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hawkfalcon Group Title

The height of triangle ACE is 12 and base AE = 20. A rectangle is inscribed in triangle ACE as shown below.? a) Express the rectangle’s area as a function of x and y. Use the fact that the triangle ACE is similar to triangle BCD to write y as a function of x. c)Express the rectangle’s area as a function of only x. d) Find the maximum possible area of the rectangle.

  • one year ago
  • one year ago

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  1. hawkfalcon Group Title
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    |dw:1345995812545:dw|

    • one year ago
  2. hawkfalcon Group Title
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    Nobody knows what to do?:#

    • one year ago
  3. hawkfalcon Group Title
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    @Zekarias ?

    • one year ago
  4. Zekarias Group Title
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    a) (12-y)x b) 12(x-0.1x^2) c) 30 sq units

    • one year ago
  5. hawkfalcon Group Title
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    ...How?

    • one year ago
  6. Zekarias Group Title
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    Is "How" for all of it?

    • one year ago
  7. hawkfalcon Group Title
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    Just b and c

    • one year ago
  8. hawkfalcon Group Title
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    especially b... :O

    • one year ago
  9. Zekarias Group Title
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    consider the perpendicular line form C, we can come out with the ratio 12/y =10/x, where 10 is half the rectangles side,20. Then simplify it so as to inset the result in to the equation in 'a'. To 'c' just use the application of derivative.

    • one year ago
  10. hawkfalcon Group Title
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    Okay. Makes sense I guess:p thanks!

    • one year ago
  11. ganeshie8 Group Title
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    small catch

    • one year ago
  12. ganeshie8 Group Title
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    triangle ACE is similar to triangle BCD => height1/height2 = base1/base2

    • one year ago
  13. ganeshie8 Group Title
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    12/y = 20/x y = (3/5)x

    • one year ago
  14. ganeshie8 Group Title
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    this would give you max area 60

    • one year ago
  15. hawkfalcon Group Title
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    o.O But y needs to be written as a function of x.

    • one year ago
  16. ganeshie8 Group Title
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    y = (3/5)x

    • one year ago
  17. ganeshie8 Group Title
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    its a function of x

    • one year ago
  18. ganeshie8 Group Title
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    linear

    • one year ago
  19. hawkfalcon Group Title
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    Oh yeah :3. So why did you use the entire base and @Zekarias used 1/2?

    • one year ago
  20. ganeshie8 Group Title
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    since both are similar triangles, "ratio of bases" equals "ratio of heights"

    • one year ago
  21. hawkfalcon Group Title
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    Okay, that makes sense. :3 Can you explain how you got 60 though?

    • one year ago
  22. ganeshie8 Group Title
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    write the area equation in x and optimize

    • one year ago
  23. ganeshie8 Group Title
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    for optimizing, use either of the below two : 1) its a parabola facing down so max value = f(-b/2a) or 2) use calculus

    • one year ago
  24. ganeshie8 Group Title
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    this q from conics, or calculus ?

    • one year ago
  25. hawkfalcon Group Title
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    calculus. Going into calculus next year and they gave us some prep stuff*.*

    • one year ago
  26. ganeshie8 Group Title
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    oh ok, so we have this so far : A = x(12-y) -------(1) y = (3/5)x --------(2)

    • one year ago
  27. hawkfalcon Group Title
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    Okay, true.

    • one year ago
  28. ganeshie8 Group Title
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    hmm which one moves ?

    • one year ago
  29. ganeshie8 Group Title
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    ohhk yeah as we go down its moving a lot it seems...

    • one year ago
  30. ganeshie8 Group Title
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    substitute (2) in (1)

    • one year ago
  31. hawkfalcon Group Title
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    x(12-(3/5)x)

    • one year ago
  32. ganeshie8 Group Title
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    \(A = x(12 - \frac{3}{5}x)\) \(A = 12x- \frac{3}{5}x^2)\)

    • one year ago
  33. hawkfalcon Group Title
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    Okayy and solve for x

    • one year ago
  34. ganeshie8 Group Title
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    nope we need to optimize A

    • one year ago
  35. ganeshie8 Group Title
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    find maximum possible value of A, right ?

    • one year ago
  36. hawkfalcon Group Title
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    Oh.

    • one year ago
  37. hawkfalcon Group Title
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    Ya

    • one year ago
  38. ganeshie8 Group Title
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    theres a process for finding maximum/minimum values of any funcitons

    • one year ago
  39. ganeshie8 Group Title
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    you familiar with differentiation ?

    • one year ago
  40. hawkfalcon Group Title
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    ... I guess I havenet learned that yet..

    • one year ago
  41. ganeshie8 Group Title
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    its simple... if you knw differentiation already

    • one year ago
  42. hawkfalcon Group Title
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    I think we are learning that next year :( (monday)

    • one year ago
  43. ganeshie8 Group Title
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    just if you knw derivative of x, and x^2, its enough

    • one year ago
  44. ganeshie8 Group Title
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    oh ok then you cannot use calculus, lets switch to conics. you knw parabolas, right

    • one year ago
  45. hawkfalcon Group Title
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    Okay, I don't know how to do that.. Maybe I should make a new question asking for the dirivative of A=12x-3/4x^2

    • one year ago
  46. hawkfalcon Group Title
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    Yes.

    • one year ago
  47. hawkfalcon Group Title
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    You said f(-b/2a)

    • one year ago
  48. ganeshie8 Group Title
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    yes

    • one year ago
  49. ganeshie8 Group Title
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    A = 12x - (3/5) x^2

    • one year ago
  50. ganeshie8 Group Title
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    \(A = \frac{-3}{5}x^2 + 12x\)

    • one year ago
  51. hawkfalcon Group Title
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    Yes

    • one year ago
  52. ganeshie8 Group Title
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    a = -3/5 b = 12

    • one year ago
  53. hawkfalcon Group Title
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    Cool, thanks, just plug and chug now:D

    • one year ago
  54. ganeshie8 Group Title
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    f(-b/2a) gives the vertex y co-ordinate, which is the maximum value

    • one year ago
  55. hawkfalcon Group Title
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    y=10

    • one year ago
  56. ganeshie8 Group Title
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    |dw:1345999525420:dw|

    • one year ago
  57. ganeshie8 Group Title
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    -b/2a = 10 f(-b/2a) = ?

    • one year ago
  58. ganeshie8 Group Title
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    put x = -b/2a = 10, in area function

    • one year ago
  59. hawkfalcon Group Title
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    Okay.

    • one year ago
  60. hawkfalcon Group Title
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    60!:D

    • one year ago
  61. ganeshie8 Group Title
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    if you remember, for any parabola, -b/2a is the x-coordinate of vertex f(-b/2a) is the y-coordinate of vertex

    • one year ago
  62. ganeshie8 Group Title
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    great !!

    • one year ago
  63. hawkfalcon Group Title
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    Thank you so much! Now I can do the rest of these problems:D

    • one year ago
  64. ganeshie8 Group Title
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    glad to hear ! calculus wud be much fun :) good luck !!

    • one year ago
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