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:
3 <_ x
Step-by-step explanation:
multiply both sides by 15
1/5 * 15 <_ x
15/5 <_ x
3 <_ x
Answer:
10 miles per hour.
Step-by-step explanation:
Let x represent athlete's walking speed.
We have been given that her jogging rate is 5 mph faster than her walking rate, so athlete's jogging speed would be
miles per hour.

10 minutes = 1/6 hour.
20 minutes = 1/3 hour
While walking, we will get 

While jogging, we will get 

Since athlete is covering same distance while walking and jogging, so we can equate both expressions as:

Cross multiply:




Therefore, athlete's walking speed is 5 miles per hour.
Jogging speed: 
Therefore, athlete's jogging speed is 10 miles per hour.
Answer:
to do it 5 x 10 x 4 x 5 x 6 x 7 x 3 x 2 3 x 4 x5
Step-by-step explanation:
x 3x 3x 3x3 x4 x4x4 x4x to the power of 5 million
Answer:
Label the y-axis Charms and the x-axis Beads
Step-by-step explanation: