Atank initially contains 120l of pure water. a mixture continuing a concentration of γγ g/l of salt 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 in terms of γγ for the amount of salt in the tank at any time tt.

The amount of salt in the tank at any time t is

Explanation:

By definition, we have that the change rate of salt in the tank is , where is the rate of salt entering and is the rate of salt going outside.

Then we have, , and

So we obtain.  , then

, and using the integrating factor , therefore

, we get   , after integrating both sides , therefore , to find we know that the tank initially contains 120L of pure water, that means the initial conditions , so

Finally we can write an expression in terms of γγ for the amount of salt in the tank at any time t, it is

i already answered it by 34/s

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y