A tank in the shape of a cylinder standing on end leaks water through a circular hole in its bottom. If friction is considered, the height h of the water in the tank as a function of time is given by dh Ar /2gh dt where A, and Ap are the cross-sectional areas of the water in the tank and of the hole, respectively, g is the gravitational coefficient, and 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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5. A tank in the shape of a cylinder standing on end leaks water through a circular hole in its
bottom. If friction is considered, the height h of the water in the tank as a function of time
is given by
dh
A
V2gh
dt
where A, and A are the cross-sectional areas of the water in the tank and of the hole,
respectively, g is the gravitational coefficient, and 0 < c < 1 is a constat. Solve for h(t),
given that the initial height of water is H. Sketch the graph of h(t) and give its interval I of
definition in terms of the given initial constants.
Transcribed Image Text:5. A tank in the shape of a cylinder standing on end leaks water through a circular hole in its bottom. If friction is considered, the height h of the water in the tank as a function of time is given by dh A V2gh dt where A, and A are the cross-sectional areas of the water in the tank and of the hole, respectively, g is the gravitational coefficient, and 0 < c < 1 is a constat. Solve for h(t), given that the initial height of water is H. Sketch the graph of h(t) and give its interval I of definition in terms of the given initial constants.
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