Πr^2(h)
π(1.2)^2)(4)=18.1 ft^3
22*18.1=398.2
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
1/2, 3/8, 1/7 hopefully I am right I’m not sure
Answer:
$14.8
Step-by-step explanation:
There is a mistype in the question. It should say: ... <em>si cada uno de ellos hicieron una contribución de </em><em>dieciseis</em><em> pesos...</em>
So if everybody contributes $14, they make a total of 14*x, where x denotes the number of students. In this scenario, $4 are left, calling y to the cost of the trip, then:
14*x = y - 4 (eq. 1)
In the other scenario, everybody contributes $16 and $6 are in excess, so
16*x = y + 6 (eq. 2)
subtracting eq. 1 to eq. 2:
16*x - 14*x = y + 6 - (y - 4)
2*x = y + 6 - y + 4
2*x = 10
x = 10/2 = 5
Replacing this value in eq. 1:
14*5 = y - 4
70 + 4 = y
y = $74
If every student pays: 74/5 = $14.8, then they would get altogether the exact cost of the trip
Answer:
1 and 3, 2 and 4
Step-by-step explanation:
Supplementary angles total to 180° or should form a straight line. 1 and 3, 2 and 4 are vertical angles which equal one another and are not supplementary.
