shes.radical
  • shes.radical
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Nnesha
  • Nnesha
A[r(t)] means substitute r for r(t) function into A(r)
shes.radical
  • shes.radical
...what? so then its \[A[r(t)]=3.14(10^2)+3t ?\] i dont get it..
Nnesha
  • Nnesha
don't add r(t) = what ?

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More answers

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

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