Contemporary Mathematics for Business & Consumers
8th Edition
ISBN: 9781305886803
Author: Brechner
Publisher: Cengage
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Chapter 13, Problem 11CR
To determine
To fill: The blanks provided for the statement, “A popular method for calculating the interest on an installment is known as _____ interest.”
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The final answer is 8/π(sinx) + 8/3π(sin 3x)+ 8/5π(sin5x)....
Keity
x२
1. (i)
Identify which of the following subsets of R2 are open and which
are not.
(a)
A = (2,4) x (1, 2),
(b)
B = (2,4) x {1,2},
(c)
C = (2,4) x R.
Provide a sketch and a brief explanation to each of your answers.
[6 Marks]
(ii)
Give an example of a bounded set in R2 which is not open.
[2 Marks]
(iii)
Give an example of an open set in R2 which is not bounded.
[2 Marks
2.
(i)
Which of the following statements are true? Construct coun-
terexamples for those that are false.
(a)
sequence.
Every bounded sequence (x(n)) nEN C RN has a convergent sub-
(b)
(c)
(d)
Every sequence (x(n)) nEN C RN has a convergent subsequence.
Every convergent sequence (x(n)) nEN C RN is bounded.
Every bounded sequence (x(n)) EN CRN converges.
nЄN
(e)
If a sequence (xn)nEN C RN has a convergent subsequence, then
(xn)nEN is convergent.
[10 Marks]
(ii)
Give an example of a sequence (x(n))nEN CR2 which is located on
the parabola x2 = x², contains infinitely many different points and converges
to the limit x = (2,4).
[5 Marks]
Chapter 13 Solutions
Contemporary Mathematics for Business & Consumers
Ch. 13.I - Mike Dennis has a Bank of America account with an...Ch. 13.I - Kendra Wolf has a Bank of America revolving credit...Ch. 13.I - Angler Marine has a $75,000 line of credit with...Ch. 13.I - Calculate the missing information on the following...Ch. 13.I - Calculate the missing information on the following...Ch. 13.I - Calculate the missing information on the following...Ch. 13.I - Calculate the missing information on the following...Ch. 13.I - Prob. 5RECh. 13.I - Calculate the missing information on the following...Ch. 13.I - Anny Winslow has a Bank of America revolving...
Ch. 13.I - Kathy Hansen has a revolving credit account. The...Ch. 13.I - Kathy Hansen has a revolving credit account. The...Ch. 13.I - Kathy Hansen has a revolving credit account. The...Ch. 13.I - Prob. 11RECh. 13.I - Kathy Hansen has a revolving credit account. The...Ch. 13.I - Prob. 13RECh. 13.I - 14. Calculate the average daily balance for...Ch. 13.I - 15. Calculate the average daily balance for...Ch. 13.I - Carolyn Salkind has a Bank of America revolving...Ch. 13.I - Prob. 17RECh. 13.I - The Jewelry Exchange has a $30,000 line of credit...Ch. 13.II - Bob Johnson found a car he wanted to buy at...Ch. 13.II - Prob. 5TIECh. 13.II - Prob. 6TIECh. 13.II - Prob. 7TIECh. 13.II - Prob. 8TIECh. 13.II - Prob. 9TIECh. 13.II - Calculate the amount financed, the finance charge,...Ch. 13.II - Calculate the amount financed, the finance charge,...Ch. 13.II - Prob. 3RECh. 13.II - Prob. 4RECh. 13.II - Calculate the amount financed, the finance charge,...Ch. 13.II - Prob. 6RECh. 13.II - Prob. 7RECh. 13.II - Calculate the amount financed, the finance charge,...Ch. 13.II - Prob. 9RECh. 13.II - Calculate the amount financed, the finance charge,...Ch. 13.II - Calculate the amount financed, the finance charge,...Ch. 13.II - Calculate the amount financed, the finance charge,...Ch. 13.II - Calculate the amount financed, the finance charge,...Ch. 13.II - Calculate the amount financed, the finance charge,...Ch. 13.II - Calculate the finance charge, the finance charge...Ch. 13.II - Prob. 16RECh. 13.II - Prob. 17RECh. 13.II - Calculate the finance charge, the finance charge...Ch. 13.II - Calculate the finance charge, the finance charge...Ch. 13.II - Calculate the finance charge, the finance charge...Ch. 13.II - Prob. 21RECh. 13.II - Prob. 22RECh. 13.II - Prob. 23RECh. 13.II - Calculate the finance charge and the annual...Ch. 13.II - Prob. 25RECh. 13.II - Prob. 26RECh. 13.II - Prob. 27RECh. 13.II - Calculate the finance charge and the monthly...Ch. 13.II - Calculate the finance charge and the monthly...Ch. 13.II - Calculate the finance charge and the monthly...Ch. 13.II - Prob. 31RECh. 13.II - Prob. 32RECh. 13.II - Calculate the missing information for the...Ch. 13.II - Calculate the missing information for the...Ch. 13.II - Prob. 35RECh. 13.II - Calculate the missing information for the...Ch. 13.II - Calculate the missing information for the...Ch. 13.II - Prob. 38RECh. 13.II - You are the loan department supervisor for the...Ch. 13.II - Prob. 40RECh. 13.II - You are the loan department supervisor for the...Ch. 13.II - You are the loan department supervisor for the...Ch. 13.II - You are the loan department supervisor for the...Ch. 13.II - Prob. 44RECh. 13.II - Prob. 45RECh. 13.II - 46. Meghan Pease purchased a small sailboat for...Ch. 13.II - Prob. 47RECh. 13.II - 48. Doug Black bought a jet ski with a 9% add-on...Ch. 13.II - Olivia Fast found a timeshare offer entitling her...Ch. 13.II - Tim Houston purchased a wall unit for $2,400. He...Ch. 13.II - First National Bank offers a 36-month installment...Ch. 13.II - At a recent boat show, Nautica Bank was offering...Ch. 13.II - Prob. 53RECh. 13.II - 54. a. What is the rebate fraction of a 36-month...Ch. 13.II - Charlie Allen financed a $3,500 Nautilus home gym...Ch. 13 - ____ credit is a loan arrangement in which there...Ch. 13 - The effective or true annual interest rate being...Ch. 13 - Loans that are backed by the borrowers promise to...Ch. 13 - 4. Loans made on a continuous basis and billed...Ch. 13 - 5. Name the two most common methods used to...Ch. 13 - Prob. 6CRCh. 13 - Prob. 7CRCh. 13 - Prob. 8CRCh. 13 - Prob. 9CRCh. 13 - Prob. 10CRCh. 13 - Prob. 11CRCh. 13 - Prob. 12CRCh. 13 - 13. The finance charge ________ is the unearned...Ch. 13 - Prob. 14CRCh. 13 - Prob. 1ATCh. 13 - Prob. 2ATCh. 13 - Prob. 3ATCh. 13 - 4. Calculate the average daily balance for January...Ch. 13 - Mel Arrandt has a Bank of America account with a...Ch. 13 - Alpine Construction, Inc. has a $100,000 line of...Ch. 13 - George Bell bought an ultralight airplane for...Ch. 13 - 8. David Sporn bought a saddle from Linville...Ch. 13 - 9. Buster Blaster Recording Studio purchased a new...Ch. 13 - Chris Manning purchased a $7,590 motorcycle with a...Ch. 13 - 11. SkyHigh Aircraft Sales uses the Executive...Ch. 13 - 12. After making 11 payments on a 36-month loan,...Ch. 13 - An Auntie Annes franchise financed a $68,000...Ch. 13 - 14. You are a salesperson for Mega Marine Boat...Ch. 13 - 15. Joe Keener found the accompanying ad for a...
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- 2. (i) What does it mean to say that a sequence (x(n)) nEN CR2 converges to the limit x E R²? [1 Mark] (ii) Prove that if a set ECR2 is closed then every convergent sequence (x(n))nen in E has its limit in E, that is (x(n)) CE and x() x x = E. [5 Marks] (iii) which is located on the parabola x2 = = x x4, contains a subsequence that Give an example of an unbounded sequence (r(n)) nEN CR2 (2, 16) and such that x(i) converges to the limit x = (2, 16) and such that x(i) # x() for any i j. [4 Marksarrow_forward1. (i) which are not. Identify which of the following subsets of R2 are open and (a) A = (1, 3) x (1,2) (b) B = (1,3) x {1,2} (c) C = AUB (ii) Provide a sketch and a brief explanation to each of your answers. [6 Marks] Give an example of a bounded set in R2 which is not open. (iii) [2 Marks] Give an example of an open set in R2 which is not bounded. [2 Marks]arrow_forwardsat Pie Joday) B rove: ABCB. Step 1 Statement D is the midpoint of AC ED FD ZEDAZFDC Reason Given 2 ADDC Select a Reason... A OBB hp B E F D Carrow_forward
- 2. if limit. Recall that a sequence (x(n)) CR2 converges to the limit x = R² lim ||x(n)x|| = 0. 818 - (i) Prove that a convergent sequence (x(n)) has at most one [4 Marks] (ii) Give an example of a bounded sequence (x(n)) CR2 that has no limit and has accumulation points (1, 0) and (0, 1) [3 Marks] (iii) Give an example of a sequence (x(n))neN CR2 which is located on the hyperbola x2 1/x1, contains infinitely many different Total marks 10 points and converges to the limit x = (2, 1/2). [3 Marks]arrow_forward3. (i) Consider a mapping F: RN Rm. Explain in your own words the relationship between the existence of all partial derivatives of F and dif- ferentiability of F at a point x = RN. (ii) [3 Marks] Calculate the gradient of the following function f: R2 → R, f(x) = ||x||3, Total marks 10 where ||x|| = √√√x² + x/2. [7 Marks]arrow_forward1. (i) (ii) which are not. What does it mean to say that a set ECR2 is closed? [1 Mark] Identify which of the following subsets of R2 are closed and (a) A = [-1, 1] × (1, 3) (b) B = [-1, 1] x {1,3} (c) C = {(1/n², 1/n2) ER2 | n EN} Provide a sketch and a brief explanation to each of your answers. [6 Marks] (iii) Give an example of a closed set which does not have interior points. [3 Marks]arrow_forward
- Function: y=xsinx Interval: [ 0 ; π ] Requirements: Draw the graphical form of the function. Show the coordinate axes (x and y). Choose the scale yourself and show it in the flowchart. Create a flowchart based on the algorithm. Write the program code in Python. Additional requirements: Each stage must be clearly shown in the flowchart. The program must plot the graph and save it in PNG format. Write the code in a modular way (functions and main section should be separate). Expected results: The graph of y=xsinx will be plotted in the interval [ 0 ; π ]. The algorithm and flowchart will be understandable and complete. When you test the code, a graph file in PNG format will be created.arrow_forwardA company specializing in lubrication products for vintage motors produce two blended oils, Smaza and Nefkov. They make a profit of K5,000.00 per litre of Smaza and K4,000.00 per litre of Nefkov. A litre of Smaza requires 0.4 litres of heavy oil and 0.6 litres of light oil. A litre of Nefkov requires 0.8 litres of heavy oil and 0.2 litres of light oil. The company has 100 litres of heavy oil and 80 litres of light oil. How many litres of each product should they make to maximize profits and what level of profit will they obtain? Show all your workings.arrow_forwardUse the graphs to find estimates for the solutions of the simultaneous equations.arrow_forward
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