average rate of change practice\ncomplete this assessment to review what youve learned. it will not count…

average rate of change practice\ncomplete this assessment to review what youve learned. it will not count toward your grade.\ntyrekis is an engineer and needs to design a rocket for an experiment. he has calculated that the height of the rocket, in feet, with respect to time, in seconds, can be modeled by the function h(t)= - 16t² + 160t. find the average rate of change of the rocket over the interval 4,5. (1 point)\nthe average rate of change is feet per second.\ncheck answer remaining attempts : 3

average rate of change practice\ncomplete this assessment to review what youve learned. it will not count toward your grade.\ntyrekis is an engineer and needs to design a rocket for an experiment. he has calculated that the height of the rocket, in feet, with respect to time, in seconds, can be modeled by the function h(t)= - 16t² + 160t. find the average rate of change of the rocket over the interval 4,5. (1 point)\nthe average rate of change is feet per second.\ncheck answer remaining attempts : 3

Answer

Explanation:

Step1: Definir la fórmula

La fórmula para el cambio promedio de una función $y = f(x)$ en el intervalo $[a,b]$ es $\frac{f(b)-f(a)}{b - a}$. Aquí, $a = 4$, $b = 5$ y $h(t)=-16t^{2}+160t$.

Step2: Calcular $h(5)$

Sustituir $t = 5$ en $h(t)$: $h(5)=-16\times5^{2}+160\times5=-16\times25 + 800=-400 + 800=400$.

Step3: Calcular $h(4)$

Sustituir $t = 4$ en $h(t)$: $h(4)=-16\times4^{2}+160\times4=-16\times16+640=-256 + 640 = 384$.

Step4: Calcular el cambio promedio

Usar la fórmula: $\frac{h(5)-h(4)}{5 - 4}=\frac{400 - 384}{1}=16$.

Answer:

16