Tank 1 initially contains 8 kg of salt dissolved into 1 kl. of water. Tank 2...
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Tank 1 initially contains 8 kg of salt dissolved into 1 kl. of water. Tank 2 initially contains 1 kg of salt dissolved into 1 kL of water. Both tanks are well mixed. A solution concentrated at 3kg/kL is flowing into the first tank and pure water is flowing into the second tank at the flow rates specified in the figure. Similarly, the figure shows the rate the mixtures are flowing between each tank and being drained. Let r(t) be the amount of salt in tank 1 in kg, and y(t) be the amount of salt in tank 2 in kg. 1 kl./hr-> 1 kl/hr Tank 1 1 KL x = -2x+y +3, v=x-2y, 1 kl/hr →→ ←1 kl/hr Tank 2 y(t) 1 kl ←1 kl/hr 1 kl/hr-> (0)=8 y(0) = 1. Use the substitution = y + 2y to convert the system to a second order initial value problem and solve for y(t). Then substitute your solution y(t) back into = y + 2y to solve for r(t). Tank 1 initially contains 8 kg of salt dissolved into 1 kl. of water. Tank 2 initially contains 1 kg of salt dissolved into 1 kL of water. Both tanks are well mixed. A solution concentrated at 3kg/kL is flowing into the first tank and pure water is flowing into the second tank at the flow rates specified in the figure. Similarly, the figure shows the rate the mixtures are flowing between each tank and being drained. Let r(t) be the amount of salt in tank 1 in kg, and y(t) be the amount of salt in tank 2 in kg. 1 kl./hr-> 1 kl/hr Tank 1 1 KL x = -2x+y +3, v=x-2y, 1 kl/hr →→ ←1 kl/hr Tank 2 y(t) 1 kl ←1 kl/hr 1 kl/hr-> (0)=8 y(0) = 1. Use the substitution = y + 2y to convert the system to a second order initial value problem and solve for y(t). Then substitute your solution y(t) back into = y + 2y to solve for r(t).
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Related Book For
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
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