Contemporary Mathematics for Business & Consumers
8th Edition
ISBN: 9781305886803
Author: Brechner
Publisher: Cengage
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Chapter 7.I, Problem 11RE
To determine
To calculate: The date of the invoice, invoice subtotal and invoice total if unit price of
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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?
(a) State, without proof, Cauchy's theorem, Cauchy's integral formula and Cauchy's
integral formula for derivatives. Your answer should include all the conditions
required for the results to hold.
(8 marks)
(b) Let U{z EC: |z| -1}. Let 12 be the triangular contour with vertices at
0, 2-2 and 2+2i, parametrized in the anticlockwise direction. Calculate
dz.
You must check the conditions of any results you use.
(d) Let U C. Calculate
Liz-1ym dz,
(z - 1) 10
(5 marks)
where 2 is the same as the previous part. You must check the conditions of any
results you use.
(4 marks)
(a) Suppose a function f: C→C has an isolated singularity at wЄ C. State what it
means for this singularity to be a pole of order k.
(2 marks)
(b) Let f have a pole of order k at wЄ C. Prove that the residue of f at w is given
by
1
res (f, w):
=
Z
dk
(k-1)! >wdzk−1
lim
-
[(z — w)* f(z)] .
(5 marks)
(c) Using the previous part, find the singularity of the function
9(z) =
COS(πZ)
e² (z - 1)²'
classify it and calculate its residue.
(5 marks)
(d) Let g(x)=sin(211). Find the residue of g at z = 1.
(3 marks)
(e) Classify the singularity of
cot(z)
h(z) =
Z
at the origin.
(5 marks)
Chapter 7 Solutions
Contemporary Mathematics for Business & Consumers
Ch. 7.I - From the following FotoFair invoice, identify the...Ch. 7.I - Prob. 2TIECh. 7.I - What word is represented by each of the following...Ch. 7.I - Prob. 2RECh. 7.I - What word is represented by each of the following...Ch. 7.I - Prob. 4RECh. 7.I - Prob. 5RECh. 7.I - Prob. 6RECh. 7.I - Prob. 7RECh. 7.I - Prob. 8RE
Ch. 7.I - Using the Panorama Products invoice below, extend...Ch. 7.I - Prob. 10RECh. 7.I - Prob. 11RECh. 7.I - Using the Panorama Products invoice below, extend...Ch. 7.I - Prob. 13RECh. 7.I - Using the Panorama Products invoice below, extend...Ch. 7.I - Prob. 15RECh. 7.I - Prob. 16RECh. 7.I - Prob. 17RECh. 7.I - Prob. 18RECh. 7.I - Prob. 19RECh. 7.I - Prob. 20RECh. 7.I - Prob. 21RECh. 7.I - Prob. 22RECh. 7.II - Gifts Galore, a retail gift shop, buys merchandise...Ch. 7.II - Prob. 4TIECh. 7.II - Wilson Sporting Goods recently sold tennis rackets...Ch. 7.II - Calculate the following trade discounts. Round all...Ch. 7.II - Calculate the following trade discounts. Round all...Ch. 7.II - Prob. 3RECh. 7.II - Prob. 4RECh. 7.II - Calculate the following trade discounts. Round all...Ch. 7.II - 6. Calculate the following trade discounts and net...Ch. 7.II - Calculate the following trade discounts and net...Ch. 7.II - Calculate the following trade discounts and net...Ch. 7.II - Calculate the following trade discounts and net...Ch. 7.II - Calculate the following net price factors and net...Ch. 7.II - Calculate the following net price factors and net...Ch. 7.II - Prob. 12RECh. 7.II - Prob. 13RECh. 7.II - Calculate the following trade discounts and trade...Ch. 7.II - Calculate the following trade discounts and trade...Ch. 7.II - Calculate the following trade discounts and trade...Ch. 7.II - Calculate the following trade discounts and trade...Ch. 7.II - Calculate the following trade discounts and trade...Ch. 7.II - Prob. 19RECh. 7.II - Calculate the following trade discounts and trade...Ch. 7.II - Calculate the following trade discounts and trade...Ch. 7.II - Prob. 22RECh. 7.II - Calculate the following trade discounts and trade...Ch. 7.II - Calculate the following trade discounts and trade...Ch. 7.II - Calculate the following trade discounts and trade...Ch. 7.II - Calculate the following trade discounts and trade...Ch. 7.III - Northwest Publishers sold an order of books to The...Ch. 7.III - Prob. 7TIECh. 7.III - The Rainbow Appliance Center purchased an order of...Ch. 7.III - Prob. 1RECh. 7.III - Prob. 2RECh. 7.III - Prob. 3RECh. 7.III - Prob. 4RECh. 7.III - Prob. 5RECh. 7.III - Calculate the following net price factors and net...Ch. 7.III - Prob. 7RECh. 7.III - Prob. 8RECh. 7.III - Calculate the following net price factors and...Ch. 7.III - Calculate the following net price factors and...Ch. 7.III - Calculate the following net price factors and...Ch. 7.III - Prob. 12RECh. 7.III - Prob. 13RECh. 7.III - Prob. 14RECh. 7.III - Complete the following table. Round net price...Ch. 7.III - Prob. 16RECh. 7.III - Prob. 17RECh. 7.III - Prob. 18RECh. 7.III - Prob. 19RECh. 7.III - Prob. 20RECh. 7.III - Complete the following table. Round net price...Ch. 7.III - Complete the following table. Round net price...Ch. 7.III - Complete the following table. Round net price...Ch. 7.III - Prob. 24RECh. 7.III - Complete the following table. Round net price...Ch. 7.III - Complete the following table. Round net price...Ch. 7.III - Prob. 27RECh. 7.IV - Valiant Plumbing ordered sinks from a supplier....Ch. 7.IV - All Pro Sports Center purchases $45,300 in...Ch. 7.IV - Prob. 11TIECh. 7.IV - Prob. 12TIECh. 7.IV - Prob. 13TIECh. 7.IV - Prob. 14TIECh. 7.IV - Prob. 15TIECh. 7.IV - Calculate the cash discount and the net amount due...Ch. 7.IV - Calculate the cash discount and the net amount due...Ch. 7.IV - Prob. 3RECh. 7.IV - Prob. 4RECh. 7.IV - Prob. 5RECh. 7.IV - For the following transactions, calculate the...Ch. 7.IV - For the following transactions, calculate the...Ch. 7.IV - Prob. 8RECh. 7.IV - Prob. 9RECh. 7.IV - Using the ordinary dating method, calculate the...Ch. 7.IV - Using the ordinary dating method, calculate the...Ch. 7.IV - Prob. 12RECh. 7.IV - Using the ordinary dating method, calculate the...Ch. 7.IV - Using the ordinary dating method, calculate the...Ch. 7.IV - Using the EOM, ROG, and Extra dating methods,...Ch. 7.IV - Using the EOM, ROG, and Extra dating methods,...Ch. 7.IV - Using the EOM, ROG, and Extra dating methods,...Ch. 7.IV - Using the EOM, ROG, and Extra dating methods,...Ch. 7.IV - Using the EOM, ROG, and Extra dating methods,...Ch. 7.IV - Using the EOM, ROG, and Extra dating methods,...Ch. 7.IV - 21. The Apollo Company received an invoice from a...Ch. 7.IV - An invoice is dated August 21 with terms of 4/18...Ch. 7.IV - An invoice dated January 15 has terms of 3/20 ROG....Ch. 7.IV - Prob. 24RECh. 7.IV - 25. Red Tag Furniture received a SeaLand container...Ch. 7.IV - 26. City Cellular purchased $28,900 in cell phones...Ch. 7 - 1. The document detailing a sales transaction is...Ch. 7 - F.O.B. shipping point and F.O.B. destination are...Ch. 7 - 3. To extend an invoice, for each line, we...Ch. 7 - 4. To calculate the amount of a single trade...Ch. 7 - 5. The _____ price is the amount a business...Ch. 7 - 6. To calculate the net price factor, we subtract...Ch. 7 - Write the formula for the trade discount rate....Ch. 7 - In a chain or of trade discounts, we calculate the...Ch. 7 - 9. As a shortcut, we can use the net price _____...Ch. 7 - To calculate the net price factor, we subtract...Ch. 7 - A single trade discount that equates to all the...Ch. 7 - Prob. 12CRCh. 7 - To calculate the credit given for a partial...Ch. 7 - Prob. 14CRCh. 7 - Prob. 1ATCh. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...Ch. 7 - Answer the following questions based on the...
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