The base of the triangle shown in the figure is also the radius of a circular arc.
Question:
(a) Find the area A of the shaded region as a function of θ for 0 (b) Use a graphing utility to graph the area function over the given domain. Interpret the graph in the context of the problem.
12
Step by Step Answer:
a tan x 2 x 12 tan Area Area if triang...View the full answer
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 Calculus questions
-
A page that is x inches wide and y inches high contains 30 square inches of print. The top and bottom margins are each 2 inches deep and the margins on each side are 2 inches wide. (a) Show that the...
-
A golf ball is hit with an initial velocity of 130 feet per second at an inclination of 45° to the horizontal. In physics, it is established that the height h of the golf ball is given by the...
-
Use a graphing utility to graph the region corresponding to the system of constraints. Then find the minimum and maximum values of the objective function and the points where they occur, subject to...
-
Management is responsible for establishing effective internal control for its organization, including measures to prevent, deter, and detect fraud. Appendix 7A on pages 294296 describes antifraud...
-
An air stream at a specified temperature and relative humidity undergoes evaporative cooling by spraying water into it at about the same temperature. The lowest temperature the air stream can be...
-
A manufacturer receives N units of a certain raw material that are initially placed in storage and then withdrawn and used at a constant rate until the supply is exhausted 1 year later. Suppose...
-
A compressor of mass \(120 \mathrm{~kg}\) has a rotating unbalance of \(0.2 \mathrm{~kg}-\mathrm{m}\). If an isolator of stiffness \(0.5 \mathrm{MN} / \mathrm{m}\) and damping ratio 0.06 is used,...
-
Deer Creek Inc. bottles and distributes spring water. On April 27 of the current year, Deer Creek reacquired 15,000 shares of its common stock at $60 per share. On July 13, Deer Creek sold 9,000 of...
-
Enter the forum and write a post discussing the role of government and compliance with foreign laws regarding buyer and supplier agreements. Your response must be substantial and analyze the topic...
-
You have $250,000 to invest in a stock portfolio. Your choices are Stock H, with an expected return of 12.3 percent, and Stock L, with an expected return of 10.2 percent. If your goal is to create a...
-
1. When graphing the sine and cosine functions, determining the amplitude is part of the analysis. Explain why this is not true for the other four trigonometric functions. 2. A weight is suspended...
-
Convert the radian measure to degree measure. Round to three decimal places, if necessary. 1. 3 / 10 2. 7 / 5 3. -3 / 5 4. -11 /6 5. 5.2 6. 7 7. -2.15 8. -4.63
-
Research shows that in a job interview, the interviewer is likely to be strongly influenced by first impressions of the interviewee. In many cases a decision is made within the first minute of the...
-
Can fashion be protected is an ongoing subject of debate both in and outside of our industry. 1. Go to LinkedIn Learning and watch the video "Intellectual Property Fundamentals" by Dana Robinson for...
-
To complete the film assignment using Conversation on the Constitution , paper of approximately 1000 words ( 12 point font, proper citations to any works cited in the paper) using the following...
-
Watch the full Martin Luther King Jr. I Have a Dream speech (16 minutes). What was your reaction to the speech? Describe how the speech moved you? Did you feel the crescendo ending?
-
Read the brief case summary below, "Government Contracts and Third-Party Beneficiaries." Kremen also alleged that NSI had breached an implied-in-fact contract with him, but the court dismissed this...
-
With some understanding of the legal system, the Viral Clean ("Clean") owners can now shift their focus to examining specific areas of law that create potential risks and liabilities for their...
-
Access the 2017 10-K of Advanced BioEnergy, LLC, which is available from SEC.gov, and identifyits unconsolidated statements on pages 5355 of the 10-K filing. This companys business consists of...
-
1. What are some current issues facing Saudi Arabia? What is the climate for doing business in Saudi Arabia today? 2. Is it legal for Auger's firm to make a payment of $100,000 to help ensure this...
-
Use the Product Rule twice to prove that if , g, and h are differentiable functions of x, then xp *(x),y(x)8(x) + (x)y(x),8(x) + (x)y(x)8(x), = [(x}y(x)8(x)]}
-
Let and g be functions whose first and second derivatives exist on an interval I. Which of the following formulas is (are) true? (a) g" - "g = (g'- 'g)' (b) g" + "g = (g)"
-
Find the derivative of (x) = x|x|. Does "(0) exist?
-
When owning and operating any business, whether it's a caf or a pool cleaning business, it's very important that you know exactly what your income and expenditure is. Is your business making money or...
-
Resources Unlimited Corporation was formed in 1985 through the merger of two natural pipeline companies. The result was the largest gas distribution network in the United States, with 38,000 miles of...
-
Toyota was the world's first automobile manufacturer to produce more than 10 million vehicles per year, which it has done since 2012, when it also reported the production of its 200-millionth...
Study smarter with the SolutionInn App