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A trough at the end of a gutter spout is meant to direct water away from a house. The homeowner makes the trough from a rectangular piece of aluminum that is 24 in. long and 8 in. wide. He makes a fold along the two long sides a distance of x inches from the edge. 38) 24 in. 8 - 2x a. Write a function to represent the volume in terms of x. b. What value of x will maximize the volume of water that can be carried by the gutter?

A trough at the end of a gutter spout is meant to direct water away from a house. The homeowner makes the trough from a rectangular piece of aluminum that is 24 in. long and 8 in. wide. He makes a fold along the two long sides a distance of x inches from the edge. 38) 24 in. 8 - 2x a. Write a function to represent the volume in terms of x. b. What value of x will maximize the volume of water that can be carried by the gutter?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve the problem. 38) A trough at the end of a gutter spout is meant to direct water away from a house. The homeowner makes the trough from a rectangular piece of aluminum that is 24 in. long and 8 in. wide. He makes a fold along the two long sides a distance of x inches from the edge. 38) 24 in. 8 - 2x a. Write a function to represent the volume in terms of x. b. What value of x will maximize the volume of water that can be carried by the gutter?
Transcribed Image Text:Solve the problem. 38) A trough at the end of a gutter spout is meant to direct water away from a house. The homeowner makes the trough from a rectangular piece of aluminum that is 24 in. long and 8 in. wide. He makes a fold along the two long sides a distance of x inches from the edge. 38) 24 in. 8 - 2x a. Write a function to represent the volume in terms of x. b. What value of x will maximize the volume of water that can be carried by the gutter?
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