Question

I seriously need help with question with polynomials. Please help me? Medal and fan!

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. (6 points)

Part B: How large is the area of spilled paint after 10 minutes? You may use 3.14 to approximate π in this problem. (4 points)

Answer 2

Hello?

Answer 3

Um, Haseeb? Are you there?

Answer 4

@Hero If you have the time can you help me out with this?

Answer 5

Can you calculate A for a given value of t? Say t = 2, what will be the painted area?

Answer 6

Yes.

Answer 7

Ok, so you can solve part B.

Answer 8

Yes, but Part A is what I'm having trouble with.

Answer 9

Cool. Take the same steps as for part B, but instead of using 10 just keep t. You won't get a number but an expression involving t.

Answer 10

So it would A[r(t)]=πr2+3t?

Answer 11

Just to check, what result did you get for part B?

Answer 12

I haven't done Part B yet.

Answer 13

You should. It will help with part A. It also makes it easier to understand someone else's explaination, if you'll still need help.

Answer 14

Okay, I'll try.

Answer 15

Wait, but what is the radius of the spilled paint?

Answer 16

r(t) = 3t, where t represents time in minutes and r represents how far the paint is spreading.

Answer 17

so r is meant to be the radius

Answer 18

Oh, so the paint is spreading equivalent to the radius of the circle?

Answer 19

The radius of the painted circle is increasing as time goes on. So it's 3 after 1 minute, 6 after 2 minutes, etc.

Answer 20

So it's 282.6?

Answer 21

what did you get for the radius after 10 minutes?

Answer 22

30.

Answer 23

Oh.

Answer 24

295.788?

Answer 25

Let me check how I can write pretty expressions real quick. :)

Answer 26

\[A =\pi r ^{2}\]

Answer 27

Is that what you used?

Answer 28

Yes

Answer 29

With 30 as r

Answer 30

Because 30 is the radius after 10 minutes.

Answer 31

When I plug in r = 30 I get\[\pi (30)^{2} = 900\pi= 900x3.14 = 2826\]

Answer 32

Hm, seems like your first answer was almost right, just off by a factor of 10 for some reason.

Answer 33

Oh.

Answer 34

So part B is 2826

Answer 35

Yes. Now for part A.

Answer 36

The idea is the same, but now instead of pluging in 30 into

A = πr2

you plug in 3t

Answer 37

A[r(t)] = pi*3t^2?

Answer 38

More like

pi*(3t)^2

Answer 39

Probably should be simplified to 9*pi*t^2

Answer 40

Oh.

Answer 41

And that's part A?

Answer 42

Yes.

It gives you an expression to calculate the area directly from time. Without having to calculate the radius first.

Answer 43

Thank you. :)

Answer 44

No problem :)