Question

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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

i dont understand this one at all

Answer 3

@welshfella

Answer 4

@Photon336

Answer 5

\[r(t) = 3t \]

\[A(r) = \pi*r^{2}\]

so we need to find the area spilled as a function of time.

since r = 3t, we can easily plug this equation into the second equation.

\[A(r) = \pi*r^{2}\]


\[A(t) = \pi*(3t)^{2}\]


\[A(t) = \pi*9t^{2}\]

now you can express the area in terms of time (t)

Answer 6

we've now built the appropriate function, do you get what I did?

Answer 7

@fantageplayer

Answer 8

yah

Answer 9

i think

Answer 10

so you can easily just plug in now t = 10 minutes into the new equation that we've built.

Answer 11

282.74334

Answer 12

? im not so sure

Answer 13

solving for a:
at=(3.141593)(9)t2
Divide both sides by t.
at
t
=
28.274334t2
t
a=28.274334t
Answer:
a=28.274334t then if t=10 then a=282.74334

Answer 14

@Photon336