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Fresh water flows into tank 1; mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and out of tank 3; all at the given flow rate r gallons per minute. The initial amounts x₁(0)=xo (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 maximal amount of salt that tank 3 ever contains. Finally, construct a figure showing the graphs of x₁ (t), x₂ (t), and x3 (t). r = 60, x₁ = 45, V₁ =15, V₂ = 12, V3 = 20 X₁ (t) = X₂ (t)= X3 (t)=

Fresh water flows into tank 1; mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and out of tank 3; all at the given flow rate r gallons per minute. The initial amounts x₁(0)=xo (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 maximal amount of salt that tank 3 ever contains. Finally, construct a figure showing the graphs of x₁ (t), x₂ (t), and x3 (t). r = 60, x₁ = 45, V₁ =15, V₂ = 12, V3 = 20 X₁ (t) = X₂ (t)= X3 (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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Fresh water flows into tank 1; mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and out of tank 3; all at the given flow rate r gallons per minute. The initial amounts X₁ (0)=xo (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 maximal amount of salt that tank 3 ever contains. Finally, construct a figure showing the graphs of x₁ (t), x₂(t), and x3 (t). r=60, xo = 45, V₁ =15, V₂ = 12, V3 = 20 X₁ (t) = X₂ (t) = X3 (t) =
Transcribed Image Text:Fresh water flows into tank 1; mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and out of tank 3; all at the given flow rate r gallons per minute. The initial amounts X₁ (0)=xo (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 maximal amount of salt that tank 3 ever contains. Finally, construct a figure showing the graphs of x₁ (t), x₂(t), and x3 (t). r=60, xo = 45, V₁ =15, V₂ = 12, V3 = 20 X₁ (t) = X₂ (t) = X3 (t) =
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