Difference between revisions of "2004 AMC 10A Problems/Problem 2"

Revision as of 17:22, 11 September 2007

Problem

For any three real numbers $a$ , $b$ , and $c$ , with $b\neq c$ , the operation $\otimes$ is defined by: $\otimes(a,b,c)=\frac{a}{b-c}$ What is $\otimes$ $( \otimes$ $(1,2,3),$ $\otimes$ $(2,3,1),$ $\otimes$ $(3,1,2))$ ?

$\mathrm{(A) \ } -\frac{1}{2}\qquad \mathrm{(B) \ } -\frac{1}{4} \qquad \mathrm{(C) \ } 0 \qquad \mathrm{(D) \ } \frac{1}{4} \qquad \mathrm{(E) \ } \frac{1}{2}$

Solution

$\otimes$ $\left(\frac{1}{2-3}, \frac{2}{3-1}, \frac{3}{1-2}\right)=\displaystyle$ $\otimes$ $(-1,1,-3)=\frac{-1}{1+3}=-\frac{1}{4}\Longrightarrow\mathrm{(B)}$

2004 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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All AMC 10 Problems and Solutions

@@ Line 1: / Line 1: @@
 == Problem ==
-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:
+For any three [[real number]]s <math>a</math>, <math>b</math>, and <math>c</math>, with <math>b\neq c</math>, the [[operation]] <math>\otimes</math> is defined by:
 <math>
 \otimes(a,b,c)=\frac{a}{b-c}
@@ Line 9: / Line 9: @@
 == Solution ==
-<math>\otimes</math><math>(\frac{1}{2-3}, \frac{2}{3-1}, \frac{3}{1-2})=</math><math>\otimes</math><math>(-1,1,-3)=\frac{-1}{1+3}=-\frac{1}{4}\Longrightarrow\mathrm{(B)}</math>
+<math>\otimes</math><math> \left(\frac{1}{2-3}, \frac{2}{3-1}, \frac{3}{1-2}\right)=\displaystyle</math><math>\otimes</math><math>(-1,1,-3)=\frac{-1}{1+3}=-\frac{1}{4}\Longrightarrow\mathrm{(B)}</math>
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Difference between revisions of "2004 AMC 10A Problems/Problem 2"

Revision as of 17:22, 11 September 2007

Problem

Solution

See also