Step-by-step explanation:
(a + b)² = 9
(b + c)² = 25
(a + c)² = 81
Taking the square root:
a + b = ±3
b + c = ±5
a + c = ±9
By adding these three equations together and dividing both sides by 2, we get the value of a + b + c.
Possible combinations for a + b + c such that the sum is greater than or equal to 1 are:
a + b + c = (-3 + 5 + 9)/2 = 11/2
a + b + c = (3 − 5 + 9)/2 = 7/2
a + b + c = (3 + 5 + 9)/2 = 17/2
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
Answer:
0.4
Step-by-step explanation:
15 = 5p - 13
-13 = 5p -13
---------------- ( subtract 13 on both sides )
<u> 2 = 5p</u>
5 = 5p
---------------- ( divide 2 by 5 )
p = 0.4
( p equals 0.4 )
Answer:
2.4 hours or 2 hours and 24 minutes
Step-by-step explanation:
Jack mows 1/6 of the lawn per hour while Marilyn mows 1/4 of the lawn together. Adding up those rates yields in their combined mowing rate:
The time required for them to mow the entire lawn is:
It would take them both 2.4 hours to mow the lawn together.
