Answer:
Minimum angle = 108°
Step-by-step explanation:
From the figure attached,
Minimum angle to overlap the star onto itself is the angle of rotation from point A to B.
Let the angle between A and B measure a°.
If we complete a star pentagon by joining the vertices of the star,
Formula to measure the internal angle of a polygon is,
Measure of internal angle = 
Measure of ∠ABC = 
= 108°
Since, one side star divides the interior angle into three equal parts,
Measure of interior angle = 
= 36°
From ΔAOB,
m(∠OAB) + m(∠AOB) + m(∠ABO) = 180° [Sum of interior angles of a triangle = 180°]
36° + a + 36° = 180°
a + 72° = 180°
a = 180 - 72
a = 108°
Therefore, by the minimum angle of rotation of 108° star will overlap onto itself.
Answer:
Step-by-step explanation:
x^2=-6
x=
Answer:
Solution : Option D
Step-by-step explanation:
Let's start by listing two cases made possible when r is positive, in ( r, θ ). Remember that in polar coordinates a point is expressed in an ordered pair, where r is the distance from the pole (in this case 9, as it lies on the 9th circle) and theta is the directed angle from the positive x - axis.
( 9, θ ) here theta will be the angle to the terminal side with respect to the positive x - axis. This angle will be 60 degrees more than 90, or 90 + 60 = 150 degrees
( 9, θ ) and here theta will be the remaining degrees, or 360 - 150 = 210 degrees. Right away your solution will be (9, 210°)
Based on the terms of the invoice, the gross amount on the invoice and the date of payment, the cash discount is $19 and the net amount paid is $931.
<h3 /><h3>What is the cash discount?</h3>
The terms of the invoice are such that if the person pays within 10 days they get a 3% discount. If they pay in 15 days, they get a 2% discount.
The person paid on the 22nd after buying on the 8th so they qualify for the 2% for paying within 15 days.
The cash discount is:
= 2% x 950
= $19
The net amount paid is:
= 950 - 19
= $931
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