Question

2. (16 points) Two large tanks, each holding 24 liters of a brine solution, are interconnected by pipes as shown in the figure. Pure water flows into tank A at a rate of 6 L/min, and fluid is drained out of tank B at the same rate. Also, 8 L/min of fluid are pumped from tank A to tank B, and 2 L/min from tank B to tank A. The liquids inside each tank are kept well stirred so that each mixture is homogeneous. Initially the brine solution in tank A contains 2 kg of salt and that in tank B contains 1 kg of salt. Let x(t) represent the mass of salt in tank A at time t and y(t) the mass of salt in tank B. (a) Show that the rates of change of the mass of the salt are described by the system of DEs dx/dt = -1/3x + 1/12y dy/dt = 1/3x - 1/3y (b) Use systematic elimination to solve the system of equations subject to the initial conditions x(0) = 2, y(0) = 1 (c) Use a graphing utility to graph both solution curves for 0 ? t ? 15 minutes.

          2. (16 points) Two large tanks, each holding 24 liters of a brine solution, are interconnected by pipes as shown in the figure. Pure water flows into tank A at a rate of 6 L/min, and fluid is drained out of tank B at the same rate. Also, 8 L/min of fluid are pumped from tank A to tank B, and 2 L/min from tank B to tank A. The liquids inside each tank are kept well stirred so that each mixture is homogeneous. Initially the brine solution in tank A contains 2 kg of salt and that in tank B contains 1 kg of salt. Let x(t) represent the mass of salt in tank A at time t and y(t) the mass of salt in tank B.
(a) Show that the rates of change of the mass of the salt are described by the system of DEs
dx/dt = -1/3x + 1/12y
dy/dt = 1/3x - 1/3y
(b) Use systematic elimination to solve the system of equations subject to the initial conditions x(0) = 2, y(0) = 1
(c) Use a graphing utility to graph both solution curves for 0 ? t ? 15 minutes.

2. (16 points) Two large tanks, each holding 24 liters of a brine solution, are interconnected by pipes as shown in the figure. Pure water flows into tank A at a rate of 6 L/min, and fluid is drained out of tank B at the same rate. Also, 8 L/min of fluid are pumped from tank A to tank B, and 2 L/min from tank B to tank A. The liquids inside each tank are kept well stirred so that each mixture is homogeneous. Initially the brine solution in tank A contains 2 kg of salt and that in tank B contains 1 kg of salt. Let x(t) represent the mass of salt in tank A at time t and y(t) the mass of salt in tank B.
(a) Show that the rates of change of the mass of the salt are described by the system of DEs
dx/dt = -1/3x + 1/12y
dy/dt = 1/3x - 1/3y
(b) Use systematic elimination to solve the system of equations subject to the initial conditions x(0) = 2, y(0) = 1
(c) Use a graphing utility to graph both solution curves for 0 ? t ? 15 minutes.

Added by Heather W.

Question

Please give Ace some feedback