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Math Help - Optimization Problem

  1. #1
    Member ~berserk's Avatar
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    Optimization Problem

    This problem has been giving me a lot of trouble, mostly because I am unsure how to set it up in order to find the minimum value.

    Two posts, one 12ft high and one 28ft high, stand 30ft apart. They are to be stayed by two wires attached to a single stake, running from ground level to the top of each post. Where should the stake be placed to use the least amount of wire?

    I'm not really sure how to set this up besides this diagram:Optimization Problem-triangles.jpg
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by ~berserk View Post
    This problem has been giving me a lot of trouble, mostly because I am unsure how to set it up in order to find the minimum value.

    Two posts, one 12ft high and one 28ft high, stand 30ft apart. They are to be stayed by two wires attached to a single stake, running from ground level to the top of each post. Where should the stake be placed to use the least amount of wire?

    I'm not really sure how to set this up besides this diagram:Click image for larger version. 

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    This should get you started

    let x be the distace the peg is from the 12ft pole. Then the distance from the peg to the 28ft pole is 30-x

    Now use the pythogrean theorem to find the lenth of each hypotenuse.

    Good luck!
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