Two tanks are connected as in Figure 1.6. Tank 1initially contains 20 pounds of salt dissolved in 100gallons of brine. Tank 2 initially contains 150 gallonsof brine in which 90 pounds of salt are dissolved. Attime zero, a brine solution containing 1/2 pound ofsalt per gallon is added to tank I at the rate of 5 gallonsper minute, Tank 1 has an output that discharges brineinto tank 2 at the rate of 5 gallons per minute, and tank2 also has an output of 5 gallons per minute. Deter-mine the amount of salt in each tank at any time. Also,determine when the concentration of salt in tank 2 is aminimum and how much salt is in the tank at that time.Hint: Solve for the amount of salt in tank 1 at time tand use this solution to help determine the amount intank 2.S prl min: 12 Ih gelS gil tainTaukpal min

Answered: Two tanks are connected as in Figure…

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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Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km3, and water flows from lake A into lake B, and from lake B into lake C, both inflows and outflows at the same rate of 525 km3/year. Suppose that at time t=0 (years), the pollutant concentration of lake B, caused by past industrial pollution that has now been ordered to cease, is five times that of lake A. If the outflow from lake B to lake C is perfectly mixed lake water, how long will it take to reduce the pollution concentration in lake B to twice that of lake A? Choose all correct answers. B Approximately 6.3 years. Approximately 4.4 years. Approximately 5 years. Approximately 8.3 years. Approximately 7 years.
Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: The vat contains 230 gallons of liquid, which never changes. Sugar water with a concentration of 7 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. • Sugar water with a concentration of 3 tablespoons/gallon flows through pipe B into the vat at the rate of 25 gallons/minute. The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 30 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 22 tablespoons of sugar in the vat at t = 0. How many tablespoons…
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
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
If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second.How long will it take for the rocket to return to the ground?
Part 1 Homing pigeons avoid flying over water. Suppose a homing pigeon is released on an island at point C, which is 7 mi directly out in the water from a point B on shore. Point B is 16 mi downshore from the pigeon's home loft at point A. Assume that a pigeon flying over water uses energy at a rate 1.23 times the rate over land. Toward what point S downshore from A should the pigeon fly in order to minimize the total energy required to get to the home loft at A?
1. Consider two interconnected tanks as shown below. Tank 1 initially contains 600 gal of water with 3 lb of salt, and Tank 2 initially contains 400 gal of water with 1 lb of salt. Water containing 0.4 lb/gal of salt flows into Tank 1 at a rate of 3 gal/min. The well stirred mixture in Tank 1 flows into Tank 2 at a rate of 4 gal/min. The well stirred mixture in Tank 2 leaves the tank at a rate of 6 gal/min and additionally, flows back into Tank 1 at a rate of 2 gal/min. Let Q₁(t) and Q₂(t) denote the amounts of salt (in lb) in Tank 1 and Tank 2 at time t in minutes. Let V₁ (t) and V₂(t) denote the volumes of solutions (in gal) in Tank 1 and Tank 2 at time t in minutes. Set up the initial value problem satisfied by Q₁(t) and Q₂(t) describing the mixing process. (Show your work to get a full credit) Tank 1 72 Tank 2 T4

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