Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 25, Problem 8AR
Express these ratios in lowest fractional form.
8.16to
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9. Establish the identity
1-
1+z+z² +
2n+1
...
+z" =
1- z
(z1)
and then use it to derive Lagrange's trigonometric identity:
1
1+ cos cos 20 +... + cos no =
+
2
sin[(2n+1)0/2]
2 sin(0/2)
(0 < 0 < 2л).
Suggestion: As for the first identity, write S = 1+z+z² +...+z" and consider
the difference S - zS. To derive the second identity, write z =
eie in the first one.
8. Prove that two nonzero complex numbers z₁ and Z2 have the same moduli if and only if
there are complex numbers c₁ and c₂ such that Z₁ = c₁C2 and Z2 = c1c2.
Suggestion: Note that
(i≤
exp (101+0) exp (01-02)
and [see Exercise 2(b)]
2
02
Ꮎ
-
= = exp(i01)
exp(101+0) exp (i 01 - 02 ) = exp(102).
i
2
2
numerical ana
Chapter 25 Solutions
Mathematics For Machine Technology
Ch. 25 - Prob. 1ARCh. 25 - Express these ratios in lowest fractional form. 2....Ch. 25 - Express these ratios in lowest fractional form. 3....Ch. 25 - Express these ratios in lowest fractional form. 4....Ch. 25 - Express these ratios in lowest fractional form. 5....Ch. 25 - Express these ratios in lowest fractional form. 6....Ch. 25 - Express these ratios in lowest fractional form. 7....Ch. 25 - Express these ratios in lowest fractional form....Ch. 25 - Express these ratios in lowest fractional form. 9....Ch. 25 - Express these ratios in lowest fractional form....
Ch. 25 - Express these ratios in lowest fractional form....Ch. 25 - Bronze is an alloy of copper, zinc, and tin with...Ch. 25 - Solve for the unknown value in each of the...Ch. 25 - Analyze each of the following problems to...Ch. 25 - Express each value as a percent. a. 1 b. 112 c....Ch. 25 - Express each value as a percent. a. 0.72 b.2.037...Ch. 25 - Express each percent as a decimal fraction or...Ch. 25 - Express each percent as a common fraction or mixed...Ch. 25 - Find each percentage. Round the answers to 2...Ch. 25 - Find each percent (rate). Round the answers to 2...Ch. 25 - Prob. 21ARCh. 25 - Prob. 22ARCh. 25 - The carbon content of machine steel for gages...Ch. 25 - A piece of machinery is purchased for $8792. In 1...Ch. 25 - Engine pistons and cylinder heads are made of an...Ch. 25 - Before starting two jobs, a shop has an inventory...Ch. 25 - An alloy of stainless steel contains 73.6% iron,...Ch. 25 - Prob. 28AR
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