There are three interconnected tanks, each with volume 10 liters and containing saline solution. Fresh water is pumped into tank 3 at 1liter/min. Solution from tank 3 is pumped to tank 2 at 1 liter/min. Solution from tank 2 is pumped to tank 1 at 1 liter/min. Solution ispumped from tank 1 at 1 liter per min. At time t=0, tank 3 has 1 gram of salt per liter, tank 2 has fresh water, and tank 1 has 2 grams ofsalt per per liter, Let x(t) be the amount of salt in tank 1 at time t, y(t) the amount of salt in tank 2 at time t, and z(t) the amount of salt intank 3 at timet.The system of differential equations describing the tank system is%3Dx(0) =y(0) =z(0) =Characteristic polynomial:Eigenvalue:Matrix exponential:The solution isx(t) =y(t) =z(t) =Find the approximate time required to reduce the concentration in tank 3 to half the original concentration.

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Answered: There are three interconnected tanks,…

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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A 100-gal tank initially contains 25 gal of 50% salt solution. Fresh water is then poured into the tank at the rate of 4 gal/min, while the well-stirred mixture leaves the tank at the rate of 2 gal/min. Find (a) the amount of time required for overflow to occur and (b) the percentage of salt in the tank at the moment of overflow.
Find the derivative using the methods of Example 6 in the text. y = x8x y =
Two well-mixed tanks are interconnected. Tank A contains 60 grams of salt in 40 liters of water, and Tank B contains 70 grams of salt in 20 liters of water. A briny solution with concentration 2 gram/L flows into Tank A at a rate of 7 L/min, while a solution with concentration 3 grams/L flows into Tank B at a rate of 5 L/min. The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 1 L/min flows from Tank B to Tank A. An additional 12 L/min drains from Tank B. Letting x1 represent the grams of salt in Tank A, and x2 represent the grams of salt in Tank B, set up the IVP for amount of salt in these two tanks. x2 x1(0) = ' 23(0) =
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16. A solution is made that contains 9 pounds of salt per every 10 gallons and flows into a half tank of water that holds 2021 gallons at time 3D0. Then the solution enters the tank from one side at a rate of 12 gallons per minute and exits the tank from the other side at a rate of 11 gallons per minute. a. How much salt is in the tank when full?
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