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 59, Problem 49A
The shaded piece shown is cut from a circular disk. Find the area of the piece. Round the answer to 1 decimal place. Dimensions are in inches.
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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 59 Solutions
Mathematics for Machine Technology
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Ch. 59 - Find the unknown area, or diameter for each of the...Ch. 59 - Find the unknown area, or diameter for each of the...Ch. 59 - Find the unknown area, or diameter for each of the...Ch. 59 - Find the unknown area, or diameter for each of the...Ch. 59 - Find the unknown area, or diameter for each of the...Ch. 59 - Find the unknown area, or diameter for each of the...Ch. 59 - Find the unknown area, or diameter for each of the...Ch. 59 - Find the unknown area, or diameter for each of the...Ch. 59 - A rectangular steel plate 15.10 inches long and...Ch. 59 - Hydraulic pressure of 705.0 pounds per square inch...Ch. 59 - A circular base is shown. The base is cut from a...Ch. 59 - Find the area of the template shown. Round the...Ch. 59 - A force of 62,125 pounds pulls on a steel rod that...Ch. 59 - A piece shown by the shaded portion is to be cut...Ch. 59 - Find the unknown area, radius, or central angle...Ch. 59 - Find the unknown area, radius, or central angle...Ch. 59 - Find the unknown area, radius, or central angle...Ch. 59 - Find the unknown area, radius, or central angle...Ch. 59 - Find the unknown area, radius, or central angle...Ch. 59 - Find the unknown area, radius, or central angle...Ch. 59 - Find the unknown area, radius, or central angle...Ch. 59 - Find the unknown area, radius, or central angle...Ch. 59 - Prob. 33ACh. 59 - Prob. 34ACh. 59 - Prob. 35ACh. 59 - Find the unknown area, radius, or central angle...Ch. 59 - A section of a piece of round stock with a...Ch. 59 - Three pieces, each in the shape of a sector, are...Ch. 59 - Prob. 39ACh. 59 - Prob. 40ACh. 59 - Find the area of each of the segments ACE for...Ch. 59 - Prob. 42ACh. 59 - Prob. 43ACh. 59 - Prob. 44ACh. 59 - Prob. 45ACh. 59 - Prob. 46ACh. 59 - Compute the area of the steel insert (shaded...Ch. 59 - A pattern is shown. a. Find the surface area of...Ch. 59 - The shaded piece shown is cut from a circular...
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