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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Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km3, and water flows from lake A into lake B, and from lake B into lake C, both inflows and outflows at the same rate of 525 km3/year. Suppose that at time t=0 (years), the pollutant concentration of lake B, caused by past industrial pollution that has now been ordered to cease, is five times that of lake A. If the outflow from lake B to lake C is perfectly mixed lake water, how long will it take to reduce the pollution concentration in lake B to twice that of lake A? Choose all correct answers. B Approximately 6.3 years. Approximately 4.4 years. Approximately 5 years. Approximately 8.3 years. Approximately 7 years.
A 200-liter tank initially contains 100 liters of brine solution containing 25kg of salt. A brine solution containing 0.5 kg/ liter of salt flows into the container at a rate of 1 liter/min. The solution is kept thoroughly mixed, and the mixture flows out at a rate of 0.5 liters/min. How much salt is in the container after 10 minutes? When the tank is about to overflow, another drain is opened at 1 liter/min. How much salt is in the tank when the volume returns to what it was initially?
Two chemicals A and B are combined to form a chemical C. The rate of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially there are 48 grams of A and 89 grams of B, and for each gram of B, 1 grams of A is used. It has been observed that 34,25 grams of C is formed in 15 minutes. How much is formed in 40 minutes? What is the limiting amount of C after a long time? 83.89 inf grams of C are formed in 40 minutes grams is the limiting amount of C after a long time
Tank A initially holds 200 liters of brine containing 225 N of salt. Eight liters of fresh water per minute enter tank A and the mixture assumed uniform, flows from tank A to tank B initially containing 200 liters of fresh water, at 8 liters per minute. The resulting mixture, also kept uniform runs out of tank B at the rate of 8 liters/min. At what time "t" that tank B reached its maximum amount of salt? 15 minutes 50 minutes 60 minutes 25 minutes
A cylindrical tank holds 22 liters of water. At time t = 0, two taps are opened simultaneously, the upper tap that feeds the water tank with a constant speed of v1 liters per minute and the lower tap that expels the water from the tank with a constant speed of v2 liters per minute . Suppose that v1 = 11 liters / minute and v2 = 3 liters / minute. If the tank has a capacity of 75 liters, when will the tank be filled?
solve and draw a diagram of the problem Two large tanks, each holding 100L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 3L/min and from tank B into tank A at a rate of 1L/min. The liquid inside each tank is kept well stirred. Pure water flows into tank A at a rate of 6L/min. The solution flows out of the system from tank A at 4L/min and from tank B at 2L/min. If, initially, tank A contains pure water and tank B contains 20kg of salt, determine the mass of salt in each tank at time t ≥ 0.
A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially contains 100 liters of pure water. The mixed solution is drained at 3 liters per minute. At what time will the solution contain 10% ammonia?
"MixtureA tank contains 100 gallons of a solution composed of 70% water and 30% alcohol. A second solution containing 75% alcohol and 25% water is added to the tank at a rate of 12 gallons per minute. As the second solution is being added, the tank is being drained at a rate of 15 gallons per minute. The solution in the tank is stirred constantly. How much alcohol is in the tank after 15 minutes"

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