Let's take a look at the first few numbers in the sequence based on the given rule:

Inspecting this pattern it seems like the power

is being raised to is always one less than the number of the sequence, so if we were on the nth number in the sequence, that part of the expression would be

. We also know that we'll be multiplying whatever we get from that by 6, so we can write the full explicit rule for our sequence as

Where

is the nth number in our sequence.
Answer:
2 x 2 x 7 = 28 2 x 2 x 2 x 5 = 40 2 x 2 x 2 x 2 x 3 x 3 = 144 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 = 504... ... The LCM of the given two numbers using prime factorization is 36 ...
Step-by-step explanation:
Cone details:
Sphere details:
================
From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.
<u>Using Pythagoras Theorem</u>
(a)
TO² + TU² = OU²
(h-10)² + r² = 10² [insert values]
r² = 10² - (h-10)² [change sides]
r² = 100 - (h² -20h + 100) [expand]
r² = 100 - h² + 20h -100 [simplify]
r² = 20h - h² [shown]
r = √20h - h² ["r" in terms of "h"]
(b)
volume of cone = 1/3 * π * r² * h
===========================




To find maximum/minimum, we have to find first derivative.
(c)
<u>First derivative</u>

<u>apply chain rule</u>

<u>Equate the first derivative to zero, that is V'(x) = 0</u>




<u />
<u>maximum volume:</u> <u>when h = 40/3</u>


<u>minimum volume:</u> <u>when h = 0</u>


Step-by-step explanation:

The variance of a distribution is the square of the standard deviation
The variance of the data is 2.2
<h3>How to calculate the variance</h3>
Start by calculating the expected value using:

So, we have:

This gives

Next, calculate E(x^2) using:

So, we have:


The variance is then calculated as:

So, we have:


Approximate

Hence, the variance of the data is 2.2
Read more about variance at:
brainly.com/question/15858152