EBK MATHEMATICS FOR MACHINE TECHNOLOGY
7th Edition
ISBN: 9780100548169
Author: SMITH
Publisher: YUZU
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Textbook Question
Chapter 50, Problem 8A
Name each of the following angles in two additional ways.
a.
b.
c.
d.
e.
f.
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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 50 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 50 - What is the complement of a 2741'19" angle?Ch. 50 - Express 721252 as decimal degrees. Round the...Ch. 50 - Prob. 3ACh. 50 - Solve for F in the proportion...Ch. 50 - Prob. 5ACh. 50 - Prob. 6ACh. 50 - Prob. 7ACh. 50 - Name each of the following angles in two...Ch. 50 - Identify each of the following angles as acute,...Ch. 50 - Prob. 10A
Ch. 50 - Prob. 11ACh. 50 - Solve the following exercises: Determine the...Ch. 50 - Determine the values of 2,3, and 4 for these given...Ch. 50 - Given: ABCD. Determine the values of 2 through 8...Ch. 50 - Given: Hole centerlines EFGH and MPKL. Determine...Ch. 50 - Given: Hole centrelines ABCD and EFGH . Determine...Ch. 50 - Given: ABCD,AEED. Determine the value of 2 and 3...Ch. 50 - Given: FHGSKM and FGHK . Determine the value of ...
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