Question

Help!!! Medal and Fan

A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function r(t) = 3t, where t represents time in minutes and r 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(r) = πr2.

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

Part B: How large is the area of spilled paint after 10 minutes? You may use 3.14 to approximate π in this problem.

Answer 1

@heretohelpalways @Hero @GIL.ojei @DanJS @dan815 @pooja195

Answer 2

Replace r in \[\Large A = \pi*r^2\] with r(t)

then replace r(t) with 3t

Answer 3

after all of those replacements, simplify as much as possible

Answer 4

so would it be 28.26t

Answer 5

the t should be t^2

if you leave it in terms of pi, which is what I would do, it would be \[\Large A(t) = 9\pi*t^2\]

Answer 6

when you square 3t, you square both pieces

3 squared = 9
t squared is written as t^2

Answer 7

so it would be 28.26t^2 for the area of the spill

Answer 8

correct, if you go with using pi = 3.14

Answer 9

in part B, you replace t with 10 and evaluate

Answer 10

so i would multiply 28.26 by 100??

Answer 11

yes

Answer 12

so 2826

Answer 13

correct

Answer 14

okay thank you

Answer 15

you're welcome