9. Given the tank system, setup the system of equations. Assuming they all have different amounts...
B. Set up a system of equations for the following situation and then use MATLAB to solve the system Tank A contains 50 gallons of water in which 25 pounds of salt are dissolved. A second tank, B, contains 50 gallons of pure water. Liquid is pumped in and out of the tanks at the rates shown in Figure 8.9. Derive the differential equations taerihe themuunds and B, respectively d tm in tanks A mixture pure water 3 gal/min 1...
Consider two brine tanks connected as shown in figure I below. Tank 1 contains xit) pounds of salt in 100 wal of brine and tank 2 contains vit) pounds of salt in 200 gal of brine. The brine in each tank is kept uniform by stirring, and brine is pumped from each tank to the other at the rates indicated in figure 1. In addition, fresh water flows into tank 1 at 20 gal/min, and the brine in tank 2...
I just need help understand
where I get the 7 for the dx/dt
1. (5 points) Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from Tank A into Tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min. The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into Tank A...
same question, just 3 different lettered sections
Write the given system of equations as a matrix equation and solve by using inverses. X1 + X2 = k1 3x + 2x2 = kz a. What are X1 and X2 when kı = - 3 and k2= - 4? X1 X2= b. What are xı and x2 when ki = 5 and k2 = - 3? X1 = X2 = c. What are X1 and x2 when ki = - 1 and...
This is all one question.
3. Suppose Romeo and Juliet's love obeys the following differential equations: :/which has the following eigenvectors: 2 adwth egmao The matrix of this system is with eigenvalue 2, and 1 with eigenvalue-4 We wil use these two eigenvectors to define a new coordinate system, and we will use u and v to represent these coordinates. However, in this problem, we will treat u and v as new variables. Your goal is to rewrite this system...
Notre Dame University Faculty of Engineering seawater jet hits a tank aluminum (p 280o kg/m3) that is subme attached through a pulley system to a cylindrical solid block of s submerged in a pool of sea water as shown in Figure P The diar-stance between the eseawaterjet is A = 0.15m2 and θ-70". The coefficient of 1. l area of the n the wheels of the cart and the ground is assumed to be equal to 0.04. num block is...
e) From the vector equation in part d, we get this system of linear equations (I changed the variables from ci, c2, and cs to x, y, z so they are easier to use in Geogebra and more familiar): x+3y+z e 0 Originally we solved e 0. Try picking 4 different sets of values for 0 e and using Row Reduction to solve the system of equations. This is good practice. Here is a calculator where you can check your...
3. There are three ponds, each occupied by a large number of frogs. Every day, a certain fraction of the frogs from each pond migrate to one of the two neighbouring ponds according to the diagram at the right. Thus the number of frogs in each pond changes from day to day according to the following dynamical system: 0 Xn+1 Zr The eigenvalues of this matrix are λ-1,A-0.6 and λ-05. 0.1 (a) Find eigenvectors for each of these eigenvalues. (b)...
(7 10 Two connected tanks, each with a capacity of 60 liters, contain brine (salt water) Initially the firs tank contains 40 liters and the second tank contains 30 liers. Brine with a salt conccntration of 1 grams per litcr flows into the first tank at S litcrs per hour. Well-stirred brine flows from the first tank into the second at 7 liters per hour from the second nto the fist at3 lters per honr, from the first into a...
Please note that all the steps
are meant to help solve the problem.
Question A1: We have yet to discover what happens when the matrix that defines our system has a repeated real eigenvalue. Let's start with the case of a system defined by a diagonal matrix, which has the twice repeated real eigenvalue A 3. Follow the steps below to analyze the shape of the trajectories and draw the phase plane portrait: 1. Write down the explicit solution to...