**Problem Statement:**Two tanks, each holding 100 L of liquid, are interconnected by pipes with liquid flowing from tank A into tank B at a rate of 12 L/min and from tank B into tank A at 3 L/min, as shown in the figure. The liquid inside each tank is kept well stirred. Pure water flows into tank A at a rate of 9 L/min, and the solution flows out of tank B at 9 L/min. If, initially, tank A contains 2.6 kg of salt and tank B contains no salt (only water), determine the mass of salt in each tank at time \( t \geq 0 \). Graph on the same axes the two quantities \( x_1(t) \) and \( x_2(t) \), where \( x_1(t) \) is the mass of salt in tank A and \( x_2(t) \) is the mass in tank B.**Diagram Explanation:**- **Tanks Diagram:** - **Tank A:** - Input: 9 L/min of pure water - Internal flow: 12 L/min to Tank B - Initial salt mass: \( x_1(0) = 2.6 \) kg - **Tank B:** - Input: 12 L/min from Tank A and 3 L/min back to Tank A - Output: Tank B outputs solution at 9 L/min - Initial salt mass: \( x_2(0) = 0 \) kg**Questions:**What are the equations for the mass of salt in each tank at time \( t \geq 0 \)?- \( x_1(t) = \) - \( x_2(t) = \)**Note:** The diagram is included to assist in understanding the flow of liquids and the initial conditions in each tank. It shows the rates of flow and the initial amount of salt present, providing a visual representation to support the problem requirements.

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Answered: Two tanks, each holding 100 L of…

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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