Question

The path of a baseball thrown at an angle of 40 degrees can be modeled by y=-0.05x^2+3.2x+8y=−0.05x 2 +3.2x+8 where x is the horizontal distance in feet from the release point and y is the corresponding height, in feet. Calculate the average rate of change of the height over the interval 8\le x\le208≤x≤20.

Answer 1

Answer:

The average rate of change of the height $A_{rate}=1.8$

Step-by-step explanation:

The average rate of change of a function is given by:

$A_{rate}=\frac{f(b)-f(a)}{b-a}$

Where:

f(x) is the funtion, in our case $f(x) = y = -0.05x^{2}+3.2x+8$

f(b) is the function evaluated in b, when b = 20

f(a) is the funtion evaluated in a, when a = 8

Let's find f(a) and f(b):

$f(8) = -0.05(8)^{2}+3.2(8)+8=30.4$

$f(20) = -0.05(20)^{2}+3.2(20)+8=52$

Therefore, using the average rate of change equation.

$A_{rate}=\frac{52-30.4}{20-8}=1.8$

I hope it helps you!