In this assignment, you examine a process that links polygons and circles. You will reach some quantitative conclusions about their respective areas and the relationship between the two.

As you know, a regular polygon has sides of equal length and angles that are the same. This confers a high degree of symmetry to these figures. A circle may be thought of as the logical limit of an n-sided polygon as n goes to infinity; the sides become infinitesimally small, and the interior angle between adjacent sides continues toward 180°.

A circumscribed polygon is a regular polygon that surrounds a circle. The radius of the circle is the length of the apothem of the polygon; both share the same center. This means the circle touches the polygon on the inside in the middle of each side of the polygon.

Similarly, an inscribed polygon is surrounded by a circle sharing the same center and goes through each vertex of the polygon.

A sample of inscribed and circumscribed pentagons is shown below: [pic]
Questions

For this exercise, consider a circle of radius 1, and corresponding inscribed and circumscribed polygons with the number of sides n = 3, 4, 5, 6, and 8.

A: For each n = 3, 4, 5, 6 and 8, what are the areas of the inscribed and circumscribed polygons with n sides? Inscribed: 3= 1.299 4= 2.000 5= 2.378 6= 2.598 8= 2.828

B: As n gets larger, what happens to the ratio of these pairs of areas? Use the larger area as the numerator and the smaller area as the denominator. As n gets larger, the ratios of the pairs of areas gets closer to 1.

C: Both areas approach a limiting value as n gets larger and larger. What number would this be? As n gets larger, the areas get closer to π which is the area of the circle.

...Week Three PracticalProblem
In this assignment, you examine a practical procedure used in computer-aided design and computational fluid dynamics. You will make some assessments regarding this procedure.
The word triangulation has two definitions. The first, and most common, is the use of trigonometry to establish the position of an object relative to two or more fixed, known locations. This is common in navigation. The second definition is the decomposition of a polygon into triangles. This provides a convenient representation of a polygon that can be used in a variety of computational contexts, such as those mentioned above. For this assignment you will not be concerned about computer science; rather, you will study the variety of ways in which polygons may be triangulated.
For the first three questions, consider the polygons to be convex. If you select any pair of points inside or on the boundary of the polygon, and join them with a line segment, that line segment will remain inside or on the boundary of the polygon; it will never cross the boundary and be outside the polygon. The final question asks you to consider what sort of effect the loosening of this restriction might have on your efforts.
Below is a series of diagrams showing the ways in which the first few polygons may be triangulated. At the start of this task, consider the vertices of the polygon as distinct; that is, they are distinguished...

...Week7Problems—30 points
10 points each. Place answers in the following table:
1. 20.16%; 28.4%; 14.83%
2. 0.3889; 2.571; 0.1512
3. 7.68; 1.44; 9.12
A cohort study is conducted to assess the association between clinical characteristics and the risk of stroke. The study involves n=1,250 participants who are free of stroke at the study start. Each participant is assessed at study start (baseline) and every year thereafter for five years. The following table displays data on hypertension status measured at baseline and hypertension status measured two years later.
2 Years: Not Hypertensive 2 Years: Hypertensive
Baseline: Not Hypertensive 850 148
Baseline: Hypertensive 45 207
Compute the prevalence of hypertension at baseline.
Prevalence = __20.16%______
Compute the prevalence of hypertension at 2 years.
Prevalence = ___28.4%_____
Compute the cumulative incidence of hypertension over 2 years.
Incidence = ___14.83%_____
A case-control study is conducted to assess the relationship between heavy alcohol use during the first trimester of pregnancy and miscarriage. Fifty women who suffered miscarriage are enrolled along with 50 who delivered full term. Each participant’s use of alcohol during pregnancy is ascertained. Heavy drinking is defined as 4 or more drinks on one occasion. The data are shown below.
Miscarriage Delivered Full Term
Heavy Alcohol Use 14 4
No Heavy...

...ECO 550 WEEK 4 CHAPTER 7 AND CHAPTER 8 PROBLEMS
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Chapter 7
In the deep creek mining company described in this chapter table 7.1 suppose again that labor is the variable input and capital is the fixed input. Specifically, assume that the firm owns a piece of equipment having a 500-bhp rating. A. Complete the following tableLabor input L(#of workers
Total production TPL (=Q)
Marginal Product (MPL)
Average Product APL
1
2
3
4
5
6
7
8
9
10
`
B. Plot the (i) total product, (ii) marginal product, (iii) average product functions.
C. Determine the boundaries of these three stages of production.
6. Consider the following short-Run production function (where input, ):
A. Determine the marginal product
B. Determine the average product function
C. Find the value of L that maximizes Q
D. Find the value of L at which the marginal product function takes on its maximum value
E. Find the value of L at which the average product function takes on its maximum value.
8. Based on the production function parameter estimates reported in Table 7.4:
A. Which industry (or industries) appears to exhibit decreasing returns to scale? (Ignore the issue of statistical significance.)
B. Which industry comes closest to exhibiting constant returns to scale?
C. In which will a given percentage increase in capital result in the largest percentage increase in output?
D. In what industry will a given...

...Week7 (12) The Instruments of Trade Policy Chapters 9
Problem set
Exercise 7.1
Use your knowledge about trade policy to evaluate each of the following statements:
a. “An excellent way to reduce unemployment is to enact tariffs on imported goods.”
b. “Tariffs have a more negative effect on welfare in large countries than in small countries.”
c. “Automobile manufacturing jobs are heading to Mexico because wages are so much lower there than in the United States. As a result, we should implement tariffs on automobiles equal to the difference between US and Mexican wage rates.”
Exercise 7.2
Home and Foreign produce and consume wheat.
a) Assume the demand for wheat in Home is: D = 100 - 20P
And the supply of wheat in Home is: S = 20 + 20P.
Numerically calculate the demand equation for imported wheat in Home. Draw the corresponding curve. What is the price of wheat in Home if there is no trade with Foreign?
b) Now add Foreign. The demand for wheat in Foreign is: D* = 80 – 20P, while the supply of wheat in Foreign equals S* = 40 + 20P.
Numerically calculate the supply equation for wheat exported by Foreign. Draw in the corresponding curve in the figure you drew for a). What is the price of wheat in Foreign if there would be no trade with Home?
c) Now assume that Home and Foreign start trading wheat. There are no costs of transport. Calculate the equilibrium price of wheat in case of open-border trade. What is the...

...Week7Problem Set
Chapter 26 (page 903):
1. Answer the following questions:
a. What is the difference between a firm’s cash cycle and its operating cycle?
b. How will a firm’s cash cycle be affected if a firm increases its inventory, all else being equal?
c. How will a firm’s cash cycle be affected if a firm begins to take the discounts offered by its suppliers, all else being equal?
4. The Greek Connection had sales of $32 million in 2012, and a cost of goods sold of $20 million. A simplified balance sheet for the firm appears below:
THE GREEK CONNECTIONBalance SheetAs of December 31, 2012 (in $ thousand) |
Assets | Liabilities and Equity |
CashAccounts receivableInventory | $ 2,000 3,950 1,300 | Accounts payableNotes payableAccruals | $ 1,500 1,000 1,220 |
Total current assets | $ 7,250 | Total current liabilitiesLong-term debt | $ 3,720 3,000 |
Net plant, property,and equipment | $ 8,500 | Total liabilitiesCommon equity | $ 6,720 9,030 |
Total assets | $ 15,750 | Total liabilities and equity | $ 15,750 |
a. Calculate The Greek Connection’s net working capital in 2012.
Net working capital = current assets - its current liabilities
= $7,250 - $3,720 = $3,530
b. Calculate the cash conversion cycle of The Greek Connection in 2012.
The cash conversion cycle (CCC) is defined as
CCC = Accounts Receivable Days + Inventory Days − Accounts Payable Days
Accounts Receivable Days = 3,950,000/(32,000,000/365) = 45.054687...

...Business system anaylsis
Problems and Exercises
Week7 Homework
Tom Sanders
DeVry University
Professor Girten
October 14, 2014
Problems and Exercises
Appendix A
Question 1 - The use-case diagram shown in Figure A-1 F captures the Student billing function but does not contain any function for accepting tuition payment from students. Revise the diagram to capture this functionality. Also, express some common behavior among two use cases in the revised diagram by using include relationships.
The diagram should look like this.
1. Student to the billing counter
2. Billing counter to the acceptance of registration
3. Registration to verification of subjects and courses
4. Validate whether the student has completed pre-requisite courses
5. Approval from the respective course coordinators
6. Final billing given to the student to make payment of his or her fees.
Appendix B
Question 1 - When should you use an Agile method, and when should you use an engineering-based method for developing a system? Support your answer.
An agile method lessens the workload, which also saves more time. It is adaptive in nature and they also focus on people rather than process, so in a case where a system needs to be developed and can be changed rapidly this can be a good method to use.
Engineering-based methods are well detailed and require a lot of documentation; they can also be predictive and don’t usually support changes. They are...

...
In this document ACC 306 Week 3 Problem 16-7 you will find:
Sherrod, Inc. - Multiple differences; a. calculate taxable income; balance sheet classification
Business - Accounting
Week 3
Required Readings
a. Chapter 16: Accounting for Income Taxes
b. Chapter 17: Pensions and Other Postretirement Benefits
Discussions
1. 1st Posting Due by Day 3. Accounting Changes and Error Correction. From Chapter 16 complete Integrating Case 16-5 and post the answers to the discussion board by Day 3.
2. 1st Posting Due by Day 3. 401(k) plan contributions. From Chapter 17 complete Ethics Case 17-6 and post the answers to the discussion board by Day 3.
Quiz
Assignments
1. Due by Day 7. Week 3 Exercises. Complete these problems and turn them in via the dropbox: E16-24, E16-25, P16-7, E17-10, E17-19, and P17-16.
Reserve your ambitions for a position in the student government for your sophomore or junior year of college. Freshman are largely ignored by the SGA. You can use your freshman year to learn about campus politics and discover what role you'd like to play in them.
In this document ACC 306 Week 3 Problem 16-7 you will find:
Sherrod, Inc. - Multiple differences; a. calculate taxable income; balance sheet classification
Business -...

...ECO 550 WEEK 6 CHAPTER 11 AND CHAPTER 12 PROBLEMS
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Chapter 11
2. Ajax Cleaning Products is a medium-sized firm operating in an industry dominated by one large firm Tile King. Ajax produces a multi-headed tunnel wall scrubber that is similar to a model produced by Tile King. Ajax decides to charge the same price as Tile King to avoid the possibility of a price war. The price charged by Tile King is $20,000.
Ajax has the following short-run cost curve:
,000 - 5,000Q + 100Q2.
A. Computer the marginal cost curve for Ajax.
B. Given Ajax’s pricing strategy, what is the marginal revenue function for Ajax?
4. Unique Creations holds a monopoly position in the production and sale of manometers. The cost function facing Unique is estimated to be
TC = $100,000 + 20Q
A. What is the marginal cost for Unique?
C. What is the marginal revenue at the price computed in Part (b)?
6. Wyandotte Chemical Company sells various chemicals to the automobile industry. Wyandotte currently sells 30,000 gallons of polyol per year at an average price of $15 per gallon. Fixed costs of manufacturing polyol are $90,000 per year and total variable costs equal $180,000. The operations research department has estimated that a 15 percent increase in output would not affect fixed costs but would reduce average variable costs by 60 cents per gallon. The marketing department has estimated the arc elasticity of demand for polyol to be –2.0.
A. How much would...