## help_people one year ago Please check if this is right???

1. help_people

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.

2. help_people

Part A: You will plug in 3t to A(r) = pir^2 When you plug in the 3t you get: A[r(t)]= pi(3t)^2 =pi * (3t)^2 =pi * (3t * 3t) =28.274334t^2 ( I was just simplifying). Part B: 30 is r, because 30 is the radius after 10 minutes: π(30)2=900π = 900 x 3.14=2826

3. help_people

@hartnn @Elsa123

4. hartnn

part A, don't simplify, write $$9\pi t^2$$ as the answer. part B, writing units would be better 2826 sq. units

5. help_people

it also says show your work for part a so what would i put and ok for part b

6. hartnn

you did show your work for part A properly, just keep the final answer as 9pi t^2 and instead of writing answer for part B as 2826 write 2826 sq. units

7. hartnn

Part B: 10 is r, because 10 is the radius after 10 minutes: 9π(10^2)=900π = 900 x 3.14=2826 sq units. ^^^

8. help_people

yes i saw :)

9. hartnn

wait

10. help_people

I'm here :)

11. hartnn

Part B: 10 is t, because we need area after 10 minutes: 9π(10^2)=900π = 900 x 3.14=2826 sq units. ------------------ t =10, 10 is actually time :P

12. help_people

Is this what you would like me to do with Part A? : Part A: You will plug in 3t to A(r) = pir^2 When you plug in the 3t you get: A[r(t)]= pi(3t)^2 =pi * (3t)^2 =pi * (3t * 3t) =9pit^2

13. hartnn

yep

14. help_people

ok so is 30 still radius or ?

15. help_people

(just out of curiosity)

16. hartnn

where did you get 30 from?? i don't even see 30 in the question :P

17. hartnn

but yes, 30 will be the radius after 10 minutes :)

18. triciaal

yes

19. help_people

I believe i multiplied 10 x 3 in 3(t) to get 30 and called it radius. To think about it that was stupid.

20. triciaal

@hartnn r(t) = 3t and 10 = 10 so r = 30

21. hartnn

yes, i agreed, r =30

22. help_people

Is this what you wanted me to do with part a: Part A: You will plug in 3t to A(r) = pir^2 When you plug in the 3t you get: A[r(t)]= pi(3t)^2 =pi * (3t)^2 =pi * (3t * 3t) =9pit^2

23. hartnn

yes, part A is perfect

24. help_people

wait so what about pt b?

25. help_people

Part B: 10 is t, because we need area after 10 minutes: 9π(10^2)=900π = 900 x 3.14=2826 So, the answer is 2826 sq. units.

26. hartnn

Part B: 10 is t, because we need area after 10 minutes: 9π(10^2)=900π = 900 x 3.14=2826 sq units. yesss

27. help_people

ok so everything is bueno?

28. hartnn

bueno? yes, everything is okay :)