4. Two 100 litre tanks are completely filled with a mixture of salt and water with each tank containing a different conc

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4 Two 100 Litre Tanks Are Completely Filled With A Mixture Of Salt And Water With Each Tank Containing A Different Conc 1 (249.08 KiB) Viewed 200 times

4. Two 100 litre tanks are completely filled with a mixture of salt and water with each tank containing a different concentration of salt. Fresh water is pumped into Tank A at a rate of 8 litres per minute. The water mixes in the two tanks as described by the diagram below, with water being pumped out of Tank B at a rate of 8 litres per minute. Initially Tank A contains no salt and Tank B contains 6kg of salt. 8L/min 9 L/min Pure water Tank A 100 Litres Tank B 100 Litres 1 L/min 8L/min The problem is to find the amount of salt (in kilograms) in Tank A and Tank B at time t. (a) Let x(t) be the amount of salt in Tank A at time t and let y(t) be the amount of salt (in kilograms) in Tank B at time t minutes. Explain why (5)=(-0.00 0.01 -0.09 })(;). (b) Find explicit formulas for x(t) and y(t) at time t given that -0.09 0.01 0.09 -0.09 ¹)(-³) = −0.12(_3) and -0.09 0.01 0.09 -0.09 ) ( ³ ) = −0.06( ¹ ). (c) Confirm that the concentration of salt in each tank approaches zero over a long period of time.