1 Answer

Richard Morgan · Answer 1 · 2023-07-03T15:22:36+0000

It is given that

A stone is thrown into a pond, A circular ripple spreads over the pond in such a way that the radius is increasing at a rate of 2.5 feet per second.

In one second the increment in radius is 2.5 feet

After t seconds, the increment in radius is given by

The area of the circular ripple is

$A(r)=\pi r^2$

$(A\circ r)(t)=A\lbrack r(t)\rbrack$

Substitute r(t)=2.5t, we get

$(A\circ r)(t)=A\lbrack2.5t\rbrack$

$UseA(r)=\pi r^2,\text{ we get}$

$(A\circ r)(t)=\pi(2.5t)^2$

The required function is

$(A\circ r)(t)=6.25\pi t^2$

Hence the fourth option is correct.

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