12.A certain polluted lake holds 50kL of water. Pure water flows into the lake at arate of 2kL per hour, and water flows out of the lake at the same rate. The lake is polluted withcyanide, the initial concentration of which is 3g per kL. In order to be deemed safe to swim in, theconcentration of cyanide has to decrease to 1g per kL. Assuming instantaneous mixing, how longwill it be before the water is safe to swim in?25 ln 3 hours

Lets say amount of cyanide at time 't' be x(t) gram The rate of change of amount of cyanide is…

Answered: 12. A certain polluted lake holds 50kL…

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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3. A large tank with the capacity of 500 gallons is fully filled with pure water. Brine containing 2 pounds of salt per gallons is pumped into the tank at a rate of 5 gal/min. Find the amount A(t) pounds of salt in the tank at timer minutes, if the well-mixed solution is pumped out (a) with the same rate as the entering one; and (b) with the rate of 10 gal/min. In case (a), how much salt is in the tank after a long time? In case (b), what is the concentration of the solution in the tank by the time it is empty? (c) Let everything be the same except that, initially, the tank is filled with 250 gallons of pure water, while the well-stirred solution is pumped out with the flow rate of 2.5 gal/min. Find (t). What is the concentration of the solution in the tank by the time it is fully filled? Hint: (a) The volume of the solution in the tank at time (b) The volume of the solution in the tank at time minutes is V(t)= 500 gallons minutes is V(t)=500-5r gallons (c) The volume of the solution…
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?
2. A large tank initially contains 100 gallons of brine in which 10 lb of salt is dissolved. Starting at t = 0, pure water flows into the tank at the rate of 5 gal/min. The mixture is kept uniform by stirring, and the well-stirred mixture simultaneously flows out at the slower rate of 2 gal/min. a) How much salt is in that tank at the end of 15 min and what is the concentration at that time? b) If the capacity of the tank is 250 gallons, what is the concentration at the instant the tank overflows?
3. What will the flow rate be in milliliters per hour for vancomycin 1g/500 mL IV, if it is to be infused for 90 minutes? 333
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 contains 1800 liters (L) of fluid in which 180 grams (g) of salt is dissolved. Solution containing 20 g/L then pumped into the tank at a rate of 30 L/min; the tank is maintained well mixed and pumped out at the same rate. How many grams of salt are in the tank 20 minutes after the inlet supply is opened? а. 10830 b. 11304 C. 11324 d. 10434 е. 10334

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