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# Deal with the closed three-tank system of Fig. 5.2.5, which is described by the equations in (24, Mixed brine flows from tank 1 into tank 2, from tank 2 int \$operat...

## Question

###### Deal with the closed three-tank system of Fig. 5.2.5, which is described by the equations in (24, Mixed brine flows from tank 1 into tank 2, from tank 2 int \$operatorname{tank} 3\$, and from tank 3 into tank 1, all at the given flow rate gallons per minute. The initial amounts \$x_{1}(0)=x_{0}\$ (pounds, \$x_{2}(0)=0\$, and \$x_{3}(0)=0\$ of salt in the three tanks are giver as are their volumes \$V_{1}, V_{2}\$, and \$V_{3}(\$ in gallons \$) .\$ First solve for the amounts of salt in the three tanks at time

Deal with the closed three-tank system of Fig. 5.2.5, which is described by the equations in (24, Mixed brine flows from tank 1 into tank 2, from tank 2 int \$operatorname{tank} 3\$, and from tank 3 into tank 1, all at the given flow rate gallons per minute. The initial amounts \$x_{1}(0)=x_{0}\$ (pounds, \$x_{2}(0)=0\$, and \$x_{3}(0)=0\$ of salt in the three tanks are giver as are their volumes \$V_{1}, V_{2}\$, and \$V_{3}(\$ in gallons \$) .\$ First solve for the amounts of salt in the three tanks at time \$t\$, then determine the limiting amount (as \$t ightarrow+infty)\$ of salt in each tank Finally, construct a figure showing the graphs of \$x_{1}(t), x_{2}(t)\$ and \$x_{3}(t)\$. \$\$ r=10, x_{0}=18, V_{1}=20, V_{2}=50, V_{3}=20 \$\$

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