Answer:
32767 distinct color grouping
Step-by-step explanation:
Given data:
Total tube is 13
for distinct color, group can be 1,2,3,4,.... 15
For total number of ways we have following relation
here n = 13 so we have
for at least one
= 32767 distinct color grouping
Answer:
The Pythagorean identity states that
Using that we can rewrite the left denominator as:
Which can be factored as
The numerator we can expand as:
On the right hand side, let's multply numerator and denominator with (1 - sin t):
The total formula then becomes:
There you go... left and right are equal.