Select the best alternative 1. (6 points) A 100-liter tank initially contains 40 liters of water with 4 grams of dissolved sodium chloride. A solution of 1 gram per liter of sodium chloride flows into the tank at the rate of 3 liters per minute. Both solutions mix perfectly. The mixture is extracted by means of a pump at a rate of 5 liters per second. Let ? (?) be the mass of sodium chloride present in the tank at any time ? ≥ 0 before the tank eventually empties. Which of the following initial value problems best describes ? (?)?
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1.
(6 points) A 100-liter tank initially contains 40 liters of water...
please help me with this asap 08 - A 200-liter tank initially contains 40 liters of...
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08 - A 200-liter tank initially contains 40 liters of a potassium chloride solution with a concentration of 3 grams/liter. At t = 0. potassium chloride solution with a concentration of 6 grams/liter begins to flow into the tank at the rate of 4 liters/min. The thoroughly mixed content of the tank is drawn off at the rate of 2 liters/min. Which of the initial value problems below best describes the quantity of potassium...
-2t A tank initially contains 10 liters of water and 5 grams of salt. Salt water...
-2t A tank initially contains 10 liters of water and 5 grams of salt. Salt water containing 3+ e grams of salt per liter is pumped into the tank at a rate of 2 liters per minute. The solution of salt water is instantaneously, perfectly mixed and then pumped out at a rate of 2 liters per minute. Determine when, to three decimal places, the concentration of the salt leaving the tank is within 0.01 grams/liter of the salt entering...
(1 point) A tank initially contains 25 liters of salt water solution with 10 grams of...
(1 point) A tank initially contains 25 liters of salt water solution with 10 grams of salt dissolved in it. Salt water containing one gram of salt per liter pours in at the rate of one liter per minute and the well-stired mixture drains out at the rate of 2 liters per minute. How many grams of salt will be in the tank after one minute? Answer: grams of salt.
(1 point) A large tank contains 500 liters of a salt solution which has a concentration...
(1 point) A large tank contains 500 liters of a salt solution which has a concentration of 0.55 kilograms per liter. A salt solution which has a concentration of 0.7 kilograms per liter is added to the solution at a rate of 40 liters per minute. At the same time, the solution drains from the tank at 40 liters per minute. Find the amount of the salt in the solution as a function of t: S = kilograms
11. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved....
11. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 L/min. The well-mixed solution is pumped out at the same rate. Find the number of grams of salt in the tank at time t.
(3 points) Consider the two tank apparatus shown in the figure. Each tank has capacity 950950 liters and initially c...
(3 points)
Consider the two tank apparatus shown in the figure. Each tank
has capacity 950950 liters and initially contains 100100 liters of
fresh water. At time t=0t=0, the well-stirred mixing process
begins. Suppose that the concentration of brine flowing into Tank 1
via the top tube is 11 kilograms per liter, and that the flow rates
are r1=r3=4r1=r3=4 liters per minute, and r2=r4=13r2=r4=13 liters
per minute.
(a) Determine the volume of solution in each tank as a function of...
5. (20 points) A tank with a capacity of 500 liters contains 200 liters of water...
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.
A Water Tank Problem with Discontinuous Source A water tank contains V, > 0 liters of...
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...
4. A tank initially contains 100 liters (L) of water with a salt concentration of 20...
4. A tank initially contains 100 liters (L) of water with a salt concentration of 20 g/L. A mixture with a salt concentration of 5 g/L flows into the tank at a rate of 5 Umin while the well-mixed fuid in the tank flows out at the rate of 3 L/min. Determine the concentration of salt (g/L) in the tank when the volume in the tank reaches 400 liters.
A tank initially contains 500 gallons of water in which 40 pounds of salt is initially dissolved in the water
A tank initially contains 500 gallons of water in which 40 pounds of salt is initially dissolved in the water. Brine (a water-salt mixture) containing 0.4 pounds of salt per gallon flows into the tank at the rate of 5 gal/min, and the mixture (which is assumed to be perfectly mixed) flows out of the tank at the same rate of 5 gal/min. Let y(t) be the amount of salt (in pounds) in the tank at time t. a) Set up...
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08 - A 200-liter tank initially contains 40 liters of a potassium chloride solution with a concentration of 3 grams/liter. At t = 0. potassium chloride solution with a concentration of 6 grams/liter begins to flow into the tank at the rate of 4 liters/min. The thoroughly mixed content of the tank is drawn off at the rate of 2 liters/min. Which of the initial value problems below best describes the quantity of potassium...
-2t A tank initially contains 10 liters of water and 5 grams of salt. Salt water containing 3+ e grams of salt per liter is pumped into the tank at a rate of 2 liters per minute. The solution of salt water is instantaneously, perfectly mixed and then pumped out at a rate of 2 liters per minute. Determine when, to three decimal places, the concentration of the salt leaving the tank is within 0.01 grams/liter of the salt entering...
(1 point) A tank initially contains 25 liters of salt water solution with 10 grams of salt dissolved in it. Salt water containing one gram of salt per liter pours in at the rate of one liter per minute and the well-stired mixture drains out at the rate of 2 liters per minute. How many grams of salt will be in the tank after one minute? Answer: grams of salt.
(1 point) A large tank contains 500 liters of a salt solution which has a concentration of 0.55 kilograms per liter. A salt solution which has a concentration of 0.7 kilograms per liter is added to the solution at a rate of 40 liters per minute. At the same time, the solution drains from the tank at 40 liters per minute. Find the amount of the salt in the solution as a function of t: S = kilograms
11. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 L/min. The well-mixed solution is pumped out at the same rate. Find the number of grams of salt in the tank at time t.
(3 points)
Consider the two tank apparatus shown in the figure. Each tank
has capacity 950950 liters and initially contains 100100 liters of
fresh water. At time t=0t=0, the well-stirred mixing process
begins. Suppose that the concentration of brine flowing into Tank 1
via the top tube is 11 kilograms per liter, and that the flow rates
are r1=r3=4r1=r3=4 liters per minute, and r2=r4=13r2=r4=13 liters
per minute.
(a) Determine the volume of solution in each tank as a function of...
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.
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...
4. A tank initially contains 100 liters (L) of water with a salt concentration of 20 g/L. A mixture with a salt concentration of 5 g/L flows into the tank at a rate of 5 Umin while the well-mixed fuid in the tank flows out at the rate of 3 L/min. Determine the concentration of salt (g/L) in the tank when the volume in the tank reaches 400 liters.
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