Question

Please check if this is right???

Answer 1

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 2

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

Answer 3

@hartnn @Elsa123

Answer 4

part A,
don't simplify,
write \(9\pi t^2\) as the answer.

part B,
writing units would be better
2826 sq. units

Answer 5

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

Answer 6

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

Answer 7

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

^^^

Answer 8

yes i saw :)

Answer 9

wait

Answer 10

I'm here :)

Answer 11

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

Answer 12

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

Answer 13

yep

Answer 14

ok so is 30 still radius or ?

Answer 15

(just out of curiosity)

Answer 16

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

Answer 17

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

Answer 18

yes

Answer 19

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

Answer 20

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

Answer 21

yes, i agreed, r =30

Answer 22

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

Answer 23

yes,
part A is perfect

Answer 24

wait so what about pt b?

Answer 25

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.

Answer 26

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

yesss

Answer 27

ok so everything is bueno?

Answer 28

bueno?

yes, everything is okay :)