Difference between revisions of "2004 AMC 10A Problems/Problem 2"
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\otimes(a,b,c)=\frac{a}{b-c} | \otimes(a,b,c)=\frac{a}{b-c} | ||
</math> | </math> | ||
| − | What is <math>\otimes< | + | What is <math>\otimes<cmath>( \otimes</cmath>(1,2,3),<cmath>\otimes</cmath>(2,3,1),<cmath>\otimes</cmath>(3,1,2))</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> | <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> | ||
== Solution == | == Solution == | ||
| − | <math>\otimes< | + | <math>\otimes<cmath> \left(\frac{1}{2-3}, \frac{2}{3-1}, \frac{3}{1-2}\right)=</cmath>\otimes</math><math>(-1,1,-3)=\frac{-1}{1+3}=-\frac{1}{4}\Longrightarrow\mathrm{(B)}</math> |
== See also == | == See also == | ||
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[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Revision as of 10:27, 4 July 2013
Problem
For any three real numbers 
, 
, and 
, with 
, the operation 
is defined by:
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. 
