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a bucket of paint has spilled on a tile floor. the paint flow can be expressed with the function p(t) = 6t, 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 8 minutes? you may use 3.14 to approximate π in this problem. (4 points)

A:A(6t)=πp^2

B: about 7234.56

Step-by-step explanation:

First find A[p(t)], Since this is a composite function so whenever you see p(t), you replace it with 6t, that is the value of p(t).

This is a simplified version of the area of the circle as a function of time A(6t)=πp^2

To find how large the area of paint spilled plug in 8 for t because t represents time.

A(48)≈3.14(48)^2

A(48)≈3.14*2304

A(48)≈7234.56

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi