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3. (25 pts) A tank with 60 gallons of wine contains 11% alcohol by volume. Wine...
Question 4 2.5 pts Beer with 6% alcohol (by volume) is pumped into a 500 gallon tank at a rate of 5 gal/min, and the mixture is pumped out at the same rate. Let y(t) denote the percentage of alcohol in the tank at time t (in minutes). Write a differential equation for y(t). O (t) = 100(g(t) - 6) O 4 (t) = 6(gt) - 0.01) O 4 (t) = 0.01(6 – (t)) y(t) = 6+ Ce-.01t
B. Set up a system of equations for the following situation and then use MATLAB to solve the system Tank A contains 50 gallons of water in which 25 pounds of salt are dissolved. A second tank, B, contains 50 gallons of pure water. Liquid is pumped in and out of the tanks at the rates shown in Figure 8.9. Derive the differential equations taerihe themuunds and B, respectively d tm in tanks A mixture pure water 3 gal/min 1...
(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...
(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...
15. Consider a two tank system pictured below. Suppose tank A contains 100 gallons of water in which 120 pounds of salt are dissolved initially. Suppose tank B has 100 gallons of water in which zero pounds of salt are dissolved initially. Liquid is pumped into 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 are assumed to be well mixed. How many pounds...
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)...
(you can give youtr als we A tank contains initially (t 0) 200 gallons of water in which 80 pounds of salt are dissolved. Pure water (i.e. no salt) runs into the tank at the rate of 4 gal/min. The mixture is drained out from bottom of tank at the rate of 6 gal/min. How much salt is there in the tank after 66 minutes?
83. Suppose that a tank contains 20 gal of a solution of a certain chemical and that 5 lb of the chemical are in the solution. Starting at a certain instant, a solution of the same chemical, with concentration of 2 lb/gal, is allowed to flow into the tank at the rate of 3 gal/min. The mixture is drained off at the same rate so that the volume of the solution in the tank remains constant. How many gallons 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...
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.)