EBK MATHEMATICS FOR MACHINE TECHNOLOGY
8th Edition
ISBN: 9781337798396
Author: SMITH
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Textbook Question
Chapter 1, Problem 18A
Express the mixed numbers in Exercises 17 and 18 as improper fractions. Then express the improper fractions as the equivalent fractions indicated.
18.
a.
b.
c.
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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 1 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 1 - Write the fractional part that each length, A...Ch. 1 - A welded support base is cut into four pieces as...Ch. 1 - The circle in Figure 1-5 is divided into equal...Ch. 1 - The circle in Figure 1-5 is divided into equal...Ch. 1 - Reduce to halves. a. 48 b. 918 c. 100200 d. 121242Ch. 1 - Reduce to halves. a. 2510 b. 1812 c. 12636 d....Ch. 1 - Reduce numbers to lowest terms in Exercises 7 and...Ch. 1 - Reduce numbers to lowest terms in Exercises 7 and...Ch. 1 - Express the fractions in Exercises 9 and 10 as...Ch. 1 - Express the fractions in Exercises 9 and 10 as...
Ch. 1 - In Exercises 11 and 12, express the given...Ch. 1 - In Exercises 11 and 12, express the given...Ch. 1 - Express the mixed numbers in Exercises 13 and 14...Ch. 1 - Express the mixed numbers in Exercises 13 and 14...Ch. 1 - Express the improper fractions in Exercises 15 and...Ch. 1 - Express the improper fractions in Exercises 15 and...Ch. 1 - Express the mixed numbers in Exercises 17 and 18...Ch. 1 - Express the mixed numbers in Exercises 17 and 18...Ch. 1 - Sketch and redimension the plate shown in Figure...
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