CE 565 QUIZ NO. 1 (TAKE HOME) SPRING 2012 NAME: Problem No. 1 (30 points) Economic formulas are available to compute annual payments for loans. Suppose that you borrow an amount of money P and agree to repay it in a n annual payments at an interest rate of i. The formula to computer the annual payment A is: (1 ) 1 (1 )? ? ? ? n n i A P i i Using the flowcharting symbols located on Figure 2.1 in your text book (Page 27), develop a flowchart to implement this formula in a program that can accept any value of i, P and n. If you wanted a monthly payment of $2,400 per month on a $500,000 loan over 30 years, what interest rate do you need to get from the bank? Problem No. 2 (30 points) Manning’s formula for a rectangular channel can be written as: 2 1 3 2 3 5( 2 ) 1 ( ) S B H BH n Q ? ? Given this equation, which parameter do you think you need to pay close attention to during field measurements? Now, given that Q = flow (m3/s), n = a roughness coefficient, B = width (m), H = depth (m), and S = slope. You know the width to be 20 m and the depth to be 0.3 m. Unfortunately, you know the roughnes coefficient and the slope to a +/-10% accuracy. Assume the roughness is 0.03 and the slope is 0.0003. Using the first order error analysis, determine the accuracy of your flow. Given this new information, which parameter should you try to measure with more precision? CE 565 QUIZ NO. 1 (TAKE HOME) SPRING 2012 NAME: Problem No. 3 (20 points) Using Cramers Rule to solve the following systems of linear equations. Then use Gauss-Seidel Method to solve the same set of equations (no, you can not start with an initial guess that is the same as the answer). Provide a brief comparison of the two methods. 3X1 + 3X2 -2X3 = 7.6 2X1 -4X2 + X3 = 1.4 -X1 -2X2 + 5X3 = -6.3 Problem No. 4(20 points) In a statistical fitting of a linear equation of the form Y = a +bX, values for the fitting coefficients a and b can obtained by solving two simultaneous equations in the form of: ? ?? ? ? ? n i i n i an...