Answer:
- The shaded region is 9.83 cm²
Step-by-step explanation:
<em>Refer to attached diagram with added details.</em>
<h2>Given </h2>
Circle O with:
- OA = OB = OD - radius
- OC = OD = 2 cm
<h2>To find</h2>
<h2>Solution</h2>
Since r = OC + CD, the radius is 4 cm.
Consider right triangles OAC or OBC:
- They have one leg of 2 cm and hypotenuse of 4 cm, so the hypotenuse is twice the short leg.
Recall the property of 30°x60°x90° triangle:
- a : b : c = 1 : √3 : 2, where a- short leg, b- long leg, c- hypotenuse.
It means OC: OA = 1 : 2, so angles AOC and BOC are both 60° as adjacent to short legs.
In order to find the shaded area we need to find the area of sector OADB and subtract the area of triangle OAB.
Area of <u>sector:</u>
- A = π(θ/360)r², where θ- central angle,
- A = π*((mAOC + mBOC)/360)*r²,
- A = π*((60 + 60)/360))(4²) = 16.76 cm².
Area of<u> triangle AO</u>B:
- A = (1/2)*OC*(AC + BC), AC = BC = OC√3 according to the property of 30x60x90 triangle.
- A = (1/2)(2*2√3)*2 = 4√3 = 6.93 cm²
The shaded area is:
- A = 16.76 - 6.93 = 9.83 cm²
8x - 3/x
x = 1/2
(8 • 1/2) - 3/0.5
4 - 1.5
2.5
Answer:
1/8
Step-by-step explanation:
(6(3)⁻¹(1))⁻³ n⁰=1
(6/3)⁻³
(2)⁻³
1/(2)³
1/8
Hope it helps
Take the price of pears (£1.30 per kilogram) and multiply it by the amount of pears (7kg). You get 9.1 so now you take the total amount spent (£12.70) and subtract the 9.1 and you get 3.6 now that is the amount you spent on the apples. So take 3.6 and divide it by the amount of apples you got (2kg) you will get 1.8 and that is your overall answer.