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shes.radical

  • one year ago

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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  1. Nnesha
    • one year ago
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    A[r(t)] means substitute r for r(t) function into A(r)

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

  3. Nnesha
    • one year ago
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    don't add r(t) = what ?

  4. shes.radical
    • one year ago
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    3t

  5. Nnesha
    • one year ago
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    yes right so you can replace r(t) with 3t A(3t) =pi r^2 replace r with 3t don't add 3t

  6. shes.radical
    • one year ago
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    oh..is that it?

  7. Nnesha
    • one year ago
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    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

  8. shes.radical
    • one year ago
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    ....so then its \[A(3t)=3.14*3^2?\]

  9. Nnesha
    • one year ago
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    not just 3 it's (3t)^2

  10. shes.radical
    • one year ago
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    okay so then its \[A(3t)=3.14(3t^2)\] now what .-.

  11. Nnesha
    • one year ago
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    (3t)^2 means 3^2 * t^2

  12. shes.radical
    • one year ago
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    which is \[9(t^2)\]

  13. Nnesha
    • one year ago
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    yes right \[\huge\rm A(\color{red}{r(t)})=A(\color{ReD}{3t})= 9t^2\pi\]

  14. Nnesha
    • one year ago
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    part B substitute t for 10

  15. Nnesha
    • one year ago
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    use 3.14 for pi

  16. shes.radical
    • one year ago
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    \[9(10^2)(3.14)=2826\]

  17. Nnesha
    • one year ago
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    looks good

  18. shes.radical
    • one year ago
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    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

  19. Nnesha
    • one year ago
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    yep

  20. Nnesha
    • one year ago
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    or you can say 9pit^2 :D

  21. shes.radical
    • one year ago
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    you're awesome..thank you thank you thank you!!

  22. Nnesha
    • one year ago
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    np :=)

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