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Mixing Problems and Separable Differential Equations - Calculus 2

Quoc Dat Phung 20,221 lượt xem 1 year ago
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In this video, I will go over many examples about typical mixing problem that students often see in Calculus 2 classes. There is also another kind of mixing problem that involves percentages. I will cover this type of mixing problem in the next video. There are three formulas that you need to know. They will result in a separable differential equation that you can easily solve.

A tank contains 20 kg of salt dissolved in 5000 L of water.
Brine that contains 0.03 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 salt will there be in the tank after half an hour?

A vat with 500 gallons of beer contains 4% alcohol (by volume).
Beer with 6% alcohol is pumped into the vat at a rate of 5 gal/min.
The mixture is pumped out at the same rate.
The solution is kept thoroughly mixed.
What is the percentage of alcohol after an hour?

A tank contains 1000 L of pure water.
Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min
Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10L/min
The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min.
How much salt is in the tank:
(a) after t minutes
(b) after 1 hour?

A tank contains 1000L of brine with 15 kg of dissolved salt.
Pure water enters the tank at a rate of 10 L/min.
The solution is kept thoroughly mixed and drains from the tank at the same rate.
How much salt is in the tank a) after t min? b) after 20 min?

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