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(7 points) 8. A tank initially contains 80 L of a solution in which 20 g...
A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially hel...
A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.1 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.02 kg/L, determine the mass of salt in the tank after t min. When will the...
A tank contains 100L of water. A solution with a salt concentration of 0.6kg/L is added...
A tank contains 100L of water. A solution with a salt concentration of 0.6kg/L is added at a rate of 7L/min. The solution is kept thoroughly mixed and is drained from the tank at a rate of 5L/min. Answer the following questions. 1. If is the amount of salt (in kilograms) after t minutes, what is the differential equation for which y is satisfied? Use the variable y for y(t). Answer (in kilograms per minute): dy/dt = 4.2-(5y/100+2t) 2. How...
(2 points) A tank contains 80 kg of salt and 1000 L of water. Pure water...
(2 points) A tank contains 80 kg of salt and 1000 L of water. Pure water enters a tank at the rate 12 L/min. The solution is mixed and drains from the tank at the rate 6 L/min. (a) What is the amount of salt in the tank initially? amount = (kg) (b) Find the amount of salt in the tank after 4.5 hours. amount = (kg) (c) Find the concentration of salt in the solution in the tank as...
A brine solution of salt flows at a constant rate of 9 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.2 kg of salt. The solution inside the tank is kept...
A brine solution of salt flows at a constant rate of 9 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.2 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.04 kg/L, determine the mass of salt in the tank after t min. When will the...
2. A tank initially contains 100 gallons of salt solution in which 20 pounds of salt is dissolved. Starting at time 0, a solution containing 3 pounds of salt per gallon flows into the tank at a...
2. A tank initially contains 100 gallons of salt solution in which 20 pounds of salt is dissolved. Starting at time 0, a solution containing 3 pounds of salt per gallon flows into the tank at a rate of 4 gallons per minute. The mixture is kept uniform by stirring and the well-mixed solution simultancously flows out of the tank at the same rate. Determine the amount of salt in the tank after 10 minutes, when the amount of salt...
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 980 gal of pure water.
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...
6. A 500 L tank initially contains 10 g of salt dissolved in 200 L of...
6. A 500 L tank initially contains 10 g of salt dissolved in 200 L of water. Water containing 1/4 g of salt per liter is poured into the tank at the rate of 4 L/min and the mixture is drained from the tank at the rate of 2 L/min. Find an initial value problem that solve for x(t), the mass of salt in the tank at time t prior to when the tank overflows, then solve for x(t).
Salt water flows at a constant rate of 6 L/min into a tank that initially held...
Salt water flows at a constant rate of 6 L/min into a tank that initially held 100 L of salt solution in which was dissolved 0.3 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the solution entering the tank is 0.03 kg/L. a) Dtermine the mass of salt in the tank after t min. b) When will the concentration of...
Salt water flows at a constant rate of 6 L/min into a tank that initially held...
Salt water flows at a constant rate of 6 L/min into a tank that initially held 100 L of salt solution in which was dissolved 0.15 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the solution entering the tank is 0.03 kg/L. a) Dtermine the mass of salt in the tank after t min. b) When will the concentration of...
A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.1 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.02 kg/L, determine the mass of salt in the tank after t min. When will the...
A tank contains 100L of water. A solution with a salt concentration of 0.6kg/L is added at a rate of 7L/min. The solution is kept thoroughly mixed and is drained from the tank at a rate of 5L/min. Answer the following questions. 1. If is the amount of salt (in kilograms) after t minutes, what is the differential equation for which y is satisfied? Use the variable y for y(t). Answer (in kilograms per minute): dy/dt = 4.2-(5y/100+2t) 2. How...
(2 points) A tank contains 80 kg of salt and 1000 L of water. Pure water enters a tank at the rate 12 L/min. The solution is mixed and drains from the tank at the rate 6 L/min. (a) What is the amount of salt in the tank initially? amount = (kg) (b) Find the amount of salt in the tank after 4.5 hours. amount = (kg) (c) Find the concentration of salt in the solution in the tank as...
A brine solution of salt flows at a constant rate of 9 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.2 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.04 kg/L, determine the mass of salt in the tank after t min. When will the...
2. A tank initially contains 100 gallons of salt solution in which 20 pounds of salt is dissolved. Starting at time 0, a solution containing 3 pounds of salt per gallon flows into the tank at a rate of 4 gallons per minute. The mixture is kept uniform by stirring and the well-mixed solution simultancously flows out of the tank at the same rate. Determine the amount of salt in the tank after 10 minutes, when the amount of salt...
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.
6. A 500 L tank initially contains 10 g of salt dissolved in 200 L of water. Water containing 1/4 g of salt per liter is poured into the tank at the rate of 4 L/min and the mixture is drained from the tank at the rate of 2 L/min. Find an initial value problem that solve for x(t), the mass of salt in the tank at time t prior to when the tank overflows, then solve for x(t).
Salt water flows at a constant rate of 6 L/min into a tank that initially held 100 L of salt solution in which was dissolved 0.3 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the solution entering the tank is 0.03 kg/L. a) Dtermine the mass of salt in the tank after t min. b) When will the concentration of...
Salt water flows at a constant rate of 6 L/min into a tank that initially held 100 L of salt solution in which was dissolved 0.15 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the solution entering the tank is 0.03 kg/L. a) Dtermine the mass of salt in the tank after t min. b) When will the concentration of...
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