Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Textbook Question
Chapter 64, Problem 24A
Find the number of cubic centimeters of material contained in the jig bushing shown. Round the answer to the nearest tenth cubic centimeter.
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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 64 Solutions
Mathematics For Machine Technology
Ch. 64 - In order to make a conical duct a circular sheet...Ch. 64 - Prob. 2ACh. 64 - Prob. 3ACh. 64 - Convert 12.02 sq in. to square centimeters.Ch. 64 - Prob. 5ACh. 64 - Prob. 6ACh. 64 - Prob. 7ACh. 64 - Compute the volume of each sphere 7 through 14....Ch. 64 - Prob. 9ACh. 64 - Compute the volume of each sphere 7 through 14....
Ch. 64 - Prob. 11ACh. 64 - Compute the volume of each sphere 7 through 14....Ch. 64 - Prob. 13ACh. 64 - Compute the volume of each sphere 7 through 14....Ch. 64 - Prob. 15ACh. 64 - Solve these exercise. A vat in the shape of a...Ch. 64 - Prob. 17ACh. 64 - Solve these exercises. A company produces...Ch. 64 - Solve these exercises. Pieces in the shape of...Ch. 64 - Solve these exercises. A plastic products...Ch. 64 - Solve these exercises. Find the weight of the...Ch. 64 - Compute the capacity, in liters, of the container...Ch. 64 - A seamless brass tube and brass flange assembly is...Ch. 64 - Find the number of cubic centimeters of material...Ch. 64 - Find the weight of the cast-iron angle iron shown....Ch. 64 - Prob. 26ACh. 64 - Prob. 27ACh. 64 - Compute the number of cubic centimeters of...
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