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mathcoral

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Mixing with a Common Drain. Two tanks, each holding 1 L of liquid, are connected by a pipe through which liquid flows from tank A into tank B at a rate of 3-a L/min (0<a<3). The liquid inside each tank is kept well stirred. Pure water flows into tank A at a rate of 3 L/min. Solution flows out of tank A at a L/min and out of tank B at 3-a L/min. If, initially, tank B contains no salt (only water) and tank A contains 0.1 kg of salt, determine the mass of salt in each tank at time T>=0. How does the mass of salt in tank A depend on the choice of a? What is the maximum mass of salt in tank B?Here is picture of the tank View attachment 8094

I was going to make a normal equation x'=Ax to find the eigenvectors.

I got stuck on the set up

x

x

x

The rate in is 0 because the liquid is pure water.

x

x

I am unsure how to put the 3 L/min coming out of from both tanks (bottom pipe).

I was going to make a normal equation x'=Ax to find the eigenvectors.

I got stuck on the set up

x

_{1}=rate in - rate outx

_{1}(t)=0 - (3-a)x_{1}(t) - ax_{1}(t)x

_{1}(t)= -3x_{1}(t)The rate in is 0 because the liquid is pure water.

x

_{2}(t) =rate in - rate outx

_{2}(t)= (3-a)x_{1}(t) - (3-a)x_{2}(t)I am unsure how to put the 3 L/min coming out of from both tanks (bottom pipe).