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 65, Problem 31A
For each function of an angle, write the cofunction of the complement of the angle.
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Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
p-1
2
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
23
32
how come?
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
The set T is the subset of these residues exceeding
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
2
p-1
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
23
The set T is the subset of these residues exceeding
2°
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
how come?
Shading a Venn diagram with 3 sets: Unions, intersections, and...
The Venn diagram shows sets A, B, C, and the universal set U.
Shade (CUA)' n B on the Venn diagram.
U
Explanation
Check
A-
B
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Chapter 65 Solutions
Mathematics for Machine Technology
Ch. 65 - If tan A=4.13792 , determine the value of angle A...Ch. 65 - Find the number of cubic inches of material...Ch. 65 - Find the number of cubic inches of material...Ch. 65 - The sector of a circle has an area of 231.3 sq in....Ch. 65 - Determine the arc length ABC if r=5.75in. and...Ch. 65 - Identify each of the following angles as acute....Ch. 65 - Prob. 7ACh. 65 - Refer to Figure 65-3 in answering exercises 1...Ch. 65 - Prob. 9ACh. 65 - Refer to Figure 65-3 in answering exercises 1...
Ch. 65 - Prob. 11ACh. 65 - Refer to Figure 65-3 in answering exercises 1...Ch. 65 - Prob. 13ACh. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - Prob. 25ACh. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - Prob. 41ACh. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - Prob. 45ACh. 65 - For each exercise, functions and cofunctions of...Ch. 65 - Prob. 47ACh. 65 - For each exercise, functions and cofunctions of...Ch. 65 - Prob. 49ACh. 65 - For each exercise, functions and cofunctions of...Ch. 65 - Prob. 51ACh. 65 - For each exercise, functions and cofunctions of...Ch. 65 - Prob. 53ACh. 65 - For each exercise, functions and cofunctions of...Ch. 65 - Prob. 55ACh. 65 - For each exercise, functions and cofunctions of...Ch. 65 - Prob. 57A
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