Posted by :) on .
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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:),
i'm sorry, this is about optimization problems.

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Damon,
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 = (10x)/4
As = s^2 = (10020 x + x^2)/16
A= Ac+As = x^2/4pi + (1/16)(x^220x+100)
dA/dx = 0 for max or min
0= x/2pi +1/16 (2x20)
0= .16 x + .125 x  1.25
0= .285 x  1.25
x = 4.4 
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Kassahun,
5inches