Question

I really do not get this :/

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 1

A[r(t)] means substitute r for r(t) function into A(r)

Answer 2

...what? so then its \[A[r(t)]=3.14(10^2)+3t ?\]
i dont get it..

Answer 3

don't add
r(t) = what ?

Answer 4

3t

Answer 5

yes right so you can replace r(t) with 3t
A(3t) =pi r^2
replace r with 3t don't add 3t

Answer 6

oh..is that it?

Answer 7

yes right \[\huge\rm A(\color{red}{r(t)})=A(\color{ReD}{3t})= \pi\color{Red}{ r}^2\]

^replace r with 3t and then take square

Answer 8

....so then its \[A(3t)=3.14*3^2?\]

Answer 9

not just 3 it's (3t)^2

Answer 10

okay so then its \[A(3t)=3.14(3t^2)\]
now what .-.

Answer 11

(3t)^2 means 3^2 * t^2

Answer 12

which is \[9(t^2)\]

Answer 13

yes right \[\huge\rm A(\color{red}{r(t)})=A(\color{ReD}{3t})= 9t^2\pi\]

Answer 14

part B substitute t for 10

Answer 15

use 3.14 for pi

Answer 16

\[9(10^2)(3.14)=2826\]

Answer 17

looks good

Answer 18

so,
Part A: \[A[r(t)]=A(3t)=9t^2 \pi\]
and Part B:
\[9(10^2)(3.14)=2826\]
right? thats the answer right?? :D

Answer 19

yep

Answer 20

or you can say 9pit^2 :D

Answer 21

you're awesome..thank you thank you thank you!!

Answer 22

np :=)