What is 70-(-671) divided by 12
1 answer:
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Answer:
The length of one side of the octagon is 7.65 cm
Step-by-step explanation:
The parameters given are;
A regular octagon inscribed in a circle of radius, r, of 10 cm.
The length of each side is found from the isosceles triangle formed by the radius and one side of the octagon
The sum of interior angles in a polygon, ∑θ = 180 × (n - 2)
Where;
n = The number of sides of the polygon
θ = The interior angle of the polygon
For the octagon, we have;
n = 8, therefore;
∑θ = 180 × (8 - 2) = 1080
Given that there are eight equal angles in a regular octagon, we have;
∑θ = 8 × θ
= 1080
θ = 1080/8 = 135°
The sum of angles at the center of the circle = 360
Therefore, the angle at the center (tip angle) of the isosceles triangle formed by the radius and one side of the octagon = 360/8 = 45°
The base angles of the isosceles triangle is therefore, (180 - 45)/2 = 67.5° = θ/2
The length of the base of the isosceles triangle formed by the radius and one side of the octagon = The length of one side of the octagon
From trigonometric ratios, the length of the base of the isosceles triangle is therefore;
2 × r × cos(θ/2) = 2×10 × cos(67.5°) = 7.65 cm
The length of the base of the isosceles triangle = 7.65 cm = The length of one side of the octagon.
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following equation:
The inverse is the following (we calculate it by replacing f(x) by x and x by f(x)):
The domain would be the range of the original equation, and it would be the range of values that f(x) could take, which was from -4 to positive infinity, that is, f(x) ≥ -4.
Therefore, the domain is x ≥ -4.
So the correct answer is D.