Let <em>a</em> be the first term in the sequence. If <em>r</em> is the ratio between consecutive terms, then the second term is <em>ar</em>, the third term is <em>ar </em>^2, the fourth is <em>ar</em> ^3, and so on, up to the <em>n</em>-th term <em>ar</em> ^(<em>n</em> - 1).
So the third, fourth, and fifth terms are such that
<em>ar</em> ^2 = 18
<em>ar</em> ^3 = 27
<em>ar</em> ^4 = 81/2
Solve for <em>a</em> and <em>r</em> :
(<em>ar</em> ^3) / (<em>ar</em> ^2) = 27/18 => <em>r</em> = 3/2
<em>ar</em> ^2 = <em>a</em> (3/2)^2 = 9/4 <em>a</em> = 18 => <em>a</em> = 8
Then the <em>n</em>-th term in the sequence is
<em>ar</em> ^(<em>n</em> - 1) = 9 (3/2)^(<em>n</em> - 1)
You can rewrite this by first rewriting 9 = 3^2, then
9 (3/2)^(<em>n</em> - 1) = 3^2 * 3^(<em>n</em> - 1) / 2^(<em>n</em> - 1) = 3^(<em>n</em> + 1)/2^(<em>n</em> - 1)
The drain pipe can drain (1/2) of the tank in 1 hour.
The fill pipe can fill (1/6) of the tank in 1 hour.
Working together, the pipes will drain the tank in (1/2) - (1/6) hours.
(1/2) - (1/6) = (3/6) -(1/6) = (2/6) or (1/3) of an hour.
So, working together, it will take 3 hours.
Uh idek but i think the relationship is that x is plus 1 every time and y is plus 4 every time
Answer:
119.64m^3
Step-by-step explanation:
Given that
The height is 12.7 m
And the base with the circumference is 18.9 m
We need to find out the volume of the right circular cone
As for determining it first compute the radius
As we know that
Circumference = 2πr
18.9 = 2 × 3.14 × r
r = 3m
Now the volume is
= 1 ÷ 3πr^2h
= 1 ÷ 3 × 3.14 × 3^2 × 12.7
= 119.64m^3
