Prove that the area of a sector of a circle of radius r associated with a central

Question:

Prove that the area of a sector of a circle of radius r associated with a central angle θ (measured in radians) is A = 1/2 r² θ.

Prove that the area of a sector of a circle

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

See More Books

Question Posted: Jan 22, 2019 08:02 AM

See More Questions

(a) Show that this gives the equation of a line in R2 thru (x2, y2) and (x3, y3). (b) Prove that the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is (c) Prove that the area of a...
1. Is a degree or a radian the larger unit of measure? Explain. 2. Prove that the area of a circular sector of radius r with central angle is A = 1/2 r2, where is measured in radians.
A trough in the shape of a half cylinder has length 5 m and radius 1 m. The trough is full of water when a valve is opened, and water flows out of the bottom of the trough at a rate of 1.5 m 3 /hr...
If f(x) = 5x + 1, find and simplify each of the following in Problem. f(f( -1))
Dollar Department Stores has received an offer from Harris Diamonds to purchase Dollar's store on Grove Street for $120,000. Dollar has determined probability estimates of the store's future...
In 2019, Rylan Enterprises' net income increased by $2.5 million while its depreciation expense decreased by $500,000, accounts receivable increased by $2,000,000 and accounts payable increased by...
In Exercises 1 to 4, it may be helpful to draw a figure such as Figure 5.5. Figure 5.5. Using the normal curve table, determine the area of the standard normal distribution that is greater than the...
A commercial fisherman notices the following relationship between hours spent fishing and the quantity of fish caught: Hours Quantity of Fish (in pounds) 0 hours ......0 lb 1.........10 2.........18...
How do ethical considerations factor into the governance frameworks of collaborative consortia, particularly concerning data privacy, intellectual property rights, and equitable distribution of...
1. Toronto- based Mercedes- Benz Canada, with a network of 55 dealers, did not know enough about its customers. Dealers provided customer data to the company on an ad hoc basis. Mercedes did not...
An auditorium with a flat floor has a large flatpanel television on one wall. The lower edge of the television is 3 ft above the floor, and the upper edge is 10 ft above the floor (see figure)....
Use the figure to prove the law of cosines (which is a generalization of the Pythagorean theorem): c 2 = a 2 + b 2 - 2ab cos . (b cos 0, b sin 0) b' a (a, 0)
What company did Bristol Myers Squibb acquire in 2019? What happened to the companys stock price when the merger was announced?
A pressure vessel of 250-mm inner diameter and 6-mm wall thickness is fabricated from a 1.2- m section of spirally welded pipe AB and is equipped with two rigid end plates. The gage pressure inside...
The preliminary survey results just came back on the specialty catalog project, and they look great! The average planned order size was $42.33, well above the $15 that was hoped for. The group leader...
2) An opening bridge takes 60 seconds to open. The opening motion is shown on the angular velocity time diagram (Figure 14). Figure 14 Angular Velocity (rad.s) 0.03 0.02 0.01 0 10 20 30 40 40 50 60...
What is the meaning of all of these? "Transforming the complex to the simple is pure genius" "Complexity that works is built up out of modules that work perfectly, layered one over the other"
Why do we employ perceptual screens to filter the ads to which we are exposed? 2. What does the term consumer behavior refer to, and why is it important to advertisers? What is the difference...
How is internal application integration accomplished?
Why can wastewater treatment requirements in Hawaii be less stringent than those in most locations on the U.S. mainland?
The graph of the derivative f of a function f is shown. (a) On what intervals is f increasing or decreasing? (b) At what values of x does f have a local maximum or minimum? y= f'(x) 0 4
Suppose the derivative of a function f is f'(x) = (x + 1)2 (x - 3)5 (x - 6)4. On what interval is increasing?
(a) Use a graph of f to estimate the maximum and minimum values. Then find the exact values. (b) Estimate the value of x at which f increases most rapidly. Then find the exact value. f(x) = x + 1/ x2...
Lake Incorporated and the River, Incorporated reported net incomes of $205,000 and $164,000, respectively, for the most recent fiscal year. Both companies had 41,000 shares of common stock issued and...
What effect Eventually, BREXIT will make on EU? How it will benefit UK? What will be the possible outcome?
Merchant Company purchased property for a building site. The costs associated with the property were: Purchase price Real estate commissions Legal fees Expenses of clearing the land Expenses to...

Prove that the area of a sector of a circle of radius r associated with a central

Question:

Step by Step Answer:

The area of the entire circle is r 2 The ra...View the full answer

Calculus Early Transcendentals

Related Video

Students also viewed these Mathematics questions