I need to know the anawer
2 answers:
You might be interested in
Answer:
Yes, i believe that the generalization about the measure of a point angle of a star polygon is true.
First we find sum of interior angle of an n-sided star polygon.
number of triangle in a polygon = n - 2
sum of interior angle of a triangle = 180°
sum of interior angle of an n-sided star polygon = ( n - 2 ) × 180°
To find measure of a point angle, we use:
× 180°
To find a point angle we eliminate density by multiplying d by 2 in the formula for finding number of triangle, divide the whole by total number of sides and then multiply by the sum of interior angle of triangle(180°).
Since all the angle of a regular star polygon are equal, we can calculate each pointy interior angle of a regular star polygon using the formula given below:
× 180°
The expression as given doesn't make much sense. I think you're trying to describe an infinitely nested radical. We can express this recursively by
Then you want to know the value of
if it exists.
To show the limit exists and that converges to some limit, we can try showing that the sequence is bounded and monotonic.
Boundedness: It's true that . Suppose
. Then
. So by induction,
is bounded above by 7 for all
.
Monontonicity: We have and
. It should be quite clear that
. Suppose
. Then
. So by induction,
is monotonically increasing.
Then because is bounded above and strictly increasing, the limit exists. Call it
. Now,
Solve for :
We omit because our analysis above showed that
must be positive.
So the value of the infinitely nested radical is 7.