Answer:
The numbers of measure of music played are 1 and 7
Step-by-step explanation:
Given
Required
Solve for x when s = 80
Substitute 80 for x
Subtract 50 from both sides
Divide through by 10
Reorder
This can be split into
or
Solve for x
or
or
Hence:
<em>The numbers of measure of music played are 1 and 7</em>
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.