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...

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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...

...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...

...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...

...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...

...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...

...
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...

...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...