Please help with part b) ASAP! DiscussionThe system of mixing tanks shown in Figure is a closed system. The tanks A, B, and C initially contain the number of gallons ofbrine indicated in the figure.mixture5 gal/minBC100 gal100 gal50 galmixturemixture5 gal/min5 gal/mina. Construct a mathematical model in the form of a linear system of first-order differential equations for the number of pounds ofsalt x1 (t), x2 (t) and x3 (t) in the tanks A, B, and C at time t, respectively. Write the system in matrix form.b. Use the eigenvalue method of this section to solve the linear system in part (a) subject tox1 (0) = 30, x2 (0) = 20, and x3 (0) = 5.c. Show that xi (t) + x2 (t) + x3 (t) = 55. Interpret this result.lim x1 (t) lim x2 (t)andlim *3 (t) Interpret this result.n >0d. What are> n->0

Given, the system of mixing tanks shown in the figure is a closed system. The tanks A, B, and C…

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The system of mixing tanks shown in Figure is a closed system. The

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.5: Systems Of Equations

Problem 5SBE: Setting Up System of Equations In Exercises S-3 through S-6, you are asked to write a system of two...

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Question

Please help with part b) ASAP!

Discussion
The system of mixing tanks shown in Figure is a closed system. The tanks A, B, and C initially contain the number of gallons of
brine indicated in the figure.
mixture
5 gal/min
B
C
100 gal
100 gal
50 gal
mixture
mixture
5 gal/min
5 gal/min
a. Construct a mathematical model in the form of a linear system of first-order differential equations for the number of pounds of
salt x1 (t), x2 (t) and x3 (t) in the tanks A, B, and C at time t, respectively. Write the system in matrix form.
b. Use the eigenvalue method of this section to solve the linear system in part (a) subject to
x1 (0) = 30, x2 (0) = 20, and x3 (0) = 5.
c. Show that xi (t) + x2 (t) + x3 (t) = 55. Interpret this result.
lim x1 (t) lim x2 (t)
and
lim *3 (t) Interpret this result.
n >0
d. What are
> n->0

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