EBK MATHEMATICS FOR MACHINE TECHNOLOGY
7th Edition
ISBN: 9780100548169
Author: SMITH
Publisher: YUZU
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Chapter 27, Problem 7A
To determine
(a)
To find the tolerance from the help of given data in the table.
To determine
(b)
To find the tolerance from the help of given data in the table.
To determine
(c)
To find the minimum limitfrom the help of given data in the table.
To determine
(d)
To find the maximum limitfrom the help of given data in the table..
To determine
(e)
To find the tolerancefrom the help of given data in the table..
To determine
(f)
To find the maximum limitfrom the help of given data in the table..
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Without evaluating the Legendre symbols, prove the following.
(i) 1(173)+2(2|73)+3(3|73) +...+72(72|73) = 0.
(Hint: As r runs through the numbers 1,2,.
(ii) 1²(1|71)+2²(2|71) +3²(3|71) +...+70² (70|71)
= 71{1(1|71) + 2(2|71) ++70(70|71)}.
72, so does 73 – r.)
By considering the number N = 16p²/p... p² - 2, where P1, P2, … … … ‚ Pn
are primes, prove that there are infinitely many primes of the form
8k - 1.
(c) (i) By first considering the case where n is a prime power, prove that
n
μ² (d)
=
ø(n)
(d)'
n≥ 1.
d\n
(ii) Verify the result of part (c)(i) when n =
20.
Chapter 27 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
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