Question

Help!! 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)

Answer 1

A) A(p(t)) = 25πt²

B) 314 square units.

Explanation:

Part A)

Flow of paint can be expressed by the function:

p(t) = 5t

Area of the pattern is expressed as:

A(p) = πp²

Since area is given in terms of p, we can use the expression of p to express the area of pattern in terms of time(t). Using the value, we get:

A(p(t)) = π (5t)²

A(p(t)) = 25πt²

Part B)

We have to calculate the area of the pattern after time t. Substituting the value of t in above expression, we get:

A(p(2)) = 25 x 3.14 x 4 = 314 square units.

Therefore, the area of spilled paint after 2 minutes will be 314 square units.