Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 22, Problem 12A
Finding Percentage, Percent, and Base in Practical Applications
Solve the following problems.
12. An engine loses 4.2 horsepower through friction. The power loss is 6% of the total rated horsepower. What is the total horsepower rating?
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5. (a) State the Residue Theorem. Your answer should include all the conditions required
for the theorem to hold.
(4 marks)
(b) Let y be the square contour with vertices at -3, -3i, 3 and 3i, described in the
anti-clockwise direction. Evaluate
に
dz.
You must check all of the conditions of any results that you use.
(5 marks)
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L
You must check all of the conditions of any results that you use.
ཙ
x sin(Tx)
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da.
(11 marks)
3. (a) Lety: [a, b] C be a contour. Let L(y) denote the length of y. Give a formula
for L(y).
(1 mark)
(b) Let UCC be open. Let f: U→C be continuous. Let y: [a,b] → U be a
contour. Suppose there exists a finite real number M such that |f(z)| < M for
all z in the image of y. Prove that
<
||, f(z)dz| ≤ ML(y).
(3 marks)
(c) State and prove Liouville's theorem. You may use Cauchy's integral formula without
proof.
(d) Let R0. Let w € C. Let
(10 marks)
U = { z Є C : | z − w| < R} .
Let f UC be a holomorphic function such that
0 < |ƒ(w)| < |f(z)|
for all z Є U. Show, using the local maximum modulus principle, that f is constant.
(6 marks)
3. (a) Let A be an algebra. Define the notion of an A-module M. When is a module M
a simple module?
(b) State and prove Schur's Lemma for simple modules.
(c) Let AM(K) and M = K" the natural A-module.
(i) Show that M is a simple K-module.
(ii) Prove that if ƒ € Endд(M) then ƒ can be written as f(m) = am, where a
is a matrix in the centre of M, (K).
[Recall that the centre, Z(M,(K)) == {a Mn(K) | ab
M,,(K)}.]
= ba for all bЄ
(iii) Explain briefly why this means End₁(M) K, assuming that Z(M,,(K))~
K as K-algebras.
Is this consistent with Schur's lemma?
Chapter 22 Solutions
Mathematics for Machine Technology
Ch. 22 - What is 7.25% of 43.80? Round your answer to 2...Ch. 22 - Express 3.5% as a common fraction.Ch. 22 - Solve the proportion A12=2745 . If necessary,...Ch. 22 - Prob. 4ACh. 22 - Prob. 5ACh. 22 - Prob. 6ACh. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Finding Percentage, Percent, and Base in Practical...
Ch. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Prob. 17ACh. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Prob. 21ACh. 22 - Prob. 22ACh. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Prob. 25ACh. 22 - Prob. 26ACh. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Finding Percentage, Percent, and Base in Practical...Ch. 22 - Prob. 31ACh. 22 - A manufacturer estimates that 15,500 pieces per...Ch. 22 - The average percent defective product of a...Ch. 22 - Prob. 34ACh. 22 - Prob. 35ACh. 22 - The cost of one dozen cutters is listed as $525. A...Ch. 22 - A manufacturer's production this week is 3620...Ch. 22 - Two machines are used to produce the same product....Ch. 22 - Allowing for scrap, a firm produced 1890 pieces....Ch. 22 - A manufacturing company receives $122,000 upon the...Ch. 22 - Prob. 41A
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