6. Tank A initially holds 500 liters ofpure water and tank B 1000 liters of90% alcohol mixture (you can thinkof it as 900 liters of alcohol mixedwith 100 liters of water). 10%mixture of alcohol enters the tank Aat a rate of 10 L/min and wellmixed solution leaves tank B withthe same rate. The water/alcohol mixture is transferred from tank A to tank B with the rate 15L/min and from tank B to tank A with the rate 5 L/min. Write the initial value problemdescribing alcohol content of each tank. Write it in the matrix form. DO NOT SOLVE.100/min of Alcohol Sclution10min Alcohol Solutionwith 10% of Alcohol concentrationTank Asonë0 % of Alcotiul50/min152/minTank B100090% of Ainahal

Let, x1(t) and x2(t) be the alcohol concentrations in tanks A and B at time t, respectively,…

Answered: 6. Tank A initially holds 500 liters 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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The initial mass of a certain species of fish is 3 million tons. The mass of fish, if left alone, would increase at a rate proportional to the mass, with a proportionality constant of 5/yr. However, commercial fishing removes fish mass at a constant rate of 18 million tons per year. When will all the fish be gone? If the fishing rate is changed so that the mass of fish remains constant, what should that rate be? When will all the fish be gone? The fish will all be gone in years. (Round to three decimal places as needed.)
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.
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The initial mass of a certain species of fish is 3 million tons. The mass of fish, if left alone, would increase at a rate proportional to the mass, with a proportionality constant of 5/yr. However, commercial fishing removes fish mass at a constant rate of 17 million tons per year. When will all the fish be gone? If the fishing rate is changed so that the mass of fish remains constant, what should that rate be? When will all the fish be gone? The fish will all be gone in years. (Round to three decimal places as needed.)
Consider the mixing process shown in the figure. A mixing chamber initially contains 4 liters of a clear liquid. Clear liquid flows into the chamber at a rate of 10 liters per minute. A dye solution having a concentration of 0.6 kilograms per liter is injected into the mixing chamber at a constant rate of r liters per minute. When the mixing process is started, the well-stirred mixture is pumped from the chamber at a rate of 10 + r liters per minute. (a) Develop a mathematical model for the mixing process. Let Q represent the amount of dye in kilograms in the mixture. dQ kg/min dt (b) The objective is to obtain a dye concentration in the outflow mixture of 0.5 kilograms per liter. What injection rate r is required to achieve this equilibrium solution? 7 = L/min Would this equilibrium value of r be different if the fluid in the chamber at time t = 0 contained some dye? no (c) Assume the mixing chamber contains 4 liters of clear liquid at time t = 0. How many minutes will it take for the…
x2 + 3x + 2 y' У (1) %3D 4 у — 2 v(2) - 1
3. A tank contains 400 liters of brine holding 300 kg of salt in solution. Water containing 125 g of salt per liter flows into the tank at the rate of 12 liters per minute, and the mixture kept uniform by stirring, flows out at the same rate. Find the among of salt at the end of 90 minutes. Hint: = Pinin dt - Tout s+ (Fin-Tout))
The brine solution is recycled using a series of mixing tanks before being released outside of the tanks. Tank A receives pure water at a rate of 4 L/min. The solution is pumped to Tanks B and C at rates of 2 L/min and x L/min, respectively, from Tank A, which originally contains 500 L of brine solution in which 200 g of salt is first dissolved. At a rate of 4 L/min, Tank B from its original 400 L of brine solution in which 1000 g of salt has been dissolved pumps the solution to Tank C. At a rate of y L/min, Tank C, which originally holds 400 L of pure water, pumps the solution back to Tank B. Meanwhile, Tank C releases z L/min of solution out of the system. a. Determine the values of x, y, and z if the volume of the solution within each tank stays constant throughout time. b. Find out the brine solution's concentration coming out of each tank at time t-8 minutes. 2 L/min TANK B TANKA 4 L/min y L/min Pure water @4 L/min x L/min TANK C z L/min
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