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anonymous

  • one year ago

I seriously need help with question with polynomials. Please help me? Medal and fan!

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  1. anonymous
    • one year ago
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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)

  2. anonymous
    • one year ago
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    Hello?

  3. anonymous
    • one year ago
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    Um, Haseeb? Are you there?

  4. anonymous
    • one year ago
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    @Hero If you have the time can you help me out with this?

  5. beginnersmind
    • one year ago
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    Can you calculate A for a given value of t? Say t = 2, what will be the painted area?

  6. anonymous
    • one year ago
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    Yes.

  7. beginnersmind
    • one year ago
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    Ok, so you can solve part B.

  8. anonymous
    • one year ago
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    Yes, but Part A is what I'm having trouble with.

  9. beginnersmind
    • one year ago
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    Cool. Take the same steps as for part B, but instead of using 10 just keep t. You won't get a number but an expression involving t.

  10. anonymous
    • one year ago
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    So it would A[r(t)]=πr2+3t?

  11. beginnersmind
    • one year ago
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    Just to check, what result did you get for part B?

  12. anonymous
    • one year ago
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    I haven't done Part B yet.

  13. beginnersmind
    • one year ago
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    You should. It will help with part A. It also makes it easier to understand someone else's explaination, if you'll still need help.

  14. anonymous
    • one year ago
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    Okay, I'll try.

  15. anonymous
    • one year ago
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    Wait, but what is the radius of the spilled paint?

  16. beginnersmind
    • one year ago
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    r(t) = 3t, where t represents time in minutes and r represents how far the paint is spreading.

  17. beginnersmind
    • one year ago
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    so r is meant to be the radius

  18. anonymous
    • one year ago
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    Oh, so the paint is spreading equivalent to the radius of the circle?

  19. beginnersmind
    • one year ago
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    The radius of the painted circle is increasing as time goes on. So it's 3 after 1 minute, 6 after 2 minutes, etc.

  20. anonymous
    • one year ago
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    So it's 282.6?

  21. beginnersmind
    • one year ago
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    what did you get for the radius after 10 minutes?

  22. anonymous
    • one year ago
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    30.

  23. anonymous
    • one year ago
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    Oh.

  24. anonymous
    • one year ago
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    295.788?

  25. beginnersmind
    • one year ago
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    Let me check how I can write pretty expressions real quick. :)

  26. beginnersmind
    • one year ago
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    \[A =\pi r ^{2}\]

  27. beginnersmind
    • one year ago
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    Is that what you used?

  28. anonymous
    • one year ago
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    Yes

  29. anonymous
    • one year ago
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    With 30 as r

  30. anonymous
    • one year ago
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    Because 30 is the radius after 10 minutes.

  31. beginnersmind
    • one year ago
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    When I plug in r = 30 I get\[\pi (30)^{2} = 900\pi= 900x3.14 = 2826\]

  32. beginnersmind
    • one year ago
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    Hm, seems like your first answer was almost right, just off by a factor of 10 for some reason.

  33. anonymous
    • one year ago
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    Oh.

  34. anonymous
    • one year ago
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    So part B is 2826

  35. beginnersmind
    • one year ago
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    Yes. Now for part A.

  36. beginnersmind
    • one year ago
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    The idea is the same, but now instead of pluging in 30 into A = πr2 you plug in 3t

  37. anonymous
    • one year ago
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    A[r(t)] = pi*3t^2?

  38. beginnersmind
    • one year ago
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    More like pi*(3t)^2

  39. beginnersmind
    • one year ago
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    Probably should be simplified to 9*pi*t^2

  40. anonymous
    • one year ago
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    Oh.

  41. anonymous
    • one year ago
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    And that's part A?

  42. beginnersmind
    • one year ago
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    Yes. It gives you an expression to calculate the area directly from time. Without having to calculate the radius first.

  43. anonymous
    • one year ago
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    Thank you. :)

  44. beginnersmind
    • one year ago
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    No problem :)

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