Abucket 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.

part b: how large is the area of spilled paint after 2 minutes? you may use 3.14 to approximate π in this problem.

Given the paint flow can be expressed with the function as:

where, t represents time in minutes and p represents  how far the paint is spreading.

It is also given that: The flowing paint is creating a circular pattern on the tile

The area of the pattern can be expressed as:

A

To find the area of the circle of spilled paint as a function of time.

⇒

therefore,  the area of the circle of spilled paint as a function of time .         ......[1]

B

To find how large is the area of spilled paint after 2 minutes.

Substitute t = 2 minutes and in [1] we have;

square units.

Therefore, 314 square units large is  the area of spilled paint after 2 minutes.

the distance between the school and her home is 3.6km.

12 mins = 0.2 hours = 1/5 hour

54 ÷ 3 = 18km per hour

1/5 of 18 = 3.6km per 12 mins