Three large tanks contain brine, as shown in the figure below. pure water 4 gal/min 国国回 a gal b gal egal mixture mixture mixture 4 gal/min 4 gal/min 4 gal/min Use the information in the figure to construct a mathematical model for the number of pounds of salt x,(t), x(e), and xg(t) at time t in tanks A, 8, and C respectively. (Assume a = 250, b= 200, and e 150.)

Three large tanks contain brine, as shown in the figure below. pure water 4 gal/min 国国回 a gal b gal egal mixture mixture mixture 4 gal/min 4 gal/min 4 gal/min Use the information in the figure to construct a mathematical model for the number of pounds of salt x,(t), x(e), and xg(t) at time t in tanks A, 8, and C respectively. (Assume a = 250, b= 200, and e 150.)

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Three large tanks contain brine, as shown in the figure below.
pure water
4 gal/min
A
В
a gal
b gal
c gal
mixture
mixture
mixture
4 gal/min
4 gal/min
4 gal/min
Use the information in the figure to construct a mathematical model for the number of pounds of salt x, (t), x,(t), and x,(t) at time t in tanks A, B, and C respectively. (Assume a = 250, b = 200, and c = 150.)
dx,
dt
dx2
dt
dx 3
dt
Without solving the system, predict limiting values of x,(t), x,(t), and x3(t) as t → co.
lim x,(t) =
lim x2(t) =
lim x(t) =
t- 00

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