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Math Help - Calculus and Geometry problem

  1. #1
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    Calculus and Geometry problem

    Please help me with this problem, I got a solution but I don't think it's correct.

    A, B and C are computers. A Printer needs to be connected to each of them. Where does P need to be placed in order to minimize the total cable length AP + BP + CP?

    Sketch:
    [img=http://img233.imageshack.us/img233/1386/sketchml6.th.jpg]

    The equation I got is:

    Square root of (4 + P) + Square root of (5+ P) + 8-P.

    However, this does not seem to be correct and if I try to find the minimum I get strange values. Please tell me my mistake and help me. Thank you very much for your help.

    There's another similar problem, but the coordinates confuse me. P has to be on the line and the question is where to place P so that the sum of the length of the lines from AP BP and CP is as short as possible.

    Last edited by Instigator; September 30th 2007 at 08:33 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Instigator View Post
    Please help me with this problem, I got a solution but I don't think it's correct.

    A, B and C are computers. A Printer needs to be connected to each of them. Where does P need to be placed in order to minimize the total cable length AP + BP + CP?

    Sketch:
    [img=http://img233.imageshack.us/img233/1386/sketchml6.th.jpg]

    The equation I got is:

    Square root of (4 + P) + Square root of (5+ P) + 8-P.

    However, this does not seem to be correct and if I try to find the minimum I get strange values. Please tell me my mistake and help me. Thank you very much for your help.

    There's another similar problem, but the coordinates confuse me. P has to be on the line and the question is where to place P so that the sum of the length of the lines from AP BP and CP is as short as possible.

    Assign the point P the coordinates (x,y), then compute the sum of the
    distances from A, B and C:

    <br />
d= \sqrt{(x-1)^2+(y-2)^2} + \sqrt{(x-3)^2+(y-11)^2} + \sqrt{(x-7)^2+(y-3)^2}<br />

    Now find (x,y) which minimises d

    RonL
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