EBK MATHEMATICS FOR MACHINE TECHNOLOGY
7th Edition
ISBN: 9780100548169
Author: SMITH
Publisher: YUZU
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Chapter 42, Problem 65A
Solve each of the following equations using the addition principle of equality. Check each answer.
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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 42 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 42 - Write the expression "A number divided by 7 plus...Ch. 42 - Use scientific notation to solve (6.325 108)(9.4...Ch. 42 - Prob. 3ACh. 42 - If a=7.5 and b=9.45 , what is the value of a+4bb2a...Ch. 42 - Prob. 5ACh. 42 - Prob. 6ACh. 42 - Prob. 7ACh. 42 - Prob. 8ACh. 42 - Prob. 9ACh. 42 - Solve each of the following equations using the...
Ch. 42 - Prob. 11ACh. 42 - Solve each of the following equations using the...Ch. 42 - Prob. 13ACh. 42 - Prob. 14ACh. 42 - Prob. 15ACh. 42 - Prob. 16ACh. 42 - Prob. 17ACh. 42 - Prob. 18ACh. 42 - Prob. 19ACh. 42 - Prob. 20ACh. 42 - Prob. 21ACh. 42 - Prob. 22ACh. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Prob. 26ACh. 42 - Prob. 27ACh. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Write an equation for each of the following...Ch. 42 - Write an equation for each of the following...Ch. 42 - Prob. 33ACh. 42 - Write an equation for each of the following...Ch. 42 - Write an equation for each of the following...Ch. 42 - Write an equation for each of the following...Ch. 42 - Prob. 37ACh. 42 - Prob. 38ACh. 42 - Prob. 39ACh. 42 - A Shaft rotates in a bearing that is 0.3968 inch...Ch. 42 - For each of the following problems, substitute the...Ch. 42 - For each of the following problems, substitute the...Ch. 42 - Prob. 43ACh. 42 - For each of the following problems, substitute the...Ch. 42 - Prob. 45ACh. 42 - Prob. 46ACh. 42 - Prob. 47ACh. 42 - Prob. 48ACh. 42 - Prob. 49ACh. 42 - Prob. 50ACh. 42 - Prob. 51ACh. 42 - Solve each of the following equations using the...Ch. 42 - Prob. 53ACh. 42 - Prob. 54ACh. 42 - Prob. 55ACh. 42 - Prob. 56ACh. 42 - Prob. 57ACh. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Prob. 60ACh. 42 - Prob. 61ACh. 42 - Solve each of the following equations using the...Ch. 42 - Prob. 63ACh. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Prob. 66ACh. 42 - Solve each of the following equations using the...Ch. 42 - Prob. 68ACh. 42 - Prob. 69ACh. 42 - Prob. 70ACh. 42 - Prob. 71ACh. 42 - Prob. 72ACh. 42 - Prob. 73ACh. 42 - Prob. 74ACh. 42 - Prob. 75ACh. 42 - For each of the following problems, substitute the...Ch. 42 - Prob. 77ACh. 42 - Prob. 78ACh. 42 - Prob. 79ACh. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Solve each of the following equations using the...Ch. 42 - Write an equation for each of the following...Ch. 42 - Write an equation for each of the following...Ch. 42 - Write an equation for each of the following...Ch. 42 - The feed of a drill is the depth of material that...Ch. 42 - Prob. 109ACh. 42 - For each of the following problems, substitute the...Ch. 42 - For each of the following problems, substitute the...Ch. 42 - For each of the following problems, substitute the...Ch. 42 - Solve each of the following equations using either...Ch. 42 - Solve each of the following equations using either...Ch. 42 - Solve each of the following equations using either...Ch. 42 - Solve each of the following equations using either...Ch. 42 - Solve each of the following equations using either...Ch. 42 - Prob. 118ACh. 42 - Prob. 119ACh. 42 - Prob. 120ACh. 42 - Prob. 121ACh. 42 - Prob. 122ACh. 42 - Prob. 123ACh. 42 - Prob. 124ACh. 42 - Solve each of the following equations using either...Ch. 42 - Prob. 126ACh. 42 - Solve each of the following equations using either...Ch. 42 - Prob. 128ACh. 42 - Prob. 129ACh. 42 - Prob. 130A
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