The diagram shows the sector OAB of a circle of radius r cm. The area of the

Question:

The diagram shows the sector OAB of a circle of radius r cm. The area of the sector is 15 cm² and ∠AOB = 1.5 radians.

a. Prove that r = 2√5.

b. Find, in cm, the perimeter of the sector OAB. The segment R, shaded in the diagram, is enclosed by the arc AB and the straight line AB.

c. Calculate, to 3 decimal places, the area of R.

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

Step by Step Answer:

Related Book For book-img-for-question

Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

ISBN: 9781292183404

1st Edition

Authors: Greg Attwood, Jack Barraclough, Ian Bettison, David Goldberg, Alistair Macpherson, Joe Petran

See More Books

Question Posted: Aug 10, 2023 04:43 AM

See More Questions

The diagram shows the sector OAB of a circle with centre O, radius 12 cm and angle 1.2 radians. The line AC is a tangent to the circle with centre O, and OBC is a straight line. The region R is...
The diagram shows a sector OAB of a circle with centre O and radius r. Angle AOB is radians. The point C on OA is such that BC is perpendicular to OA. The point D is on BC and the circular arc AD...
The diagram shows a sector OAB of a circle with centre O and radius r cm. The angle AOB is radians and the perimeter of the sector is 30 cm. a) Show that = 30/r 2. b) Find the area of the sector...
Three years ago, Witt Gas Controls purchased equipment for $80,000 that was expected to have a useful life of 5 years with a $9000 salvage value . Increased demand necessitated an upgrade costing...
The following cost behavior patterns describe anticipated manufacturing costs for 2013: raw material, $7/unit; direct labor, $10/unit; and manufacturing overhead, $240,000 + $8/unit. Required: If...
Steinberg Company had the following direct materials costs for the manufacturing of product T in March: Actual purchase price per pound.........................................................$7.50...
The voltage-to-current ratio in the primary coil of a transformer can be thought of as the transformer's effective resistance. A step-down transformer converts $120 \mathrm{~V}$ at the primary to...
Roger Ginde is developing a program in supply chain management certification for managers. Ginde has listed a number of activities that must be completed before a training program of this nature...
What kind of organization might want to follow a different political model of IT than the federal model? Describe how a manager provides leadership with respect to infonnation technology in the...
Solve, for 0 < x < 2, a cos (x - 2) = /2 12 b sin 3x = 2
In the diagram, AB is the diameter of a circle of radius r cm and BOC = radians. Given that the area of COB is equal to that of the shaded segment, show that + 2 sin = . 0 0 C B
How would entrance fees be treated in the financial statements accounts of a club?
Discuss the nature, type and possible locations of sensors that need to be used for safety as well as control of a thermal system, which heat short metal rods in a gas furnace and then bend them into...
The Stonebridge Tire Co. manufactures passenger car tires. The manufacturing process results in tires that are either first-quality tires, blemished tires, or defective tires. The proportions of the...
The FLAMES-ARE-US Co. manufactures butane cigarette lighters. Your top-of-the-line lighter, which has the brand name "SURE-FLAME," costs $\$ 29.95$. As a promotional strategy, the SURE-FLAME...
Central limit theorems have important applications in the area of quality control. One such application concerns so-called control charts, and in particular, $\bar{X}$ charts, which are used to...
The Central Processing Unit (CPU) in a laptop computer that your company manufactures is known to have the following service life characteristics: $P(x>s+t \mid x>s)=P(x>t) \forall s$ and...
Listed below are altitudes (thousands of feet) and outside air temperatures (F) recorded by the author during Delta Flight 1053 from New Orleans to Atlanta. For the prediction interval, use a 95%...
Question 6.10 Current and deferred tax worksheets and tax entries From the hip Ltd?s statement of profit or loss for the year ended 30 June 2007 and extracts from its statements of financial position...
The study reported 45 injuries to the upper extremity on a dry field consisting of artificial turf over the course of 10,112 games. What procedure can be used to assess whether the risk of injury is...
Provide a 95% CI for the rate of injury to the upper extremity on artificial turf. Express each rate as the number of injuries per 1000 games? Sports Medicine Injuries are common in football and may...
Her doctor is considering taking her off antihypertensive medications but wants to be fairly certain that her true DBP is less than 90 mm Hg. Use a statistical approach to answer this question....
7.) The COVID 19 epidemic has spurred the development of contactless check-in at hotels, which allows guests to carry out the entire check-in process using a smartphone. What effect might this new...
On May 1 of the current year, Grace, Laura, and Ann opened a business called Three Gals. Prior to opening Three Gals, they incurred the following costs: Purchase of fixtures $ 480 Accounting fees...
Define the political motivation behind New Deal Spending. Explain why political factors might lead to New Deal expenditures not going to the most needy. This question relates to the New Deal and...

The diagram shows the sector OAB of a circle of radius r cm. The area of the

Question:

T R 0 B

Step by Step Answer:

a x 151...View the full answer

Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

Students also viewed these Mathematics questions