HELP PLEASE ASAP!!!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)

Accepted Solution

A. It's a composite function, so basically, wherever you see a p, replace it with 5t, because we are given that information. So, your answer is:
[tex]A[p(t)] = 5t \pi 2=10t \pi [/tex]

B. Let's use the function we created, and just plug in 2 for t:
[tex]A[p(2)] = 10(2) \pi [/tex]
[tex]A[p(2)] = 62.83[/tex]

So, your answer is (approximately) 62.83 units².