Question

1.For the "closed "system of three brine tanks with volumes V1 = 50gal,V2 = 25gal,V3 = 50gal and constant flow rate r = 10gal / min Find the amounts of salt x1(t), x2(t), x3(t) at time t in the three brine tanks, if the initial amount in each of the tanks is: x1(0) = 50, x2(0) = x3(0) = 0. (The difference between this system and "open" system is that now the inflow to tank 1 is the outflow from tank 3)

          1.For the "closed "system of three brine tanks with volumes
V1 = 50gal,V2 = 25gal,V3 = 50gal and constant flow rate r = 10gal / min
Find the amounts of salt x1(t), x2(t), x3(t) at time t in the three brine tanks, if the initial
amount in each of the tanks is: x1(0) = 50, x2(0) = x3(0) = 0.
(The difference between this system and "open" system is that now the inflow to tank 1 is
the outflow from tank 3)

1.For the "closed "system of three brine tanks with volumes
V1 = 50gal,V2 = 25gal,V3 = 50gal and constant flow rate r = 10gal / min
Find the amounts of salt x1(t), x2(t), x3(t) at time t in the three brine tanks, if the initial
amount in each of the tanks is: x1(0) = 50, x2(0) = x3(0) = 0.
(The difference between this system and "open" system is that now the inflow to tank 1 is
the outflow from tank 3)

Added by Natalie V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shaiju T

05/07/2022

Step 1

Step 1: Write the differential equations in matrix form: The differential equations for the system can be written in matrix form as: \[ \begin{bmatrix} x_1' \\ x_2' \\ x_3' \end{bmatrix} = \begin{bmatrix} -\frac{1}{5} & 0 & 0 \\ \frac{1}{5} & -\frac{2}{5} & 0 \\ 0 Show more…

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For the "closed" system of three brine tanks with volumes V1 = 50 gal, V2 = 25 gal, V3 = 50 gal, and constant flow rate r = 10 gal/min, find the amounts of salt x1(t), x2(t), and x3(t) at time t in the three brine tanks, if the initial amount in each of the tanks is: x1(0) = 50, x2(0) = x3(0) = 0. (The difference between this system and "open" system is that now the inflow to tank 1 is the outflow from tank 3.)