Answer:
190 possibilities.
Step-by-step explanation:
The problem is called 20 choose 2, given by the formula for combinations
C(20,2) = 20! / (2! (20-2)!) = 190
alternatively, we can reason it this way:
there are 20 choices to choose a captain and 19 choices for an alternate captain for a total of 380 ways.
However, there are 20 choices to choose an alternate captain and 19 choices for a captain for a total of 380 ways.
Since we are essentially double counting every choice of the posts, we need to divide 380 by 2 to get 190 ways.
 
        
             
        
        
        
This is completing the square:
(x^2+12x+36)+42-36
Answer: (x+6)^2 +6
        
             
        
        
        
Remember, 

, where 

 is circumference and tex]d[/tex] is the diameter. They are related by a constant 

 (pi).
We can solve the above equation for d and then substitute our known values.

 
 
        
        
        
A translation of right 3 up 1