*Using Differential Equations 3. A solution containing 0.2 kg/l of salt is pumped into a tank...
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...
Water 12 L/min Mixture 4 L/min 100 L 100 L Mixture 16 L/min Mixture 12 L/min Mixing tank A holds 100 L of water in which 0.04 kg of salts is dissolved. Suppose tank B contains 100 L of water which has 0.02 kg of salt. Liquid is pumped in and out of the tanks as indicated in the figure. The mixture exchanged between the two tanks and the liquid pumped out of tank B is assumed to be well...
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...
Couipaiy 27, A large tank is partially filled with 400 L of fluid in which 5 kg of salt is dissolved. Brine containing 0.25 kg of salt per liter is pumped into the tank at a rate of 20 Lmin. The well-mixed solution is then pumped out at a slower rate of 15 L/min. Find the number of kilograms of salt in the tank after 30 minutes. Couipaiy 27, A large tank is partially filled with 400 L of fluid...
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)
10. Suppose a brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt. The brine enters the tank at a rate of 5 L/Min. The mixture, kept uniform by stirring, is flowing out at the rate of 5 L/min. Let A(t) be the amount of salt in the tank at time t (in minutes), then set up an IVP for the scenario, then find the concentration,...
(1) A tank is filled with 300 liters (L) of contaminated water initially containing 3 kg of toxin. Pure water is pumped in to the tank at a rate of 40 L/min, mixes instantaneously, and the mixture is pumped out at the same rate (40 L/min). Let y(t) be the amount of toxin present in the tank at time t. Write the differential equation and the initial value that models this scenario. (a) Find the particular solution, y(t). Put a...
4. Suppose there are two tanks, each containing 200 l of fluid. Tank 1 initially contains pure water and tank 2 initially contains water with 200 kg of salt dissolved. The tanks are stirred constantly so their solutions have uniform concentration. There is a pipe which takes 10 l/min from tank 1 to tank 2, and another pipe which takes 5 l/min from tank 2 to tank 1. Also, pure water is being pumped into tank 1 at a rate...
I just need help understand where I get the 7 for the dx/dt 1. (5 points) Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from Tank A into Tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min. The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into Tank A...
Question 2 (1 point) A tank contains1,500 L of water in which 20 kg of salt has been dissolved. Fresh water is pumped into the tank at a rate of 15 L/min. The solution is well mixed and then pumped out at a rate of 10 L/min. How much salt is in the tank at t minutes and at 10 minutes?