anonymous one year ago 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.

1. anonymous

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

2. jim_thompson5910

Replace r in $\Large A = \pi*r^2$ with r(t) then replace r(t) with 3t

3. jim_thompson5910

after all of those replacements, simplify as much as possible

4. anonymous

so would it be 28.26t

5. jim_thompson5910

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

6. jim_thompson5910

when you square 3t, you square both pieces 3 squared = 9 t squared is written as t^2

7. anonymous

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

8. jim_thompson5910

correct, if you go with using pi = 3.14

9. jim_thompson5910

in part B, you replace t with 10 and evaluate

10. anonymous

so i would multiply 28.26 by 100??

11. jim_thompson5910

yes

12. anonymous

so 2826

13. jim_thompson5910

correct

14. anonymous

okay thank you

15. jim_thompson5910

you're welcome