Question: Two brine tanks are connected with volumes Upper V 1 and Upper V 2. Water with a salt concentration of c 0 flows into tank1,
Two brine tanks are connected with volumes Upper V 1 and Upper V 2. Water with a salt concentration of c 0 flows into tank1, while mixed brine flows from tank 1 to tank2, and out of tank 2. Let x Subscript i Baseline left parenthesis t right parenthesis denote the amount(in pounds) of salt in tank i at time t. If each flow rate is r gallons per minute, then an accounting of salt concentrations yields the following first-order system, where k Subscript iequalsStartFraction r Over Upper V Subscript i EndFraction . x 1 prime equals rc 0negative k 1 x 1 x 2 prime equals k 1 x 1 minus k 2 x 2 Use the values Upper V 1equals80, Upper V 2equals160, requals8, and c 0equals4
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