e6exam1secBsolnsW06

e6exam1secBsolnsW06 - Engineering 6 Winter 2006 Midterm...

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Engineering 6, Winter 2006 Midterm Solutions Lecture Section B (MWF4-5) Regrade requests: Regrade requests must be submitted in writing to Dr. Lagerstrom no later than the lecture section on Friday, March 3. Regrades will only be considered in cases where it looks like the grader missed something. That is, requests along the lines of "I think I deserve more points" will not get very far, because the the grading scale on each problem was applied consistently for all students. Note also : Your exam may have been photocopied before it was returned, so please don't risk your engineering career here at UCD by changing an answer and submitting it for a regrade. Exam Version A (Version A is indicated by the first problem being worth 22 points; the first problem on Version B is worth 14 points.) Problem 1. (22 points total) (a) (10 points) List the five steps of the problem-solving process (as defined in lecture and the lecture notes) and give a 1-2 sentence explanation of each. 1. Problem definition: recognize and define the problem, collect relevant data, etc. 2. Mathematical model: determine fundamental principles, express in mathematical terms, make simplifying assumptions if necessary, etc. 3. Computational method: develop computational algorithm (step by step method). 4. Implementation of method: choose appropriate programming language and computer. 5. Test and assess the solution: input test data and check results, check assumptions, perform reality check, etc. (b) (6 points) Briefly explain the difference between the precision of a measurement and the accuracy of the measurement. Accuracy is a measure of the nearness of a measurement to the actual value. Precision refers to the repeatability of a measurement (as often expressed in terms of number of significant digits or decimal places). (c) (6 points) What are the basic rules of thumb for determining significant digits when you are multiplying two numbers and when you are adding two numbers? That is, how do you figure out how many significant digits the result has? Show how it works in each case using the numbers 3.21 and 14.6, where 3.21+14.6 yields 17.81 and 3.21*14.6 yields 46.866, i.e., how should these results be written with the correct number of significant digits? For addition: The result should show significant digits only as far to the right as the least precise number in the calculation. So 3.21 + 14.6 = 17.8 For multiplication: The product should contain the same number of significant digits as are contained in the number with the fewest significant digits. So 3.21*14.6 = 46.9
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Problem 2. (24 points total) (a) (6 points) Convert the following equation to a Matlab assignment statement (i.e., write it in Matlab notation). Use built-in functions where possible. Assume all variables are scalars. π 8 ) ln( 54 ) 82 . 0 arccos( x D = Answer: D = acos(0.82)/(54*log(x))*sqrt(8*pi); (The answer as shown has the minimum parentheses; more parentheses may be used; dot operators may also be used, but they're not necessary because x is a scalar; semicolon optional) (b) (6 points) Write the Matlab code that would create a vector named x with 75 values from 1 to 50 and
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