Asked by :)
                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?
            
            
        Answers
                    Answered by
            :)
            
    i'm sorry, this is about optimization problems.
    
                    Answered by
            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 = (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
    
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
                    Answered by
            Kassahun
            
    5inches
    
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