Answer:
StartFraction pi Over 3 EndFraction
Step-by-step explanation:
we know that
The circumference of a circle subtends a central angle of 360 degrees or 2π radians
so
by proportion
Find out the central angle for an arc equal to One-sixth of the circumference of a circle
Let
x -----> the measure of the central angle in radians for an arc equal to One-sixth of the circumference

Simplify

therefore
StartFraction pi Over 3 EndFraction
A fact family is a group of math facts using the same numbers. In the case of addition/subtraction, you use three numbers and get four facts. For example, you canform a fact family using the threenumbers 10, 2, and 12: 10 + 2 = 12, 2 + 10 = 12, 12 − 10 = 2, and 12 − 2 = 10.
Answer:
D
Step-by-step explanation:
The diagram is composed of one large right triangle and inside it it's divided into 2 small right triangles. Since these triangles all have the same shape but not the same size, they are similar triangles. Using similar triangles, create a proportion of side lengths. A proportion is an equation with equal ratios from the large triangle to a small. Notice the large triangle has a hypotenuse of 6+7 = 13 and a leg of x. The small triangle has a hypotenuse of x and a leg of 7.


To solve for x, cross multiply the numerator with the denominator.

Answer:
Seventeen
Step-by-step explanation:
Answer:
Convergent
Step-by-step explanation:
This is an alternating series where bn = 2n / eⁿ. Apply the alternating series test:
lim(n→∞) bn
= lim(n→∞) (2n / eⁿ)
Use L'hopital's rule:
= lim(n→∞) (2 / eⁿ)
= 0
For n ≥ 1, the series is decreasing. 2(n+1) / eⁿ⁺¹ < 2n / eⁿ.
Therefore, the series converges.