the height (in feet) of a soccer ball that was kicked is modeled by the function $f(x)=-x^{2}+9x$, where $x$…

the height (in feet) of a soccer ball that was kicked is modeled by the function $f(x)=-x^{2}+9x$, where $x$ is time (in seconds) that the ball was in the air. estimate the average rate of change over the interval $0.7,4.3$. (1 point)\n\n$\\square$ feet per second

the height (in feet) of a soccer ball that was kicked is modeled by the function $f(x)=-x^{2}+9x$, where $x$ is time (in seconds) that the ball was in the air. estimate the average rate of change over the interval $0.7,4.3$. (1 point)\n\n$\\square$ feet per second

Answer

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0.7$, $b=4.3$ and $f(x)=-x^{2}+9x$.

Step2: Calculate $f(4.3)$

$f(4.3)=-(4.3)^{2}+9\times4.3=-18.49 + 38.7=20.21$.

Step3: Calculate $f(0.7)$

$f(0.7)=-(0.7)^{2}+9\times0.7=- 0.49+6.3 = 5.81$.

Step4: Calculate the average rate of change

$\frac{f(4.3)-f(0.7)}{4.3 - 0.7}=\frac{20.21 - 5.81}{3.6}=\frac{14.4}{3.6}=4$.

Answer:

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