Contemporary Mathematics for Business & Consumers
8th Edition
ISBN: 9781305585447
Author: Robert Brechner, Geroge Bergeman
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 17.I, Problem 12RE
To determine
To calculate: The sum-of-the-years’ digits and depreciation rate fraction for year 1, year 3 and year 5 when the useful life is 7 years.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
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)
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 17 Solutions
Contemporary Mathematics for Business & Consumers
Ch. 17.I - Wild Flour Bakery purchased a new bread oven for...Ch. 17.I - Prob. 2TIECh. 17.I - Prob. 3TIECh. 17.I - Prestige Limousine Sen ice purchased a limousine...Ch. 17.I - Prob. 1RECh. 17.I - Prob. 2RECh. 17.I - Prob. 3RECh. 17.I - Prob. 4RECh. 17.I - Prob. 5RECh. 17.I - Prob. 6RE
Ch. 17.I - Prob. 7RECh. 17.I - Prob. 8RECh. 17.I - The Huffy Laundromat purchased new washing...Ch. 17.I - Prob. 10RECh. 17.I - Prob. 11RECh. 17.I - Prob. 12RECh. 17.I - Prob. 13RECh. 17.I - Prob. 14RECh. 17.I - Prob. 15RECh. 17.I - Prob. 16RECh. 17.I - Prob. 17RECh. 17.I - Complete Exercises 18-23 as they relate to the...Ch. 17.I - Prob. 19RECh. 17.I - Prob. 20RECh. 17.I - Complete Exercises 18-23 as they relate to the...Ch. 17.I - Prob. 22RECh. 17.I - Complete Exercises 18-23 as they relate to the...Ch. 17.I - Prob. 24RECh. 17.I - Prob. 25RECh. 17.I - Prob. 26RECh. 17.I - Prob. 27RECh. 17.I - Prob. 28RECh. 17.I - Prob. 29RECh. 17.I - Prob. 30RECh. 17.I - Prob. 31RECh. 17.I - You are the accountant for Raleigh Industries, a...Ch. 17.I - BUSINESS DECISION: REPLACING AN ASSET Supreme Auto...Ch. 17.II - Prob. 5TIECh. 17.II - Prob. 6TIECh. 17.II - 1. Ink Masters Printing purchased a new printing...Ch. 17.II - Prob. 2RECh. 17.II - Prob. 3RECh. 17.II - Prob. 4RECh. 17.II - Prob. 5RECh. 17.II - All-That-Glitters Mining Company paid $49.250.000...Ch. 17.II - 7. Sequoia Timber Company purchased land...Ch. 17.II - Prob. 8RECh. 17 - Prob. 1CRCh. 17 - Prob. 2CRCh. 17 - 3. The useful _____ is the length of time an asset...Ch. 17 - Prob. 4CRCh. 17 - 5. Depreciation methods that assume an asset...Ch. 17 - Prob. 6CRCh. 17 - Prob. 7CRCh. 17 - 8. A method of accelerated depreciation that uses...Ch. 17 - Prob. 9CRCh. 17 - Prob. 10CRCh. 17 - Prob. 11CRCh. 17 - Prob. 12CRCh. 17 - Prob. 13CRCh. 17 - When natural resources are depleted, the average...Ch. 17 - Calculate the total cost, total depreciation, and...Ch. 17 - Calculate the total cost, total depreciation, and...Ch. 17 - Oxford Manufacturing. Inc., purchased new...Ch. 17 - Prob. 4ATCh. 17 - Prob. 5ATCh. 17 - Prob. 6ATCh. 17 - Prob. 7ATCh. 17 - Prob. 8ATCh. 17 - Prob. 9ATCh. 17 - Prob. 10ATCh. 17 - Prob. 11ATCh. 17 - Screen Gems Movie Theater purchased a new...Ch. 17 - Stone Age Concrete, Inc. MACRS Depreciation...Ch. 17 - Prob. 14ATCh. 17 - In January 2002. Marine Science Corporation was...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- (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_forward1. 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_forward
- Please 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_forwardLet 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_forward
- No 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(a) Define the notion of an ideal I in an algebra A. Define the product on the quotient algebra A/I, and show that it is well-defined. (b) If I is an ideal in A and S is a subalgebra of A, show that S + I is a subalgebra of A and that SnI is an ideal in S. (c) Let A be the subset of M3 (K) given by matrices of the form a b 0 a 0 00 d Show that A is a subalgebra of M3(K). Ꮖ Compute the ideal I of A generated by the element and show that A/I K as algebras, where 0 1 0 x = 0 0 0 001arrow_forward
- (a) Let HI be the algebra of quaternions. Write out the multiplication table for 1, i, j, k. Define the notion of a pure quaternion, and the absolute value of a quaternion. Show that if p is a pure quaternion, then p² = -|p|². (b) Define the notion of an (associative) algebra. (c) 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 (iii) a² = b, b² = abba = 0. = b, b² = b, ab = ba = 0. (d) Let u1, 2 and 3 be in the Temperley-Lieb algebra TL4(8). ገ 12 13 Compute (u3+ Augu2)² where A EK and hence find a non-zero x € TL4 (8) such that ² = 0.arrow_forwardQ1: Solve the system x + x = t², x(0) = (9)arrow_forwardCo Given show that Solution Take home Су-15 1994 +19 09/2 4 =a log суто - 1092 ж = a-1 2+1+8 AI | SHOT ON S4 INFINIX CAMERAarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillElementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice UniversityAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Elementary Algebra
Algebra
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:OpenStax - Rice University
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Use of ALGEBRA in REAL LIFE; Author: Fast and Easy Maths !;https://www.youtube.com/watch?v=9_PbWFpvkDc;License: Standard YouTube License, CC-BY
Compound Interest Formula Explained, Investment, Monthly & Continuously, Word Problems, Algebra; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=P182Abv3fOk;License: Standard YouTube License, CC-BY
Applications of Algebra (Digit, Age, Work, Clock, Mixture and Rate Problems); Author: EngineerProf PH;https://www.youtube.com/watch?v=Y8aJ_wYCS2g;License: Standard YouTube License, CC-BY