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1) A tank contains 200 gallons of water in which 50 pounds of salt are dissolved. A brine solutio...
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...
A 120-gallon tank initially contains 90 pounds of salt dissolved in 90 gallons of water. Brine...
A 120-gallon tank initially contains 90 pounds of salt dissolved in 90 gallons of water. Brine containing 2 1b/gal of salt flows into the tank at the rate of 4 cal/min, and the well-stirred mixture flows out of the tank at the rate of 3 gal/min. How much salt does the tank contain when it is full? (At 30 minutes, there is approximately 202 pounds of salt present in the tank.)
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...
(1 point) A tank holds 250 gallons of water than contains 50 pounds of dissolved salt. Pure water...
(1 point) A tank holds 250 gallons of water than contains 50 pounds of dissolved salt. Pure water is flowing into the tank at the rate of 1/2 gal/min while the solution flows out of the tank at the rate of 4 gal/min. (a) Write down a differential equation describing this situation. Use y for the amount of salt in the tank dy 4y/250-3.5t) dt (b) Write this equation in the correct form for using the method of separation of...
A tank contains 150 gallons of brine whose salt concentration is 2 pounds per gallon. Three...
A tank contains 150 gallons of brine whose salt concentration is 2 pounds per gallon. Three gallons of brine whose salt concentration is 4 pounds per gallon flow into the tank each minute. At the same time 3 gallons of the mixture flows out each minute. If the mixture is kept uniform by constant stirring, find the salt content of the brine as a function of the time t. Approximately how long will it take until there are 240 pounds...
2. A tank contains a 100 gallons of pure water. Brine containing pound salt per gallon...
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...
(1 point) A tank holds 280 gallons of water than contains 35 pounds of dissolved salt....
(1 point) A tank holds 280 gallons of water than contains 35 pounds of dissolved salt. Pure water is flowing into the tank at the rate of 1/2 gal/min while the solution flows out of the tank at the rate of 2 gal/min. (a) Write down a differential equation describing this situation. Use y for the amount of salt in the tank. dy dt = (b) Write this equation in the correct form for using the method of separation of...
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...
1) Given a tank initially contains 200 gallons of brine (salt mixed with water) in which...
1) Given a tank initially contains 200 gallons of brine (salt mixed with water) in which 150 lbs of salt is dissolved. A salt solution consisting of 0.5×(1 + e^(-0.02t)) lb. of salt per gallon (where t is time in unit of minute) is flowing into the tank at a rate of 10 gal./min and the mixed solution is drained from tank at the same rate. Find the amount of the salt in the tank after 1 hour. (10 points)...
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...
A 120-gallon tank initially contains 90 pounds of salt dissolved in 90 gallons of water. Brine containing 2 1b/gal of salt flows into the tank at the rate of 4 cal/min, and the well-stirred mixture flows out of the tank at the rate of 3 gal/min. How much salt does the tank contain when it is full? (At 30 minutes, there is approximately 202 pounds of salt present in the tank.)
(1 point) A tank holds 250 gallons of water than contains 50 pounds of dissolved salt. Pure water is flowing into the tank at the rate of 1/2 gal/min while the solution flows out of the tank at the rate of 4 gal/min. (a) Write down a differential equation describing this situation. Use y for the amount of salt in the tank dy 4y/250-3.5t) dt (b) Write this equation in the correct form for using the method of separation of...
A tank contains 150 gallons of brine whose salt concentration is 2 pounds per gallon. Three gallons of brine whose salt concentration is 4 pounds per gallon flow into the tank each minute. At the same time 3 gallons of the mixture flows out each minute. If the mixture is kept uniform by constant stirring, find the salt content of the brine as a function of the time t. Approximately how long will it take until there are 240 pounds...
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...
(1 point) A tank holds 280 gallons of water than contains 35 pounds of dissolved salt. Pure water is flowing into the tank at the rate of 1/2 gal/min while the solution flows out of the tank at the rate of 2 gal/min. (a) Write down a differential equation describing this situation. Use y for the amount of salt in the tank. dy dt = (b) Write this equation in the correct form for using the method of separation of...
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...
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...
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