∆BOC is equilateral, since both OC and OB are radii of the circle with length 4 cm. Then the angle subtended by the minor arc BC has measure 60°. (Note that OA is also a radius.) AB is a diameter of the circle, so the arc AB subtends an angle measuring 180°. This means the minor arc AC measures 120°.
Since ∆BOC is equilateral, its area is √3/4 (4 cm)² = 4√3 cm². The area of the sector containing ∆BOC is 60/360 = 1/6 the total area of the circle, or π/6 (4 cm)² = 8π/3 cm². Then the area of the shaded segment adjacent to ∆BOC is (8π/3 - 4√3) cm².
∆AOC is isosceles, with vertex angle measuring 120°, so the other two angles measure (180° - 120°)/2 = 30°. Using trigonometry, we find
where 
is the length of the altitude originating from vertex O, and so
where 
is the length of the base AC. Hence the area of ∆AOC is 1/2 (2 cm) (4√3 cm) = 4√3 cm². The area of the sector containing ∆AOC is 120/360 = 1/3 of the total area of the circle, or π/3 (4 cm)² = 16π/3 cm². Then the area of the other shaded segment is (16π/3 - 4√3) cm².
So, the total area of the shaded region is
(8π/3 - 4√3) + (16π/3 - 4√3) = (8π - 8√3) cm²
Answer:
The value of 
is 16.
Step-by-step explanation:
The given expression is 
.
Put x = 2 in the above expression as follows :
Hence, the final answer is 16.
12-3x+4y
You just have to simplify the equation
When the gradient of the slope is negative or positive, the slope is negative or positive respectively.
or if u wanna tell by looking at the straight line graph, then if it makes an acute angle with the x-axis it's positive, if it makes an obtuse angle with x-axis its negative.
the slope is zero when the graph is horizontal
then slope is undefined when eh graph is vertical.
hope this helps
