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Math Help - Find the value of p (with graph)

  1. #1
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    Find the value of p (with graph)

    In the figure below, ABCD is a rectangle. Points A and C lie on the graph of y=px^3, where p is a constant. If the area of ABCD is 4, what is the value of p?

    Sorry for the sloppy graph! Can you please explain how you got the answer?

    Thanks in advance!!

    - - - -599
    Attached Thumbnails Attached Thumbnails Find the value of p (with graph)-599.jpg  
    Last edited by fabxx; September 25th 2008 at 11:34 PM. Reason: sorry i made a mistake :)
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  2. #2
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    In y = p^3,
    if p is constant, then y = p^3 should be a horizontal line only....not an "S"-curve, or cubic curve, as shown in the diagram.
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  3. #3
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    i made a mistake. it should be y=px^3
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  4. #4
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    So it is y = p(x^3). Now it makes sense.

    Given, area of ABCD = 4 sq.units.
    AD = BC = |-1/2| +|1/2| = 1 unit
    So, AB = CD = 4/1 = 4 units ----------**

    At point A(-1/2,a)
    y = px^3
    a = p(-1/2)^3 = -p/8

    At point B(-1/2,b)
    b = p(-1/2)^3 = -p/8

    So a = b = -p/8
    That means "a" and b are equidistant from the x-axis.

    Since AB = 4 = (a +b), then,
    a +b = 4
    |-p/8| +|-p/8| = 4
    2|-p/8| = 4
    |-p/8| = 2
    Square both sides to eliminate the absolute sign,
    p^2 / 64 = 4
    p^2 = 4*64
    Take the square roots of both sides,
    p = +,-2*8
    p = +,-16 -----------answer.

    EDIT:
    The rectangle corner points distracted me.
    The p is concerned about the cubic curve only, I forgot.
    The p = sqrt(4*64) = 2*8 = 16 only. Not +,-16.
    Last edited by ticbol; September 26th 2008 at 04:34 AM.
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