A tank contains 70 kg of salt and 2000 L of water. Water containing 0.4kg/L of...

A tank contains 70 kg of salt and 2000 L of water. Water containing 0.4kg/L of salt enters the tank at the rate 16L/min. The solution is mixed and drains from the tank at the rate 4L/min. A(t) is the amount of salt in the tank at time t measured in kilograms.
(a) A(0) =  (kg)
(b) A differential equation for the amount of salt in the tank is  =0=0. (Use t,A, A', A'', for your variables, not A(t), and move everything to the left hand side.)
(c) The integrating factor is
(d) A(t) =  (kg)
(e) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.)
concentration =  kgL

Expert Solution

Colby Messinger answered 1 year ago

A tank contains 90 kg of salt and 2000 L of water: Pure water enters a...

A tank contains 90 kg of salt and 2000 L of water: Pure water enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the rate 4 L/min. What is the amount of salt in the tank initially? Find the amount f salt in the tank after 4.5 hours. Find the concentration of salt in the solution in the tank as the time approaches infinity. (Assume your tank is large enough to...

A tank contains 60 kg of salt and 1000 L of water. Pure water enters a...

A tank contains 60 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 3 hours. amount = (kg) (c) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume...

A tank contains 365 gallons of water and 50 oz of salt. Water containing a salt...

A tank contains 365 gallons of water and 50 oz of salt. Water containing a salt concentration of 1/6(1 + 1/4 sin t) oz/gal flows into the tank at a rate of 8 gal/min, and the mixture in the tank flows out at the same rate. The long-term behavior of the solution is an oscillation about a certain constant level. a) What is this level? b) What is the amplitude of the oscillation?

A tank contains 200 gal of water and 50oz of salt. Water containing a salt concentration...

A tank contains 200 gal of water and 50oz of salt. Water containing a salt concentration of 1/8(1+1/2 sint) oz/gal flows into the tank at a rate of 4 gal/min, the mixture flows out at the same rate. A) find the amount of salt in the tank at any moment. Q(t) = B) the amplitude of oscillation is C) level of the amplitude is

A tank contains 360 gallons of water and 50 oz of salt. Water containing a salt...

A tank contains 360 gallons of water and 50 oz of salt. Water containing a salt concentration of 1 6 (1 + 1 4 sin t) oz/gal flows into the tank at a rate of 8 gal/min, and the mixture in the tank flows out at the same rate. The long-term behavior of the solution is an oscillation about a certain constant level. a) What is this level? b) What is the amplitude of the oscillation? (Round your answers to...

A tank contains 20 kg of salt dissolve in 7000 L of water. Brine that contain...

A tank contains 20 kg of salt dissolve in 7000 L of water. Brine that contain 0.041 kg of salt per liter of water enters the tank at a rate of 25 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much Kg salt remains in the tank if as time approaches to infinite?

2. A tank initially contains 120 L of pure water. A salt mixture containing a concentration of...

2. 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 →∞.

A tank contains 9,000 L of brine with 11 kg of dissolved salt. Pure water enters...

A tank contains 9,000 L of brine with 11 kg of dissolved salt. Pure water enters the tank at a rate of 90 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. (a) How much salt is in the tank after t minutes? (b) How much salt is in the tank after 10 minutes? (Round your answer to one decimal place.)

A tank contains 10 gallons of water. Salt water containing a concentration of 4t ounces per...

A tank contains 10 gallons of water. Salt water containing a concentration of 4t ounces per gallon flows into the tank at a rate of 4 gallons per minute and the mixture in the tank flows out at the same rate. (a)Construct the mathematical model for this flow process (b)Use integrating factors to solve for Q(t). (c)If the tank contains Q0 amount of salt at time t = 0, use this as an initial condition to solve for the constant...

A tank originally contains 120 gal of fresh water. Then water containing 1/2 lb of salt...

A tank originally contains 120 gal of fresh water. Then water containing 1/2 lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at the same rate. After 11 min the process is stopped, and fresh water is poured into the tank at a rate of 2 gal/min, with the mixture again leaving at the same rate. Find the amount of salt Q(11) in the tank at...

Question