- help_people

Please check if this is right???

- jamiebookeater

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- 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.

- 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

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## More answers

- hartnn

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

- help_people

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

- 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

- 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.
^^^

- help_people

yes i saw :)

- hartnn

wait

- help_people

I'm here :)

- 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

- 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

- hartnn

yep

- help_people

ok so is 30 still radius or ?

- help_people

(just out of curiosity)

- hartnn

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

- hartnn

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

- triciaal

yes

- 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.

- triciaal

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

- hartnn

yes, i agreed, r =30

- 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

- hartnn

yes,
part A is perfect

- help_people

wait so what about pt b?

- 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.

- 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

- help_people

ok so everything is bueno?

- hartnn

bueno?
yes, everything is okay :)

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