AD is an arc of a circle with centre C 1 and radius 6 cm. AB is
Question:
AD is an arc of a circle with centre C1 and radius 6 cm. AB is an arc of a circle with centre C2. The size of angle AC2D is 2π/3 radians.
Calculate
a) The radius of the circle with centre C2
b) The area of the shaded region ABD.
A 6 cm C₁ 2 rad 3 C₂ D B
Step by Step Answer:
ANSWER To solve this problem we will need to use some basic principles of circle geometry and trigonometry a To find the radius of the circle with cen...View the full answer
Complete Pure Mathematics 1 For Cambridge International AS & A Level
ISBN: 9780198427438
2nd Edition
Authors: Jean Linsky, Brian Western, James Nicholson
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
-
In the diagram, AB is an arc of a circle with centre O and radius 4cm. Angle AOB is radians. The point D on OB is such that AD is perpendicular to OB. The arc DC, with centre O, meets OA at C. i....
-
The diagram below shows a triangle ABC with AB = 10 cm, AC = 13 cm and angle BAC = 0.5 rad. BD is an arc of a circle with centre A and radius 10 cm. Find a) The length of arc BD b) The perimeter of...
-
The diagram shows a shape ABCD. The curve AB is an arc of a circle with centre D. Angle ADB is 0.75 rad. Find a) The length of the arc AB b) The area of the sector ADB c) The area of ABCD. A B 10 cm...
-
Answer the following question based on the information presented for Cloud 9 in the appendix to this text and the current and earlier chapters. You should also consider your answers to the case study...
-
Michael and Kevin want to buy chocolates. They can't agree on whether they want chocolatecovered almonds, chocolate-covered peanuts, or chocolate-covered raisins.They agree to create a mix. They...
-
The cable is subjected to a uniform loading of w = 250 lb/ft. Determine the maximum and minimum tension in the cable. 50 ft 6 ft
-
Design the suspension of a car such that the maximum vertical acceleration felt by the driver is less than \(2 g\) at all speeds between \(70 \mathrm{~km} / \mathrm{h}\) and \(140 \mathrm{~km} /...
-
Financial StatementsPrivate University. The following is the pre-closing trial balance for Horton University as of June 30, 2011. Additional information related to net assets and the statement of...
-
Examine the concept of process prioritization in the context of real-time operating systems. How do real-time processes differ in terms of scheduling, and what mechanisms are used to ensure that...
-
On December 31, 2023, Stilton Service Companys year-end, the unadjusted trial balance included the following items: Required 1. Prepare the adjusting entry on the books of Stilton Service Company to...
-
Express 4 cosx sinx in terms of cos x.
-
Given that sin 40 = 0.643 (3 s.f.) a) Write down another angle between 0 and 360 whose sine is 0.643 b) Write down two angles between 360 and 720 whose sine is 0.643.
-
Should estimation of the deadweight loss (DWL) be included in antitrust cases? Explain why the language of the Sherman Act is not necessarily an economic measurement of the deadweight loss. Is the...
-
Proponents of tort reform argue that increased tort liability has increased the practice of ____________ medicine.
-
If an insured is injured while driving a motor vehicle owned by someone other than the insured, whose coverage is considered primary and whose coverage is considered secondary?
-
What factors should be considered when assessing statistics?
-
True Or False If an insured is injured while in a vehicle owned by someone else, the insureds coverage will be used to pay her medical expenses up to the limits of their coverage.
-
True Or False The problems of the tort system cannot be resolved by simply gathering empirical evidence.
-
Calculate the heat released when 4.000 L Cl2 with a density of 2.46 g/L at 25oC reacts with an excess of sodium metal to form solid sodium chloride at 25oC.
-
Calculate Total Contribution Margin for the same items. Total Revenue Total Variable Costs Total Contribution Margin $50.00 a. $116.00 $329.70 b. $275.00 $14,796.00 $7,440.00 c. $40,931.25 d....
-
The total reserves of oil in the world are 1,689,078,618,100 barrels. The total reserves of the top 15 countries listed in Exercise 2.13 are 1,563,350,000,000 barrels. Use a graphical technique that...
-
The following table lists the average oil consumption per day of the top 20 oil-consuming nations. Use a graphical technique to display this information. Consumption of Oil (Barrels per Day) Country...
-
The production of steel has often been used as a measure of the economic strength of a country. The next table lists the steel produced in the 20 largest steel-producing nations in 2014. The units...
-
Mar 1 . Pasta House signed an $ 1 5 , 0 0 0 contract with Cosby Renovations to remodel the inside of the building. Pasta House paid $ 4 , 0 0 0 down and agreed to pay the remainder when Cosby...
-
On January 1, 2012, Adam Corp signed a 5-year non-cancellable lease for one (non-specialized) machine. The terms of this contract require annual payments of $9,968 at the beginning of each year...
-
On January 1, Dora purchases 175 of the $1,000, 7%, 15-year bonds issued by Splash City, with interest receivable semiannually on June 30 and December 31 each year. Assuming the market interest rate...
Study smarter with the SolutionInn App