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:
$7562.50
Step-by-step explanation:
4700 (1.0825)^7-1
Answer:cab
Step-by-step explanation:
Answer:
1: n > -75
2: n < -12
Step-by-step explanation:
1: n/-3 - 8 < 17
n/-3 (- 8 + 8) < 17 + 8
n/-3 < 25
n/-3(-3) < 25(-3)
n < -75
n > -75 (switch symbol when you divide or multiply by a negative number)
2: n/-2 + 11 > 17
n/-2 (+ 11 - 11) > 17 - 11
n/-2 > 6
n/-2(-2) > 6(-2)
n > -12
n < -12 (switch symbol when you divide or multiply by a negative number)
Answer:
Step-by-step explanation:
y^2-22y+c
complete the square ax^2+bx+c is our old formula quadratic equation
we know that to find c we will divide b/2 and square it
22/2=11
c^2=121
we have y^2-22y+121
