Promedio Móvil 4 H

Estrategias FOREX Estrategia Forex, Estrategia simple, Estrategia Forex Trading, Forex Scalping

Estrategia Forex 4H Fibo + MA & # 8212; Funcionó bien al negociar para todos los pares de divisas en un marco de tiempo H4. Hay solamente un indicador forex & # 8212; MTF Moving Average (te permite ver visualmente la tendencia actual diaria) y una de las herramientas más útiles para el comerciante, creo - Fibonacci.

El indicador de instalación MTF Moving Average es el siguiente: TimeFrame & # 8212; 1440, MAPeriod & # 8212; 1950, Shift & # 8212; 0, Método & # 8212; 1, Precio & # 8212; 0.

La estrategia 4H Fibo + MTF MA es la siguiente:

1) El gráfico para el par de divisas elegido (en el rango H4), encontramos el último movimiento ascendente o descendente, que no restaura el Fibonacci 38.2%.

2) Rasstyagivaem Fibonacci en los extremos del movimiento (máximo y mínimo) en este momento.

3) Solo nos interesan dos niveles importantes: el 38,2% y el 61,8% Fibonacci, o mejor dicho el precio otboi de estos niveles.

4) Si el mercado es hacia abajo, fijamos dos órdenes pendientes:

Venta Limite el nivel de 38,2% de Fibonacci. Y stop-loss fijado en el nivel de 61,8%.

Límite de venta en uroven61, 8% de Fibonacci. Y stop-loss establecido en 100 puntos.

Para las transacciones para comprar (el mercado hacia arriba) & # 8212; Instale una orden de compra de límites a los mismos niveles y con la misma stop-loss.

5) Mira siempre la pantalla MTF Moving Average y el acuerdo debe ser concluido sólo en la dirección de la tendencia diaria (este indicador y se muestra).

Si te atreves a comerciar contra la tendencia & # 8212; A continuación, poner una toma fija de beneficio que debe ser garazdo menos que para el comercio con la tendencia y también no se olvide lo más rápido posible para traducir la posición de cero & # 187; nivel.

Aunque es mejor sólo el comercio con la tendencia!

6) Para el beneficio recomendamos usar una parada de arrastre a una distancia de 75 puntos. Para pares más volátiles & # 8212; Una parada de arrastre a 100 puntos.

La transacción debe cubrirse únicamente con stop-loss o stop stop. Pero si lo desea, puede cerrar parte del acuerdo en los niveles importantes, o en el nivel del censo y # 171; 0.0 & # 187; En la secuencia de Fibonacci (por ejemplo 50-70% de la transacción).

Aquí hay algunas estadísticas, y aunque es un poco viejas, pero creo que en este momento, esta estrategia funcionará tan bien como importante Fibonacci siempre funciona bien:

Advertencia: Plantilla y luz pre-necesidad descomprimir!

Consiga el movimiento - consiga sano

Get Moving - Get Healthy con New Jersey 4-H es una manera interactiva y divertida de aprender hábitos alimenticios saludables, tamaño de las porciones, la nueva pirámide alimenticia y ejercicios simples. El programa se enfoca en entender MyPyramid, identificar tamaños de porciones y aprender maneras fáciles de hacer ejercicio.

Un componente clave del programa son los kits de actividades que incluyen las siguientes actividades: Desafío del ejercicio, Encontrar su pirámide, Placa saludable, Medir, Distorsión de porciones, Leer la etiqueta, Servir el partido, Piensa en lo que bebe y Qué cuenta. Cada uno tiene un plan de lección y ofrece opciones para ampliar la experiencia de aprendizaje.

Se pueden hacer arreglos para pedir prestado un kit o hacer que los profesionales de extensión de su condado lleven a cabo un programa educativo para un club, escuela o programa después de la escuela. El kit también es ideal para ferias de salud comunitaria ya que ofrece lecciones rápidas y fáciles. Para obtener más información sobre el programa, póngase en contacto con cualquiera de los miembros de Get Moving - Get Healthy con New Jersey 4-H Team que se enumeran a continuación:

Rutgers, la Universidad Estatal de Nueva Jersey. Una institución de igualdad de oportunidades y acción afirmativa. Última actualización: 10/1/2012, webmaster & # 64; njaes & # 46; rutgers & # 46; edu

¡Guauu! Estamos en funcionamiento con este año FLL Challenge & # 8220; Natures & # 8217; Fury & # 8221 ;. Las últimas semanas han sido una locura. Tuvimos que comprar 2 nuevas computadoras (Ugh Windows 8), y obtener todos ellos la configuración.

El año pasado, el Club de Robótica 4-H del Condado de Orleans tenía un equipo de FLL (12 niños todos juntos, los dos de 8 años de edad vinieron a las reuniones, pero no estuvieron involucrados en el proyecto o el robot & # 8212; Pero nos dieron camisas de equipo / sombreros y vinieron a la competencia como nuestras animadoras.) Tratando de planificar con antelación, pre-registró dos equipos de FLL en mayo (Equipos 1071 & # 038; 1405) .. y ordenó 2 nuevos Lego EV3 y 2 kits de instalación de campo.

Al entrar en la semana 2, actualmente tenemos por lo menos 26 niños comprometidos, y tal vez algunos otros que están tratando de determinar si nuestro horario se relaciona con sus propias vidas ocupadas. Mientras mi esposa y yo nos apresuramos a registrar un tercer equipo (Team 15629), e intentamos ver si tenemos el presupuesto para comprar un 3er EV3.

Hemos logrado que los obstáculos se construyan (y algunos de ellos reconstruidos y reconstruidos de nuevo) y hemos montado los primeros 2 EV3 (y nuestros 2 robots NXT originales) en robots básicos para que los niños puedan empezar Intentando las misiones.

El próximo fin de semana, estaremos formalmente seleccionando equipos, nombres y colores. Que debería amp-up el proyecto de trabajo, y tal vez empezar a ver algunos coopertition.

¡La temporada está sobre nosotros para la primera Liga Lego!

Nos reuniremos por primera vez este año el sábado 7 de septiembre. Comenzaremos a la 1pm con los niños que se encuentran con Erik en el edificio de oficinas Justo hasta 4pm y en 1:15 con los padres que se encuentran con Marlene en el Centro de Educación por aproximadamente media hora. Por favor venga preparado para completar el papeleo de membresía 4-H (se le pedirá información de seguro). La cuota es de $ 5 por miembro.

Los niños comenzarán una investigación y terminarán de construir los elementos del juego de este año.

Se distribuirá mucha información y se contestarán las preguntas. Padres / tutor (es) nuevo (s) y regreso (s) por favor haga todo lo posible para asistir a esta sesión de 30-45 minutos. Si tengo que repetirlo varias veces, puedo olvidar a quién he dicho. También preguntaré, si usted tiene una pregunta que se puede hacer en la reunión, por favor escríbala y tráigala con usted.

La temporada de construcción comenzará la semana siguiente con sesiones el lunes y el miércoles 6:30 & # 8211; 8:00 en la oficina de la feria. Incluyo esta información sólo en caso de que no sea posible que alguien asista a la séptima.

Si desea echar un vistazo temprano a lo que el tema y el desafío son para este año, por favor vaya al siguiente enlace:

Padres que regresan: habrá algunos cambios desde el año pasado & # 8230; ¡por favor venga!

Ésta es la mitad más joven & # 82221; Del club de robótica del condado de Orleans 4-H. Para unirse debe tener por lo menos 8 años de edad por 1/1/14. (Cualquier persona que ingrese al 9no grado este septiembre pasará a nuestro equipo de FRC) La composición del equipo de FLL será explicada en la reunión.

Esperamos ver a todos y tener otra temporada de campeonato.

A medida que entramos en el verano, nuestros miembros más jóvenes del Club de Robótica se están preparando para este primer desafío de la Liga de Lego (FLL) de otoño, la Furia de la Naturaleza & # 8221 ;.

Este año, hemos registrado dos equipos de FLL. Equipo 1071 y 1405. Cada equipo consistirá de hasta 10 4-Hers (menores de 14 años). Durante NATURE'S FURY los equipos construirán, probarán y programarán un robot autónomo utilizando LEGO MINDSTORMS® para resolver un conjunto de misiones en el Juego de Robots. Además, cada equipo desarrollará un proyecto único para resolver un problema del mundo real.

Si tiene preguntas o desea obtener más información, póngase en contacto con nosotros. (Envíe un e-mail a & # 8220; robótica & # 8222; en wiksclan. com & # 8221;)

El equipo de FRC está trabajando en mudarse a un nuevo sitio web.

Las 4-H Moving Images consisten en películas, cintas de video y un DVD documentando los programas y actividades de los clubes 4-H en Oregon, especialmente la escuela de verano en el campus del estado de Oregon. El programa de la juventud 4-H se administra a través del servicio de la extensión de la universidad del estado de Oregon y fue establecido en los 1910s tempranos.

Cantidad

1,4 pies cúbicos, incluyendo 14 películas, 8 cintas de video y 2 DVDs; 4 cajas

Papeles Relacionados

Los registros de servicio de extensión (RG 111) incluyen los registros administrativos de los programas Oregon 4-H. Fotografías de actividades 4-H y participantes están disponibles en la Colección de fotografías 4-H (P 146). Ejemplares de Extensión Colección de fotografías (P 020). Las fotografías de comunicaciones de extensión y estación de experimentación (P 120) y la colección de Harriet. Otras imágenes en movimiento de programas y actividades de 4-H forman parte de las Imágenes de Movimiento de Comunicaciones (FV P 120) de Extensión y Experimento y las Películas y Cintas de Vídeo de Educación Superior Continua (FV P 048).

Más información

La velocidad de un objeto es la velocidad a la que cubre la distancia. La fórmula general para la velocidad es la distancia dividida por el tiempo. Nosotros escribimos

Velocidad = distancia / tiempo, v = d / t.

Para mayor comodidad usamos las abreviaturas d = distancia, t = tiempo y v = velocidad. Si usted cubre una distancia de 80 millas en dos horas, entonces su velocidad promedio es

V = (80 millas) / (2 horas) = ​​40 millas / hora.

Usted probablemente va más lento que el promedio durante algunos períodos de tiempo, y más rápido durante otros períodos. El velocímetro del coche muestra la velocidad inmanente del coche. Es decir, qué tan rápido se está yendo en cualquier momento.

De acuerdo con las reglas del álgebra, podemos reescribir la fórmula v = d / t de dos formas diferentes.

Si queremos saber hasta dónde llega un coche a 55 millas / hora de viaje en 3 horas escribimos d = vt = (55 millas / hora) * (3 horas) = ​​165 millas.

Si queremos saber cuánto tiempo tomará este coche para cubrir una distancia de 220 millas escribimos t = d / v = (220 millas) / (55 millas / hora) = 4 horas.

Las unidades, como millas y horas, siempre se llevan en los cálculos y se tratan como cantidades algebraicas ordinarias.

El resultado de cada medición tiene dos partes, un número y una unidad. El número es la respuesta a & quot; ¿Cuántas? & Quot; Y la unidad es la respuesta a & quot; De qué & quot ;. Las unidades son cantidades estándar tales como un segundo, un metro, una milla. Las unidades más utilizadas actualmente son las del sistema internacional, abreviado SI (Sistema Internacional de Unidades). Ejemplos de unidades SI son el metro (m) para la longitud, el segundo (s) para el tiempo y el kilogramo (kg) para la masa.

La velocidad de un objeto es una cantidad escalar. Sólo nos dice qué tan rápido se mueve el objeto, pero no en qué dirección se dirige. La cantidad vectorial que especifica tanto la velocidad como la dirección se denomina velocidad. (Notación: velocidad = v, velocidad = v.)

Problema:

En un intervalo de tiempo de 5 minutos, un corredor corre una vez alrededor de una pista de una milla. ¿Cuál es su velocidad promedio? ¿Cuál es su velocidad promedio?

Solución: Después de 5 minutos el corredor vuelve a su posición inicial. El desplazamiento es cero, por lo que su velocidad media es cero. La velocidad media es la distancia recorrida en el intervalo de tiempo Dt. Esta distancia es de una milla. La velocidad media por lo tanto es (1 milla) / (5 minutos) = (12 millas) / (60 minutos) = 12 millas / hora. Nota: La velocidad es un escalar, la velocidad es un vector. La velocidad media no es en general igual a la magnitud de la velocidad media.

Problema:

Un motorista conduce al norte por 35 minutos a 85 km / h y luego se detiene durante 15 minutos. Luego continúa hacia el norte, viajando 130 km en 2 horas. A) ¿Cuál es su desplazamiento total? B) ¿Cuál es su velocidad media?

Solución: (a) En los primeros 35 minutos el motorista viaja d 1 = v 1 t 1 = 85 km / h ґ 35 min ґ 1 h / (60 min) = 49,6 km. En las próximas 2 horas viaja 130 km. La distancia total recorrida es de 179,6 km. Su desplazamiento es de 179,6 km (norte). (B) Su velocidad media es v = d / t. Viaja durante 170 minutos (incluyendo su parada). Por lo tanto, su velocidad media es v = (179,6 km / (170 min)) ґ (60 min / h) (norte) = 63,4 km / h (norte).

Velocidad

La velocidad es escalar. Los escalares son cantidades con magnitud única. La dirección no importa. Si usted está en la carretera si viaja 100 km / h sur o 100 km / h al norte, su velocidad sigue siendo 100 km / h. Otros ejemplos de cantidades escalares son el tamaño del zapato, la masa, el área, la energía. (Velocidad media) = (distancia total) y división; (tiempo total)

Ejemplo 1

Si alguien caminaba 400 m en línea recta en 5 min, su velocidad media sería (400 m) & dividir; (5 min) = 80 m / min. Si la misma persona caminaba 100 m [Norte] luego 300 m [Sur] en 5 minutos, su velocidad media seguiría siendo (400 & divide; 5) = 80 m / min. Si esa persona caminaba 100 m [E] en .75 min, 100 m [N] en 1.50 min, 100 m [W] en 1.00 min y finalmente 100 m [S] en 1.75 min, su velocidad promedio sería (400 m ) & Dividir; (5 min) = 80 m / min.

Ejemplo 2

Usted conduce un automóvil durante 2,0 h a 40 km / h, luego durante otras 2,0 h a 60 km / h. a. ¿Cuál es su velocidad promedio? segundo. ¿Obtiene la misma respuesta si maneja 100 km en cada una de las dos velocidades?

a. La distancia total recorrida = [(2 h) (40 km / h) + (2 h) (60 km / h)] = 200 km

El tiempo total = 2 + 2 = 4 h

Velocidad media = (200 km) / (4 h) = 50 km / h

segundo. Distancia total = 100 + 100 = 200 km

Tiempo total = [100 km) / (40 km / h) + (100 km) / 60 km / h)] = 4,17 h

Velocidad media = (200 km) / (4,17 h) = 48 km / h

Velocidad media

(Velocidad media) = desplazamiento y división; hora.

La velocidad es un vector. Se debe indicar tanto la dirección como la cantidad. Un tren tiene una velocidad de 100km / h al norte, y un segundo tren tiene una velocidad de 100km / h al sur, los dos trenes tienen diferentes velocidades, aunque su velocidad es la misma. Otros ejemplos de vectores son fuerza e intensidad de campo.

Ejemplo 3

Si una persona caminaba 400 m en línea recta en 5 min, la velocidad de esa persona sería (400 m [adelante]) y dividir; (5 min) = 80 m / min [adelante].

Si la misma persona caminó 100 m [Norte] luego 300 m [Sur] en 5 minutos, primero encontramos su desplazamiento. Desplazamiento = 200 m [S] velocidad = 200 y división; 5 = 40 m / min [S]

Si esa persona caminaba 100 m [E] en .75 min, 100 m [N] en 1.50 min, 100 m [W] en 1.00 min y finalmente 100 m [S] en 1.75 min, esa persona terminaría de regreso donde ellos empezado. Puesto que su desplazamiento es cero, su velocidad es cero.

Recuerde, (velocidad media) = desplazamiento y división; hora.

Ejemplo 4

Un excursionista viajó 80,0 m [S] a 1,00 m / s, luego 80,0 m [S] a 5,00 m / s. ¿Cuál es la velocidad media del excursionista?

Desplazamiento = 160.0 m [S] tiempo para la primera parte es 80.0 & divide; 1.00 = 80.0 s, tiempo para la segunda parte es 80.0 m & divide; 5,00 m / s = 16,0 s. Tiempo total = 80.0 + 16.0 = 96.0 s Por lo tanto, la velocidad es (160.0 m [S]) & divide; 96.0 s = 1.67 m / s [S]

Ejemplo 5

Un tren en una vía recta viajó 60,0 km / h [E] durante 2,00 h, se detuvo durante 15 minutos y luego viajó 100,0 km [W] a 133 km / h. a. ¿Cuál fue la velocidad media del tren durante todo el viaje? a. ¿Cuál fue la velocidad promedio del tren para todo el viaje?

a. Para encontrar la velocidad media, necesitamos la distancia total y el tiempo total. Durante la primera parte del viaje, el tren cubrió 60.0x2.00 = 120 km en 2.00 h. Durante la segunda parte del viaje el tren viajó 0,00 km en 0,25 h. Durante la tercera parte del viaje, el tren viajó 100,0 km en 0,75 h. En total el tren viajó 220 km en 3,00 h. Velocidad media = (220 km) y división; 3.00 = 73,3 km / h

segundo. Para encontrar la velocidad media, necesitamos desplazamiento y tiempo total. Durante la primera parte del viaje, el tren cubrió 60.0x2.00 = 120 km [E] en 2.00 h. Durante la segunda parte del viaje el tren viajó 0,00 km en 0,25 h. Durante la tercera parte del viaje, el tren viajó 100.0 km [W] en (100.0 km & división; 133 km / h) = 0.75 h. El desplazamiento del tren fue (120-100) = 20 km [E] en 3,00 h. Velocidad media = (20 km [E]) y división, 3.00h = 6,7 km / h [E]

Ejemplo 6

Un corredor cubre una vuelta de una pista circular de 40,0 m de diámetro en 62,5 s. Para esa vuelta, ¿cuál era su velocidad media y velocidad media?

Velocidad media = (distancia total) / (tiempo total) = (& # 960; * 40.0) / (62.5) = 2.01m / s

Velocidad media = desplazamiento / tiempo = 0 / 62.5 = 0 m / s

Aceleración

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Aceleración = (cambio de velocidad) y división; hora .

La aceleración es un vector cuando se refiere a la velocidad de cambio de velocidad. La aceleración es escalar cuando se refiere a la velocidad de cambio de velocidad. Un coche que se desacelera para parar en una señal de la parada se está acelerando porque su velocidad está cambiando. Podríamos referirnos a este tipo de aceleración como desaceleración o aceleración negativa. Un coche que va a una velocidad constante alrededor de una curva todavía está acelerando porque su dirección está cambiando.

Ejemplo 7

Un lanzador entrega una bola rápida con una velocidad de 43 m / s al sur. El bateador golpea la bola y le da una velocidad de 51m / s al norte. ¿Cuál fue la aceleración promedio de la pelota durante los 1.0ms cuando estuvo en contacto con el bate?

(51 m / s hacia el norte - 43 m / s hacia el sur) / (1,0 x 10 -3 s)

Deje que el sur sea positivo y la aceleración de los rendimientos negativos del norte = (-51m / s - 43 m / s) / (1.0x10 -3 s) = -94000 m / s / s aceleración = 94000 m / s / s al norte

Problemas de velocidad, velocidad y aceleración

A. Velocidad media, problemas de velocidad media

1. Un automóvil viaja en una carretera recta durante 40 km a 30 km / h. A continuación, continúa en la misma dirección para otros 40 km a 60 km / h. A) ¿Cuál es la velocidad media del coche durante este viaje de 80 km? B) Cuál es la velocidad media.

2. Un camión en una carretera recta comienza desde el reposo y acelera a 2,0 m / s 2 hasta alcanzar una velocidad de 20 m / s. A continuación, el camión se desplaza durante 20 s a una velocidad constante hasta que se aplican los frenos, deteniendo el automóvil de manera uniforme en 5,0 s adicionales. ¿Cuánto tiempo está el camión en movimiento y cuál es su velocidad media durante el movimiento?

3. Mientras viaja a casa desde la escuela, viaja a 95 km / h durante 130 km y luego a 65 km / h. Llegas a casa en 3 horas y 20 min. ¿Qué tan lejos está su ciudad natal de la escuela y cuál es la velocidad promedio?

4. Una persona toma un viaje, conduciendo con una velocidad constante de 89.5 km / h, a excepción de una parada de descanso de 22 minutos. Si la velocidad media de la persona es de 77,8 km / h, ¿cuánto tiempo se gasta en el viaje y en qué medida la persona viaja?

5. De t = 0 a t = 4,21 min, un hombre se detiene, y desde t = 4,21 min a t = 8,42 min, camina enérgicamente en línea recta a una velocidad constante de 1,91 m / s. En el intervalo de tiempo de 1,00 min a 5,21 min

a. Su velocidad media

segundo. Su aceleración promedio?

6. Un observador de aves serpentea por los bosques, caminando 0,684 km hacia el este, 0,486 km hacia el sur y 3,56 km en una dirección 61,7 grados al norte del oeste. El tiempo necesario para este viaje es de 1.124 h. Determine el desplazamiento del observador de aves (a) y (b) la velocidad media.

7. Un conductor de camión se apresura a recoger una carga de huevos. Viaja 40 millas a 80 millas por hora, regresando con un camión completo a lo largo de la misma ruta a 40 millas por hora. ¿Cuál fue su velocidad promedio para el viaje?

8. Un piloto de autos de carreras se pone en una carrera de 100 millas. En el marcador a mitad de camino, sus radios de equipo de boxes que ella ha promediado sólo 50 millas / hora. ¿Qué tan rápido debe conducir sobre la distancia restante con el fin de un promedio de 100 millas por hora para toda la carrera?

9. Al llegar a su destino, un mochilero camina con una velocidad media de 1,34 m / s, hacia el oeste. Esta velocidad promedio se debe a que ella sube 6,44 km con una velocidad media de 2,68 m / s, al oeste, se da vuelta y alza con una velocidad promedio de 0,447 m / s, hacia el este. ¿A qué distancia caminaba?

10. Usted correr a 6 mi / h para 5 millas, luego conducir otros 5 mi en un coche. ¿Con qué velocidad promedio debe conducir si su velocidad promedio para las 10 millas enteras es de 10,8 mi / h?

a. La distancia de una vuelta alrededor de una pista ovalada es de 1,50 km. Si un ciclista que va a una velocidad constante hace una vuelta en 1.10 min, ¿cuál es la velocidad de la moto y ciclista en metros por segundo?

segundo. ¿La velocidad de la moto también es constante? Explique.

B. Problemas de aceleración constante

1. Si la posición de un bicho viene dada por x = 4m - (12m / s) t + (3m / s 2) t 2 (donde t es en segundos y x en metros), cual es su velocidad en t = 1 s ?

2. Un OVNI viaja con una velocidad de 3250 m / s. De repente, el cohete retro se dispara, el OVNI se detiene a una parada con una aceleración cuya magnitud es igual a 10m / s 2. ¿Cuál es la velocidad del OVNI cuando el desplazamiento de la embarcación es de 215 km, en relación con el punto donde el retro El cohete comenzó a disparar?

3. Un vehículo que viaja 60 km / h se aproxima a una intersección justo cuando el semáforo se vuelve amarillo. La luz amarilla dura sólo 2,0 s antes de volver a rojo. La distancia hasta el lado cercano de la intersección es de 30 my la intersección es de 15 m de ancho. El vehículo puede desacelerar a -6.4 m / s 2. mientras que puede acelerar de 60 km / h a 70 km / h en 3.0 s. a. Si se aplican los frenos, ¿hasta dónde viajará el vehículo antes de parar? segundo. Si el vehículo se acelera, ¿hasta dónde viajará antes de que la luz se vuelva roja?

4. Un automóvil acelera a una velocidad de 0.6 m / s 2. ¿Cuánto tiempo toma este automóvil pasar de una velocidad de 55 millas por hora a 60 millas por hora?

5. Un jalopy con una velocidad inicial de 23,7 km / h acelera a una velocidad uniforme de 0,92 m / s 2 durante 3,6 s. Encuentre la velocidad final y el desplazamiento del jalopy durante este tiempo.

6. Un chorro adquiere una velocidad de despegue de 112 m / s en 20.0 s, comenzando desde el descanso y viajando hacia el este. ¿Cuál es la magnitud y la dirección de su aceleración media?

7. Un bobsledder que comienza del resto acelera uniformemente abajo de una colina de 30 grados en 3.30 m / s 2. ¿Cuánto tiempo tomará para alcanzar la parte inferior de la colina si su cambio en la elevación es 110 m?

8. Dos marcadores separados por 0,30 km colocados en una carretera. Un guzzler de gas pasó el primer marcador con una velocidad de 5,0 m / s [E] y pasó el segundo marcador con una velocidad de 33,0 m / s [E]. Calcule la aceleración media del coche.

9. Un jalopy se desacelera de 48m / s a ​​12m / s en 5 s. ¿Cuál es el desplazamiento de la jalopía durante este tiempo?

10. ¿Cuánto tiempo tomará un jalopy, comenzando del resto, para alcanzar una velocidad de 24 m / s sobre una distancia de 315 m?

11. Un jalopy viaja en una carretera recta de largo nivel a 50 km / h y luego acelera hasta 90 km / h en 15 segundos. Calcule la aceleración del jalopy en m / s / s.

12. Un canguro se mueve con una velocidad de 5,0 m / s en un ángulo de 30 & ordm; Norte del Este. El canguro, 4.0 segundos después, se mueve con una velocidad de 6.0 m / s en un ángulo de 45 & ordm; Al sur de este. ¿Cuál es la aceleración promedio del canguro?

13. Un bobsledder está acelerando abajo de un 30.0 & ordm; Colina en a = 2,80 m / s 2. a. ¿Cuál es el componente vertical de su aceleración? segundo. ¿Cuánto tiempo le llevará a llegar al fondo de la colina, asumiendo que comienza desde el resto y se acelera uniformemente, si el cambio de elevación es 315 m?

14. Supongamos que el vector de posición para un error se da como una función del tiempo por r (t) = x (t) + y (t), con x (t) = at + byy (t) = ct 2 + D, donde a = 1,00 m / s, b = 1,00 m, c = 0,125 m / s 2 y d = 1,00 m. Determine una ecuación para la velocidad instantánea en función de t.

15. Una thingamajig se mueve a lo largo del eje x de acuerdo con la ecuación x (t) = (2.60t 2 -2.00t + 3.00) m, donde t es en segundos y x está en m. a. Encuentre la velocidad media entre t = 1.90s y 2.90s. segundo. Encuentre velocidad instantánea en t = 1,90 s y 2,90 s. do. Hallar la aceleración media entre t = 1.90s y t = 2.90s. re. Encuentre la aceleración instantánea en t = 1.90s y 2.90s.

16. Un conductor que viaja 40 km / h ve a un niño correr a la carretera 13 m por delante de su jalopy. Él aplica los frenos, y el jalopy desacelera uniformemente en 8.0 m / s / s. El tiempo de reacción del conductor es de 0,25 s. ¿El jalopy golpeará al niño?

17. Una jalopy que viaja 70 km / h llega a una parada a 120 m. Encuentra la aceleración del jalopy.

C. Problemas de dos objetos

1. Un biólogo corre en línea recta hacia su coche a una velocidad de 4.0 m / s. El coche está a una distancia de distancia. Un oso hambriento está a 23 metros detrás del biólogo y lo persigue a 6,0 m / s. El biólogo llega al coche con seguridad. ¿Cuál es el valor máximo posible para d?

2. Dos mármoles están separados por 400 cm. El mármol azul comienza a viajar 26 cm / s hacia el mármol azul. El mármol rojo comienza a viajar 4.0s más tarde hacia el mármol azul a 31.25 m / s. Aproximadamente, ¿cuántos segundos tarda el mármol rojo en viajar antes de chocar de frente? ¿Cuán lejos se mueve cada mármol desde su posición inicial?

3. Una mujer está corriendo a una velocidad constante de 5 m / s en un intento de coger un autobús parado 11 m por delante de ella. Sin embargo, se aleja de ella con una aceleración constante de 1 m / s 2. ¿Cuánto tiempo le toma llegar al autobús si sigue corriendo a la misma velocidad?

4. Dos sprinters terminan con tiempos de 3: 53.58 y 3: 55.66. Suponiendo que ambos funcionan 1609 m a velocidad constante. ¿Qué distancia los separa al final de la carrera?

5. Una mujer en un puente a 86.8 m sobre un arroyo ve una botella flotando a una velocidad constante. Ella deja caer una piedra del resto cuando la botella tiene 5.88 m más para viajar antes de pasar debajo del puente. La piedra golpea el agua 2.18 m delante de la botella. Calcule la velocidad de la botella.

6. Después de una parada de reabastecimiento un coche de carreras acelera a 6m / s 2. y después de 4 s vuelve a entrar en la pista. En ese instante, otro automóvil de carrera que viaja a una velocidad constante de 70 m / s se adelanta y pasa el coche reabastecido. Si el coche reabastecido mantiene su aceleración, ¿cuánto tiempo se requiere para que pueda coger el otro coche?

7. Cuando usted está a 20m de distancia de un hummer detenido que comienza a acelerar lejos de usted a 3 m / s / s. ¿Con qué velocidad constante deberías correr para atrapar al hummer?

8. Un scooter que viaja a 1,00 m / s pasa a un ciclista parado. En el instante en que el scooter pasa al ciclista, el ciclista comienza a acelerar a 0.200 m / s 2 en la dirección del scooter. a. ¿Cuánto tiempo tarda el ciclista en alcanzar el scooter? segundo. ¿Cuál es la velocidad del ciclista cuando alcanza el scooter? do. ¿Hasta dónde viajan antes de reunirse?

D. Otros problemas

1. Un clunker tenía una aceleración, a, y una desaceleración de 1.84 * a. El clunker debe viajar una distancia corta, L, en el tiempo mínimo. ¿Empezando y terminando en reposo, en qué parte de L el conductor debe comenzar a frenar?

2. Un velocista que comienza una carrera de 100 yardas acelera desde el descanso a 9 ft / s 2. Después de adquirir la velocidad máxima, corre a velocidad constante. Si termina en 11s, ¿hasta dónde corre mientras se acelera?

3. Un ascensor se desplaza hacia arriba como se describe por:

T = (3,0 m / s 2) t + (0,20 m / s 3) t 2 ¿Cuál es la aceleración del ascensor 4,0 s después de partir del reposo?

4. A 1350 kg cuatro por cuatro moviéndose con una velocidad de 15.0 m / s comienza a acelerarse a (1.5t + 2.60) m / s 2. Determine (a) su velocidad y (b) su posición después de 6.00 segundos. (C) ¿Qué fuerza resultante actuó sobre el cuatro por cuatro en t = 3.00s?

5. Un convoy viaja a una velocidad de 72 km / h. El convoy debe detenerse durante 2,0 minutos. Si el convoy se desacelera a una velocidad uniforme de 1,0 m / s 2 y, después de la parada, se acelera a una velocidad de .50 m / s 2. cuánto más tiempo es el tiempo del viaje comparado con el tiempo si el convoy Había mantenido una velocidad constante?

6. Resuelve m (d 2 x / dt 2) + b (dx / dt) - kx = 0 dado que es una ecuación de movimiento de un cuerpo que no está en vibración amortiguada. Traducir la ecuación.

Respuestas a los problemas de velocidad, velocidad y aceleración

Dado que 10 millas debían cubrirse a 10,8 mi / h, el tiempo para el viaje, t para. Se encuentra por t tot = d tot / v avg = 10 / 10,8 = 0,926 h

Dado que 5 millas fueron trotadas a 6 mi / h, el tiempo de jogging fue t j = 5/6 = 0.833 h

El tiempo restante para conducir los 5 mi restantes es por lo tanto 0.926 - 0.833 = 0.0926 h

Dado que hay 5 millas para conducir, la velocidad media requerida es v d = 5 / 0.0926 = 54 mi / h

(70 km / h) (1000 m / km) (1h / 3600s) = 19,4 m / s

Aplicación de v f 2 = v i 2 + 2ad: 0 2 = (19,4) 2 + 2a (120) a = -1,58 m / s / s

a. Tiempo perdido durante la deceleración: velocidad inicial = 72 km / h * 1000/3600) = 20 m / s

Velocidad final = 0 t = (0-20) / (- 1,0 m / s / s) = 20 s

Distancia recorrida = v i t + (1/2) a 2 = (20 m / s) (20 s) + (1/2) (- 1,0) (20) 2 = 200 m

Tiempo para viajar 200 m si el tren mantiene 20 m / s = 200/20 = 10 s

Tiempo perdido = 20 - 10 = 10 s

segundo. Tiempo perdido durante la parada = 2,0 minutos = 120 s

do. Tiempo perdido durante la aceleración

Velocidad inicial = 0

Velocidad final = 20 m / s

T = (20 -0) / (0,50 m / s / s) = 40 s

Distancia recorrida = v i t + (1/2) a 2 = (0 m / s) (40 s) + (1/2) (0.50) (40) 2 = 400 m

Tiempo para viajar 400 m si el tren mantiene 20 m / s = 400/20 = 20 s

Tiempo perdido = 40 - 20 = 20 s

re. Tiempo total perdido

10 + 120 + 20 = 150 s o 2,5 minutos

SOLUCIÓN: es un coche se mueve con una velocidad media de 60 km / h por hora. Recorrerá una distancia de 60 km. a. ¿Hasta dónde viajaría si se moviera a esta velocidad durante 4 h? segundo. Para 10 m h?

Pregunta 224504. es un coche que se mueve con una velocidad media de 60 km / h por hora. Recorrerá una distancia de 60 km. a. ¿Hasta dónde viajaría si se moviera a esta velocidad durante 4 h? segundo. Para 10m h?

Lo intenté como dijiste que probar y creo que es por a. La velocidad media es distanciada con el tiempo. 60 x 4 = 240ºC. 240% 4 = 6o tal vez. Quiero la respuesta hoy plzzz y gracias u :) Respuesta de drj (1380) "/>" /> Usted puede poner esta solución en su sitio web! Si un coche se mueve con una velocidad media de 60 km / hora. Recorrerá una distancia de 60 km en 1 hora. a. ¿Qué tan lejos se desplazaría si se moviera a esta velocidad durante 4 h? segundo. Durante 10 h?

Paso 2. Para el problema a, 60 km / h * 4 h = 240 km.

Paso 3. Para el problema b, 60 km / h * 10 h = 600 km.

Espero que los pasos anteriores sean útiles.

Para los videos paso a paso LIBRES en la introducción al álgebra, visite http://www. FreedomUniversity. TV/courses/IntroAlgebra y para la visita de la trigonometría http://www. FreedomUniversity. TV/courses/Trigonometry.

¡Buena suerte en tus estudios!

Respetuosamente, el Dr. J

Imágenes en movimiento 4-H, 1939-2009

Abstracto:

Las 4-H Moving Images consisten en películas, videos y un DVD que documenta los programas, proyectos y participantes de Oregon 4-H, especialmente el programa de la escuela de verano en el campus del estado de Oregon en Corvallis. La colección incluye 14 carretes de película; Cinco de las películas documentan actividades y programas durante la semana escolar de verano de 1939, 1960 y 1967. Otras películas muestran un club de tiro con arco, actividades para hacer terrarios, la conferencia 4-H y el Congreso Nacional 4-H. Una película que describe los programas y actividades 4-H a nivel nacional (4-H is More) fue producida por el Consejo Nacional 4-H. Cuatro videocintas forman parte de la colección. Estos incluyen un video promocional para la conferencia de verano 4-H en el campus del estado de Oregon; Una cinta de video para el entrenamiento de jueces de caballos 4-H; EM Power, una cinta de vídeo para un programa de gestión ambiental (de residuos) para jóvenes; Y la juventud de América: el reto y la oportunidad, una producción de 1989 sobre cómo el programa nacional 4-H puede abordar los muchos problemas que enfrentan los niños y jóvenes. El DVD de Wagon Trek Movie and Pictures fue preparado en honor al 50 aniversario de una caminata en 1959 de 4-H de Jacksonville a Corvallis. El DVD incluye imágenes de la película de 1959, así como fotografías que representan a los participantes de la caminata con sus carros y caballos, desfiles a lo largo de la ruta, y sus campings.

Comentarios

Agregar una reseña y compartir sus pensamientos con otros lectores. Sé el primero.

Nota histórica:

4-H es el programa juvenil administrado en Oregon por el Servicio de Extensión con el objetivo de desarrollar la ciudadanía, liderazgo y habilidades para la vida a través de programas de aprendizaje experiencial en agricultura, economía doméstica, ciencias naturales, ingeniería y arte. Oregon 4-H se desarrolló a partir de los clubes industriales establecidos por las escuelas individuales a principios del siglo XX. El primer líder estatal, F. L. Griffin, fue contratado en 1914. La Semana de Verano 4-H en el campus del Estado de Oregon comenzó en 1916 y trajo a jóvenes de todo Oregon al campus de Corvallis.

Guillermo C. (Bill) Smith trabajó en las comunicaciones de la extensión del estado de Oregon como especialista de las comunicaciones de la transmisión a partir de 1954 hasta su retiro en 1978. Él filmó una o más de las películas en la colección.

La caminata 1959 del carro fue organizada por el condado de Jackson 4-H Empire Builders Club y los agentes de extensión Glenn Klein y Marilou Garner Perris. La caminata tomó 13 días para completar y cubrió 225 millas de Jacksonville, Oregon, a Corvallis, donde los participantes de la caminata se unieron a la escuela de verano 4-H en el campus del estado de Oregon.

4-H ayuda a los jóvenes de Missouri a seguir en movimiento

Longtime Benton County 4-H volunteer Tina Ives and son Dylan Carver have lost more than 50 pounds each since they resolved to keep active and eat better.

COLE CAMP, Mo.—It's time to get moving. That's the message of the "Move Across Missouri" program to 4-H youth and their families.

By keeping a running tally, 4-H'ers can see how a few minutes or an hour here and there quickly adds up. In 2010, more than 460 people signed up for Move Across Missouri. About 300 of them regularly recorded their activity throughout a four-month competition period. Participants logged almost 100,000 hours—nearly 6 million minutes—of physical activity.

When Tina Ives and son Dylan Carver's 4-H club started participating in Move Across Missouri last year, the club began to incorporate physical activity into meetings and events. Healthier food was served at club events: fruit kebabs instead of donuts, for example, and lean ground beef, courtesy of the Missouri Beef Industry Council, which sponsors the program.

During one outing, Ives realized she needed to do a better job of practicing what she preached. "We took them for a walk up to the top of a hill," she recalls. "Halfway up the hill, we had to stop just so I could catch my breath. I realized that I can't teach a child to eat healthy and live healthy if I'm not an example of doing that myself. I didn't feel good. I was embarrassed, and I decided it was time to get right."

Posted on Apr 28, 2011.

Value of Adult Volunteer Leaders in the New Mexico 4-H Program

Economic Value of Volunteer Time

Using the 1999 average hourly wage for nonagricultural workers ($14.30) provided by the Independent Sector (1999) and the median hours contributed, the economic value of the average New Mexico adult 4-H leaders' time was $5283.65. Applying this figure, New Mexico volunteers (N = 1,134) contributed an estimated 6.5 million dollars to the New Mexico 4-H program in 1998.

Other Monetary Contributions

4-H leaders in New Mexico made fewer than 25 phone calls per year and spent under $50 on long distance/pay phone charges. They also spent less the $50 of their own money on program supplies. New Mexico 4-H leaders, however, drove more than 500 miles in a year for related 4-H activities. New Mexico is a very rural state with only a few major urban centers, thus requiring greater driving distances and more time to attend both in - and out-of-county events. Nationally, in 1996, the average 4-H volunteer drove 300 to 400 miles and spent approximately $50.00 of their own money (4-H Statistics, 1998).

Implications and Recommendations

Based on the findings of the study, the following recommendations were made.

Given the study's findings, the 4-H program should be expanded by implementing recruitment strategies that target under-utilized populations, including male and minority populations, college students, senior citizens, urban based families, and individuals identified as lower economic status.

Volunteers are important resources to the 4-H program. They are used to teach, plan, and implement many programs. Extension should continue to emphasize leader involvement in the areas found to have had the most time served because research shows that volunteers are more motivated and effective in serving areas they have an investment in. However, 4-H faculty and staff should invest more time in promoting leader involvement, recruitment, and volunteer training if they wish to expand and increase the educational program relativity of these areas.

The economic value of the average New Mexico adult 4-H volunteer leader's time for the period of 1 year was determined to be $5283.85. In 1998, 1,134 volunteers who had served at least 4 years were enrolled in the New Mexico 4-H program. Using these figures, New Mexico volunteers contributed an estimated $6.5 million in time and talent to the state 4-H program for 1998. 4-H administrators should use this information to demonstrate the significance and relevance volunteer have to the New Mexico 4-H program. These figures should also be used to address additional funding needs for the 4-H Youth Development Program.

4-H leaders made less than 25 calls per year and spent under $50 on long distance/pay phone charges and under $50 on program supplies. Extension should continue to keep these "out of pocket" expenses to a minimum by allowing leaders to make long distance phone calls from their local office and through providing project materials at a low cost.

Leaders drove more than 500 miles in a year for related to 4-H programs. This is higher than the national average. A mileage reimbursement program should be initiated for volunteers driving their personal vehicles who drive 500 miles per year or more. The reimbursement program could be initiated through 4-H County Councils or fundraising events.

When recruiting volunteers, findings from this study should be used to help answer questions such as, "How much time would I be spending?" "What activities would I be expected to be involved with?" and "When would I be expected to serve?"

Volunteer leaders spent the least amount of time receiving or giving volunteer orientation and training. 4-H program faculty and staff should provide high-quality, frequent volunteer orientations and training throughout the year.

Other states should collect data to determine a profile of their volunteer 4-H leaders. Data collected can be used to make decisions about recruiting, orienting/training, management, and evaluation of the overall volunteer program.

The information collected from this study is useful to both state and county staff to help improve programs, recruit volunteers, and justify the spending of public dollars for 4-H Youth Development programming. Study findings can be used for program planning, recruitment, and accountability purposes. The program planning and recruitment aspects are primarily useful to Extension staff. For example, average hours spent by adult volunteer leaders in different program areas will be available to use in recruiting when potential volunteers ask, "How much time would I likely be spending?" Monthly patterns of activity for adult leaders will help to determine months when most leaders would be active and open to respond to surveys, attend training sessions, and receive information concerning new aspects of certain projects and to identify when recruitment of extra help might be needed.

Data related to the nature and extent of leader involvement can be used for accountability purposes (impact figures related to time spent by volunteer leaders in support of their leadership activities) and can be shared with funding agencies, donors, and sponsors, as well as provide recognition to volunteers serving in the program. Finally, general background data on volunteer leaders will enable a "volunteer leader profile" to be formulated containing characteristics of 4-H volunteer leaders to aid in recruitment efforts.

Referencias

Brudney, J. (1990). Fostering volunteer programs in the public sector: Planning, initiating, and managing voluntary activities. San Francisco, CA: Jossey-Bass Publishers.

Culp, K. III (1997). Motivating and retaining adult volunteer 4-H leaders. Journal of Agricultural Education . 38, (2) 1-7.

Fritz, S. (2000). Motivation and recognition preferences of 4-H volunteers. Journal of Agricultural Education . 41 (3) 40-49.

Rouse, S. B. & Clawson, B. (1992). Motives and incentives of older adult volunteers: tapping an aging population for youth development workers. Journal of Extension [On-line]. 30(3). Available at: http://www. joe. org/joe/1992fall/a1.html

Steele, S. M. Finley, C. & Edgerton, C. A. (1989). Partners for action: The roles of key volunteers . Madison, WI. University of Wisconsin-Madison.

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Notable ETF Outflow Detected - ITB, DHI, LEN, NVR Tuesday, January 26, 11:03 AM ET, by Market News Video Staff Symbols mentioned in this story: ITB, DHI, LEN, NVR Exchange traded funds (ETFs) trade just.

Ex-Dividend Reminder: Starbucks, KB Home and Northwest Bancshares Friday, January 29, 9:56 AM ET, by Market News Video Staff On 2/2/16, Starbucks Corp. (SBUX), KB Home (KBH), and Northwest Bancshares, Inc.

Analysts Forecast 28% Upside For The Holdings of ITB Thursday, February 4, 8:05 AM ET, by Market News Video Staff Looking at the underlying holdings of the ETFs in our coverage universe at ETF Channel.

March 24th Options Now Available For iShares Dow Jones U. S. Home Construction Index Fund (ITB) Thursday, February 4, 11:11 AM ET, by Market News Video Staff Investors in iShares Dow Jones U. S. Home Construction Index Fund (ITB) saw new options begin.

Oversold Conditions For Lennar (LEN) Monday, February 8, 11:57 AM ET, by Market News Video Staff Legendary investor Warren Buffett advises to be fearful when others are greedy, and be greedy.

KBH Crosses Above Key Moving Average Level

By Market News Video Staff, Friday, March 18, 11:14 AM ET

Play Video: Learn About The 200 DMA

Start slideshow: 10 Stocks Crossing Above Their 200 Day Moving Average »

In trading on Friday, shares of KB Home (NYSE:KBH ) crossed above their 200 day moving average of $13.71, changing hands as high as $13.89 per share. KB Home shares are currently trading up about 1.9% on the day. The chart below shows the one year performance of KBH shares, versus its 200 day moving average:

Looking at the chart above, KBH's low point in its 52 week range is $9.04 per share, with $17.42 as the 52 week high point — that compares with a last trade of $13.75. Can your brain be trained to become a chart-predicting wizard? Click here to find out

According to the ETF Finder at ETF Channel, KBH makes up 2.23% of the iShares U. S. Home Construction ETF (AMEX:ITB ) which is trading higher by about 1.4% on the day Friday.

Top Six Most Viewed Stories This Week @ Market News Video :

This Article's Word Cloud: AMEX Above According Click Crossing ETFs Finder Friday Home Looking NYSE Start Stocks Their about above average below brain changing chart compares contain currently find hands held here high iShares last makes moving other point predicting range raquo share shares slideshow that trading versus week what which with year your

1 By admin | August 27, 2017

Dear Stark County 4-H Families and Friends:

Please post and share this information. The Stark County, OSUE Office is relocating to RG Drage Campus, but first to fair grounds for fair week… Please feel free to call me to discuss this great opportunity we have with the opportunity for growth, storage and connections with schools throughout the county and RG Drage Campus.

Let’s have a great Stark County fair 2017. See you at the Fair.

Gracias. David Crawford

We will be packing and moving offices August 27-28 and 31 (Thursday-Monday). If you need 4-H Books for fair - last day is Wednesday (8-26)

Ohio State University Extension, Stark County

First to the STARK COUNTY FAIR…

The Ohio State University Extension Office will operate a mobile office at the Stark County Fair, September 1-7, 2017. To connect with 4-H Youth Development and Expanded Food and Nutrition Program professionals, visit the 4-H Exhibits building at the fair; to connect with the Agriculture and Natural Resource professional or the Stark County Master Gardener Volunteers, visit the Stark County Farm Bureau Building at the fair. The office will reopen for regular business at a new location on Tuesday, September 8 at the RG Drage Campus located at 2800 Richville Drive SE, Suite 100, Massillon, OH 44646.

We will be packing and moving offices August 27-28 and 31 (Thursday-Monday).

Second to our new office location at the

The Ohio State University Extension, Stark County Office will be relocating from this location in the USDA Service Center to the RG Drage Campus. Our new address will be:

Ohio State University Extension, Stark County

RG Drage Campus

28 00 Richville Drive SE, Suite 100

Massillon, OH 44646

The office will re-open for regular business following the Stark County Fair ( September 1-7 ) at our new location on Tuesday, September 8.

Thanks for your patience and understanding during this transition!

The OSU Extension Stark County Office Team

For many youth involved in 4-H. traveling to various events becomes quite common. Some trips may be short, only an hour or two drive, while others may take much longer, crossing several state or country lines to reach the final destination. Through all of these miles and hours on the road or in the air, youth have the opportunity to learn a great deal about themselves, their peers and the volunteers they travel with. These experiences help to set 4-H members up for success by opening their mind to new experiences, people and locations outside of their own home.

4-H members take trips for multiple purposes. Some are trips to educational contests, such as the Junior Dairy Management Contest or 4-H and FFA Dairy Forum held during the All-American Dairy Show in Harrisburg, Pennsylvania; others are to youth conferences, like the National 4-H Dairy Conference in Madison, Wisconsin, or the National 4-H Conference in Washington, D. C.; while others may be to different parts of their home state for camps, such as Michigan State University Extension ’s 4-H Great Lakes Natural Resources Camp or 4-H Animal and Veterinary Science Camp. Whatever the reason, the time spent traveling affords youth the opportunity for conversations they might not otherwise engage in with peers and adults. They are able to better know and understand other club members from their counties or different parts of the state en route to the event. The travel becomes a unifying experience for the group as they laugh, learn and perhaps troubleshoot new routes or unexpected changes in during the trip.

The events themselves provide numerous opportunities to grow and refine skills, generally in a specific project area, such as animal science or leadership and citizenship. At the same time, youth are simultaneous developing life skills. like independence and confidence, which will serve them throughout the rest of their lives. They are also engaged in global and cultural education as they meet new people, see new parts of the world and appreciate both the many similarities and differences that exist.

Traveling with 4-H provides youth a safe and supportive environment to break out of their comfort zone and explore something new. These trips may inspire future educational or career choices as horizons are expanded to the endless possibilities that exist in the future.

This article was published by Michigan State University Extension . For more information, visit http://www. msue. msu. edu. To have a digest of information delivered straight to your email inbox, visit http://www. msue. msu. edu/newsletters. To contact an expert in your area, visit http://expert. msue. msu. edu. or call 888-MSUE4MI (888-678-3464).

Related Events

Mar 19, 2017 | The Palace of Auburn Hills, 6 Championship Drive, Auburn Hills, MI 48326

Mar 26, 2017 – Mar 26, 2017 | Kent County Sheriff's Mounted Unit Equestrian Training Center, 4687 Kroes Street NE, Rockford, MI 49441

Apr 4, 2017 – Apr 8, 2017 | MSU Tollgate Farm and Education Center, 28115 Meadowbrook Road, Novi, MI 48377

Apr 4, 2017 – Apr 8, 2017 | Thompson Community Center, 11370 Hupp Street, Warren, MI 48089

Apr 15, 2017 | MSU Extension Tollgate Farm and Education Center, 28115 Meadowbrook Road, Novi, MI 48377

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February 23, 2017 | Karen L. Pace | Building resilience through the 7 Cs of positive youth development.

February 16, 2017 | Katie Ockert | Several animal science quiz bowls and skill-a-thons are held throughout the year and are a great way to teach youth about animal science.

February 16, 2017 | Jackelyn Martin | The Real Colors personality assessment tool helps with interpersonal interactions amongst individuals.

February 12, 2017 | Betty Jo Krosnicki | 4-H teen leaders are being sought to help meet the challenge of educating the next generation of young people on money management and agri-science career exploration topics.

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Related Resources

4-H center renovations slowly moving forward

A long-term renovation project to upgrade facilities at the Northern Virginia 4-H Educational Center in Front Royal has been a slow-moving effort so far.

Ann Marlow, chairwoman for the James Swart Animal Renovation Committee, said the project is a massive undertaking and that the committee is “doing it in stages.”

Joan Moore, a member of the board of directors as well as the committee, said, “We seem to be stuck in early phases, but it all revolves around funds.”

The committee, Marlow said, is essentially leading the renovation efforts for the center in what is being called the “Dreams Need Heroes Campaign.”

The whole campaign has been estimated to cost as much as $5 million, with the actual renovation costs estimated at $2 million.

The Northern Virginia 4-H Educational Center serves 18 counties in Virginia, including Shenandoah, Warren and Frederick.

At the moment, Marlow said the facility holds most of its events during the summer.

“We’ve got horse classes and horse camps and some other groups using the facility, but we want to do more,” Marlow said.

Both Moore and Marlow indicated that the renovation committee will look to reach out to other state horse breeders groups as well as the Wounded Warrior Project in order to enhance the facility’s uses.

Moore said the project’s next phase includes a $385,600 total upgrade of the stables.

For the immediate future, Moore said the committee will be focused on “making the stalls more habitable.”

Simply upgrading the stall doors will cost the center an estimated $48,400. Moore said the committee has raised between $80,000 and $90,000 since 2004.

The “Dreams Need Heroes” campaign has goals of enhancing the facility for the purposes of holding more events year-round as well as more use as an equestrian facility, Marlow said.

“We need to make the place available, acceptable and attractive enough to have horsemen come in,” Moore said.

In exchange for funding, Moore said the committee is offering donors the opportunity to have site buildings branded in their name.

However, one issue in tackling the renovation efforts, Moore said, is that the committee only has around five or six members. So far, Moore said that the center has been able to upgrade in a few areas since the campaign began. One major upgrade was the addition of frost-proof fire hydrants in 2017.

“The Welsh Pony Association has a show here twice a year and they used to have hoses all over the place,” Moore said.

Still, Moore and the rest of the Animal Renovation Committee are looking to reach more residents in the area and around the state to receive funding.

“We have lists of people that have never even heard of this place,” Moore said, adding that contacting potential donors is “an ongoing process.”

Due to full-time jobs and prior obligations, Moore said it is “very difficult to follow-up on all of the suggested people that we need to meet.”

In addition, Moore said they are working on getting more volunteers for the facility.

“We need them desperately. It could be menial jobs … whether licking envelopes, I don’t care,” she said, “We need interested people, who are not on payroll and who just want to be part of this.”

Moore said that they hope to complete the stall upgrades this spring and will be looking to work with King Construction out of Charlottesville.

In addition, Marlow said that the committee will “purchase a PA system and some judge’s stands” for the stable area.

“The idea is that we want to renovate this facility to make it more usable for people,” Marlow said.

Contact staff writer Kevin Green at 540-465-5137 ext. 155, or kgreen@nvdaily. com

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Average Velocity Formula

Below are problems based on Average Velocity:

Solved Examples

Question 1: Calculate the average velocity at a particular time interval of a particle if it is moves 5 m at 2 s and 15 m at 4s along x-axis? Solución:

Given: Initial distance traveled, x i = 5 m, Final distance traveled, x f = 15 m, Initial time interval t i = 2s, Final time interval t f = 4s. Average Velocity V av = $\frac - x_ > - t_ >$ = $\frac $ = $\frac $ = 5m/s.

Question 2: A car is moving with initial velocity of 20 m/s and it reaches its destiny at 50 m/s. Calculate its average velocity. Solución:

Given: Initial Velocity U = 20 m/s, Final velocity V = 50 m/s. Average Velocity V av = $\frac $ = $\frac $ = 35 m/s.

During a tennis match, a player serves the ball at 23.6 m/s, with the center of the ball leaving the racquet horizontally 2.37 m above the court surface. The net is 12 m away and 0.90 m high. When the ball reaches the net, (a) does the ball clear it and (b) what is the distance between the center of the ball and the top of the net? Suppose that, instead, the ball is served as before but now it leaves the racquet at 5.00° below the horizontal. When the ball reaches the net, (c) does the ball clear it and (d) what now is the distance between the center of the ball and the top of the net?

In a jump spike, a volleyball player slams the ball from overhead and toward the opposite floor. Controlling the angle of the spike is difficult. Suppose a ball is spiked from a height of 2.30 m with an initial speed of 20.0 m/s at a downward angle of 18.00°. How much farther on the opposite floor would it have landed if the downward angle were, instead, 8.00°?

A baseball leaves a pitcher’s hand horizontally at a speed of 161 km/h. The distance to the batter is 18.3 m. (a) How long does the ball take to travel the first half of that distance? (b) The second half? (c) How far does the ball fall freely during the first half? (d) During the second half? (e) Why aren’t the quantities in (c) and (d) equal?

In Fig. 4-39. a ball is thrown leftward from the left edge of the roof, at height h above the ground. The ball hits the ground 1.50 s later, at distance from the building and at angle with the horizontal. (a) Find h ( Hint: One way is to reverse the motion, as if on videotape.) What are the (b) magnitude and (c) angle relative to the horizontal of the velocity at which the ball is thrown? (d) Is the angle above or below the horizontal?

Two seconds after being projected from ground level, a projectile is displaced 40 m horizontally and 53 m vertically above its launch point. What are the (a) horizontal and (b) vertical components of the initial velocity of the projectile? (c) At the instant the projectile achieves its maximum height above ground level, how far is it displaced horizontally from the launch point?

In Fig. 4-48. a baseball is hit at a height and then caught at the same height. It travels alongside a wall, moving up past the top of the wall 1.00 s after it is hit and then down past the top of the wall 4.00 s later, at distance farther along the wall. (a) What horizontal distance is traveled by the ball from hit to catch? What are the (b) magnitude and (c) angle (relative to the horizontal) of the ball’s velocity just after being hit? (d) How high is the wall?

When a large star becomes a supernova. its core may be compressed so tightly that it becomes a neutron star. with a radius of about 20 km (about the size of the San Francisco area). If a neutron star rotates once every second, (a) what is the speed of a particle on the star’s equator and (b) what is the magnitude of the particle’s centripetal acceleration? (c) If the neutron star rotates faster, do the answers to (a) and (b) increase, decrease, or remain the same?

An Earth satellite moves in a circular orbit 640 km above Earth’s surface with a period of 98.0 min. What are the (a) speed and (b) magnitude of the centripetal acceleration of the satellite?

A carnival merry-go-round rotates about a vertical axis at a constant rate. A man standing on the edge has a constant speed of 3.66 m/s and a centripetal acceleration of magnitude . Position vector locates him relative to the rotation axis. (a) What is the magnitude of ? What is the direction of when is directed (b) due east and (c) due south?

A rotating fan completes 1200 revolutions every minute. Consider the tip of a blade, at a radius of 0.15 m. (a) Through what distance does the tip move in one revolution? What are (b) the tip’s speed and (c) the magnitude of its acceleration? (d) What is the period of the motion?

A purse at radius 2.00 m and a wallet at radius 3.00 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is . At that instant and in unit-vector notation, what is the acceleration of the wallet?

A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time , it is at point (5.00 m, 6.00 m) with velocity and acceleration in the positive x direction. At time , it has velocity and acceleration in the positive y direction. What are the (a) x and (b) y coordinates of the center of the circular path if is less than one period?

At , the acceleration of a particle in counterclockwise circular motion is . It moves at constant speed. At time , its acceleration is . What is the radius of the path taken by the particle if is less than one period?

A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (4.00 m, 4.00 m) with a velocity of and an acceleration of . What are the (a) x and (b) y coordinates of the center of the circular path?

A boy whirls a stone in a horizontal circle of radius 1.5 m and at height 2.0 m above level ground. The string breaks, and the stone flies off horizontally and strikes the ground after traveling a horizontal distance of 10 m. What is the magnitude of the centripetal acceleration of the stone during the circular motion?

A cameraman on a pickup truck is traveling westward at 20 km/h while he videotapes a cheetah that is moving westward 30 km/h faster than the truck. Suddenly, the cheetah stops, turns, and then runs at 45 km/h eastward, as measured by a suddenly nervous crew member who stands alongside the cheetah’s path. The change in the animal’s velocity takes 2.0 s. What are the (a) magnitude and (b) direction of the animal’s acceleration according to the cameraman and the (c) magnitude and (d) direction according to the nervous crew member?

A boat is traveling upstream in the positive direction of an x axis at 14 km/h with respect to the water of a river. The water is flowing at 9.0 km/h with respect to the ground. What are the (a) magnitude and (b) direction of the boat’s velocity with respect to the ground? A child on the boat walks from front to rear at 6.0 km/h with respect to the boat. What are the (c) magnitude and (d) direction of the child’s velocity with respect to the ground?

A suspicious-looking man runs as fast as he can along a moving sidewalk from one end to the other, taking 2.50 s. Then security agents appear, and the man runs as fast as he can back along the sidewalk to his starting point, taking 10.0 s. What is the ratio of the man’s running speed to the sidewalk’s speed?

A rugby player runs with the ball directly toward his opponent’s goal, along the positive direction of an x axis. He can legally pass the ball to a teammate as long as the ball’s velocity relative to the field does not have a positive x component. Suppose the player runs at speed 4.0 m/s relative to the field while he passes the ball with velocity relative to himself. If has magnitude 6.0 m/s, what is the smallest angle it can have for the pass to be legal?

Two ships, A and B. leave port at the same time. Ship A travels northwest at 24 knots, and ship B travels at 28 knots in a direction 40° west of south. (1 knot = 1 nautical mile per hour; see Appendix D.) What are the (a) magnitude and (b) direction of the velocity of ship A relative to B. (c) After what time will the ships be 160 nautical miles apart? (d) What will be the bearing of B (the direction of B ’s position) relative to A at that time?

A 200-m-wide river flows due east at a uniform speed of 2.0 m/s. A boat with a speed of 8.0 m/s relative to the water leaves the south bank pointed in a direction 30° west of north. What are the (a) magnitude and (b) direction of the boat’s velocity relative to the ground? (c) How long does the boat take to cross the river?

Two highways intersect as shown in Fig. 4-49. At the instant shown, a police car P is distance from the intersection and moving at speed . Motorist M is distance from the intersection and moving at speed . (a) In unit-vector notation, what is the velocity of the motorist with respect to the police car? (b) For the instant shown in Fig. 4-49. what is the angle between the velocity found in (a) and the line of sight between the two cars? (c) If the cars maintain their velocities, do the answers to (a) and (b) change as the cars move nearer the intersection?

Ship A is located 4.0 km north and 2.5 km east of ship B. Ship A has a velocity of 22 km/h toward the south, and ship B has a velocity of 40 km/h in a direction 37° north of east. (a) What is the velocity of A relative to B in unit-vector notation with toward the east? (b) Write an expression (in terms of and ) for the position of A relative to B as a function of t. where when the ships are in the positions described above. (c) At what time is the separation between the ships least? (d) What is that least separation?

A 200-m-wide river has a uniform flow speed of 1.1 m/s through a jungle and toward the east. An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 4.0 m/s with respect to the water. There is a clearing on the north bank 82 m upstream from a point directly opposite the clearing on the south bank. (a) In what direction must the boat be pointed in order to travel in a straight line and land in the clearing on the north bank? (b) How long will the boat take to cross the river and land in the clearing?

You are kidnapped by political-science majors (who are upset because you told them political science is not a real science). Although blindfolded, you can tell the speed of their car (by the whine of the engine), the time of travel (by mentally counting off seconds), and the direction of travel (by turns along the rectangular street system). From these clues, you know that you are taken along the following course: 50 km/h for 2.0 min, turn 90° to the right, 20 km/h for 4.0 min, turn 90° to the right, 20 km/h for 60 s, turn 90° to the left, 50 km/h for 60 s, turn 90° to the right, 20 km/h for 2.0 min, turn 90° to the left, 50 km/h for 30 s. At that point, (a) how far are you from your starting point, and (b) in what direction relative to your initial direction of travel are you?

Curtain of death. A large metallic asteroid strikes Earth and quickly digs a crater into the rocky material below ground level by launching rocks upward and outward. The following table gives five pairs of launch speeds and angles (from the horizontal) for such rocks, based on a model of crater formation. (Other rocks, with intermediate speeds and angles, are also launched.) Suppose that you are at when the asteroid strikes the ground at time and position (Fig. 4-51 ). (a) At , what are the x and y coordinates of the rocks headed in your direction from launches A through E. (b) Plot these coordinates and then sketch a curve through the points to include rocks with intermediate launch speeds and angles. The curve should indicate what you would see as you look up into the approaching rocks and what dinosaurs must have seen during asteroid strikes long ago.

A woman who can row a boat at 6.4 km/h in still water faces a long, straight river with a width of 6.4 km and a current of 3.2 km/h. Let point directly across the river and point directly downstream. If she rows in a straight line to a point directly opposite her starting position, (a) at what angle to must she point the boat and (b) how long will she take? (c) How long will she take if, instead, she rows 3.2 km down the river and then back to her starting point? (d) How long if she rows 3.2 km up the river and then back to her starting point? (e) At what angle to should she point the boat if she wants to cross the river in the shortest possible time? (f) How long is that shortest time?

In Fig. 4-55. a radar station detects an airplane approach ing directly from the east. At first observation, the airplane is at distance from the station and at angle above the horizon. The airplane is tracked through an angular change in the vertical east–west plane; its distance is then . Find the (a) magnitude and (b) direction of the airplane’s displacement during this period.

The fast French train known as the TGV (Train à Grande Vitesse) has a scheduled average speed of 216 km/h. (a) If the train goes around a curve at that speed and the magnitude of the acceleration experienced by the passengers is to be limited to 0.050g, what is the smallest radius of curvature for the track that can be tolerated? (b) At what speed must the train go around a curve with a 1.00 km radius to be at the acceleration limit?

A magnetic field can force a charged particle to move in a circular path. Suppose that an electron moving in a circle experiences a radial acceleration of magnitude in a particular magnetic field. (a) What is the speed of the electron if the radius of its circular path is 15 cm? (b) What is the period of the motion?

The position vector for a proton is initially and then later is , all in meters. (a) What is the proton’s displacement vector, and (b) to what plane is that vector parallel?

A particle P travels with constant speed on a circle of radius (Fig. 4-56 ) and completes one revolution in 20.0 s. The particle passes through O at time . State the following vectors in magnitude-angle notation (angle relative to the positive direction of x ). With respect to O. find the particle’s position vector at the times t of (a) 5.00 s, (b) 7.50 s, and (c) 10.0 s.

(d) For the 5.00 s interval from the end of the fifth second to the end of the tenth second, find the particle’s displacement. For that interval, find (e) its average velocity and its velocity at the (f) beginning and (g) end. Next, find the acceleration at the (h) beginning and (i) end of that interval.

Long flights at midlatitudes in the Northern Hemisphere encounter the jet stream, an eastward airflow that can affect a plane’s speed relative to Earth’s surface. If a pilot maintains a certain speed relative to the air (the plane’s airspeed ), the speed relative to the surface (the plane’s ground speed ) is more when the flight is in the direction of the jet stream and less when the flight is opposite the jet stream. Suppose a round-trip flight is scheduled between two cities separated by 4000 km, with the outgoing flight in the direction of the jet stream and the return flight opposite it. The airline computer advises an airspeed of 1000 km/h, for which the difference in flight times for the outgoing and return flights is 70.0 min. What jet-stream speed is the computer using?

A particle starts from the origin at with a velocity of and moves in the xy plane with constant acceleration . When the particle’s x coordinate is 29 m, what are its (a) y coordinate and (b) speed?

A wooden boxcar is moving along a straight railroad track at speed . A sniper fires a bullet (initial speed ) at it from a high-powered rifle. The bullet passes through both lengthwise walls of the car, its entrance and exit holes being exactly opposite each other as viewed from within the car. From what direction, relative to the track, is the bullet fired? Assume that the bullet is not deflected upon entering the car, but that its speed decreases by 20%.Take and . (Why don’t you need to know the width of the boxcar?)

You are to throw a ball with a speed of 12.0 m/s at a target that is height above the level at which you release the ball (Fig. 4-60 ). You want the ball’s velocity to be horizontal at the instant it reaches the target. (a) At what angle above the horizontal must you throw the ball? (b) What is the horizontal distance from the release point to the target? (c) What is the speed of the ball just as it reaches the target?

A graphing surprise. At time , a burrito is launched from level ground, with an initial speed of 16.0 m/s and launch angle . Imagine a position vector continuously directed from the launching point to the burrito during the flight. Graph the magnitude r of the position vector for (a) and (b) . For , (c) when does r reach its maximum value, (d) what is that value, and how far (e) horizontally and (f) vertically is the burrito from the launch point? For , (g) when does r reach its maximum value, (h) what is that value, and how far (i) horizontally and (j) vertically is the burrito from the launch point?

In Sample Problem 4-7 b, a ball is shot through a horizontal distance of 686 m by a cannon located at sea level and angled at 45° from the horizontal. How much greater would the horizontal distance have been had the cannon been 30 m higher?

(a) If an electron is projected horizontally with a speed of , how far will it fall in traversing 1.0 m of horizontal distance? (b) Does the answer increase or decrease if the initial speed is increased?

The magnitude of the velocity of a projectile when it is at its maximum height above ground level is 10 m/s. (a) What is the magnitude of the velocity of the projectile 1.0 s before it achieves its maximum height? (b) What is the magnitude of the velocity of the projectile 1.0 s after it achieves its maximum height? If we take and to be at the point of maximum height and positive x to be in the direction of the velocity there, what are the (c) x coordinate and (d) y coordinate of the projectile 1.0 s before it reaches its maximum height and the (e) x coordinate and (f) y coordinate 1.0 s after it reaches its maximum height?

A frightened rabbit moving at 6.0 m/s due east runs onto a large area of level ice of negligible friction. As the rabbit slides across the ice, the force of the wind causes it to have a constant acceleration of , due north. Choose a coordinate system with the origin at the rabbit’s initial position on the ice and the positive x axis directed toward the east. In unitvector notation, what are the rabbit’s (a) velocity and (b) position when it has slid for 3.0 s?

The pilot of an aircraft flies due east relative to the ground in a wind blowing 20 km/h toward the south. If the speed of the aircraft in the absence of wind is 70 km/h, what is the speed of the aircraft relative to the ground?

The pitcher in a slow-pitch softball game releases the ball at a point 3.0 ft above ground level. A stroboscopic plot of the position of the ball is shown in Fig. 4-63. where the readings are 0.25 s apart and the ball is released at . (a) What is the initial speed of the ball? (b) What is the speed of the ball at the instant it reaches its maximum height above ground level? (c) What is that maximum height?

The New Hampshire State Police use aircraft to enforce highway speed limits. Suppose that one of the airplanes has a speed of 135 mi/h in still air. It is flying straight north so that it is at all times directly above a north–south highway. A ground observer tells the pilot by radio that a 70.0 mi/h wind is blowing but neglects to give the wind direction. The pilot observes that in spite of the wind the plane can travel 135 mi along the highway in 1.00 h. In other words, the ground speed is the same as if there were no wind. (a) From what direction is the wind blowing? (b) What is the heading of the plane; that is, in what direction does it point?

The position of a particle moving in the xy plane is given by , where is in meters and t is in seconds. (a) Calculate the x and y components of the particle’s position at , and 4.0 s and sketch the particle’s path in the xy plane for the interval . (b) Calculate the components of the particle’s velocity at , 2.0, and 3.0 s. Show that the velocity is tangent to the path of the particle and in the direction the particle is moving at each time by drawing the velocity vectors on the plot of the particle’s path in part (a). (c) Calculate the components of the particle’s acceleration at , 2.0, and 3.0 s.

A golfer tees off from the top of a rise, giving the golf ball an initial velocity of 43 m/s at an angle of 30° above the horizontal. The ball strikes the fairway a horizontal distance of 180 m from the tee. Assume the fairway is level. (a) How high is the rise above the fairway? (b) What is the speed of the ball as it strikes the fairway?

A track meet is held on a planet in a distant solar system. A shot-putter releases a shot at a point 2.0 m above ground level. A stroboscopic plot of the position of the shot is shown in Fig. 4-64. where the readings are 0.50 s apart and the shot is released at time . (a) What is the initial velocity of the shot in unit-vector notation? (b) What is the magnitude of the free-fall acceleration on the planet? (c) How long after it is released does the shot reach the ground? (d) If an identical throw of the shot is made on the surface of Earth, how long after it is released does it reach the ground?

More than your average project: A day in the life of a 4-H member

Feeding time in the lamb barn is a twice-daily routine throughout the summer for Geauga County 4-H member Anna Montazzoli. And in the morning, she spends roughly an hour walking the lambs.

CHAGRIN FALLS, Ohio — The sun is just up, and Leah Fine is exhausted. She tries to sleep until the last possible minute, but she knows that Bella, Vinnie and Lugnut are surely up and waiting for her.

While it seems like she just left the barn, the 12-year-old pulls on her boots and heads across her family’s 20-acre farm outside Chagrin Falls.

Bella, a one-year-old heifer, is part of the family’s breeding program, but her 4-H project steers Vinnie and Lugnut will both be taken to market after the county fair.

Leah works inside the stall, tucked into a corner of the roughly 200-year-old barn on the former dairy farm, feeding the trio, giving them hay, then cleaning the stall.

“It’s gross if you don’t do it in the morning,” she says of the latter duty, pointing out that she will repeat the entire process before dinner.

As the remaining three head of cattle on her family’s small beef-hog-sheep and alpaca operation look on, Leah swings open the doors leading to a fenced area between the barn and a shed, and leads the massive Lugnut, the 2017 4-H project she will bring to the Great Geauga County Fair Aug. 28 through Sept. 1, out of the barn.

The 1,200-pound Angus cross hesitates a moment as the pair exit the dimly lit barn, planting his front hooves and pulling back in his halter when he notices a stranger in the yard.

“They can be antsy,” Leah says as she coaxes Lugnut through the barn door, repeating “walk, walk” in a gentle, yet firm, tone.

The steer is even less cooperative when Leah leads him into a wash stand, pushing and pulling him into position.

“He knows how to do this,” Leah grunts as the animal finally steps into the stand and Leah runs toward the shed for a hose.

Following his bath, Leah will walk Lugnut for the next two hours.

“They have to get to know you,” Leah said later of exercise routine. “You can tell the difference during competition.”

Lugnut has lived on the Fine farm since September, when Leah bought him from a 4-H member in Chardon. The name, according to Leah’s father, Dan, was given because of the steer’s propensity for acting like “a 600-pound rabbit” when he first arrived on the farm.

Unlike smaller 4-H projects, raising steers has left Leah with time for little else this summer. Still, the busy Kenston Middle School seventh-grader manages to work in soccer and, as soon as school begins again, homework.

Short break

Today, Leah will return to the barn around 5:30 p. m. to repeat the feeding-cleaning-walking rotation. Taking a break after her morning duties, she leans back on a rocking chair on the front porch and explains how it all pays off.

“I know how to buy, raise and sell a steer, but you have to put the work into it, and it can be tough,” she said. “Sometimes I’m so tired when I come home, but I have to go straight to the barn. It is a big responsibility, but it pays off. If your animal doesn’t trust you, they can be jumpy.”

Leah, who has had rabbit, poultry and hog 4-H projects, decided to raise steers after seeing her sister, Elise ­— now a sophomore at the University of Akron — raise them for years. Leah has already begun working with her 2017 project, a steer named Simba.

And the work doesn’t end in the barn.

“In the project books, you have to record things like what grain you used, adding up all your expenses,” she said. “And you have to attend a quality assurance (seminar) and keep up on shots and tagging in December. And I sent out 150 hand-written letters to potential buyers at the fair.”

Dan, a small business owner himself, said that while Leah does the work and pays back all of her project-related expenses, 4-H has become a family effort.

“The lessons it teaches are huge,” Dan said. “And I get to spend quality time with my daughter.”

Leah is using both the work experience and profit to augment her chosen career path, to become a second grade teacher.

“4-H teaches you a lot about completing a project, working on it every day, responsibility and time management,” she said. “But the best, I think, is the friendships I’ve made.”

Then she added with a giggle, “And I like being the person behind the gate at the fair, seeing all the fairgoers walking by and saying ‘yeah, that’s my animal.’”

Down the road in Auburn Township, some of Leah’s fellow Geauga County Junior Fair Livestock Sale Ambassadors group are hard at work on their 4-H projects as well.

Family affair

Members of the Montazzoli family describe themselves as suburban. But since moving to Ohio from Atlanta, 4-H has become all encompassing for Todd and Liz Montazzoli and their four children.

Todd, a marketing professional for Nestle in Solon, said when his oldest daughter, Jennifer, expressed an interest in a 4-H pygmy goat project seven years ago, his support was immediate.

“It was what they wanted to do, so I built them a barn,” he laughed.

Now, each of the Montazzoli children — Jennifer, 18; Anna, 15; Matthew, 12; and Phillip, 8 — spend up to six hours a day in the barn with their various projects.

Todd himself has become the adviser for the Junior Fair Livestock Sale Ambassadors group, which gives community presentations to encourage businesses and individuals to attend the junior fair livestock sale, as well as promote their businesses through the livestock sale.

Rutina diaria

While smaller animal projects don’t take up as much of the year as larger projects such as steer and hogs — lambs, for instance, are purchased in May, chickens in July, and ducks in June — the day-to-day care is equally time consuming and there is even less time to ready the animals for the fair.

Jennifer and Anna are up by 7:30 a. m. each day, feeding their four lambs — Emmit, Cody, Captain and Trooper — which share barn space with Phillip’s lamb Griffin, and Jennifer’s pygmy goats. Anna also shows ducks and both girls have shown rabbits in the past.

Following the morning feeding, the girls spend roughly an hour walking the lambs, both for exercise and practice for the fair’s showmanship competition.

Meanwhile, Matthew and Phillip are able to sleep in a bit longer than their sisters before tending to their coops of meat chickens and layers. But the boys have much do much more than simple twice-per-day feeding, watering and collecting eggs three times each day.

“You want to bring the ones that are most calm when you hold them and don’t flip out,” he said, holding Sadie, which took first in open class at last year’s fair. “You keep a record of each chicken to pick which four you bring to the fair. You’re looking for a list of defects (judges consider) like an uneven keel or missing a certain feather.”

Future plans

All four of the Montazzoli children return to the barn in the evening, when it is cooler for another round of feeding, watering and showmanship practice, sometimes well into the night, Jennifer said. In addition, detailed records must be kept in each project book.

Even friends must get in on the act.

“Oh yeah,” Jennifer laughed. “All our friends know that we’ll make them work.”

Like all 4-H clubs, the groups the children belong to — including Junior Fair Board, Junior Leadership, Feathers and Fleece, Pygmy Connection, and The Bunny Bunch — are completely member-driven, and community service projects range from yard work to visiting area nursing homes with smaller animals like rabbits.

The 32 Junior Fair Ambassadors members write, refine, and ultimately present a marketing plan encouraging businesses and civic groups to attend the fair and make a purchase at the market livestock sales.

“I don’t know if I’ll be a farmer, but there is so much 4-H has taught me about discipline,” Anna said. “Even when you don’t want to put in the work, they are animals, so you have to.”

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Susan | April 15th, 2002

By Larry Cote, Associate Provost and Director

It’s truly stating the obvious that the 4-H camping program has occupied almost all of our collective efforts and energy over the past month. Many of you have seen, or will have the opportunity to view, the videotape of the April 9 news conference in which we announced that we are slowing down the process, holding camps as usual this summer, and taking our time to do our own thorough and thoughtful review of the use of Native American customs in our 4-H camping program. This news was well-received within Extension as well as throughout the state.

Also well-received was the appointment of Sue Jones and Dave Snively to lead us, and our many 4-H members, volunteers, and alumni, in the next steps. I have confidence in Dave’s and Sue’s judgment, their keen understanding of 4-H and West Virginia, and their commitment to Extension. They will be providing regular updates on their actions and plans; I ask you to give them your full support.

Many of you have shared your thoughts with me over recent weeks, and for that candor I thank you. There are so many things from the past month that I would do over if I had the chance; such is the benefit of hindsight. Now we begin to rebuild trust and bring together the many groups and individuals who will be part of the process of moving forward. I’ve been humbled and almost overwhelmed by the passion and commitment associated with the 4-H program in our state and want to make the most of every opportunity in the coming days and months to “make the best better.” Thank you for everything you’ve done–and will continue to do–in support of our 4-H educational program. I know it has been a difficult time for many of you within your own counties as well as your own families as you’ve attempted to support the decision to make changes.

I have met and talked about this issue with many people and groups over the past month, and I will continue to do so. While we have made a conscious effort to focus forward and not to dwell on the misdirection and ambiguity from the USDA. there are some who need to hear that information from me before they are satisfied. If you have specific volunteers or community members who remain angry or need clarification, I would urge you to contact Dave, Sue, or me, and we will contact them.

Many of you have expressed your concern over the accusations and speculation made by hosts and callers of Metronews’ “Talkline” radio show. As an update, we did provide “Talkline” co-host Stephen Reed with detailed documentation about this issue, as requested through the Freedom of Information Act (FOIA). In particular, he had stated that he was skeptical that the USDA really did direct us to change our program by June 1 or risk a civil rights investigation and potential loss of funding. When Mr. Reed received his packet of information, which included a draft letter from the USDA outlining the potential sanctions if we did not comply, he responded via e-mail to me last week: “We all now realize that the draft copy of the fax you received from the USDA really did exist, and while we may differ on certain points, I can certainly understand how this correspondence could make you feel a sense of urgency about the matter.” Mr. Reed has offered his assistance with our “4-H Forward” proceso.

There is so much energy and commitment being generated in our state (and beyond) right now for 4-H. I ask each of you to help us take this energy and turn it toward the celebration of the true power of youth and the many exciting opportunities for growth of our program.

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A compact way to describe position is with a graph of position x plotted as a function of time t —a graph of x ( t ). (The notation x ( t ) represents a function x of t . not the product x times t .) As a simple example, Figure 2-2 shows the position function x ( t ) for a stationary armadillo (which we treat as a particle) over a 7 s time interval. The animal's position stays at x = -2 m.

Higo. 2-2 The graph of x( t) for an armadillo that is stationary at x = -2 m. The value of x is -2 m for all times t.

Figure 2-3 a is more interesting, because it involves motion. The armadillo is apparently first noticed at t = 0 when it is at the position x = -5 m. It moves toward x = 0, passes through that point at t = 3 s, and then moves on to increasingly larger positive values of x . Figure 2-3 b depicts the straight-line motion of the armadillo and is something like what you would see. The graph in Figure 2-3 a is more abstract and quite unlike what you would see, but it is richer in information. It also reveals how fast the armadillo moves.

Higo. 2-3 ( a) The graph of x( t) for a moving armadillo. ( b) The path associated with the graph. The scale below the x axis shows the times at which the armadillo reaches various x values.

Actually, several quantities are associated with the phrase “how fast.” One of them is the average velocity v avg . which is the ratio of the displacement D x that occurs during a particular time interval D t to that interval:

The notation means that the position is x 1 at time t 1 and then x 2 at time t 2 . A common unit for v avg is the meter per second (m/s). You may see other units in the problems, but they are always in the form of length/time.

On a graph of x versus t . v avg is the slope of the straight line that connects two particular points on the x ( t ) curve: one is the point that corresponds to x 2 and t 2 . and the other is the point that corresponds to x 1 and t 1 . Like displacement, v avg has both magnitude and direction (it is another vector quantity). Its magnitude is the magnitude of the line's slope. A positive v avg (and slope) tells us that the line slants upward to the right; a negative v avg (and slope) tells us that the line slants downward to the right. The average velocity v avg always has the same sign as the displacement D x because D t in Equation 2-2 is always positive.

Figure 2-4 shows how to find v avg in Figure 2-3 for the time interval t = 1 s to t = 4 s. We draw the straight line that connects the point on the position curve at the beginning of the interval and the point on the curve at the end of the interval. Then we find the slope D x / D t of the straight line. For the given time interval, the average velocity is

Higo. 2-4 Calculation of the average velocity between t = 1 s and t = 4 s as the slope of the line that connects the points on the x( t) curve representing those times.

Average speed s avg is a different way of describing “how fast” a particle moves. Whereas the average velocity involves the particle's displacement D x . the average speed involves the total distance covered (for example, the number of meters moved), independent of direction; es decir,

You drive a beat-up pickup truck along a straight road for 8.4 km at 70 km/h, at which point the truck runs out of gasoline and stops. Over the next 30 min, you walk another 2.0 km farther along the road to a gasoline station.

(a) What is your overall displacement from the beginning of your drive to your arrival at the station?

Solution: Assume, for convenience, that you move in the positive direction of an x axis, from a first position of x 1 = 0 to a second position of x 2 at the station. That second position must be at x 2 = 8.4 km + 2.0 km = 10.4 km. Then the Key Idea here is that your displacement D x along the x axis is the second position minus the first position. From Equation 2-1. tenemos

Thus, your overall displacement is 10.4 km in the positive direction of the x axis.

(b) What is the time interval D t from the beginning of your drive to your arrival at the station?

Solution: We already know the walking time interval D t wlk (= 0.50 h), but we lack the driving time interval D t dr . However, we know that for the drive the displacement D x dr is 8.4 km and the average velocity v avg, dr is 70 km/h. A Key Idea to use here comes from Equation 2-2. This average velocity is the ratio of the displacement for the drive to the time interval for the drive:

Rearranging and substituting data then give us

(c) What is your average velocity v avg from the beginning of your drive to your arrival at the station? Find it both numerically and graphically.

Solution: The Key Idea here again comes from Equation 2-2. v avg for the entire trip is the ratio of the displacement of 10.4 km for the entire trip to the time interval of 0.62 h for the entire trip. Here we find

To find v avg graphically, first we graph the function x ( t ) as shown in Figure 2-5. where the beginning and arrival points on the graph are the origin and the point labeled as “Station.” The Key Idea here is that your average velocity is the slope of the straight line connecting those points; that is, v avg is the ratio of the rise ( D x = 10.4 km) to the run ( D t = 0.62 h), which gives us v avg = 16.8 km/h.

Higo. 2-5 The lines marked “Driving” and “Walking” are the position-time plots for the driving and walking stages. (The plot for the walking stage assumes a constant rate of walking.) The slope of the straight line joining the origin and the point labeled “Station” is the average velocity for the trip, from the beginning to the station.

(d) Suppose that to pump the gasoline, pay for it, and walk back to the truck takes you another 45 min. What is your average speed from the beginning of your drive to your return to the truck with the gasoline?

Solution: The Key Idea here is that your average speed is the ratio of the total distance you move to the total time interval you take to make that move. The total distance is 8.4 km + 2.0 km + 2.0 km = 12.4 km. The total time interval is 0.12 h + 0.50 h + 0.75 h = 1.37 h. Thus, Equation 2-3 gives us

TACTIC 1: Do You Understand the Problem?

For beginning problem solvers, no difficulty is more common than simply not understanding the problem. The best test of understanding is this: Can you explain the problem?

Write down the given data, with units, using the symbols of the chapter. (In Sample Problem 2-1. the given data allow you to find your net displacement D x in part (a) and the corresponding time interval D t in part (b).) Identify the unknown and its symbol. (In the sample problem, the unknown in part (c) is your average velocity v avg .) Then find the connection between the unknown and the data. (The connection is provided by Equation 2-2. the definition of average velocity.)

TACTIC 2: Are the Units OK?

Be sure to use a consistent set of units when putting numbers into the equations. In Sample Problem 2-1. the logical units in terms of the given data are kilometers for distances, hours for time intervals, and kilometers per hour for velocities. You may sometimes need to convert units.

TACTIC 3: Is Your Answer Reasonable?

Does your answer make sense, or is it far too large or far too small? Is the sign correct? Are the units appropriate? In part (c) of Sample Problem 2-1. for example, the correct answer is 17 km/h. If you find 0.00017 km/h, -17 km/h, 17 km/s, or 17000 km/h, you should realize at once that you have done something wrong. The error may lie in your method, in your algebra, or in your keystroking of numbers on a calculator.

TACTIC 4: Reading a Graph

Figure 2-2. Figure 2-3. Figure 2-4 and Figure 2-5 are graphs you should be able to read easily. In each graph, the variable on the horizontal axis is the time t . with the direction of increasing time to the right. In each, the variable on the vertical axis is the position x of the moving particle with respect to the origin, with the positive direction of x upward. Always note the units (seconds or minutes; meters or kilometers) in which the variables are expressed.

2.9 Interactive Learningware

PBJ Makes Bullish Cross Above Critical Moving Average

By The Online Investor Staff, Monday, March 14, 4:06 PM ET

Start slideshow: 10 Stocks Crossing Above Their 200 Day Moving Average »

In trading on Monday, shares of the PowerShares Dynamic Food & Beverage Portfolio ETF (AMEX:PBJ ) crossed above their 200 day moving average of $32.29, changing hands as high as $32.37 per share. PowerShares Dynamic Food & Beverage Portfolio shares are currently trading up about 0.4% on the day. The chart below shows the one year performance of PBJ shares, versus its 200 day moving average:

This Article's Word Cloud: AMEX Above Average Beverage Crossing Dave Dynamic Find Flexible Food Free Growth Investment Looking Offer Portfolio PowerShares Special Start Stocks Their Trial about above average below changing chart compares currently from hands high holding last moving offer point range raquo share shares special that their trading versus week what with

PBJ Makes Bullish Cross Above Critical Moving Average | www. TheOnlineInvestor. com | Copyright y copia; 1998 - 2017, All Rights Reserved

Nothing in The Online Investor is intended to be investment advice, nor does it represent the opinion of, counsel from, or recommendations by BNK Invest Inc. or any of its affiliates, subsidiaries or partners. Ninguna de las informaciones contenidas en el presente documento constituye una recomendación de que cualquier estrategia de inversión, estrategia de cartera, transacción particular sea adecuada para cualquier persona en particular. Todos los espectadores están de acuerdo en que bajo ninguna circunstancia BNK Invest, Inc. sus subsidiarias, socios, funcionarios, empleados, afiliados o agentes serán responsables por cualquier pérdida o daño causado por su confianza en la información obtenida. Al visitar, usar o ver este sitio, usted acepta los siguientes Términos y Condiciones: Términos de servicio. Video widget and stock market videos powered by Market News Video. Quote data delayed at least 20 minutes, powered by Ticker Technologies. Y Mergent. Contact The Online Investor ; Conozca a nuestro equipo editorial.

Getting average bit rate of a MPEG-4/H.264 movie

Subject . Getting average bit rate of a MPEG-4/H.264 movie

From: Nikita Zhuk <email@hidden >

Date: Mon, 6 Nov 2006 18:04:47 +0200

Delivered-to: email@hidden

Delivered-to: email@hidden

I would like to estimate an average data bit rate of the first (and only) video track in a movie which has been encoded with H.264 MPEG-4 codec. Currently I've been trying to estimate this by this simple calculation:

bitRate = dataSizeInBits / durationInSeconds, where dataSizeInBits = GetMediaDataSize(myVideoMedia, 0, GetMediaDisplayDuration(myVideoMedia)) * 8 durationInSeconds = GetMediaDisplayDuration(myVideoMedia) / GetMediaTimeScale(myVideoMedia)

I've tested this code with various movie files and in most cases the results seem reasonable. However, in some cases, especially with short (1-2 sec) movies the estimated bitrate is 1.5 - 3 times higher than the bitrate which was used when these videos were encoded.

So, does GetMediaDataSize() call include some "extra" size (e. g. container, header data..) which shouldn't be included in the bitrate calculation? Are there any better ways to calculating this? I'm using Objective-C & QTKit when possible and C & Carbon QuickTime when necessary.

4-H GET MOVING, HEEL, FOOD PYRAMID EDUCATION

Scott County CES utilized a variety of educational resources and methods to reach K-5 students and their families with healthy living curriculum. Throughout the school year 1,420 students were reached each month with the HEEL newsletter sent home via Friday Folders. Lessons from the newsletters provided by CES were reinforced by school nurses, family resource center personnel and on school announcements.

110 5th grade 4-H members participated in a 5 part series of lessons utilizing the Get Moving Kentucky for Youth curriculum. Pre and post test evaluations where administered and consistent improvement is indicated on the post test with scores averaging above 90% for all tests and test takers.

The Get Moving lesson series provided review time and the most popular lesson was “group exercise at your desk”. Teachers reinforced this lesson prior to testing and indoor physical activity during inclement weather was a repeated request.

Selecting healthy food and snacks based on the food pyramid was a series shared via the 4-H Newsletter. The Scott County 4-H Newsletter reaches 1,320 families each month. A five-part series included in our monthly newsletter received positive feed back from parents. During a 4-H Council meeting one leader remarked that this information was posted on their refrigerator. Another 4-H parent remarked that her inactive daughter showed her the exercises they learned at school during 4-H time and she felt the positive nature of the lesson (non-competitive) would encourage her child to continue exercising.

Greenbush, Maine

Other production occupations including supervisors (10%)

Driver/sales workers and truck drivers (9%)

Electrical equipment mechanics and other installation, maintenance, and repair occupations including supervisors (7%)

Vehicle and mobile equipment mechanics, installers, and repairers (5%)

Building and grounds cleaning and maintenance occupations (5%)

Laborers and material movers, hand (5%)

Carpenters (5%)

Cashiers (9%)

Secretaries and administrative assistants (9%)

Other production occupations including supervisors (5%)

Registered nurses (5%)

Other office and administrative support workers including supervisors (5%)

Building and grounds cleaning and maintenance occupations (4%)

Preschool, kindergarten, elementary and middle school teachers (4%)

Average climate in Greenbush, Maine

Based on data reported by over 4,000 weather stations

Earthquake activity:

Greenbush-area historical earthquake activity is slightly below Maine state average. It is 93% smaller than the overall U. S. average.

On 10/3/2006 at 00:07:38 , a magnitude 4.3 (3.8 MB , 3.8 MW , 4.3 LG , Depth: 4.0 mi , Class: Light , Intensity: IV - V) earthquake occurred 55.0 miles away from the city center On 4/20/2002 at 10:50:47 , a magnitude 5.2 (5.2 MB , 4.2 MS , 5.2 MW , 5.0 MW , Depth: 6.8 mi , Class: Moderate , Intensity: VI - VII) earthquake occurred 255.0 miles away from Greenbush center On 10/7/1983 at 10:18:46 , a magnitude 5.3 (5.1 MB , 5.3 LG , 5.1 ML) earthquake occurred 294.1 miles away from the city center On 1/19/1982 at 00:14:42 , a magnitude 4.7 (4.5 MB , 4.7 MD , 4.5 LG) earthquake occurred 184.6 miles away from the city center On 2/26/1999 at 03:38:43 , a magnitude 3.8 (3.8 LG , Depth: 2.0 mi , Class: Light , Intensity: II - III) earthquake occurred 61.5 miles away from Greenbush center On 9/16/1994 at 04:22:42 , a magnitude 3.6 (3.6 LG , Depth: 3.1 mi) earthquake occurred 24.0 miles away from the city center Magnitude types: regional Lg-wave magnitude (LG), body-wave magnitude (MB), duration magnitude (MD), local magnitude (ML), surface-wave magnitude (MS), moment magnitude (MW)

Natural disasters:

The number of natural disasters in Penobscot County (17) is greater than the US average (12). Major Disasters (Presidential) Declared: 10 Emergencies Declared: 7

Causes of natural disasters: Floods: 8 , Storms: 7 , Snows: 5 , Heavy Rains: 2 , Blizzard: 1 , Hurricane: 1 , Ice Storm: 1 , Snowfall: 1 , Wind: 1 , Winter Storm: 1 , Other: 1 (Note: Some incidents may be assigned to more than one category).

Hospitals and medical centers near Greenbush:

CUMMINGS HEALTH CARE FACILITY (Nursing Home, about 13 miles away; HOWLAND, ME)

ORONO COMMONS (Nursing Home, about 14 miles away; ORONO, ME)

TREATS FALLS HOUSE (Hospital, about 14 miles away; ORONO, ME)

Colleges/universities with over 2000 students nearest to Greenbush:

University of Maine ( about 14 miles; Orono, ME ; Full-time enrollment: 8,931)

Husson University ( about 20 miles; Bangor, ME ; FT enrollment: 2,421)

University of Maine at Augusta ( about 79 miles; Augusta, ME ; FT enrollment: 3,204)

University of Maine at Farmington ( about 82 miles; Farmington, ME ; FT enrollment: 2,036)

Saint Joseph's College of Maine ( about 128 miles; Standish, ME ; FT enrollment: 2,010)

Southern Maine Community College ( about 128 miles; South Portland, ME ; FT enrollment: 4,666)

University of Southern Maine ( about 129 miles; Portland, ME ; FT enrollment: 6,647)

Public elementary/middle school in Greenbush:

Notable locations in Greenbush: Scotts Corners (A). Greenbush Volunteer Fire Department Codville Station (B). Greenbush Volunteer Fire Department Oloman Station (C). Display/hide their locations on the map

Churches in Greenbush include: Cardville Church (A). United Pentecostal Church (B). Display/hide their locations on the map

Cemeteries: Welles Cemetery (1). Cardville Cemetery (2). Dennis Cemetery (3). Display/hide their locations on the map

Streams, rivers, and creeks: Stevens Brook (A). Smart Brook (B). Whitney Brook (C). Parker Meadow Brook (D). Otter Brook (E). Poplar Brook (F). Display/hide their locations on the map

Penobscot County has a predicted average indoor radon screening level greater than 4 pCi/L (pico curies per liter) - Highest Potential

Air pollution and air quality trends (lower is better)

Air Quality Index (AQI) level in 2012 was 54.3 . This is better than average.

Greenbush compared to Maine state average:

Median house value significantly below state average.

Unemployed percentage below state average.

Black race population percentage significantly below state average.

Hispanic race population percentage significantly below state average.

Foreign-born population percentage significantly below state average.

Renting percentage below state average.

Length of stay since moving in significantly above state average.

Number of rooms per house significantly below state average.

House age significantly below state average.

Percentage of population with a bachelor's degree or higher significantly below state average.

Educational Attainment (%) in 2000

School Enrollment by Level of School (%) in 2000

Education Gini index (Inequality in education)

Most commonly used house heating fuel:

Presidential Elections Results

1996 Presidential Elections Results

2000 Presidential Elections Results

2004 Presidential Elections Results

2008 Presidential Elections Results

2012 Presidential Elections Results

Religion statistics for Greenbush town (based on Penobscot County data)

Source: Clifford Grammich, Kirk Hadaway, Richard Houseal, Dale E. Jones, Alexei Krindatch, Richie Stanley and Richard H. Taylor. 2012. 2010 U. S.Religion Census: Religious Congregations & Membership Study. Association of Statisticians of American Religious Bodies. Jones, Dale E. et al. 2002. Congregations and Membership in the United States 2000. Nashville, TN: Glenmary Research Center. Graphs represent county-level data

Food Environment Statistics:

Number of grocery stores: 34

Number of supercenters and club stores: 2

Number of convenience stores (no gas): 38

Number of convenience stores (with gas): 85

Number of full-service restaurants: 110

11.02 / 10,000 pop.

Adult diabetes rate:

Adult obesity rate:

4.81% of this county's 2011 resident taxpayers lived in other counties in 2010 ($34,478 average adjusted gross income )

0.04% of residents moved from foreign countries ($304 average AGI )

Top counties from which taxpayers relocated into this county between 2010 and 2011:

0.44% ($29,886 average AGI)

5.52% of this county's 2010 resident taxpayers moved to other counties in 2011 ($36,804 average adjusted gross income )

0.03% of residents moved to foreign countries ($387 average AGI )

Top counties to which taxpayers relocated from this county between 2010 and 2011:

0.56% ($32,990 average AGI)

Strongest AM radio stations in Greenbush:

WZON (620 AM; 5 kW; BANGOR, ME; Owner: THE ZONE CORPORATION)

WABI (910 AM; 5 kW; BANGOR, ME; Owner: CLEAR CHANNEL BROADCASTING LICENSES, INC.)

WNZS (1340 AM; 1 kW; VEAZIE, ME; Owner: WATERFRONT COMMUNICATIONS INC.)

WSKW (1160 AM; 10 kW; SKOWHEGAN, ME; Owner: MOUNTAIN WIRELESS, INCORPORATED)

WDEA (1370 AM; 5 kW; ELLSWORTH, ME; Owner: CUMULUS LICENSING CORP.)

WRKO (680 AM; 50 kW; BOSTON, MA; Owner: ENTERCOM BOSTON LICENSE, LLC)

WTME (780 AM; 10 kW; RUMFORD, ME; Owner: MOUNTAIN VALLEY BROADCASTING, INC.)

WEEI (850 AM; 50 kW; BOSTON, MA; Owner: ENTERCOM BOSTON LICENSE, LLC)

WBZ (1030 AM; 50 kW; BOSTON, MA; Owner: INFINITY BROADCASTING OPERATIONS, INC.)

WCRN (830 AM; 50 kW; WORCESTER, MA; Owner: CARTER BROADCASTING CORPORATION)

WNNZ (640 AM; 50 kW; WESTFIELD, MA; Owner: CLEAR CHANNEL BROADCASTING LICENSES, INC.)

WCHP (760 AM; 35 kW; CHAMPLAIN, NY; Owner: CHAMPLAIN RADIO, INC.)

WREM (710 AM; daytime; 5 kW; MONTICELLO, ME; Owner: ALLAN H WEINER)

Strongest FM radio stations in Greenbush:

WVOM (103.9 FM; HOWLAND, ME; Owner: CLEAR CHANNEL BROADCASTING LICENSES, INC.)

WHCF (88.5 FM; BANGOR, ME; Owner: BANGOR BAPTIST CHURCH)

WBZN (107.3 FM; OLD TOWN, ME; Owner: CUMULUS LICENSING CORP.)

WMEH (90.9 FM; BANGOR, ME; Owner: MAINE PUBLIC BROADCASTING CORPORATION)

WEZQ (92.9 FM; BANGOR, ME; Owner: CUMULUS LICENSING CORP.)

WQCB (106.5 FM; BREWER, ME; Owner: CUMULUS LICENSING CORP.)

WWMJ (95.7 FM; ELLSWORTH, ME; Owner: CUMULUS LICENSING CORP.)

WWBX (97.1 FM; BANGOR, ME; Owner: CLEAR CHANNEL BROADCASTING LICENSES, INC.)

WKIT-FM (100.3 FM; BREWER, ME; Owner: THE ZONE CORPORATION)

WHMX (105.7 FM; LINCOLN, ME; Owner: BANGOR BAPTIST CHURCH)

WBFB (104.7 FM; BELFAST, ME; Owner: CLEAR CHANNEL BROADCASTING LICENSES, INC.)

WMEB-FM (91.9 FM; ORONO, ME; Owner: UNIVERSITY OF MAINE SYSTEM)

WNSX (97.7 FM; WINTER HARBOR, ME; Owner: CLEAR CHANNEL BROADCASTING LICENSES, INC.)

WGUY (102.1 FM; DEXTER, ME; Owner: CONCORD MEDIA GROUP, INC.)

TV broadcast stations around Greenbush:

WMEB-TV ( Channel 12; ORONO, ME; Owner: MAINE PUBLIC BROADCASTING CORPORATION)

WBGR-LP ( Channel 33; BANGOR/DEDHAM, ME; Owner: MAINE FAMILY BROADCASTING, INC.)

W66CL ( Channel 66; BANGOR, ME; Owner: MS COMMUNICATIONS, LLC)

Greenbush, Maine

Fatal accident count 9

Vehicles involved in fatal accidents 15

Fatal accidents involving drunken persons: 1

Fatalities 12

Persons involved in fatal accidents 22

Pedestrians involved in fatal accidents 0

Maine average

Fatal accident count 58

Vehicles involved in fatal accidents 82

Fatal accidents involving drunken persons 23

Fatalities 63

Persons involved in fatal accidents 140

Pedestrians involved in fatal accidents 4

National Bridge Inventory (NBI) Statistics

4 Number of bridges

8m 26ft Total length

$124,000 Total costs

4,720 Total average daily traffic

391 Total average daily truck traffic

6,841 Total future (year 2031) average daily traffic

FCC Registered Antenna Towers:

FCC Registered Private Land Mobile Towers:

1

Lat: 45.100333 Lon: -68.637250, Call Sign: WQBH225 Assigned Frequencies: 151.745 MHz Grant Date: 10/05/2004, Expiration Date: 10/05/2017, Certifier: Janis Madden Registrant: Atlantic Communications, Inc. 40 Freedom Parkway, Hermon, Maine 04401, Bangor, ME 04402-0596, Phone: (207) 848-7590, Fax: (207) 974-3151, Email:

FCC Registered Amateur Radio Licenses:

2

Call Sign: KD1QX, Previous Call Sign: N1NKO, Licensee ID: L00805901 Grant Date: 01/30/2004, Expiration Date: 02/01/2017 Registrant: Frank L Hoskins Jr, 1032 Cardville Road, Greenbush, ME 04418

Call Sign: KB1WLU, Licensee ID: L01678166 Grant Date: 12/15/2011, Expiration Date: 12/15/2021, Certifier: Bruce M Johnson Registrant: Bruce M Johnson, 1517 Greenfied Rd, Greenbush, ME 04418

FAA Registered Aircraft:

1

Aircraft: DENNEY AIRCRAFT KITFOX 2 ( Category: Land, Seats: 2, Weight: Up to 12,499 Pounds), Engine: ROTAX 521 (80 HP) (2 Cycle) N-Number: 602TR. Serial Number: 196, Year manufactured: 1990, Airworthiness Date: 05/22/2007 Registrant (Individual): Ryan P Severance, 958 Cardville Rd, Greenbush, ME 04418

2006 National Fire Incident Reporting System Incidents:

Incident types - Greenbush

Volunteers Essential To Successful 4-H Programs

Volunteer leaders are essential to the successful delivery of 4-H programs to youth. Last year, more than 660,000 4-H volunteer leaders worked directly or indirectly with youth in the United States. In Alabama, more than 3300 volunteers helped with 4-H projects and/or programs.

Due to downsizing and economic cuts from government sources, 4-H programs will depend on help from volunteers more and more, in the coming years, says Dr. Bob Drakeford, Extension 4-H Specialist, volunteer programs.

In Alabama, we are using volunteers in a number of ways in Extension programs to benefit communities and youth. We have an active 4-H Volunteer Association which is directed by Tommy Williams of Albertville.

Four-H adult volunteers know what it means to make a difference in a young person's life. They are valuable to 4-H because they share their knowledge and skills with young people and give youths the guidance needed to grow into good, productive citizens.

People of all ages can be volunteers for 4-H, says Drakeford. Young or old men and women can become 4-H volunteers. Mothers, fathers, grandparents, working or retired businessmen and businesswomen, teachers and college students can become active volunteers.

Four-H also provides ways for older youths to become volunteer leaders for children's programs.

The average 4-H volunteer donates 220 hours per year in preparing for and teaching youth. Estimated value of the total time and resources volunteers devote to 4-H is about $1.1 billion annually.

If you are interested in becoming a 4-H volunteer leader, contact your county Extension office. If you are interested in joining the Alabama 4-H Volunteer Association, write to Tommy Williams, 1860 Courtland, Albertville, AL.

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Moving Forward with 4-H SET

By: Andrew Yuan & Melissa Sharp 4-H Youth Mentors, Pinellas County Extension

What does 4-H mean to you? Do you think it’s all about agriculture and animal care? Not anymore it’s not. 4-H programs and clubs have progressed to include project areas outside the traditional agricultural beginnings. 4-H has evolved to keep up with modern times. As 4-H looks even more towards the future, it has adopted a new initiative: developing and implementing programs for 4-H Science, Engineering, and Technology, better known as 4-H SET.

The 4-H SET initiative is being carried out through the 4-H Youth Development Program in response to increasing global competition in the field of science. In the United States only about 18 percent of high school seniors are proficient in science according to a 2005 National Assessment of Educational Program study. In addition, only 5 percent of college graduates earn degrees in science, engineering, and technology compared to 66 percent in Japan and 59 percent in China. 4-H SET could be the solution. With resources and connections to 106 land-grant universities and colleges, 4-H is in the perfect position to educate today’s youth.

In conjunction with the new SET initiative, last year 4-H successfully launched the national public service campaign, One Million New Scientists. One Million New Ideas.™ The goal of this campaign is to attract youth to the sciences and have one million new youth in 4-H SET programs by the year 2017. To date, 4-H Science, Engineering, and Technology programs reach roughly 5 million youth with hands-on learning experiences with more than half a million adult volunteers providing their devoted support. These programs capture all sorts of subjects including but not limited to rocketry, computer science, bio-fuels, robotics, and renewable energy.

Another product of this initiative is 4-H National Youth Science Day (NYSD). The first NYSD ever was held last year on October 8, 2008. It was an official day recognized by Congress that emphasizes the importance of science and sparks interest in youth to pursue careers in science, engineering, and technology. The 2008 National Science Experiment featured on that day focused on environmental science and water conservation. Look for upcoming details later this month on the second annual 4-H National Youth Science Day.

The 4-H SET initiative will ultimately increase science literacy and aptitude among the 4-H youth, spark their interest in careers in science, engineering, and technology, and prepare them to compete in a global community. 4-H SET will breed the next generation of global thinkers and technological innovation as we head into the future.

An example of a new 4-H SET curriculum is The Power of the Wind . This is a fun hands on book that teaches middle and high school youth the value of critical thinking and different ways of going green.

The Power of the Wind has many different activities. One activity is about making a wind power boat that could slide along a smooth surface when a fan was activated. This teaches youth the engineering process of planning, building, testing and then modifying an idea. By using interactive methods, youth learn fundamental engineering principles while having a great time! Another example in to build pinwheels in order to learn how turbines work.

Critical thinking is stressed heavily in this book. The activities encourage youth to come up with their own ideas about a problem, or design. For example, in one activity youth are asked to design and then build a wind power machine.

Going green is a big theme in society now, and this curriculum definitely fits into the green movement. The book discusses the benefit and workings of turbines and other wind powered machines as well as how much money turbines save on electricity cost, and why it’s so clean. The curriculum even touches briefly on solar energy, and why going green is good.

If you are interested in more information about 4-H SET, The Power of the Wind . or other project areas for the 21st century, please contact the 4-H office at 582-2215, ayuan@pinellascounty. org. or msharp@pinellascounty. org .

Storage Unit Conversion Chart

ABF's 28 foot trailers are approximately 8 feet 6 inches wide and 9 feet high. This is significantly larger than most rental trucks. ReloCubes are approximately 6'3"D x 7'W x 8'4"H. In general, allow 200 cubic feet of loading space for each room of your house. You'll want to allow extra room for bulky pieces of furniture. Remember to include outdoor furniture and large appliances.

Storage Unit Size

Storage Unit Space

Equivalent ABF Trailer Space

Equivalent ABF ReloCubes

5' x 10' Storage

5' x 15' Storage

10' x 10' Storage

10' x 15' Storage

1200 cubic feet

10' x 20' Storage

1600 cubic feet*

* If your storage unit is 10’ x 20’ or larger, we recommend you call our toll free number at 800-355-1696 to speak with an ABF U-Pack representative.

Note: These figures are for estimation only. Your freight bill will be based on the actual space your shipment uses.

Average cycling speed for new and experienced cyclists

One of the most common questions among new cyclists - and one of the hardest to give a sensible answer to - is the average speed of a cyclist.

There are lots of reasons why average speed can't be used as a reliable measure of comparison, which mostly come down to the following:

Riding conditions

If you live in Norfolk, where hills are few and far between, your experience will bear little comparison with a rider setting off to the Lake District each week. The rolling hills of the Cotswolds are not the same as the Scottish highlands.

So hearing from someone else that their average is, say, 20 miles per hour, means very little if you don't know where they are riding.

Some areas are naturally and frequently exposed to high winds. Wind has a very significant impact on cycling speed, even quite gentle wind. Likewise temperature is a factor, with very hot and cold weather both acting to reduce average speed.

Equipo

It's not about the bike? Well perhaps just a bit, especially where weight is concerned. Cyclists who have changed to carbon fibre bikes have told me their speed increased immediately by 5-10%. This was a greater improvement than I expected, and perhaps would only make such an important difference for cyclists in great shape.

Peripheral equipment like tyres can also make a small difference in weight and speed.

I suspect, but can't prove it, that the psychological impact of buying a lighter / more expensive bike also plays a role - if you think you will go faster. you will go faster.

But if you are overweight yourself, saving a kilo on the bike will make a smaller difference.

Distance covered

Average speed varies to an extent with distance covered. Rides less than an hour or so in length will usually have a slightly lower average, because the first part of a ride is slower as your legs warm up. Rides between one and two hours usually have the greatest overall speed. Then for longer rides the average will often start to fall slightly, as fatigue plays an increasing role. For many of us rides over about three hours can become very tiring (assuming a reasonable sustained effort during those three hours!)

Cyclist age

Cyclist age is important, but often less so than the number of years experience that the cyclist has.

Over the years cyclists accumulate a greater proportion of 'slow twitch' muscle fibres in their legs. Heart and lungs will often be strong and efficient. But age counts against all of us!

Older riders will usually be less strong at fast sprints or bursts up short hills, but very good at maintaining steady speed over longer distances. There are lots of 40-50 year old cyclists who can hold their own in rides with 25 year olds.

Teamwork

Cycling in a group - paceline riding - has very significant benefits. For much of the time you will be 'drafting' the person in front ie experiencing limited wind resistance yourself. Although the benefits this provides will vary with conditions and the number of people in the group, it is often said that the average cyclist's speed will increase 20-30% as a result of cycling in a group, even more.

So it is very unlikely your average solo speed will be comparable with the local cycling group. The Tour de France riders achieve 25 miles per hour over 125 miles, but that is very much due to the large size of the peloton (group of cyclists).

Average speed - indications

Bearing in mind all the provisos above, you still want to know the 'average cycling speed? Hear are some general guidelines, all for solo riders on general 'mixed' terrain (ie rolling hills about 30% of the time, and pretty flat the rest of the time):

Beginner, short distance (say 10-15 miles): average speed 12 mph. Most cyclists can achieve 10-12 mph average very quickly with limited training

More experienced, short-medium distance (say 20-30 miles): average 15-16 mph

Reasonable experience, medium (say 40 miles): average around 16-19 mph

Quite competent club rider, some regular training likely, medium-long distances (say 50-60 miles): 20-24 mph

Many cyclists never get to an average over 13-15 mph, don't worry about it, enjoy yourself. Plenty of cyclists can maintain 25+ mph over long distances, especially if conditions are flat or they are cycling in groups.

Get your family moving with 4-H, experts say

Special to The Commercial

FERNDALE — In a world over-saturated by electronic devices, people, more than ever, need to get up and move! That’s why the C. A. Vines 4-H Center, west of Little Rock, is hosting a 5K Fun Run for families.

The 5K run will be held April 13. At-the-door registration for the race will begin at 7:30 a. m. with the race start set for 9:30 a. m. Awards will be presented at 11 a. m.

Advance registration is $5 for children and $15 for adults. At-the-door admission is $10 for children and $20 for adults.

The brochure, which has directions to the 4-H center and the pre-registration form, can be found at http://www. kidsarus. org/5KRun/5k_trail_run_brochure. pdf

For more information, contact Tony Baker at tbaker@uaex. edu or at (501) 821-4444.

The Cooperative Extension Service is part of the University of Arkansas System Division of Agriculture and offers its programs to all eligible persons regardless of race, color, national origin, religion, gender, age, disability, marital or veteran status, or any other legally protected status, and is an Affirmative Action/Equal Opportunity Employer.

John Cartwright is a correspondent for the Cooperative Extension Service, U of A System Division of Agriculture.

Dear 4-H Colleagues,

March had been a hectic but highly energizing and educational month for me. The month started with a trip to Albany to participate in the Legislative Breakfast component of 4-H Capital Days. It was exciting to return to a program that I was very involved with during my first Extension position as a 4-H Educator in Rockland County all these years later in the State Leader role! Congratulations to the 4-H Educator Association for continuing to provide strong leadership to this program. I was impressed by the high level of engagement between the Legislators and your 4-H teens. The youth participants were clearly well prepared for the opportunity to share their 4-H experiences with the elected officials.

Thanks to the staff here and all of you I am learning more and more about our vibrant and complex 4-H system at the Local, State and National level. Visits this month to Broome County, New York City, a NYS 4-H Foundation Board Meeting, and a trip to National 4-H Council for the meeting of the State Leaders have all helped to expand my knowledge of our resources, challenges and the many opportunities that are heading our way. One such opportunity emerged this month through National Council in the form of a funding opportunity from the Disney Corporation. Working quickly to respond to a very short turnaround time and with strong support from Jackie Davis-Manigaulte (NYC), Tim Davis (Ontario) and Shawn Tiede (Wyoming) we were able to submit a proposal that will hopefully allow NYS 4-H to be one of five pilot sites nationally for the implementation of a 4-H Exploring Your Environment project this summer and into the fall that will reach underserved youth from NYC, Rochester and Buffalo, including the opportunity for 100 youth to participate in a week of summer 4-H Camp at Bristol Hills or Camp Wyomoco.

Finally, I am looking forward to digesting the responses to the online 4-H survey that we launched early in the month and sent to your Association Executive Director. If your Association has not responded you still have a few more days to participate!

Assistant Director – Interim State 4H Leader

Governor Andrew Cuomo’s proposed 2017 State Budget demonstrates a growing commitment to expanding quality Afterschool programming across the State. The State 4-H Office, with a great deal of support and input from CCE Association-based 4-H programs that already are engaged in afterschool efforts as well as the NYC 4-H program, has been working closely with the New York State Afterschool Network (NYSAN) to contribute to the effort to seize on this opportunity by educating the NYS Senate and Assembly about the importance of this investment of behalf of NYS families and children. 4-H is a strong player already with a number of programs stretching across the State, and this new funding would provide many additional opportunities for us to bring our research-based and hands-on philosophy to many more NYS youth.

The research is clear that high-quality afterschool and summer programs not only keep children safe and parents working, but also helps close the achievement gap for low-income students. Additionally, these programs support development of the critical thinking and social skills needed for long-term success in the workplace and in life. According to NYSAN Executive Director, Nora Niedzielski-Eichner, “New York has a tremendous foundation of high-quality programs that can be quickly scaled up under the Governor’s proposal to reach more than 100,000 students who currently have no access to afterschool experiences. These new programs have the potential to change lives for children all across the state as they have the opportunity to explore new interests, develop healthy relationships, and receive academic support—all components of high-quality programs that have been shown to increase the chances that students will stay in school and out of trouble.” The Governor’s proposal would initially almost triple the state’s current investment in afterschool programs and, over the next five years, promises to continue to grow support for these crucial programs. Meeting the needs of the 21st Century workforce is a crucial challenge for New York, and increasing access to afterschool programs is a cost-effective approach for both families and students.

Looking at the various ways 4-H is already engaged in afterschool programming, it is clear that we have the capacity to serve in the role as direct providers in some situations, providers of targeted programming at existing sites that fit with our 4-H mission mandates, and also potentially to provide technical assistance and educational support toward the goal of ensuring that programs are research-based and promote positive youth development principles. I have been communicating with a small group of 4-H educators who are already highly engaged in the afterschool setting, sharing information from NYSAN and asking for their input as we make sure that the good work 4-H is already doing is well understood by our policy makers in Albany. If you would like to be added to this informal list of interested 4-H educators please just send me an email and I will add you to the conversation!

Andrew S. Turner CCE Assistant Director, Interim 4H State Leader

After just a few days in the role of interim 4H State Leader I am far more interested in listening and learning, but I do have the following initial observations to share:

1) 4H is an incredibly strong brand that we should take pride in and work hard to protect, promote and expand to more young people. The 4H clover is well-known, highly regarded and elicits incredibly positive feedback from people when they see it. This is not something to take for granted. We should probably all think about it often and remember that we all have a responsibility to maintain this status and expand it moving forward. Read more…

2) Our statewide 4H community (youth participants and their guardians, 4H alumnus, volunteer leaders, 4H staff and team members both on and off campus and our funding partners) are very passionate about the 4H program, its capability to provide positive youth development and its potential to grow and remain highly relevant in the 21st century. I do not sense much of any cynicism, defeatism or belief that “our best days are behind us.” This is exciting and something we should capitalize on.

3) There is a willingness to explore our own strengths, weaknesses, opportunities and threats and make some challenging decisions. There is, to be fair, also frustration that although we have had many conversations, strategic planning sessions and survey opportunities, the ability to actually make some commitments and move together as one system has seemed a bit out of reach. In my administrative experience, to date, this often indicates that it is not a lack of vision necessarily or lack of will but more a lack of a clear understanding of roles and process. How do we make decisions as a statewide 4H program? How do we hold each other accountable to the vision, goals and priorities? I am looking forward to the opportunity to explore these questions with you in the coming months.

Working with the team here I plan to develop a brief survey in the near future that captures some basic information about the 4H team in the field and how you are feeling about these issues and the questions I posed in my email message at the end of the year which are included again below. I do not think a drawn-out planning process is required; we have quite a bit of information already to consider, but I would like to capture some very new input and perspective from all of you and learn more about your local association 4H goals and staffing structures. I am also interested in getting out to visit and discuss some of these issues face to face. Please consider inviting me to regional/district 4H staff meetings in the coming months, and I will make every effort to attend a meeting of each district during my tenure as the interim State Leader. Here are the three questions again from my December message.

What can the NYS 4H Youth Development program provide to the youth of NYS that is unique, effective and highly valued by youth participants and their families? What can we do better than anyone else?

What program goals can our educators, volunteers and campus-based partners all get equally passionate about in a way that can propel our efforts forward in a more unified and focused way?

Where do we think the resources will be coming from in the future to support our efforts, and what does this mean for the way we are organized and structured?

I believe that if we can focus on these and related questions in the coming weeks and months we will be in a good position to make wise decisions about the leadership position and many other questions related to the 4H program in NYS. Thanks for listening!

Andrew S. Turner CCE Assistant Director, Interim 4H State Leader

During this holiday season I am thankful for all of the accomplishments of 4-H across New York State. The state office has been successfully expanding collaborative efforts on campus and off. Among the accomplishments, we have 5 active Youth PWTs, a 4-H Youth Development Advisory Committee that includes 4 on-campus faculty, 4 active Federal Formula Funds projects directly linking the state office, campus faculty and staff to county programming, we are now a prominent active member of NYSAN, partnering with Ulster County we are re-establishing participation with State Exchange, we have secured the Washington State 4-H e-volunteering modules and will continue to offer additional modules as they become available, our National Mentoring Project involvement has expanded from 3 to 6 sites, and through national efforts, we’re working to identify a set of common measures for NYS that compliments national and regional reporting. Our county and state programming advances align well with the CCE Strategic Plan and the educator’s success stories we receive exemplify the depth and variety of 4-H programming.

As I complete my tenure, I appreciate the opportunity to have been a part of this complex system. I have learned a wealth of information about the dynamic resources and richness of the Cornell Cooperative Extension system. It has been a pleasure to build on the legacy of NYS and to take steps towards accessible 4-H programming for all of the children and youth of New York. I wish continued success and advancement for the CCE 4-H system.

Have a peaceful, restorative holiday season!

This FFN is full of great information about opportunities for 4-H’ers, volunteers, educators, updates on 4-H evaluation activities that have been occurring throughout the past year, grant opportunities that could support programming, upcoming workshops and training on-campus. There is a lot of good information in this issue-I encourage you to read through it from start to finish.

October was full of conferences and workshops virtual and in-person that many educators attended, including the Galaxy and NYSACCE4-HE conferences. Most exciting for me was the participation of two important 4-H partners at the Educator’s conference. Liz Searle, NYS 4-H Foundation Director and Nora Niedzielski-Eichner, NYSAN Director. The growth of these partnerships will allow for more support of NYS 4-H.

The NYS Foundation is willing to collaborate with you on funding efforts beneficial to county programming, including some of the grants described in this edition. The Foundation is also available to support and collaborate on larger funding efforts. Consider meeting with Liz to discuss development opportunities, beyond the annual Foundation grant opportunity.

Our involvement with NYSAN is expanding, according to Nora, we have 4-H participation in at least three of the regional networks, Corning/Elmira, Westchester, and Rochester. June Mead and Vicki Giarratano have been invited to participate in a meeting this month to launch a network in the Binghamton area, which would bring our involvement up to participation in four of eight regional networks. This is very good news for us, because one of many benefits of partnering with NYSAN is engaging in conversations with legislators about after-school/out-of-school programs. On January 14th, NYSAN is hosting the first Expanding Learning Opportunities for New York’s Students: A Statewide Summit on Afterschool and Summer Programs for state legislators. I am delighted to share with you that The Bronfenbrenner Center for Translational Research will be a sponsor of the summit and New York State 4-H will have a delegation! Stay tune for more details.

Enjoy the beauty of the changing fall colors and have a great weekend!

Valerie Adams - Bass, PhD

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Escambia Moving Forward With $1.5 Million 4-H Facility

December 30, 2012

The Escambia County Commission is set to move forward with design work on a new Escambia County 4-H Center located at the Escambia County Extension Office on Stefani Road.

Earlier this year, the children and teens on the 4-H County Council voted to sell their 240 acre Langley Bell 4-H Center to Navy Federal Credit Union. Navy Federal will pay $3.6 million for the property next to the credit union’s campus in Beulah, and the Escambia County Commission is constructing the new 4-H Center on Stefani Road with $1.5 million in local option sales tax funds.

At their January 3 meeting, the Escambia Commission is expected to approve a $170,000 contract with Hernandez Calhoun Design International for architectural and engineering services for the new 4-H Center. The design project is expected to be complete in 105 days, plus an additional 30 days for construction bids and 240 days for construction administration.

The new 4-H Center will be a single story building just under 10,000 square feet that will include a multi-purpose room/auditorium with stage, kitchen, offices, reception area, life skills room, science room with wet lab, volunteer room with technology lab, county council, club meeting room and storage. Plans also call for a potential 500 square foot exterior teaching pavilion.

A 12-member 4-H Task Force is currently holding meetings to study the needs of the local 4-H Youth Development program by evaluating options to compliment the 4-H Center on Stefani Road.

During the next six months, the task force will develop viable options that may be considered to meet the animal science, natural resources, and outdoor education needs of the UF/IFAS Extension 4-H Youth Development Program in Escambia County. The Task Force will present its findings to the UF/IFAS Dean of Extension, who will in turn use the information provided by the task force to make decisions for the 4-H program.

Pictured top: The Langley Bell 4-H Center was sold to Navy Federal Credit Union for $3.6 million. A portion of the neighboring Navy Federal complex in Beulah can be seen in the background of this photograph of the Langley Bell Building. Pictured below: A new 4-H Center will be constructed adjacent to the Escambia County Extension Office on Stefani Road. NorthEscambia. com photos, click to enlarge.

Comentarios

23 Responses to “Escambia Moving Forward With $1.5 Million 4-H Facility”

4-H Alumni on January 1st, 2017 1:18 pm

Speechless….for a sec…….This is such a travesty of justice….what was intended for a perpetual gift for past, present and future youth of our county has morphed into a fight over $$$’s for the mighty and powerful “system” to receive gain… If we don’t do it right – right now – the present and future youth will not have resources available to learn important life skills in the agricultural and animal husbandry fields. A student does not learn with only classroom experience….there are enough “college grads” in the system who don’t do the “in - field” calls necessary to properly facilitate the duties of the current Ex. Office system. Visual and hands on lessons are so important to most of our youth for the complete learning cycle. To restrict the field and barn lessons would stifle the determination and resolve, the ability to process all of the skills necessary to adequately become a true 4-Her…head, heart, hands and health. Ironic…..the very motto we are trying to preserve is the very one that is being tragically yanked away. Without the land, environment, space, agricultural equipment and other related resources…our kids will not have the necessary tools of learning as a springboard for the future of agriculture…in our town, our county, or our country. Sad….

Whatthehay on January 1st, 2017 11:49 am

THE WHOLE POINT IS: this land was never ever suppose to sold to begin with, it did not belong to the aka county it was donated in good faith to the 4H, the cc would not encourage anything ifit had not been sold to begin with. This land was to be there long after all of us are gone. You tell me how you could ever replace the nature and beauty of this piece of land, it wasn’t just about livestock and growing things, some children have never seen land like this and sadly now they never will.

david lamb on January 1st, 2017 10:40 am

Nick Place sounds reasonable. In my conversations with him, he has stated that he wants all the possibi;lities and info before he makes a decision. WRE need to keep the pressure on him, but write/call/email the commisio0ners too! I was told by a person in the know that dear Pam asked him if 10 acres would suffice and if he knew where there was 10 acres for sale. His answer was a resounding NO. If you want to discuss the Bayer property I AM ALL FOR THAT! Bet Miss Allen went away mad! Spending money on Stefani Rd is Pams way of getting what SHE wants. The MOU appears to be an appeasement with no legality behind it. It took away the right of the youth to have any say in what Pam Allen does or what IFAS does.

Gulf Coast on December 31st, 2012 10:28 am

I encourage each and everyone of you to show your displeasure by calling the county commissioners and telling them to hold that money up.

Sandra on December 31st, 2012 10:17 am

Surprised? Hardly, we all knew this was going to happen. It boils down to the mighty dollar and we would sell our own children for that green stuff.

Molino lady on December 31st, 2012 8:40 am

I think its a crying shame that the 4-H children will miss out on all their activities until the higher ups make up their minds on how to spend the money they receive from the sale of their land to Navy Federal. The Bayer land on Crabtree Church in Molino would have been the piece of land I would have chosen. What’s wrong, don”t the big wigs making the decision on what land to buy, want to drive to Molino. 4-H is suppose to be about the children’s projects. Stephani Road is residenal property. Not a place for the kids to enjoy nature and their surroundings. I think its a shame, myself.

concerned. citizen on December 31st, 2012 5:51 am

I agree with gulf coast. Its not the county commissioners its the leadership with the extension office. Every decision falls on the dean Nick place. However the county commissioners should hold up the money that they are over which is the lost dollars that is the only leverage we have. We will end up with no land and a gold empire of a building if this money is not held up. They will use all the 1.5 plus another million leaving not enough money to replace what we once had. I plead with the public to stand up for our kids like you did for the library system. We need your support. Don’t be silent email your commissioners and dr place

429SCJ on December 31st, 2012 2:19 am

@ Molino Jim. These Commissioners have no shame. They only seek to advance their own interest at the cost of others.

Time will wash away these commissioners and the world will be shed of them.

gulfcoast on December 30th, 2012 9:00 pm

Whatthehay, It wasnt the CC fault, in fact they did support the resolution “encouraging” extension to find a suitable replacement. Two brand new commissioners as well, hopefully even more supportive of what the kids did for this county.

Show your displeasure with extension with an email to Nick Place, dont bother with Diem, Allen, or Vergot they want nothing to do with a new Langley Bell Property.

molino jim on December 30th, 2012 8:53 pm

To the 4H members– welcome to Civics 101. You have just learn how government 101 works. As of yesterday one of the members of the “select committee” was ask about what was being done about the 4H property, he stated there had been no decision made. I guess he’s one of the CC’s hand picked movers and shakers. My daughter was a member of 4H when she was young, my wife had to take her to meetings because of my job. She fussed about having to drive home at night and now the same thing is still going to happen. How many members of 4H live south of Cantonment as compared to the north end. How much live stock can be kept on the property the CC want 4H to use? I know the other people living in the area are going to enjoy the smell and sounds of live stock next door to them. Also is this property the county already owns or has WD and the rest of the good old boys returned. THE COUNTY COMMISSION SHOULD BE ASHAME OF THIS AND OF OF THEIR SELVES.

Whatthehay on December 30th, 2012 8:29 pm

GulfCoast, contact your County Commisioner, really? They were the trustees and they allowed this to happen to begin with thats who it all started with.

Gulf Coast on December 30th, 2012 7:12 pm

If you are truly concerned about the future of 4H, I encourage each and every one of your to contact your county commissioner’s office, voice those concerns. Also and probably most importantly you need to contact Dr. Nick Place, the new Dean of Extension, his email is:

Dr. Place is the one who will ultimately decide what will happen with the $1.6 million dollars allocated from the sale of the Langley Bell property. If enough citizens show their displeasure with the way Ms. Allen, and Mr. Diem is handling this situation, it can only help.

The Task Force does not even get to vote on their favorite proposal, another way Ms Allen has taken the citizens voice away from them. I repeat the Task Force doesnt get a vote.

The 4Hers of this county did their civic duty to support economic job growth in this county. The taxpayers need to voice their displeasure with the people WE pay to grow the 4H program in this county. They have failed miserably at their job, and we need to make sure the CC and Dr. Place know this.

david lamb on December 30th, 2012 7:01 pm

one more thing! Economic development got their wishes chamber of commers got their wishes Navy Federal got their wishes commissioner got brownie points for sale All the muckity muck got sonmething when does 4Hfamilies get what they want good ole boy network at work.

Carl on December 30th, 2012 6:56 pm

I do not have any ties with 4H but it seems the kids are being took advantage of. Going from 240 acres to 20 acres, what kind of deal is that? I wish the public would rally around the kids and make the County Commission and whoever else is in charge do the right thing. Seems like the 4H needs a Good Lawyer.

david lamb on December 30th, 2012 6:39 pm

THIS IS ONE HUGE MISTAKE! The youth of Escambia 4H deserve better representation than this! IFAS, Pam Allen and Keith Diem are trying to ram their desires down our throats! NO money shoulkd be spent on Stephani RD until the results, conclusions and desires of the 4H families/members of Escambia county are determined. As a former 4Her and member of 4H alumni, I want to see Bayer property bought and all Extension activities moved to that location. I also make no bones about supporting new management in the Escambia extension office. For any state, local or federal funds to be spent on the Current extension office is dead wrong and Commissioners need to be careful with spending monies on that location.

russ on December 30th, 2012 12:53 pm

Now it looks like the cc’s are gonna stick it to the children just like they stuck it to the employees.

Jodie on December 30th, 2012 11:52 am

I find it hard to believe that the 4-H Kids sold their 240 acres and are settling for a few acres next to the extension office. And now they have to spend more money to build facilities on this small amount of land.

Whatever happened to the Bayer land. It has all the buildings on it needed for livestock, meetings, etc, etc.

Sounds like the “Task Force” and adults took over and are giving the kids the shaft.

dick tracy on December 30th, 2012 11:17 am

There isn’t nothing surprizing me anymore with our dictatorship. Just another chicken soup sandwich…….

SANDI on December 30th, 2012 10:46 am

This might be a dumb question but if they are getting $3.6 million for the land why are we using local option sales tax money to build their building?

whatthehay on December 30th, 2012 10:24 am

Dear Mr. Matt Langley Bell, you set that property aside for the future of the children of Escambia County, your wishes were not honored and now the 240 that were left after the first sale is now being squeezed on to 20. I apologize for the carelessness that was forced upon a legacy and trust, this is so sad. Idon’t want to hear about it brought jobs and other stuf blah, blah. blah there is hundreds of acres of federal land right next to the navy federal ( for a few helicopters to train on) and also other lands available for purchase this is a crying shame.

Sandra on December 30th, 2012 9:19 am

So the Bayer property on Crabtree is out? I thought that that property was better suited. I guess in the end the extension service will dictate this deal as none of them want to drive to Molino.

Bama54 on December 30th, 2012 8:08 am

I did not know this a done deal! I thought the 4-h were looking for area to build!

concerned. citizen on December 30th, 2012 7:12 am

I will be asking commissioners to hold off on approving this until the task force had time to do their job and the dean has selected where the livestock and the “camp” is going to go. They 4-H is planning one using the 1.5 million lost dollars on the facility plus portions of the 1.6 that everyone thought was allocated for land. The MOU had loop holes in its wording but they played it off as the total 1.6 could be used for land. The public is being led to believe 4H is doing the right thing and that is by far not the truth. I urge you to get involved and insure its a win win for all. At this point the kids are getting the shaft

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Introduction: Average Rate of Change

The average rate of change of any function is a concept that is not new to you. You have studied it in relation to a line. That's right! The slope is the average rate of change of a line. For a line, it was unique in the fact that the slope was constant. It didn't change no matter what two points you calculated it for on the line. Take a look at the following graph and we will discuss the slope of a function. Demo: Slope of a Secant/Tangent Line (Walter Fendt) The function is in red. The blue line connects the two points that we want to find the average rate of change (slope of the blue line). The two points are (x, f(x)) and (x+h, f(x+h)). To find the slope, the definition is the change in y over the change of x. Does this sound familiar. Applying this definition we get the following formula:

Notice on the graph that the line we are finding the slope of crosses the graph twice. Do you remember from geometry what you call a line that crosses a circle twice? You got it. It's a secant line . When you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points.

As an example, let's find the average rate of change ( slope of the secant line ) for any point on a given function. This is finding the general rate of change. The general rate of change is good for any two points on the function. Find the general rate of change for f(x) = x 2

f(x) = x 2 and f(x + h) = (x + h) 2 Therefore, the slope of the secant line between any two points on this function is 2x + h. To find the specific rate of change between two given values of x, is a simple matter of substitution. Let's say we are asked to find the average rate of change between the points x 1 = 2 and x 2 = 4. Then in our general answer, we will replace x with x 1 and h = x 2 - x 1 . Replacing these values in the formula yields 2(2) + (4 - 2) = 4 + 2 = 6. Thus, the slope of the secant line connecting the two points of the function is 6. Note that the answer is a positive number. That means what? That's right, you know! The line is going uphill or increasing as you look at it from left to right. Be careful that you put the values for determining h in the correct order. You already know that slope can be positive, negative or zero.

Now using the same function as above, find the average rate of change between x 1 = -1 and x 2 = -3. The answer is 2(-1) + ( -3 + 1) = -2 + -2 = -4. This means that the secant line is going downhill or decreasing as you look at it from left to right.

Sample problems

1) Find the general rate of change for the function f(x) = 2x 2 + 1. Then find the specific rate of change for x 1 = 2 to x 2 = 5.

2) Find the general rate of change for the function f(x) = x 3. Then find the specifice rate of change for x 1 = 0 to x 2 = 2. Look for the answers worked out somewhere below!

Fly into the next section with Snoopy! Look down here for the answers to the sample problems. Specific rate of change = 4(2) +2(5 - 2) = 8 + 6 = 14 Specific rate of change = 3(0) + 3(0)(2) + (2) 2 = 4 Ready for the next section! Go back up and hit the yes button.

Rory Eldridge, of Stanton, makes eye contact with judge Adam Conover while showing his pig Tuesday morning at the Montcalm County 4-H Fair. Making eye contact with the judge while showing your pig is one of the points that a contestant is scored on in competition. (The Daily News | Mike Taylor)

Bayley Wolfe works her hog around the arena for one final showing after winning grand supreme in the Swine Show Tuesday at the Montcalm County 4-H Fair.

GREENVILLE — Organizers at this year’s Montcalm County 4-H Swine Show were originally concerned that contestant numbers might be somewhat reduced this year due to a nationwide outbreak of porcine epidemic diarrhea (PED) virus that decimated (as of April) about 10 percent of the country’s piglets. From June, 2017 to April, 2017 about seven million pigs nationwide succumbed to the illness, which is not transferable to humans.

According to Lisa Johnson, of the Montcalm County 4-H board, the number of contestants in this year’s show is about the same as in previous years, despite the epidemic.

“They’re about the same as has been in the past,” Johnson said. “It’s been a little difficult finding feeder pigs this year for projects because of the swine virus going around.”

Johnson added that many pig farmers have become incredibly cautious about letting “outsiders,” basically, anyone not directly related to the farm, get near their animals. Since there is still not much known about exactly how the disease is spread, that caution is well considered.

Volunteers help corral a pig toward the winners area for a photo Tuesday at the Montcalm County 4-H Fair.

“I’ve even heard of breeders who ask someone to wait down at the roadside and then bring their pig to them, rather than let them go up to the barns,” Johnson said.

For all the worry over the virus, however, the mood was festive and exciting at this year’s swine show. Young 4-H members paraded their neatly groomed hogs past the judges exactly as in years past. Though “paraded” may be too formal a word.

Pigs, after all, have minds of their own and even the trainers of the best hogs present sometimes found themselves chasing their recalcitrant, squealing charges around the pen.

Turnout was excellent for the event, despite grey skies and frequent cloudbursts.

Judges based their decisions on several factors, two of the most important being presentation of the pig — how well it is groomed — and the trainer’s ability to control the animal. All the hours of hard work back home at the farm paid off for several blue ribbon winners throughout the day.

Colin Hough, 12, of Lakeview, lets out a yell of excitement after taking first place in the heavyweight hog round of Tuesday’s Swine Show at the Montcalm County 4-H Fair.

The less well-trained animals frequently elicited chuckles from the gathered spectators as they dashed around the pen in an effort to avoid being corralled.

County 4-H member Hannah Patin, 16, has been involved in 4-H since she was 10 and was showing a “backup” hog. The pig she had been training for the past several months came in just one pound below the minimum required by the judges.

“My first pig was one pound under,” Hannah said. “So I’m showing a backup. I’m not sure what my chances will be.”

But like most of the other contestants milling around the barn waiting for their turn in the arena, Hannah was enjoying her moment in the spotlight, her chance to see the end result of months of hard work and dedication.

National 4-H Shooting Sports Joins NSSF’s Project ChildSafe® to Emphasize Responsible Firearm Storage

NEWTOWN, Conn. and TRAPPE, MD – The National Shooting Sports Foundation (NSSF®) announced today that National 4-H Shooting Sports, a leading shooting education and youth development program administered by the U. S. Department of Agriculture, will join forces with Project ChildSafe to emphasize the importance of responsible firearm storage across the country.

COLORADO SPRINGS, Colorado (June 1, 2017) - At only 18 years old, Lydia Paterson (Kansas City, Kansas) has solidified herself as a world-class pistol athlete by earning an Olympic Quota in Women’s Air Pistol at the International Shooting Sports Federation (ISSF) World Cup in Munich, Germany. Lydia started in 4-H shooting sports when she was eight years old. Having been in the program until this year when she ages out. She held the 2010 Daisy National BB gun title; broke the National Jr air pistol record by two points that has been held since 1995 a year before she was born; and now has earned an Olympic quota for the United States of America in air pistol that has not been earned since 2005. Lydia’s brother, Caleb has won three 4-H National Shooting titles and is now helping coach the Kansas National 4-H team. Her father, Ron and mother Letha have been active in 4-H since 2006. Lydia’s mom says that “We believe in this program and what it has done for our family bringing us together and teaching us a lifestyle of helping others to achieve their own goals in life.”

The 4-H Name and Emblem

The 4-H Name and Emblem is a federally protected mark, 4-H programs are subject to federal regulations, including that the 4-H Name and Emblem shall not be used in any way to imply endorsement of commercial firms, products or services. Inclusion of the following websites is indicative of a partnership between 4-H and these entities, and does not imply endorsement or exclusivity.

Focusing on Youth Development

The focus of all 4-H programs is the development of youth as individuals and as responsible and productive citizens. The National 4-H Shooting Sports Program stands out as an example. Youth learn marksmanship, the safe and responsible use of firearms, the principles of hunting and archery, and much more. The activities of the program and the support of caring adult leaders provide young people with opportunities to develop life skills, self-worth, and conservation ethics.

Additional problems from Serway's fourth edition

(4 ed) 2.1 The position-time graph for a particle moving along the z-axis is as shown in an old Figure P2.1. Determine whether the velocity is positive, negative, or zero at times t 1 . t 2 . t 3 . and t 4

(4 ed) 2.2 The new BMW M3 can accelerate from zero to 60 mi/h in 5.6 s

(a) What is the resulting acceleration in m/s 2 ?

(b) How long would it take the BMW to go from 60 mi/h to 130 mi/h at this rate?

(4 ed) 2.3 A hot air balloon is traveling vertically upward at a constant speed of 5.00 m/s. When it is 21.0 m above the ground, a package is released from the balloon.

(a) After it is released, for how long is the package in the air?

(b) What is its velocity just before impact with the ground!

(c) Repeat (a) and (b) for the case of the baloon descending at 5.0 m/s.

(4 ed) 2.4 A hockey player is standing on his skates on a frozen pond when an opposing player skates by with the puck, moving with a uniform speed of 12.0 m/s. After 3.00 s, the first player makes up his mind to chase his opponent. If the first player accelerates uniformly at 4.00 m/s 2 ,

(a) how long does it take him to catch the opponent?

(b) How far has the first player traveled in this time?

2.Q4 Is it possible to have a situation in which the velocity and acceleration have opposite signs? If so, sketch a velocity-time graph to prove your point.

Certainly. Consider a car moving to the right but slowing down. Moving to the right means its velocity is positive. Slowing down means its velocity is de creasing or the change in velocity is negative and that means the acceleration is negative.

2.Q5 If the velocity of a particle is nonzero, can its acceleration be zero? Explain.

If the velocity is constant the acceleration is zero .

2.Q6 If the velocity of a particle is zero, can its acceleration be nonzero? Explain.

A velocity of zero is also a constant velocity and that means the acceleration is zero .

2.Q9 A student at the top of a building of height h throws one ball upward with an initial speed v yi and then throws a second ball downward wit the same initial speed. How do the final speeds of the balls compare when they reach the ground?

This one will be fun or interesting to talk about again after we have studied Energy Conservation.

When the ball that was initially thrown up ward comes back to the height of the top of the building, its speed is again v yi . It will have the same speed . Of course its velocity will be - v yi because it is moving down . That means that it has exactly the same speed and velocity at the ball that is initially thrown down ward with initial speed v yi so the two balls hit the ground with exactly the same speed (and velocity!).

2.Q16 A pebble is dropped into a water well and the splash is heard sixteen seconds later; as illustrated in the "BC" cartoon in Figure !2.16. Estimate the distance from the top of the well to the water's surface.

We can use the equation

We are measuring distances from the top of the well so y i = 0 and we drop the pebble so v yi = 0 so this equation reduces to

y = (1/2) ( - 9.8 m/s 2 ) (16 s) 2

That is a very deep "well", indeed! But, maybe, wells were deeper in such prehistoric times. If we had used the approximation that a y = - g = - 10 m/s 2. then our value would have been

Problems from the current (5th) edition of Serway and Beichner.

2.4 A particle moves according to the equation x = 10 t 2 where x is in meters and t is in seconds.

(a) Find the average velocity for the time interval from 2.0 s to 3.0 s.

x(2 s) = 10 (2) 2 = 10 (4) = 40 m

x(3 s) = 10 (3) 2 = 10 (9) = 90 m

x = x f - x i = x(3 s) - x(2 s) = 90 m - 40 m = 50 m

(b) Find the average velocity for the time interval 2.0 s to 2.1 s

x(2 s) = 10 (2) 2 = 10 (4) = 40 m

x(2.1 s) = 10 (2.1) 2 = 10 (4.41) = 44.1 m

x = x f - x i = x(2.1 s) - x(2 s) = 44.1 m - 40 m = 4.1 m

[[ (c) Find the instantaneous velocity at t = 2.0 s

v = dx/dt = dx / dt = 10 [ d(t 2 )/dt ] = 10 [ 2t ] = 20 t

2.9 The position-time graph for a particle moving along the x-axis is shown in Figure P2.9

(a) Find the average velocity in the time interval t = 1.5 s to t = 4.0 s.

From the graph, we can find x (1.5 s) = 8 m

x = x f - x i = x(4.0 s) - x(1.5 s) = 2 m - 8 m = - 6 m

Remember, anything means (final value) - (initial value)

(b) Determine the instantaneous velocity at t = 2.0 s by measuring the slope of the tangent line shown in the graph.

To measure the slope of the line drawn tangent to the curve at t = 2.0 s, we can pick two points on the line.

We might choose

(t = 1.0 s, x = 9.0 m)

(t = 3.5 s, x = 1.0 m)

Now we calculate v = x / t

(c) At what value of t is the velocity zero?

The velocity is zero when the slope of the tangent line (on an x-, t - graph) is zero.

That happens on this graph for t = 4.0 s .

2.12 A particle is moving with a velocity v o = 60.0 m/s in the positive x direction at t = 0. Between t = 0 and t = 15 s, the velocity decreases uniformly to zero. What is the average acceleration during this 15-s interval. What is the significance of the sign in your answer?

a = v / t = [ - 60 m / s ] / [ 15 s ] = - 4 (m/s)/s = - 4 m/s 2

The minus sign means the particle is slowing down . Its velocity is decreasing . It is decelerating .

2.14 A particle starts from rest and accelerates as shown in Figure P2.14.

Determine the following:

(a) the particle's speed at t = 10 s and at t = 20 s and

From the graph, we can see that from t = 0 to t = 10 s, the acceleration is a constant 2.0 m/s 2 v = v i + a t

v(10 s) = 0 + (2 m/s 2 ) (10 s)

For the next five seconds, from t = 10 s to t = 15 s, the acceleration is zero which means the velocity remains constant ,

For the next five seconds, from t = 15 s to t = 20 s, the acceleration is negative, a = - 3.0 m/s 2

v i = v(15 s) = 20 m/s

v(20 s) = 20 m/s + (- 3 m/s 2 ) (5 s)

(b) the distance traveled in the first 20 s

We have already determined the values of the acceleration for various time intervals x = x i + v i t + ( 1 / 2 ) a t 2

x(10 s) = 0 + 0 + ( 1 / 2 ) (2 m/s 2 )(10 s) 2

The acceleration remains constant (at a = 0) for the next five seconds (until t = 15 s) so we can, again, apply this equation which describes distance with constant acceleration.

x i = x(10 s) = 100 m

v i = v(10 s) = 20 m/s

x(15 s) = 100 m + (20 m/s)(5 s) + ( 1 / 2 ) (0)(5 s) 2

The acceleration again remains constant (at a = - 3 m/s 2 ) for the next five seconds (until t = 20 s) so we can, again, apply this equation which describes distance with constant acceleration.

x i = x(15 s) = 200 m

v i = v(15 s) = 20 m/s

x(20 s) = 200 m + (20 m/s)(5 s) + ( 1 / 2 ) ( - 3 m/s 2 )(5 s) 2

2.19 Figure P2.19 shows a graph of v versus t for the motion of a motocyclist as she starts from rest and moves along the road in a straight line.

(a) Find the average acceleration for the time interval t o = 0 to t 1 = 6.0 s.

From the graph, we can read the velocities for these times v 1 = v(t 1 ) = v(6 s) = 8 m/s

a = v / t = [8 m/s ] / [6 s] = 1.33 m/s 2

(b) Estimate the time at which the acceleration has its greatest positive value and the value of the acceleration at this instant.

Acceleration is the slope of the line on a velocity-time graph like Figure P2.23. The slope seems greatest at about t = 3 s

And, there, I estimate the slope by sketching a tangent line which goes through the points

(t = 1 s, v = 0) and (t = 6 s, v = 10 m/s)

a = v / t = [10 m/s ] / [6 s] = 1.67 m/s 2

(c) When is the acceleration zero?

Zero acceleration means the slope of the line tangent to the curve on a v-t graph is zero . a = 0 for t = 6 s

(d) Estimate the maximum negative value of the acceleration and the time at which it occurs.

Acceleration is the slope of the line on a velocity-time graph like Figure P2.23. The slope is negative from t = 0 to about t = 10 seconds. During that time, the slope seems greatest (negatively) at about t = 8 s. T here, I estimate the slope by sketching a tangent line which goes through the points (t = 6 s, v = 10 m/s) and (t = 11 s, v = 0 m/s)

a = v / t = [- 10 m/s ] / [5 s] = - 1.8 m/s 2

2.21 Jules Verne in 1865 proposed sending people to the Moon by firing a space capsule from a 220-m-long cannon with a final velocity of 10.97 km/s. What would have been the unrealistically large acceleration experienced by the space travelers during launch? Compare your answer with the free-fall acceleration of 9.8 m/s 2 .

First, let's change the final velocity to units of m/s; we can almost do that in our heads.

2.29 A drag racer starts her car from rest and accelerates at 10.0 m/s 2 for the entire distance of 400 m ( 1 / 4 mile).

(a) How long did it take the car to travel this distance?

400 m = 0 + 0 + ( 1 / 2 ) (10 m/s 2 ) t 2

(b) What is its speed at the end of the run?

v = 0 + (10 m/s 2 )(8.94 s)

2.39 A ball accelerates at 0.5 m/s 2 while moving down an inclined plane 9.0 m long. When it reaches the bottom, the ball rolls up another plane, where, after moving 15 m, it comes to rest.

(a) What is the speed of the ball at the bottom of the first plane?

v 2 = 0 2 + 2 (0.5 m/s 2 )(9 m) = 9 m 2 /s 2

(b) How long doe is take to roll down the first plane?

3 m/s = 0 + (0.5 m/s 2 ) t

(c) What is the acceleration along the second plane?

What value of a brings the ball to rest, having

when it started with

after traveling a distance of

0 2 = (3 m/s) 2 + 2 a (15 m)

(d) What is the ball's speed 8.0 m along the second plane?

v 2 = (3 m/s) 2 + 2 ( - 0.3 m/s 2 ) ( 8 m)

v 2 = ( 9 - 4.8 ) (m 2 /s 2 ) = 4.2 m 2 /s 2

2.40 Speedy Sue driving at 30 m/s enters a one-lane tunnel. She then observes a slow-moving van 155 m ahead traveling at 5.0 m/s. Sue applies her brakes but can decelerate only at 2.0 m/s 2 because the road is wet. Will there be a collision?

If yes, determine how far into the tunnel and at what time the collision occurs.

If no, determine the distance of closest approache between Sue's car and the van.

We will measure distances from the tunnel's entrance.

The position of the v an is given by

x v = 155 m + (5.0 m/s) t + 0

x v = 155 m + (5.0 m/s) t

The position of Speedy Sue's c ar is given by

To determine if there is a collision, we can set these two positions equal to each other (as they will be if there is a collision) and solve for t, the time at which that collision occurs.

(30 m/s) t + ( 1 / 2 ) (- 2.0 m/s 2 ) t 2 = 155 m + (5.0 m/s) t

(1 m/s 2 ) t 2 + ( - 25 m/s) t + 155 m = 0

This is now in the "standard form" of a quadratic equation,

a x 2 + b x + c = 0

So we can now use the quadratic equation to solve for t. We can explicitly keep the units or we can ensure that the units are consistent and simply write

a = 1, b = - 25, and c = 155

t = 11.4 seconds or t = 13.6 seconds

The collision occurs 11.4 seconds after entering the tunnel. Mathematically, t = 13.6 s is also a solution, but the collision has already occured about two seconds before that!

Solutions to the additional problems from Serway's fourth edition

(4 ed) 2.1 The position-time graph for a particle moving along the z-axis is as shown in an old Figure P2.14. Determine whether the velocity is positive, negative, or zero at times

a) t 1 ; the velocity, as the slope of the tangent line, is zero

b) t 2 ; the velocity, as the slope of the tangent line, is negative

c) t 3 ; the velocity, as the slope of the tangent line, is positive

d) t 4 ; the velocity, as the slope of the tangent line, is zero

(4 ed) 2.2 The new BMW M3 can accelerate from zero to 60 mi/h in 5.6 s

(a) What is the resulting acceleration in m/s 2 ?

a = v / t = [ 60 mi/h ] / 5.6 s = 10.7 (mi/h)/s

(b) How long would it take the BMW to go from 60 mi/h to 130 mi/h at this rate?

t = [ 130 mi/h - 60 mi/h ] / (10.7 mi/h/s )

t = [ 70 mi/h ] / (10.7 mi/h/s )

That is 6.45 seconds beyond the 5.6 s required to reach 60 mi/h. The total time will be

t tot = 5.6 s + 6.54 s

(4 ed) 2.3 A hot air balloon is traveling vertically upward at a constant speed of 5.00 m/s. When it is 21.0 m above the ground, a package is released from the balloon.

(a) After it is released, for how long is the package in the air?

Once released, the package is in free fall with an acceleration of a = - g = - 9.8 m/s 2

We know its initial velocity and initial position

The later position of the package is given by

y = 21 m + (5 m/s) t + ( 1 / 2 ) ( - 9.8 m/s 2 ) t 2

Now we set y = 0 and solve for t

y = 0 = 21 m + (5 m/s) t + ( 1 / 2 ) ( - 9.8 m/s 2 ) t 2

As before, we can carry the units explicitly or we can ensure that we have consistent units and drop them and write only

4.9 t 2 - 5 t - 21 = 0

From the quadradic equation, we find the two solutions of t

Physically, we are only interested in solutions for t > 0. Mathematically, our equation is only valid for t > 0 since it is valid only after the package is released. So we use only t 1 .

(b) What is its velocity just before impact with the ground!

Once released, the velocity of the package is given by v = v i + a t

v = 5 m/s + ( - 9.8 m/s 2 ) t

v = 5 m/s + ( - 9.8 m/s 2 ) (2.64 s)

Of course, the minus sign indicates that the velocity is directed downward .

(c) Repeat (a) and (b) for the case of the baloon descending at 5.0 m/s.

As before, once released, the package is in free fall with an acceleration of a = - g = - 9.8 m/s 2

We know its initial velocity and initial position

The package, along with the balloon, is now moving downward and this shows up as the negative sign on the velocity

The later position of the package is given by

y = 21 m + ( - 5 m/s) t + ( 1 / 2 ) ( - 9.8 m/s 2 ) t 2

Now we set y = 0 and solve for t

y = 0 = 21 m + ( - 5 m/s) t + ( 1 / 2 ) ( - 9.8 m/s 2 ) t 2

As before, we can carry the units explicitly or we can ensure that we have consistent units and drop them and write only

4.9 t 2 + 5 t - 21 = 0

From the quadradic equation, we find the two solutions of t

Physically, we are only interested in solutions for t > 0. Mathematically, our equation is only valid for t > 0 since it is valid only after the package is released. So we use only t 1 .

Once released, the velocity of the package is given by

v = - 5 m/s + ( - 9.8 m/s 2 ) t

v = - 5 m/s + ( - 9.8 m/s 2 ) (1.62 s)

Notice that the velocities are the same. Later on, we can describe this in terms of energy conservation. The kinetic energy of the package is the same whether it is thrown up with v = + 5 m/s or if it is thrown down with v = - 5 m/s.

(4 ed) 2.4 A hockey player is standing on his skates on a frozen pond when an opposing player skates by with the puck, moving with a uniform speed of 12.0 m/s. After 3.00 s, the first player makes up his mind to chase his opponent. If the first player accelerates uniformly at 4.00 m/s 2 ,

(a) how long does it take him to catch the opponent?

We know the initial velocities and accelerations of the two players, a 1 = 4 m/s 2. a 2 = 0

The position of player #2 is given by

Be careful with the time . We must account for player #1's wait of 3 s. With this accounted for, we can calculate the position of player #1 from

Of course, this equation only makes sense for t > 3 s.

x 1 = 0 + 0 + ( 1 / 2 ) (4 m/s 2 ) (t - 3 s) 2 = (2 m/s 2 ) (t 2 - 6 s t + 9 s 2 )

Now we set x 1 = x 2 and solve for the time t.

(2 m/s 2 ) (t 2 - 6 s t + 9 s 2 ) = (12 m/s) t

We can either keep the units in explicitly or ensure that we have consistent units and simply write

2 (t 2 - 6t + 9) = 12t

2 t 2 - 12 t + 18 = 12 t

2 t 2 - 24 t + 18 = 0

t 2 - 12 t + 9 = 0

There are two solutions to this quadratic equation,

However, the equation for the position of player #1 is not valid for t 2 < 3 s, so we keep only t x ,

(b) How far has the first player traveled in this time?

Now where is player #2 (and, therefore, player #1 as well) at this time? x 2 = x 2i + v 2i t + ( 1 / 2 ) a 2 t 2

(Is a hockey rink that large?)

Energy. gov

How important is carbon capture and storage (CCS) to U. S. and global greenhouse gas mitigation efforts? What’s the status of FE’s CCS research and development (R&D)? And how do we move these important technologies forward?

These are some of the questions that Dr. Julio Friedmann, FE’s Deputy Assistant Secretary for Clean Coal, tackled during his keynote address at the Global Carbon Capture and Storage Institute's Third Annual Americas Forum, hosted by the Canadian Embassy on February 28.

CCS is the process of capturing and storing or re-using carbon dioxide (CO 2 ) from coal-fired power plants and industrial sources, and is an important part of President Obama’s all-of-the-above plan to secure America’s energy future. Applied to coal-fired electricity generation, CCS is expected to play an important role in achieving national and global CO 2 reduction goals.

The technical community broadly supports CCS as a critical tool for reducing carbon emissions, and a number of studies have underscored the importance of CCS to any CO 2 mitigation strategy. For instance, a 2012 study by the International Energy Administration showed that CCS would account for roughly one-sixth of the CO 2 reduction required in 2050 to meet global carbon emission targets.

"Take any option off the table today,” Dr. Friedmann said, and “the cost of greenhouse gas abatement goes up. It doesn't matter what that option is, whether you take off efficiency or renewables or nuclear or CCS or fuel switching. In the context of CCS, if you take CCS off the table, the cost of abatement goes up 50 to 80 percent.”

DOE’s research and development initiatives have helped the U. S. become a leader in CCS development. The Department is currently supporting eight 1 st Generation commercial-scale CCS demonstration projects underway across the country, including the commercial-scale Kemper Project in Mississippi – which will begin operation later this year. At the same time, the Office of Fossil Energy is pursuing R&D on lower cost 2 nd Generation technologies.

Developing those more cost effective technologies will be critical to widespread commercialization of CCS.

“We need more 2 nd Generation pilots,” Dr. Friedmann told the audience of 120 people. “And that means we will be trying to figure out how to create budgets, create solicitations, create opportunities, so that people inside this room and outside this room can take those kinds of investments and develop these commercial technologies.”

Reflecting his commitment to CCS, President Obama’s Energy Department budget request for Fiscal Year 2017 includes more than $277 million for the FE’s CCS and Power Systems R&D program. This is on top of the $6 billion that the 2009 Recovery Act targeted for CCS – as well as the Department’s new $8 billion loan guarantee program to support advanced fossil energy technologies that reduce greenhouse gas emissions, including carbon capture technologies.

Going forward, many experts believe that CCS will not only be required for coal plants and industrial facilities, but for natural gas plants, as well. That’s why the President’s FY 2017 budget request includes $25 million for a new Natural Gas CCS demonstration program to support projects to capture and store carbon emissions from natural gas power systems.

"It is an all of the above world," Dr. Friedmann noted. “We also have to envision a world in which we're not just doing CCS …for stationary power plants fired by coal. We will be doing this for natural gas plants. We will be doing this at cement plants and steel mills and refineries. We're going to be doing this in a lot of different contexts and a lot of places. It's simply required to get to where we need to get."

4-H Youth Development

Welcome to Strafford County 4-H!

Tractor Supply Company

12 Two Rod Road, Rochester NH

Over 15,000 youth statewide have been involved in one or more aspects of the 4-H Youth Development Program and Strafford County boasts over one dozen active, year-round clubs for youth focusing on a variety of topics like STEM, gardening, textiles, and archery!

4-H has over 50 project areas which are connected to nationally reviewed curriculum and activity guides. In 4-H you can get involved in projects from animal husbandry to robotics and technology! If you are a youth, or parent of a youth, between the ages of 5 and 18, find out how you can get involved by visiting:

4-H involves hundreds of dedicated and caring adult volunteers who commit thousands of hours annually to improving the lives of youth in New Hampshire. We believe strongly in positive youth-adult partnerships and are always looking for new volunteers for a variety of roles ranging from one time event support to on-going club leaders. If you are an adult looking to make an impact in the lives of youth, visit:

Already involved? Then you know what an amazing role 4-H can play in your life and the lives of others! To find forms, scholarship applications and event information, visit:

If you would like more information please call the Strafford County 4-H office at (603) 749-4445, or e-mail Kristen Lyons, 4-H Program Coordinator at Kristen. Lyons@unh. edu

STANTON — Rebecca McCafferty may be resigning as 4-H coordinator for Ionia and Montcalm counties, but she is going to continue her career with 4-H … albeit in the deep south.

McCafferty was hired as 4-H coordinator for Ionia and Montcalm counties in the spring of 2012. Two years later, she is stepping down to accept an extension agent position with the Sarasota County 4-H program in Florida.

Her final day with Ionia-Montcalm 4-H will be June 13.

McCafferty has a lengthy history with 4-H. She previously participated in 4-H for seven years in Michigan’s Upper Peninsula before traveling to Japan in the summer of 2001 via a 4-H exchange program. She said the decision to relocate from Michigan to Florida wasn’t an easy one.

“Working with the Ionia-Montcalm volunteers has been such a wonderful experience,” she said. “There is so much talent and passion with all of these volunteers and the youth of both Ionia and Montcalm are lucky to have such a motivated and dedicated community. I am constantly amazed at how when something needs to get done, someone is willing to step up and get it done.

“4-H is such a wonderful program for youth and I have been so lucky to have a great community of volunteers to work with,” she added. “They have been so patient and adaptable, adjusting to me being split between both counties and have put up with my million and one questions, dual-county random learning opportunities and funky sunglasses.”

MSU Extension Educator/Supervisor Pat Dignum, who also works for both Ionia and Montcalm counties, said the new job is a wonderful opportunity for McCafferty.

“We wish her well in her new 4-H role and take pride in her choice of Extension as an ongoing career,” Dignum said. “We will miss her energy and spontaneity.”

McCafferty’s duties in both counties included recruiting, interviewing and orienting new volunteers and leaders promoting club activities and events and helping with the fair.

The Montcalm County 4-H Fair is scheduled for June 22-28 while the Ionia County Free Fair is scheduled for July 17-26. Dignum doesn’t believe McCafferty’s resignation won’t have a major impact on the fairs, as much of the planning and prep work has already been completed and many 4-H club and committee volunteers will lend a helping hand.

“Fair week is truly the culmination of a year of preparation,” Dignum noted.

Dignum said she will meet with MSU Extension Children & Youth Institute Director Dr. Julie Chapin and MSU Extension District 8 Coordinator Don Lehman soon to discuss the future of the 4-H coordinator position in Ionia and Montcalm counties. McCafferty had been working part-time for each county, which equated to a full-time position.

“Of course, our best case scenario would be to restore both counties to each having their own full-time coordinator,” Dignum theorized. “The dual county 50-50 role has proven most challenging. Elsewhere in the state, dual positions have been re-split into two part-time positions, yet retention remains an issue. Anything less than full-time results in reduced educational programming when management tasks consume the majority of a half-time program coordinator’s hours.”

McCafferty agrees with Dignum.

“I think the biggest challenge will remain if there is a dual-county coordinator serving both counties,” she said. “A lot of time is spent on administrative and management work and programming and educational opportunities are missed. It has also been a challenge to meet the varying needs of the program, so reviewing the split role would be beneficial for both counties.”

Jason Kilmer Jamie Gardner Tracey Ramsey

Intended Audience : The 4-H sheep project is intended for those individuals who are interested in showing sheep. There is not a need for previous sheep experience, just a willingness to learn more about sheep in general. These projects are intended to give an individual a chance to follow their special interest as well as explore new ones in the sheep industry. In the end the project will hopefully serve as a learn experience for the individual, one that can be taken away and applied in the real world. Membership is typically open to all youth ages from 5-19 who meet certain membership guidelines.

4-H is the largest youth serving organization in the world. It began in rural America but has spread to major urban centers, suburban communities, and rural non-farm settings. The fact is that all 50 states have 4-H programs and more than 80 countries worldwide are now involved in the activity. It is a project designated for both boys and girls with many different projects areas such as large or small animal, foods, clothing, wood science, horticulture etc.

4-H is not just an individual project but actually has family involvement. Typically youth are enrolled as members, but other family members are involved as club leaders, help with meetings, or head projects. Families work together to fulfill projects as they learn together.

4-H is a community affair. The community provides resources for 4-H members such as field trips or fairs.

4-H is an educational and learning experience for today’s youth.

4-H Sheep Project

In 4-H sheep project member become familiar with the many areas concerning sheep. This usually is dependent upon level of members such as beginner intermediate and advanced.

They become familiar with management, selection, production, and health of sheep.

They learn how to keep financial and performance records for management purposes.

Exhibiting sheep is a main focus including identification of major breeds, identification of parts of the sheep, and present speeches and presentations on sheep.

Plus while doing all of this they begin to explore career opportunities with sheep.

"Learning by doing"

I pledge by Head to clearer thinking

my Heart to greater loyalty

my hands to larger service

and my Health to better living

for my club, my community, my country and my world.

To Make the Best Better

Contacts to Get Started

Knowing who to go to for someone that is interested in knowing more about 4-H and how to get involved in showing sheep as a 4-H project is one of the first steps that every 4-Her goes through. It is not difficult to find someone that is willing and able to help a 4-Her become involved in an organization where friendships can be made and responsibilities can be learned. The possibilities are endless as to who to visit or call. You could get in touch with your county extension office, 4-H leader, an older 4-H member, or local producers to help you learn more about the 4-H sheep project.

Your county extension office can give you information on the 4-H sheep project. A book is usually distributed and will contain a variety of information on nutrition, management, etc. for sheep. Someone will assist you in determining who your 4-H leader is for your particular township for a further reference. You can also find out how, when, and where to become involved in showing sheep as a 4-H project.

As previously mentioned, your county extension office will inform you as to who your 4-H leader is in your township. You may already know your local 4-H leader, but have never spoken with him or her about showing sheep as a 4-H project. This is the person that you become quite aquatinted with during your 4-H membership. It is the 4-H leader’s responsibility to hold monthly meetings, sign up 4-H members in their project of interest, keep the 4-Her informed about important dates, and let the 4-Her know about his or her responsibilities concerning their 4-H project.

Older 4-H members can also give a prospect 4-Her a lot of information on what is involved with showing sheep as a 4-H project. These are the people that have actively participated and have experienced what is involved with showing sheep firsthand. It is older 4-H members that can give you many tips on grooming, nutrition, and general management. These 4-Hers can also give you information on who to call and what to do to get enrolled in 4-H.

Many times one doesn’t think about turning to a local sheep producer for tips on how to find out more about showing sheep as a 4-H project. It is many of these producers that have shown sheep as a 4-H project in past years that helped them get started raising sheep. These producers often can provide a lamb for you to purchase for your 4-H project and can offer helpful advice concerning the care of your lamb.

Where to Purchase Lambs

There are two main ways to purchase you lambs private treaty and auction. Private treaty is where you go to a producers farm and purchase lambs privately. This is the best way for a new showman to purchase lambs. The producer can take time to help the 4-Her and point out what they should be looking for. Many times the producer will give the first year 4-Her a break on price. A good price on an average lamb is $100-$150 and the price goes higher for better lambs.

Auctions or Club Lamb Sales are another place for purchasing animals. The auction is fast paced and many people are biding on the animal all at the same time. It is very easy for a first year member to get lost during an auction. The price of lambs are normally higher at auctions, however the lambs are usually very good. To find where and when auctions are held ask your county extension agent.

Basic Daily Care

Now that you have your lambs bought you need to take care of them. The most basic thing to do is feed and water your lamb. When deciding what to feed go to your local feed mill there are knowledgeable people there willing to help. The easiest thing to do is feed a complete show feed ration. This way you know your lamb will be receiving a well balanced diet. Follow the directions with the feed for the amount you are to feed each day. Also get a couple bales of hay and feed each lamb a couple hand fulls each day. The single most important idem for your lamb is a good supply of fresh water. A five gallon bucket works good for supplying water and be sure you change it every day.

Getting your lamb out of the pen and exercising it is a very good idea. You need to purchase a halter to put on your lamb. Halter breaking your lamb will prove to be quite a challenge but stick with it. Walking your lamb 1-2 miles a day will help with muscle development and muscle firmness. The more you walk you lambs the more you may need to feed you don't want to get you lambs to skinny. Also be careful walking you lambs on hot days, it may be best to only do short walks on extremely hot days.

When you have your lambs out for a walk it is good to practice your showing skills. Practice walking your lamb around by holding on to its head and guiding it around. Stop and set up the lambs feet by placing the front legs straight down and the back legs slightly back form the rear not right under the lamb. The more you practice with your lamb the better you and your lamb will do on show day.

Show Day Preparation

There is a lot to do to get your lamb ready for show day. The best thing to do is start the day before the show. The equipment used on your lamb can be quite expensive so it may be best to share the cost with another member or ask a fellow 4-Her if you could borrow their equipment. The most important step in getting your lamb ready is shearing and the closer you can get to the skin the better. Because you are shearing the lamb so close you need to wash the lamb first to get the dirt and oils out so your clippers will run good. Many people use dish soap or Woolite, however livestock soap it best. After your lamb is all clean your need to dry your sheep with a towel or livestock blower. The livestock blower is best at taking the water off the lamb, however they can be very expensive. When you go to shear your lamb it is best to put it on a blocking stand. This is a stand that holds the lamb still while you work on it. It allows you to go slow and do a good job. There are many different types of clippers that can be used to shear your sheep and as mentioned above the closer to the skin you get the better. The reason for this is so the muscle can stand out and the lamb will feel hard when touched.

After your lamb is cleaned and sheared you may wish to put a blanket or sock on you lamb to keep it clean until show day. If you do not cover you lamb when done you will probable have to wash you lamb on the day of show. When you put your lamb back into the pen put some fresh bedding down so your lamb will stay clean.

On the day of show just before you go into the ring inspect you lamb for any dirt marks and clean them up. Also clean out the inside of there ears with a wet rag and be sure you wipe all of the bedding off of the lamb.

Important Show Day Information

The day has finally come for you to exhibit all of the hard work that you have put into your 4-H sheep project. Show day is the day when you are in competition with other fellow 4-H members. Many awards are given out according to how well your animal competes against all of the other animals that have been entered. There is a lot of important information that your need to know before you step into the show ring as an exhibitor.

When the day begins, it is always important that your check what class your lamb will be showing in. After you know what class you’re in, you can usually estimate when you need to start getting your lamb prepared for the show. Next, it is always a good idea to watch some of the classes that show before you. Watching other exhibitors show will give you an idea of how to show in a show ring with a judge (it may also calm some of your nerves). It is also important to listen to all announcements that are made. These announcements will usually inform you of when to come to the make-up ring. Other information such as the judge’s comments after he is finished placing a class and final placing will also be given. Finally, it is also important to check over your lamb one final time before your proceed up to the make-up ring.

Now it is time to sell your 4-H lamb. Sale day is the day when you get to exhibit your animal to many buyers that have come to purchase your animal. It is always important to make sure that your lamb is well groomed (as if it were show day). Each animal will sell at a particular time during the sale, so it is important to know the sale order for that day. Many times announcements will be make to let the 4-Hers know where they are in the sale order. You may also hear the auctioneers sell the animals, who has purchased the animals, and for how much the animal was purchased. When it is your turn to sell your lamb, the auctioneer will bid your animal up to a specific dollar amount per pound according to who is bidding on your animal. A sale will be made when your lamb is no longer being bid up. The buyer of your lamb is the last person that has bid on your animal. It is always important to remember to thank your buyer after the sale for purchasing your lamb. This also a time for you to invite the buyer back next year to the sale. Finally, every buyer always enjoys getting a hand written thank you in the mail for purchasing an animal.

Identification of sheep:

Sheep are identified in many ways in order to keep accurate records and also so they can be identified at show day. Each sheep or lamb must have health papers which provides an accurate record of a sheep’s health history. Also usually a few days before the event or the day of a sheep will be weighed in. This is another way of identification by means of weight. Other ways of identification include:

*Some sheep owners will use only one of the above while others will use a combination.

Five-decade Gloucester County 4-H volunteer keeps the annual fair moving

As the clock ticked down to today’s opening ceremonies, club leaders marked items on their check lists, and participants carried supplied across fields to the barns where they’ll spent the next four fair days.

Through the light chaos, a golf cart buzzed up and down the paved and gravel paths, and the driver, Wally, slowly passed the Wallace Warren pavilion where Little Miss Peach and Peach Queen will be crowned Friday night.

The name of the pavilion isn’t a coincidence. Wallace Warren — well, Wally, as he’s known on the fairgrounds — earned the honor over the last half-century.

Wally, a North Carolina native, has been a Gloucester County 4-H volunteer for 50 years, although was an active 4-H member since he was a kid.

In five decades, the 80-year-old has seen the fair grow, relocate, and change. Through the annual farm life-centered festival’s transformation, however, it’s always remained a place where Gloucester County folks — from full-time farmers to emergency room doctors and newspaper owners — converge.

And stop by to see Wally, who’s been the grounds keeper at the Mullica Hill fairgrounds for 20 years.

“Sixty hours a week donated. Ain’t got nothing else to do,” Él rió. “Been retired 20 years.”

Wally transplanted his Southern charm to Yankee soul in 1952 when his service in the Army brought him to Philadelphia, to protect the City of Brotherly Love during the Korean War.

He returned to North Carolina for three months before coming back north for his wife Elaine, who couple married on a CBS TV show “Bride and Groom” after regularly scheduled couple cancelled. They won a honeymoon, stove, refrigerator, freezer and washing machine.

Elaine died seven years ago.

Wally, who lives on his Mantua farm, remembers when dairy farms were “real big” in Gloucester County. That was near the time he got involved with the county’s 4-H program.

He helped start the horse club with 90 girls and 10 boys, each owning their own horse.

Wally remembers the early days of the fair, which was once held at a church campground in Paulsboro and a barn on county property in Clayton.

He also remembers the first show at the Mullica HIll fairgrounds. The arena in 1967 stood at the top of a hill where Wally’s pavillion now stands.

“Buildings going up are the biggest changes,” él dijo.

Buildings, the information booth, bathrooms and barns have been added over the years. Currently, the 4-H association is fundraising to expand Wally’s barn and add dressing room areas to the alread-existing stage.

“We just need volunteers,” él dijo. “Theyre hard to come by nowadays. parents are interessted as long as their kids are in 4-H. Then they disappear.”

It could be hard for other volunteers to measure up to Wally, though. He’s been maintaining the grounds for two decades. Cutting the grass is a full-time job, he said.

“I wish we could clone Wally into a 100 different people,” said Linda Strieter, 4-H program coordinator. “He’s one in a million.”

Despite slowing down just a bit since his 80th birthday, Wally’s still “extremely dependable,” Strieter added.

He’ll fix it. He’ll make it. He’ll help haul it across the fairgrounds.

And if for some reason it’s not in his wheelhouse, he knows someone who can help, Strieter said.

“I try,” Wally blushed.

“No. You make sure it happens,” Strieter said.

This year Wally is helping make happen all of the annual events — the swine, beef and sheep shows — and some new ones like Saturday’s Mud Run which will have competitor’s racing through piles of peaches and over obstacles.

After 10 years, the interactive children’s “Day on the Farm” exhibit is back to teach young kids about growing food and caring for farm animals.

The fair starts at 8:30 a. m. today, but ceremoniously opens at 5:30 p. m. tonight with the parade of clubs. The Gloucester County 4H Fair runs through Sunday.

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4-H helps Missouri Youth Keep Moving

Longtime Benton County 4-H volunteer Tina Ives and son Dylan Carver have lost more than 50 pounds each since they resolved to keep active and eat better.

COLE CAMP, Mo.—It's time to get moving. That's the message of the "Move Across Missouri" program to 4-H youth and their families.

By keeping a running tally, 4-H'ers can see how a few minutes or an hour here and there quickly adds up. In 2010, more than 460 people signed up for Move Across Missouri. About 300 of them regularly recorded their activity throughout a four-month competition period. Participants logged almost 100,000 hours—nearly 6 million minutes—of physical activity.

When Tina Ives and son Dylan Carver's 4-H club started participating in Move Across Missouri last year, the club began to incorporate physical activity into meetings and events. Healthier food was served at club events: fruit kebabs instead of donuts, for example, and lean ground beef, courtesy of the Missouri Beef Industry Council, which sponsors the program.

During one outing, Ives realized she needed to do a better job of practicing what she preached. "We took them for a walk up to the top of a hill," she recalls. "Halfway up the hill, we had to stop just so I could catch my breath. I realized that I can't teach a child to eat healthy and live healthy if I'm not an example of doing that myself. I didn't feel good. I was embarrassed, and I decided it was time to get right."

Can't find what you are looking for?

Extension Education in Wise County

Wise County Youth Fair

For more Wise County Youth Fair information check out their website http://www. wcyouthfair. org

MONDAY, FEBRUARY 29 8:00 am Horse – Check registration papers 8:30 am Horse Show (NRS Arena) 7:00 pm Queen Contest

TUESDAY, MARCH 1 7:00 am Arrival of: Broilers & Breeding Poultry, Breeding Dairy Goats, Longhorn Cattle (Check papers on arrival) Arrival of Breeding Swine (In place by 3:00 pm) 8:00 am Broiler Show Breeding Poultry Show (Released following shows) 8:00-4:00 pm Arrival of: Market Lambs & Market Wethers Must be in place by 4:00 pm. - Weight/Breed cards are due to Superintendents by 4:30 pm. 8:30 am Horse Show (NRS Arena) 10:00 am Breeding Dairy Goat Show (Release following shows) 12:00 noon Arrival of Rabbits 1:00 pm Meat Pen Rabbits judged 2:00 pm Longhorn Show - Steers followed by heifers (Released following show)

4:00 pm Breeding Swine Show (Released following show) 5:00 pm Classifying of Market Lambs & Classifying of Market Wethers 6:30 pm 4-H Parade of Fashion

WEDNESDAY, MARCH 2 8:00 am Market Lamb Show Followed by: Market Wether Show 8:00-4:00 Arrival of Market Hogs Must be in place by 4:00 pm.

Weight/Breed cards are due to Superintendents by 4:30 pm.

Arrival of Market Steers - Weight/Breed cards are due to Superintendents by 7:00 pm. 10:00 am Dog Show 5:00 pm Classifying of: Market Hogs 8:00 pm Classifying of: Market Steers 8:00 pm Registration papers & tattoos checked on Beef Heifers

THURSDAY, MARCH 3 11:00 am Market Swine Show Followed by: Invitational Celebrity Showmanship 7:30—10:00 am Arrival of: 4-H Foods, Crafts, and Photography, FCCLA Foods and Crafts, Horticulture 10:30 am 4-H Food, Crafts and Horticulture judged & FCCLA Food & Crafts judged 4:00 pm Agricultural Product Identification—Poultry Barn 5:00 pm Ag Mechanics begin moving in (must be in place by 8 am Friday) 5:00—7:00 pm Viewing of: 4-H, FCCLA and Horticulture exhibits

FRIDAY, MARCH 4 8:00 am Prospect Steer Show Immediately followed by: Market Steer Show 10:00 noon Agricultural Mechanics judged 12:00 noon Release of: Market Goats, Lambs, & Hogs 1:00 pm Breeding Beef Heifer Show (All Beef Animals released at conclusion of show) 4:00 pm Pictures taken of:4-H Food, Crafts, and Photography winning entries 4:15 pm Pictures taken of: FCCLA winning entries 3:00—4:00 pm Release of:4-H & FCCLA Food, Craft, Clothing, Photography and Horticulture 5:00 pm Wise County Heart of a Champion Show

SATURDAY, MARCH 5 9:00—11:00 am Judging Contest 10:00 am Pet Show 11:00—12:30 pm Bar-B-Q Meal 12:30 pm Awards 1:00 pm 2017 WCYF Auction 2:00 pm Release of all remaining animals & Ag Mech

Good Luck Wise County 4-H’ers.

Jim Frank Hornback Scholarship

Any Wise County graduating senior Ag. students who plans on majoring in agriculture at a Texas College or University are eligible for the $2,000 Hornback Scholarship.

Interested students must complete the Scholarship Application and a copy of the high school transcript by Friday, April 15 2017 . Materials can be mailed to our office Texas A&M AgriLife Extension, 206 S. State, Decatur, TX 76234 or hand delivered to the same address. Fax or emailed copies are not acceptable. Signatures must be original. Interviews will be set up with students after applications are received.

Please contact our office at 940/627-3341 if we can be of assistance.

Scholarship Recipient’s Requirements

Recipient must bring to the Wise County Extension office:

Proof of college enrollment for both fall and spring semesters (student schedule)

A transcript or report card showing completion of 12 hours for your first college semester, with a minimum GPA: 2.5 on a scale of 4.0.

Scholarship will be $1000 for freshman fall and spring semesters.

Committee requires a “Letter of Progress” from the scholarship recipient after completing their fall semester.

Welcome to Wise County

Wise County is Not Out Of The Way, Just Out Of The Ordinary . Until recently, Wise County has been one the best-kept secrets in north central Texas. As with any secret, however, word is getting out. The expansion in recent years of the Alliance Corridor in northwest Tarrant County, and the Texas Motor Speedway in Denton County, have brought unparalleled growth to our area.

Just north of the heart of the Fort Worth metropolitan area, and less than an hour from DFW International Airport, Wise County provides convenient access to any product your heart desires. But what makes Wise County out of the ordinary is our community culture.

Come and visit Wise County. You can shop in our stores, study our history, and meet some friendly people. Take a look at our homes, new and old, and you will be amazed at the value. Visit our banks where you get to talk to a real, live banker that can handle your financial needs in a personal way. And don’t worry if you fall in love with our way of life because, whether for a day or a lifetime, you’re welcome in Wise County.

Click the Icon above to Join 4-H

40 Gallon Challenge

What is the 40 Gallon Challenge ?

The 40 Gallon Challenge is a call for residents and businesses to reduce our region’s water use on average by 40 gallons per person, per day. The challenge began in 2011 as a voluntary campaign to increase water conservation.

The 40 Gallon Challenge encourages people to save a minimum of 40 gallons a day by adopting new water-saving techniques. The pledge card outlines water-saving practices and the daily water-savings to expect. You can use the pledge to review the water-saving practices that you or your family currently puts to use. By pledging new practices, you will see the total daily savings expected for your household

To start saving water and take the challenge, go to the website and complete the checklist of water-saving practices. The checklist includes both indoor and outdoor water-saving tips.

County Population: 60,939

Retail Sales Tax: 8.25%

Annual Average Temperature: 65.7 degrees F

Monthly Average High Temperature: 84 degrees F

Monthly Average Low Temperature: 42 degrees F

Annual Average Precipitation: 42″

Annual Average Snowfall: 3.9″

Tunica 4-H club gets moving to lose weight

By Kaitlyn Byrne MSU Ag Communications

MMISSISSIPPI STATE -- Tunica County 4-H is striving to help kids and teens achieve healthier lifestyles through a new program called Move to Lose.

Before (top photo): Charity Womack (front row, left) wanted a healthier lifestyle so she joined other members of the Tunica County 4-H Club in the Move to Lose program, with encouragement from 4-H agent Ebony Jones (far right).

After (bottom photo): Charity Womack, a 4-H senior at Rosa Fort High School in Tunica, has lost 74 pounds since September with the Move to Lose program. (Submitted photos)

Ebony Jones, Tunica County 4-H agent, started the Move to Lose program in September after she saw an interest in a healthier lifestyle among her 4-H’ers.

“A lot of the kids would ask me about ways they could exercise and improve their diets and their overall health, so I decided we needed a structured program to help with that, ” she said. “I wanted to be able to provide them with the information and support they needed to make positive changes for their health. ”

Jones said Tunica County 4-H partnered with Tunica County Parks and Recreation to allow Move to Lose participants to exercise as a group with a trainer at the Tunica Health and Wellness Center. The group does water aerobics and cardio workout sessions on alternating weekdays.

Jones said the program requires participants to keep a food journal to monitor what they eat.

“The kids write down everything they eat so we can discuss it and talk about what is healthy and what isn’t. It really helps them stay on track when they have to explain why they ate certain things, ” she said. “We watch calories, but we don’t necessarily do diets. We focus on lifestyle changes. ”

Charity Womack, a 4-H senior at Rosa Fort High School, has lost 74 pounds since September with the Move to Lose program.

Womack said Move to Lose gave her the motivation she needed to stick to a healthy lifestyle.

“Because of Move to Lose, I now have people on my side to help me lose weight, and they ask me questions to hold me accountable, ” she said. “It really helped to have a group of people supporting me like that. ”

Jones said Womack went above and beyond the expectations of the program.

“Most of the kids go to the workout twice a week, but Charity did double time, ” Jones said. “Charity would go with me to exercise every day after work. She’s very enthusiastic and dedicated to having a healthier lifestyle, and that’s what the program is all about. ”

Womack said she was hesitant to join the program at first, but Jones encouraged her to give it a try.

“I really thought about not doing it because I wasn’t sure if I could stick with it, but Mrs. Ebony gave me so much motivation to just give it a shot, ” she said. “She helps push me to keep going and stay on track. ”

Womack said Move to Lose has helped change her life, and she wants to encourage her peers to make healthy decisions, too.

“If someone’s having doubts about getting started with an exercise plan, I would tell them to just go out and do what they have to do, ” she said. “Push forward, and if you all work together, you can achieve great results. Having support is a big help. ”

Released: March 8, 2012 Contact: Ebony Jones, (662-363-2911)

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Get step-by-step solutions for your textbook problems from www. math4u. us

Jon Rogawski, Calculus: Early Transcendentals, W. H. Freeman and Company, 2008

1. A ball is dropped from a state of rest at time t = 0. The distance traveled after t seconds is s(t) = 16t 2 ft. (a) How far does the ball travel during the time interval [2, 2.5]? (b) Compute the average velocity over [2, 2.5]. (c) Compute the average velocity over time intervals [2, 2.01], [2, 2.005], [2, 2.001], [2, 2.00001]. Use this to estimate the object’s instantaneous velocity at t = 2.

2. A wrench is released from a state of rest at time t = 0. Estimate the wrench’s instantaneous velocity at t = 1, assuming that the distance traveled after t seconds is s(t) = 16t 2.

3. Let v = 20√T as in Example 2. Estimate the instantaneous ROC of v with respect to T when T = 300 K.

4. Compute D y / D x for the interval [2, 5], where y = 4x − 9. What is the instantaneous ROC of y with respect to x at x = 2?

In Exercises 5–6, a stone is tossed in the air from ground level with an initial velocity of 15 m/s. Its height at time t is h(t) = 15t − 4.9t 2 m.

5. Compute the stone’s average velocity over the time interval [0.5, 2.5] and indicate the corresponding secant line on a sketch of the graph of h(t).

6. Compute the stone’s average velocity over the time intervals [1, 1.01], [1, 1.001], [1, 1.0001] and [0.99, 1], [ 0.999, 1]. [0.9999, 1]. Use this to estimate the instantaneous velocity at t = 1.

7. With an initial deposit of $100, the balance in a bank account after t years is f(t) = 100(1.08) t dollars. (a) What are the units of the ROC of f(t)? (b) Find the average ROC over [0, 0.5] and [0, 1]. (c) Estimate the instantaneous rate of change at t = 0.5 by computing the average ROC over intervals to the left and right of t = 0.5.

8. The distance traveled by a particle at time t is s(t) = t 3 + t. Compute the average velocity over the time interval [1, 4] and estimate the instantaneous velocity at t = 1.

In Exercises 9–16, estimate the instantaneous rate of change at the point indicated.

9. P(x) = 4x 2 − 3; x = 2

17. The atmospheric temperature T (in ◦F) above a certain point on earth is T = 59 − 0.00356h, where h is the altitude in feet (valid for h ≤ 37,000). What are the average and instantaneous rates of change of T with respect to h? Why are they the same? Sketch the graph of T for h ≤ 37,000.

18. The height (in feet) at time t (in seconds) of a small weight oscillating at the end of a spring is h(t) = 0.5 cos (8t). (a) Calculate the weight’s average velocity over the time intervals [0, 1] and [3, 5]. (b) Estimate its instantaneous velocity at t = 3.

19. The number P(t) of E. coli cells at time t (hours) in a petri dish is plotted in Figure 9. (a) Calculate the average ROC of P ( t ) over the time interval [ 1. 3 ] and draw the corresponding secant line. (b) Estimate the slope m of the line in Figure 9. What does m represent?

24. An epidemiologist finds that the percentage N(t) of susceptible children who were infected on day t during the first three weeks of a measles outbreak is given, to a reasonable approximation, by the formula

A graph of N ( t ) appears in Figure 13. (a) Draw the secant line whose slope is the average rate of increase in infected children over the intervals between days 4 and 6 and between days 12 and 14. Then compute these average rates (in units of percent per day). (b) Estimate the ROC of N ( t ) on day 12.

25. The fraction of a city’s population infected by a flu virus is plotted as a function of time (in weeks) in Figure 14. (a) Which quantities are represented by the slopes of lines A and B? Estimate these slopes. (b) Is the flu spreading more rapidly at t = 1, 2, or 3? (c) Is the flu spreading more rapidly at t = 4, 5, or 6?

26. The fungus fusarium exosporium infects a field of flax plants through the roots and causes the plants to wilt. Eventually, the entire field is infected. The percentage f(t) of infected plants as a function of time t (in days) since planting is shown in Figure 15. (a) What are the units of the rate of change of f(t) with respect to t? What does this rate measure? (b) Use the graph to rank (from smallest to largest) the average infection rates over the intervals [0, 12], [20, 32], and [40, 52]. (c) Use the following table to compute the average rates of infection over the intervals [30, 40], [40, 50] ,[30, 50] (d) Draw the tangent line at t = 40 and estimate its slope. Choose any two points on the tangent line for the computation.

27. Let v = 20√T as in Example 2. Is the ROC of v with respect to T greater at low temperatures or high temperatures? Explain in terms of the graph.

28. If an object moving in a straight line (but with changing velocity) covers D s feet in D t seconds, then its average velocity is v 0 = D s / D t ft/s. Show that it would cover the same distance if it traveled at constant velocity v 0 over the same time interval of D t seconds. This is a justification for calling D s / D t the average velocity.

29. Sketch the graph of f(x) = x(1 − x) over [0, 1]. Refer to the graph and, without making any computations, find: (a) The average ROC over [0, 1] (b) The (instantaneous) ROC at x = 1/2 (c) The values of x at which the ROC is positive

30. Which graph in Figure 16 has the following property: For all x, the average ROC over [ 0, x] is greater than the instantaneous ROC at x? Explain.

31. The height of a projectile fired in the air vertically with initial velocity 64 ft / s is h (t) = 64t − 16t 2 ft. (a) Compute h(1). Show that h(t) − h(1) can be factored with (t − 1) as a factor. (b) Using part (a), show that the average velocity over the interval [1, t] is −16(t − 3). (c) Use this formula to find the average velocity over several intervals [1, t] with t close to 1. Then estimate the instantaneous velocity at time t = 1.

32. Let Q(t) = t 2. As in the previous exercise, find a formula for the average ROC of Q over the interval [1, t] and use it to estimate the instantaneous ROC at t = 1. Repeat for the interval [2. t] and estimate the ROC at t = 2.

33. Show that the average ROC of f(x) = x 3 over [1, x] is equal to x 2 + x + 1. Use this to estimate the instantaneous ROC of f (x) at x = 1.

34. Find a formula for the average ROC of f(x) = x 3 over [2, x] and use it to estimate the instantaneous ROC at x = 2.

58. Investigate numerically for several values of n and then guess the value in general.

59. Show numerically that for b = 3, 5 appears to equal ln 3, ln 5, where ln x is the natural logarithm. Then make a conjecture (guess) for the value in general and test your conjecture for two additional values of b.

60. Investigate for (m. n) equal to (2, 1), (1, 2), (2, 3), and (3, 2). Then guess the value of the limit in general and check your guess for at least three additional pairs.

2. Find the points of discontinuity of f(x) and state whether f (x) is left - or right-continuous (or neither) at these points.

3. At which point c does f(x) have a removable discontinuity? What value should be assigned to f(c) to make f continuous at x = c?

4. Find the point c 1 at which f (x) has a jump discontinuity but is left-continuous. What value should be assigned to f (c 1 ) to make f right-continuous at x = c 1 .

5. (a) For the function shown in Figure 16, determine the one-sided limits at the points of discontinuity. (b) Which of these discontinuities is removable and how should f be redefined to make it continuous at this point?

In Exercises 37–50, determine the domain of the function and prove that it is continuous on its domain using the Laws of Continuity and the facts quoted in this section.

51. Suppose that f (x) = 2 for x > 0 and f (x) = − 4 for x < 0. What is f (0) if f is left-continuous at x = 0? What is f (0) if f is right-continuous at x = 0?

52. Sawtooth Function Draw the graph of f (x) = x − [x]. At which points is f discontinuous? Is it left - or right-continuous at those points?

In Exercises 53–56, draw the graph of a function on [0, 5] with the given properties.

53. f (x) is not continuous at x = 1, but and exist and are equal.

54. f(x) is left-continuous but not continuous at x = 2 and right-continuous but not continuous at x = 3.

55. f (x) has a removable discontinuity at x = 1, a jump discontinuity at x = 2, and . .

56. f (x) is right - but not left-continuous at x = 1, left - but not right-continuous at x = 2, and neither left - nor right-continuous at x = 3.

57. Each of the following statements is false. For each statement, sketch the graph of a function that provides a counterexample.

(a) If exists, then f (x) is continuous at x = a.

(b) If f(x) has a jump discontinuity at x = a, then f(a) is equal to either or .

(c) If f (x) has a discontinuity at x = a, then and exist but are not equal.

(d) The one-sided limits and always exist, even if does not exist.

1. Use the IVT to show that f (x) = x 3 + x takes on the value 9 for some x in [1, 2].

2. Show that takes on the value 0.499 for some t in [0, 1].

3. Show that g(t) = t 2 tan t takes on the value ½ for some t in [0. π/4].

4. Show that takes on the value 0.4.

5. Show that cos x = x has a solution in the interval [0, 1].

6. Use the IVT to find an interval of length ½ containing a root of f(x) = x 3 + 2x + 1.

In Exercises 7–16, use the IVT to prove each of the following statements.

7. for some number c.

8. For all integers n, sin nx = cos x for some x Î [0 ,π].

9. √2 exists. Hint: Consider f(x) = x 2

10. A positive number c has an nth root for all positive integers n. (This fact is usually taken for granted, but it requires proof.)

11. For all positive integers k, there exists x such that cos x = x k.

12. 2 x = bx has a solution if b > 2.

13. 2 x = b has a solution for all b > 0 (treat b ≥ 1 first).

14. tan x = x has infinitely many solutions.

15. The equation e x + ln x = 0 has a solution in (0, 1).

16. tan −1 x = cos −1 x has a solution.

17. Carry out three steps of the Bisection Method for f(x) = 2 x − x 3 as follows: (a) Show that f(x) has a zero in [1, 1.5]. (b) Show that f(x) has a zero in [1.25, 1.5]. (c) Determine whether [1.25, 1.375] or [1.375, 1.5] contains a zero.

18. Figure 4 shows that f(x) = x 3 − 8x − 1 has a root in the interval [2.75, 3]. Apply the Bisection Method twice to find an interval of length 1/16 containing this root.

19. Find an interval of length ¼ in [0, 1] containing a root of x 5 − 5x + 1 = 0.

20. Show that tan 3 θ − 8tan 2 θ + 17tan θ − 8 = 0 has a root in [0.5, 0.6]. Apply the Bisection Method twice to find an interval of length 0.025 containing this root.

In Exercises 21–24, draw the graph of a function f (x) on [0, 4] with the given property.

21. Jump discontinuity at x = 2 and does not satisfy the conclusion of the IVT.

22. Jump discontinuity at x = 2, yet does satisfy the conclusion of the IVT on [0, 4].

23. Infinite one-sided limits at x = 2 and does not satisfy the conclusion of the IVT.

24. Infinite one-sided limits at x = 2, yet does satisfy the conclusion of the IVT on [0, 4].

26. Take any map (e. g. of the United States) and draw a circle on it anywhere. Prove that at any moment in time there exists a pair of diametrically opposite points on that circle corresponding to locations where the temperatures at that moment are equal. Hint: Let θ be an angular coordinate along the circle and let f (θ) be the difference in temperatures at the locations corresponding to θ and θ + π.

27. Assume that f(x) is continuous and that 0 ≤ f (x) ≤ 1 for 0 ≤ x ≤ 1 (see Figure 5). Show that f(c) = c for some c in [0, 1].

28. Use the IVT to show that if f (x) is continuous and one-to-one on an interval [a, b], then f(x) is either an increasing or a decreasing function.

2. Let f (x) = 2x 2 − 3x − 5. Show that the slope of the secant line through (2. f (2)) and (2 + h. f (2 + h)) is 2h + 5. Then use this formula to compute the slope of: (a) The secant line through (2, f(2)) and (3, f(3)) (b) The tangent line at x = 2 (by taking a limit)

22. First find the slope and then an equation of the tangent line to the graph of f (x) = √x at x = 4.

In Exercises 23–40, compute the derivative at x = a using the limit definition and find an equation of the tangent line.

23. f (x) = 3x 2 + 2x, a = 2

41. What is an equation of the tangent line at x = 3, assuming that f (3) = 5 and f ' ( 3 ) = 2?

42. Suppose that y = 5x + 2 is an equation of the tangent line to the graph of y = f(x) at a = 3. What is f(3)? What is f ' (3)?

43. Consider the “curve” y = 2x + 8. What is the tangent line at the point (1, 10). Describe the tangent line at an arbitrary point.

44. Suppose that f (x) is a function such that f (2 + h) − f (2) = 3h 2 + 5h. (a) What is f ' (2)? (b) What is the slope of the secant line through (2, f (2)) and (6, f(6))?

49. The vapor pressure of water is defined as the atmospheric pressure P at which no net evaporation takes place. The following table and Figure 13 give P (in atmospheres) as a function of temperature T in kelvins. (a) Which is larger: P ' (300) or P ' (350). Answer by referring to the graph. (b) Estimate P ' ( T ) for T = 303, 313, 323, 333, 343 using the table and the average of the difference quotients for h = 10 and − 10:

In Exercises 50–51, traffic speed S along a certain road (in mph) varies as a function of traffic density q (number of cars per mile on the road). Use the following data to answer the questions:

50. Estimate S ' (q) when q = 120 cars per mile using the average of difference quotients at h and − h as in Exercise 48.

51. The quantity V = q S is called traffic volume. Explain why V is equal to the number of cars passing a particular point per hour. Use the data to compute values of V as a function of q and estimate V ' (q) when q = 120.

52. For the graph in Figure 14, determine the intervals along the x-axis on which the derivative is positive.

59. Sketch the graph of f (x) = sin x on [ 0 ,π ] and guess the value of f ' (π/2). Then calculate the slope of the secant line between x = π/2 and x = π/2 + h for at least three small positive and negative values of h. Are these calculations consistent with your guess?

60. Figure 15(A) shows the graph of f (x) =√x. The close-up in (B) shows that the graph is nearly a straight line near x = 16. Estimate the slope of this line and take it as an estimate for f ' (16). Then compute f ' (16) and compare with your estimate.

65. Apply the method of Example 6 to f (x) = sin x to determine f ' ( p /4) accurately to four decimal places.

66. Apply the method of Example 6 to f(x) = cos x to determine f ' (π/5) accurately to four decimal places. Use a graph of f(x) to explain how the method works in this case.

In Exercises 70–72, i ( t ) is the current (in amperes) at time t (seconds) flowing in the circuit shown in Figure

69. According to Kirchhoff’s law, i(t) = Cv ' ( t ) + R −1 v(t). where v(t) is the voltage (in volts) at time t, C the capacitance (in farads), and R the resistance (in ohms).

70. Calculate the current at t = 3 if v( t ) = 0.5t + 4 V, C = 0.01 F, and R = 100 W.

71. Use the following table to estimate v ¢ (10). For a better estimate, take the average of the difference quotients for h and −h as described in Exercise 48. Then estimate i(10), assuming C = 0.03 and R = 1000.

72. Assume that R = 200 W but C is unknown. Use the following data to estimate v ' (4) as in Exercise 71 and deduce an approximate value for the capacitance C.

52. Sketch the graph of f(x) = x − 3x 2 and find the values of x for which the tangent line is horizontal.

53. Find the points on the curve y = x 2 + 3x − 7 at which the slope of the tangent line is equal to 4.

54. Sketch the graphs of f(x) = x 2 − 5x + 4 and g(x) = −2x + 3. Find the value of x at which the graphs have parallel tangent lines.

55. Find all values of x where the tangent lines to y = x 3 and y = x 4 are parallel.

56. Show that there is a unique point on the graph of the function f(x) = ax 2 + bx + c where the tangent line is horizontal (assume a > 0). Explain graphically.

57. Determine coefficients a and b such that p(x) = x 2 + ax + b satisfies p(1) = 0 and p ' (1) = 4.

58. Find all values of x such that the tangent line to the graph of y = 4x 2 + 11x + 2 is steeper than the tangent line to y = x 3

59. Let f(x) = x 3 − 3x + 1. Show that f ' (x) ≥ −3 for all x, and that for every m > −3, there are precisely two points where f ' (x) = m. Indicate the position of these points and the corresponding tangent lines for one value of m in a sketch of the graph of f (x).

60. Show that if the tangent lines to the graph of at x = a and at x = b are parallel, then either a = b or a + b = 2.

61. Compute the derivative of f (x) = x −2 using the limit definition.

63. Find an approximation to m4 using the limit definition and estimate the slope of the tangent line to y = 4 x at x = 0 and x = 2.

64. Let f(x) = xe x. Use the limit definition to compute f ¢ (0) and find the equation of the tangent line at x = 0.

65. The average speed (in meters per second) of a gas molecule is . where T is the temperature (in kelvin), M is the molar mass (kg /mol) and R = 8.31. Calculate dv avg /dT at T = 300 K for oxygen, which has a molar mass of 0.032 kg/mol.

66. Biologists have observed that the pulse rate P (in beats per minute) in animals is related to body mass (in kilograms) by the approximate formula P = 200m −1/4. This is one of many allometric scaling laws prevalent in biology. Is the absolute value |dP/dm| increasing or decreasing as m increases? Find an equation of the tangent line at the points on the graph in Figure 17 that represent goat (m = 33) and man (m = 68).

67. Some studies suggest that kidney mass K in mammals (in kilograms) is related to body mass m (in kilograms) by the approximate formula K = 0.007m 0.85. Calculate dK/dm at m = 68. Then calculate the derivative with respect to m of the relative kidney-to-mass ratio K/m at m = 68.

68. The relation between the vapor pressure P (in atmospheres) of water and the temperature T (in kelvin) is given by the Clausius–Clapeyron law:

where k is a constant. Use the table below and the approximation to estimate dP/dT for T = 303, 313, 323, 333, 343. Do your estimates seem to confirm the Clausius–Clapeyron law? What is the approximate value of k? What are the units of k?

69. Let L be a tangent line to the hyperbola xy = 1 at x = a, where a > 0. Show that the area of the triangle bounded by L and the coordinate axes does not depend on a.

70. In the notation of Exercise 69, show that the point of tangency is the midpoint of the segment of L lying in the first quadrant.

71. Match the functions (A)–(C) with their derivatives (I)–(III) in Figure 18.

94. Two small arches have the shape of parabolas. The first is given by f(x) = 1 − x 2 for −1 ≤ x ≤ 1 and the second by g(x) = 4 − (x − 4) 2 for 2 ≤ x ≤ 6. A board is placed on top of these arches so it rests on both (Figure 22). What is the slope of the board?

95. A vase is formed by rotating y = x 2 around the y-axis. If we drop in a marble, it will either touch the bottom point of the vase or be suspended above the bottom by touching the sides (Figure 23). How small must the marble be to touch the bottom?

98. Verify the Power Rule for the exponent 1/n, where n is a positive integer, using the following trick: Rewrite the difference quotient for y = x 1/n at x = b in terms of u = (b + h) 1/n and a = b 1/n.

99. Infinitely Rapid Oscillations Define

Show that f(x) is continuous at x = 0 but f ' (0) does not exist (see Figure 12).

100. Prove that f(x) = e x is not a polynomial function. Hint: Differentiation lowers the degree of a polynomial by 1.

101. Consider the equation e x = λx, where λ is a constant. (a) For which λ does it have a unique solution? For intuition, draw a graph of y = e x and the line y = λx. (b) For which λ does it have at least one solution?

1. Find the ROC of the area of a square with respect to the length of its side s when s = 3 and s = 5.

2. Find the ROC of the volume of a cube with respect to the length of its side s when s = 3 and s = 5.

3. Find the ROC of y = x −1 with respect to x for x = 1, 10.

4. At what rate is the cube root changing with respect to x when x = 1, 8, 27?

In Exercises 5–8, calculate the ROC.

5. dV/dr, where V is the volume of a cylinder whose height is equal to its radius (the volume of a cylinder of height h and radius r is πr 2 h)

6. ROC of the volume V of a cube with respect to its surface area A

7. ROC of the volume V of a sphere with respect to its radius.

8. . where A is the surface area of a sphere of diameter D (the surface area of a sphere of radius r is 4πr 2 )

9. (a) Estimate the average velocity over [0.5, 1]. (b) Is average velocity greater over [1, 2] or [2, 3]? (c) At what time is velocity at a maximum?

10. Match the description with the interval (a)–(d). (i) Velocity increasing (ii) Velocity decreasing (iii) Velocity negative (iv) Average velocity of 50 mph

11. Figure 11 displays the voltage across a capacitor as a function of time while the capacitor is being charged. Estimate the ROC of voltage at t = 20 s. Indicate the values in your calculation and include proper units. Does voltage change more quickly or more slowly as time goes on? Explain in terms of tangent lines.

12. Use Figure 12 to estimate dT/dh at h = 30 and 70, where T is atmospheric temperature (in degrees Celsius) and h is altitude (in kilometers). Where is dT/dh equal to zero?

13. A stone is tossed vertically upward with an initial velocity of 25 ft /s from the top of a 30-ft building. (a) What is the height of the stone after 0.25 s? (b) Find the velocity of the stone after 1 s. (c) When does the stone hit the ground?

14. The height (in feet) of a skydiver at time t (in seconds) after opening his parachute is h(t) = 2000 − 15t ft. Find the skydiver’s velocity after the parachute opens.

15. The temperature of an object (in degrees Fahrenheit) as a function of time (in minutes) is for 0 ≤ t ≤ 20. At what rate does the object cool after 10 min (give correct units)?

16. The velocity (in centimeters per second) of a blood molecule flowing through a capillary of radius 0.008 cm is given by the formula v = 6.4 × 10 −8 − 0.001r 2. where r is the distance from the molecule to the center of the capillary. Find the ROC of velocity as a function of distance when r = 0.004 cm.

17. The earth exerts a gravitational force of (in Newtons) on an object with a mass of 75 kg, where r is the distance (in meters) from the center of the earth. Find the ROC of force with respect to distance at the surface of the earth, assuming the radius of the earth is 6.77 × 10 6 m

18. The escape velocity at a distance r meters from the center of the earth is v esc = (2.82 × 10 7 )r –1/2 m/s. Calculate the rate at which v esc changes with respect to distance at the surface of the earth.

19. The power delivered by a battery to an apparatus of resistance R (in ohms) is W. Find the rate of change of power with respect to resistance for R = 3 and R = 5 W.

20. The position of a particle moving in a straight line during a 5-s trip is s(t) = t 2 − t + 10 cm. (a) What is the average velocity for the entire trip? (b) Is there a time at which the instantaneous velocity is equal to this average velocity? If so, find it.

21. By Faraday’s Law, if a conducting wire of length l meters moves at velocity v m/s perpendicular to a magnetic field of strength B (in teslas), a voltage of size V = − Blv is induced in the wire. Assume that B = 2 and l = 0.5. (a) Find the rate of change dV/dv. (b) Find the rate of change of V with respect to time t if v = 4t + 9.

22. The height (in feet) of a helicopter at time t (in minutes) is s(t) = −3t + 400t for 0 ≤ t ≤ 10. (a) Plot the graphs of height s(t) and velocity v(t). (b) Find the velocity at t = 6 and t = 7. (c) Find the maximum height of the helicopter.

23. The population P(t) of a city (in millions) is given by the formula P(t) = 0.00005t 2 + 0.01t + 1, where t denotes the number of years since 1990. (a) How large is the population in 1996 and how fast is it growing? (b) When does the population grow at a rate of 12,000 people per year?

24. According to Ohm’s Law, the voltage V, current I, and resistance R in a circuit are related by the equation V = IR, where the units are volts, amperes, and ohms. Assume that voltage is constant with V = 12 V. Calculate (specifying the units): (a) The average ROC of I with respect to R for the interval from R = 8 to R = 8.1 (b) The ROC of I with respect to R when R = 8 (c) The ROC of R with respect to I when I = 1.5

25. Ethan finds that with h hours of tutoring, he is able to answer correctly S (h) percent of the problems on a math exam. What is the meaning of the derivative S ¢ (h)? Which would you expect to be larger: S ' (3) or S ' (30). Explain.

26. Suppose θ(t) measures the angle between a clock’s minute and hour hands. What is θ ' (t) at 3 o’clock?

27. Table 2 gives the total U. S. population during each month of 1999 as determined by the U. S. Department of Commerce. (a) Estimate P ¢ (t) for each of the months January–November. (b) Plot these data points for P ¢ (t) and connect the points by a smooth curve. (c) Write a newspaper headline describing the information contained in this plot.

28. The tangent lines to the graph of f(x) = x 2 grow steeper as x increases. At what rate do the slopes of the tangent lines increase?

29. According to a formula widely used by doctors to determine drug dosages, a person’s body surface area (BSA) (in meters squared) is given by the formula BSA = /60, where is the height in centimeters and w the weight in kilograms. Calculate the ROC of BSA with respect to weight for a person of constant height h = 180. What is this ROC for w = 70 and w = 80? Express your result in the correct units. Does BSA increase more rapidly with respect to weight at lower or higher body weights?

30. A slingshot is used to shoot a pebble in the air vertically from ground level with an initial velocity 200 m/s. Find the pebble’s maximum velocity and height.

31. What is the velocity of an object dropped from a height of 300 m when it hits the ground?

32. It takes a stone 3 s to hit the ground when dropped from the top of a building. How high is the building and what is the stone’s velocity upon impact?

33. A ball is tossed up vertically from ground level and returns to earth 4 s later. What was the initial velocity of the stone and how high did it go?

34. An object is tossed up vertically from ground level and hits the ground T s later. Show that its maximum height was reached after T/2 s.

35. A man on the tenth floor of a building sees a bucket (dropped by a window washer) pass his window and notes that it hits the ground 1.5 s later. Assuming a floor is 16 ft high (and neglecting air friction), from which floor was the bucket dropped?

36. Which of the following statements is true for an object falling under the influence of gravity near the surface of the earth? Explain. (a) The object covers equal distance in equal time intervals. (b) Velocity increases by equal amounts in equal time intervals. (c) The derivative of velocity increases with time.

37. Show that for an object rising and falling according to Galileo’s formula in Eq. (3), the average velocity over any time interval [t 1 . t 2 ] is equal to the average of the instantaneous velocities at t 1 and t 2 .

38. A weight oscillates up and down at the end of a spring. Figure 13 shows the height y of the weight through one cycle of the oscillation. Make a rough sketch of the graph of the velocity as a function of time.

In Exercises 39–46, use Eq. (2) to estimate the unit change.

39. Estimate and . Compare your estimates with the actual values.

40. Suppose that f(x) is a function with f ¢ (x) = 2 −x. Estimate f (7) − f (6). Then estimate f(5), assuming that f (4) = 7.

41. Let F(s) = 1.1s + 0.03s 2 be the stopping distance as in Example 3. Calculate F(65) and estimate the increase in stopping distance if speed is increased from 65 to 66 mph. Compare your estimate with the actual increase.

42. According to Kleiber’s Law, the metabolic rate P (in kilocalories per day) and body mass m (in kilograms) of an animal are related by a three-quarter power law P = 73.3m 3/4. Estimate the increase in metabolic rate when body mass increases from 60 to 61 kg.

43. The dollar cost of producing x bagels is C(x) = 300 + 0.25x − 0.5(x/1000) 3. Determine the cost of producing 2,000 bagels and estimate the cost of the 2001st bagel. Compare your estimate with the actual cost of the 2001st bagel.

44. Suppose the dollar cost of producing x video cameras is C(x) = 500x − 0.003x 2 + 10 −8 x 3. (a) Estimate the marginal cost at production level x = 5000 and compare it with the actual cost C(5001) − C(5000). (b) Compare the marginal cost at x = 5000 with the average cost per camera, defined as C(x)/x.

45. The demand for a commodity generally decreases as the price is raised. Suppose that the demand for oil (per capita per year) is D(p) = 900/p barrels, where p is the price per barrel in dollars. Find the demand when p = $40. Estimate the decrease in demand if p rises to $41 and the increase if p is decreased to $39.

46. The reproduction rate of the fruit fly Drosophila melanogaster, grown in bottles in a laboratory, decreases as the bottle becomes more crowded. A researcher has found that when a bottle contains p flies, the number of offspring per female per day is f(p) = (34 − 0.612p)p −0.658 (a) Calculate f(15) and f ' (15). (b) Estimate the decrease in daily offspring per female when p is increased from 15 to 16. Is this estimate larger or smaller than the actual value f(16) − f(15)? (c) Plot f (p) for 5 ≤ p ≤ 25 and verify that f(p) is a decreasing function of p. Do you expect f ' (p) to be positive or negative? Plot f ' (p) and confirm your expectation.

47. Let A = s 2. Show that the estimate of A(s + 1) − A(s) provided by Eq. (2) has error exactly equal to 1. Explain this result using Figure 14.

48. According to Steven’s Law in psychology, the perceived magnitude of a stimulus (how strong a person feels the stimulus to be) is proportional to a power of the actual intensity I of the stimulus. Although not an exact law, experiments show that the perceived brightness B of a light satisfies B = kI 2/3. where I is the light intensity, whereas the perceived heaviness H of a weight W satisfies H = kW 3/2 (k is a constant that is different in the two cases). Compute dB/dI and dH/dW and state whether they are increasing or decreasing functions. Use this to justify the statements: (a) A one-unit increase in light intensity is felt more strongly when I is small than when I is large. (b) Adding another pound to a load W is felt more strongly when Wis large than when W is small.

49. Let M(t) be the mass (in kilograms) of a plant as a function of time (in years). Recent studies by Niklas and Enquist have suggested that for a remarkably wide range of plants (from algae and grass to palm trees), the growth rate during the life span of the organism satisfies a three-quarter power law, that is, dM/dt = CM 3/4 for some constant C. (a) If a tree has a growth rate of 6 kg/year when M = 100 kg, what is its growth rate when M = 125 kg? (b) If M = 0.5 kg, how much more mass must the plant acquire to double its growth rate?

50. As an epidemic spreads through a population, the percentage p of infected individuals at time t (in days) satisfies the equation (called a differential equation) dp/dt = 4p − 0.06p 2. 0 ≤ p ≤ 100 (a) How fast is the epidemic spreading when p = 10% and when p = 70%? (b) For which p is the epidemic neither spreading nor diminishing? (c) Plot dp/dt as a function of p. (d) What is the maximum possible rate of increase and for which p does this occur?

51. The size of a certain animal population P(t) at time t (in months) satisfies dP/dt = 0.2(300 − P). (a) Is P growing or shrinking when P = 250? when P = 350? (b) Sketch the graph of dP/dt as a function of P for 0 ≤ P ≤ 300. (c) Which of the graphs in Figure 15 is the graph of P(t) if P(0) = 200?

In Exercises 53–54, the average cost per unit at production level x is defined as C avg (x) = C(x)/x, where C(x) is the cost function. Average cost is a measure of the efficiency of the production process.

53. Show that C avg (x) is equal to the slope of the line through the origin and the point (x, C(x)) on the graph of C(x). Using this interpretation, determine whether average cost or marginal cost is greater at points A, B, C, D in Figure 16.

54. The cost in dollars of producing alarm clocks is C(x) = 50x 3 − 750x 2 + 3740x + 3750 where x is in units of 1,000. (a) Calculate the average cost at x = 4, 6, 8, and 10. (b) Use the graphical interpretation of average cost to find the production level x 0 at which average cost is lowest. What is the relation between average cost and marginal cost at x 0 (see Figure 17)?

37. (a) Find the acceleration at time t = 5 min of a helicopter whose height (in feet) is h(t) = − 3t 3 + 400t. (b) Plot the acceleration h ² (t) for 0 ≤ t ≤ 6. How does this graph show that the helicopter is slowing down during this time interval?

38. Find an equation of the tangent to the graph of y = f ¢ (x) at x = 3, where f(x) = x 4.

39. Figure 5 shows f. f '. and f ' '. Determine which is which.

40. The second derivative f ' ' is shown in Figure 6. Determine which graph, (A) or (B), is f and which is f ' '.

41. Figure 7 shows the graph of the position of an object as a function of time. Determine the intervals on which the acceleration is positive.

42. Find the second derivative of the volume of a cube with respect to the length of a side.

43. Find a polynomial f(x) satisfying the equation x f '' (x) + f (x) = x 2.

44. Find a value of n such that y = x n e x satisfies the equation xy ' = (x − 3)y.

45. Which of the following descriptions could not apply to Figure 8? Explain. (a) Graph of acceleration when velocity is constant (b) Graph of velocity when acceleration is constant (c) Graph of position when acceleration is zero

46. A servomotor controls the vertical movement of a drill bit that will drill a pattern of holes in sheet metal. The maximum vertical speed of the drill bit is 4 in ./s, and while drilling the hole, it must move no more than 2.6 in ./s to avoid warping the metal. During a cycle, the bit begins and ends at rest, quickly approaches the sheet metal, and quickly returns to its initial position after the hole is drilled. Sketch possible graphs of the drill bit’s vertical velocity and acceleration. Label the point where the bit enters the sheet metal.

52. Find the 100th derivative of p(x) = (x + x 5 + x 7 ) 10 (1 + x 2 ) 11 (x 3 + x 5 + x 7 )

54. Use the Product Rule twice to find a formula for (f g) '' in terms of the first and second derivative of f and g.

55. Use the Product Rule to find a formula for (f g) '' and compare your result with the expansion of (a + b) 3. Then try to guess the general formula for (f g) (n)

42. Find the values of x between 0 and 2 π where the tangent line to the graph of y = sin x cos x is horizontal.

43. Calculate the first five derivatives of f(x) = cos x. Then determine f (8) and f (37).

44. Find y (157). where y = sin x.

48. Show that no tangent line to the graph of f(x) = tan x has zero slope. What is the least slope of a tangent line? Justify your response by sketching the graph of (tan x) '.

49. The height at time t (s) of a weight, oscillating up and down at the end of a spring, is s(t) = 300 + 40 sin t cm. Find the velocity and acceleration at t = π.

50. The horizontal range R of a projectile launched from ground level at an angle θ and initial velocity v 0 m/s is . Calculate dR/dθ. If θ = 7π /24, will the range increase or decrease if the angle is increased slightly? Base your answer on the sign of the derivative.

51. If you stand 1 m from a wall and mark off points on the wall at equal increments δ of angular elevation (Figure 4), then these points grow increasingly far apart. Explain how this illustrates the fact that the derivative of tan θ is increasing.

52. Use the limit definition of the derivative and the addition law for the cosine to prove that (cos x) ' = −sin x.

53. Show that a nonzero polynomial function y = f (x) cannot satisfy the equation y ² = − Y. Use this to prove that neither sin x nor cos x is a polynomial.

56. Show that if π / 2 < θ < π. then the distance along the x-axis between θ and the point where the tangent line intersects the x-axis is equal to |tan θ| (Figure 5).

74. The average molecular velocity v of a gas in a certain container is given by v = 29√T m/s, where T is the temperature in kelvins. The temperature is related to the pressure (in atmospheres) by T = 200P.

76. Assume that f(0) = 2 and f ' (0) = 3. Find the derivatives of (f (x)) 3 and f (7x ) at x = 0.

77. Compute the derivative of h(sin x) at x = π/6, assuming that h ' (0.5) = 10.

78. Let F(x) = f(g(x)), where the graphs of f and g are shown in Figure 1. Estimate g ' (2) and f ' (g(2)) from the graph and compute F ' (2).

88. Use the Chain Rule to express the second derivative of f ◦ g in terms of the first and second derivatives of f and g.

89. Compute the second derivative of sin (g(x)) at x = 2, assuming that g (2) = π/4, g ' (2) = 5, and g ' ' (2) = 3.

90. An expanding sphere has radius r = 0.4t cm at time t (in seconds). Let V be the sphere’s volume. Find dV/dt when (a) r = 3 and (b) t = 3.

91. The power P in a circuit is P = Ri 2. where R is resistance and i the current. Find dP/dt at t = 2 if R = 1000 W and i varies according to i = sin(4πt) (time in seconds).

92. The price (in dollars) of a computer component is P = 2C − 18C −1. where C is the manufacturer’s cost to produce it. Assume that cost at time t (in years) is C = 9 + 3t −1 and determine the ROC of price with respect to time at t = 3.

93. The force F (in Newtons) between two charged objects is F = 100/r 2. where r is the distance (in meters) between them. Find dF/dt at t = 10 if the distance at time t (in seconds) is r = 1 + 0.4t 2.

94. According to the U. S. standard atmospheric model, developed by the National Oceanic and Atmospheric Administration for use in aircraft and rocket design, atmospheric temperature T (in degrees Celsius), pressure P (kPa = 1000 Pascals), and altitude h (meters) are related by the formulas (valid in the troposphere h ≤ 11000):

Calculate dP/dh. Then estimate the change in P (in Pascals, Pa) per additional meter of altitude when h = 3000.

35. Find the points on the graph of y 2 = x 3 − 3x + 1 (Figure 6) where the tangent line is horizontal. (a) First show that 2yy ¢ = 3x 2 − 3, where y ¢ = dy/dx. (b) Do not solve for y ¢. Rather, set y ¢ = 0 and solve for x. This gives two possible values of x where the slope may be zero. (c) Show that the positive value of x does not correspond to a point on the graph. (d) The negative value corresponds to the two points on the graph where the tangent line is horizontal. Find the coordinates of these two points.

36. Find all points on the graph of 3x 2 + 4y 2 + 3xy = 24 where the tangent line is horizontal (Figure 7). (a) By differentiating the equation of the curve implicitly and setting y ¢ = 0, show that if the tangent line is horizontal at (x. y). then y = −2x. (b) Solve for x by substituting y = −2x in the equation of the curve.

37. Show that no point on the graph of x 2 − 3xy + y 2 = 1 has a horizontal tangent line.

38. Figure 1 shows the graph of y 4 + xy = x 3 − x + 2. Find dy/dx at the two points on the graph with x-coordinate 0 and find an equation of the tangent line at (1, 1).

39. If the derivative dx/dy exists at a point and dx/dy = 0, then the tangent line is vertical. Calculate dx/dy for the equation y 4 + 1 = y 2 + x 2 and find the points on the graph where the tangent line is vertical.

40. Differentiate the equation xy = 1 with respect to the variable t and derive the relation .

44. The volumeV and pressure P of gas in a piston (which vary in time t) satisfy PV 3/2 = C, where C is a constant. Prove that The ratio of the derivatives is negative. Could you have predicted this from the relation PV 3/2 = C?

46. Find all points on the folium x 3 + y 3 = 3xy at which the tangent line is horizontal.

58. Show that if P lies on the intersection of the two curves x 2 − y 2 = c and xy = d (c, d constants), then the tangents to the curves at P are perpendicular.

79. The energy E (in joules) radiated as seismic waves from an earthquake of Richter magnitude M is given by the formula log 10 E = 4.8 + 1.5M. (a) Express E as a function of M. (b) Show that when M increases by 1, the energy increases by a factor of approximately 31. (c) Calculate dE/dM

1. How fast is the water level rising if water is filling the tub at a rate of 0.7 ft 3 /min?

2. At what rate is water pouring into the tub if the water level rises at a rate of 0.8 ft/min?

3. The radius of a circular oil slick expands at a rate of 2 m/min. (a) How fast is the area of the oil slick increasing when the radius is 25 m? (b) If the radius is 0 at time t = 0, how fast is the area increasing after 3 min?

4. At what rate is the diagonal of a cube increasing if its edges are increasing at a rate of 2 cm/s?

In Exercises 5–8, assume that the radius r of a sphere is expanding at a rate of 14 in./min. The volume of a sphere is .

5. Determine the rate at which the volume is changing with respect to time when r = 8 in.

6. Determine the rate at which the volume is changing with respect to time at t = 2 min, assuming that r = 0 at t = 0.

7. Determine the rate at which the surface area is changing when the radius is r = 8 in.

8. Determine the rate at which the surface area is changing with respect to time at t = 2 min, assuming that r = 3 at t = 0.

9. A road perpendicular to a highway leads to a farmhouse located 1 mile away (Figure 9). An automobile travels past the farmhouse at a speed of 60 mph. How fast is the distance between the automobile and the farmhouse increasing when the automobile is 3 miles past the intersection of the highway and the road?

10. A conical tank has height 3 m and radius 2 m at the top. Water flows in at a rate of 2 m 3 /min. How fast is the water level rising when it is 2 m?

11. Follow the same set-up as Exercise 10, but assume that the water level is rising at a rate of 0. 3 m / min when it is 2 m. At what rate is water flowing in?

12. Sonya and Isaac are in motorboats located at the center of a lake. At time t = 0, Sonya begins traveling south at a speed of 32 mph. At the same time, Isaac takes off, heading east at a speed of 27 mph. (a) How far have Sonya and Isaac each traveled after 12 min? (b) At what rate is the distance between them increasing at t = 12 min?

13. Answer (a) and (b) in Exercise 12 assuming that Sonya begins moving 1 minute after Isaac takes off.

14. A 6-ft man walks away from a 15-ft lamppost at a speed of 3 ft /s (Figure 10). Find the rate at which his shadow is increasing in length.

15. At a given moment, a plane passes directly above a radar station at an altitude of 6 miles. (a) If the plane’s speed is 500 mph, how fast is the distance between the plane and the station changing half an hour later? (b) How fast is the distance between the plane and the station changing when the plane passes directly above the station?

16. In the setting of Exercise 15, suppose that the line through the radar station and the plane makes an angle θ with the horizontal. How fast is θ changing 10 min after the plane passes over the radar station?

17. A hot air balloon rising vertically is tracked by an observer located 2 miles from the lift-off point. At a certain moment, the angle between the observer’s line-of-sight and the horizontal is π/5, and it is changing at a rate of 0.2 rad/min. How fast is the balloon rising at this moment?

18. As a man walks away from a 12-ft lamppost, the tip of his shadow moves twice as fast as he does. What is the man’s height?

In Exercises 19–23, refer to a 16-ft ladder sliding down a wall, as in Figures 1 and 2. The variable h is the height of the ladder’s top at time t, and x is the distance from the wall to the ladder’s bottom.

19. Assume the bottom slides away from the wall at a rate of 3 ft/s. Find the velocity of the top of the ladder at t = 2 if the bottom is 5 ft from the wall at t = 0.

20. Suppose that the top is sliding down the wall at a rate of 4 ft/s. Calculate dx/dt when h = 12.

21. Suppose that h(0) = 12 and the top slides down the wall at a rate of 4 ft/s. Calculate x and dx/dt at t = 2 s.

22. What is the relation between h and x at the moment when the top and bottom of the ladder move at the same speed?

23. Show that the velocity dh / dt approaches infinity as the ladder slides down to the ground (assuming dx / dt is constant). This suggests that our mathematical description is unrealistic, at least for small values of h. What would, in fact, happen as the top of the ladder approaches the ground?

24. The radius r of a right circular cone of fixed height h = 20 cm is increasing at a rate of 2 cm/s. How fast is the volume increasing when r = 10?

25. Suppose that both the radius r and height h of a circular cone change at a rate of 2 cm/s. How fast is the volume of the cone increasing when r = 10 and h = 20?

26. A particle moves counterclockwise around the ellipse 9x 2 + 16y 2 = 25 (Figure 11). (a) In which of the four quadrants is the derivative dx / dt positive? Explain your answer. (b) Find a relation between dx/dt and dy/dt. (c) At what rate is the x-coordinate changing when the particle passes the point (1, 1) if its y-coordinate is increasing at a rate of 6 ft /s? (d) What is dy/dt when the particle is at the top and bottom of the ellipse?

27. A searchlight rotates at a rate of 3 revolutions per minute. The beam hits a wall located 10 miles away and produces a dot of light that moves horizontally along the wall. How fast is this dot moving when the angle θ between the beam and the line through the searchlight perpendicular to the wall is π/6?

28. A rocket travels vertically at a speed of 800 mph. The rocket is tracked through a telescope by an observer located 10 miles from the launching pad. Find the rate at which the angle between the telescope and the ground is increasing 3 min after lift-off.

29. A plane traveling at an altitude of 20,000 ft passes directly overhead at time t = 0. One minute later you observe that the angle between the vertical and your line of sight to the plane is 1.14 rad and that this angle is changing at a rate of 0.38 rad/min. Calculate the velocity of the airplane.

30. Calculate the rate (in cm 2 /s) at which area is swept out by the second hand of a circular clock as a function of the clock’s radius.

31. A jogger runs around a circular track of radius 60 ft. Let (x, y) be her coordinates, where the origin is at the center of the track. When the jogger’s coordinates are (36, 48), her x-coordinate is changing at a rate of 14 ft/s. Find dy/dt.

32. A car travels down a highway at 55 mph. An observer is standing 500 ft from the highway. (a) How fast is the distance between the observer and the car increasing at the moment the car passes in front of the observer? Can you justify your answer without relying on any calculations? (b) How fast is the distance between the observer and the car increasing 1 min later?

In Exercises 33–34, assume that the pressure P (in kilopascals) and volume V (in cubic centimeters) of an expanding gas are related by PV b = C, where b and C are constants (this holds in adiabatic expansion, without heat gain or loss).

33. Find dP/dt if b = 1.2, P = 8 kPa, V = 100 cm 2. and dV/dt = 20 cm 3 /min.

34. Find b if P = 25 kPa, dP/dt = 12 kPa/min, V = 100 cm 2. and dV/dt = 20 cm 3 /min.

35. A point moves along the parabola y = x 2 + 1. Let l(t) be the distance between the point and the origin. Calculate l ¢ (t). assuming that the x-coordinate of the point is increasing at a rate of 9 ft/s.

36. The base x of the right triangle in Figure 12 increases at a rate of 5 cm/s, while the height remains constant at h = 20. How fast is the angle θ changing when x = 20?

37. A water tank in the shape of a right circular cone of radius 300 cm and height 500 cm leaks water from the vertex at a rate of 10 cm 3 /min. Find the rate at which the water level is decreasing when it is 200 cm.

38. Two parallel paths 50 ft apart run through the woods. Shirley jogs east on one path at 6 mph, while Jamail walks west on the other at 4 mph. If they pass each other at time t = 0, how far apart are they 3 s later, and how fast is the distance between them changing at that moment?

39. Henry is pulling on a rope that passes through a pulley on a 10-ft pole and is attached to a wagon (Figure 13). Assume that the rope is attached to a loop on the wagon 2 ft off the ground. Let x be the distance between the loop and the pole. (a) Find a formula for the speed of the wagon in terms of x and the rate at which Henry pulls the rope. (b) Find the speed of the wagon when it is 12 ft from the pole, assuming that Henry pulls the rope at a rate of 1. 5 ft/s.

40. A roller coaster has the shape of the graph in Figure 14. Show that when the roller coaster passes the point ( x, f (x)), the vertical velocity of the roller coaster is equal to f ¢ (x) times its horizontal velocity.

41. Using a telescope, you track a rocket that was launched 2 miles away, recording the angle θ between the telescope and the ground at half-second intervals. Estimate the velocity of the rocket if θ(10) = 0 .205 and θ(10.5) = 0.225.

42. Two trains leave a station at t = 0 and travel with constant velocity v along straight tracks that make an angle θ. (a) Show that the trains are separating from each other at a rate . (b) What does this formula give for θ = π?

43. A baseball player runs from home plate toward first base at 20 ft/s. How fast is the player’s distance from second base changing when the player is halfway to first base? See Figure 15.

44. As the wheel of radius r cm in Figure 16 rotates, the rod of length L attached at the point P drives a piston back and forth in a straight line. Let x be the distance from the origin to the point Q at the end of the rod as in the figure. (a) Use the Pythagorean Theorem to show that (b) Differentiate Eq. (8) with respect to t to prove that (c) Calculate the speed of the piston when θ = π/2, assuming that r = 10 cm, L = 30 cm, and the wheel rotates at 4 revolutions per minute.

45. A spectator seated 300 m away from the center of a circular track of radius 100 m watches an athlete run laps at a speed of 5 m/s. How fast is the distance between the spectator and athlete changing when the runner is approaching the spectator and the distance between them is 250 m?

46. A cylindrical tank of radius R and length L lying horizontally as in Figure 17 is filled with oil to height h. (a) Show that the volume V(h) of oil in the tank as a function of height h is

(b) Show that (c) Suppose that R = 4 ft and L = 30 ft, and that the tank is filled at a constant rate of 10 ft 3 /min. How fast is the height h increasing when h = 5?

CHAPTER REVIEW EXERCISES

113. Water pours into the tank in Figure 7 at a rate of 20 m 3 /min. How fast is the water level rising when the water level is h = 4 m?

114. The minute hand of a clock is 4 in. long and the hour hand is 3 in. long. How fast is the distance between the tips of the hands changing at 3 o’clock?

115. A light moving at 3 ft / s approaches a 6-ft man standing 12 ft from a wall (Figure 8). The light is 3 ft above the ground. How fast is the tip P of the man’s shadow moving when the light is 24 ft from the wall?

116. A bead slides down the curve xy = 10. Find the bead’s horizontal velocity if its height at time t seconds is y = 80 − 16t 2 cm.

117. (a) Side x of the triangle in Figure 9 is increasing at 2 cm/s and side y is increasing at 3 cm/s. Assume that θ decreases in such a way that the area of the triangle has the constant value 4 cm 2. How fast is θ decreasing when x = 4, y = 4? (b) How fast is the distance between P and Q changing when x = 2, y = 3?

In exercises 1-6 use the linear approximation to estimate D f = f(3.02) – f(3) for the given function 1. f (x) = x 2

25. The cube root of 27 is 3. How much larger is the cube root of 27.2? Estimate using the Linear Approximation.

26. Which is larger: √2.1 − √2 or √9.1 − √9? Explain using the Linear Approximation.

27. Estimate sin 61◦ − sin 60◦ using the Linear Approximation.

28. A thin silver wire has length L = 18 cm when the temperature is T = 30◦C. Estimate the length when T = 25◦C if the coefficient of thermal expansion is k = 1.9 × 10 −5 ◦C −1.

29. The atmospheric pressure P (in kilopascals) at altitudes h (in kilometers) for 11 ≤ h ≤ 25 is approximately P(h) = 128e −0.157h. (a) Use the Linear Approximation to estimate the change in pressure at h = 20 when D h = 0.5. (b) Compute the actual change and compute the percentage error in the Linear Approximation.

30. The resistance R of a copper wire at temperature T = 20◦C is R = 15 W. Estimate the resistance at T = 22◦C, assuming that

31. The side s of a square carpet is measured at 6 ft. Estimate the maximum error in the area A of the carpet if s is accurate to within half an inch.

32. A spherical balloon has a radius of 6 in. Estimate the change in volume and surface area if the radius increases by 0.3 in.

33. A stone tossed vertically in the air with initial velocity v ft/s reaches a maximum height of h = v 2 /64 ft. (a) Estimate D h if v is increased from 25 to 26 ft / s. (b) Estimate D h if v is increased from 30 to 31 ft / s. (c) In general, does a 1 ft / s increase in initial velocity cause a greater change in maximum height at low or high initial velocities? Explain.

34. If the price of a bus pass from Albuquerque to Los Alamos is set at x dollars, a bus company takes in a monthly revenue of R(x) = 1.5x − 0.01x 2 (in thousands of dollars). (a) Estimate the change in revenue if the price rises from $50 to $53. (b) Suppose that x = 80. How will revenue be affected by a small increase in price? Explain using the Linear Approximation.

35. The stopping distance for an automobile (after applying the brakes) is approximately F(s) = 1.1s + 0.054s 2 ft, where s is the speed in mph. Use the Linear Approximation to estimate the change in stopping distance per additional mph when s = 35 and when s = 55.

36. Juan measures the circumference C of a spherical ball at 40 cm and computes the ball’s volume V. Estimate the maximum possible error in V if the error in C is at most 2 cm. Recall that C = 2πr and . where r is the ball’s radius.

37. Estimate the weight loss per mile of altitude gained for a 130-lb pilot. At which altitude would she weigh 129.5 lb? See Example 4.

38. How much would a 160-lb astronaut weigh in a satellite orbiting the earth at an altitude of 2,000 miles? Estimate the astronaut’s weight loss per additional mile of altitude beyond 2,000.

39. The volume of a certain gas (in liters) is related to pressure P (in atmospheres) by the formula PV = 24. Suppose that V = 5 with a possible error of ± 0.5 L. (a) Compute P and estimate the possible error. (b) Estimate the maximum allowable error in V if P must have an error of at most 0.5 atm.

40. The dosage D of diphenhydramine for a dog of body mass w kg is D = k w 2/3 mg, where k is a constant. A cocker spaniel has mass w = 10 kg according to a veterinarian’s scale. Estimate the maximum allowable error in w if the percentage error in the dosage D must be less than 5%.

In Exercises 41–50, find the linearization at x = a.

41. y = cos x sin x, a = 0

51. Estimate √16.2 using the linearization L(x) of f(x) = √x at a = 16. Plot f(x) and L(x) on the same set of axes and determine if the estimate is too large or too small.

52. Estimate 1/√15 using a suitable linearization of f(x) = 1/√x. Plot f(x) and L(x) on the same set of axes and determine if the estimate is too large or too small. Use a calculator to compute the percentage error.

In Exercises 53–61, approximate using linearization and use a calculator to compute the percentage error.

62. Plot f(x) = tan x and its linearization L(x) at a = π/4 on the same set of axes. (a) Does the linearization overestimate or underestimate f(x)? (b) Show, by graphing y = f(x) − L(x) and y = 0.1 on the same set of axes, that the error |f(x) − L(x)| is at most 0.1 for 0.55 ≤ x ≤ 0.95. (c) Find an interval of x-values on which the error is at most 0.05.

63. Compute the linearization L(x) of f(x) = x 2 − x 3/2 at a = 2. Then plot f(x) − L(x) and find an interval around a = 1 such that |f(x) − L(x)| ≤ 0.1.

In Exercises 64–65, use the following fact derived from Newton’s Laws: An object released at an angle θ with initial velocity v ft/s travels a total distance

64. A player located 18.1 ft from a basket launches a successful jump shot from a height of 10 ft (level with the rim of the basket), at an angle θ = 34 o and initial velocity of v = 25 ft/s. (a) Show that the distance s of the shot changes by approximately 0.255 D θ ft if the angle changes by an amount D θ. Remember to convert the angles to radians in the Linear Approximation. (b) Is it likely that the shot would have been successful if the angle were off by 2◦?

65. Estimate the change in the distance s of the shot if the angle changes from 50◦ to 51◦ for v = 25 ft / s and v = 30 ft / s. Is the shot more sensitive to the angle when the velocity is large or small? Explain.

66. Compute the linearization of f (x) = 3x − 4 at a = 0 and a = 2. Prove more generally that a linear function coincides with its linearization at x = a for all a.

67. According to (3), the error in the Linear Approximation is of “order two” in h. Show that the Linear Approximation to f(x) =√x at x = 9 yields the estimate . Then compute the error E for h = 10 −n. 1 ≤ n ≤ 4, and verify numerically that E ≤ 0.006h 2.

68. Show that the Linear Approximation to f(x) = tan x at x = π/4 yields the estimate tan (π/4 + h) – 1 » 2h. Compute the error E for h = 10 −n. 1 ≤ n ≤ 4, and verify that E satisfies the Error Bound (3) with K = 6.2.

69. Show that for any real number k, (1 + x) k ≈ 1 + kx for small x. Estimate (1.02) 0.7 and (1.02) −0.3.

70. (a) Show that f(x) = sin x and g(x) = tan x have the same linearization at a = 0. (b) Which function is approximated more accurately? Explain using a graph over [0, π/6]. (c) Calculate the error in these linearizations at x = π/6. Does the answer confirm your conclusion in (b)?

71. Let D f = f(5 + h) − f(5). where f(x) = x 2. and let E = | D f − f ¢ (5)h| be the error in the Linear Approximation. Verify directly that E satisfies (3) with K = 2 (thus E is of order two in h).

1. The following questions refer to Figure 15. (a) How many critical points does f(x) have? (b) What is the maximum value of f(x) on [0, 8]? (c) What are the local maximum values of f(x)? (d) Find a closed interval on which both the minimum and maximum values of f(x) occur at critical points. (e) Find an interval on which the minimum value occurs at an endpoint.

In Exercises 3–14, find all critical points of the function.

3. f(x) = x 2 − 2x + 4

15. Let f(x) = x 2 − 4x + 1. (a) Find the critical point c of f(x) and compute f(c). (b) Compute the value of f(x) at the endpoints of the interval [0, 4]. (c) Determine the min and max of f(x) on [0, 4]. (d) Find the extreme values of f(x) on [0, 1].

16. Find the extreme values of 2x 3 − 9x 2 + 12x on [0, 3] and [0, 2].

17. Find the minimum value of y = tan −1 (x 2 − x).

18. Find the critical points of f(x) = sin x + cos x and determine the extreme values on [0, π/2].

19. Compute the critical points of h(t) = (t 2 − 1) 1/3. Check that your answer is consistent with Figure 17. Then find the extreme values of h(t) on [0, 1] and [0, 2].

20. Plot f(x) = 2√x − x on [0, 4] and determine the maximum value graphically. Then verify your answer using calculus.

21. Plot f (x) = ln x − 5 sin x on [0, 2π] (choose an appropriate viewing rectangle) and approximate both the critical points and extreme values.

22. Approximate the critical points of g(x) = x arccos x and estimate the maximum value of g(x).

In Exercises 23–56, find the maximum and minimum values of the function on the given interval. 23. y = 2x 2 − 4x + 2, [0, 3].

63. Let f(x) = 3x − x 3. Check that f (−2) = f(1). What may we conclude from Rolle’s Theorem? Verify this conclusion.

In Exercises 64–67, verify Rolle’s Theorem for the given interval.

64. f (x) = x + x −1. [1/2, 2]

68. Use Rolle’s Theorem to prove that f(x) = x 5 + 2x 3 + 4x − 12 has at most one real root.

69. Use Rolle’s Theorem to prove that f (x) = x 3 /6 + x 2 /2 + x + 1 has at most one real root.

70. The concentration C ( t ) (in mg/cm 3 ) of a drug in a patient’s bloodstream after t hours is . Find the maximum concentration and the time at which it occurs.

84. Show, by considering its minimum, that f(x) = x 2 − 2x + 3 takes on only positive values. More generally, find the conditions on r and s under which the quadratic function f(x) = x 2 + rx + s takes on only positive values. Give examples of r and s for which f takes on both positive and negative values.

85. Show that if the quadratic polynomial f(x) = x 2 + rx + s takes on both positive and negative values, then its minimum value occurs at the midpoint between the two roots.

88. Find the minimum and maximum values of f(x) = x p (1 − x) q on [0, 1], where p and q are positive numbers.

In Exercises 1–10, find a point c satisfying the conclusion of the MVT for the given function and interval.

1. y = x −1. [1, 4]

11. Let f(x) = x 5 + x 2. Check that the secant line between x = 0 and x = 1 has slope 2. By the MVT, f ' (c) = 2 for some c Î in the interval (0,1). Estimate c graphically as follows. Plot f(x) and the secant line on the same axes. Then plot the lines y = 2x + b for different values of b until you find a value of b for which it is tangent to y = f(x). Zoom in on the point of tangency to find its x-coordinate.

12. Determine the intervals on which f (x) is positive and negative, assuming that Figure 12 is the graph of f(x).

13. Determine the intervals on which f ( x ) is increasing or decreasing, assuming that Figure 12 is the graph of the derivative f ' (x).

14. Plot the derivative f ' (x) of f(x) = 3x 5 − 5x 3 and describe the sign changes of f ' (x). Use this to determine the local extreme values of f(x). Then graph f(x) to confirm your conclusions.

In Exercises 15–18, sketch the graph of a function f(x) whose derivative f ' (x) has the given description.

15. f ' (x) > 0 for x > 3 and f ' (x) < 0 for x < 3.

In Exercises 19–22, use the First Derivative Test to determine whether the function attains a local minimum or local maximum (or neither) at the given critical point.

19. y = 7 + 4x − x 2. c = 2

In Exercises 25–52, find the critical points and the intervals on which the function is increasing or decreasing, and apply the First Derivative Test to each critical point.

25. y = −x 2 + 7x − 17

53. Show that f(x) = x 2 + bx + c is decreasing on (−∞, −b/2) and increasing on (−b/2, ∞).

54. Show that f(x) = x 3 − 2x 2 + 2x is an increasing function.

55. Find conditions on a and b that ensure that f(x) = x 3 + ax + b is increasing on (−∞, ∞) .

57. Sam made two statements that Deborah found dubious. (a) “Although the average velocity for my trip was 70 mph, at no point in time did my speedometer read 70 mph.” (b) “Although a policeman clocked me going 70 mph, my speedometer never read 65 mph.” In each case, which theorem did Deborah apply to prove Sam’s statement false: the Intermediate Value Theorem or the Mean Value Theorem? Explain.

58. Determine where f(x) = (1000 − x) 2 + x 2 is increasing. Use this to decide which is larger: 1000 2 or 998 2 + 2 2.

59. Show that f(x) = 1 − |x| satisfies the conclusion of the MVT on [a, b] if both a and b are positive or negative, but not if a < 0 and b > 0.

60. Which values of c satisfy the conclusion of the MVT on the interval [a, b] if f(x) is a linear function?

61. Show that if f is a quadratic polynomial, then the midpoint c = (a + b)/2 satisfies the conclusion of the MVT on [a, b] for any a and b.

62. Suppose that f(0) = 4 and f ¢ (x) ≤ 2 for x > 0. Apply the MVT to the interval [0, 3] to prove that f(3) ≤ 10. Prove more generally that f(x) ≤ 4 + 2x for all x > 0.

63. Suppose that f(2) = −2 and f ¢ ( x ) ≥ 5. Show that f(4) ≥ 8.

64. Find the minimum value of f(x) = x x for x > 0.

65. Show that the cubic function f(x) = x 3 + ax 2 + bx + c is increasing on (−∞, ∞) if b > a 2 /3.

66. Prove that if f(0) = g(0) and f ' (x) ≤ g ' (x) for x ≥ 0, then f(x) ≤ g(x) for all x ≥ 0.

67. Use Exercise 66 to prove that sin x ≤ x for x ≥ 0.

19. Sketch the graph of f(x) = x 4 and state whether f has any points of inflection. Verify your conclusion by showing that f ² (x) does not change sign.

20. Through her website, Leticia has been selling bean bag chairs with monthly sales as recorded below. In a report to investors, she states, “Sales reached a point of inflection when I started using pay-per-click advertising.” In which month did that occur? Explain.

22. Figure 16 shows the graph of the derivative f ¢ (x) on [0, 1.2]. Locate the points of inflection of f(x) and the points where the local minima and maxima occur. Determine the intervals on which f(x) has the following properties: (a) Increasing (b) Decreasing (c) Concave up (d) Concave down

In Exercises 23–36, find the critical points of f(x) and use the Second Derivative Test (if possible) to determine whether each corresponds to a local minimum or maximum.

23. f (x) = x 3 − 12x 2 + 45x

In Exercises 37–50, find the intervals on which f is concave up or down, the points of inflection, and the critical points, and determine whether each critical point corresponds to a local minimum or maximum (or neither).

37. f (x) = x 3 − 2x 2 + x

51. An infectious flu spreads slowly at the beginning of an epidemic. The infection process accelerates until a majority of the susceptible individuals are infected, at which point the process slows down. (a) If R(t) is the number of individuals infected at time t, describe the concavity of the graph of R near the beginning and end of the epidemic. (b) Write a one-sentence news bulletin describing the status of the epidemic on the day that R(t) has a point of inflection.

52. Water is pumped into a sphere at a constant rate (Figure 17). Let h(t) be the water level at time t. Sketch the graph of h(t) (approximately, but with the correct concavity). Where does the point of inflection occur?

53. Water is pumped into a sphere at a variable rate in such a way that the water level rises at a constant rate c (Figure 17). Let V(t) be the volume of water at time t. Sketch the graph of V(t) (approximately, but with the correct concavity). Where does the point of inflection occur?

1. Find the dimensions of the rectangle of maximum area that can be formed from a 50-in. piece of wire. (a) What is the constraint equation relating the lengths x and y of the sides? (b) Find a formula for the area in terms of x alone. (c) Does this problem require optimization over an open interval or a closed interval? (d) Solve the optimization problem.

2. A 100-in. piece of wire is divided into two pieces and each piece is bent into a square. How should this be done in order to minimize the sum of the areas of the two squares? (a) Express the sum of the areas of the squares in terms of the lengths x and y of the two pieces. (b) What is the constraint equation relating x and y? (c) Does this problem require optimization over an open or closed interval? (d) Solve the optimization problem.

3. Find the positive number x such that the sum of x and its reciprocal is as small as possible. Does this problem require optimization over an open interval or a closed interval?

4. The legs of a right triangle have lengths a and b satisfying a + b = 10. Which values of a and b maximize the area of the triangle?

5. Find positive numbers x, y such that xy = 16 and x + y is as small as possible.

6. A 20-in. piece of wire is bent into an L-shape. Where should the bend be made to minimize the distance between the two ends?

7. Let S be the set of all rectangles with area 100. (a) What are the dimensions of the rectangle in S with the least perimeter? (b) Is there a rectangle in S with the greatest perimeter? Explain.

8. A box has a square base of side x and height y. (a) Find the dimensions x, y for which the volume is 12 and the surface area is as small as possible. (b) Find the dimensions for which the surface area is 20 and the volume is as large as possible.

9. Suppose that 600 ft of fencing are used to enclose a corral in the shape of a rectangle with a semicircle whose diameter is a side of the rectangle as in Figure 10. Find the dimensions of the corral with maximum area.

10. Find the rectangle of maximum area that can be inscribed in a right triangle with legs of length 3 and 4 if the sides of the rectangle are parallel to the legs of the triangle, as in Figure 11.

11. A landscape architect wishes to enclose a rectangular garden on one side by a brick wall costing $30/ft and on the other three sides by a metal fence costing $10/ft. If the area of the garden is 1000 ft 2. find the dimensions of the garden that minimize the cost.

12. Find the point on the line y = x closest to the point (1, 0).

13. Find the point P on the parabola y = x 2 closest to the point (3, 0) (Figure 12).

15. A box is constructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $1/ft 2 and the metal for the sides costs $2/ft 2. Find the dimensions that minimize cost if the box has a volume of 20 ft 3.

16. Find the dimensions of the rectangle of maximum area that can be inscribed in a circle of radius r (Figure 14).

17. Problem of Tartaglia (1500–1557) Among all positive numbers a. b whose sum is 8, find those for which the product of the two numbers and their difference is largest.

18. Find the angle θ that maximizes the area of the isosceles triangle whose legs have length l (Figure 15).

19. The volume of a right circular cone is and its surface area is . Find the dimensions of the cone with surface area 1 and maximal volume (Figure 16).

20. Rice production requires both labor and capital investment in equipment and land. Suppose that if x dollars per acre are invested in labor and y dollars per acre are invested in equipment and land, then the yield P of rice per acre is given by the formula P =100√x + 150√y. If a farmer invests $40/ acre, how should he divide the $40 between labor and capital investment in order to maximize the amount of rice produced?

22. Find the dimensions x and y of the rectangle inscribed in a circle of radius r that maximizes the quantity xy 2.

23. Find the angle θ that maximizes the area of the trapezoid with a base of length 4 and sides of length 2, as in Figure 17.

24. Consider a rectangular industrial warehouse consisting of three separate spaces of equal size as in Figure 18. Assume that the wall materials cost $200 per linear ft and the company allocates $2,400,000 for the project. (a) Which dimensions maximize the total area of the warehouse? (b) What is the area of each compartment in this case?

25. Suppose, in the previous exercise, that the warehouse consists of n separate spaces of equal size. Find a formula in terms of n for the maximum possible area of the warehouse.

26. The amount of light reaching a point at a distance r from a light source A of intensity I A is I A /r 2. Suppose that a second light source B of intensity I B = 4I A is located 10 ft from A. Find the point on the segment joining A and B where the total amount of light is at a minimum.

27. Find the area of the largest rectangle that can be inscribed in the region bounded by the graph of y = (4 − x)/(2+ x) and the coordinate axes (Figure 19).

28. According to postal regulations, a carton is classified as “oversized” if the sum of its height and girth (the perimeter of its base) exceeds 108 in. Find the dimensions of a carton with square base that is not oversized and has maximum volume.

29. Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis, and a tangent line to the graph of y = ( x + 1 ) −2.

30. What is the area of the largest rectangle that can be circumscribed around a rectangle of sides L and H? Hint: Express the area of the circumscribed rectangle in terms of the angle θ (Figure 20).

31. Optimal Price Let r be the monthly rent per unit in an apartment building with 100 units. A survey reveals that all units can be rented when r = $900 and that one unit becomes vacant with each $10 increase in rent. Suppose that the average monthly maintenance per occupied unit is $100 / month. (a) Show that the number of units rented is n = 190 − r/10 for 900 ≤ r ≤ 1900. (b) Find a formula for the net cash intake (revenue minus maintenance) and determine the rent r that maximizes intake.

32. An 8-billion-bushel corn crop brings a price of $2.40/bushel. A commodity broker uses the following rule of thumb: If the crop is reduced by x percent, then the price increases by 10x cents. Which crop size results in maximum revenue and what is the price per bushel?

34. Let P = (a, b) be a point in the first quadrant. (a) Find the slope of the line through P such that the triangle bounded by this line and the axes in the first quadrant has minimal area. (b) Show that P is the midpoint of the hypotenuse of this triangle.

35. A truck gets 10 mpg (miles per gallon) traveling along an interstate highway at 50 mph, and this is reduced by 0.15 mpg for each mile per hour increase above 50 mph. (a) If the truck driver is paid $30 / hour and diesel fuel costs P = $3/gal, which speed v between 50 and 70 mph will minimize the cost of a trip along the highway? Notice that the actual cost depends on the length of the trip but the optimal speed does not. (b) Plot cost as a function of v (choose the length arbitrarily) and verify your answer to part (a). (c) Do you expect the optimal speed v to increase or decrease if fuel costs go down to P = $2/gal? Plot the graphs of cost as a function of v for P = 2 and P = 3 on the same axis and verify your conclusion.

36. Figure 21 shows a rectangular plot of size 100 × 200 feet. Pipe is to be laid from A to a point P on side BC and from there to C. The cost of laying pipe through the lot is $30/ft (since it must be underground) and the cost along the side of the plot is $15/ft. (a) Let f(x) be the total cost, where x is the distance from P to B. Determine f(x), but note that f is continuous at x = 0 (when x = 0, the cost of the entire pipe is $15/ft). (b) What is the most economical way to lay the pipe? What if the cost along the sides is $24/ft?

37. Find the dimensions of a cylinder of volume 1 m 3 of minimal cost if the top and bottom are made of material that costs twice as much as the material for the side.

38. In Example 6 in this section, find the x-coordinate of the point P where the light beam strikes the mirror if h 1 = 10, h 2 = 5, and L = 20.

In Exercises 39–41, a box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out squares of length h from the corners and folding up the sides (Figure 22).

39. Find the value of h that maximizes the volume of the box if A = 15 and B = 24. What are the dimensions of the resulting box?

40. Which value of h maximizes the volume if A = B?

41. Suppose that a box of height h = 3 in. is constructed using 144 in. 2 of cardboard (i. e. AB = 144). Which values A and B maximize the volume?

42. The monthly output P of a light bulb factory is given by the formula P = 350LK, where L is the amount invested in labor and K the amount invested in equipment (in thousands of dollars). If the company needs to produce 10,000 units per month, how should the investment be divided among labor and equipment to minimize the cost of production? The cost of production is L + K.

43. Use calculus to show that among all right triangles with hypotenuse of length 1, the isosceles triangle has maximum area. Can you see more directly why this must be true by reasoning from Figure 23?

44. Janice can swim 3 mph and run 8 mph. She is standing at one bank of a river that is 300 ft wide and wants to reach a point located 200 ft downstream on the other side as quickly as possible. She will swim diagonally across the river and then jog along the river bank. Find the best route for Janice to take.

46. (a) Find the radius and height of a cylindrical can of total surface area A whose volume is as large as possible. (b) Can you design a cylinder with total surface area A and minimal total volume?

47. Find the area of the largest isosceles triangle that can be inscribed in a circle of radius r.

48. A billboard of height b is mounted on the side of a building with its bottom edge at a distance h from the street. At what distance x should an observer stand from the wall to maximize the angle of observation θ (Figure 24)? ( a) Find x using calculus. (b) Solve the problem again using geometry (without any calculation!). There is a unique circle passing through points B and C whichis tangent to the street. Let R be the point of tangency. Show that θ is maximized at the point R. Hint: The two angles labeled ψ are, in fact, equal because they subtend equal arcs on the circle. Let A be the intersection of the circle with PC and show that ψ = θ + PBA > θ. (c) Prove that the two answers in (a) and (b) agree.

49. Use the result of Exercise 48 to show that θ is maximized at the value of x for which the angles Ð QPB and Ð QCP are equal.

52. A poster of area 6 ft 2 has blank margins of width 6 in. on the top and bottom and 4 in. on the sides. Find the dimensions that maximize the printed area.

54. Find the minimum length l of a beam that can clear a fence of height h and touch a wall located b ft behind the fence (Figure 27).

55. Let (a, b) be a fixed point in the first quadrant and let S(d) be the sum of the distances from (d, 0) to the points (0, 0). (a, b). and (a, −b). (a) Find the value of d for which S ( d ) is minimal. The answer depends on whether b < √3a or b ≥√3a. (b) Let a = 1. Plot S(d) for b = 0.5, √3, 3 and describe the position of the minimum.

56. The minimum force required to drive a wedge of angle α into a block (Figure 28) is proportional to

where f is a positive constant. Find the angle α for which the least force is required, assuming f = 0.4.

57. In the setting of Exercise 56, show that for any f the minimal force required is proportional to .

58. The problem is to put a “roof” of side s on an attic room of height h and width b. Find the smallest length s for which this is possible. See Figure 29.

59. Find the maximum length of a pole that can be carried horizontally around a corner joining corridors of widths 8 ft and 4 ft (Figure 30).

60. Redo Exercise 59 for corridors of arbitrary widths a and b.

61. Find the isosceles triangle of smallest area that circumscribes a circle of radius 1 (from Thomas Simpson’s The Doctrine and Application of Fluxions, a calculus text that appeared in 1750). See Figure 31.

In Exercises 1–4, use Newton’s Method with the given function and initial value x 0 to calculate x 1 . x 2 . x 3 .

1. f (x) = x 2 − 2, x 0 = 1

5. Use Figure 6 to choose an initial guess x 0 to the unique real root of x 3 + 2x + 5 = 0. Then compute the first three iterates of Newton’s Method.

6. Use Newton’s Method to find a solution to sin x = cos 2x in the interval [0, π/2] to three decimal places. Then guess the exact solution and compare with your approximation.

7. Use Newton’s Method to find the two solutions of e x = 5x to three decimal places (Figure 7).

8. Use Newton’s Method to approximate the positive solution to the equation ln(x + 4) = x to three decimal places.

In Exercises 9–12, use Newton’s Method to approximate the root to three decimal places and compare with the value obtained from a calculator.

13. Use Newton’s Method to approximate the largest positive root of f(x) = x 4 − 6x 2 + x + 5 to within an error of at most 10 −4. Refer to Figure 5.

14. Sketch the graph of f(x) = x 3 − 4x + 1 and use Newton’s Method to approximate the largest positive root to within an error of at most 10 −3.

15. Use a graphing calculator to choose an initial guess for the unique positive root of x 4 + x 2 − 2x − 1 = 0. Calculate the first three iterates of Newton’s Method.

16. The first positive solution of sin x = 0 is x = π. Use Newton’s Method to calculate π to four decimal places.

69. Show that f(x) = tan 2 x and g(x) = sec 2 x have the same derivative. What can you conclude about the relation between f and g? Verify this conclusion directly.

70. Show, by computing derivatives, that for some constant C. Find C by setting x = 0.

71. A particle located at the origin at t = 0 begins moving along the x-axis with velocity ft/s. Let s(t) be its position at time t. State the differential equation with initial condition satisfied by s(t) and find s(t).

72. Repeat Exercise 71, but replace the initial condition s(0) = 0 with s(2) = 3.

73. A particle moves along the x-axis with velocity v(t) = 25t −t 2 ft/s. Let s(t) be the position at time t. (a) Find s(t), assuming that the particle is located at x = 5 at time t = 0. (b) Find s(t), assuming that the particle is located at x = 5 at time t = 2.

74. A particle located at the origin at t = 0 moves in a straight line with acceleration ft / s. Let v(t) be the velocity and s(t) the position at time t. (a) State and solve the differential equation for v( t ) assuming that the particle is at rest at t = 0. (b) Find s(t).

75. A car traveling 84 ft/s begins to decelerate at a constant rate of 14 ft/s 2. After how many seconds does the car come to a stop and how far will the car have traveled before stopping?

76. Beginning at rest, an object moves in a straight line with constant acceleration a, covering 100 ft in 5 s. Find a.

77. A 900-kg rocket is released from a spacecraft. As the rocket burns fuel, its mass decreases and its velocity increases. Let v( m ) be the velocity (in meters per second) as a function of mass m. Find the velocity when m = 500 if dv/dm = −50m −1/2. Assume that v(900) = 0.

78. As water flows through a tube of radius R = 10 cm, the velocity of an individual water particle depends on its distance r from the center of the tube according to the formula dv/dr = −0.06r. Determine v(r), assuming that particles at the walls of the tube have zero velocity.

79. Find constants c 1 and c 2 such that F(x) = c 1 x sin x + c 2 cos x is an antiderivative of f(x) = x cos x.

80. Find the general antiderivative of (2x + 9) 10.

1. An athlete runs with velocity 4 mph for half an hour, 6 mph for the next hour, and 5 mph for another half-hour. Compute the total distance traveled and indicate on a graph how this quantity can be interpreted as an area.

2. Figure 14 shows the velocity of an object over a 3-min interval. Determine the distance traveled over the intervals [0, 3] and [1, 2.5] (remember to convert from miles per hour to miles per minute).

3. A rainstorm hit Portland, Maine, in October 1996, resulting in record rainfall. The rainfall rate R ( t ) on October 21 is recorded, in inches per hour, in the following table, where t is the number of hours since midnight. Compute the total rainfall during this 24-hour period and indicate on a graph how this quantity can be interpreted as an area.

4. The velocity of an object is v( t ) = 32 t ft / s. Use Eq. (2) and geometry to find the distance traveled over the time intervals [ 0 , 2 ] and [ 2 , 5 ].

5. Compute R 6 . L 6 . and M 3 to estimate the distance traveled over [ 0 , 3 ] if the velocity at half-second intervals is as follows:

6. Use the following table of values to estimate the area under the graph of f ( x ) over [ 0 , 1 ] by computing the average of R 5 and L 5 .

7. Consider f ( x ) = 2 x + 3 on [ 0 , 3 ]. (a) Compute R 6 and L 6 over [ 0 , 3 ]. (b) Find the error in these approximations by computing the area exactly using geometry.

1. An airplane makes the 350-mile trip from Los Angeles to San Francisco in 1 hour. Assuming that the plane’s velocity at time t is v( t ) mph, what is the value of the integral .

2. A hot metal object is submerged in cold water. The rate at which the object cools (in degrees per minute) is a function f ( t ) of time. Which quantity is represented by the integral .

3. Which of the following quantities would be naturally represented as derivatives and which as integrals? (a) Velocity of a train (b) Rainfall during a 6-month period (c) Mileage per gallon of an automobile (d) Increase in the population of Los Angeles from 1970 to 1990

4. Two airplanes take off at t = 0 from the same place and in the same direction. Their velocities are v 1 ( t ) and v 2 ( t ) . respectivamente. What is the physical interpretation of the area between the graphs of v 1 ( t ) and v 2 ( t ) over an interval [ 0 , T ].

1. Water flows into an empty reservoir at a rate of 3 , 000 + 5 t gal / hour. What is the quantity of water in the reservoir after 5 hours?

2. Find the displacement of a particle moving in a straight line with velocity v( t ) = 4 t − 3 ft / s over the time interval [ 2 , 5 ].

3. A population of insects increases at a rate of 200 + 10 t + 0 . 25 t 2 insects per day. Find the insect population after 3 days, assuming that there are 35 insects at t = 0.

4. A survey shows that a mayoral candidate is gaining votes at a rate of 2 , 000 t + 1 , 000 votes per day, where t is the number of days since she announced her candidacy. How many supporters will the candidate have after 60 days, assuming that she had no supporters at t = 0?

5. A factory produces bicycles at a rate of 95 + 0 . 1 t 2 − t bicycles per week ( t in weeks). How many bicycles were produced from day 8 to 21?

6. Find the displacement over the time interval [ 1 , 6 ] of a helicopter whose (vertical) velocity at time t is v( t ) = 0 . 02 t 2 + t ft / s.

7. A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall between t = 0 . 5 and t = 1 s? Use Galileo’s formula v( t ) = − 32 t ft / s.

8. A projectile is released with initial (vertical) velocity 100 m / s. Use the formula v( t ) = 100 − 9. 8 t for velocity to determine the distance traveled during the first 15 s.

In Exercises 9–12, assume that a particle moves in a straight line with given velocity. Find the total displacement and total distance traveled over the time interval, and draw a motion diagram like Figure 3 (with distance and time labels).

13. The rate (in liters per minute) at which water drains from a tank is recorded at half-minute intervals. Use the average of the left - and right-endpoint approximations to estimate the total amount of water drained during the first 3 min.

14. The velocity of a car is recorded at half-second intervals (in feet per second). Use the average of the left - and right-endpoint approximations to estimate the total distance traveled during the first 4 s.

15. Let a ( t ) be the acceleration of an object in linear motion at time t . Explain why is the net change in velocity over [ t 1 , t 2 ]. Find the net change in velocity over [ 1 , 6 ] if a ( t ) = 24 t − 3 t 2 ft / s 2.

16. Show that if acceleration a is constant, then the change in velocity is proportional to the length of the time interval.

17. The traffic flow rate past a certain point on a highway is q ( t ) = 3 , 000 + 2 , 000 t − 300 t 2. where t is in hours and t = 0 is 8 AM. How many cars pass by during the time interval from 8 to 10 AM?

18. Suppose that the marginal cost of producing x video recorders is 0 . 001 x 2 − 0 . 6 x + 350 dollars. What is the cost of producing 300 units if the setup cost is $20,000 (see Example 4)? If production is set at 300 units, what is the cost of producing 20 additional units?

19. Carbon Tax To encourage manufacturers to reduce pollution, a carbon tax on each ton of CO 2 released into the atmosphere has been proposed. To model the effects of such a tax, policymakers study the marginal cost of abatement B ( x ) . defined as the cost of increasing CO 2 reduction from x to x + 1 tons (in units of ten thousand tons—Figure 4). Which quantity is represented by .

20. Power is the rate of energy consumption per unit time. A megawatt of power is 10 6 W or 3 . 6 × 10 9 J / hour. Figure 5 shows the power supplied by the California power grid over a typical 1-day period. Which quantity is represented by the area under the graph?

21. Figure 6 shows the migration rate M ( t ) of Ireland during the period 1988–1998. This is the rate at which people (in thousands per year) move in or out of the country.

(a) What does represent? (b) Did migration over the 11-year period 1988–1998 result in a net influx or outflow of people from Ireland? Base your answer on a rough estimate of the positive and negative areas involved. (c) During which year could the Irish prime minister announce, “We are still losing population but we’ve hit an inflection point—the trend is now improving.”

22. Figure 7 shows the graph of Q ( t ) . the rate of retail truck sales in the United States (in thousands sold per year). (a) What does the area under the graph over the interval [ 1995 , 1997 ] represent? (b) Express the total number of trucks sold in the period 1994–1997 as an integral (but do not compute it). (c) Use the following data to compute the average of the right - and left-endpoint approximations as an estimate for the total number of trucks sold during the 2-year period 1995–1996.

23. Heat Capacity The heat capacity C ( T ) of a substance is the amount of energy (in joules) required to raise the temperature of 1 g by 1 ◦ C at temperature T . (a) Explain why the energy required to raise the temperature from T 1 to T 2 is the area under the graph of C ( T ) over [ T 1 , T 2 ].

(b) How much energy is required to raise the temperature from 50 to 100 ◦ C if C ( T ) = 6 + 0 . 2 √ T .

In Exercises 24 and 25, consider the following. Paleobiologists have studied the extinction of marine animal families during the phanerozoic period, which began 544 million years ago. A recent study suggests that the extinction rate r ( t ) may be modeled by the function r ( t ) = 3 , 130 /( t + 262 ) for 0 ≤ t ≤ 544 . Here, t is time elapsed (in millions of years) since the beginning of the phanerozoic period. Thus, t = 544 refers to the present time, t = 540 is 4 million years ago, etc.

24. Use R N or L N with N = 10 (or their average) to estimate the total number of families that became extinct in the periods 100 ≤ t ≤ 150 and 350 ≤ t ≤ 400.

25. Estimate the total number of extinct families from t = 0 to the present, using M N with N = 544.

26. Cardiac output is the rate R of volume of blood pumped by the heart per unit time (in liters per minute). Doctors measure R by injecting A mg of dye into a vein leading into the heart at t = 0 and recording the concentration c ( t ) of dye (in milligrams per liter) pumped out at short regular time intervals (Figure 8).

(a) The quantity of dye pumped out in a small time interval [ t , t + Δ t ] is approximately Rc ( t ) Δ t . Explicar por qué.

(b) Show that . where T is large enough that all of the dye is pumped through the heart but not so large that the dye returns by recirculation. (c) Use the following data to estimate R . assuming that A = 5 mg:

27. A particle located at the origin at t = 0 moves along the x - axis with velocity v( t ) = ( t + 1 ) − 2. Show that the particle will never pass the point x = 1.

2 8. A particle located at the origin at t = 0 moves along the x - axis with velocity v(t) = ( t + 1 ) −1 / 2. Will the particle be at the point x = 1 at any time t . If so, find t .

1. Two quantities increase exponentially with growth constants k = 1 . 2 and k = 3 . 4, respectively. Which quantity doubles more rapidly?

2. If you are given both the doubling time and the growth constant of a quantity that increases exponentially, can you determine the initial amount?

3. A cell population grows exponentially beginning with one cell. Does it take less time for the population to increase from one to two cells than from 10 million to 20 million cells?

4. Referring to his popular book A Brief History of Time . the renowned physicist Stephen Hawking said, “Someone told me that each equation I included in the book would halve its sales.” If this is so, write a differential equation satisfied by the sales function S ( n ) . where n is the number of equations in the book.

5. Carbon dating is based on the assumption that the ratio R of C 14 to C 12 in the atmosphere has been constant over the past 50,000 years. If R were actually smaller in the past than it is today, would the age estimates produced by carbon dating be too ancient or too recent?

6. Which is preferable: an interest rate of 12% compounded quarterly, or an interest rate of 11% compounded continuously?

7. Find the yearly multiplier if r = 9% and interest is compounded (a) continuously and (b) quarterly.

8. The PV of N dollars received at time T is (choose the correct answer): (a) The value at time T of N dollars invested today (b) The amount you would have to invest today in order to receive N dollars at time T

9. A year from now, $1 will be received. Will its PV increase or decrease if the interest rate goes up?

10. Xavier expects to receive a check for $1,000 1 year from today. Explain, using the concept of PV, whether he will be happy or sad to learn that the interest rate has just increased from 6% to 7%.

1. A certain bacteria population P obeys the exponential growth law P ( t ) = 2 , 000 e 1 . 3 t ( t in hours). (a) How many bacteria are present initially? (b) At what time will there be 10,000 bacteria?

2. A quantity P obeys the exponential growth law P ( t ) = e 5 t ( t in years). (a) At what time t is P = 10? (b) At what time t is P = 20? (c) What is the doubling time for P .

3. A certain RNA molecule replicates every 3 minutes. Find the differential equation for the number N ( t ) of molecules present at time t (in minutes). Starting with one molecule, how many will be present after 10 min?

4. A quantity P obeys the exponential growth law P ( t ) = Ce kt ( t in years). Find the formula for P ( t ) . assuming that the doubling time is 7 years and P ( 0 ) = 100.

5. The decay constant of Cobalt-60 is 0 . 13 years − 1. What is its halflife?

6. Find the decay constant of Radium-226, given that its half-life is 1,622 years.

7. Find all solutions to the differential equation y ' = − 5 y . Which solution satisfies the initial condition y ( 0 ) = 3 . 4?

8. Find the solution to y ' = √ 2 y satisfying y ( 0 ) = 20.

9. Find the solution to y ' = 3 y satisfying y ( 2 ) = 4.

10. Find the function y = f ( t ) that satisfies the differential equation y ' = − 0 . 7 y and initial condition y ( 0 ) = 10.

11. The population of a city is P ( t ) = 2 · e 0 . 06 t (in millions), where t is measured in years. (a) Calculate the doubling time of the population. (b) How long does it take for the population to triple in size? (c) How long does it take for the population to quadruple in size?

12. The population of Washington state increased from 4 . 86 million in 1990 to 5 . 89 million in 2000. Assuming exponential growth, (a) What will the population be in 2010? (b) What is the doubling time?

13. Assuming that population growth is approximately exponential, which of the two sets of data is most likely to represent the population (in millions) of a city over a 5-year period?

14. Light Intensity The intensity of light passing through an absorbing medium decreases exponentially with the distance traveled. Suppose the decay constant for a certain plastic block is k = 2 when the distance is measured in feet. How thick must the block be to reduce the intensity by a factor of one-third?

15. The Beer–Lambert Law is used in spectroscopy to determine the molar absorptivity α or the concentration c of a compound dissolved in a solution at low concentrations (Figure 12). The law states that the intensity I of light as it passes through the solution satisfies ln ( I / I 0 ) = α cx . where I 0 is the initial intensity and x is the distance traveled by the light. Show that I satisfies a differential equation dI / dx = − kx for some constant k .

16. An insect population triples in size after 5 months. Assuming exponential growth, when will it quadruple in size?

17. A 10-kg quantity of a radioactive isotope decays to 3 kg after 17 years. Find the decay constant of the isotope.

18. Measurements showed that a sample of sheepskin parchment discovered by archaeologists had a C 14 to C 12 ratio equal to 40% of that found in the atmosphere. Approximately how old is the parchment?

20. A paleontologist has discovered the remains of animals that appear to have died at the onset of the Holocene ice age. She applies carbon dating to test her theory that the Holocene age started between 10,000 and 12,000 years ago. What range of C 14 to C 12 ratio would she expect to find in the animal remains?

21. Atmospheric Pressure The atmospheric pressure P ( h ) (in pounds per square inch) at a height h (in miles) above sea level on earth satisfies a differential equation P ' = − kP for some positive constant k .

(a) Measurements with a barometer show that P ( 0 ) = 14 . 7 and P ( 10 ) = 2 . 13. What is the decay constant k ? (b) Determine the atmospheric pressure 15 miles above sea level.

22. Inversion of Sugar When cane sugar is dissolved in water, it converts to invert sugar over a period of several hours. The percentage f ( t ) of unconverted cane sugar at time t decreases exponentially. Suppose that f ' = − 0 . 2 f . What percentage of cane sugar remains after 5 hours? After 10 hours?

23. A quantity P increases exponentially with doubling time 6 hours. After how many hours has P increased by 50%?

24. Two bacteria colonies are cultivated in a laboratory. The first colony has a doubling time of 2 hours and the second a doubling time of 3 hours. Initially, the first colony contains 1,000 bacteria and the second colony 3,000 bacteria. At what time t will sizes of the colonies be equal?

25. Moore’s Law In 1965, Gordon Moore predicted that the number N of transistors on a microchip would increase exponentially. (a) Does the table of data below confirm Moore’s prediction for the period from 1971 to 2000? If so, estimate the growth constant k . (b) Plot the data in the table. (c) Let N ( t ) be the number of transistors t years after 1971. Find an approximate formula N ( t ) ≈ Ce kt . where t is the number of years after 1971. (d) Estimate the doubling time in Moore’s Law for the period from 1971 to 2000. (e) If Moore’s Law continues to hold until the end of the decade, how many transistors will a chip contain in 2010? (f) Can Moore have expected his prediction to hold indefinitely?

26. Assume that in a certain country, the rate at which jobs are created is proportional to the number of people who already have jobs. If there are 15 million jobs at t = 0 and 15.1 million jobs 3 months later, how many jobs will there be after two years?

28. To model mortality in a population of 200 laboratory rats, a scientist assumes that the number P ( t ) of rats alive at time t (in months) satisfies the Gompertz equation with M = 204 and k = 0 . 15 months − 1 (Figure 13). Find P ( t ) [note that P ( 0 ) = 200] and determine the population after 20 months.

29. A certain quantity increases quadratically: P ( t ) = P 0 t 2. (a) Starting at time t 0 = 1, how long will it take for P to double in size? How long will it take starting at t 0 = 2 or 3? (b) In general, starting at time t 0 . how long will it take for P to double in size?

30. Verify that the half-life of a quantity that decays exponentially with decay constant k is equal to ln 2 / k .

31. Compute the balance after 10 years if $2,000 is deposited in an account paying 9% interest and interest is compounded (a) quarterly, (b) monthly, and (c) continuously.

32. Suppose $500 is deposited into an account paying interest at a rate of 7%, continuously compounded. Find a formula for the value of the account at time t . What is the value of the account after 3 years?

33. A bank pays interest at a rate of 5%. What is the yearly multiplier if interest is compounded (a) yearly? (b) three times a year? (c) continuously?

34. How long will it take for $4,000 to double in value if it is deposited in an account bearing 7% interest, continuously compounded?

35. Show that if interest is compounded continuously at a rate r . then an account doubles after ( ln 2 )/ r years.

36. How much must be invested today in order to receive $20,000 after 5 years if interest is compounded continuously at the rate r = 9%?

37. An investment increases in value at a continuously compounded rate of 9%. How large must the initial investment be in order to build up a value of $50,000 over a seven-year period?

38. Compute the PV of $5,000 received in 3 years if the interest rate is (a) 6% and (b) 11%. What is the PV in these two cases if the sum is instead received in 5 years?

39. Is it better to receive $1,000 today or $1,300 in 4 years? Consider r = 0 . 08 and r = 0 . 03.

40. Find the interest rate r if the PV of $8,000 to be received in 1 year is $7,300.

41. If a company invests $2 million to upgrade its factory, it will earn additional profits of $500 , 000 / year for 5 years. Is the investment worthwhile, assuming an interest rate of 6% (assume that the savings are received as a lump sum at the end of each year)?

42. A new computer system costing $25,000 will reduce labor costs by $7 , 000 / year for 5 years. (a) Is it a good investment if r = 8%? (b) How much money will the company actually save?

43. After winning $25 million in the state lottery, Jessica learns that she will receive five yearly payments of $5 million beginning immediately. (a) What is the PV of Jessica’s prize if r = 6%? (b) How much more would the prize be worth if the entire amount were paid today?

44. An investment group purchased an office building in 1998 for $17 million and sold it 5 years later for $26 million. Calculate the annual (continuously compounded) rate of return on this investment.

45. Use Eq. (3) to compute the PV of an income stream paying out R ( t ) = $5 , 000 / year continuously for 10 years and r = 0 . 05.

46. Compute the PV of an income stream if income is paid out continuously at a rate R ( t ) = $5 , 000 e 0 . 1 t / year for 5 years and r = 0 . 05.

47. Find the PV of an investment that produces income continuously at a rate of $800 / year for 5 years, assuming an interest rate of r = 0 . 08.

48. The rate of yearly income generated by a commercial property is $50 , 000 / year at t = 0 and increases at a continuously compounded rate of 5%. Find the PV of the income generated in the first four years if r = 8%.

49. Show that the PV of an investment that pays out R dollars / year continuously for T years is R ( 1 − e − rT )/ r . where r is the interest rate.

50. Explain this statement: If T is very large, then the PV of the income stream described in Exercise 49 is approximately R / r .

51. Suppose that r = 0 . 06. Use the result of Exercise 50 to estimate the payout rate R needed to produce an income stream whose PV is $20,000, assuming that the stream continues for a large number of years.

53. Use Eq. (6) to compute the PV of an investment that pays out income continuously at a rate R ( t ) = ( 5 , 000 + 1 , 000 t ) e 0 . 02 t dollars / year for 10 years and r = 0 . 08.

54. Banker’s Rule of 70 Bankers have a rule of thumb that if you receive R percent interest, continuously compounded, then your money doubles after approximately 70 / R years. For example, at R = 5%, your money doubles after 70 / 5 or 14 years. Use the concept of doubling time to justify the Banker’s Rule.

55. Isotopes for Dating Which of the following isotopes would be most suitable for dating extremely old rocks: Carbon-14 (half-life 5,570 years), Lead-210 (half-life 22.26 years), and Potassium-49 (half-life 1.3 billion years)? Explicar por qué.

56. Let P = P ( t ) be a quantity that obeys an exponential growth law with growth constant k . Show that P increases m - fold after an interval of ( ln m )/ k years.

57. Average Time of Decay Physicists use the radioactive decay law R = R 0 e − kt to compute the average or mean time M until an atom decays. Let F ( t ) = R / R 0 = e − kt be the fraction of atoms that have survived to time t without decaying. (a) Find the inverse function t ( F ) . (b) The error in the following approximation tends to zero as N →∞.

39. On a typical day, a city consumes water at the rate of r ( t ) = 100 + 72 t − 3 t 2 (in thousands of gallons per hour), where t is the number of hours past midnight. What is the daily water consumption? How much water is consumed between 6 PM and midnight?

40. The learning curve for producing bicycles in a certain factory is L ( x ) = 12 x − 1 / 5 (in hours per bicycle), which means that it takes a bike mechanic L ( n ) hours to assemble the n th bicycle. If 24 bicycles are produced, how long does it take to produce the second batch of 12?

41. Cost engineers at NASA have the task of projecting the cost P of major space projects. It has been found that the cost C of developing a projection increases with P at the rate dC / dP ≈ 21 P − 0 . 65. where C is in thousands of dollars and P in millions of dollars. What is the cost of developing a projection for a project whose cost turns out to be P = $35 million?

42. The cost of jet fuel increased dramatically in 2005. Figure 6 displays Department of Transportation estimates for the rate of percentage price increase R ( t ) (in units of percentage per year) during the first 6 months of the year. Express the total percentage price increase I during the first 6 months as an integral and calculate I . When determining the limits of integration, keep in mind that t is in years since R ( t ) is a yearly rate.

1. Find the area of the region between y = 3 x 2 + 12 and y = 4 x + 4 over [− 3 , 3 ] (Figure 8).

2. Compute the area of the region in Figure 9(A), which lies between y = 2 − x 2 and y = − 2 over [− 2 , 2 ].

3. Let f ( x ) = x and g ( x ) = 2 − x 2 [Figure 9(B)]. (a) Find the points of intersection of the graphs. (b) Find the area enclosed by the graphs of f and g .

4. Let f ( x ) = 8 x − 10 and g ( x ) = x 2 − 4 x + 10. (a) Find the points of intersection of the graphs. (b) Compute the area of the region below the graph of f and above the graph of g .

19. Find the area of the region enclosed by the curves y = x 3 − 6 x and y = 8 − 3 x 2.

20. Find the area of the region enclosed by the semicubical parabola y 2 = x 3 and the line x = 1.

23. Find the area of the region lying to the right of x = y 2 + 4 y − 22 and the left of x = 3 y + 8.

24. Find the area of the region lying to the right of x = y 2 − 5 and the left of x = 3 − y 2.

25. Calculate the area enclosed by x = 9 − y 2 and x = 5 in two ways: as an integral along the y - axis and as an integral along the x - axis.

26. Figure 15 shows the graphs of x = y 3 − 26 y + 10 and x = 40 − 6 y 2 − y 3. Match the equations with the curve and compute the area of the shaded region.

50. Find the area enclosed by the curves y = c − x 2 and y = x 2 − c as a function of c . Find the value of c for which this area is equal to 1.

57. Find the line y = mx that divides the area under the curve y = x ( 1 − x ) over [ 0 , 1 ] into two regions of equal area.

58. Let c be the number such that the area under y = sin x over [ 0 , π ] is divided in half by the line y = cx (Figure 18). Find an equation for c and solve this equation numerically using a computer algebra system.

1. What is the average value of f ( x ) on [ 1 , 4 ] if the area between the graph of f ( x ) and the x - axis is equal to 9?

2. Find the volume of a solid extending from y = 2 to y = 5 if the cross section at y has area A ( y ) = 5 for all y .

1. Let V be the volume of a pyramid of height 20 whose base is a square of side 8. (a) Use similar triangles as in Example 1 to find the area of the horizontal cross section at a height y . (b) Calculate V by integrating the cross-sectional area.

2. Let V be the volume of a right circular cone of height 10 whose base is a circle of radius 4 (Figure 16). (a) Use similar triangles to find the area of a horizontal cross section at a height y . (b) Calculate V by integrating the cross-sectional area.

3. Use the method of Exercise 2 to find the formula for the volume of a right circular cone of height h whose base is a circle of radius r (Figure 16).

4. Calculate the volume of the ramp in Figure 17 in three ways by integrating the area of the cross sections: (a) Perpendicular to the x - axis (rectangles) (b) Perpendicular to the y - axis (triangles) (c) Perpendicular to the z - axis (rectangles)

5. Find the volume of liquid needed to fill a sphere of radius R to height h (Figure 18).

6. Find the volume of the wedge in Figure 19(A) by integrating the area of vertical cross sections.

7. Derive a formula for the volume of the wedge in Figure 19(B) in terms of the constants a . b . and c .

8. Let B be the solid whose base is the unit circle x 2 + y 2 = 1 and whose vertical cross sections perpendicular to the x - axis are equilateral triangles. Show that the vertical cross sections have area and compute the volume of B .

In Exercises 9–14, find the volume of the solid with given base and cross sections.

9. The base is the unit circle x 2 + y 2 = 1 and the cross sections perpendicular to the x - axis are triangles whose height and base are equal.

10. The base is the triangle enclosed by x + y = 1, the x - axis, and the y - axis. The cross sections perpendicular to the y - axis are semicircles.

11. The base is the semicircle . where − 3 ≤ x ≤ 3. The cross sections perpendicular to the x - axis are squares.

12. The base is a square, one of whose sides is the interval [ 0,l ] along the x - axis. The cross sections perpendicular to the x - axis are rectangles of height f ( x ) = x 2.

13. The base is the region enclosed by y = x 2 and y = 3. The cross sections perpendicular to the y - axis are squares.

14. The base is the region enclosed by y = x 2 and y = 3. The cross sections perpendicular to the y - axis are rectangles of height y 3.

15. Find the volume of the solid whose base is the region | x | +| y | ≤ 1 and whose vertical cross sections perpendicular to the y - axis are semicircles (with diameter along the base).

16. Show that the volume of a pyramid of height h whose base is an equilateral triangle of side s is equal to .

17. Find the volume V of a regular tetrahedron whose face is an equilateral triangle of side s (Figure 20).

18. The area of an ellipse is π ab, where a and b are the lengths of the semimajor and semiminor axes (Figure 21). Compute the volume of a cone of height 12 whose base is an ellipse with semimajor axis a = 6 and semiminor axis b = 4.

20. A plane inclined at an angle of 45◦ passes through a diameter of the base of a cylinder of radius r. Find the volume of the region within the cylinder and below the plane (Figure 23).

21. Figure 24 shows the solid S obtained by intersecting two cylinders of radius r whose axes are perpendicular. (a) The horizontal cross section of each cylinder at distance y from the central axis is a rectangular strip. Find the strip’s width. (b) Find the area of the horizontal cross section of S at distance y. (c) Find the volume of S as a function of r.

2 2. Let S be the solid obtained by intersecting two cylinders of radius r whose axes intersect at an angle θ. Find the volume of S as a function of r and θ.

23. Calculate the volume of a cylinder inclined at an angle θ = 30◦ whose height is 10 and whose base is a circle of radius 4 (Figure 25).

24. Find the total mass of a 1-m rod whose linear density function is ρ(x) = 10(x + 1) −2 kg/m for 0 ≤ x ≤ 1.

25. Find the total mass of a 2-m rod whose linear density function is ρ(x) = 1 + 0.5sin(πx) kg/m for 0 ≤ x ≤ 2.

26. A mineral deposit along a strip of length 6 cm has density s(x) = 0.01x(6 − x) g/cm for 0 ≤ x ≤ 6. Calculate the total mass of the deposit.

27. Calculate the population within a 10-mile radius of the city center if the radial population density is ρ(r) = 4(1 + r 2 ) 1/3 (in thousands per square mile).

28. Odzala National Park in the Congo has a high density of gorillas. Suppose that the radial population density is ρ(r) = 52(1 + r 2 ) −2 gorillas per square kilometer, where r is the distance from a large grassy clearing with a source of food and water. Calculate the number of gorillas within a 5-km radius of the clearing.

9. Table 1 lists the population density (in people per squared kilometer) as a function of distance r (in kilometers) from the center of a rural town. Estimate the total population within a 2-km radius of the center by taking the average of the left - and right-endpoint approximations.

10. Find the total mass of a circular plate of radius 20 cm whose mass density is the radial function ρ(r) = 0.03 + 0.01cos (πr 2 ) g/cm 2.

31. The density of deer in a forest is the radial function ρ(r) = 150(r 2 + 2) −2 deer per km 2. where r is the distance (in kilometers) to a small meadow. Calculate the number of deer in the region 2 ≤ r ≤ 5 km.

32. Show that a circular plate of radius 2 cm with radial mass density ρ(r) = 4/r g/cm has finite total mass, even though the density becomes infinite at the origin.

33. Find the flow rate through a tube of radius 4 cm, assuming that the velocity of fluid particles at a distance r cm from the center is v(r) = 16 − r 2 cm/s.

34. Let v(r) be the velocity of blood in an arterial capillary of radius R = 4 × 10 −5 m. Use Poiseuille’s Law (Example 6) with k = 10 6 (m-s) −1 to determine the velocity at the center of the capillary and the flow rate (use correct units).

35. A solid rod of radius 1cm is placed in a pipe of radius 3cm so that their axes are aligned. Water flows through the pipe and around the rod. Find the flow rate if the velocity of the water is given by the radial function v(r) = 0.5(r − 1)(3 − r) cm/s.

36. To estimate the volume V of Lake Nogebow, the Minnesota Bureau of Fisheries created the depth contour map in Figure 26 and determined the area of the cross section of the lake at the depths recorded in the table below. EstimateV by taking the average of the right - and left-endpoint approximations to the integral of cross-sectional area.

53. The temperature T(t) at time t (in hours) in an art museum varies according to T(t) = 70 + 5cos(πt/12). Find the average over the time periods [0, 24] and [2, 6].

54. A ball is thrown in the air vertically from ground level with initial velocity 64 ft/s. Find the average height of the ball over the time interval extending from the time of the ball’s release to its return to ground level. Recall that the height at time t is h(t) = 64t − 16t 2.

5. What is the average area of the circles whose radii vary from 0 to 1?

6. An object with zero initial velocity accelerates at a constant rate of 10 m/s 2. Find its average velocity during the first 15 s.

57. The acceleration of a particle is a(t) = t − t 3 m/s 2 for 0 ≤ t ≤ 1. Compute the average acceleration and average velocity over the time interval [0, 1], assuming that the particle’s initial velocity is zero.

58. Let M be the average value of f(x) = x 4 on [0, 3]. Find a value of c in [0, 3] such that f(c) = M.

29. Use both the Shell and Disk Methods to calculate the volume of the solid obtained by rotating the region under the graph of f(x) = 8 − x 3 for 0 ≤ x ≤ 2 about: (a) the x-axis (b) the y-axis

46. Use the Shell Method to calculate the volume V of the “bead” formed by removing a cylinder of radius r from the center of a sphere of radius R (compare with Exercise 51 in Section 6.3).

50. The surface area of a sphere of radius r is 4πr 2. Use this to derive the formula for the volume V of a sphere of radius R in a new way. (a) Show that the volume of a thin spherical shell of inner radius r and thickness D x is approximately 4πr 2 D x. (b) Approximate V by decomposing the sphere of radius R into N thin spherical shells of thickness D x = R/N. (c) Show that the approximation is a Riemann sum which converges to an integral. Evaluate the integral.

1. How much work is done raising a 4-kg mass to a height of 16 m above ground?

2. How much work is done raising a 4-lb mass to a height of 16 ft above ground?

In Exercises 3–6, compute the work (in joules) required to stretch or compress a spring as indicated, assuming that the spring constant is k = 150 kg/s 2.

3. Stretching from equilibrium to 12 cm past equilibrium

4. Compressing from equilibrium to 4 cm past equilibrium

5. Stretching from 5 to 15 cm past equilibrium

6. Compressing the spring 4 more cm when it is already compressed 5 cm

7. If 5 J of work are needed to stretch a spring 10 cm beyond equilibrium, how much work is required to stretch it 15 cm beyond equilibrium?

8. If 5 J of work are needed to stretch a spring 10 cm beyond equilibrium, how much work is required to compress it 5 cm beyond equilibrium?

9. If 10 ft-lb of work are needed to stretch a spring 1 ft beyond equilibrium, how far will the spring stretch if a 10-lb weight is attached to its end?

10. Show that the work required to stretch a spring from position a to position b is . where k is the spring constant. How do you interpret the negative work obtained when |b| < |a|?

In Exercises 11–14, calculate the work against gravity required to build the structure out of brick using the method of Examples 2 and 3. Assume that brick has density 80 lb/ft 3.

11. A tower of height 20 ft and square base of side 10 ft

12. A cylindrical tower of height 20 ft and radius 10 ft

13. A 20-ft-high tower in the shape of a right circular cone with base of radius 4 ft

14. A structure in the shape of a hemisphere of radius 4 ft

15. Built around 2600 BCE, the Great Pyramid of Giza in Egypt is 485 ft high (due to erosion, its current height is slightly less) and has a square base of side 755.5 ft (Figure 6). Find the work needed to build the pyramid if the density of the stone is estimated at 125 lb/ft 3.

In Exercises 16–20, calculate the work (in joules) required to pump all of the water out of the tank. Assume that the tank is full, distances are measured in meters, and the density of water is 1000 kg/m 3.

16. The box in Figure 7; water exits from a small hole at the top.

17. The hemisphere in Figure 8; water exits from the spout as shown.

18. The conical tank in Figure 9; water exits through the spout as shown.

19. The horizontal cylinder in Figure 10; water exits from a small hole at the top.

20. The trough in Figure 11; water exits by pouring over the sides.

21. Find the work W required to empty the tank in Figure 7 if it is half full of water.

22. Assume the tank in Figure 7 is full of water and let W be the work required to pump out half of the water. Do you expect W to equal the work computed in Exercise 21? Explain and then compute W.

23. Find the work required to empty the tank in Figure 9 if it is half full of water.

24. Assume the tank in Figure 9 is full of water and find the work required to pump out half of the water.

26. How much work is done lifting a 25-ft chain over the side of a building (Figure 12)? Assume that the chain has a density of 4 lb/ft.

27. How much work is done lifting a 3-m chain over the side of a building if the chain has mass density 4 kg/m?

28. An 8-ft chain weighs 16 lb. Find the work required to lift the chain over the side of a building.

29. A 20-ft chain with mass density 3 lb/ft is initially coiled on the ground. How much work is performed in lifting the chain so that it is fully extended (and one end touches the ground)?

30. How much work is done lifting a 20-ft chain with mass density 3 lb/ft (initially coiled on the ground) so that its top end is 30 ft above the ground?

31. A 1,000-lb wrecking ball hangs from a 30-ft cable of density 10 lb/ft attached to a crane. Calculate the work done if the crane lifts the ball from ground level to 30 ft in the air by drawing in the cable.

In Exercises 32–34, use Newton’s Universal Law of Gravity, according to which the gravitational force between two objects of mass m and M separated by a distance r has magnitude GMm/r 2. where G = 6.67 × 10 −11 m 3 kg −1 s −1. Although the Universal Law refers to point masses, Newton proved that it also holds for uniform spherical objects, where r is the distance between their centers.

32. Two spheres of mass M and m are separated by a distance r 1 . Show that the work required to increase the separation to a distance r 2 is equal to .

33. Use the result of Exercise 32 to calculate the work required to place a 2,000-kg satellite in an orbit 1,200 km above the surface of the earth. Assume that the earth is a sphere of mass M e = 5.98 × 10 24 kg and radius r e = 6.37 × 10 6 m. Treat the satellite as a point mass.

34. Use the result of Exercise 32 to compute the work required to move a 1,500-kg satellite from an orbit 1,000 to 1,500 km above the surface of the earth.

35. Assume that the pressure P and volume V of the gas in a 30-in. cylinder of radius 3 in. with a movable piston are related by PV 1.4 = k, where k is a constant (Figure 13). When the cylinder is full, the gas pressure is 200 lb/in. 2. (a) Calculate k. (b) Calculate the force on the piston as a function of the length x of the column of gas (the force is PA, where A is the piston’s area). (c) Calculate the work required to compress the gas column from 30 to 20 in.

36. A 20-ft chain with linear mass density ρ(x) = 0.02x(20 − x) lb/ft lies on the ground. (a) How much work is done lifting the chain so that it is fully extended (and one end touches the ground)? (b) How much work is done lifting the chain so that its top end has a height of 30 ft?

38. A model train of mass 0.5 kg is placed at one end of a straight 3-m electric track. Assume that a force F(x) = 3x − x 2 N acts on the train at distance x along the track. Use the Work-Kinetic Energy Theorem (Exercise 37) to determine the velocity of the train when it reaches the end of the track.

39. With what initial velocity v 0 must we fire a rocket so it attains a maximum height r above the earth? Hint: Use the results of Exercises 32 and 37. As the rocket reaches its maximum height, its KE decreases from to zero.

40. With what initial velocity must we fire a rocket so it attains a maximum height of r = 20 km above the surface of the earth?

54. An airplane’s velocity is recorded at 5-min intervals during a 1-hour period with the following results, in mph: 550, 575, 600, 580, 610, 640, 625, 595, 590, 620, 640, 640, 630 Use Simpson’s Rule to estimate the distance traveled during the hour.

55. Use Simpson’s Rule to determine the average temperature in a museum over a 3-hour period, if the temperatures (in degrees Celsius), recorded at 15-min intervals, are 21, 21.3, 21.5, 21.8, 21.6, 21.2, 20.8, 20.6, 20.9, 21.2, 21.1, 21.3, 21.2.

54. Find the average height of a point on the semicircle for − 1 ≤ x ≤ 1.

55. Find the volume of the solid obtained by revolving the graph of over [0, 1] about the y-axis.

56. Find the volume of the solid obtained by revolving the region between the graph of y 2 − x 2 = 1 and the line y = 2 about the line y = 2.

57. Find the volume of revolution for the region in Exercise 56, but revolve around y = 3.

58. A charged wire creates an electric field at a point P located at a distance D from the wire (Figure 7). The component E ^ of the field perpendicular to the wire (in volts) is

75. An investment pays a dividend of $250/year continuously forever. If the interest rate is 7%, what is the present value of the entire income stream generated by the investment?

76. An investment is expected to earn profits at a rate of 10000e 0.01t dollars/year forever. Find the present value of the income stream if the interest rate is 4%.

77. Compute the present value of an investment that generates income at a rate of 5000te 0.01t dollars/year forever, assuming an interest rate of 6%.

78. Find the volume of the solid obtained by rotating the region below the graph of y = e −x about the x-axis for 0 ≤ x < ∞.

1. Express the arc length of the curve y = x 4 between x = 2 and x = 6 as an integral (but do not evaluate).

In Exercises 5–10, calculate the arc length over the given interval.

1. A box of height 6 ft and square base of side 3 ft is submerged in a pool of water. The top of the box is 2 ft below the surface of the water. (a) Calculate the fluid force on the top and bottom of the box. (b) Write a Riemann sum that approximates the fluid force on a side of the box by dividing the side into N horizontal strips of thickness D y = 6/N. (c) To which integral does the Riemann sum converge? (d) Compute the fluid force on a side of the box.

2. A plate in the shape of an isosceles triangle with base 1 ft and height 2 ft is submerged vertically in a tank of water so that its vertex touches the surface of the water (Figure 7). (a) Show that the width of the triangle at depth y is f(y) = y/2. (b) Consider a thin strip of thickness D y at depth y. Explain why the fluid force on a side of this strip is approximately equal to where w = 62.5 lb/ft 3. (c) Write an approximation for the total fluid force F on a side of the plate as a Riemann sum and indicate the integral to which it converges. (d) Calculate F.

3. Repeat Exercise 2, but assume that the top of the triangle is located 3 ft below the surface of the water.

4. The thin plate R in Figure 8, bounded by the parabola y = x 2 and y = 1, is submerged vertically in water. Let F be the fluid force on one side of R.

(a) Show that the width of R at height y is f(y) = 2√y and the fluid force on a side of a horizontal strip of thickness D y at height y is approximately . (b) Write a Riemann sum that approximates F and use it to explain why . (c) Calculate F.

5. Let F be the fluid force (in Newtons) on a side of a semicircular plate of radius r meters, submerged in water so that its diameter is level with the water’s surface (Figure 9).

(a) Show that the width of the plate at depth y is . (b) Calculate F using Eq. (2).

6. Calculate the force on one side of a circular plate with radius 2 ft, submerged vertically in a tank of water so that the top of the circle is tangent to the water surface.

7. A semicircular plate of radius r, oriented as in Figure 9, is submerged in water so that its diameter is located at a depth of m feet. Calculate the force on one side of the plate in terms of m and r.

8. Figure 10 shows the wall of a dam on a water reservoir. Use the Trapezoidal Rule and the width and depth measurements in the figure to estimate the total force on the wall.

9. Calculate the total force (in Newtons) on a side of the plate in Figure 11(A), submerged in water.

10. Calculate the total force (in Newtons) on a side of the plate in Figure 11(B), submerged in a fluid of mass density ρ = 800 kg/m 3.

11. The plate in Figure 12 is submerged in water with its top level with the surface of the water. The left and right edges of the plate are the curves y = x 1/3 and y = − x 1/3. Find the fluid force on a side of the plate.

12. Let R be the plate in the shape of the region under y = sin x for 0 ≤ x ≤ π/2 in Figure 13(A). Find the fluid force on a side of R if it is rotated counterclockwise by 90◦ and submerged in a fluid of density 140 lb/ft 3 with its top edge level with the surface of the fluid as in (B).

13. In the notation of Exercise 12, calculate the fluid force on a side of the plate R if it is oriented as in Figure 13(A). You may need to use Integration by Parts and trigonometric substitution.

14. Let A be the region under the graph of y = ln x for 1 ≤ x ≤ e (Figure 14). Calculate the fluid force on one side of a plate in the shape of region A if the water surface is at y = 1.

15. Calculate the fluid force on one side of the “infinite” plate B in Figure 14.

16. A square plate of side 3 m is submerged in water at an incline of 30◦ with the horizontal. Its top edge is located at the surface of the water. Calculate the fluid force (in Newtons) on one side of the plate.

17. Repeat Exercise 16, but assume that the top edge of the plate lies at a depth of 6 m.

18. Figure 15(A) shows a ramp inclined at 30◦ leading into a swimming pool. Calculate the fluid force on the ramp.

19. Calculate the fluid force on one side of the plate (an isosceles triangle) shown in Figure 15(B).

20. The trough in Figure 16 is filled with corn syrup, whose density is 90 lb/ft 3. Calculate the force on the front side of the trough.

21. Calculate the fluid pressure on one of the slanted sides of the trough in Figure 16, filled with corn syrup as in Exercise 20.

22. Figure 17 shows an object whose face is an equilateral triangle with 5-ft sides. The object is 2 ft thick and is submerged in water with its vertex 3 ft below the water surface. Calculate the fluid force on both a triangular face and a slanted rectangular edge of the object.

23. The end of the trough in Figure 18 is an equilateral triangle of side 3. Assume that the trough is filled with water to height y. Calculate the fluid force on each side of the trough as a function of the level y and the length l of the trough.

24. A rectangular plate of side l is submerged vertically in a fluid of density w, with its top edge at depth h. Show that if the depth is increased by an amount D h, then the force on a side of the plate increases by wA D h, where A is the area of the plate.

25. Prove that the force on the side of a rectangular plate of area A submerged vertically in a fluid is equal to p 0 A, where p 0 is the fluid pressure at the center point of the rectangle.

26. If the density of a fluid varies with depth, then the pressure at depth y is a function p ( y ) (which need not equal w y as in the case of constant density). Use Riemann sums to argue that the total force F on the flat side of a submerged object submerged vertically is . where f(y) is the width of the side at depth y.

1. Four particles are located at points (1, 1), (1, 2), (4, 0), (3, 1) (a) Find the moments M x and M y and the center of mass of the system, assuming that the particles have equal mass m. (b) Find the center of mass of the system, assuming the particles have mass 3, 2, 5, and 7, respectively.

2. Find the center of mass for the system of particles of mass 4, 2, 5, 1 located at (1, 2), (−3, 2), (2, −1), (4, 0).

3. Point masses of equal size are placed at the vertices of the triangle with coordinates (a, 0), (b, 0), and (0, c). Show that the center of mass of the system of masses has coordinates .

4. Point masses of mass m 1 . m 2 . and m 3 are placed at the points (−1, 0), ( 3, 0), and (0, 4). (a) Suppose that m 1 = 6. Show that there is a unique value of m 2 such that the center of mass lies on the y-axis. (b) Suppose that m 1 = 6 and m 2 = 4. Find the value of m 3 such that y CM = 2.

5. Sketch the lamina S of constant density ρ = 3 g/cm 2 occupying the region beneath the graph of y = x 2 for 0 ≤ x ≤ 3. (a) Use formulas (1) and (2) to compute M x and M y . (b) Find the area and the center of mass of S.

6. Use Eqs. (1) and (3) to find the moments and center of mass of the lamina S of constant density ρ = 2 g/cm 2 occupying the region between y = x 2 and y = 9x over [0, 3]. Sketch S, indicating the location of the center of mass.

7. Find the moments and center of mass of the lamina of uniform density ρ occupying the region underneath y = x 3 for 0 ≤ x ≤ 2.

8. Calculate M x (assuming ρ = 1) for the region underneath the graph of y = 1 − x 2 for 0 ≤ x ≤ 1 in two ways, first using Eq. (2) and then using Eq. (3).

9. Let T be the triangular lamina in Figure 17.

(a) Show that the horizontal cut at height y has length and use Eq. (2) to compute M x (with ρ = 1). (b) Use the Symmetry Principle to show that M y = 0 and find the center of mass.

In Exercises 10–17, find the centroid of the region lying underneath the graph of the function over the given interval.

10. f (x) = 6 − 2x, [0, 3]

18. Calculate the moments and center of mass of the lamina occupying the region between the curves y = x and y = x 2 for 0 ≤ x ≤ 1.

19. Sketch the region between y = x + 4 and y = 2 − x for 0 ≤ x ≤ 2. Using symmetry, explain why the centroid of the region lies on the line y = 3. Verify this by computing the moments and the centroid.

In Exercises 34–36, use the additivity of moments to find the COM of the region.

34. Isosceles triangle of height 2 on top of a rectangle of base 4 and height 3 (Figure 19)

35. An ice cream cone consisting of a semicircle on top of an equilateral triangle of side 6 (Figure 20)

In Exercises 1–14, calculate the Taylor polynomials T 2 (x) and T 3 (x) centered at x = a for the given function and value of a.

1. f (x) = sin x, a = 0

19. Show that the nth Maclaurin polynomial for f(x) = e x is

27. Plot y = e x together with the Maclaurin polynomials T n (x) for n = 1, 3, 5 and then for n = 2, 4, 6 on the interval [−3, 3]. What difference do you notice between the even and odd Maclaurin polynomials?

29. Use the Error Bound to find the maximum possible size of |cos 0.3 − T 5 (0.3)|, where T 5 (x) is the Maclaurin polynomial. Verify your result with a calculator.

32. Let and let T n (x) be the Taylor polynomial centered at a = 8. (a) Find T 3 (x) and calculate T 3 (8.02). (b) Use the Error Bound to find a bound for |T 3 (8.02) − √9.02|.

37. Find n such that |T n (1.3) − ln(1.3)| ≤ 10 −4. where T n is the Taylor polynomial for f(x) = ln x at a = 1.

42. Verify that the third Maclaurin polynomial for f(x) = e x sin x is equal to the product of the third Maclaurin polynomials of e x and sin x (after discarding terms of degree greater than 3 in the product).

43. Find the fourth Maclaurin polynomial for f(x) = sin x cos x by multiplying the fourth Maclaurin polynomials for f(x) = sin x and f(x) = cos x.

44. Find the Maclaurin polynomials T n (x) for f(x) = cos (x 2 ). You may use the fact that T n (x) is equal to the sum of the terms up to degree n obtained by substituting x 2 for x in the nth Maclaurin polynomial of cos x.

45. A cylindrical tank filled with water has height 10 ft and a base of area 30 ft 2. Water leaks through a hole in the bottom of area 1/3 ft 2. How long does it take (a) for half of the water to leak out and (b) for the tank to empty?

46. A conical tank filled with water has height 12 ft [Figure 7(A)]. Assume that the top is a circle of radius 4 ft and that water leaks through a hole in the bottom of area 2 in 2. Let y ( t ) be the water level at time t. (a) Show that the cross-sectional area of the tank at height y is A ( y ) = (π/9)y 2 . (b) Find the differential equation satisfied by y ( t ) and solve for y ( t ). Use the initial condition y(0) = 12. (c) How long does it take for the tank to empty?

47. The tank in Figure 7(B) is a cylinder of radius 10 ft and length 40 ft. Assume that the tank is half-filled with water and that water leaks through a hole in the bottom of area B = 3 in 2. Determine the water level y(t) and the time t e when the tank is empty.

Online homework help for college and high school students. Get homework help and answers to your toughest questions in math, algebra, trigonometry, precalculus, calculus, physics. Homework assignments with step-by-step solutions.

Hunterdon 4-H and rest of Cooperative Extension moving to building on Rt. 12, Raritan Twp.

Hunterdon's Rutgers Cooperative Extension offices are moving from Route 31 to the former youth shelter at the county complex off Route 12 in Raritan Township and officials promised Tuesday night that it will be good move for the program.

4-H is part of Cooperative Extension, which also includes the county agricultural agents, Master Gardeners and Family and Community Health Sciences (once called home economics).

Around two dozen 4-H club leaders, parents of 4-H members and county agricultural leaders attended the Freeholders meeting in Flemington to ask questions about the move.

Dan Mundy, president of the county 4-H Leaders Association, had brought up a number of concerns in a letter to the Freeholders.

Before letting the people in the audience speak, Freeholder Director Matt Holt explained the move, saying advantages of the new location include a patio, garden, lawn area and commercial kitchen. The Extension offices won’t have to share the building, he added.

He said that while former shelter is about 200 square feet smaller than the existing location, the county’s Building 1 with its various rooms, including a large assembly space, is only about 100 yards away and can be used for 4-H meetings, as can meeting rooms in the nearby county library.

The shelter was closed 15 months ago. Children who would have been placed there are now sent to a Morris County shelter. Responding to a concern raised Tuesday about lack of storage space, George Wagner, county director of public safety, said it has a “huge attic” that can be used for that purpose.

There are just over 400 4-H members in Hunterdon in 23 clubs, and 59 project leaders as well as 100 other volunteers.

The move is designed to free up more space for the Social Services department. According to Holt, the county’s public health nursing service will be moved into the former Extension offices, making it more convenient for Human Services clients who have need for the nurses.

Of the new location, “I think you’re going to love the space,” said County Administrator Cindy Yard, noting that she was a three-club 4-H member and “I certainly know the value” of the organization.

Holt, a former 4-H sheep club member, added “it’s going to be a delight.”

Several people had questions about moving office furnishings to the new location. Anna Pinkerton, who works in the 4-H department, asked “can we take out old desks?”

Yard replied that some of the furniture already at Route 12 is modular, and it would be pointless to take it apart so items could be moved from Route 31. But everybody can keep their chairs, she promised. “Generic” furniture might stay at the old location, Holt said.

Some employees had thought that their new offices would be furnished with cast-offs from county surplus. Not to worry.

“We’re not putting people on milk crates,” Yard said, noting that the county has purchased used furniture from a pharmaceutical company and it’s in good shape.

The move is scheduled for the second week of October, said County Architect Frank Bell, who is overseeing the project.

4-H alum Irv Hockenbury of Reaville, a director of the county 4-H and Agricultural Fair, asked how long Extension can plan to stay in the former shelter.

Yard indicated it cold be a long time; the arrangement with Morris to house Hunterdon youths “is working very well,” ella dijo.

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This week our 4-H group had the privilege of serving at Feed My Starving Children. FMSC is a non-profit christian organization that utilizes volunteers to make food packets to send to starving people around the world. They have shifts available where people can sign up for to help make Manna Packs. The Manna Pack consists of Chicken (flavoring with vitamins), Veggies, Soy, and Rice. Each pack holds enough for about 6 meals.

When we got there we signed in and put our hairnets on. We sat down and learned about what we would do and who we were helping. We also got to watch a short video that showed testimonies about people that receive the food and how needed it is.

We washed our hands and then went to pick our jobs. They have a system in place that makes it easy for anyone to come in and volunteer and several jobs to choose from.

The kids chose the scooping job because it’s fun

and easy for them to do.

They each had their own scoop and poured the chicken, veggies, soy, and rice into the funnel.

I held a bag under the funnel to catch the food and then weighed it to make sure we had the right amount.

Jonathan sealed the bags shut and got them ready to put in a box.

The room was filled with many volunteers from several different businesses, families, and groups. We were able to fill enough bags to feed 59 children for one whole year! They told us that the food would be going to Zimbabwe. When it was all done we got to gather around those boxes of food and pray. What a great way to end.

This service was a great reminder that there are many people out there that don’t have anything to eat. This was just one simple way we can help and live out scripture.

For I was hungry and you gave me food, I was thirsty and you gave me drink, I was a stranger and you welcomed me, Matthew 25:35

We all had a great time, serving for a great cause, and we can’t wait to go back again.

What ways does your family like to serve together?

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Last summer Abby and Jonathan attended our County Fair. As you always see at any county fair, there was a display of 4-H projects. Jonathan suggested that maybe 4-H would be a good thing for us to check out for the kids.

I had looked their website over and made a couple calls. I kind of drug my feet into checking it out, so here we are in March and we finally attended our first 4-H club meeting.

We went to the meeting and there were a variety of ages attending. I was told that each meeting there is usually a demonstration of some sort usually done by the kids. This week was different because one of the leaders was doing the demonstration. He did different activities where they got to see how light worked using special glasses, boxes, and lasers. It was a really fun learning experience for them and they enjoyed the hands on activities.

After the demonstration was over the real meeting started. The older members (high school age) called the meeting to order and started with the pledges. Then they went over the last meeting minutes, treasury report, old business, and new business. This is almost totally kid run, while the leaders sit on the side lines for assistance as needed. If the president (again a high schooler) asks for an idea it is expected that all the kids speak out. This was something new for my kids to see and experience. They loved it!

As the meeting was going on, the younger kids had received a worksheet with ideas on it and they were supposed to circle what they liked to do. When the meeting was about done each of the younger kids got to stand up. say their name, share what they liked, and why. After watching a couple others do it my kids were ready. I thought at least Joel would need a little prodding but he was the first one and he just stood up, said his business, and sat down. Abigail and Lydia followed and they did just great. I was so proud of them. I loved that they had this opportunity to practice speaking in front of others.

I think 4-H will be a great opportunity for my kids to learn leadership and speaking skills. They will also enjoy serving the community and getting to make new friends.

They had such a good time and are looking forward to many more adventures with 4-H. I look forward to sharing them with you.

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First Trust NYSE Arca Biotechnology Index Fund Experiences Big Outflow Tuesday, January 19, 11:51 AM ET, by Market News Video Staff Symbols mentioned in this story: FBT, NKTR, CRL, ILMN Exchange traded funds (ETFs) trade just.

First Trust NYSE Arca Biotechnology Index Fund -- Insider Buying Index Registering 12.9% Wednesday, January 20, 10:05 AM ET, by Market News Video Staff A look at the weighted underlying holdings of the First Trust NYSE Arca Biotechnology Index.

Myriad Genetics Enters Oversold Territory (MYGN) Thursday, January 21, 4:22 PM ET, by Market News Video Staff Legendary investor Warren Buffett advises to be fearful when others are greedy, and be greedy.

FBT, CRL, QGEN, GRFS: Large Outflows Detected at ETF Wednesday, January 27, 10:56 AM ET, by Market News Video Staff Symbols mentioned in this story: FBT, CRL, QGEN, GRFS Exchange traded funds (ETFs) trade just.

Oversold Conditions For Celldex Therapeutics (CLDX) Wednesday, January 27, 4:23 PM ET, by Market News Video Staff Legendary investor Warren Buffett advises to be fearful when others are greedy, and be greedy.

NKTR Crosses Above Key Moving Average Level

By Market News Video Staff, Friday, March 11, 4:32 PM ET

Play Video: Learn About The 200 DMA

Start slideshow: 10 Stocks Crossing Above Their 200 Day Moving Average »

In trading on Friday, shares of Nektar Therapeutics (NASDAQ:NKTR ) crossed above their 200 day moving average of $12.66, changing hands as high as $12.94 per share. Nektar Therapeutics shares are currently trading up about 7% on the day. The chart below shows the one year performance of NKTR shares, versus its 200 day moving average:

Looking at the chart above, NKTR's low point in its 52 week range is $9.16 per share, with $17.55 as the 52 week high point — that compares with a last trade of $12.87. Special Offer: Free Sample Issue to the Preferred Stock List Newsletter

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By: Misha Dillon Justin Sellon Joy Petscher

The 4-H sheep project is intended for individuals who are interested in showing sheep. You don't have to have any prior experience, just be willing to learn more about sheep. With this in mind lets get started learning about sheep!

Let's first define 4-H. 4-H is the largest youth serving organization in the world. It began in rural America but has spread to major urban center, suburban communities, and rural non-farm settings. All 50 states have 4-H programs and more than 80 countries worldwide. 4-H provides a family atmosphere with youth of age's third grade to twelfth grade being the primary members. However, family members are encouraged to get involved as club leaders and help work together with kids to fulfill projects as they learn together. 4-H is an educational and learning experience for today's youth.

You want to try to choose a high-quality, healthy, muscular lamb with some style. The main thing to remember is that the most expensive lamb is not always the best lamb. The lamb should be free of parasites when you buy it. If you don't know if it has been wormed you should worm it. Lambs should be vaccinated for CD/T before going on full feed. There are a number of different breeds you can choose from to show. Some of the more common breeds shown in Indiana are Suffolk, Hampshire, Dorset, Southdown, Shropshire, and Natural Color. You can see pictures of these breeds and many others at: http://www. ansi. okstate. edu/breeds/sheep/ Some of the breeds are shown below.

There are two main ways to purchase lambs. One is through private treaty which is off the farm, while the other is in a sale. A sale although not always, is generally more expensive. You can see list of upcoming sales by looking here: http://www. clublambpage. com/

Some important factors to remember when selecting a market lamb are the age of the lamb, conformation, growthiness, muscling, breed characteristics, wool quality, soundness and substance of bone. Not anyone of these characteristics will make a great sheep, but the best combination of all of them will allow for a complete and very competitive sheep.

Feeding is one of the most important aspects of the project next to selecting your lamb. You don't have to feed the most expensive feed to get the most out of your lamb. Textured or pellet feed are both acceptable. You should feed a feed that contains 16%-18% protein. This is an area that can be played with as you gain more experience in the project. A market lamb should gain anywhere from .5-.8 pounds per day an average of 6-8 pounds of feed. Lambs are also ruminants and require some sort of roughage such as hay. A regular feeding schedule should be adopted. A good routine would be feeding early in the morning and later at night to avoid as many problems with heat as possible. Water is also very important. A clean, fresh source of water should be available at all times. Some websites that have sources of show lamb feeds are listed:

There are many different exercise programs that can be utilized when working with sheep. To get started a good rule of thumb is to walk your lambs at least 15 minutes a day. There are many reasons why exercise is important. A good exercise program can help build muscle and tone muscle that is already there. Also, a lamb that is exercised on a regular basis will hold up better in the show ring. Some other methods of exercise involve tracks with jumps set up and treadmills. For a beginner to the sheep industry it is easier just to start out with regular old walking. As you progress increase the distance and time of walking. Another important thing to remember is that with increased exercise feed intake will also increase.

The first thing to work on when training a show lamb is getting it halter broke. When a lamb is halter broke it can be tied for exercising, cleaning, examining and can make it easier to lead when not on a halter. There are numerous techniques to showing and it's up to you to develop your own technique. Some ways to get your lamb to stick are to practice backing it up until it pushes back into you. Backing them into a shallow hole or off the back of a lamb stand is another practical way. The most important thing to remember when training your lamb is the more hours you spend with your lamb the more comfortable each of you will be with each other.

Ok, you've made it to the show ring now what do you do? This is the fun and exciting part where all of your hard work finally pays off. First of all, remember that this is your time to show your accomplishments to the judge. If you are in a market lamb class it is important to show the sheep to the judge. Make sure the lamb is always between the judge and you. Always walk around the front of the lamb. Set legs on the judges side of the lamb first. Be patient and calm. If you get nervous or anxious the lamb will sense this and possibly not cooperate. Also, be confident in yourself. If you have put in the time and effort every day then you will have no problems when it comes to the show ring.

Different ways of showing sheep!

On a final note, don't ever forget if you need help ask. There are numerous resources to get help. Go to producers, extension agents, old 4-Her's, or 4-H leaders. If they don't have the answers they can find someone that will be able to help you.

Last but not least remember to have fun.

recurso

Calculating the cost of moving in activity

Wouldn’t it be great if whenever we decided to move to a new home, we could just pick up and go with no costs involved? Unfortunately moving into a new place doesn’t work this way, especially for people who are making the transition from renter to homeowner. Aside from the cost of buying a home, there are other costs to be considered: deposits for utilities, hiring movers or renting a truck, purchasing lawn care equipment, buying furniture, and having tools on hand for basic home safety, repair and maintenance.

This exercise helps youth understand the costs associated with moving and provides the basis for discussing the impact these costs have for low wage earners. The list of items below does not necessarily illustrate a comprehensive list of what every new homeowner must have but includes common items that new homeowners either need to have on hand or might consider purchasing prior to their move.

Worksheet

How much does it cost to move in? Put on your detective caps to find out! Do some research and determine the cost for each line item in the worksheet. Some places to look for prices include the internet, catalogs, or a local hardware store.

Follow up questions

Were you surprised by some of the items on the list? If so, why?

Can you think of ways you could cut costs if you are on a limited budget?

Which items are вЂ˜must-haves’ that would be absolutely necessary for you to have as a homeowner? Why are these items needed?

Have questions? В Contact copelanda@missouri. edu or 573-882-8807

The Missouri 4-H website contains many PDF documents that require the free Adobe Reader. В You may need to download the newer version of Adobe Reader if you encounter problems reading the PDF documents. В

Western Union

We are a leader in global payment services. From small businesses and global corporations, to families near and far away, to NGOs in the most remote communities on Earth, Western Union helps people and businesses move money - to help grow economies and realize a better world. In 2017, we moved over $150 billion dollars for our consumer and business clients. We continue to innovate, developing new ways to send money through digital, mobile, and retail channels, with an array of convenient pay-out options to meet business and consumer needs.

500,000+ Agent locations . and 100,000 ATMs and kiosks around the globe

In over 200 countries and territories

We moved more than $150 Billion in principal in 2017 for our consumer and business clients

Transacting in more than 130 currencies

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What we do

We are a business centered on the needs of our customers, and over the years, we’ve invested and innovated to provide consumers and businesses with even more choices – in products, in services, and in how and where they can access Western Union when moving money across borders.

We connect people

We move money for better, enabling individuals, families and friends to securely and seamlessly transfer money in the ways that are most convenient for them, whether that is walking into a retail location or using our Western Union website or app to move money in minutes.

Our customers use our services to send money to family members in nearly every part of the world, to provide support, recognize a special occasion, and enable entrepreneurship or education.

We connect businesses

As businesses have a growing need to move money around the globe and transact in different currencies, we’ve answered these needs with Western Union Business Solutions to help navigate the global economy, including solutions for International Payments, Risk Management, and Cash Management Solutions. We offer a wide range of industry-specific solutions that today help over 100,000 clients including financial institutions, educational institutions, NGOs, and small/medium sized businesses needing to make cross-border payments.

Our purpose

We believe that when money moves, better things can happen. A business expands. A child goes to college. Emergency aid arrives when it’s needed. An economy prospers, an opportunity opens, a community heals and relationships endure.

Moving money for better means moving money for a better world –creating value for individuals, businesses and for society.

Western Union Foundation

The Western Union Foundation with the support of The Western Union Company, its employees, Agents, and business partners, works to realize the Education for Better vision by supporting education and disaster relief efforts as pathways toward a better future.

Since its inception in 2001, the Western Union Foundation has contributed over $102 million to more than 2,500 nongovernmental organizations in 137 countries and territories.

The Western Union Foundation, is a separate В§501(c)(3) recognized United States charity.

Education for Better

Education is one of the surest paths to economic opportunity and financial inclusion, which is why it’s both the Western Union Company and the Western Union Foundation cause of choice. Education for Better leverages Western Union services, cause marketing, advocacy, strategic philanthropy, employee engagement, and communications to support secondary and vocational education programs around the world.

Launched in 2012, Education for Better is our commitment to support education around the world in conjunction with the Western Union Foundation.

To date, we have moved over $7 billion in principal for education through Western Union Business Solutions and raised $60K through the consumer donation match initiative supporting UNICEF education programs for Syrian children. We’ve also supported one million days of schooling through our PASS initiative.

Chain of Betters

Our vision of moving money for better sits at the center of the Chain of Betters initiative, empowering people to change lives and shape communities through small gifts that make a big difference.

Our Chain of Betters initative is live in over 140 countries and has helped fund various initatives in countries across the globe, from transforming the fortunes of a fishing village in the Philippines to using technology to connect parents in Europe with their son in China.

Elementary School

Looking Back and Moving Forward-Doves of Peace

New Year's Eve has always been a time for looking back to the past, and more importantly, looking forward to the coming year. It's a time to reflect on the changes we want (or need) to make and resolve to follow through on those changes. Here are some of 3/4H's resolutions, goals and reflections that help to make our class community a peaceful place of learning in 2017.

I loved going to the lo'i field at UH; I learned a lot about the past. - C. M.

I really enjoyed the "Hour of Code" and now I think I want to make computer games. - S. H.

I look forward to going to Camp Erdman and being with my friends. - N. S.

I can't wait for Field Day! - R. K.

I can't wait to learn new strategies in math. - P. S.

My goal is to know all my multiplication facts by the end of the year. - A. S

I (by myself) will pack my bag before leaving in the morning.-R. K.

I am going to try to be on time for things. - P. Y.

Error 403 Access to our site has been rejected due to the following: Your browser appears to be a spam bot, adware, unauthorized spider or a browser that is trying to collect or distribute unauthorized information or your browser may have an add-on utility or toolbar that is acting like adware or a spam bot. Try accessing our site with a clean version of FireFox, Chrome, Internet Explorer, Safari or other major desktop, tablet or smart device browser - or - If you feel you are receiving this message in error, please contact the site adminstrator networkadmin@sref. info for assistance in accessing our site.

Access to our site has been rejected due to the following: Your browser appears to be a spam bot, adware, unauthorized spider or a browser that is trying to collect or distribute unauthorized information or your browser may have an add-on utility or toolbar that is acting like adware or a spam bot. Try accessing our site with a clean version of FireFox, Chrome, Internet Explorer, Safari or other major desktop, tablet or smart device browser - or - If you feel you are receiving this message in error, please contact the site adminstrator networkadmin@sref. info for assistance in accessing our site.

Guru Meditation:

TruColorXP - 4"H X 48"W

The ultimate in indoor color display technology. Has built-in entertaining and attention getting features such as “Trivia in Motion” and the ability to receive satellite updates with an optional receiver to display stock quotes, sports scores and news which makes it ideal for welcoming and entertaining guests at lobbies, sports bars and more. With the included Infrared Wireless Remote, the display may be programmed in a matter of minutes. Also easily programmable via PC through direct connection, LAN or Internet e-mail!

16 Characters

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Programmable via Infrared Remote Keyboard with password protection

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Turn Trivia ON/OFF w/ the Wireless Remote Keyboard or PC

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64K Jumbo Memory with 52 Pages of memory bank

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10 Year Warranty on the LED with 160 Degree viewing angle

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*Software and MiniWeb™ required **Internet access and software required ***Optional receiver required, monthly fees apply

1 TruColorXP programmable LED Display

1 Wireless Infrared Remote Keyboard

1 Serial cable for RS232 communication

1 User’s Manual

1 30-Day trial software CD

1 set of wall mounting bracket

ReloCube ® Size & Delivery

Move Easy in a U-Pack ReloCube ®

When you choose to move or store in a ReloCube, U-Pack delivers an easy-to-load portable moving and storage container right to your door. Reserve one, or as many as you think you'll need, and pay only for the Cubes you actually use. Simply load it, lock it, and keep the key; we'll move it, or store it until you're ready for delivery.

It's just one of the reasons so many customers choose U-Pack. Get a free moving quote today and see how the U-Pack ReloCube makes moving easy and affordable.

ReloCube Internal & External Dimensions

Interior dimensions are approximately 70" x 82" x 93" (DWH)

Exterior dimensions are approximately 6'3" x 7' x 8'4" (DWH)

Loading capacity is approximately 305 cubic feet

ReloCube Specifics

ReloCubes are custom-built, weatherproof, metal containers

They sit flat on the ground for convenient loading and unloading

They fit easily into a standard-size parking space

Each Cube can hold a maximum of 2,500 pounds of household goods

Cubes are equipped with logistics tracking throughout the interior, making securing your belongings easy

You can place your own padlock on the ReloCube for added security, and it stays on until you remove it at the destination

ReloCube Delivery

With U-Pack door-to-door service, we’ll deliver ReloCubes right to your door. The type of equipment we use to get them there differs by service center. In some locations they’ll be delivered using a flatbed trailer, and in some locations we’ll deliver using a drop-deck trailer. With both types of equipment, the Cubes are positioned using a forklift, and we’ll place them right where you want them—as long as it’s a hard, level surface.

ReloCube Delivery With a Flatbed Trailer

In areas where we use a flatbed trailer to deliver ReloCubes, we can deliver up to four Cubes at one time. These trailers are approximately 43 feet long (51 feet with the tractor), so they require plenty of room for both turning and parking.

ReloCube Delivery With a Drop-Deck Trailer

In areas where we use a drop-deck trailer to deliver ReloCubes, we can deliver up to two Cubes at one time. These trailers are approximately 39 feet long (47 feet with the tractor), so they also require plenty of room for both turning and parking.

If you have questions about the type of equipment used in your location, call a helpful U-Pack moving consultant at 844-611-4586 .

Learn More About Moving in a ReloCube

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Inspections for Ownership aka Brand Inspections

Arizona, California, Colorado, Idaho, Montana, Nebraska, Nevada, New Mexico,

North Dakota, Oregon, South Dakota, Utah, Washington, and Wyoming

Horses in these states must be registered with the B rand Inspector and the paperwork

should accompany your horse anytime you are away from your barn.

This is an inspection of ownership. You must prove that you own the horse

and the paperwork is required whether or not your horse has a brand.

If you have breed registration papers listing you as the horse's owner, it makes the process easier.

Brands aren't necessary -- but the paperwork is.

Should I Ship My Horse Overseas with Me?

by Lynn Cairney

The expense is a major factor. In February of 2007, the cost was about $5,000 for one horse, $10,000 for two horses. And this is only one-way. But this includes vet exams and vaccines, horse passport, airport quarantine, international paperwork, customs paperwork, customs vet check, trailering door to door, meaning picking up at current stables, airplane flight, then trailering to your new stable in Germany, hay and water for the entire journey.

Here’s a quick checklist.

The rest of this article will walk you through how to do all of this.

√ Contact Guido Klatte (or your transport of choice) to start the entire process.

√ Apply for equine passports through USEF.

√ Find stable in Germany.

√ Follow instructions for vet vaccinations.

√ Clean tack and pack for flight. Get out the military duffle bags!

√ List all tack on the ATA Carnet provided by transport co. for customs.

Dogs: We also shipped our two dogs on the flight with the horses. The cost was about $100 for our 25 lb. Cocker Spaniel and $200 for our 120 lb Labrador. The shipping company gave us the special paperwork to be filled out by our vet. Besides the vaccines, they both had to get a micro-chip.

Military tax note: If you ship your horse or other pet, you can deduct the entire cost on your income taxes. It is an “unreimbursed moving expense” and completely legal to claim as a deduction. We confirmed this through the Legal Office on base.

The decision to bring our horses was a no-brainer for us; our horses bring an immense amount of joy to our lives. Riding is what my husband and I do together. Our horses are family. I couldn’t imagine living without them for 2-3 years. So our budget was simply allocated toward that. But because I’m a very practical person, I sat down and crunched some numbers….and did a how-crazy-am-I sanity check!

What if we don’t take them? …just board them at a good barn and save the shipping cost. For 2 years, we added up the cost of board, grain, seasonal shots, farrier, floating and discovered we’d still be spending thousands of dollars, but not one second of enjoying our horses. If we were to hire a trainer, more $$$. Or without a trainer, letting them be put out to pasture for a couple of years, at their young age of 3 ½ we were sure they would lose a lot of their training, so there goes a wasted year and a half to get them where they were.

Leasing your horse: A manager at my barn offered to help me lease our horses while we were away to offset the cost of board, etc. and keep up their training. She was so kind to offer this and I’m sure she would have only recommended someone completely reliable. This may work for others who want to keep up their horse’s training and exercise program, but it didn’t work for us. It may be something for others to consider while stationed overseas, though. If you know you’ll be back to the States, that may be enough for you to stop in on your horse and have a nice ride while in town once or twice a year.

Health questions: Our horses were 3 years old at the time, young and healthy and pretty docile with all their groundwork training, definitely not “hot”. My vet still prescribed an ulcer medicine to be given a few weeks before travel, which simply coats their stomach lining to prevent ulcers or irritation caused by the stress of travel. If your horse is older, consult your vet on the stress of travel and if your horse is healthy enough to handle the trip. Trailering to the airport can be the most stressful portion. Our horses were trailered for about 4 days from Colorado to New York. Once on the plane from NY to Amsterdam it took only 7 hours to fly. Then another 5 hours to drive to our stables in Dudeldorf.

How does the flight work?

Unlike setting up a flight with cargo for your dog or cat, it is mandatory that you go through a horse transport company. They will take care of all documents and setting up the door to door service – transport from your barn to the airport, flight from the US to Amsterdam, then transport to your barn in Germany.

We used the company Guido Klatte Equine Services . www. gklatte. de (at the bottom of photo, click on the American flag for English). They use The Dutta Corp. to handle the Stateside journey. The Dutta Corp . Ph: 914-276-3880 FAX 914-276-3883

I believe they only fly out of JFK (New York). But returning, they fly into JFK, Miami, and Los Angeles. Other carriers have other ports, but I only know about Klatte.

For the Klatte / Dutta Corp. they fly year-round with no restrictions on seasons. This is very helpful when you usually have to work around summer restrictions on commercial flights.

Find Stable in Germany: Before your horse can be booked on a flight, you must be approved at a stable in Germany. They will need this address for the paperwork. I went to Germany about 5 months before the flight and drove around with my husband who was already living there. There was a barn on every corner and we literally pulled over and inquired about boarding our two horses. I should interject that my husband speaks German quite well. He doesn’t know the horse world lingo, and has trouble with the dialect in this region, but I believe this helped us get answers and referrals. All the barn owners were very friendly and let us know if they would have availability or not. We were then referred to Dohm stables, and once we saw the grounds, amenities and met Maria and Klaus Dohm, we were finished looking!

Quarantine: The pre-export quarantine at JFK airport was a minimum of 6 hours. Our horses arrived the night before to rest before the flight. The cost of this is factored into the estimate above. Your horse will be in a stall at the cargo portion of the airport where there is a vet clinic. The good news is that once they land in Amsterdam and complete the customs check, there is no quarantine for geldings or mares! You immediately head to your barn and enjoy your horses!

W hen you return to the States, there is a 3-day quarantine for geldings, 2-week quarantine for mares.

Here’s information from the Klatte website.

I was a groom on the flight with my horses and I can confirm these details are correct.

Your horses travel with the best available airlines. KLM and Lufthansa are preferred partners. Some airlines offer their own horse stewards. With other carriers members of the Klatte team take care of your valuable freight.

There is always a horse steward on board, mostly with a veterinary background. Guido Klatte: "Qualified personnel is of highest concern to me." Water and hay are served on board. Varying dividers changes the available space. Two horses can travel "business class" and enjoy more room. Without the divider and extra cargo your horse can travel "first class".

On some carriers your own groom may be able to accompany your horse during the flight. The client decides on the level of comfort. The flight box, which is lifted into the freight deck of the air plane, offers room for three horses.

This is my personal photo, not from the site.

This Klatte transport truck is carrying me, my husband, our two dogs, and our two horses!

The driver had cctv so we could watch our guys over the 5-hour trip.

Equine Passport : Since all horses in Germany are required to have a passport, you’ll have to apply for a passport through the United States Equestrian Federation (USEF), the national governing body for equestrian sport. This is mandatory, you will not be able to ship your horse to Germany without a passport. A brand inspection will not suffice. To obtain a passport, you will also need to become a member with USEF, which expires in one year. You do not need to renew if you do not wish to. I included this cost in the original estimate.

USEF Website: www. usef. org Phone: 859-258-2472

Information may have changed since I applied for my passports in 2006. Please call their office to confirm the process.

You should apply for the passport 6 months out. It will need to be sent back again with the horses sketches for approval, so allow for delivery time and their processing backlog. It is quite an intense process and it's best to find a vet who has done this before. My vet had not, but he read all the rules, was meticulous about it and was able to check in and make sure he was filling it out correctly. For his time, series of shots, sketches of the horses, and filling out the passport correctly in two different colors of red and blue ink, it was about $425 for both horses. I believe the price of the passport was $50 each. You also need to join the FEI which will cost about $100 per horse. I've included all of this in the estimate for shipping.

Important Customs Tax Info: Ask your shipper to set up your horse’s stay as “temporary entrance to Germany”. We found out that if we were to bring our horses on a “permanent basis”, we’d have to pay 25% of their value in taxes. This wouldn’t have been a problem with the low cost of our horses, but customs didn’t “believe” the low value, even though we sent documentation. And we were boarding the plane in days and didn’t have time to argue. They had assigned their own value in taxes, which came to about $3,000! To avoid this, we had to bring them into Germany on a “temporary basis”. Be sure to ask your shipper about this, they will need to prepare different paperwork for you. In 2006, “temporary” allowed for a one-year stay. Then you must go to the customs office and ask for an extension, which is usually 6 months at a time. And this is what we have done our entire stay here. We used the customs office in Wittlich. If you are not stationed at Spangdahlem, you can ask your customs office on base for the nearest office. Be sure to have your horse’s passport when you go. This has not been a problem for us to keep them in Germany an additional year and a half. When you leave the country, you must call the customs office and tell them your horses are now leaving the country and they will record it in their system.

Packing your tack for the flight: I made the mistake of packing all our tack into our tack trunks. I wasn't informed that when they tell you that you can bring your tack, there is a limited amount of space. The box carries three horses side by side. In front of them is a narrow space where you can put your tack for no extra charge.

However, it fits more of a duffle size, or saddle bag carrier, not large, square tack trunks. My trunks had to be placed elsewhere on the cargo plane and I was actually charged extra for this. Be sure to ask for the measurements when you speak to the transport company. Also ask if you can bring a bag of grain in the duffle bag. The transport company will provide you with what is called an ATA Carnet. This is customs paperwork you will fill out before the flight listing every piece of tack you are bringing with you. They can send you a sample of someone else's to give you an idea for the wording.

Be sure to read Lynn's picture / story of her horses return trip to the United States from Germany (below). Information has been updated since their flight to Germany two years before.

Bankston, Iowa

For population 25 years and over in Bankston:

High school or higher: 93.1%

Bachelor's degree or higher: 9.8%

Graduate or professional degree: 0.0%

Unemployed: 20.0%

Mean travel time to work (commute): 21.3 minutes

For population 15 years and over in Bankston city:

Median real estate property taxes paid for housing units with mortgages in 2017: $224 (0.1%)

Nearest city with pop. 50,000+: Dubuque, IA (13.9 miles , pop. 57,686).

Nearest city with pop. 200,000+: Madison, WI (88.6 miles , pop. 208,054).

Nearest city with pop. 1,000,000+: Chicago, IL (174.4 miles , pop. 2,896,016).

Nearest cities: Graf, IA (2.1 miles). Epworth, IA (2.2 miles ), Farley, IA (2.3 miles ), Rickardsville, IA (2.6 miles). Holy Cross, IA (2.6 miles ), Centralia, IA (2.6 miles). Peosta, IA (2.7 miles ), New Vienna, IA (2.9 miles ).

Latitude: 42.51 N , Longitude: 90.96 W

Area code commonly used in this area: 563

Building and grounds cleaning and maintenance occupations (84%)

Transportation occupations (11%)

Material moving occupations (4%)

Management occupations (0%)

Business and financial operations occupations (0%)

Computer and mathematical occupations (0%)

Architecture and engineering occupations (0%)

Office and administrative support occupations (50%)

Business and financial operations occupations (47%)

Sales and related occupations (3%)

Management occupations (0%)

Computer and mathematical occupations (0%)

Architecture and engineering occupations (0%)

Life, physical, and social science occupations (0%)

Average climate in Bankston, Iowa

Based on data reported by over 4,000 weather stations

Tornado activity:

Bankston-area historical tornado activity is near Iowa state average. It is 78% greater than the overall U. S. average.

On 3/13/1990 , a category F4 ( max. wind speeds 207-260 mph) tornado 11.1 miles away from the Bankston city center caused between $5,000,000 and $50,000,000 in damages.

On 8/12/1974 , a category F4 tornado 28.7 miles away from the city center injured 12 people and caused between $500,000 and $5,000,000 in damages.

Earthquake activity:

Bankston-area historical earthquake activity is slightly below Iowa state average. It is 86% smaller than the overall U. S. average.

On 4/18/2008 at 09:36:59 , a magnitude 5.4 (5.1 MB , 4.8 MS , 5.4 MW , 5.2 MW , Depth: 8.9 mi , Class: Moderate , Intensity: VI - VII) earthquake occurred 323.8 miles away from the city center On 6/28/2004 at 06:10:52 , a magnitude 4.2 (4.0 MB , 4.2 MW , Depth: 6.2 mi , Class: Light , Intensity: IV - V) earthquake occurred 128.4 miles away from Bankston center On 6/10/1987 at 23:48:54 , a magnitude 5.1 (4.9 MB , 4.4 MS , 4.6 MS , 5.1 LG) earthquake occurred 301.8 miles away from the city center On 6/18/2002 at 17:37:15 , a magnitude 5.0 (4.3 MB , 4.6 MW , 5.0 LG , Depth: 3.1 mi) earthquake occurred 354.9 miles away from the city center On 4/18/2008 at 15:14:16 , a magnitude 4.8 (4.5 MB , 4.8 MW , 4.6 MW , Depth: 6.2 mi) earthquake occurred 323.4 miles away from Bankston center On 4/3/1974 at 23:05:02 , a magnitude 4.7 (4.5 MB , 4.7 LG) earthquake occurred 310.0 miles away from the city center Magnitude types: regional Lg-wave magnitude (LG), body-wave magnitude (MB), surface-wave magnitude (MS), moment magnitude (MW)

Natural disasters:

The number of natural disasters in Dubuque County (15) is greater than the US average (12). Major Disasters (Presidential) Declared: 14 Emergencies Declared: 1

Causes of natural disasters: Floods: 14 , Storms: 11 , Tornadoes: 4 , Heavy Rain: 1 , Hurricane: 1 (Note: Some incidents may be assigned to more than one category).

Hospitals and medical centers near Bankston:

HERITAGE MANOR (Nursing Home, about 11 miles away; DUBUQUE, IA)

HACIENDA COMMUNITY LIVING HOME (Hospital, about 12 miles away; DUBUQUE, IA)

HOSPICE OF DUBUQUE (Hospital, about 13 miles away; DUBUQUE, IA)

ENNOBLE SKILLED NURSING AND REHABILITATION CENTER (Nursing Home, about 13 miles away; DUBUQUE, IA)

WEST 32ND COMMUNITY LIVING HOME (Hospital, about 13 miles away; DUBUQUE, IA)

LUTHER MANOR RETIREMENT HOME (Nursing Home, about 13 miles away; DUBUQUE, IA)

DUBUQUE NURSING AND REHAB CENTER (Nursing Home, about 13 miles away; DUBUQUE, IA)

Colleges/universities with over 2000 students nearest to Bankston:

University of Wisconsin-Platteville ( about 29 miles; Platteville, WI ; Full-time enrollment: 7,679)

Upper Iowa University ( about 49 miles; Fayette, IA ; FT enrollment: 5,275)

Kirkwood Community College ( about 55 miles; Cedar Rapids, IA ; FT enrollment: 11,503)

Ashford University ( about 60 miles; Clinton, IA ; FT enrollment: 73,330)

Northeast Iowa Community College-Calmar ( about 66 miles; Calmar, IA ; FT enrollment: 3,365)

University of Iowa ( about 66 miles; Iowa City, IA ; FT enrollment: 24,735)

Kaplan University-Davenport Campus ( about 70 miles; Davenport, IA ; FT enrollment: 60,376)

Dubuque County has a predicted average indoor radon screening level greater than 4 pCi/L (pico curies per liter) - Highest Potential

Air pollution and air quality trends (lower is better)

No gay or lesbian households reported

Bankston compared to Iowa state average:

Median household income above state average.

Black race population percentage significantly below state average.

Hispanic race population percentage significantly below state average.

Median age significantly below state average.

Foreign-born population percentage significantly below state average.

Length of stay since moving in significantly below state average.

Number of rooms per house above state average.

House age significantly below state average.

Number of college students significantly above state average.

Percentage of population with a bachelor's degree or higher below state average.

Educational Attainment (%) in 2017

School Enrollment by Level of School (%) in 2017

Education Gini index (Inequality in education)

Most commonly used house heating fuel:

Presidential Elections Results

1996 Presidential Elections Results

2000 Presidential Elections Results

2004 Presidential Elections Results

2008 Presidential Elections Results

2012 Presidential Elections Results

Religion statistics for Bankston city (based on Dubuque County data)

Source: Clifford Grammich, Kirk Hadaway, Richard Houseal, Dale E. Jones, Alexei Krindatch, Richie Stanley and Richard H. Taylor. 2012. 2010 U. S.Religion Census: Religious Congregations & Membership Study. Association of Statisticians of American Religious Bodies. Jones, Dale E. et al. 2002. Congregations and Membership in the United States 2000. Nashville, TN: Glenmary Research Center. Graphs represent county-level data

Food Environment Statistics:

Number of grocery stores: 11

Number of supercenters and club stores: 1

Number of convenience stores (no gas): 4

Number of convenience stores (with gas): 49

Number of full-service restaurants: 90

Adult diabetes rate:

Adult obesity rate:

Low-income preschool obesity rate:

Local government employment and payroll (March 2012)

Monthly full-time payroll

Average yearly full-time wage

Monthly part-time payroll

Bankston government finances - Expenditure in 2002 (per resident):

Current Operations - Central Staff Services: $3,000 ($120.00) Sewerage: $3,000 ($120.00) Financial Administration: $1,000 ($40.00) Fire Protection: $1,000 ($40.00) Regular Highways: $1,000 ($40.00) General - Other: $1,000 ($40.00) Water Utilities: $1,000 ($40.00)

Total Salaries & Wages: $2,000 ($80.00)

Bankston government finances - Revenue in 2002 (per resident):

Charges - Sewerage: $3,000 ($120.00)

Revenue - Water Utilities: $2,000 ($80.00)

State Intergovernmental - Highways: $2,000 ($80.00)

Tax - Total General Sales: $3,000 ($120.00)

Bankston government finances - Cash and Securities in 2002 (per resident):

Other Funds - Cash & Deposits: $4,000 ($160.00)

4.53% of this county's 2011 resident taxpayers lived in other counties in 2010 ($42,754 average adjusted gross income )

Strongest AM radio stations in Bankston:

KDTH (1370 AM; 5 kW; DUBUQUE, IA; Owner: RADIO DUBUQUE, INC.)

KXEL (1540 AM; 50 kW; WATERLOO, IA; Owner: KXEL BROADCASTING COMPANY, INC.)

WMT (600 AM; 5 kW; CEDAR RAPIDS, IA; Owner: CITICASTERS LICENSES, L. P.)

WDBQ (1490 AM; 1 kW; DUBUQUE, IA; Owner: CUMULUS LICENSING CORP.)

WTMJ (620 AM; 50 kW; MILWAUKEE, WI; Owner: JOURNAL BROADCAST CORPORATION)

WSCR (670 AM; 50 kW; CHICAGO, IL; Owner: INFINITY BROADCASTING OPERATIONS, INC.)

WGN (720 AM; 50 kW; CHICAGO, IL; Owner: WGN CONTINENTAL BROADCASTING CO.)

WBBM (780 AM; 50 kW; CHICAGO, IL; Owner: INFINITY BROADCASTING OPERATIONS, INC.)

WHO (1040 AM; 50 kW; DES MOINES, IA; Owner: CITICASTERS LICENSES, L. P.)

KKHQ (950 AM; 5 kW; OELWEIN, IA; Owner: CUMULUS LICENSING CORP.)

WISN (1130 AM; 50 kW; MILWAUKEE, WI; Owner: CAPSTAR TX LIMITED PARTNERSHIP)

WSPT (1010 AM; 50 kW; STEVENS POINT, WI)

WMVP (1000 AM; 50 kW; CHICAGO, IL; Owner: ABC, INC.)

Strongest FM radio stations in Bankston:

KGRR (97.3 FM; EPWORTH, IA; Owner: RADIO DUBUQUE, INC.)

KATF (92.9 FM; DUBUQUE, IA; Owner: RADIO DUBUQUE, INC.)

K239AB (95.7 FM; DUBUQUE, IA; Owner: AUGUSTANA COLLEGE)

KOEL-FM (92.3 FM; OELWEIN, IA; Owner: CUMULUS LICENSING CORP.)

KFMW (107.9 FM; WATERLOO, IA; Owner: KXEL BROADCASTING COMPANY, INC.)

WJOD (103.3 FM; ASBURY, IA; Owner: CUMULUS LICENSING CORP.)

KLYV (105.3 FM; DUBUQUE, IA; Owner: CUMULUS LICENSING CORP.)

KUNI (90.9 FM; CEDAR FALLS, IA; Owner: UNIVERSITY OF NORTHERN IOWA)

WVRE (101.1 FM; DICKEYVILLE, WI; Owner: RADIO DUBUQUE, INC.)

K254AE (98.7 FM; DUBUQUE, IA; Owner: UNIVERSITY OF NORTHERN IOWA)

KXGE (102.3 FM; DUBUQUE, IA; Owner: CUMULUS LICENSING CORP.)

KDST (99.3 FM; DYERSVILLE, IA; Owner: DESIGN HOMES, INC.)

K269EK (101.7 FM; DUBUQUE, IA; Owner: THE UNIVERSITY OF IOWA)

KIYX (106.1 FM; SAGEVILLE, IA; Owner: QUEENB RADIO WISCONSIN, INC.)

WPVL-FM (107.1 FM; PLATTEVILLE, WI; Owner: QUEENB RADIO WISCONSIN, INC.)

WGLR-FM (97.7 FM; LANCASTER, WI; Owner: QUEENB RADIO WISCONSIN, INC.)

KMCH (94.7 FM; MANCHESTER, IA; Owner: FIFE COMMUNICATION COMPANY, L. C.)

TV broadcast stations around Bankston:

KFXB ( Channel 40; DUBUQUE, IA; Owner: DUBUQUE TV LTD. PARTNERSHIP)

KWWL ( Channel 7; WATERLOO, IA; Owner: RAYCOM AMERICA, INC.)

KGAN ( Channel 2; CEDAR RAPIDS, IA; Owner: KGAN LICENSEE, LLC)

KCRG-TV ( Channel 9; CEDAR RAPIDS, IA; Owner: CEDAR RAPIDS TELEVISION CO.)

KRIN ( Channel 32; WATERLOO, IA; Owner: IOWA PUBLIC BROADCASTING BOARD)

KFXA ( Channel 28; CEDAR RAPIDS, IA; Owner: SECOND GENERATION OF IOWA, LTD.)

W22CI ( Channel 22; BLOOMINGTON, WI; Owner: STATE OF WISCONSIN - EDUCATIONAL COMMUNICATIONS BOARD)

FCC Registered Private Land Mobile Towers:

1

Center Town ( Lat: 42.518611 Lon: -90.960972), Call Sign: KNFD395 Assigned Frequencies: 464.775 MHz Grant Date: 08/20/2012, Expiration Date: 09/10/2022 Registrant: Cara Enterprises Inc, Las Vegas, NV 89140-0124, Phone: (702) 838-9728, Fax: (702) 363-4607, Email:

Home Mortgage Disclosure Act Aggregated Statistics For Year 2009 (Based on 1 partial tract)

David Halliday, Robert Resnick, Jearl Walker, Fundamentals of Physics, 9th edition, Wiley 2010

37. A typical sugar cube has an edge length of 1 cm. If you had a cubical box that contained a mole of sugar cubes, what would its edge length be? (One mole = 6.02 x 10 23 units.)

38. An old manuscript reveals that a landowner in the time of King Arthur held 3.00 acres of plowed land plus a livestock area of 25.0 perches by 4.00 perches. What was the total area in (a) the old unit of roods and (b) the more modern unit of square meters? Here, 1 acre is an area of 40 perches by 4 perches, 1 rood is an area of 40 perches by 1 perch, and 1 perch is the length 16.5 ft.

39. A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car's fuel consumption was at the rate of 40 miles per gallon on the open road. The tourist does not realize that the u. K. gallon differs from the U. S. gallon: 1 U. K. gallon = 4.5460900 liters 1 U. S. gallon = 3.7854118 liters. For a trip of 750 miles (in the United States), how many gallons of fuel does (a) the mistaken tourist believe she needs and (b) the car actually require?

40. Using conversions and data in the chapter, determine the number of hydrogen atoms required to obtain 1.0 kg of hydrogen. A hydrogen atom has a mass of 1.0 U.

41. A cord is a volume of cut wood equal to a stack 8 ft long, 4 ft wide, and 4 ft high. How many cords are in 1.0 m 3 ?

42. One molecule of water (H 2 O) contains two atoms of hydrogen and one atom of oxygen. A hydrogen atom has a mass of 1.0 u and an atom of oxygen has a mass of 16 u, approximately. (a) What is the mass in kilograms of one molecule of water? (b) How many molecules of water are in the world's oceans, which have an estimated total mass of 1.4 x 10 21 kg?

43. A person on a diet might lose 2.3 kg per week. Express the mass loss rate in milligrams per second, as if the dieter could sense the second-by-second loss.

44. What mass of water fell on the town in Problem 7? Water has a density of 1.0 x 10 3 kg/m 3 .

46. A unit of area often used in measuring land areas is the hectare, defined as 10 4 m 2. An open-pit coal mine consumes 75 hectares of land, down to a depth of 26 m, each year. What volume of earth, in cubic kilometers, is removed in this time?

47. An astronomical unit (AU) is the average distance between Earth and the Sun, approximately 1.50 x 10 8 km. The speed of light is about 3.0 x 10 8 m/s. Express the speed of light in astronomical units per minute.

48. The common Eastern mole, a mammal, typically has a mass of 75 g, which corresponds to about 7.5 moles of atoms. (A mole of atoms is 6.02 x 10 23 atoms.) In atomic mass units (u), what is the average mass of the atoms in the common Eastern mole?

50. You receive orders to sail due east for 24.5 mi to put your salvage ship directly over a sunken pirate ship. However, when your divers probe the ocean floor at that location and find no evidence of a ship, you radio back to your source of information, only to discover that the sailing distance was supposed to be 24.5 nautical miles, not regular miles.

1. During a hard sneeze, your eyes might shut for 0.50 s. If you are driving a car at 90 km/h during such a sneeze, how far does the car move during that time?

2. Compute your average velocity in the following two cases: (a) You walk 73.2 m at a speed of 1.22 m/s and then run 73.2 m at a speed of 3.05 m/s along a straight track. (b) You walk for 1.00 min at a speed of 1.22 m/s and then run for 1.00 min at 3.05 m/s along a straight track. (c) Graph x versus t for both cases and indicate how the average velocity is found on the graph.

3. An automobile travels on a straight road for 40 km at 30 km/h.1t then continues in the same direction for another 40 km at 60 km/h. (a) What is the average velocity of the car during the full 80 km trip? (b) What is the average speed? (c) Graph x versus t and indicate how the average velocity is found on the graph.

4. A car travels up a hill at a constant speed of 40 km/h and returns down the hill at a constant speed of 60 km/h. Calculate the average speed for the round trip.

5. The position of an object moving along an x axis is given by x = 3t – 4t 2 + t 3. where x is in meters and t in seconds. Find the position of the object at the following values of t: (a) 1 s, (b) 2 s, (c) 3 s, and (d) 4 s. (e) What is the object's displacement between t = 0 and t = 4 s? (f) What is its average velocity for the time interval from t = 2 s to t = 4 s? (g) Graph x versus t for 0. t. 4 s and indicate how the answer for (f) can be found on the graph.

6. The 1992 world speed record for a bicycle (human-powered vehicle) was set by Chris Huber. His time through the measured 200 m stretch was a sizzling 6.509 s, at which he commented, "Cogito ergo zoom!" (I think, therefore I go fast!). In 2001, Sam Whittingham beat Huber's record by 19.0 km/h. What was Whittingham's time through the 200 m?

7. Two trains, each having a speed of 30 km/h, are headed at each other on the same straight track. A bird that can fly 60 km/h flies off the front of one train when they are 60 km apart and heads directly for the other train. On reaching the other train, the bird flies directly back to the first train, and so forth. (We have no idea why a bird would behave in this way.) What is the total distance the bird travels before the trains collide?

8. Figure 2-21 shows a general situation in which a stream of people attempt to escape through an exit door that turns out to be locked. The people move toward the door at speed Vs = 3.50 m/s, are each d = 0.25 m in depth, and are separated by L = 1.75 m. The arrangement in Fig. 2-21 occurs at time t = 0. (a) At what average rate does the layer of people at the door increase? (b) At what time does the layer's depth reach 5.0m?

9. In 1 km races, runner 1 on track 1 (with time 2 min, 27.95 s) appears to be faster than runner 2 on track 2 (2 min, 28.15 s). However, length Lz of track 2 might be slightly greater than length LI of track 1. How large can Lz - LI be for us still to conclude that runner 1 is faster?

11. You are to drive to an interview in another town, at a distance of 300 km on an expressway. The interview is at 11:15 A. M. You plan to drive at 100 km/h, so you leave at 8:00 A. M. to allow some extra time. You drive at that speed for the first 100 km, but then construction work forces you to slow to 40 km/h for 40 km. What would be the least speed needed for the rest of the trip to arrive in time for the interview?

12. An abrupt slowdown in concentrated traffic can travel as a pulse, termed a shock wave, along the line of cars, either downstream (in the traffic direction) or upstream, or it can be stationary. Figure 2-22 shows a uniformly spaced line of cars moving at speed v = 25.0 m/s toward a uniformly spaced line of slow cars moving at speed Vs = 5.00 m/s. Assume that each faster car adds length L = 12.0 m (car length plus buffer zone) to the line of slow cars when it joins the line, and assume it slows abruptly at the last instant. (a) For what separation distance d between the faster cars does the shock wave remain stationary? If the separation is twice that amount, what are the (b) speed and (c) direction (upstream or downstream) of the shock wave?

13. You drive on Interstate 10 from San Antonio to Houston, half the time at 55 km/h and the other half at 90 km/h. On the way back you travel half the distance at 55 km/h and the other half at 90 km/h. What is your average speed (a) from San Antonio to Houston, (b) from Houston back to San Antonio, and ( c) for the entire trip? (d) What is your average velocity for the entire trip? (e) Sketch x versus t for (a), assuming the motion is all in the positive x direction. Indicate how the average velocity can be found on the sketch.

14. An electron moving along the x axis has a position given by x = 16te - t m, where t is in seconds. How far is the electron from the origin when it momentarily stops?

15. (a) If a particle's position is given by x = 4 - 12t + 3t 2 (where t is in seconds and x is in meters), what is its velocity at t = 1 s? (b) Is it moving in the positive or negative direction of x just then? (c) What is its speed just then? (d) Is the speed increasing or decreasing just then? (e) Is there ever an instant when the velocity is zero? If so, give the time t; if not, answer no. (f) Is there a time after t = 3 s when the particle is moving in the negative direction of x? If so, give the time t; if not, answer no.

16. The position function x(t) of a particle moving along an x axis is x = 4.0 - 6.0t 2. with x in meters and t in seconds. (a) At what time and (b) where does the particle (momentarily) stop? At what (c) negative time and (d) positive time does the particle pass through the origin? (e) Graph x versus t for the range - 5 s to + 5 s. (f) To shift the curve rightward on the graph, should we include the term +20t or the term -20t in x(t)? (g) Does that inclusion increase or decrease the value of x at which the particle momentarily stops?

17. The position of a particle moving along the x axis is given in centimeters by x = 9.75 +1.50t 3. where t is in seconds. Calculate (a) the average velocity during the time interval t = 2.00 s to t = 3.00 s; (b) the instantaneous velocity at t = 2.00 s; (c) the instantaneous velocity at t = 3.00 s; (d) the instantaneous velocity at t = 2.50 s; and (e) the instantaneous velocity when the particle is midway between its positions at t = 2.00 sand t = 3.00 s. (f) Graph x versus t and indicate your answers graphically.

18. The position of a particle moving along an x axis is given by x = 12t 2 - 2t 3. where x is in meters and t is in seconds. Determine (a) the position, (b) the velocity, and (c) the acceleration of the particle at t = 3.0 s. (d) What is the maximum positive coordinate reached by the particle and (e) at what time is it reached? (f) What is the maximum positive velocity reached by the particle and (g) at what time is it reached? (h) What is the acceleration of the particle at the instant the particle is not moving (other than at t = 0)? (i) Determine the average velocity of the particle between t = 0 and t = 3 s.

19. At a certain time a particle had a speed of 18 m/s in the positive x direction, and 2.4 s later its speed was 30 m/s in the opposite direction. What is the average acceleration of the particle during this 2.4 s interval?

20. (a) If the position of a particle is given by x = 20t - 5t 3. where x is in meters and t is in seconds, when, if ever, is the particle's velocity zero? (b) When is its acceleration a zero? (c) For what time range (positive or negative) is a negative? (d) Positive? (e) Graph x(t), v(t), and a(t).

21. From t = 0 to t = 5.00 min, a man stands still, and from t = 5.00 min to t = 10.0 min, he walks briskly in a straight line at a constant speed of 2.20 m/s. What are (a) his average velocity v avg and (b) his average acceleration a avg in the time interval 2.00 min to 8.00 min? What are (c) v avg and (d) a avg in the time interval 3.00 min to 9.00 min? (e) Sketch x versus t and v versus t, and indicate how the answers to (a) through (d) can be obtained from the graphs.

22. The position of a particle moving along the x axis depends on the time according to the equation x = ct 2 - bt 3. where x is in meters and t in seconds. What are the units of (a) constant e and (b) constant b? Let their numerical values be 3.0 and 2.0, respectively. (c) At what time does the particle reach its maximum positive x position? From t = 0.0 s to t = 4.0 s, (d) what distance does the particle move and (e) what is its displacement? Find its velocity at times (f) 1.0 s, (g) 2.0 s, (h) 3.0 s, and (i) 4.0 s. Find its acceleration at times (j) 1.0 s, (k) 2.0 s, (1) 3.0 s, and (m) 4.0 s.

23. An electron with an initial velocity Vo = 1.50 x 10 5 m/s enters a region of length L = 1.00 cm where it is electrically accelerated (Fig. 2-23). It emerges with v = 5.70 x 10 6 m/s. What is its acceleration, assumed constant?

24. Catapulting mushrooms. Certain mushrooms launch their spores by a catapult mechanism. As water condenses from the air onto a spore that is attached to the mushroom, a drop grows on one side of the spore and a film grows on the other side. The spore is bent over by the drop's weight, but when the film reaches the drop, the drop's water suddenly spreads into the film and the spore springs upward so rapidly that it is slung off into the air. Typically, the spore reaches a speed of 1.6 m/s in a 5.0?m launch; its speed is then reduced to zero in 1.0 mm by the air. Using that data and assuming constant accelerations, find the acceleration in terms of g during (a) the launch and (b) the speed reduction.

25. An electric vehicle starts from rest and accelerates at a rate of 2.0 m/s 2 in a straight line until it reaches a speed of 20 m/s. The vehicle then slows at a constant rate of 1.0 m/s 2 until it stops. (a) How much time elapses from start to stop? (b) How far does the vehicle travel from start to stop?

26. A muon (an elementary particle) enters a region with a speed of 5.00 x 10 6 m/s and then is slowed at the rate of 1.25 x 10 14 m/s 2. (a) How far does the muon take to stop? (b) Graph x versus t and v versus t for the muon.

27. An electron has a constant acceleration of +3.2 m/s 2. At a certain instant its velocity is +9.6 m/s. What is its velocity (a) 2.5 s earlier and (b) 2.5 s later?

28. On a dry road, a car with good tires may be able to brake with a constant deceleration of 4.92 m/s 2. (a) How long does such a car, initially traveling at 24.6 m/s, take to stop? (b) How far does it travel in this time? (c) Graph x versus t and v versus t for the deceleration.

29. A certain elevator cab has a total run of 190 m and a maximum speed of 305 m/min, and it accelerates from rest and then back to rest at 1.22 m/s 2. (a) How far does the cab move while accelerating to full speed from rest? (b) How long does it take to make the nonstop 190 m run, starting and ending at rest?

30. The brakes on your car can slow you at a rate of 5.2 m/s 2. (a) If you are going 137 km/h and suddenly see a state trooper, what is the minimum time in which you can get your car under the 90 km/h speed limit? (The answer reveals the futility of braking to keep your high speed from being detected with a radar or laser gun.) (b) Graph x versus t and v versus t for such a slowing.

31. Suppose a rocket ship in deep space moves with constant acceleration equal to 9.8 m/s 2. which gives the illusion of normal gravity during the flight. (a) If it starts from rest, how long will it take to acquire a speed one-tenth that of light, which travels at 3.0 x 10 8 m/s? (b) How far will it travel in so doing?

32. A world's land speed record was set by Colonel John P. Stapp when in March 1954 he rode a rocket-propelled sled that moved along a track at 1020 km/h. He and the sled were brought to a stop in 1.4 s. (See Fig. 2-7.) In terms of g, what acceleration did he experience while stopping?

33. A car traveling 56.0 km/h is 24.0 m from a barrier when the driver slams on the brakes. The car hits the barrier 2.00 s later. (a) What is the magnitude of the car's constant acceleration before impact? (b) How fast is the car traveling at impact?

34. In Fig. 2-24, a red car and a green car, identical except for the color, move toward each other in adjacent lanes and parallel to an x axis. At time t = 0, the red car is at x r = 0 and the green car is at x g = 220 m. If the red car has a constant velocity of 20 km/h, the cars pass each other at x = 44.5 m, and if it has a constant velocity of 40 km/h, they pass each other at x = 76.6 m. What are (a) the initial velocity and (b) the constant acceleration of the green car?

35. Figure 2-24 shows a red car and a green car that move toward each other. Figure 2-25 is a graph of their motion, showing the positions x g0 = 270 m and x r0 = -35.0 m at time t = 0. The green car has a constant speed of 20.0 m/s and the red car begins from rest. What is the acceleration magnitude of the red car?

36. A car moves along an x axis through a distance of 900 m, starting at rest (at x = 0) and ending at rest (at x = 900 m). Through the first 1/4 of that distance, its acceleration is +2.25 m/s 2. Through the rest of that distance, its acceleration is -0.750 m/s 2. What are (a) its travel time through the 900 m and (b) its maximum speed? (c) Graph position x, velocity v, and acceleration a versus time t for the trip.

37. Figure 2-26 depicts the motion x(m) of a particle moving along an x axis with a constant acceleration. The figure's vertical scaling is set by Xs = 6.0 m. What are the (a) magnitude and (b) direction of the particle's acceleration?

38. (a) If the maximum acceleration that is tolerable for passengers in a 0,t (s) subway train is 1.34 m/s 2 and subway stations are located 806 m apart, what is the maximum speed a subway train can attain between stations? (b) What is the travel time between stations? (c) If a subway train stops for 20 s at each station, what is the maximum average speed of the train, from one start-up to the next? (d) Graph x, v, and a versus t for the interval from one start-up to the next.

39. Cars A and B move in the same direction in adjacent lanes. The position x of car A is given in Fig. 2-27, from time t = 0 to t = 7.0 s. The figure's vertical scaling is set by x s = 32.0 m. At t = 0, car B is at x = 0, with a velocity of 12 m/s and a negative constant acceleration a b. (a) What must a b be such that the cars are (momentarily) side by side (momentarily at the same value of x) at t = 4.0 s? (b) For that value of a b. how many times are the cars side by side? (c) Sketch the position x of car B versus time t on Fig. 2-27. How many times will the cars be side by side if the magnitude of acceleration a b is (d) more than and (e) less than the answer to part (a)?

40. You are driving toward a traffic signal when it turns yellow. Your speed is the legal speed limit of Va = 55 km/h; your best deceleration rate has the magnitude a = 5.18 m/s 2. Your best reaction time to begin braking is T = 0.75 s. To avoid having the front of your car enter the intersection after the light turns red, should you brake to a stop or continue to move at 55 km/h if the distance to the intersection and the duration of the yellow light are (a) 40 m and 2.8 s, and (b) 32 m and 1.8 s? Give an answer of brake, continue, either (if either strategy works), or neither (if neither strategy works and the yellow duration is inappropriate).

41. As two trains move along a track, their conductors suddenly notice that they are headed toward each other. Figure 2-28 gives their velocities V as functions of time t as the conductors slow the trains. The figure's vertical scaling is set by Vs = 40.0 m/s. The slowing processes begin when the trains are 200 m apart. What is their separation when both trains have stopped?

42. You are arguing over a cell phone while trailing an unmarked police car by 25 m; both your car and the police car are traveling at 110 km/h. Your argument diverts your attention from the police car for 2.0 s (long enough for you to look at the phone and yell, "1 won't do that!"). At the beginning of that 2.0 s, the police officer begins braking suddenly at 5.0 m/s 2. (a) What is the separation between the two cars when your attention finally returns? Suppose that you take another 0.04 s to realize your danger and begin braking. (b) If you too brake at 5.0 m/s 2. what is your speed when you hit the police car?

43. When a high-speed passenger train traveling at 161 km/h rounds a bend, the engineer is shocked to see that a locomotive has improperly entered onto the track from a siding and is a distance D = 676 m ahead (Fig. 2-29). The locomotive is moving at 29.0 km/h. The engineer of the high-speed train immediately applies the brakes. (a) What must be the magnitude of the resulting constant deceleration if a collision is to be just avoided? (b) Assume that the engineer is at x = 0 when, at t = 0, he first spots the locomotive. Sketch x(t) curves for the locomotive and high speed train for the cases in which a collision is just avoided and is not quite avoided.

44. When startled, an armadillo will leap upward. Suppose it rises 0.544 m in the first 0.200 s. (a) What is its initial speed as it leaves the ground? (b) What is its speed at the height of 0.544 m? (c) How much higher does it go?

45. (a) With what speed must a ball be thrown vertically from ground level to rise to a maximum height of 50 m? (b) How long will it be in the air? (c) Sketch graphs of y, v, and a versus t for the ball. On the first two graphs, indicate the time at which 50 m is reached.

46. Raindrops fall 1700 m from a cloud to the ground. (a) If they were not slowed by air resistance, how fast would the drops be moving when they struck the ground? (b) Would it be safe to walk outside during a rainstorm?

47. At a construction site a pipe wrench struck the ground with a speed of 24 m/s. (a) From what height was it inadvertently dropped? (b) How long was it falling? (c) Sketch graphs of y, v, and a versus t for the wrench.

48. A hoodlum throws a stone vertically downward with an initial speed of 12.0 m/s from the roof of a building, 30.0 m above the ground. (a) How long does it take the stone to reach the ground? (b) What is the speed of the stone at impact?

49. A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground?

50. At time t = 0, apple 1 is dropped from a bridge onto a roadway beneath the bridge; somewhat later, apple 2 is thrown down from the same height. Figure 2-30 gives the vertical positions y of the apples versus t during the falling, until both apples have hit the roadway. The scaling is set by ts = 2.0 s. With approximately what speed is apple 2 thrown down?

51. As a runaway scientific balloon ascends at 19.6 m/s, one of its instrument packages breaks free of a harness and free-falls. Figure 2-31 gives the vertical velocity of the package versus time, from before it breaks free to when it reaches the ground. (a) What maximum height above the break-free point does it rise? b) How high is the break-free point above the ground?

52. A bolt is dropped from a bridge under construction, falling 90 m to the valley below the bridge. (a) In how much time does it pass through the last 20% of its fall? What is its speed (b) when it begins that last 20% of its fall and (c) when it reaches the valley beneath the bridge?

53. A key falls from a bridge that is 45 m above the water. It falls directly into a model boat, moving with constant velocity, that is 12 m from the point of impact when the key is released. What is the speed of the boat?

54. A stone is dropped into a river from a bridge 43.9 ill above the water. Another stone is thrown vertically down 1.00 s after the first is dropped. The stones strike the water at the same time. (a) What is the initial speed of the second stone? (b) Plot velocity versus time on a graph for each stone, taking zero time as the instant the first stone is released.

55. A ball of moist clay falls 15.0 m to the ground. It is in contact with the ground for 20.0 ms before stopping. (a) What is the magnitude of the average acceleration of the ball during the time it is in contact with the ground? (Treat the ball as a particle.) (b) Is the average acceleration up or down?

56. Figure 2-32 shows the speed v versus height y of a ball tossed directly upward, along a y axis. Distance d is 0.40 m. The speed at height Y A is V A The speed at height Y B is 1/3 V A What is speed V A ?

57. To test the quality of a tennis ball, you drop it onto the floor from a height of 4.00 m. It rebounds to a height of 2.00 m. If the ball is in contact with the floor for 12.0 ms, (a) what is the magnitude of its average acceleration during that contact and (b) is the average acceleration up or down?

58. An object falls a distance h from rest. If it travels 0.50h in the last 1.00 s, find (a) the time and (b) the height of its fall. (c) Explain the physically unacceptable solution of the quadratic equation in t that you obtain.

59. Water drips from the nozzle of a shower onto the floor 200 cm below. The drops fall at regular (equal) intervals of time, the first drop striking the floor at the instant the fourth drop begins to fall. When the first drop strikes the floor, how far below the nozzle are the (a) second and (b) third drops?

60. A rock is thrown vertically upward from ground level at time t = 0. At t = 1.5 s it passes the top of a tall tower, and 1.0 s later it reaches its maximum height. What is the height of the tower?

61. A steel ball is dropped from a building's roof and passes a window, taking 0.125 s to fall from the top to the bottom of the window, a distance of 1.20 m. It then falls to a sidewalk and bounces back past the window, moving from bottom to top in 0.125 s. Assume that the upward flight is an exact reverse of the fall. The time the ball spends below the bottom of the window is 2.00 s. How tall is the building?

62. A basketball player grabbing a rebound jumps 76.0 cm vertically. How much total time (ascent and descent) does the player spend (a) in the top 15.0 cm of this jump and (b) in the bottom 15.0 cm? Do your results explain why such players seem to hang in the air at the top of a jump?

63. A drowsy cat spots a flowerpot that sails first up and then down past an open window. The pot is in view for a total of 0.50 s, and the top-to-bottom height of the window is 2.00 m. How high above the window top does the flowerpot go?

64. A ball is shot vertically upward from the surface of another planet. A plot of Y versus t for the ball t (s) is shown in Fig. 2-33, where Y is the height of the ball above its starting point and t = 0 at the instant the ball is shot. The figure's vertical scaling is set by ys = 30.0 m. What are the magnitudes of (a) the free-fall acceleration on the planet and (b) the initial velocity of the ball?

65. Figure 2-13a gives the acceleration of a volunteer's head and torso during a rear-end collision. At maximum head acceleration, what is the speed of (a) the head and (b) the torso?

66. In a forward punch in karate, the fist begins at rest at the waist and is brought rapidly forward until the arm is fully extended. The speed v(t) of the fist is given in Fig. 2-34 for someone skilled in karate. The vertical scaling is set by v s = 8.0 m/s. How far has the fist moved at (a) time t = 50 ms and (b) when the speed of the fist is maximum?

67. When a soccer ball is kicked toward a player and the player deflects the ball by "heading" it, the acceleration of the head during the collision can be significant. Figure 2-35 gives the measured acceleration a(t) of a soccer player's head for a bare head and a helmeted head, starting from rest. The scaling on the vertical axis is set by as a s = 200 m/s 2. At time t = 7.0 ms, what is the difference in the speed acquired by the bare head and the speed acquired by the helmeted head?

68. A salamander of the genus Hydromantes captures prey by launching its tongue as a projectile: The skeletal part of the tongue is shot forward, unfolding the rest of the tongue, until the outer portion lands on the prey, sticking to it. Figure 2-36 shows the acceleration magnitude a versus time t for the acceleration phase of the launch in a typical situation. The indicated accelerations are a 2 = 400 m/s 2 and a l = 100 m/s 2. What is the outward speed of the tongue at the end of the acceleration phase?

69. How far does the runner whose velocity - time graph is shown in Fig. 2-37 travel in 16 s? The figure's vertical scaling is set by vs = 8.0 m/s.

70. Two particles move along an x axis. The position of particle 1 is given by x = 6.00t 2 + 3.00t + 2.00 (in meters and seconds); the acceleration of particle 2 is given by a = -8.00t (in meters per second squared and seconds) and, at t = 0, its velocity is 20 m/s. When the velocities of the particles match, what is their velocity?

71. In an arcade video game, a spot is programmed to move across the screen according to x = 9.00t – 0.750t 3. where x is distance in centimeters measured from the left edge of the screen and t is time in seconds. When the spot reaches a screen edge, at either x = 0 or x = 15.0 cm, t is reset to 0 and the spot starts moving again according to x(t). (a) At what time after starting is the spot instantaneously at rest? (b) At what value of x does this occur? (c) What is the spot's acceleration (including sign) when this occurs? (d) Is it moving right or left just prior to coming to rest? (e) Just after? (f) At what time t > 0 does it first reach an edge of the screen?

72. A rock is shot vertically upward from the edge of the top of a tall building. The rock reaches its maximum height above the top of the building 1.60 s after being shot. Then, after barely missing the edge of the building as it falls downward, the rock strikes the ground 6.00 s after it is launched. In SI units: (a) with what upward velocity is the rock shot, (b) what maximum height above the top of the building is reached by the rock, and (c) how tall is the building?

73. At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.2 m/s 2. At the same instant a truck, traveling with a constant speed of 9.5 m/s, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the automobile be traveling at that instant?

74. A pilot flies horizontally at 1300 km/h, at height h = 35 m above initially level ground. However, at time t = 0, the pilot begins to fly over ground sloping upward at angle θ = 4.3° (Fig. 2-38). If the pilot does not change the airplane's heading, at what time t does the plane strike the ground?

75. To stop a car, first you require a certain reaction time to begin braking; then the car slows at a constant rate. Suppose that the total distance moved by your car during these two phases is 56.7 m when its initial speed is 80.5 km/h, and 24.4 m when its initial speed is 48.3 km/h. What are (a) your reaction time and (b) the magnitude of the acceleration?

76. Figure 2-39 shows part of a street where traffic flow is to be controlled to allow a platoon of cars to move smoothly along the street. Suppose that the platoon leaders have just reached intersection 2, where the green appeared when they were distance d from the intersection. They continue to travel at a certain speed vp (the speed limit) to reach intersection 3, where the green appears when they are distance d from it. The intersections are separated by distances D 23 and D 12 (a) What should be the time delay of the onset of green at intersection 3 relative to that at intersection 2 to keep the platoon moving smoothly? Suppose, instead, that the platoon had been stopped by a red light at intersection 1. When the green comes on there, the leaders require a certain time t, to respond to the change and an additional time to accelerate at some rate a to the cruising speed vp. (b) If the green at intersection 2 is to appear when the leaders are distance d from that intersection, how long after the light at intersection 1 turns green should the light at intersection 2 turn green?

77. A hot rod can accelerate from 0 to 60 km/h in 5.4 s. (a) What is its average acceleration, in m/s 2. during this time? (b) How far will it travel during the 5.4 s, assuming its acceleration is constant? (c) From rest, how much time would it require to go a distance of 0.25 km if its acceleration could be maintained at the value in (a)?

78. A red train traveling at 72 km/h and a green train traveling at 144 km/h are headed toward each other along a straight, level track. When they are 950 m apart, each engineer sees the other's train and applies the brakes. The brakes slow each train at the rate of 1.0 m/s 2. Is there a collision? If so, answer yes and give the speed of the red train and the speed of the green train at impact, respectively. If not, answer no and give the separation between the trains when they stop.

79. At time t = 0, a rock climber accidentally allows a piton to fall freely from a high point on the rock wall to the valley below him. Then, after a short delay, his climbing partner, who is 10 m higher on the wall, throws a piton downward. The positions y of the pitons versus t during the falling are given in Fig.2-40. With what speed is the second piton thrown?

80. A train started from rest and moved with constant acceleration. At one time it was traveling 30 m/s, and 160 m farther on it was traveling 50 m/s. Calculate (a) the acceleration, (b) the time required to travel the 160 m mentioned, (c) the time required to attain the speed of 30 m/s, and (d) the distance moved from rest to the time the train had a speed of 30 m/s. (e) Graph x versus t and v versus t for the train, from rest.

81. A particle's acceleration along an x axis is a = 5.0t, with t in seconds and a in meters per second squared. At t = 2.0 s, its velocity is +17 m/s. What is its velocity at t = 4.0 s?

82. Figure 2-41 gives the acceleration a versus time t for a particle moving along an x axis. The a-axis scale is set by as = 12.0 m/s 2. At t = -2.0 s, the particle's velocity is 7.0 m/s. What is its velocity at t = 6.0 s?

83. Figure 2-42 shows a simple device for measuring your reaction time. It consists of a cardboard strip marked with a scale and two large dots. A friend holds the strip vertically, with thumb and forefinger at the dot on the right in Fig. 2-42. You then position your thumb and forefinger at the other dot (on the left in Fig. 2-42), being careful not to touch the strip. Your friend releases the strip, and you try to pinch it as soon as possible after you see it begin to fall. The mark at the place where you pinch the strip gives your reaction time. (a) How far from the lower dot should you place the 50.0 ms mark? How much higher should you place the marks for (b) 100, (c) 150, (d) 200, and (e) 250 ms?

84. A rocket-driven sled running on a straight, level track is used to investigate the effects of large accelerations on humans. One such sled can attain a speed of 1600 km/h in 1.8 s, starting from rest. Find (a) the acceleration (assumed constant) in terms of g and (b) the distance traveled.

85. A mining cart is pulled up a hill at 20 km/h and then pulled back down the hill at 35 km/h through its original level. (The time required for the cart's reversal at the top of its climb is negligible.) What is the average speed of the cart for its round trip, from its original level back to its original level?

86. A motorcyclist who is moving along an x axis directed toward the east has an acceleration given by a = (6.1 - 1.2t) m/s 2 for 0 ≤ t ≤ 6.0 s. At t = 0, the velocity and position of the cyclist are 2.7 m/s and 7.3 m. (a) What is the maximum speed achieved by the cyclist? (b) What total distance does the cyclist travel between t = 0 and 6.0 s?

87. When the legal speed limit for the New York Thruway was increased from 55 mi/h to 65 mi/h, how much time was saved by a motorist who drove the 700 km between the Buffalo entrance and the New York City exit at the legal speed limit?

88. A car moving with constant acceleration covered the distance between two points 60.0 m apart in 6.00 s. Its speed as it passed the second point was 15.0 m/s. (a) What was the speed at the first point? (b) What was the magnitude of the acceleration? (c) At what prior distance from the first point was the car at rest? (d) Graph x versus t and v versus t for the car, from rest (t = 0).

89. A certain juggler usually tosses balls vertically to a height H. To what height must they be tossed if they are to spend twice as much time in the air?

90. A particle starts from the origin at t = 0 and moves along the positive x axis. A graph of the velocity of the particle as a function of the g time is shown in Fig. 2-43; the v-axis scale is set by v s = 4.0 m/s. (a) What is the coordinate of the particle at t = 5.0 s? (b) What is the velocity of the particle at t = 5.0 s? (c) What is the acceleration of the particle at t = 5.0 s? (d) What is the average velocity of the particle between t = 1.0 sand t = 5.0 s? (e) What is the average acceleration of the particle between t = 1.0 s and t = 5.0 s?

91. A rock is dropped from a 100-m-high cliff. How long does it take to fall (a) the first 50 m and (b) the second 50 m?

92. Two subway stops are separated by 1100 m. If a subway train accelerates at +1.2 m/s 2 from rest through the first half of the distance and decelerates at -1.2 m/s 2 through the second half, what are (a) its travel time and (b) its maximum speed? (c) Graph x, v, and a versus t for the trip.

93. A stone is thrown vertically upward. On its way up it passes point A with speed v, and point B, 3.00 m higher than A, with speed ½v. Calculate (a) the speed v and (b) the maximum height reached by the stone above point B.

94. A rock is dropped (from rest) from the top of a 60-m-tall building. How far above the ground is the rock 1.2 s before it reaches the ground?

95. An iceboat has a constant velocity toward the east when a sudden gust of wind causes the iceboat to have a constant acceleration toward the east for a period of 3.0 s. A plot of x versus t is shown in Fig. 2-44, where t = 0 is taken to be the instant the wind starts to blow and the positive x axis is toward the east. (a) What is the acceleration of the iceboat during the 3.0 s interval? (b) What is the velocity of the iceboat at the end of the 3.0 s interval? (c) If the acceleration remains constant for an additional 3.0 s, how far does the iceboat travel during this second 3.0 s interval?

96. A lead ball is dropped in a lake from a diving board 5.20 m above the water. It hits the water with a certain velocity and then sinks to the bottom with this same constant velocity. It reaches the bottom 4.80 s after it is dropped. (a) How deep is the lake? What are the (b) magnitude and (c) direction (up or down) of the average velocity of the ball for the entire fall? Suppose that all the water is drained from the lake. The ball is now thrown from the diving board so that it again reaches the bottom in 4.80 s. What are the (d) magnitude and (e) direction of the initial velocity of the ball?

97. The single cable supporting an unoccupied construction elevator breaks when the elevator is at rest at the top of a 120-m-high building. (a) With what speed does the elevator strike the ground? (b) How long is it falling? (c) What is its speed when it passes the halfway point on the way down? (d) How long has it been falling when it passes the halfway point?

98. Two diamonds begin a free fall from rest from the same height, 1.0 s apart. How long after the first diamond begins to fall will the two diamonds be 10 m apart?

99. A ball is thrown vertically downward from the top of a 36.6-m-tall building. The ball passes the top of a window that is 12.2 m above the ground 2.00 s after being thrown. What is the speed of the ball as it passes the top of the window?

100. A parachutist bails out and freely falls 50 m. Then the parachute opens, and thereafter she decelerates at 2.0 m/s 2. She reaches the ground with a speed of 3.0 m/s. (a) How long is the parachutist in the air? (b) At what height does the fall begin?

101. A ball is thrown down vertically with an initial speed of v0 from a height of h. (a) What is its speed just before it strikes the ground? (b) How long does the ball take to reach the ground? What would be the answers to (c) part a and (d) part b if the ball were thrown upward from the same height and with the same initial speed? Before solving any equations, decide whether the answers to (c) and (d) should be greater than, less than, or the same as in (a) and (b).

102. The sport with the fastest moving ball is jai alai, where measured speeds have reached 303 km/h. If a professional jai alai player faces a ball at that speed and involuntarily blinks, he blacks out the scene for 100 ms. How far does the ball move during the blackout?

1. The position vector for an electron is r = (5.0 m)i - (3.0 m)j + (2.0 m)k. (a) Find the magnitude of r. (b) Sketch the vector on a right-handed coordinate system.

2. A watermelon seed has the following coordinates: x = -5.0 m, y = 8.0 m, and z = 0 m. Find its position vector (a) in unit-vector notation and as (b) a magnitude and (c) an angle relative to the positive direction of the x axis. (d) Sketch the vector on a right-handed coordinate system. If the seed is moved to the xyz coordinates (3.00 m, 0 m, 0 m), what is its displacement (e) in unit-vector notation and as (f) a magnitude and (g) an angle relative to the positive x direction?

3. A positron undergoes a displacement Δr = 2.0i - 3.0j + 6.0k, ending with the position vector r = 3.0j - 4.0k, in meters. What was the positron's initial position vector?

4. The minute hand of a wall clock measures 10 cm from its tip to the axis about which it rotates. The magnitude and angle of the displacement vector of the tip are to be determined for three time intervals. What are the (a) magnitude and (b) angle from a quarter after the hour to half past, the (c) magnitude and (d) angle for the next half hour, and the (e) magnitude and (f) angle for the hour after that?

Online homework help for college and high school students. Get homework help and answers to your toughest questions in math, algebra, trigonometry, precalculus, calculus, physics, engineering mechanics. Homework assignments with step-by-step solutions.

The Georgia 4-H Project and Activity Guidebook provides up to date information concerning 4-H competitive events, policies, procedures and guidelines for 4-H activities as well as other general information for clubs and members.

The Guidebook is updated regularly. Be sure that any printed information you have from the book is the most up to date. Sections and activities will include a updated date whenever a change has been made.

Georgia 4-H Project & Activity Guidebook Sections

Project Achievement includes project objectives, project list & codes, general guidelines for cloverlea, junior and seniorf projects

Special Events & Judging Activities includes project objectives and general guidelines for other competitive 4-H events & ocupaciones

Georgia 4-H Code of Ethics Honesty, fairness, consistency, and sportsmanship are learned, not inherited traits. The most important role a 4-H leader (paid or volunteer) can play in a 4-H member's development is acting as a role model by exhibiting these characteristics. We understand, as youth educators, the only way a 4-H’er truly learns and expands his or her horizon is by making his or her own decisions. “Decisions” include preparing his or her own portfolio, demonstration, speech, or show animal.

A 4-H Leader's responsibility is teaching the 4-H’er the process by which he or she can make a decision, give a presentation, or train an animal using the resources available to him or her. Realizing that one 4-H’er may not have the experience or intellectual development that another may have, indicates to the leader that this 4-H’er may require more help on his or her project than others.

Doing the work for a 4-H member totally circumvents the learning progression which is inherent in the framework of our organization. In congruence with this philosophy, no substantially finished demonstration, including speech and posters or any other 4-H project will be provided to a 4-H’er to be presented as his or her own work in competition. If materials are shared with a 4-H’er, it is for reference and resource purposes only.

The process in 4-H work from Cloverleaf (Elementary) to Senior (High School) levels was created to challenge the young person's intellectual, creative, and emotional capacities. The Georgia 4-H Mission statement emphasizes that 4-H should encourage youth to become self - directing, productive, and contributing citizens. The role of the 4-H Leader is to support, lead, encourage, develop and teach young people. Our role is not to do the work for the 4-H’er. Original NC Agents 1980's, Revision 1999 Georgia 4-H Staff

Ch4 H1 - Exercise 4-2 (10 minutes) Weighted-Average Method.

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(10 minutes) Weighted-Average Method Equivalent Units Materials Conversion Units transferred out. 190,000 190,000 Work in process, ending: 15,000 units × 80%. 12,000 15,000 units × 40%. 6,000 Equivalent units of production. 202,000 196,000 Exercise 4-3 (10 minutes) Weighted-Average Method 1. Materials Labor Overhead Cost of beginning work in process inventory. $ 18,000 $ 5,500 $ 27,500 Cost added during the period. 238,900 80,300 401,500 Total cost (a). $256,900 $85,800 $429,000 Equivalent units of production (b). 35,000 33,000 33,000 Cost per equivalent unit (a) ÷ (b). $7.34 $2.60 $13.00 2. Cost per equivalent unit for materials. $ 7.34 Cost per equivalent unit for labor. 2.60

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Volunteers keep Tipton 4-H Fair moving along

TIPTON — Mary Day was on her fourth cup of Diet Coke. The fizzy beverage kept her going as she tackled the tasks at hand.

She’d been at the fairgrounds since 8 a. m. Monday. She sat in the back of the barn casually surveying the sheep show, while carrying on a conversation with co-worker Janie Hinds.

Day and Hinds have been busy signing children up for livestock auctions, rescheduling a dog show and helping young 4-H’ers prepare for their events since the Tipton County 4-H Fair opened last week.

From 8 a. m. to nearly midnight, Day and her co-workers seem to almost live at the fairgrounds.

“We set up a week or two before. By the time everybody gets here Friday, we’re exhausted,” Day said. “Adrenaline keeps you going.”

Nevertheless, she loves the fair.

“I like to watch the kids in the 4-H fair. It takes me back.”

Not far from the sheep show, 8-year-old Gabriel Smith and his father, Brian Teuscher, were checking out the entries in the 4-H building. This was Gabriel’s first year in mini 4-H.

Gabriel stared at the ribbon next to the cookies he made with his grandmother.

“Mom said I was going to do it,” he said.

His older brother, Klayton, 13, boasted of selling breadsticks for $70.

“I was hoping for $120,” he said.

Next year both boys want to show cattle. A former 4-H’er, Teuscher looks forward to helping his sons raise livestock.

“I’ve got a farming background and his mom grew up in the country,” he said.

Not everyone comes to the Tipton County fair to show off 4-H projects. Several people come for the food.

Workers with the Tipton County Extension Homemakers Association arrived early Monday morning to fix a chicken noodle lunch for fair goers.

There are perks to slaving away in the kitchen, according to Agnes Mitchell. “Sometimes we have a pie we don’t know what it is. So we have to try it.”

Although the fair ends today, Day and her co-workers will have little time to relax. They must now start preparations for the Indiana State Fair and plan for next year’s fair.

Day admits she’s already looking forward to a few years from now, when her son, Grant, can start competing in 4-H.

“4-H is really in your blood,” she said.

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Health At Your Desk: Moving Beyond Ergonomics Presentation

Enjoy a complimentary ergonomics presentation brought to you by Dr. Brittani Young of Airrosti Rehab Center!

Join us for an educational and interactive workshop where you'll learn simple, proven techniques to avoid repetitive strain and postural injuries associated with common workplace environments. Increase flexibility, strength, and range of motion while learning ongoing solutions to relieve tension and stress. **Airrosti will provide therabands and stretch/exercise handouts to all participants.**

About Dr. Young: I am an Airrosti provider who specializes in the prevention and treatment of sprains, strains, and chronic pain. Airrosti focuses on correcting soft tissue injuries without the use of imaging, injections, or surgery.

To register for this event, search under 'Educational Programs' at the link below. Hurry - there are only 50 spots available!

*Please only register if you can actually attend the class. Only those on the registration list will be able to participate.

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VFW Post #7850 Ladies Auxiliary Donates To 4-H Fishing Team In Support Of ‘The Moving Wall’

The Owen County 4-H Fishing Team moved $700 closer to its goal of raising $6,000 to help bring ‘The Moving Wall,’ a half-scale replica of the Vietnam War Memorial to the Owen County 4-H Fairgrounds in August thanks to a check donation from the Gosport VFW Post #7850 Ladies Auxiliary. Taking part in the special presentation were, left to right: fishing team members David and MaKayla Freeman, ladies auxiliary treasurer Arleen Crawford, and chaplain Kisha Minnick. David and MaKayla are the children of Stephanie and Shane Freeman of Spencer. (Staff Photo)

© 2009-2017 Spencer Evening World, Inc. No commercial reproduction without written consent. Electronic reproduction of any kind forbidden without written consent.

Rate of Change

In Calculus, the rate of change equation can easily be obtained from the slope equation. The slope of the equation is also called as rate of change of the equation.

The subject of calculus had its origin mainly in the geometrical problem of determination of the gradient of a curve at a point, thereby resulting in the determination of the tangent at the point. This subject has also rendered possible precise formulations of a large number of physical concepts such as velocity at an instant, acceleration at an instant, curvature at a point, density at a point, specific heat at any temperature. All these appears as local or instantaneous rate of change as against the average rate of change.

Many practical relationships involve independent and dependent quantities. For example, the volume of water in a tank changes when there is change in the depth of water in the tank. Hence, the depth of the tank is the independent quantity and the volume is the dependent quantity. When we through a stone on surface of water there are ripples whose radius increases for few sec. That is the area of the circle increases as the radius increases. Hence, we see that there is increase in area of the circles as there is increase in radius. Hence, radius is the independent variable and area is the dependent variable. These are some of the rate of change examples.

Rate of Change Definition

Basically, the ratio of the change in the output value and change in the input value of a function is called as rate of change. Rate of change is the ratio that shows the relationship between the two variables in equation. In general, the coefficient of $x$ is called as the rate of change of an equation. For example, in $y = 3x + 4$, the rate of change is $3$. $3$ is the coefficient of $x$. In this equation, the constant variable is $4$.

Rate of Change in Position

The displacement in position is known as the rate of change in position. If a particle is initially at A and after time t it is at the point B, then Rate of change in position = $\frac - \text > >$.

Rate of Change in Velocity

Velocity is the speed of a particle or object. The rate of change in velocity is described as the change in position(displacement) divided by the total change in time. Speed is always positive and velocity indicates the direction.

Rate of Change in Acceleration

Acceleration is the second order derivative of the displacement. Rate of change in acceleration = $\frac > >$

Rate of Change Examples

Given below are some of the examples on rate of change.

Solved Examples

Question 1: Find the rate of change of the given points $A(7,3)$ and $B(9,5)$ Solution:

We know that, Rate of change in point(slope) = $\frac - y_ > - x_ >$

Question 2: A man driving a bus covers $60$ miles in one hour. Over the next two hours, he drives $100$ miles. What is his velocity over the next two hours. Solución:

Here, we denoted $d$ as the distance and $t$ as the time. We use the points $(1,60)$ and $(3,100)$. Here, 2 additional hours gives us a t value of $3$ and the total number of miles is $d = 60 + 100 = 60$. So, the velocity is the rate of change of the distance with respect to time. It is given as $\frac - d_ > - t_ >$

Rate of Change Formula

In calculus, rate of change formula is easily derived from the slope of the equation. The rate of change is equal to slope of the equation.

Find the Rate of Change:

The formula for slope equation can be written as,

The formula for rate of change is given as follows: Rate of change of $x$ with respect to $y$ is given as $\frac $

Rate of change of $y$ = $\frac $

This is the relationship between rate of change and slope.

Solved Example

Question: Find the rate of change of the given points $X(3,7)$ and $Y(4,2)$ Solution:

We know that the rate of change is given by the formula, Slope = $\frac - y_ > - x_ >$

Here, $(3,7)$ and $(4,2)$ are $(x_,y_ )$ and $(x_,y_ )$ respectively. Entonces,

Average Rate of Change

In geometrical concepts, the term "rate of change" is the slope of the line joining the two points of the line. This is also called as the average rate of change.

The average rate of change between the points $(4,3)$ and $(6,7)$ is the change in the y-coordinates over the change in the x-coordinates, which is also called as the slope of the line.

Average rate of change formula is m = $\frac - y_ > - x_ >$ where, m is called the slope of the line joining the points $(x_,y_ )$ and $(x_,y_ )$. The slope of the line in the graph = m = $\frac $ = $\frac $ = $2$ Hence, the average rate of change of the line joining the points $(4,3)$ and $(6,7)$ is $2$.

Average Rate of Change Formula

For any two points $(x_,y_ )$ and $(x_,y_ )$ in the co-ordinate plane, if $\delta \text $ is the change in $x$ and if $\delta \text $ is the corresponding change in $y$, then the difference quotient $\frac $ = $\frac - y_ > - x_ >$ is called the average rate of change of $y$ with respect to $x$ over the interval $(x_,y_ )$. It is also called as the ratio of change in y-coordinates over the change in x-coordinates. We can easily find the average rate of change with the help of the average rate of change formula. A function is one where there is a relationship between $x$ and $y$ is denoted as $y = f(x)$, where $x$ is an independent quantity and $y$ a dependent quantity.

F ind the Average Rate of Change

To find the average rate of change, we can use formula shown below:

Solved Examples

Question 1: Let $y = x^ - 2$. Find the average rate of change of $y$ with respect to $x$ over the interval $[3,4]$. Solución:

We have $y = x^ - 2$. (1) For average rate of change, put $x = 3$ in (1) $f(3) = (3)^ - 2$ = $27 - 2$ = $25$

$f(4) = (4)^ - 2 = 64 - 2 = 62$

The average rate of change over the interval $[3,4]$ = $\frac $

Question 2: Area of a circle $A(x) = \pi x^ $, where $x$ is the radius. Here, $x$ can take any values. Therefore, it is called as the independent variable and $y = A(x)$ is a dependent variable which depends on the value of $x$. Find the average rate of which the area of the circle changes with $x$ as the radius which changes from $x = 3$ to $x = 5$. Solución:

We have, $A(x) = \pi x^ $ Put $x = 3$, then $A(3) = \pi (3)^ = 9 \pi$ Again, $x = 5$ then $A(5) = \pi (5)^ = 25 \pi$

Then, the average rate of change is $\frac $

Average Rate of Change of a Function

For a given function $y = f(x)$, the average rate of change from a point $x = a$ to the point $x = b$ is the difference quotient. We can easily find the average rate of change of a function with the help of the formula for the average rate of change of a function.

Find the Average Rate of Change of the Function:

Average rate of change of a function is denoted as:

Here, $(b - a)$ is the change in the input of the function $f$, $ $ is the change in the function $f$ as the input change from $a$ to $b$ and $\frac $ is the average rate of change function

Maximum Rate of Change

The maximum rate of change is obtained when vector $v$ is into the same direction of the gradient $f(x, y)$. The maximum rate of change is the magnitude of the gradient $(x, y)$. Therefore, $grad(x, y)$ is the direction of the maximum rate of change of function $f$ at the point $(x, y)$.

Solved Example

Question: If $f(t) = xy^ z^ $, then find the maximum rate of change of the function at $(2,1,3)$ Solution:

The maximum rate of change of the function at $(2,1,3)$ occurs along the direction parallel to $\triangledown f$ at $(2,1,3)$.

Then, $\triangledown f$ = $y^ z^ i + 2xyz^ j + 2xy^ zk$. Here, $i, j, k$ are the unit vectors in the direction $x, y$ and $z$ respectively. Therefore, at the point $(2,1,3)$, the $grad f = \triangledown f$ at $(2,1,3)$ = $9i + 36j + 12k$ So, the maximum rate of change of $f(t)$ is $|\text f| = \sqrt + 36^ + 12^ >$ =$\sqrt $ = $\sqrt $

Instantaneous rate of change is the limit of the function that describes the average rate of change. It is used to describe how an object travel in space or around the ground. For example, the value of a function at a point $x = c$ is $f(c)$. If there is a small increment in $x$, which is $\delta x$, then the value of the function at $c + \delta x$ is $f(c + \delta x)$. Hence, the change in the value of the function is $f(c + \delta x) - f(c)$. By the term difference of quotient, we mean the change in the value of the function over the change in the value of $x$ which is $\delta x$.

Instantaneous Rate of Change Formula:

Solved Example

Question: Find the instantaneous rate of change of the function $f(x) = 2x^ + x - 3$ at $x = 4$. Solución:

For the instantaneous rate of change, calculate the first derivative of the given function. $f'(x) = 4x + 1$ Therefore, for instantaneous rate of change at $x = 4$ $f'(4) = 4 x 4 + 1 = 17$

Constant Rate of Change

Objects moving along a straight line are said to move at constant rate of change.

Constant Rate of Change Definition

The constant rate of change definition states that "If the object moves uniformly with respect to time, then it is said to move at a constant rate of change". For example, observe the following table

In the above table, as the distance increases the time taken also increases. Rate of change = $\frac $ = $\frac $ = $50$ km/hr, which is also equal to the rate of change between $(4,200)$ and $(8,400)$. For an object moving with constant rate of change, the motion of the path will be linear. The rate of change will be the slope of the line. The path described by the above a object moving as per the table is, $y - y_ = m(x - x_ )$ [Point slope formula]

$y - 200 = 50x - 200$

$y = 50x - 200 + 200 = 50x$

$y = 50x$ is the equation of the line, which is the path described by the object.

Rate of Change of a Function

To find the rate of change of a function we may compare this function with linear function. If we have $y = mx + c$ as a function. A change of $\delta x$ in $x$ produces a change $\delta y$ = $m \delta x$ in $y$, so the rate of change of a function is given by the ratio $\frac $ is equal to $m$, independent of $x$ and $\delta x$.

Relative Rate of Change

The relative rate of change of a function $f(x)$ is given by the relation $\frac $. where $f'(x)$ is the first derivative of the function.

Solved Example

Question: If $f(x) = 3x + 1$ is the function. Then, find the relative rate of change at $x = 1$. Solución:

Rate of Change and Slope

A rate of change is a ratio that compares the amount of change in a dependent variable to the amount of change in a independent variable. So, we say that Rate of Change = $\frac > >$

Slope means gradient or incline. By the use of slope, we can easily describe the measurement of the steepness of a straight line. The slope of a line is a rate of change. Slope = $\frac > >$ = $\frac > >$

If all the connected line segment of a line have the same rate of change, then they all have the same steepness and together form a straight line. So, the constant rate of change of a line is called the slope of the line. If we find the slope, then we can easily find the rate of change over the given period.

Percentage Rate of Change

The percentage rate of change is $100 \times$ $\frac $

Solved Example

Question: If $f(x) = 3x + 1$ is the function, then find the percentage rate of change at $x = 1$. Solución:

Given that $f(x) = 3x + 1$ then $f'(x) = 3$ The percentage rate of change at $x = 1$ is $100 \times$ $\frac $

= $100 \times $ $\frac $

4-H Horse Camp

INFORMATION COMING SOON - CHECK BACK Douglas County Fairgrounds, Castle Rock Meet new friends! Practice your horsemanship skills…. and, most importantly, have fun with your horse! Horse Camp will be a day camp running from 8am – 5pm. You can come all week or pick a couple of days that work for you. Your horse can come home at night or stay at the Fairgrounds (you choose) Space is limited, so send in your registration early. ALL participants must be designated Level 1 or higher Cost: $100.00 for the three days (includes meals and T-Shirt) or $35.00/day (Level testing costs extra) Registration Deadline – For full Registration Packet click HERE

4-H Working Ranch Horse Clinic

MORE INFORMATION COMING SOON

Douglas County Fairgrounds, Castle Rock, CO Instruction in Reining, Trail, Roping and Cow Work Sponsored by the Douglas County 4-H Horse Steering Committee and Colorado State University Extension in Douglas County

Animal Care and Housing Form

If you are enrolling in ANY livestock or horse project this 4-H year you MUST have an animal care form on file for each species. These need to be in the office by your species enrollment deadline. For example, if you are carrying a beef project you will need to have your form in by February 27th in order to have a tag put in your animal’s ear at weigh in. If you have any questions about filling out this form, please contact Vickie or Brenda at the office at 720-733-6940.

4-H Horse Show Buckle Series in Douglas County

Douglas County 4-H

Open Horse Show Buckle Series Five 2017 shows for overall high point! Our thanks to sponsors: D. C. Horse Steering Committee All proceeds benefit the Douglas County 4-H Horse Program - PAC and RMQHA Outreach approved shows - Douglas County Fairgrounds - 500 Fairgrounds Rd. Castle Rock, CO 80104 February 28th – Indoor Arena, April 30th – Outdoor Arena, May 22nd – Outdoor Arena, June 18th – Outdoor Arena, July 10th – Outdoor Arena,

Watch for Working Ranch Horse Show/Clinic July 9th

Buckle Series Results

Open Riding

Equine facilities at the Douglas County Fairgrounds are available for public use, when not reserved for events. 4-H Open Ride Nights have changed and 4-H will not be hosting them. В The Ride Nights will be open to the public and the policies for use are listed below. В This decision was made by the County to allow greater opportunity for use of the facilities.

Open riding schedule is published at www. fairgrounds. douglas. co. us —click on the EVENT CALENDAR. Call first before you drive to the Fairgrounds as the open riding schedule is subject to change 720-733-6900. Douglas County reserves the right to cancel open riding at any time without notice.

Rules: No stallions allowed. Horses must be kept under control at all times. No racing, roping, barrel racing, jumping, trick riding, etc allowed. No Lunging in Indoor or Outdoor Arena. Lunging only allowed in warm-up arenas. No lessons allowed. A parent or guardian must accompany anyone under the age of 18 (riders and/or spectators). All riders must check in, sign a waiver and pay fee prior to riding. Riders ride at their own risk. Parking in designated areas only. Open riding in designated areas only. В Weather and schedule permitting, Dogs are not allowed in the open riding area. Stalls are NOT provided for open riding. Riders are expected to clean up after horses. В Wheelbarrows and shovels are provided. Do not tie horses to temporary panels. Alcohol is not permitted. Anyone not complying with these rules, will be asked to leave. $5.00 per session per horse or rider:В Cash only / no change given

Jumping Competency Test

The horse committee has added this competency test that will allow members to jump even if they haven’t passed Level 3 on their advancement tests. This will be a simple test that will prove you are capable of safely clearing fences.

If you pass this test, you will be allowed to jump fences in the Hunter Hack class at the County Fair no matter what level you are. (You must still pass Level 1 to show at the County Fair).

You can take this test from any level rater that is certified to test Hunter Hack Levels 3 and above. Or, a Douglas County horse leader who has been certified to give this test can administer it.

We will be offering opportunities to pass at certain Wenesday night rides and the Monday of Horse Camp during level testing. The competency test MUST be on file with the Extension office by the level test deadline that will be published in this newsletter for you to jump at County Fair.

Lynette Winans (303)489-6276 Jennie Slade (303)646-1957 Kelly Brown (303)646-5280

Level Testing Opportunities*

If you would like to Level test 2, contact Vickie the office at 720-733-6940. If you would like to Level test 3 and 4, you need to contact a rater yourself by looking them up on the state list. Just call them and schedule a time. Raters are typically paid $15/test and/or mileage.

Written tests for Level 1 can be taken with your horse leader. All other level tests can be taken at the Extension Office year round. Just call and set a time to take the written test 720-733-6940. Remember, the written test must be taken and passed before taking the riding test.

Horse Show Organizational Guide

Have you been thinking about holding a show, but you just don't know what all goes in to it and how to get it all done? Well, here's the guide for you with great advice, time lines, checklists and sample show bills and tabulation sheets. So, read all about it and give it a try!

Useful Horse Related Links

Sleep Rocks. get more of it!

College students, like Americans overall, are sleeping less, and if you are like most college students, chances are you are not getting enough sleep. On average, most college students get 6 - 6.9 hours of sleep per night, and the college years are notoriously sleep-deprived due to an overload of activities. Recent research on college students and sleep indicates that insufficient sleep impacts our health, our moods, our GPA and our safety. Sleep really matters.

WHY do we need sleep?

Sleep is important for a number of reasons. It restores our energy, fights off illness and fatigue by strengthening our immune system, helps us think more clearly and creatively, strengthens memory and produces a more positive mood and better performance throughout the day. Sleep isn't just a passive activity and something to fill the time when we are inactive, but rather it is an active and dynamic process vital for normal motor and cognitive function.

HOW MUCH sleep do we need?

Most adults need somewhere between 6-10 hours of sleep per night. Different people need different amount of sleep to feel rested. If you are frequently tired or irritable during the day and find yourself sleeping more than an extra 2 hours per night on weekends, then you are probably not getting enough sleep during the week. Try for 7-8 hours and see how you feel.

CONSEQUENCES of sleep loss

Lack of sleep is associated with both physical and emotional health risks. These include:

More illness, such as colds and flu, due to a lowered immune system

Feeling more stressed out

Increased weight gain and obesity

Lower GPA and decreased academic performance

Increased mental health issues, such as depression and anxiety

Increased automobile accidents due to fatigue caused by "drowsy driving"

Decreased performance in athletics and other activities that require coordination

Sleep and Physical Health Issues

Lack of sleep can cause many health issues, including death, and people are often not aware that they are at risk. Since sleep deprivation can impact the immune system function, our ability to fight off infections becomes more difficult and we are more prone to getting upper respiratory infections, such as cold and flu, and often feel "run down." That's because we are! Heart and lung function is adversely affected by lack of sleep and is associated with worsening chronic lung and heart disease and high blood pressure.

Lack of sleep has been linked to obesity. With sleep deprivation, there is an increase in the hormone, ghrelin, which is associated with hunger for high calorie foods. There is a decrease in the hormone leptin which reduces appetite. This leads to weight gain in many people. Lack of sleep impacts brain function, attention span, mood and reaction times. Excessive sleepiness is a leading cause of car and truck accidents, and research has demonstrated that many industrial accidents and disasters, such as nuclear power accidents, major oil spills and space shuttle disasters have been attributed to sleep deprived workers.

Sleep and Mental Health Issues

College students are often at risk for having mental health issues such as depression and anxiety, and researchers believe that lack of sleep is a factor. An assessment of your sleep by a mental health professional may be best if you exhibit one or more of the following symptoms.

Sleep and Depression

Insomnia (often sleeping 6 hours or less a night)

Too much sleep (often sleeping 10 hours or more a night or "escape sleeping")

Regularly feeling fatigue, constantly wishing you were sleeping or napping

Engaging in day to day responsibilities feels highly tiring or burdening

Sleep and Stress/Anxiety

Racing thoughts (very high paced) that prohibit settling into sleep

Recurrent and persistent thinking about 1-2 topics that prohibit settling into sleep

Repetitive behaviors that needed to manage anxiety that inhibits falling asleep

Pattern of stressful and anxiety-provoking thoughts that wake you up during sleep

Experiencing shortness of breath when attempting to fall or stay sleep (that can't be explained by a medical condition)

Sleep and Relationships

Trouble enjoying activities within your relationships that are typically fun

Difficulty regularly listening to what your partner has to say

Pattern of being quick to get irritated or angry with your partner (increased fighting)

Regular quality of communication is reduced or more difficult

Sleep and Academic Performance

According to a health survey administered at UGA every two years, 1 in 4 UGA students indicate that lack of sleep has impacted their academic performance in a negative way. They have made lower grades, missed a paper or project deadline, or had to withdraw from class. Some students rely on staying up most of the night to study, but pulling an all-nighter and cramming at the last minute can actually be counterproductive.

The very qualities you need to maximize in order to do well on tests, such as recall, concentration, and alertness, are decreased when you are sleep deprived. Research has shown that students who get 6 or fewer hours of sleep have a lower GPA than those who get 8 or more.

How Sleep Facilitates Learning and Memory

During sleep, the brain organizes, sorts, and stores what we have learned and experienced that day, making it easier to recall at a later time.

Sleep also helps you weed out irrelevant information and helps you make connections between your memory and information you learned that day, even if you have not made those connections while awake.

If you study a little every day, you can use this natural process of sleep to gain a better understanding of the material and to retain the information more efficiently.

If you don't understand something you have read or you can't solve a problem, look it over and then sleep on it.

To sum up, to study better, more efficiently, and to increase the likelihood of learning and retaining information, get at least 6-8 hours of sleep before your exam. Go for 8!

Establishing a Sleep Ritual

Individuals regularly getting high quality sleep often have a sleep ritual. A sleep ritual is a routine that helps the mind and body wind down at the end of the day in preparation for a good night's sleep. In evaluating your sleep, does your sleep ritual include the following?

Maintain a regular bed and wake time schedule including weekends. Sleeping more than 1-2 hours more on the weekend can wreak havoc on your circadian rhythms, so a regular wake schedule is important.

Establish a regular, relaxing bedtime routine such as soaking in a hot bath or hot tub and then reading a book or listening to soothing music.

Create a sleep-conducive environment that is dark, quiet, comfortable, and cool.

Sleep on a comfortable mattress and pillows.

Use your bedroom only for sleep and sex.

Finish eating at least 2-3 hours before your regular bedtime.

Exercise regularly. It is best to complete your workout at least 2 hours before bedtime, as exercising before you sleep can leave your body too energized to relax.

Avoid caffeine (e. g. coffee, tea, soft drinks, energy drinks, chocolate) 3-4 hours before bedtime. It can keep you awake.

Avoid nicotine (e. g. cigarettes, tobacco products). Used close to bedtime, it can lead to poor sleep.

Avoid alcohol close to bedtime.

Using a Sleep Diary

A sleep diary can help you evaluate your sleep over time. Typical things kept in a sleep diary include levels of sleepiness at different times during the day, times you sleep well, times you have difficulty staying awake, and recording the amount of sleep you get each night.

Click here for an example of a Sleep Diary (Adobe pdf)

Alcohol and Sleep

Alcohol can make you feel tired because it is a depressant and has sedative qualities, but drinking alcohol can interrupt sleep and interfere with the quality of your sleep. It can also magnify the effects of sleep deprivation.

To Nap or Not to Nap?

Approximately 30-50% of college students nap, but the effect is that nappers sleep less than non-nappers. If you do nap, nap early in the day and keep it to about 20-30 minutes.

You Can't Fake Wake: Drowsy Driving

18- 24 year old drivers have a significantly higher rate of risk of late night crashes and fatigue and drowsiness are often to blame. Alcohol use is also a risk factor.

¿Que puedo hacer?

Recognize sleepiness before you start to drive.

Take a nap before you drive.

Know when you are at greater risk for drowsy driving---when are you most likely to feel fatigue?

Drive with a friend who will stay awake with you and keep you focused on driving.

STOP---If you are falling asleep, pull over to a safe spot and sleep!

Sleep Disorders. Do I Have One?

Most of us have difficulty falling asleep or staying asleep at some point in our lives. Sometimes these problems are temporary and can be due to stress. In other cases, the problem persists for weeks or even months. If you are unable to fall asleep for more than 30 minutes after going to bed, 3 or more nights per week for 4 weeks, then you may have what is known as primary insomnia . This may be due to psychological and/or physiological causes, and if it persists for more than a month, you should see your clinician.

Other sleep disorders:

Narcolepsy is an inherited condition of excessive sleepiness that causes temporary loss of muscle control and/or uncontrollable sleep attacks". There is no cure for narcolepsy, although it can be controlled through drug treatment.

Obstructive sleep apnea is a condition in which the soft tissue of the upper airway repeatedly collapses during sleep and cuts off breathing for a short time, and then the airway opens abruptly and noisily. The constant interruptions of sleep cause excessive sleepiness during the day, but sleep apnea may go unnoticed unless someone sleeps in the same room and hears interruptions. Obesity increases the risk of this disorder.

Restless legs is a condition in which the legs jerk uncontrollably during sleep, disturbing sleep and causing daytime sleepiness.

When Should I Get Help?

Consider seeing your clinician if you:

Have trouble getting to sleep or wake up frequently during the night for a period of several weeks

Fall asleep at inappropriate times even after a night of adequate sleep

Have nightmares or night terrors (the experience of awakening in a terrified state without recollection of a dream) that interrupt your sleep

Sleep-walk

Have been told by someone that you stop breathing during sleep, especially if you have morning headaches or fall asleep easily during the day

Sleep Resources

Sleep Education -- Health Promotion. 706-542-8690

NOTE: In case you are not familiar with translating word problems into equations please go through this post first. word-problems-made-easy-87346.html

What is a ‘D/S/T’ Word Problem?

Usually involve something/someone moving at a constant or average speed.

Out of the three quantities (speed/distance/time), we are required to find one.

Information regarding the other two will be provided in the question stem.

The ‘D/S/T’ Formula: Distance = Speed x Time

I’m sure most of you are already familiar with the above formula (or some variant of it). But how many of you truly understand what it signifies?

When you see a ‘D/S/T’ question, do you blindly start plugging values into the formula without really understanding the logic behind it? If then answer to that question is yes, then you would probably have noticed that your accuracy isn’t quite where you’d want it to be.

My advice here, as usual, is to make sure you understand the concept behind the formula rather than just using it blindly.

So what’s the concept? Lets find out!

The Distance = Speed x Time formula is just a way of saying that the distance you travel depends on the speed you go for any length of time.

If you travel at 50 mph for one hour, then you would have traveled 50 miles. If you travel for 2 hours at that speed, you would have traveled 100 miles. 3 hours would be 150 miles, etc.

If you were to double the speed, then you would have traveled 100 miles in the first hour and 200 miles at the end of the second hour.

We can figure out any one of the components by knowing the other two.

For example, if you have to travel a distance of 100 miles, but can only go at a speed of 50 mph, then you know that it will take you 2 hours to get there. Similarly, if a friend visits you from 100 miles away and tells you that it took him 4 hours to reach, you will know that he AVERAGED 25 mph. ¿Derecha?

All calculations depend on AVERAGE SPEED.

Supposing your friend told you that he was stuck in traffic along the way and that he traveled at 50 mph whenever he could move. Therefore, although practically he never really traveled at 25 mph, you can see how the standstills due to traffic caused his average to reduce. Now, if you think about it, from the information given, you can actually tell how long he was driving and how long he was stuck due to traffic (assuming; what is false but what they never worry about in these problems; that he was either traveling at 50 mph or 0 mph). If he was traveling constantly at 50 mph, he should have reached in 2 hours. However, since he took 4 hours, he must have spent the other 2 hours stuck in traffic!

Now lets see how we can represent this using the formula.

We know that the total distance is 100 miles and that the total time is 4 hours. BUT, his rates were different AND they were different at different times. However, can you see that no matter how many different rates he drove for various different time periods, his TOTAL distance depended simply on the SUM of each of the different distances he drove during each time period.

P. ej. if you drive a half hour at 60 mph, you will cover 30 miles. Then if you speed up to 80 mph for another half hour, you will cover 40 miles, and then if you slow down to 30 mph, you will only cover 15 miles in the next half hour. But if you drove like this, you would have covered a total of 85 miles (30 + 40 + 15). It is fairly easy to see this looking at it this way, but it is more difficult to see it if we scramble it up and leave out one of the amounts and you have to figure it out going "backwards". That is what word problems do.

Further, what makes them difficult is that the components they give you, or ask you to find can involve variable distances, variable times, variable speeds, or any two or three of these. How you "reassemble" all this in order to use the d = s*t formula takes some reflection that is "outside" of the formula itself. You have to think about how to use the formula.

So the trick is to be able to understand EXACTLY what they are giving you and EXACTLY what it is that is missing, but you do that from thinking, not from the formula, because the formula only works for the COMPONENTS of any trip where you are going an average speed for a certain amount of time. ONCE the conditions deal with different speeds or different times, you have to look at each of those components and how they go together. And that can be very difficult if you are not methodical in how you think about the components and how they go together. The formula doesn't tell you which components you need to look at and how they go together. For that, you need to think, and the thinking is not always as easy or straightforward as it seems like it ought to be.

In the case of your friend above, if we call the time he spent driving 50 mph, T1 ; then the time he spent standing still is (4 - T1) hours, since the whole trip took 4 hours. So we have 100 miles = (50 mph x T1) + (0 mph x [4 - T1]) which is equivalent then to: 100 miles = 50 mph x T1

So, T1 will equal 2 hours. And, since the time he spent going zero is (4 - 2), it also turns out to be 2 hours.

Sometimes the right answers will seem counter-intuitive. so it is really important to think about the components methodically and systematically.

There is a famous trick problem: To qualify for a race, you need to average 60 mph driving two laps around a 1 mile long track. You have some sort of engine difficulty the first lap so that you only average 30 mph during that lap; how fast do you have to drive the second lap to average 60 for both of them?

I will go through THIS problem with you because, since it is SO tricky, it will illustrate a way of looking at almost all the kinds of things you have to think about when working any of these kinds of problems FOR THE FIRST TIME (i. e. before you can do them mechanically because you recognize the TYPE of problem it is). Intuitively it would seem you need to drive 90, but this turns out to be wrong for reasons I will give in a minute.

The answer is that NO MATTER HOW FAST you do the second lap, you can't make it. And this SEEMS really odd and that it can't possibly be right, but it is. The reason is that in order to average at least 60 mph over two one-mile laps, since 60 mph is one mile per minute, you will need to do the whole two miles in two minutes or less. But if you drove the first mile at only 30, you used up the whole two minutes just doing IT. So you have run out of time to qualify.

To see this with the d = s*t formula, you need to look at the overall trip and break it into components. and that is the hardest part of doing this (these) problem(s), because (often) the components are difficult to figure out, and because it is hard to see which ones you need to put together in which way.

In the next section we will learn how to do just that.

Resolving the Components

When you first start out with these problems, the best way to approach them is by organizing the data in a tabular form.

Use a separate column each for distance, speed and time and a separate row for the different components involved (2 parts of a journey, different moving objects, etc.). The last row should represent total distance, total time and average speed for these values (although there might be no need to calculate these values if the question does not require them).

Assign a variable for any unknown quantity.

If there is more than one unknown quantity, do not blindly assign another variable to it. Look for ways in which you can express that quantity in terms of the quantities already present. Assign another variable to it only if this is not possible.

In each row, the quantities of distance, speed and time will always satisfy d = s*t.

The distance and time column can be added to give you the values of total distance and total time but you CANNOT add the speeds. Think about it: If you drive 20 mph on one street, and 40 mph on another street, does that mean you averaged 60 mph?

Once the table is ready, form the equations and solve for what has been asked!

Warning: Make sure that the units for time and distance agree with the units for the rate. For instance, if they give you a rate of feet per second, then your time must be in seconds and your distance must be in feet. Sometimes they try to trick you by using the wrong units, and you have to catch this and convert to the correct units.

A Few More Points to Note

Motion in Same Direction (Overtaking): The first thing that should strike you here is that at the time of overtaking, the distances traveled by both will be the same.

Motion in Opposite Direction (Meeting): The first thing that should strike you here is that if they start at the same time (which they usually do), then at the point at which they meet, the time will be the same. In addition, the total distance traveled by the two objects under consideration will be equal to the sum of their individual distances traveled.

Round Trip: The key thing here is that the distance going and coming back is the same.

Now that we know the concept in theory, let us see how it works practically, with the help of a few examples. Note for tables. All values in black have been given in the question stem. All values in blue have been calculated.

Example 1. To qualify for a race, you need to average 60 mph driving two laps around a 1-mile long track. You have some sort of engine difficulty the first lap so that you only average 30 mph during that lap; how fast do you have to drive the second lap to average 60 for both of them?

Solution: Let us first start with a problem that has already been introduced. You will see that by clearly listing out the given data in tabular form, we eliminate any scope for confusion.

In the first row. we are given the distance and the speed. Thus it is possible to calculate the time.

Time(1) = Distance(1)/Speed(1) = 1/30

In the second row. we are given just the distance. Since we have to calculate speed, let us give it a variable 'x'. Now, by using the 'D/S/T' relationship, time can also be expressed in terms of 'x'.

Time(2) = Distance(2)/Speed(2) = 1/x

In the third row. we know that the total distance is 2 miles (by taking the sum of the distances in row 1 and 2) and that the average speed should be 60 mph. Thus we can calculate the total time that the two laps should take.

Time(3) = Distance(3)/Speed(3) = 2/60 = 1/30

Now, we know that the total time should be the sum of the times in row 1 and 2. Thus we can form the following equation :

Time(3) = Time(1) + Time(2) ---> 1/30 = 1/30 + 1/x

From this, it becomes clear that '1/x' must be 0.

Since 'x' is the reciprocal of 0, which does not exist, there can be no speed for which the average can be made up in the second lap.

Example 2. An executive drove from home at an average speed of 30 mph to an airport where a helicopter was waiting. The executive boarded the helicopter and flew to the corporate offices at an average speed of 60 mph. The entire distance was 150 miles; the entire trip took three hours. Find the distance from the airport to the corporate offices.

Solution: Let us see what the table looks like.

Since we have been asked to find the distance from the airport to the corporate office (that is the distance he spent flying), let us assign that specific value as 'x'.

Thus, the distance he spent driving will be '150 - x' Now, in the first row. we have the distance in terms of 'x' and we have been given the speed. Thus we can calculate the time he spent driving in terms of 'x'.

Time(1) = Distance(1)/Speed(1) = (150 - x)/30 Similarly, in the second row. we again have the distance in terms of 'x' and we have been given the speed. Thus we can calculate the time he spent flying in terms of 'x'.

Time(2) = Distance(2)/Speed(2) = x/60 Now, notice that we have both the times in terms of 'x'. Also, we know the total time for the trip. Thus, summing the individual times spent driving and flying and equating it to the total time, we can solve for 'x'.

Time(1) + Time(2) = Time(3) --> (150 - x)/30 + x/60 = 3 --> x = 120 miles Answer. 120 miles Note: In this problem, we did not calculate average speed for row 3 since we did not need it. Remember not to waste time in useless calculations!

Example 3. A passenger train leaves the train depot 2 hours after a freight train left the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the speed of the passenger train, if it overtakes the freight train in three hours.

Solution: Let us look at the tabular representation of the data :

Since this is an 'overtaking' problem, the first thing that should strike us is that the distance traveled by both trains is the same at the time of overtaking.

Next we see that we have been asked to find the speed of the passenger train at the time of overtaking. So let us represent it by 'x'.

Also, we are given that the freight train is 20 mph slower than the passenger train. Hence its speed in terms of 'x' can be written as 'x - 20'.

Moving on to the time, we are told that it has taken the passenger train 3 hours to reach the freight train. This means that the passenger train has been traveling for 3 hours.

We are also given that the passenger train left 2 hours after the freight train. This means that the freight train has been traveling for 3 + 2 = 5 hours.

Now that we have all the data in place, we need to form an equation that will help us solve for 'x'. Since we know that the distances are equal, let us see how we can use this to our advantage.

From the first row. we can form the following equation :

Distance(1) = Speed(1) * Time(1) = x*3 From the second row. we can form the following equation :

Distance(2) = Speed(2) * Time(2) = (x - 20)*5 Now, equating the distances because they are equal we get the following equation :

3*x = 5*(x - 20) --> x = 50 mph. Responder. 50 mph.

Example 4. Two cyclists start at the same time from opposite ends of a course that is 45 miles long. One cyclist is riding at 14 mph and the second cyclist is riding at 16 mph. How long after they begin will they meet?

Solution: Let us see what the tabular representation look likes :

Since this is a 'meeting' problem, there are two things that should strike you. First, since they are starting at the same time, when they meet, the time for which both will have been cycling will be the same. Second, the total distance traveled by the will be equal to the sum of their individual distances.

Since we are asked to find the time, let us assign it as a variable 't'. (which is same for both cyclists)

In the first row. we know the speed and we have the time in terms of 't'. Thus we can get the following equation :

Distance(1) = Speed(1) * Time(1) = 14*t In the second row. we know the speed and again we have the time in terms of 't'. Thus we can get the following equation :

Distance(2) = Speed(2) * Time(2) = 16*t Now we know that the total distance traveled is 45 miles and it is equal to the sum of the two distances. Thus we get the following equation to solve for 't' :

Distance(3) = Distance(1) + Distance(2) --> 45 = 14*t + 16*t --> t = 1.5 hours Answer. 1.5 hours.

Example 5. A boat travels for three hours with a current of 3 mph and then returns the same distance against the current in four hours. What is the boat's speed in calm water?

Solution: Let us see what the tabular representation looks like :

Since this is a question on round trip, the first thing that should strike us is that the distance going and coming back will be the same.

Now, we are required to find out the boats speed in calm water. So let us assume it to be 'b'. Now if speed of the current is 3 mph, then the speed of the boat while going downstream and upstream will be 'b + 3' and 'b - 3' respectively.

In the first row. we have the speed of the boat in terms of 'b' and we are given the time. Thus we can get the following equation :

Distance(1) = Speed(1) * Time(1) = (b + 3)*3 In the second row. we again have the speed in terms of 'b' and we are given the time. Thus we can get the following equation :

Distance(2) = Speed(2) * Time(2) = (b - 3)*4 Since the two distances are equal, we can equate them and solve for 'b'.

Distance(1) = Distance(2) --> (b + 3)*3 = (b - 3)*4 --> b = 21 mph. Responder. 21 mph.

Re: 'Distance/Speed/Time' Word Problems Made Easy

10 Aug 2010, 20:38

Thanks a lot for this really helpful post! I used to go for CAT coaching with TIME institute about 2 years back. and I thought the method they taught to solve DST questions was unbeatable. but urs makes it even simpler, and so quick! If I save any time on GMAT while solving DST questions, the credit will def go to you!

Re: 'Distance/Speed/Time' Word Problems Made Easy

27 Oct 2010, 22:00

rags10 wrote: Hi Srihari,

Could you please guide me in solving this problem.

A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

5 minutes 6 minutes 8 minutes 9 minutes 10 minutes

This problem involves both same direction and opposite direction motion. How do we use the tabular format for this?

Please, post the new questions in a separate thread.

27 Jul 2011, 22:01

dkj1984 wrote: Example 2. An executive drove from home at an average speed of 30 mph to an airport where a helicopter was waiting. The executive boarded the helicopter and flew to the corporate offices at an average speed of 60 mph. The entire distance was 150 miles; the entire trip took three hours. Find the distance from the airport to the corporate offices.

Can someone please let me know what would be the average sped in this case .

Will it be total distance / total time = 150 / 3 or will it be 2ab/a+b = 2(30*60) / 90

I will clear your doubt but first let me give you some unsolicited 'gyan'. When dealing with formulas, remember two things: 1. Do not learn up formulas without knowing the assumptions made to derive them. 2. Make sure you understand how they are derived and the starting point.

Average speed is always Total Distance/Total Time.

1. The formula 2ab/(a+b) assumes that the distance traveled at speed a is the same as the distance traveled at speed b. Say distance traveled in each case is 1 km. 2. Derivation: Average Speed = Total Distance/Total Time = (1+1)/(1/a + 1/b) = 2ab/(a+b) So in case you have three speeds a, b and c, you know how to get the average speed in that case too.

Coming to this question, the formula is not used here because it doesn't say that the distance traveled at the two speeds is the same. Average Speed = Total distance/Total Time = 150/3 = 50 km/hr

Now there are two ways to handle it: 1. Weighted averages 2. Using algebra

Weighted Averages Method: This now becomes a weighted average problem since you have two speeds and their average is known. The weights will be the time for which the speeds were maintained. w1/w2 = (60 - 50)/(50 - 30) = 1:2 So plane travel lasted 2 hrs and car travel lasted 1 hr. Distance traveled by plane = 2*60 = 120 km

Algebra Method: Let time for which he traveled by plane is t hrs. 50 = (t*60 + (3-t)*30)/3 150 = 60t - 30t + 90 t = 2 hrs So plane travel lasted 2 hrs. Distance traveled by plane = 2*60 = 120 km

For more on weighted averages method (which helps you solve orally), check: http://www. veritasprep. com/blog/2011/03. - averages/

Re: 'Distance/Speed/Time' Word Problems Made Easy

21 May 2017, 12:51

A very interesting doubt.

Average speed divides in the ratio of the time traveled ( not distance traveled ).

Average Speed = \(\frac + \frac \) where T1 & V1 are time taken and speed respectively for first distance (accordingly for V2 and T2)

Let T is time to cover first distance, therefore 3-T is time to cover the second distance (As total time is 3 hrs)

Therefore, T = 1 hr

So, T2 = 3-1 = 2hrs

Therefore, distance from the airport to the corporate office = 60*2 = 120 miles

Re: 'Distance/Speed/Time' Word Problems Made Easy

21 May 2017, 23:02

Hi rajatjain14. Thanks for your prompt reply. Ok - so basically I have just the wrong "base". I should have taken the totally hours and not the total distance (which is easier anyways).

I got it, thank you

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