A trough is shaped like a half cylinder with length 4 m and radius 1 m. The trough is full of water when a valve is opened and water flows out of the bottom of the trough at a rate of 6.5m°/hr. (Hint: The area of a sector of a circle of radius r subtended by an angle a is .) Complete parts (a) and (b) below. Outflow 6.5 m'/h a. How fast is the water level changing when the water level is 0.5 m from the bottom of the trough? Let x and y be the sides of the triangle that is formed in the sector, and r represent the radius. Let V be the volume, L be the length of the trough, and e be the angle between x and r. Write an equation relating V, L, r, and 0.
A trough is shaped like a half cylinder with length 4 m and radius 1 m. The trough is full of water when a valve is opened and water flows out of the bottom of the trough at a rate of 6.5m°/hr. (Hint: The area of a sector of a circle of radius r subtended by an angle a is .) Complete parts (a) and (b) below. Outflow 6.5 m'/h a. How fast is the water level changing when the water level is 0.5 m from the bottom of the trough? Let x and y be the sides of the triangle that is formed in the sector, and r represent the radius. Let V be the volume, L be the length of the trough, and e be the angle between x and r. Write an equation relating V, L, r, and 0.
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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Transcribed Image Text:A trough is shaped like a half cylinder with length 4 m and radius 1 m. The trough is full of water when a valve is opened and water flows out of the bottom of the trough at a rate of 6.5m /hr. (Hint:
4 m
Pa
The area of a sector of a circle of radius r subtended by an angle a is
--) Complete parts (a) and (b) below.
2
Outflow
6.5 m/h
a. How fast is the water level changing when the water level is 0.5 m from the bottom of the trough? Let x and y be the sides of the triangle that is formed in the sector, and r represent the radius. Let V be the volume, L be the length of the
trough, and 0 be the angle between x and r. Write an equation relating V, L, r, and 0.
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