Answer:
870
Step-by-step explanation:
$435 + $395 = $830
$830 + $10 = $840
$2 x 15 = $30
$840 + $30 = $870
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DOGE
<u>EXPLANATION</u><u>:</u>
Given set A = { 1,2,3}
n(A) = 3
Let the n(B) be n
Total number of relations from A to B = 2^(3×n) =2^3n
According to the given problem
Total relations are = 512
⇛2^3n = 512
⇛2^3n = 2⁹
If bases are equal then exponents must be equal
⇛3n = 9
⇛n = 9/3
⇛n = 3
<h3>So, Number of elements in the set B = 3</h3>
Answer:
C) 
The slope of the perpendicular line
Step-by-step explanation:
<u><em>Explanation:-</em></u>
Given that the slope of the given line is
The slope of the perpendicular line
= 
The slope of the perpendicular line
= 
<u><em>Final answer</em></u>
The slope of the perpendicular line
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
