A tank with 500 liters of water initially contains 4g of calcium. Water with a concentration of 3...
a tank with 500 liters of water initially contains 4g of calcium. Water with a concentration of 3 mg/L is pumped into the tank at a rate of 1L/min and the mixture is pumped out at the same rate.
(a) Write a differential equation and its initial condition for, y(t), the total amount of calcium in grams in the tank. (t is measured in minutes, 1g = 1000mg)
(b) Find the general solution to this differential equation.
(c) Find the particular solution satisfying the initial condition
(d) (i) Draw a sketch for all possible solutions to this differential equation and (ii) include a sketch (in bold) of the solution obtained in (c)
(e) what is the amount of calcium in the tank after 1/2 hour?
(f) According to the solution found in (c), what is the amount of calcium if we wait forever? Explain.
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A tank with 500 liters of water initially contains 4g of calcium. Water with a concentration of 3...
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please solve all three questions, will upvote thank you
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A tank initially contains 980 gal of pure water. Brine containing 3.3 lb/gal of salt is poured into the tank at a rate of 7 gal/min. Suppose the solution in the tank is instantly well mixed and drained out at a rate of 9 gal/min. Let Q = Q(t) be the quantity of salt in the tank at time t minutes. What is the initial condition? Set up the differential equation for the quantity of salt in the tank: Find the particular solution: When does...
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(1 point) Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 10 L (liters) of water and 355 g of salt, while tank 2 initially contains 90 L of water and 345 g of...
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A Water Tank Problem with Discontinuous Source A water tank contains V, > 0 liters of pure water and Qo grams of salt. At time t = 0 we start pouring water into the tank with a rate r > 0 liters per minute with a salt concentration of q> 0 grams per litter, and we let the well-stirred water leave the tank at the same rate. After T > 0 minutes the process is stopped and fresh water is...
5. (20 points) A tank with a capacity of 500 liters contains 200 liters of water with 100 grams of a material in solution. Water containing a concentration of 1 g/liter of the material enters the tank at a rate of 3 liters/min, and the well-stirred mixture leaves the tank at a rate of 2 liters/min. Find the amount of mass of the material in the tank at any given time t prior to when the tank begins to overflow.
please solve all three questions, will upvote thank you
1) A tank contains 200 gallons of water in which 50 pounds of salt are dissolved. A brine solution containing 4 pounds of salt per gallon is pumped into the tank at the rate of 6 gallons per minute. The mixture is stirred well and is pumped out of the tank at the same rate. Let A(t) represent the amount of salt in the tank at time t a) Write down...
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(1 point) Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 10 L (liters) of water and 355 g of salt, while tank 2 initially contains 90 L of water and 345 g of salt. Water containing 40 g/L of salt is poured into tank1 at a rate of 4 L/min while the mixture flowing into tank 2 contains a salt concentration of 20 g/L of salt and is flowing at the rate of 1...
2. A tank contains a 100 gallons of pure water. Brine containing pound salt per gallon enters the tank at thratof 2 Let x(t) represent the amount of salt in the tank after t min. and the well-mixed solution flows out at the rate of 4ツ· a. Find the differential equation which relates( and , the initial condition and the domain of x() dr b. Find the particular solution of this equation. c. What is the most amount of salt...
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