Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 17, Problem 24P
A material is tested for cyclic fatigue failure whereby a stress, in MPa, is applied to the material and the number of cycles needed to cause failure is measured. The results are in the table below. When a log-log plot of stress versus cycles is generated, the data trend shows a linear relationship. Use least-squares regression to determine a best-fit equation for these data.
| N, cycles | 1 | 10 | 100 | 1000 | 10,000 | 100,000 | 1,000,000 |
| Stress, MPa | 1100 | 1000 | 925 | 800 | 625 | 550 | 420 |
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Chapter 17 Solutions
Numerical Methods for Engineers
Ch. 17 - Given these data 8.8 9.5 9.8 9.4 10.0 9.4 10.1 9.2...Ch. 17 - Given these data 29.65 28.55 28.65 30.15 29.35...Ch. 17 - 17.3 Use least-squares regression to fit a...Ch. 17 - 17.4 Use least-squares regression to fit a...Ch. 17 - 17.5 Using the same approach as was employed to...Ch. 17 - Use least-squares regression to fit a straight...Ch. 17 - Fit the following data with (a) A...Ch. 17 - Fit the following data with the power model...Ch. 17 - 17.9 Fit an exponential model...Ch. 17 - 17.10 Rather than using the base-e exponential...
Ch. 17 - 17.11 Beyond the examples in Fig. 17.10, there are...Ch. 17 - 17.12 An investigator has reported the data...Ch. 17 - An investigator has reported the data tabulated...Ch. 17 - 17.14 It is known that the data tabulated below...Ch. 17 - 17.15 The following data are...Ch. 17 - Given these data x 5 10 15 20 25 30 35 40 45 50 y...Ch. 17 - 17.17 Fit a cubic equation to the following...Ch. 17 - Use multiple linear regression to fit x1 0 1 1 2 2...Ch. 17 - Use multiple linear regression to fit x1 0 0 1 2 0...Ch. 17 - Use nonlinear regression to fit a parabola to the...Ch. 17 - 17.21 Use nonlinear regression to fit a...Ch. 17 - 17.22 Recompute the regression fits from Probs....Ch. 17 - Develop, debug, and test a program in either a...Ch. 17 - A material is tested for cyclic fatigue failure...Ch. 17 - The following data show the relationship between...Ch. 17 - 17.26 The data below represents the bacterial...Ch. 17 - The concentration of E. coli bacteria in a...Ch. 17 - 17.28 An object is suspended in a wind tunnel and...Ch. 17 - 17.29 Fit a power model to the data from Prob....Ch. 17 - Derive the least-squares fit of the following...Ch. 17 - 17.31 In Prob. 17.11 we used transformations to...
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