A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p (t) = 6 (t), 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) = 3.14 (p) ^2

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

Part B: How large is the area of spilled paint after 8 minutes? You may use 3.14 to approximate pi in this problem.

Question

Mathematics

Izayah Conrad

12 June, 13:00

A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p (t) = 6 (t), 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) = 3.14 (p) ^2

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

Part B: How large is the area of spilled paint after 8 minutes? You may use 3.14 to approximate pi in this problem.

+5

Answers (2)

Know the Answer?

Dexter Hampton · Answer 1

A (p (t)) = 113.04 t^2

A (p (8)) = 7234.56

Step-by-step explanation:

p (t) = 6t

A (p) = 3.14 p^2

So A (p (t)) = means we put p (t) in the function for A

= 3.14 p^2

= 3.14 (6t) ^2

= 3.14 (36t^2)

A (p (t)) = 113.04 t^2

Let t=8

A (p (8)) = 113.04 (8) ^2

= 113.04 (64)

=7234.56

Isabela Conrad · Answer 2

A) From the function p (t) = 6 (t), we know that p is 6t, so we plug this into it, to get 3.14 * (6t) ^2, or 113.04t^2.

B) Using what we got from A), we plug it in and get 113.04 * 8 * 8, or 7234.56 (Use a calculator on this, or just bash it with pencil and paper).