chau launches a rocket straight up into the air. the table below gives the height h(t) of the rocket (in…

chau launches a rocket straight up into the air. the table below gives the height h(t) of the rocket (in meters) at a few times t (in seconds) during its flight. time t (seconds) height h(t) (meters) 0 0 2.2 110 6.6 198 8.8 44 13.2 0 (a) find the average rate of change for the height from 0 seconds to 6.6 seconds. meters per second (b) find the average rate of change for the height from 8.8 seconds to 13.2 seconds. meters per second

chau launches a rocket straight up into the air. the table below gives the height h(t) of the rocket (in meters) at a few times t (in seconds) during its flight. time t (seconds) height h(t) (meters) 0 0 2.2 110 6.6 198 8.8 44 13.2 0 (a) find the average rate of change for the height from 0 seconds to 6.6 seconds. meters per second (b) find the average rate of change for the height from 8.8 seconds to 13.2 seconds. meters per second

Answer

Explanation:

Step1: Fórmula de tasa de cambio promedio

La tasa de cambio promedio de una función $y = H(t)$ en el intervalo $[a,b]$ está dada por $\frac{H(b)-H(a)}{b - a}$.

Step2: Resolver (a)

Para el intervalo de $t = 0$ a $t=6.6$ segundos, $a = 0$, $b = 6.6$, $H(0)=0$ y $H(6.6)=198$. Entonces la tasa de cambio promedio es $\frac{H(6.6)-H(0)}{6.6 - 0}=\frac{198 - 0}{6.6}=\frac{198}{6.6}=30$.

Step3: Resolver (b)

Para el intervalo de $t = 8.8$ a $t = 13.2$ segundos, $a = 8.8$, $b = 13.2$, $H(8.8)=44$ y $H(13.2)=0$. Entonces la tasa de cambio promedio es $\frac{H(13.2)-H(8.8)}{13.2 - 8.8}=\frac{0 - 44}{4.4}=\frac{- 44}{4.4}=- 10$.

Answer:

(a) 30 (b) -10