Formulate the problem before any tank empties or overflows, but do not solve the equations.Notice we need one equation for each tank.Consider three tanks. Tank X starts with 200 gal of salt water with 55 b of salt, while Tank Ystarts with 500 gal of salt water with 35 lb of salt, and Tank Z is initially empty. Suppose thatmixture flows out of Tank X into Tank Y at the rate of 8 gal/min and the mixture flows out of TankY into Tank Z at the rate of 22 gal/min. How much salt is there in each tank at any time? Onlyconsider the process before any tank empties or overflows.

W have to form three differential equation for three tank by using rate of change in amount of…

Answered: Formulate the problem before any tank…

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 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?
Suppose: • The vat contains 270 gallons of liquid, which • • . never changes. Sugar water with a concentration of 10 tablespoons/gallon flows through pipe A into the vat at the rate of 30 gallons/minute. Sugar water with a concentration of 8 tablespoons/gallon flows through pipe B into the vat at the rate of 35 gallons/minute. • The liquid in the vat is kept well-mixed. Sugar water leaves the vat through pipe C at the rate of 65 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: dS dt (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that K > 0. S(t) = (C) Suppose that there are 32 tablespoons of sugar in the vat at t = present 4 minutes later? 0. How many tablespoons will be tablespoons
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?
My cat Pythagoras has purchased and installed in my back yard a large barrel with a 400-gallon capacity. It is initially half full of clean water. But he has three hoses feeding this barrel, each with a rate of flow of 2 gal./min. of water. Two provide the barrel with clean water, but the third contains a concentration of 2 g/gal. of liquid calculus text books. My other cat, Jolie, has decided to sabotage this process by puncturing a hole toward the bottom of this barrel that allows 4 gal./min. to leak. If we assume that there is a benevolent feline deity that blissfully stirs this barrel with a rather large spoon, then write a differential equation that mathematically models the rate at which the amount of liquid calculus text books changes in the barrel (at least up to the time it fills). Thereafter, solve this differential equation.
Turbo Coolers Inc. builds cooling systems for industrial plants. A Type A cooler takes 80 W of power and can cool 18 liters of fluid per minute under the given conditions. A Type B cooler takes 100 W of power and can cool 60 liters of fluid per minute. A Type A cooler costs $3,500 and a Type B cooler costs $12,000. The factory has up to 1,000 W of power it can supply for cooling, and must cool 300 liters of fluid per minute. How many of each type of cooler should Turbo Coolers Inc. install in the factory to minimize cost? Formulate a linear programming model for this situation. Solve this model using graphical analysis. Display your graph and the solution parameters. Create your graph using Microsoft Word or Excel and submit it to your instructor. Create your graph using Microsoft Word or Excel and submit it to your instructor.
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.
Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially, there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A is used. It is observed that 20 grams of C is formed in 6 minutes. How much (in grams) is formed in 12 minutes? (Round your answer to one decimal place.) grams What is the limiting amount (in grams) of C after a long time? grams How much (in grams) of chemicals A and B remains after a long time? A B Need Help? grams grams Read It Watch It Master
1. Suppose that a commercial truck has an efficiency of 120 – 2v m(v) miles/gallon going at speed of v miles/hour. The driver's rate is 15 dollars/hr, and gas is $3.50/gal- lon. a. Find the cost C(v) per mile to travel at speed v mph. b. Find the cheapest driving speed.
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?

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