Program Explanation Given information: The conical tank contains 16 ft water initially and then after one hour the water is dropped to 9 ft . Calculation: The given problem is of training tank. The Toricelli’s law is used for a draining tank. The Toricelli’s law can be represented as, A ( y ) d y d t = − k y ........ (1) Here, A ( y ) is the horizontal cross sectional area of the cone and k is constant. In the given problem A ( y ) = A is constant for every height. The radius of the cross-section of the cone is proportional to the height y . Therefore, the value of A ( y ) = A is y 2 . Now substitute y 2 for A ( y ) in equation (1) as, y 2 d y d t = − k y ........ (2) Now use the method of separation of the variable to solve the equation (1). y 2 d y d t = − k y y 2 y d y d t = − k y 3 2 d y = − k d t Now integrate both sides. ∫ y 3 2 d y = ∫ − k d t y 5 2 5 2 = − k t + c 2 y 5 2 = − 5 k t + c Therefore, the resultant equation is as follows, 2 y 5 2 = − 5 k t + c

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. Penney, David Calvis

Publisher: PEARSON

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Strongly Connected Components

A directed graph in which a path exists between all its pairs of vertices is called a strongly connected graph. A portion of the strongly connected directed graph that contains a path to reach from each vertex to other vertices is called a strongly conne…

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Chapter 1.4, Problem 56P

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Program Description: Purpose of the problem is to find the time when the tank goes to empty.

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Chapter 1.4, Problem 55P

Chapter 1.4, Problem 57P

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Chapter 1 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

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Program Description: Purpose of the problem is to find the time when the tank goes to empty.

Solution Summary: The author explains how the Toricelli's law is used for a draining tank.

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Program Description: Purpose of the problem is to find the time when the tank goes to empty.

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Chapter 1 Solutions