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Math Help - Help with Max/Min Problem

  1. #1
    Newbie
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    Apr 2012
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    Greenville, SC
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    Help with Max/Min Problem

    Here is the problem I need help with. I don't understand how to do it at all.

    The strength of a rectangular beam is directly proportional to the product of its width and the square of its height. Find the dimensions of the strongest beam cut from a cylindrical log of a radius 14 inches.
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  2. #2
    Senior Member
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    Mar 2012
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    Sheffield England
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    Re: Help with Max/Min Problem

    Draw a rectangle inside a circle with its corners touching the circle. Let width =2w and height=2h. Draw a radius from centre to one corner Complete to make a right angled triangle by drawing a line from centre perpendicular to the height. This triangle has sides w,h and 14. So h^2+w^2=196
    Strength is S=k(2w)(2h)^2=8kwh^2
    Replace h^2 by 196-w^2
    Find dS/dw and solve dS/dw=0
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