Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Textbook Question
Chapter 54, Problem 15A
Solve the following exercises based on Principles 18 through 21, although an exercise may require the application oftwo or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute.
a. If PS = 46°, find
(1)∠1
(2)∠2
b. If PS = 39°, find
(1)∠1
(2)∠2
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Solve the linear system of equations attached using Gaussian elimination (not Gauss-Jordan) and back subsitution.
Remember that:
A matrix is in row echelon form if
Any row that consists only of zeros is at the bottom of the matrix.
The first non-zero entry in each other row is 1. This entry is called aleading 1.
The leading 1 of each row, after the first row, lies to the right of the leading 1 of the previous row.
7. Show that for R sufficiently large, the polynomial P(z) in Example 3, Sec. 5, satisfies
the inequality
|P(z)| R.
Suggestion: Observe that there is a positive number R such that the modulus of
each quotient in inequality (9), Sec. 5, is less than |an|/n when |z| > R.
9. Establish the identity
1-
1+z+z² +
2n+1
...
+z" =
1- z
(z1)
and then use it to derive Lagrange's trigonometric identity:
1
1+ cos cos 20 +... + cos no =
+
2
sin[(2n+1)0/2]
2 sin(0/2)
(0 < 0 < 2л).
Suggestion: As for the first identity, write S = 1+z+z² +...+z" and consider
the difference S - zS. To derive the second identity, write z =
eie in the first one.
Chapter 54 Solutions
Mathematics for Machine Technology
Ch. 54 - A pipe has an inside circumference of 82.50 mm and...Ch. 54 - Determine the length of AB, AC, and ED. Round the...Ch. 54 - Prob. 3ACh. 54 - What is the complement of a 7221'47" angle?Ch. 54 - Prob. 5ACh. 54 - Prob. 6ACh. 54 - Determine the unknown value for each of the...Ch. 54 - Determine the unknown value for each of the...Ch. 54 - Determine the unknown value for each of the...Ch. 54 - Determine the unknown value for each of the...
Ch. 54 - Determine the unknown value for each of the...Ch. 54 - Determine the unknown value for each of the...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Prob. 23ACh. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Prob. 29ACh. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...Ch. 54 - Solve the following exercises based on Principles...
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