Answer:
There were 28 parents in the audience.
Step-by-step explanation:
So basically we have to find out what 1/3 of 84 is.
So to find out what 1/3 of 84 is, I will divide 84 ÷ 3 = 28
So 1/3 of 84 is 28
Answer:
v=8
Step-by-step explanation:
Answer:
The series is absolutely convergent.
Step-by-step explanation:
By ratio test, we find the limit as n approaches infinity of
|[a_(n+1)]/a_n|
a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)
a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)
[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]
= |-3n³/2(n+1)³|
= 3n³/2(n+1)³
= (3/2)[1/(1 + 1/n)³]
Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity
= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity
= 3/2 × 1
= 3/2
The series is therefore, absolutely convergent, and the limit is 3/2
Answer:
a) XY , XVY
b) 248°
c) UV , UY
d) 6√5 = 13.42
Step-by-step explanation:
a) The minor arc is XY
The major arc is XVY
b) ∵ The measure of the minor arc is 112°
∵ The measure of the circle is 360°
∴ The measure of the rest arc = 360 - 112 = 248°
c) UV is the tangent to the circle
UY is the secant to the circle
d) ∵ UV is a tangent to the circle at V
∵ UY is a secant to the circle
∴ (UV)² = (UX) × (UY)
∵ UX = 9 and XY = 11 ⇒ ∴ UY = 11 + 9 = 20
∴ (UV)² = 9 × 20 = 180
∴ UV = √180 = 6√5 = 13.42