Question

Please help! 30 points! I need help with Algebra 1!!

A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 5t, where t represents time in minutes and p represents how far the paint is spreading.

The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(p) = πp2.

Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your work. (6 points)

Part B: How large is the area of spilled paint after 2 minutes? You may use 3.14 to approximate π in this problem. (4 points)

Answer 1

Part a.

It is given in the question that, The area of the pattern can be expressed as

`A(p) = \pi p^2`

And

`p(t)=5t`

So for A(p(t)), we have to substitute 5t for p in A(p), that is

`image`

Part b .

At t=2minutes,

`A(p(2)) = 25 \pi(2^2) = 25 \pi(4) = 314`

And that's the required area at t=2 minutes .