Consider an n-sided regular polygon inscribed in a circle of radius r. Join the vertices of the
Question:
Consider an n-sided regular polygon inscribed in a circle of radius r. Join the vertices of the polygon to the center of the circle, forming n congruent triangles (see figure).(a) Determine the central angle θ in terms of n.(b) Show that the area of each triangle is 1/2 r2 sinθ.(c) Let An be the sum of the areas of the n triangles. Find lim n ∞ An.
Figure for 76
Step by Step Answer:
a The central angle is given by the formula 360n This is because the polygon is regular so all its a...View the full answer
Calculus Of A Single Variable
ISBN: 9781337275361
11th Edition
Authors: Ron Larson, Bruce H. Edwards
Related Video
The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.
Students also viewed these Mathematics questions
-
(a) Find the area of a regular hexagon inscribed in a circle of radius 1. How close is this area to that of the circle? (b) Find the area A n of an n-sided regular polygon inscribed in a circle of...
-
An equilateral triangle is inscribed in a circle of radius r. See the figure. Express the circumference C of the circle as a function of the length x of a side of the triangle. First show that r 2 =...
-
Find the shape of the triangle of maximum perimeter that can be inscribed in a circle of radius r. Let (, (, and ( be as in Figure 7 and reduce the problem to maximizing P = 2r(sin (/2 + sin (/2 +...
-
(a) Victor and Maria regularly buy and sell a number of items on eBay, Craig's List, and through the free community newspaper, from which they earn about $4,000 each year. What is the accumulated...
-
Does the rate of violent crime acts vary across different regions of the United States? Answer this with the (somewhat old), 1999 data in the file P10_34.xlsx as requested below. a. Estimate an...
-
Shine King Cleaning has decided that, in addition to providing cleaning services, it will sell cleaning products. During December, Shine King completed the following transactions: Dec 2 Purchased 600...
-
Each outcome of an experiment, in the case of a random process, is called a a. sample point b. sample space c. sample function
-
Review the comprehensive annual financial report (CAFR) you obtained. 1. Indicate the activities accounted for in both internal service funds and major enterprise funds. Comment on whether any of...
-
Bobby owns ten acres of land in rural Ohio, where he keeps a small herd of wild boar. Wild boar regularly attack humans. The attacks, which are usually unprovoked, can cause injury from bites and...
-
After Susan Wong graduated from State University with a degree in management science, she went to work for a computer systems development firm in the Washington, DC, area. As a student at State,...
-
Find the constants a and b, where a || [ (x 4) dx = So |x - 4| dx = 20. 16 and
-
Use the limit process to find the area of the region bounded by the graph of the function and the y-axis over the given y-interval. Sketch the region. y = 3y - y 2 , 2 y 3
-
The corporate charter of Gage Corporation allows the issuance of a maximum of 100,000 shares of common stock. During its first 2 years of operation, Gage sold 70,000 shares to shareholders and...
-
Evaluate the primary needs of employers for positions of interest.
-
Develop strategies for responding to common job interview questions.
-
Identify a topic of interest. Create a storyboard to outline the titles, content, and related story line of your PowerPoint slides.
-
Think about a recent team or group project you were part of. Evaluate your teams performance in the following ways: How well did your team set goals up front? How well did your team establish norms,...
-
Explain etiquette for leaving an organization with grace and foresight.
-
Solve each of the following proportions. (a) 65 : 39 = x : 12 (b) 7/6 : 35/12 = 6/5 : x
-
Some people argue that the internal control requirements of the Sarbanes-Oxley Act (SOX) put U.S. companies at a competitive disadvantage to companies outside the United States. Discuss the...
-
In Exercises sketch the graph of the function by hand. y = 2 x
-
In Exercises write the exponential equation as a logarithmic equation or vice versa. (a) log 3 1/9 = -2 (b) 49 1/2 = 7
-
In Exercises write the exponential equation as a logarithmic equation or vice versa. (a) 27 2/3 = 9 (b) 16 3/4 = 8
-
Saturation of the lower transition in a general three-level atomic system. Sup- pose a signal that produces a stimulated transition probability W12 = W21 (no degeneracy) is applied to the 12...
-
1. In the attached excel file, the sheet named "KL" shows the following table, in which KL's profits are displayed for various price combinations. Note that, in the table, different prices for KL are...
-
In the figure here, a ball is thrown up onto a roof, landing 3.70 s later at height h = 19.0 m above the release level. The ball's path just before landing is angled at 0 = 60.0 with the roof. (a)...
Study smarter with the SolutionInn App