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A 29-inch piece of wire is cut into two pieces, which are then bent into a square and a circle, respectively. Where should the wire be cut in order to minimize the sum of the areas of these two shapes? Find the length of the piece of wire that is bent into a square. Round your answer to the nearest inch. (Hint: Denote the lengths of the pieces by x and 29 – x, and use appropriate formulas from geometry.)

A 29-inch piece of wire is cut into two pieces, which are then bent into a square and a circle, respectively. Where should the wire be cut in order to minimize the sum of the areas of these two shapes? Find the length of the piece of wire that is bent into a square. Round your answer to the nearest inch. (Hint: Denote the lengths of the pieces by x and 29 – x, and use appropriate formulas from geometry.)

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter3: Triangles
Section3.5: Inequalities In A Triangles
Problem 39E
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A 29-inch piece of wire is cut into two pieces, which are then bent into a square and a circle, respectively. Where should the wire be cut in order to minimize the sum of the areas of these two shapes? Find the length of the piece of wire that is bent into a square. Round your answer to the nearest inch. (Hint: Denote the lengths of the pieces by x and 29 – x, and use appropriate formulas from geometry.)
Transcribed Image Text:A 29-inch piece of wire is cut into two pieces, which are then bent into a square and a circle, respectively. Where should the wire be cut in order to minimize the sum of the areas of these two shapes? Find the length of the piece of wire that is bent into a square. Round your answer to the nearest inch. (Hint: Denote the lengths of the pieces by x and 29 – x, and use appropriate formulas from geometry.)
Suppose that f'(x) = (x + 7)(x + 4)²(x – 6)°. By examining the zeros of f'(x), identify the x-coordinates of the local maxima and minima of f (x). Separate multiple answers with a comma. If the function doesn't have a local extremum, write None for your answer. (Hint: Recall what you know about multiplicities of zeros and sign changes of polynomials.)
Transcribed Image Text:Suppose that f'(x) = (x + 7)(x + 4)²(x – 6)°. By examining the zeros of f'(x), identify the x-coordinates of the local maxima and minima of f (x). Separate multiple answers with a comma. If the function doesn't have a local extremum, write None for your answer. (Hint: Recall what you know about multiplicities of zeros and sign changes of polynomials.)
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