EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 20, Problem 2P
You perform experiments and determine the following values of heat capacity c at various temperatures T for a gas:
| T | –50 | –30 | 0 | 60 | 90 | 110 |
| c | 1270 | 1280 | 1350 | 1480 | 1580 | 1700 |
Use regression to determine a model to predict c as a function of T.
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18. If m n compute the gcd (a² + 1, a² + 1) in terms of a. [Hint: Let A„ = a² + 1
and show that A„|(Am - 2) if m > n.]
For each real-valued nonprincipal character x mod k, let
A(n) = x(d) and F(x) = Σ
:
dn
* Prove that
F(x) = L(1,x) log x + O(1).
n
By considering appropriate series expansions,
e². e²²/2. e²³/3.
....
=
= 1 + x + x² + ·
...
when |x| < 1.
By expanding each individual exponential term on the left-hand side
the coefficient of x- 19 has the form
and multiplying out,
1/19!1/19+r/s,
where 19 does not divide s. Deduce that
18! 1 (mod 19).
Chapter 20 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 20 - 20.1 Perform the same computation as in Sec. 20.1,...Ch. 20 - You perform experiments and determine the...Ch. 20 - 20.3 It is known that the tensile strength of a...Ch. 20 - Prob. 4PCh. 20 - 20.5 The specific volume of a superheated steam is...Ch. 20 - Prob. 6PCh. 20 - In Alzheimers disease, the number of neurons in...Ch. 20 - 20.8 The following data were taken from a stirred...Ch. 20 - Prob. 9PCh. 20 - Concentration data were taken at 15 time points...
Ch. 20 - Prob. 11PCh. 20 - The molecular weight of a polymer can be...Ch. 20 - 20.13 On average, the surface area A of human...Ch. 20 - 20.14 Determine an equation to predict metabolism...Ch. 20 - 20.15 Human blood behaves as a Newtonian fluid...Ch. 20 - 20.16 Soft tissue follows an exponential...Ch. 20 - 20.17 The thickness of the retina changes during...Ch. 20 - 20.18 The data tabulated below were generated from...Ch. 20 - The shear stresses, in kilopascals (kPa), of nine...Ch. 20 - 20.20 A transportation engineering study was...Ch. 20 - The saturation concentration of dissolved oxygen...Ch. 20 - For the data in Table P20.21, use polynomial...Ch. 20 - 20.23 Use multiple linear regression to derive a...Ch. 20 - 20.24 As compared to the models from Probs. 20.22...Ch. 20 - 20.25 In water-resources engineering, the sizing...Ch. 20 - 20.26 The concentration of total phosphorus and...Ch. 20 - 20.27 The vertical stress under the corner of a...Ch. 20 - Three disease-carrying organisms decay...Ch. 20 - 20.29 The mast of a sailboat has a cross-sectional...Ch. 20 - 20.30 Enzymatic reactions are used extensively to...Ch. 20 - 20.31 Environmental engineers dealing with the...Ch. 20 - An environmental engineer has reported the data...Ch. 20 - The following model is frequently used in...Ch. 20 - 20.34 As a member of Engineers Without Borders,...Ch. 20 - 20.35 Perform the same computations as in Sec....Ch. 20 - 20.36 You measure the voltage drop V across a...Ch. 20 - Duplicate the computation for Prob. 20.36, but use...Ch. 20 - The current in a wire is measured with great...Ch. 20 - 20.39 The following data was taken from an...Ch. 20 - It is known that the voltage drop across an...Ch. 20 - Ohms law states that the voltage drop V across an...Ch. 20 - 20.42 Repeat Prob. 20.41 but determine the...Ch. 20 - 20.43 An experiment is performed to determine the...Ch. 20 - Bessel functions often arise in advanced...Ch. 20 - 20.45 The population of a small community on the...Ch. 20 - Based on Table 20.4, use linear and quadratic...Ch. 20 - 20.47 Reproduce Sec. 20.4, but develop an equation...Ch. 20 - 20.48 Dynamic viscosity of water is related to...Ch. 20 - 20.49 Hooke’s law, which holds when a spring is...Ch. 20 - 20.50 Repeat Prob. 20.49 but fit a power curve to...Ch. 20 - The distance required to stop an automobile...Ch. 20 - An experiment is performed to define the...Ch. 20 - The acceleration due to gravity at an altitude y...Ch. 20 - The creep rate is the time rate at which strain...Ch. 20 - 20.55 It is a common practice when examining a...Ch. 20 - The relationship between stress and the shear...Ch. 20 - The velocity u of air flowing past a flat surface...Ch. 20 - 20.58 Andrade’s equation has been proposed as a...Ch. 20 - Develop equations to fit the ideal specific heats...Ch. 20 - 20.60 Temperatures are measured at various points...Ch. 20 - 20.61 The data below were obtained from a creep...
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- By considering appropriate series expansions, ex · ex²/2 . ¸²³/³ . . .. = = 1 + x + x² +…… when |x| < 1. By expanding each individual exponential term on the left-hand side and multiplying out, show that the coefficient of x 19 has the form 1/19!+1/19+r/s, where 19 does not divide s.arrow_forwardLet 1 1 r 1+ + + 2 3 + = 823 823s Without calculating the left-hand side, prove that r = s (mod 823³).arrow_forwardFor each real-valued nonprincipal character X mod 16, verify that L(1,x) 0.arrow_forward
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