Question: Derive the formula A = ½ r2t for the area of a sector of a circle. Here r is the radius and t is the

Derive the formula A = ½ r2t for the area of a sector of a circle. Here r is the radius and t is the radian measure of the central angle (see Figure 17).

Step by Step Solution

★★★★★

3.30 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Recall that the area of the circle is r 2 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

955-M-C-D-E (1402).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Prove the formula A = ½r2 for the area of a sector of a circle with radius and central angle θ. y.

Use the formula for t of Exercise 14.28 to derive the following (1 Î±) 100% confidence limits for Î²: In exercise 1-12 B 1tla/2.n-2* n-2

If the surface of a cone of slant height C and base radius r is cut along a lateral edge and laid flat, it becomes the sector of a circle of radius C and central angle Î¸ (see Figure 19)....

L41_05,L41_06 Find the length of the arc of a circle of radius 12 meters subtended by a central angle 01'63 degrees. Round your answer to the nearest hundredth. The length of the arc is meters. Find...

4.1 Special Right Triangles and Trigonometric Ratios Chapter 4 Trigonometric Functions Section 4.1: Special Right Triangles and Trigonometric Ratios Special Right Triangles Trigonometric Ratios...

Math 1330 Precalculus Electronic Homework (EHW 3) Sections 4.1, 4.2 Work the following problems and choose the correct answer. The problems that refer to the Textbook may be found at www.casa.uh.edu...

Answer this: Figure 3.2 shows some special angles in standard position with the indicated terminal sides. The degree and radian measures are also given. "E. Ta nibs I 90% = 7 120 = 4 135 = 150 = 6...

Question 1 (4 points) A circle of radius 12 units is divided into 8 congruent slices. What is the area of each slice? Question 2 (4 points) A circle has radius 4 units and a central angle measuring...

i need help with tese plz 9. [-/0.9 Points] DETAILS SALGTRIG4 5.1.068. MY NOTES ASK YOUR TEACHER This exercise involves the formula for the area of a circular sector. The area of a sector of a circle...

Question 13 [3011 pt '0 3 219 G) Details Find the distance along an arc on the surface of the earth that subtends a central angle of 9 minutes (1 minute = H60 degree). The radius of the earth is 3960...

In the construction of a two-span bridge (span length = L) by using span-by-span construction, why is a length of about 1.25L bridge segment is constructed in the first phase of construction?

The Gross domestic product (GDP) in rupees grew at 7% during 2012- 2013. For international comparision, the GDP is compared in US dollars (USD) after conversion based on the market exchange rate....

When a company uses the perpetual inventory method, which of the following would be the entry to adjust inventory to lowerminus ofminus costminus orminus market ?

In the absence of a single body with responsibility for directing a destinations event tourism efforts, what approaches might be used to ensure a coordinated response to this task?

State each of the following differentiation rules both in symbols and in words. (a) The Power Rule (b) The Constant Multiple Rule (c) The Sum Rule (d) The Difference Rule (e) The Product Rule (f) The...

(a) How is the number defined? (b) Express as a limit. (c) Why is the natural exponential function y = ex used more often in calculus than the other exponential functions y = ax? (d) Why is the...

(a) Write an expression for the linearization of f at a. (b) If y = f(x), write an expression for the differential dy. (c) If dx = x, draw a picture showing the geometric meanings of y and dy.

MB Inc DOES NOT want to grow a no positive NPV projects - Profit margin =10% - Asset/Sales =150% - Debt/Equity =100% - Dividend Payout =50% 1. What is the firm's sustainable growth rate? 2. What can...

Consider a newly issued 4 - year, 3 . 1 1 % annual - pay bond trading at par. The present values of each of the bond s promised payments, discounted at 6 . 1 1 % . Its Macaulay duration is closest to

P 4-3 The accounts of Consolidated Can contain the following amounts at December 31, 2012: Cost of products sold $410,000 Dividends 3,000 Extraordinary gain (net of tax) 1,000 Income taxes 9,300...