Answer:
The diameter of the circumscribed circle is 6.92
Step-by-step explanation:
In the question, we are asked to calculate the diameter of a circle, which has a an equilateral triangle inscribed in it.
To solve this problem, let us consider the diagram attached.
Now let’s assume the point o is the center of the circle and that r is the radius of the circle. Now to calculate this radius, we need to employ the use of a trigonometrical ratio.
According to the question, we can see that we have the adjacent and the hypotenuse, so the trigonometric identity to use is the cosine.
Mathematically;
Cosine 30 = 3/r
r = 3/cosine 30
Cosine 30 = 0.866
r = 3/0.866
r = 3.46
But in the question, we were asked to calculate the diameter and not the radius.
Mathematically; d = 2r = 2 * 3.46 = 6.92
Given:
The given sequence is:
To find:
The recursive formula for , the nth term of the sequence.
Solution:
We have,
Here, the first term is 5.
The common difference is -7.
The recursive formula for the nth term of the sequence is
Where, is the common difference.
Putting in the above formula, we get
Therefore, the recursive formula for the nth term of the sequence is .