Contemporary Mathematics for Business & Consumers
8th Edition
ISBN: 9781305585447
Author: Robert Brechner, Geroge Bergeman
Publisher: Cengage Learning
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Chapter 14, Problem 13CR
To determine
The formula for the housing expense ratio.
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(b) In various places in this module, data on the silver content of coins
minted in the reign of the twelfth-century Byzantine king Manuel I
Comnenus have been considered. The full dataset is in the Minitab file
coins.mwx. The dataset includes, among others, the values of the
silver content of nine coins from the first coinage (variable Coin1) and
seven from the fourth coinage (variable Coin4) which was produced a
number of years later. (For the purposes of this question, you can
ignore the variables Coin2 and Coin3.) In particular, in Activity 8 and
Exercise 2 of Computer Book B, it was argued that the silver contents
in both the first and the fourth coinages can be assumed to be normally
distributed. The question of interest is whether there were differences in
the silver content of coins minted early and late in Manuel’s reign. You
are about to investigate this question using a two-sample t-interval.
(i) Using Minitab, find either the sample standard deviations of the
two variables…
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)
(c) Evaluate
L
You must check all of the conditions of any results that you use.
ཙ
x sin(Tx)
x²+2x+5
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)
Chapter 14 Solutions
Contemporary Mathematics for Business & Consumers
Ch. 14.I - What is the monthly payment and total interest on...Ch. 14.I - Prob. 2TIECh. 14.I - Prob. 3TIECh. 14.I - Prob. 4TIECh. 14.I - Prob. 5TIECh. 14.I - Using Table 14-1 as needed, calculate the required...Ch. 14.I - Prob. 2RECh. 14.I - Using Table 14-1 as needed, calculate the required...Ch. 14.I - Prob. 4RECh. 14.I - Prob. 5RE
Ch. 14.I - Prob. 6RECh. 14.I - Using Table 14-1 as needed, calculate the required...Ch. 14.I - Prob. 8RECh. 14.I - As one of the loan officers for Grove Gate Bank,...Ch. 14.I - As one of the loan officers for Grove Gate Bank,...Ch. 14.I - As one of the loan officers for Grove Gate Bank,...Ch. 14.I - As one of the loan officers for Grove Gate Bank,...Ch. 14.I - As one of the loan officers for Grove Gate Bank,...Ch. 14.I - As one of the loan officers for Grove Gate Bank,...Ch. 14.I - Ben and Mal Scott plan to buy a home for $272,900....Ch. 14.I - 16. Michael Sanchez purchased a condominium for...Ch. 14.I - 17. Luis Schambach is shopping for a 15-year...Ch. 14.I - 18. Phil Pittman is interested in a fixed-rate...Ch. 14.I - 19. Larry and Cindy Lynden purchased a townhome in...Ch. 14.I - Heather Gott bought a home with an adjustable-rate...Ch. 14.I - Joe and Gloria Moutran art purchasing a house in...Ch. 14.I - 22. You are a real estate broker for Aurora...Ch. 14.II - Justin Schaefer owns a home that was recently...Ch. 14.II - Roman Bass cams a gross income of $3,100 per...Ch. 14.II - For the following second mortgage applications,...Ch. 14.II - For the following second mortgage applications,...Ch. 14.II - For the following second mortgage applications,...Ch. 14.II - For the following second mortgage applications,...Ch. 14.II - For the following second mortgage applications,...Ch. 14.II - For the following second mortgage applications,...Ch. 14.II - For the following second mortgage applications,...Ch. 14.II - Calculate the housing expense ratio and the total...Ch. 14.II - Calculate the housing expense ratio and the total...Ch. 14.II - Prob. 10RECh. 14.II - Prob. 11RECh. 14.II - Prob. 12RECh. 14.II - Prob. 13RECh. 14.II - Prob. 14RECh. 14.II - Use Exhibit 14-4, Lending Ratio Guidelines, on...Ch. 14.II - 16. Ronald and Samantha Brady recently had their...Ch. 14.II - Prob. 17RECh. 14.II - Ransford and Alda Mariano own a home recently...Ch. 14.II - Prob. 19RECh. 14.II - Jamie and Alice Newmark have a combined monthly...Ch. 14.II - Prob. 21RECh. 14.II - According to moncy.CNN.com. with mortguge rates...Ch. 14 - 1. Land, including permanent improvements on that...Ch. 14 - A(n) ___________ is a loan in which real property...Ch. 14 - Mortgage ___________ points are an extra charge...Ch. 14 - Prob. 4CRCh. 14 - 5. A(n) ___________ account is a bank account used...Ch. 14 - Prob. 6CRCh. 14 - Prob. 7CRCh. 14 - Prob. 8CRCh. 14 - Prob. 9CRCh. 14 - Prob. 10CRCh. 14 - A home equity ___________ is a lump-sum second...Ch. 14 - Prob. 12CRCh. 14 - Prob. 13CRCh. 14 - Prob. 14CRCh. 14 - Prob. 1ATCh. 14 - Prob. 2ATCh. 14 - Suzanne Arthurs purchased a home with a $146,100...Ch. 14 - Prob. 4ATCh. 14 - Prob. 5ATCh. 14 - Prob. 6ATCh. 14 - Prob. 7ATCh. 14 - Prob. 8ATCh. 14 - Prob. 9ATCh. 14 - Prob. 10ATCh. 14 - Prob. 11ATCh. 14 - 12. Dale Evans bought the Lazy D Ranch with an...Ch. 14 - 13. Diversified Investments purchased a 24-unit...Ch. 14 - Larry Mager purchased a ski lodge in Telluride for...Ch. 14 - 15. A Denny’s Restaurant franchisee is looking for...Ch. 14 - Prob. 16ATCh. 14 - Adam Marsh is purchasing a $134,000 condominium...Ch. 14 - Prob. 18ATCh. 14 - Prob. 19ATCh. 14 - Prob. 20ATCh. 14 - 21. Phil Armstrong earns a gross income of $5,355...Ch. 14 - 22. Magda Leon is applying for a home mortgage...
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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?arrow_forward(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)arrow_forward(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)arrow_forward
- 1. Let z = x+iy with x, y Є R. Let f(z) = u(x, y) + iv(x, y) where u(x, y), v(x, y): R² → R. (a) Suppose that f is complex differentiable. State the Cauchy-Riemann equations satisfied by the functions u(x, y) and v(x,y). (b) State what it means for the function (2 mark) u(x, y): R² → R to be a harmonic function. (3 marks) (c) Show that the function u(x, y) = 3x²y - y³ +2 is harmonic. (d) Find a harmonic conjugate of u(x, y). (6 marks) (9 marks)arrow_forwardPlease could you provide a step by step solutions to this question and explain every step.arrow_forwardCould you please help me with question 2bii. If possible could you explain how you found the bounds of the integral by using a graph of the region of integration. Thanksarrow_forward
- Let A be a vector space with basis 1, a, b. Which (if any) of the following rules turn A into an algebra? (You may assume that 1 is a unit.) (i) a² = a, b² = ab = ba = 0. (ii) a²=b, b² = ab = ba = 0. (iii) a²=b, b² = b, ab = ba = 0.arrow_forwardNo chatgpt pls will upvotearrow_forward= 1. Show (a) Let G = Z/nZ be a cyclic group, so G = {1, 9, 92,...,g" } with g": that the group algebra KG has a presentation KG = K(X)/(X” — 1). (b) Let A = K[X] be the algebra of polynomials in X. Let V be the A-module with vector space K2 and where the action of X is given by the matrix Compute End(V) in the cases (i) x = p, (ii) xμl. (67) · (c) If M and N are submodules of a module L, prove that there is an isomorphism M/MON (M+N)/N. (The Second Isomorphism Theorem for modules.) You may assume that MON is a submodule of M, M + N is a submodule of L and the First Isomorphism Theorem for modules.arrow_forward
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