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10. A trough at the end of a gutter spout is mcant to direct water away from the house. The homeowner makes the trough from a rectangular piece of of aluminum that is 20 in. long and 12 in. wide. He makes a fold along the long sides a distance of z inches from the edge. 20 in. 12-2r a). Write a function to represent the volume as a function of r. b). What value of z will maximize the volume of the water that can be carried by the gutter? c). What is the maximum volume.

10. A trough at the end of a gutter spout is mcant to direct water away from the house. The homeowner makes the trough from a rectangular piece of of aluminum that is 20 in. long and 12 in. wide. He makes a fold along the long sides a distance of z inches from the edge. 20 in. 12-2r a). Write a function to represent the volume as a function of r. b). What value of z will maximize the volume of the water that can be carried by the gutter? c). What is the maximum volume.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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10. A trough at the end of a gutter spout is mcant to dircct water away from the house. The homcowner makes the trough from a rectangular picce of of aluminum that is 20 in. long and 12 in. wide. He makes a fold along the long sides a distance of z inches from the odge. 20 in. 12-2r a). Write a function to represent the volume as a function of r. b). What value of z will mnaximize the volume of the water that can be carried by the gutter? c). What is the maximum volume.
Transcribed Image Text:10. A trough at the end of a gutter spout is mcant to dircct water away from the house. The homcowner makes the trough from a rectangular picce of of aluminum that is 20 in. long and 12 in. wide. He makes a fold along the long sides a distance of z inches from the odge. 20 in. 12-2r a). Write a function to represent the volume as a function of r. b). What value of z will mnaximize the volume of the water that can be carried by the gutter? c). What is the maximum volume.
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