 # 1. Consider the two-loop circuit shown in gure 1. The currents I1 ...

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1. Consider the two-loop circuit shown in gure 1. The currents I1 and I2 (in Amps) satisfy the following system of equations: 16I1 − 9I2 = 110 20I2 − 9I1 + 110 = 0 a. Setup: Describe the setup of this problem (e.g. include a diagram of problem, a list of what is known/given and a list of that is being found). b. Calculation: Write the system of equations in matrix form AI = b where I =  I1 I2  Find I1 and I2 using the matrix algebra method. Perform all computations by hand and show all steps. c. Calculation: Find I1 and I2 using Cramer's Rule. Perform all computations by hand and show all steps.2. A two-bar truss supports a weight of W = 750lb as shown in gure 2. Figure 1: Circuit diagram of a two loop circuit described in problem 1 The Forces F1 and F2 satisfy the following system of equations: 0.866F1 = F2 0.5F1 = 750 a. Setup: Describe the setup of this problem (e.g. include a diagram, a list of what is known/given and list of what is being found). b. Calculation: Write the system of equations in matrix form AF = b where F =  F1 F2  Find F1 and F2 using the matrix algebra method. (N.B. for this problem some coecients and/or constants will be zero). Perform all computations by hand and show all steps. c. Calculation: Find F1 and F2 using Cramer's Rule. Perform all computations by hand and show all steps. Figure 2: Diagram of the two-bar truss described in problem 2 13. You have two sugar solutions. One is 1.2 L with concentration of 1.5 g/L. The other is 0.6 L with concentration of 1.0 g/L. These two solution are mixed together thoroughly. a. Setup: Describe the setup of this problem (e.g., include a diagram of problem, a list of what is known/given and a list of what is being found) b. Calculation: What is the nal volume and concentration of sugar in g/L of the mixture? 4. For Halloween an M and M Mars Plant wants to make up a 150 bar mixture of 3-Musketeers and Snickers bars that is 40% 3 Musketeers bars. They have stock pallets that have 70% 3-Musketeers bars and 20% 3-Musketeers bars. How many bars should they take from each stock to make the correct mixture? a. Setup: Describe the setup of this problem (e.g., include a diagram of problem, a list of what is known/given and a list of what is being found). b. Calculation: Write the total material balance and the bar component balance equations for this problem. c. Calculation: Write the system of equation in matrix form AX = b, where X has the variable for number of bars from the 70% mixture in its rst row and the variable for total number of bars from the 20% mixture in its second row. Solve using matrix algebra method. Perform all computations by hand and show all steps. 5. A stream from a well water system is owing at 1.2 liters/min. The water in this stream has a chlorine concentration of 0.2 mg/liter. To treat this water we wish to bring the concentration up to 0.5 mg/L. You can mix in a solution of chlorine that has 50 mg/L of chlorine. How much of this solution do you need to add per hour? What is the resulting total ow rate as a result of this addition? a. Setup: Describe the setup of this problem (e.g., include a diagram of problem, a list of what is known/given and a list of what is being found). b. Calculation: Write the total material balance and the chlorine component balance equations for this problem. c. Calculation: Write the system of equation in matrix form AX = b, where X has the variable for the resulting total ow rate in its rst row and the variable for the total ow rate in its second row. Solve using Cramer's rule. Perform all computations by hand and show all steps.

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