A piece of wire 16 in. long is to be cut into two pieces.

Chapter 4, Problem 45

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A piece of wire 16 in. long is to be cut into two pieces. Let x denote the length of the first piece and 16 x the length of the second. The first piece is to be bent into a circle and the second piece into a square. (a) Express the total combined area A of the circle and the square as a function of x. (b) For which value of x is the area A a minimum? (c) Using the x-value that you found in part (b), find the ratio of the lengths of the shorter to the longer piece of wire.

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