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CaHeK987 [17]
3 years ago
8

Select the correct answer from each drop down menu. Complete the statements about the closure of sets.

Mathematics
1 answer:
anygoal [31]3 years ago
4 0

Answer:

not closed

included

closed

included

Step-by-step explanation:

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A regular octagon is inscribed in a circle with a radius of 10 cm. What is the length of one side of the octagon?
Semenov [28]

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_i = 180 × (n - 2)

Where;

n = The number of sides of the polygon

θ_i = The interior angle of the polygon

For the octagon, we have;

n = 8, therefore;

∑θ_i = 180 × (8 - 2) = 1080

Given that there are eight equal angles in a regular octagon, we have;

∑θ_i = 8 × θ_i = 1080

θ_i = 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_i/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_i/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.

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3 years ago
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lakkis [162]

Answer:

16,20,24,28,32,36,40

Step-by-step explanation:

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3 years ago
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Image Above.........
Savatey [412]

Answer:

4 : 39

5 : 52

6 : 67

7 : 77

Step-by-step explanation:

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2 years ago
What is the answer for this
Lady bird [3.3K]

The equation that represents this hanger is: 4w=25

The weight of one circle is: 6.25

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3 years ago
Explain the steps you would take to complete this conversion problem.
ohaa [14]
I would multiply 46x1x1,000 to get 46,000. the. i would multiply 1x2.2x1 to get 2.2. i would then divide 46,000/2.2 to get 20,909.0909
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3 years ago
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