Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 43, Problem 27A
In each of the following problems, refer to the corresponding figure. Write an equation, solve for x, and check.
All dimensions are in inches.
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1.
2.
Define f: ZZ and 9: ZZ by f(x)=3x+1 and g(x) = x².
(a) Calculate (go f)(2).
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Verify that it is the inverse of f. Do not include a derivation for f¹ unless it is for the verification.
Suppose that two toothpaste companies compete for customers in a fixed market in which each
customer uses either Brand A or Brand B. Suppose also that a market analysis shows that the
buying habits of the customers fit the following pattern in the quarters that were analyzed:
each quarter (three-month period), 30% of A users will switch to B, while the rest stay with
A. Moreover, 40% of B users will switch to A in a given quarter, while the remaining B users
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1. The regular representation of a finite group G is a pair (Vreg, Dreg). Vreg is a vector space
and Dreg is a homomorphism.
(a) What is the dimension of Vreg?
(b) Describe a basis for Vreg and give a formula for Dreg. Hence explain why the homo-
morphism property is satisfied by Dreg.
(c) Prove that the character ✗reg (g) defined by tr Dreg (g) is zero if g is not the identity
element of the group.
(d) A finite group of order 60 has five irreducible representations R1, R2, R3, R4, R5. R₁
is the trivial representation. R2, R3, R4 have dimensions (3,3,4) respectively. What is the
dimension of R5? Explain how your solution is related to the decomposition of the regular
representation as a direct sum of irreducible representations (You can assume without proof
the properties of this decomposition which have been explained in class and in the lecture
notes).
(e) A
group element
has characters in the irreducible representations R2, R3, R4 given
as
R3
R2 (g)
= -1
X³ (g) = −1 ; XR4 (g) = 0…
Chapter 43 Solutions
Mathematics For Machine Technology
Ch. 43 - Prob. 1ACh. 43 - Prob. 2ACh. 43 - Prob. 3ACh. 43 - Prob. 4ACh. 43 - Prob. 5ACh. 43 - Prob. 6ACh. 43 - Prob. 7ACh. 43 - Express each ofthe word problems in Exercises 7...Ch. 43 - Express each ofthe word problems in Exercises 7...Ch. 43 - Express each ofthe word problems in Exercises 7...
Ch. 43 - Prob. 11ACh. 43 - Express each ofthe word problems in Exercises 7...Ch. 43 - Prob. 13ACh. 43 - Prob. 14ACh. 43 - Express each ofthe word problems in Exercises 7...Ch. 43 - Express each ofthe word problems in Exercises 7...Ch. 43 - Prob. 17ACh. 43 - Five holes are drilled in a steel plate on a bolt...Ch. 43 - The total amount of stock milled off an aluminum...Ch. 43 - Prob. 20ACh. 43 - In each of the following problems, refer to the...Ch. 43 - In each of the following problems, refer to the...Ch. 43 - In each of the following problems, refer to the...Ch. 43 - Prob. 24ACh. 43 - In each of the following problems, refer to the...Ch. 43 - In each of the following problems, refer to the...Ch. 43 - In each of the following problems, refer to the...Ch. 43 - In each of the following problems, refer to the...Ch. 43 - Prob. 29ACh. 43 - Prob. 30ACh. 43 - Solve for the unknown values in the following...Ch. 43 - Solve for the unknown values in the following...Ch. 43 - Prob. 33ACh. 43 - Prob. 34ACh. 43 - Solve for the unknown values in the following...Ch. 43 - Prob. 36ACh. 43 - Prob. 37ACh. 43 - Prob. 38ACh. 43 - Solve for the unknown values in the following...Ch. 43 - Solve for the unknown values in the following...Ch. 43 - Solve for the unknown values in the following...Ch. 43 - Solve for the unknown values in the following...Ch. 43 - Solve for the unknown values in the following...Ch. 43 - Solve for the unknown values in the following...Ch. 43 - Prob. 45ACh. 43 - Prob. 46A
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