Consider the large mixing tanks show in the figure. Suppose that both tanks A and B initially contain 100 gallons of brine. Liquid is pumped in and out of the tanks as indicated in the figure; the mixture pumped between and out of the tanks is assumed to be well-stirred. 1 (a) Starting with a mass balance, construct a mathematical model in the form of a linear system of first-order differential equations for the number of pounds rA(t) and æg(t) of salt in tanks A and B, respectively, at time t. Write the system in matrix form. (b) Use the method of undetermined coefficients to solve the linear system in (a) subject to TA (0) – 60, xB(0) = 10. (c) What are lim, r00 "A(t) and lim,0 *B(t)? Interpret this result. pure water منسلم 2 mixture 1 galmin 2 galnin mixtare mixture mixturo 3 galmin
Consider the large mixing tanks show in the figure. Suppose that both tanks A and B initially contain 100 gallons of brine. Liquid is pumped in and out of the tanks as indicated in the figure; the mixture pumped between and out of the tanks is assumed to be well-stirred. 1 (a) Starting with a mass balance, construct a mathematical model in the form of a linear system of first-order differential equations for the number of pounds rA(t) and æg(t) of salt in tanks A and B, respectively, at time t. Write the system in matrix form. (b) Use the method of undetermined coefficients to solve the linear system in (a) subject to TA (0) – 60, xB(0) = 10. (c) What are lim, r00 "A(t) and lim,0 *B(t)? Interpret this result. pure water منسلم 2 mixture 1 galmin 2 galnin mixtare mixture mixturo 3 galmin
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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![8. Consider the large mixing tanks show in the figure. Suppose that both tanks A and B initially
contain 100 gallons of brine. Liquid is pumped in and out of the tanks as indicated in the
figure; the mixture pumped between and out of the tanks is assumed to be well-stirred.
1
(a) Starting with a mass balance, construct a mathematical model in the form of a linear
system of first-order differential equations for the number of pounds TA(t) and rB(t) of
salt in tanks A and B, respectively, at time t. Write the system in matrix form.
(b) Use the method of undetermined coefficients to solve the linear system in (a) subject to
ТA (0) — 60, г в(0) — 10.
(c) What are lim-+00 TA(t) and lim +00 ªB(t)? Interpret this result.
pure water
2 gal/min
K Ibigal
2 gulmin
mixture
1 gal/min
mixhare
mixture
mixturo
1 ga/min
2 galmin
3 galimin](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69d33b94-47ab-4124-8ded-71fa51390a3f%2Ff6e10bdc-97ac-4de2-9f9d-e6e3f6bbbbfd%2Ff7lgf6r_processed.png&w=3840&q=75)
Transcribed Image Text:8. Consider the large mixing tanks show in the figure. Suppose that both tanks A and B initially
contain 100 gallons of brine. Liquid is pumped in and out of the tanks as indicated in the
figure; the mixture pumped between and out of the tanks is assumed to be well-stirred.
1
(a) Starting with a mass balance, construct a mathematical model in the form of a linear
system of first-order differential equations for the number of pounds TA(t) and rB(t) of
salt in tanks A and B, respectively, at time t. Write the system in matrix form.
(b) Use the method of undetermined coefficients to solve the linear system in (a) subject to
ТA (0) — 60, г в(0) — 10.
(c) What are lim-+00 TA(t) and lim +00 ªB(t)? Interpret this result.
pure water
2 gal/min
K Ibigal
2 gulmin
mixture
1 gal/min
mixhare
mixture
mixturo
1 ga/min
2 galmin
3 galimin
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