2. The tank shown below contains 80 lbs of salt dissolved in 500 gal of water. The inflowper minute is 20 lb of salt dissolved in 20 gal of water. The outflow is 20 gal/min of theuniform mixture. Find the time when the salt content y(t)_in the tank reaches 95% ofits limiting value (as t → *).

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Answered: 2. The tank shown below contains 80 lbs…

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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2. A.tank initially contains 100 gal of a solution that holds 25 lb of a chemical. Water runs into the tank at the rate of 3 gal/min and the solution runs out at the same rate. How much of the chemical remains in the tank after of the chemical in to reduce the amount 15 min? How long does it take the tank to 1 lb?
6. A 50 gallons tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 lb of salt per gallon is 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 b. the amount of salt in the tank at the moment of overflow
5. Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anesthetized when its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol per kilogram of the dog's body weight. Suppose also that sodium pentobarbitol is eliminated from the dog's bloodstream at a rate which is proportional to the amount of sodium pentobarbitol in the bloodstream and that after 5 hours half of the initially prescribed sodium pentobarbitol is elliminated from the bloodstream. Set up and solve an initial value differential equation. What single dose should be administered in order to anesthetize a 50-kg dog for 1 hr?
A tank with a capacity of 25 L originally contains 15 L of brine with a concentration of 5 g/L of salt. Water containing 1 g/L of salt is entering at a rate of 5 L/min, and the mixture is allowed to flow out of the tank at a rate of 4 L/min. Find the concentration (in g/L) of salt in the tank when it is on the point of overflowing.

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2. The tank shown below contains 80 lbs of salt dissolved in 500 gal of water. The inflow per minute is 20 lb of salt dissolved in 20 gal of water. The outflow is 20 gal/min of the uniform mixture. Find the time when the salt content y(t)_in the tank reaches 95% of its limiting value (as t → *).