## shes.radical one year ago I really do not get this :/ 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. Nnesha

A[r(t)] means substitute r for r(t) function into A(r)

...what? so then its $A[r(t)]=3.14(10^2)+3t ?$ i dont get it..

3. Nnesha

don't add r(t) = what ?

3t

5. Nnesha

yes right so you can replace r(t) with 3t A(3t) =pi r^2 replace r with 3t don't add 3t

oh..is that it?

7. Nnesha

yes right $\huge\rm A(\color{red}{r(t)})=A(\color{ReD}{3t})= \pi\color{Red}{ r}^2$ ^replace r with 3t and then take square

....so then its $A(3t)=3.14*3^2?$

9. Nnesha

not just 3 it's (3t)^2

okay so then its $A(3t)=3.14(3t^2)$ now what .-.

11. Nnesha

(3t)^2 means 3^2 * t^2

which is $9(t^2)$

13. Nnesha

yes right $\huge\rm A(\color{red}{r(t)})=A(\color{ReD}{3t})= 9t^2\pi$

14. Nnesha

part B substitute t for 10

15. Nnesha

use 3.14 for pi

$9(10^2)(3.14)=2826$

17. Nnesha

looks good

so, Part A: $A[r(t)]=A(3t)=9t^2 \pi$ and Part B: $9(10^2)(3.14)=2826$ right? thats the answer right?? :D

19. Nnesha

yep

20. Nnesha

or you can say 9pit^2 :D

you're awesome..thank you thank you thank you!!

22. Nnesha

np :=)