Question

Please look at the image, thank you!!if it helps im supposed to round 4 decimal places

Answer 1

Given:

The function represents the position of an object for time x.

`f(x)=√(16-x^2)`

To find:

The average velocity over the interval [2, 4].

Solution:

It is known that the average velocity over the interval [a, b] is given by:

`(f(b)-f(a))/(b-a)`

For the given position function, the average velocity over the interval [2, 4] is:

`\begin{gathered} Avg=(f(4)-f(2))/(4-2) \\ =(√(16-4^2)-√(16-2^2))/(2) \\ =(√(16-16)-√(16-4))/(2) \\ =(0-√(12))/(2) \\ =-(2√(3))/(2) \\ =-√(3) \\ =-1.7321 \end{gathered}`

Thus, the average velocity is -1.7321.