(1) A tank is filled with 300 liters (L) of contaminated water initially containing 3 kg...
(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 box around your answer.
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(1) A tank is filled with 300 liters (L) of contaminated water
initially containing 3 kg...
A tank with 500 liters of water initially contains 4g of calcium. Water with a concentration of 3...
a tank with 500 liters of water initially contains 4g of calcium. Water with a concentration of 3 mg/L is pumped into the tank at a rate of 1L/min and the mixture is pumped out at the same rate. (a) Write a differential equation and its initial condition for, y(t), the total amount of calcium in grams in the tank. (t is measured in minutes, 1g = 1000mg) (b) Find the general solution to this differential equation. (c) Find the...
*Using Differential Equations 3. A solution containing 0.2 kg/l of salt is pumped into a tank...
*Using Differential
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3. A solution containing 0.2 kg/l of salt is pumped into a tank containing 51 of pure water at a rate of 317 min. If the well stirred mixture is pumped from the tank at the same rate of 31/min, how long does it take in minutes for the liquid in the tank to contain 0.5 kg of salt?
-2t A tank initially contains 10 liters of water and 5 grams of salt. Salt water...
-2t A tank initially contains 10 liters of water and 5 grams of salt. Salt water containing 3+ e grams of salt per liter is pumped into the tank at a rate of 2 liters per minute. The solution of salt water is instantaneously, perfectly mixed and then pumped out at a rate of 2 liters per minute. Determine when, to three decimal places, the concentration of the salt leaving the tank is within 0.01 grams/liter of the salt entering...
A tank initially contains 120 L of pure water. A salt mixture containing a concentration of...
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...
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4. Suppose there are two tanks, each containing 200 l of fluid. Tank 1 initially contains...
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4. A tank initially contains 100 liters (L) of water with a salt concentration of 20...
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(1 point) Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 10 L (liters) of water and 355 g of salt, while tank 2 initially contains 90 L of water and 345 g of...
(1 point) Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 10 L (liters) of water and 355 g of salt, while tank 2 initially contains 90 L of water and 345 g of salt. Water containing 40 g/L of salt is poured into tank1 at a rate of 4 L/min while the mixture flowing into tank 2 contains a salt concentration of 20 g/L of salt and is flowing at the rate of 1...
A tank initially contains 980 gal of pure water.
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A tank initially contains 500 gallons of water in which 40 pounds of salt is initially dissolved in the water
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*Using Differential
Equations
3. A solution containing 0.2 kg/l of salt is pumped into a tank containing 51 of pure water at a rate of 317 min. If the well stirred mixture is pumped from the tank at the same rate of 31/min, how long does it take in minutes for the liquid in the tank to contain 0.5 kg of salt?
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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,...
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.
(1 point) Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 10 L (liters) of water and 355 g of salt, while tank 2 initially contains 90 L of water and 345 g of salt. Water containing 40 g/L of salt is poured into tank1 at a rate of 4 L/min while the mixture flowing into tank 2 contains a salt concentration of 20 g/L of salt and is flowing at the rate of 1...
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