A vat of volume 1000 gallons initially contains 5 lbs of salt. For t > 0...
A vat of volume 1000 gallons initially contains 5 lbs of salt. For t > 0 pure water is pumped into the vat at the rate of 2 gallons per minute; the perfectly stirred mixture is pumped out at the same flow rate. Derive a formula for the concentration of salt in the tank at any time t. Sketch a graph of the concentration versus time
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A vat of volume 1000 gallons initially contains 5 lbs of salt.
For t > 0...
2. A tank contains 100 gallons of pure water. Beginning at t O, a salt water solution containing 0.2 pounds of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. At the sa...
2. A tank contains 100 gallons of pure water. Beginning at t O, a salt water solution containing 0.2 pounds of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. At the same time, a drain is opened at the bottom of the tank which allows the mixture to leave the tank at a rate 3 gallons per minute. Assume the solution is kept perfectly mixed. (a) What will be concentration of salt...
2. A tank contains 100 gallons of pure water. Beginning at t O, a salt water...
2. A tank contains 100 gallons of pure water. Beginning at t O, a salt water solution containing 0.2 pounds of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. At the same time, a drain is opened at the bottom of the tank which allows the mixture to leave the tank at a rate 3 gallons per minute. Assume the solution is kept perfectly mixed. (a) What will be concentration of salt...
3. A 1000-gallon tank initially contains 800 gallons of water with 3 lbs of salt dissolved...
3. A 1000-gallon tank initially contains 800 gallons of water with 3 lbs of salt dissolved in it. A water-salt mixture with a concentration of 0.4 lb of salt per gallon enters the tank at a rate of 8 gal/hr. The liquid in the tank is well-mixed and is pumped out of the tank at a rate of 10 gal/hr. Suppose you were asked to find an expression for the amount of salt in the tank at time t. (a)...
Can you show all the steps please? A salt tank contains 50 lbs of salt dissolved...
Can you show all the steps please?
A salt tank contains 50 lbs of salt dissolved in a 300 gallon tank. A brine mixture with a concentration of 2 lbs of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. The mixture is distributed uniformly in the tank and the mixture is drained at the same rate of 3 gallons per minute input rate of brine 3 gal/min constant 300 gal A Set...
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...
A tank initially contains 120 L of pure water. A salt mixture containing a concentration of...
A tank initially contains 120 L of pure water. A salt mixture containing a concentration of 1.5 g/L enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves the tank at the same rate. Find an expression for the amount of salt in the tank at any time t. Also, find the limiting amount of salt in the tank as t +0. (10 points)
-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) A tank contains 200 gallons of water in which 50 pounds of salt are dissolved. A brine solutio...
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...
h A tank initially has 200 gallons of a solution that contains 25 lb. of dissolved...
h
A tank initially has 200 gallons of a solution that contains 25 lb. of dissolved salt. brine solution with a concentration of 21b of salt/gallon is admitted into the tank at a rate of 4 gallons per minute. The well-stirred solution is drained at the same rate. How long will it take for the tank to have 100 lb. of dissolved salt? Round your answer to the nearest minute.
A tank contains 200 gallons of liquid. Five gallons of brine per minute flow into the...
A tank contains 200 gallons of liquid. Five gallons of brine per minute flow into the tank, and each gallon of brine contains 2 pounds of salt. Five gallons of brine flow out of the tank per minute. Assume that the tank is kept well stirred. A. Find a differential equation for the number of pounds of salt in the tank. Assuming the tank intially contains 50 pounds of salt, solve this differential equation. B. How much salt is in...
2. A tank contains 100 gallons of pure water. Beginning at t O, a salt water solution containing 0.2 pounds of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. At the same time, a drain is opened at the bottom of the tank which allows the mixture to leave the tank at a rate 3 gallons per minute. Assume the solution is kept perfectly mixed. (a) What will be concentration of salt...
2. A tank contains 100 gallons of pure water. Beginning at t O, a salt water solution containing 0.2 pounds of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. At the same time, a drain is opened at the bottom of the tank which allows the mixture to leave the tank at a rate 3 gallons per minute. Assume the solution is kept perfectly mixed. (a) What will be concentration of salt...
3. A 1000-gallon tank initially contains 800 gallons of water with 3 lbs of salt dissolved in it. A water-salt mixture with a concentration of 0.4 lb of salt per gallon enters the tank at a rate of 8 gal/hr. The liquid in the tank is well-mixed and is pumped out of the tank at a rate of 10 gal/hr. Suppose you were asked to find an expression for the amount of salt in the tank at time t. (a)...
Can you show all the steps please?
A salt tank contains 50 lbs of salt dissolved in a 300 gallon tank. A brine mixture with a concentration of 2 lbs of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. The mixture is distributed uniformly in the tank and the mixture is drained at the same rate of 3 gallons per minute input rate of brine 3 gal/min constant 300 gal A Set...
A tank initially contains 120 L of pure water. A salt mixture containing a concentration of 1.5 g/L enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves the tank at the same rate. Find an expression for the amount of salt in the tank at any time t. Also, find the limiting amount of salt in the tank as t +0. (10 points)
-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...
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...
h
A tank initially has 200 gallons of a solution that contains 25 lb. of dissolved salt. brine solution with a concentration of 21b of salt/gallon is admitted into the tank at a rate of 4 gallons per minute. The well-stirred solution is drained at the same rate. How long will it take for the tank to have 100 lb. of dissolved salt? Round your answer to the nearest minute.
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