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A piece of wire 10 feet long is cut into two pieces. One piece is bent into the shape of a circle and the other into the shape of the square. How should the wire be cut so that the combined area of the two figures is as small as possible?

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  1. i'm sorry, this is about optimization problems.

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  2. x and (10 - x)
    x is 2 pi r
    r = x/(2 pi)
    Ac = pi r^2 = pi x^2/(4pi^2) = x^2/(4pi)

    (10 -x) = 4*side = 4 s
    so
    s = (10-x)/4
    As = s^2 = (100-20 x + x^2)/16

    A= Ac+As = x^2/4pi + (1/16)(x^2-20x+100)

    dA/dx = 0 for max or min
    0= x/2pi +1/16 (2x-20)
    0= .16 x + .125 x - 1.25
    0= .285 x - 1.25
    x = 4.4

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  3. 5inches

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