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Mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and from tank 3 into tank 1, all at the given flow rate r gallons per minute. The initial amounts x₁ (0) = x₁ (lb), and x₂ (0) = 0, and x3 (0) = 0 of salt in the three tanks are given, as are their volumes V₁, V₂, and V3. First solve for the amounts of salt in the three tanks at time t, then determine the limiting amount of salt (as t→+∞o) of salt in each tank. Finally, construct a figure showing the graphs of x₁ (t), x₂ (t), and x3 (t). r=140, x₁ = 118, V₁ =70, V₂ =20, V3 = 28 X₁ (t) =

Mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and from tank 3 into tank 1, all at the given flow rate r gallons per minute. The initial amounts x₁ (0) = x₁ (lb), and x₂ (0) = 0, and x3 (0) = 0 of salt in the three tanks are given, as are their volumes V₁, V₂, and V3. First solve for the amounts of salt in the three tanks at time t, then determine the limiting amount of salt (as t→+∞o) of salt in each tank. Finally, construct a figure showing the graphs of x₁ (t), x₂ (t), and x3 (t). r=140, x₁ = 118, V₁ =70, V₂ =20, V3 = 28 X₁ (t) =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and from tank 3 into tank 1, all at the given flow rate r gallons per minute. The initial amounts x₁ (0) = x₁ (lb), and x₂ (0) = 0, and x3 (0) = 0 of salt in the three tanks are given, as are their volumes V₁, V₂, and V3. First solve for the amounts of salt in the three tanks at time t, then determine the limiting amount of salt (as t →+∞) of salt in each tank. Finally, construct a figure showing the graphs of x₁ (t), x₂ (t), and x3 (t). r=140, x₁ = 118, V₁ =70, V₂ =20, V3 = 28 X₁ (t) =
Transcribed Image Text:Mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and from tank 3 into tank 1, all at the given flow rate r gallons per minute. The initial amounts x₁ (0) = x₁ (lb), and x₂ (0) = 0, and x3 (0) = 0 of salt in the three tanks are given, as are their volumes V₁, V₂, and V3. First solve for the amounts of salt in the three tanks at time t, then determine the limiting amount of salt (as t →+∞) of salt in each tank. Finally, construct a figure showing the graphs of x₁ (t), x₂ (t), and x3 (t). r=140, x₁ = 118, V₁ =70, V₂ =20, V3 = 28 X₁ (t) =
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