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I have a question that I cant get, help is much appreciated! Thanks in advance!
A wire 60in long is cut into 2 pieces (if optimal). One of the pieces will be bent into the shape of a circle. The other will be bent into the shape of an equilateral triangle. Where should the wire be cut so the sum of the areas is a) a maximum, b) a minimum.
Thanks!!
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We have 60 inches total of wire. Call the length of wire that we use for the triangle x. That leaves us with 60-x inches for the circle. Find an equation relating the total area of the two shapes to x. First, the area of the circle will be
The area of the triangle will be
Add them together to get the total area, then take the derivative
From here, set A'(x) = 0 and solve for x to get an absolute minimum or maximum. Then plug that value for x, along with 0 and 60, into the original equation for total area (that is, plug those values for x into A(x)). The largest value will be the max and the smallest will be the min.
Wrap it in bacon
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