Posted by Matt on Thursday, December 2, 2010 at 10:51pm.
A wire 100 inches long is to be cut into two pieces. One of the pieces will be bent into the shape of a circle and the other into the shape of a equilateral triangle. How should the wire be cut so as to maximize the sum of the area of the areas of the circle and triangle will be maximized?

Calc  MathMate, Thursday, December 2, 2010 at 11:01pm
L=total length,
x=length of piece for triangle
So
Lx=circumference of circle
At(x)=area of triangle
=√3 *x²/4
Ac(x)=area of circle
=π((Lx)/(2π))²
=(Lx)²/(4π)
Total Area, A(x)
= At(x)+Ac(x)
To find the maximum/minimum,
Equate
A'(x)=0 and solve for x.
Find A(x) = max. area.
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