A tank contains a mixture of water and salt, and at all times the solution is...

A tank contains a mixture of water and salt, and at all times the solution is kept will mixed. At time t = 0 there is 10 Liters solution in the tank, with no salt. However, being poured into the tank is a solution containing 2 grams of salt per liter, and it is entering at a rate of 5 liters per minute. Simultaneously we drain our tank at a rate of 3 liters per minute. Find the concentration of salt (measured in grams per liter) at time t.

Expert Solution

Colby Messinger answered 1 year ago

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 100kg of salt and 2000L of water. Pure water enters a tank at...

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

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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...

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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...

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A tank contains 1000L of pure water. Brine that contains 0.05kg of salt per liter enters the tank at a rate of 5L/min. Also, brine that contains 0.09kg of salt per liter enters the tank at a rate of 10L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15L/min. Answer the following questions. 1. How much salt is in the tank after t minutes? Answer (in kilograms): S(t)= 2. How much salt is...

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