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.

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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.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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A[r(t)] means substitute r for r(t) function into A(r)
...what? so then its \[A[r(t)]=3.14(10^2)+3t ?\] i dont get it..
don't add r(t) = what ?

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3t
yes right so you can replace r(t) with 3t A(3t) =pi r^2 replace r with 3t don't add 3t
oh..is that it?
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
....so then its \[A(3t)=3.14*3^2?\]
not just 3 it's (3t)^2
okay so then its \[A(3t)=3.14(3t^2)\] now what .-.
(3t)^2 means 3^2 * t^2
which is \[9(t^2)\]
yes right \[\huge\rm A(\color{red}{r(t)})=A(\color{ReD}{3t})= 9t^2\pi\]
part B substitute t for 10
use 3.14 for pi
\[9(10^2)(3.14)=2826\]
looks good
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
yep
or you can say 9pit^2 :D
you're awesome..thank you thank you thank you!!
np :=)

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