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Thread: A word Problem

  1. #1
    Oct 2007

    A word Problem

    Hi, I'm new here. Nobody in my pr-calc class could figure out how to do this problem, so hopefully you can.

    Calvin wants to make a gutter with a rectangular cross section by folding up strips of equal width on a long sheet of metal that is 26cm wide. The larger the cross sectional dimensions, the greater the capacity of the gutter. Find the dimensions that will maximize the gutter's capacity.

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  2. #2
    Eater of Worlds
    galactus's Avatar
    Jul 2006
    Chaneysville, PA
    You can do with or without calculus.

    Without calculus method:

    Let the lengths of the folded up sides be x.

    Then the base will have width 26-2x

    The area of the gutter is $\displaystyle x(26-2x) = -2x^{2}+26x$

    Now you have a quadratic to solve.

    To find the maximum capacity of the gutter, use x = -b/(2a).
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