xo (lb), and 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) = 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 = 48, xo = 60, V₁ = 12, V₂ = 8, V3 = 24 X₁ (t)= 60e-4t -61 X₂(t)=-120e + 120e X3 (t)= 180e-6-360e-4t+180 2t 41 The maximum salt ever in tank 3 is pounds. (Round to two decimal places as needed.)
xo (lb), and 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) = 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 = 48, xo = 60, V₁ = 12, V₂ = 8, V3 = 24 X₁ (t)= 60e-4t -61 X₂(t)=-120e + 120e X3 (t)= 180e-6-360e-4t+180 2t 41 The maximum salt ever in tank 3 is pounds. (Round to two decimal places as needed.)
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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Find the salt pls pounds
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 = 48, xo = 60, V₁ = 12, V₂ = 8, V3 = 24
X₁ (t)= 60e-4t
-61
X₂(t)=-120e + 120e
41
61
X3 (t)= 180e -360e-4+180e-21
The maximum salt ever in tank 3 is pounds.
(Round to two decimal places as needed.)
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