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A trough in the shape of a half cylinder has a length of 5 m and a radius of 1 m. The trough is full of water when a valve is opened, and water flows out of the bottom of the trough changing its volume. 5m. a) Identify the dependent and independent variables. b) Write a formula V(x) for the volume of the trough, where x is the level of the water measured from the bottom of the trough. (Hint: the area of a sector of a circle or radius r subtended by an angle 0 is 20/2) c) Find the domain of V according to the context of the problem given. d) Find the range of V according to the context of the problem given.

A trough in the shape of a half cylinder has a length of 5 m and a radius of 1 m. The trough is full of water when a valve is opened, and water flows out of the bottom of the trough changing its volume. 5m. a) Identify the dependent and independent variables. b) Write a formula V(x) for the volume of the trough, where x is the level of the water measured from the bottom of the trough. (Hint: the area of a sector of a circle or radius r subtended by an angle 0 is 20/2) c) Find the domain of V according to the context of the problem given. d) Find the range of V according to the context of the problem given.

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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A trough in the shape of a half cylinder has a length of 5 m and a radius of 1 m. The trough is full of water when a valve is opened, and water flows out of the bottom of the trough changing its volume. a) Identify the dependent and independent variables. b) Write a formula V(x) for the volume of the trough, where x is the level of the water measured from the bottom of the trough. (Hint: the area of a sector of a circle or radius r subtended by an angle 0 is 20/2) c) Find the domain of V according to the context of the problem given. d) Find the range of V according to the context of the problem given.
Transcribed Image Text:A trough in the shape of a half cylinder has a length of 5 m and a radius of 1 m. The trough is full of water when a valve is opened, and water flows out of the bottom of the trough changing its volume. a) Identify the dependent and independent variables. b) Write a formula V(x) for the volume of the trough, where x is the level of the water measured from the bottom of the trough. (Hint: the area of a sector of a circle or radius r subtended by an angle 0 is 20/2) c) Find the domain of V according to the context of the problem given. d) Find the range of V according to the context of the problem given.
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