30 points! i need with algebra 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)

Part a.

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

And

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

Part b .

At t=2minutes,

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

The horse traveled 439.6 feet after walking around the track 5 times

Solution:

Given that, horse walks around a circular track while its trainer stands in the center

The trainer is 14 feet from the horse at all times

Therefore, radius of circular track = 14 feet

The circumference of circle is the distance traveled by horse for 1 lap

The circumference of circle is given as:

Where, "r" is the radius and is a constant equal to 3.14

Thus the distance traveled by horse for one time in circular track is 87.92 feet

About how far had the horse traveled after walking around the track 5 times?

Multiply the circumference by 5

Thus the horse traveled 439.6 feet after walking around the track 5 times