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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)
I'm still working on Part B.
that looks right for part A
For the growing circle, The Area is a function of the radius, and the radius i a function of time...
use t=10 min in your Area function
My mom helped me with Part B, but neither of us really understand it. We kinda suck at math, unfortunately :/
@DanJS If the area is a function of the radius and the radius is a function of time, wouldn't I have to use t = 10 in my radius function and not the area function?
it doesnt matter, try it both ways, same answer
Calculating A(r(t)) is the same as first finding r(t) then using that in A(r)
Right, and the same answer if you use A(r(t)) 28.26 * 10^2 = 2826
So my work is right?
yes, looks good
Thank you so much! I really appreciate your help! :)
no prob, goodluck
what was part A?
π(3t)^2 ^ That equation will help you find the answer. You multiply 3.14 times 3^2 times t^2
So it'll look like: (3.14)(9)(t^2) Then multiply. The answer is 28.26t^2
Wait can you please explain what is part A and B? please
@DanJS please help me