Answer:
Step-by-step explanation:
GIVEN: A hotel charges a 
annual fee plus an additional 
for each night you stay there.
TO FIND: average cost per night if you stay at the hotel for 
nights.
SOLUTION:
Annual fee charged by hotel 
amount charged each night we stay there 
Total number of nights we stay 
Total amount paid for nights
Total amount paid 
average cost per night 
putting values,
average cost per night 
Hence average cost per night if we stay at hotel for days is
Answer:
15*(1+root(3))
Step-by-step explanation:
BD=5, BC=5*root(3), you can find it by using trigonometry.
AC^2=300, AC=10*root(3)
AB^2=225, AB=15.
Perimeter of ABC is AB+BC+CA=15+5*root(3)+10*root(3).
15(1+root(3))
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
