Difference between revisions of "2004 AMC 10A Problems/Problem 2"
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== Problem == | == Problem == | ||
| − | For any three | + | For any three real numbers <math>a</math>, <math>b</math>, and <math>c</math>, with <math>b\neq c</math>, the operation <math>\otimes</math> is defined by: |
| − | < | + | <cmath>\otimes(a,b,c)=\frac{a}{b-c}</cmath> |
| − | \otimes(a,b,c)=\frac{a}{b-c} | + | What is <math>\otimes(\otimes(1,2,3),\otimes(2,3,1),\otimes(3,1,2))</math>? |
| − | </ | ||
| − | What is <math>\otimes | ||
<math> \mathrm{(A) \ } -\frac{1}{2}\qquad \mathrm{(B) \ } -\frac{1}{4} \qquad \mathrm{(C) \ } 0 \qquad \mathrm{(D) \ } \frac{1}{4} \qquad \mathrm{(E) \ } \frac{1}{2} </math> | <math> \mathrm{(A) \ } -\frac{1}{2}\qquad \mathrm{(B) \ } -\frac{1}{4} \qquad \mathrm{(C) \ } 0 \qquad \mathrm{(D) \ } \frac{1}{4} \qquad \mathrm{(E) \ } \frac{1}{2} </math> | ||
Revision as of 17:21, 20 July 2014
Problem
For any three real numbers 
, 
, and 
, with 
, the operation 
is defined by:
![\[\otimes(a,b,c)=\frac{a}{b-c}\]](http://latex.artofproblemsolving.com/8/c/0/8c07fc892fc41e343f30a1c44dea8ea14edce4c9.png)
What is 
?
Solution
See also
| 2004 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
