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Math Help - Another problem

  1. #1
    Newbie Twilight's Avatar
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    Another problem

    Ok, I suck at word problems, but I have to get this done. I'm going to post the whole thing, but I probably only need the equation. After that, I should be able to do it.

    A rope is to be streched at uniform height from a tree to a fence, 20 feet from the tree, and then to the side of a building, 35 feet from the tree, at a point 30 feet from the fence.

    a. If 63 feet of rope is to be used, how far from the building wall should the rope meet the fence?

    b.How far from the building wall should the rope meet the fence if as little rope as possible is to be used?

    It's not very good, but this is the best I can do:


    Again, thanks in advance.
    Attached Thumbnails Attached Thumbnails Another problem-problem.jpg  
    Last edited by Twilight; October 2nd 2007 at 07:43 PM.
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  2. #2
    MHF Contributor
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    I'm not real clear on the orientation of things. Can you provide a picutre of a much better description of the situation?
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  3. #3
    Newbie Twilight's Avatar
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    Ok, I put a rough picture of the diagram in the textbook in the first post. Thank you for helping.
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  4. #4
    MHF Contributor
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    Very nice. The first part required only the Pythagorean Theorem and some algebra. If "x" is the desired distance form the building to the fence tie, we have:

    \sqrt{30^{2}+x^{2}}\;+\;\sqrt{20^{2}+(35-x)^{2}}\;=\;63

    Unfortunately, it appears the answer may not be unique. You tell me what to do about that.

    For the minimum, since you have posted in a generic place, I can't know what methods you are to use. Are we up to calculus or have we only analytic geometry on our side?
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  5. #5
    Newbie Twilight's Avatar
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    I am in precalulus, and this is uner the equations and inequalities section in the book.
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  6. #6
    MHF Contributor
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    Very good. You'll have to do a little algebra.

    Isolate a square root. Square things. Simplify.
    Isolate a square root. Square things. Simplify.

    Make the equation look like a parabola and you should see what to do to find the minimum.
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