Two tanks are interconnected as illustrated below:Tank 12NgalmingalminTank 2Suppose that Tank 1 contains 1 gallon of brine in which 4 pounds of salt are initially dissolved,and Tank 2 initially contains 1 gallon of pure water. At time t 0, the mixtures are pumpedbetween the two tanks, each at a rate of 2 gal/min. Assume the mixtures are well stirred. Letx₁ (t) and x₂ (t) be the amount of salt (in pounds) in Tank 1 and Tank 2, respectively, at timet.a. Formulate the system of linear differential equations that describes the amount of salt inthe tanks.b. Obtain the initial-value problem above in the matrix form X'c. Examine the solution of the system in part (b) for x₁ and x₂.d. Compute the amount of salt in each tank after 45 seconds.=AX.

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Answered: Two tanks are interconnected as…

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 tank contains 1,000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. Let y(t) be the amount of salt (in kg) in the tank after t minutes. (a) Find the rate of change of amount of salt in the tank after t minutes. dy dt kg min How much salt is in the tank when t = 0? y(0) How much salt (in kg) is in the tank after t minutes? y = = kg (b) How much salt (in kg) is in the tank after 50 minutes? (Round the answer to one decimal place.) y(50) = kg
Suppose the number of bacteria in a culture increases by 50% every hour if left on its own. Assuming that biologists decide to remove approximately one thousand bacteria from the culture every 10 minutes, which of the following equations best models the population P = P(t) of the bacteria culture, where t' is in hours? A. dP = 5P-1000 dt dP B. at dP C. dt dP D. dt E. dP at = 5P-6000 1.5P-6000 = 1.5P-1000 = -5P-1000
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?
Consider the two tank apparatus shown in the figure. Each tank has capacity 500 liters and initially contains 50 liters of fresh water. At time t = 0, the well-stirred mixing process begins. Suppose that the concentration of brine flowing into Tank 1 via the top tube is 0.75 kilograms per liter, and that the flow rates are r1 = r3 = 5 liters per minute, and r2 = r4 = 12 liters per minute. (a.) Determine the volume of solution in each tank as a function of time, t, in minutes. V1(t) = ? V2(t) = ? (b) Determine the time interval of interest (The process when a tank is full or empty) Stopping time is ? minutes (c) Let Q1(t) and Q2(t) denote the amount of salt (in kilograms) in the tanks at time t (in minutes). Derive the initial value problem with Q1(t) and Q2(t) as dependent variables describing the mixing process. Enter Q1(t) as Q1(t) and Q2(t) as Q2(t) (d/dt) (Q1(t)) = ...................................................... kg/min (d/dt) (Q2(t)) =…
Find the salt pls pounds

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