Consider two interconnected tanks. Tank 1 initially contains 55 gal of water and a oz of salt, and Tank 2 initially contains 105 gal of water and m oz of salt. Water containing b ozlgal of salt flows into Tank 1at a rate of 2 gal/min. The mixture in Tank 1 flows out at a rate of 4 gal/min, of which half flows into Tank 2, while the remainder leaves the system. Water containingn ozigal of salt also flows into Tank 2from the outside at the rate of 4 gal/min. The mixture in Tank 2 leaves the tank at a rate of 6 gal/min, of which some flows back into Tank 1 at a rate of 2 gal/min, while the rest leaves the system.(a) Draw a diagram that depicts the flow process described above. Let A(t) and B(t), respectively, be the amount of salt in each tank at time t. Write down differential equations and initial conditions thatmodel the flow process.dtA(0) =B(0) =田(b) Find the values of A(t) and B(t) for which the system is in equilibrium, that is, does not change with time. Let A and BE be the equilibrium values. Express A and BE in terms of b and n.AEBE%3D

Answered: Image /qna-images/answer/6c87cb0c-4f06-4d67-8ef3-5bdcb6ec8d08.jpg

Answered: Consider two interconnected tanks. Tank…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 16EQ

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Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the system have exactly one solution?
A transport company has two types of trucks, Type A and Type B. Type A has a refrigerated capacity of 20m and a non-refrigerated capacity of 40m while Type B has the same overall volume with equal sections for refrigerated and non-refrigerated stock. A grocer needs to hire trucks for the transport of 3,000m of refrigerated stock and 4,000m of non-refrigerated stock. The cost per kilometer of a Type A is $30, and $40 for Type B. How many trucks of each type should the grocer rent to achieve the minimum total cost? * Suppose x=type A trucks, y=type B trucks, write the objective function.
A system of two 2000L holding tanks is set up with a pipe bringing water to the first tank, another pipe taking water from the first tank to the second, and a final pipe draining away from the second tank, with each pipe moving 100L/hr. Usually, the system holds nothing but pure water, with the tanks kept half-full. One day, an apprentice spilled a 10kg bag of salt at the mouth of the pipe feeding into the first tank. To add further injury to the original injury, the bag itself flew from his grasp and partially clogged the pipe draining from the second tank. If the pile of salt is being dissolved by the water at the rate of half of the remaining pile every three hours and if the drainage pipe now only carries 90L/h. ?(?) describes the mass of salt in the pile at the mouth of the first pipe. Set up an IVP for ?(?) and explain briefly. Then find the solution ?(?).
Two connected tanks, each with a capacity of 50 liters, contain brine (saltwater). Initially, the first tank contains 18 liters of brine with a salt concentration of 3 grams per liter and the second contains 17 liters of brine with a salt concentration of 2 grams per liter. At t = 0 brine with a salt concentration of 6 grams per liter flows into the first tank at 8 liters per hour. Well-stirred brine flows from the first tank into the second at 7 liters per hour, from the second into the first at 5 liters per hour, from the first into a drain at 4 liters per hour, and from the second into a drain at 3 liters per hour. (a) Determine the volume (liters) of brine in each tank as a function of time.(b) Give an initial-value problem that governs the amount (grams) of salt in eachtank as a function of time.(c) Give the interval of definition for the solution of this initial-value problem.
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