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Math Help - Help with problem solving

  1. #1
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    Red face Help with problem solving

    Please help me with the following question:

    A sculptor commissioned to design a monument for the long reach city council, has chosen a parabolic shape that stand 15m high with supports at 45 as shown in the diagram. For aesthetic reason the sculptor chooses the shape given by the function

    Y = 15 - x
    π (pie)

    ie. y equals 15 minus x over π (pie)

    Find the length of the support beam marked A. Provide justification for your answer.

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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    do you mean

    E_1 \rightarrow y=\frac{15-x^2}{\pi}

    or

    E_2 \rightarrow y=15-\frac{x^2}{\pi}
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  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    \tan^{-1}(45^{\circ})=1

    so the equation of the line is y=x

    setting y=x equal to y=15-\frac{x^2}{\pi}

    x=15-\frac{x^2}{\pi} \iff x^2+\pi x=15 \pi

    so I will solve by completeing the square so we will add \frac{\pi^2}{4} to both sides

    x^2+\pi x +\frac{\pi^2}{4}=15 \pi +\frac{\pi^2}{4} \iff (x-\frac{\pi}{2})^2=\frac{\pi(60+\pi)}{4}


    x=\frac{\pi}{2} +\frac{\sqrt{\pi(60+\pi)}}{2}

    So this is half the distance from the diagram so if we multiply it by 2 we will get the length of the line.

    L=\pi+\sqrt{\pi(60+\pi)}
    Last edited by TheEmptySet; March 28th 2008 at 10:21 PM. Reason: typo
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