Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 45 pounds of salt are dissolved in the solution in tank. system is closed in that the well-stirred liquid is pumped only between the tanks, as shown in the figure below. (a) Use the information dx₁ dt dx2 = dt 100 gal x₁ (0) = mixture 3 gal/min 105 X₂(0) = 45 mixture 2 gal/min 2x₁ 100+t 2x₁ 100+t given in the figure to construct a mathematical model for the number of pounds of salt x₁(t) and x₂(t) at time t in tanks A and B, respectively. 3x2 100-t + B 100 gal 3x2 100-t ✓ lbs ✓ lbs (b) Find a relationship between the variables x₁(t) and x₂(t) that holds at time t. (Write an equation using x₁ for x₁(t) and x₂ for x₂(t).) |x₂(t) = (100-1)³ (100 + 1)² 300-t (100-t)² +0.45 X
Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 45 pounds of salt are dissolved in the solution in tank. system is closed in that the well-stirred liquid is pumped only between the tanks, as shown in the figure below. (a) Use the information dx₁ dt dx2 = dt 100 gal x₁ (0) = mixture 3 gal/min 105 X₂(0) = 45 mixture 2 gal/min 2x₁ 100+t 2x₁ 100+t given in the figure to construct a mathematical model for the number of pounds of salt x₁(t) and x₂(t) at time t in tanks A and B, respectively. 3x2 100-t + B 100 gal 3x2 100-t ✓ lbs ✓ lbs (b) Find a relationship between the variables x₁(t) and x₂(t) that holds at time t. (Write an equation using x₁ for x₁(t) and x₂ for x₂(t).) |x₂(t) = (100-1)³ (100 + 1)² 300-t (100-t)² +0.45 X
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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Transcribed Image Text:Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 45 pounds of salt are dissolved in the solution in tank B
system is closed in that the well-stirred liquid is pumped only between the tanks, as shown in the figure below.
dx1
dt
dx2
dt
X₁ (0)
(a) Use the information given in the figure to construct a mathematical model for the number of pounds of salt x₁(t) and x₂(t) at time t in tanks A and B, respectively.
3x2
100-t
x2(0)
=
A
100 gal
=
mixture
3 gal/min
105
45
mixture
2 gal/min
x₂(t) =
2x₁
100+ t
2x₁
100+ t
+
B
100 gal
3x2
100-t
300 t
(100-t)²
lbs
(b) Find a relationship between the variables x₁(t) and x₂(t) that holds at time t. (Write an equation using x₁ for x₁(t) and
x2
lbs
+0.45
(100 – t) ³
(100+t)²
for x₂(t).)
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