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anonymous

  • one year ago

Help!!! Medal and Fan 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. anonymous
    • one year ago
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    @heretohelpalways @Hero @GIL.ojei @DanJS @dan815 @pooja195

  2. jim_thompson5910
    • one year ago
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    Replace r in \[\Large A = \pi*r^2\] with r(t) then replace r(t) with 3t

  3. jim_thompson5910
    • one year ago
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    after all of those replacements, simplify as much as possible

  4. anonymous
    • one year ago
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    so would it be 28.26t

  5. jim_thompson5910
    • one year ago
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    the t should be t^2 if you leave it in terms of pi, which is what I would do, it would be \[\Large A(t) = 9\pi*t^2\]

  6. jim_thompson5910
    • one year ago
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    when you square 3t, you square both pieces 3 squared = 9 t squared is written as t^2

  7. anonymous
    • one year ago
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    so it would be 28.26t^2 for the area of the spill

  8. jim_thompson5910
    • one year ago
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    correct, if you go with using pi = 3.14

  9. jim_thompson5910
    • one year ago
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    in part B, you replace t with 10 and evaluate

  10. anonymous
    • one year ago
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    so i would multiply 28.26 by 100??

  11. jim_thompson5910
    • one year ago
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    yes

  12. anonymous
    • one year ago
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    so 2826

  13. jim_thompson5910
    • one year ago
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    correct

  14. anonymous
    • one year ago
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    okay thank you

  15. jim_thompson5910
    • one year ago
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    you're welcome

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