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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1. Mr. Pein has an aquarium that has a volume of 2000 mL and contains freshwater fish. One day, Mr. Pein's son accidentally spilled 1 kilogram of salt into the aquarium. The fish will die if they are in water with a salt concentration of more than 10-3 grams/mL for more than 30 minutes. So that the fish in the aquarium do not die, Mr. Pein must immediately reduce the salt concentration in the aquarium to 10-3 grams/mL by flowing fresh water at a constant rate through the aquarium, and removing the water from the aquarium at the same rate. What is the minimum water speed so that the fish don't die? In 500 А. 60000 mL/minute 2000 В. 30 In 500 mL/min 1996 С. mL/minute 30 In 500 D. 6000 mL/minute 200 Е. 30 In 500 mL/min
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?
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?
Please don't provide handwritten solution .....
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
9. A glass container can hold 35 liters of water. It currently has 10 liters of water with 15 grams of Gatorade power initially dissolved in the container. A solution is poured into the container at 3 liters per minute - the solution being poured in has 0.5 grams per liter of Gatorade powder. Assume the solution in the container is well mixed. There is an outflow at the bottom of the container which has liquid leaving at 1 liter per minute. Let G(t) denote the amount of Gatorade powder in the tank at time t. a. Setup the differential equation for G'(x). b. Solve for the general solutiont) c. Use initial condition to find the specific solution. (Write out the entire solution, with the constant(s) plugged in.) ) d. When will the container overflow?
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 technician is changing a automotbile's transmission fluid. The manual tells him the transmission hold 7.8 quarts of fluid. When He drains the transmission, it only releases 3.1 quarts. He closes the plug and puts 3.1 quarts of fresh fluid back in. The manual tells him to run the car for 10 minutes to completely mix the fresh fluid in. The manual states to repeat this process 2 more times. Knowing that some fresh fluid is lost on each of the following 2 drains, what is the final ratio of fresh fluid to old?
"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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