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Consider the two interconnected tanks shown in Figure

Elementary Differential Equations and Boundary Value Problems | 10th Edition | ISBN: 9780470458310 | Authors: William E. Boyce ISBN: 9780470458310 168

Solution for problem 22 Chapter 7.1

Elementary Differential Equations and Boundary Value Problems | 10th Edition

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Elementary Differential Equations and Boundary Value Problems | 10th Edition | ISBN: 9780470458310 | Authors: William E. Boyce

Elementary Differential Equations and Boundary Value Problems | 10th Edition

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Problem 22

Consider the two interconnected tanks shown in Figure 7.1.6. Tank 1 initially contains30 gal of water and 25 oz of salt, and Tank 2 initially contains 20 gal of water and 15 ozof salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 1.5 gal/min. Themixture flows from Tank 1 to Tank 2 at a rate of 3 gal/min.Water containing 3 oz/gal of saltalso flows into Tank 2 at a rate of 1 gal/min (from the outside). The mixture drains fromTank 2 at a rate of 4 gal/min, of which some flows back into Tank 1 at a rate of 1.5 gal/min,while the remainder leaves the system.(a) Let Q1(t) and Q2(t), respectively, be the amount of salt in each tank at time t. Writedown differential equations and initial conditions that model the flow process. Observethat the system of differential equations is nonhomogeneous.(b) Find the values of Q1 and Q2 for which the system is in equilibriumthat is, does notchange with time. Let QE1 and QE2 be the equilibrium values. Can you predict which tankwill approach its equilibrium state more rapidly?(c) Let x1 = Q1(t) QE1 and x2 = Q2(t) QE2 . Determine an initial value problem for x1and x2. Observe that the system of equations for x1 and x2 is homogeneous.

Step-by-Step Solution:
Step 1 of 3

L3 - 4 ▯ ▯ 1 ex. Sketch the graph of y = −2s n x . 2 1 −π π −1 ex. Sketch the graph of y = |sin(x − π)|. 1 −π π −1

Step 2 of 3

Chapter 7.1, Problem 22 is Solved
Step 3 of 3

Textbook: Elementary Differential Equations and Boundary Value Problems
Edition: 10
Author: William E. Boyce
ISBN: 9780470458310

This textbook survival guide was created for the textbook: Elementary Differential Equations and Boundary Value Problems, edition: 10. This full solution covers the following key subjects: . This expansive textbook survival guide covers 76 chapters, and 2039 solutions. Elementary Differential Equations and Boundary Value Problems was written by and is associated to the ISBN: 9780470458310. The answer to “Consider the two interconnected tanks shown in Figure 7.1.6. Tank 1 initially contains30 gal of water and 25 oz of salt, and Tank 2 initially contains 20 gal of water and 15 ozof salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 1.5 gal/min. Themixture flows from Tank 1 to Tank 2 at a rate of 3 gal/min.Water containing 3 oz/gal of saltalso flows into Tank 2 at a rate of 1 gal/min (from the outside). The mixture drains fromTank 2 at a rate of 4 gal/min, of which some flows back into Tank 1 at a rate of 1.5 gal/min,while the remainder leaves the system.(a) Let Q1(t) and Q2(t), respectively, be the amount of salt in each tank at time t. Writedown differential equations and initial conditions that model the flow process. Observethat the system of differential equations is nonhomogeneous.(b) Find the values of Q1 and Q2 for which the system is in equilibriumthat is, does notchange with time. Let QE1 and QE2 be the equilibrium values. Can you predict which tankwill approach its equilibrium state more rapidly?(c) Let x1 = Q1(t) QE1 and x2 = Q2(t) QE2 . Determine an initial value problem for x1and x2. Observe that the system of equations for x1 and x2 is homogeneous.” is broken down into a number of easy to follow steps, and 216 words. The full step-by-step solution to problem: 22 from chapter: 7.1 was answered by , our top Math solution expert on 12/23/17, 04:36PM. Since the solution to 22 from 7.1 chapter was answered, more than 453 students have viewed the full step-by-step answer.

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Consider the two interconnected tanks shown in Figure