The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².
The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines
b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°) ⇒ b = 96√3 cm
Call b the base of this triangle.
The vertex angle is 120°, so the other two angles have measure θ such that
120° + 2θ = 180°
since the interior angles of any triangle sum to 180°. Solve for θ :
2θ = 60°
θ = 30°
Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find
tan(30°) = h / (b/2) ⇒ h = 48 cm
Then the area of the triangle is
1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²
and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:
3072π cm² - 2304√3 cm² ≈ 5660.3 cm²
Answer: The equation parallel to the line is y=3x+8
Step-by-step explanation: Parallel lines have the same gradients, wr have a gradient for the above line which 3. The standard formula for the linear equation is y=mx+c
We have to calculate c since we have x and y.
y=mx+c
5= 3(-1)+c
c=8
The equation become y=3x+8
I would say it’s B because out of ten it makes the mean 1 point higher
Answer:
My boy or girl everyone know that its 4
Step-by-step explanation:
With pythagorean theorem and working backwards, you do 8100-1225 to get 6875, you then get the square root of that to get x=82.91 or rounded to 82.92
