. As shown in Figure 8.2.6 two large connected mixing 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 a tank is assumed to be well-stirred. Figure 8.2.6 Mixing tanks pure water mixture 2 gal/min 1 gal/min B mixture mixture mixture I gal/min 2 gal/min I gal/min (a) Construct a mathematical model in the form of a linear system of first- order differential equations for the number of pounds ¤1 (t) and #2 (t) of salt in tanks A and B, respectively, at time t. Write the system in matrix form. (b) Use the eigenvalue method of this section to solve the linear system in part (a) subject to ¤1(0) = 20, æ2(0) = 5. (c) Use a graphing utility or CAS to plot the graphs of ¤1 (t) and æ2(t) in the same coordinate plane.
. As shown in Figure 8.2.6 two large connected mixing 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 a tank is assumed to be well-stirred. Figure 8.2.6 Mixing tanks pure water mixture 2 gal/min 1 gal/min B mixture mixture mixture I gal/min 2 gal/min I gal/min (a) Construct a mathematical model in the form of a linear system of first- order differential equations for the number of pounds ¤1 (t) and #2 (t) of salt in tanks A and B, respectively, at time t. Write the system in matrix form. (b) Use the eigenvalue method of this section to solve the linear system in part (a) subject to ¤1(0) = 20, æ2(0) = 5. (c) Use a graphing utility or CAS to plot the graphs of ¤1 (t) and æ2(t) in the same coordinate plane.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Solve the exercise in the image, by using
![. As shown in Figure 8.2.6 two large connected mixing 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 a tank is
assumed to be well-stirred.
Figure 8.2.6
Mixing tanks
pure water
mixture
2 gal/min
1 gal/min
A
B
mixture
1 gal/min
mixture
mixture
2 gal/min
1 gal/min
(a) Construct a mathematical model in the form of a linear system of first-
order differential equations for the number of pounds ¤1(t) and x2 (t) of salt
in tanks A and B, respectively, at time t. Write the system in matrix form.
(b) Use the eigenvalue method of this section to solve the linear system in
part (a) subject to ¤1 (0) = 20, æ2 (0) = 5.
(c) Use a graphing utility or CAS to plot the graphs of ¤1 (t) and #2(t) in the
same coordinate plane.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffdea5bec-e634-4619-8e5f-d35b2a241bce%2F0d6a9dbe-09ca-43d2-86ad-a3e911845579%2Fu5t217_processed.png&w=3840&q=75)
Transcribed Image Text:. As shown in Figure 8.2.6 two large connected mixing 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 a tank is
assumed to be well-stirred.
Figure 8.2.6
Mixing tanks
pure water
mixture
2 gal/min
1 gal/min
A
B
mixture
1 gal/min
mixture
mixture
2 gal/min
1 gal/min
(a) Construct a mathematical model in the form of a linear system of first-
order differential equations for the number of pounds ¤1(t) and x2 (t) of salt
in tanks A and B, respectively, at time t. Write the system in matrix form.
(b) Use the eigenvalue method of this section to solve the linear system in
part (a) subject to ¤1 (0) = 20, æ2 (0) = 5.
(c) Use a graphing utility or CAS to plot the graphs of ¤1 (t) and #2(t) in the
same coordinate plane.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)