Mathematics, 11.02.2021 23:10 kelsgoat22
A tank contains 250 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.
Answers: 1
![\frac{dA}{dt}+\frac{A(t)}{50} = 5\\\\The\ integrating\ factor(IF)= e^{\int\limits \frac{1}{50}dt }=e^{\frac{t}{50} }\\\\Multiplying\ through\ by\ the\ I.F:\\\\\frac{dA}{dt}*e^{\frac{t}{50} }+\frac{A(t)}{50}*e^{\frac{t}{50} } = 5*e^{\frac{t}{50} }\\\\Integrating \ both \ sides:\\\\\int\limits[ \frac{dA}{dt}*e^{\frac{t}{50} }+\frac{A(t)}{50}*e^{\frac{t}{50} }] dt=\int\limits 5e^{\frac{t}{50} } dt\\\\A(t)e^{\frac{t}{50} } =\int\limits 5e^{\frac{t}{50} } dt\\\\](/tpl/images/1112/6507/62214.png)
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A tank contains 250 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram...
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