Difference between revisions of "2006 AMC 12A Problems/Problem 2"

Revision as of 22:03, 31 May 2009

The following problem is from both the 2006 AMC 12A #2 and 2006 AMC 10A #2, so both problems redirect to this page.

Problem

Define $x\otimes y=x^3-y$ . What is $h\otimes (h\otimes h)$ ?

$\mathrm{(A)}\ -h\qquad\mathrm{(B)}\ 0\qquad\mathrm{(C)}\ h\qquad\mathrm{(D)}\ 2h\qquad\mathrm{(E)}\ h^3$

Solution

By the definition of $\otimes$ , we have $h\otimes h=h^{3}-h$ . Then $h\otimes (h\otimes h)=h\otimes (h^{3}-h)=h^{3}-(h^{3}-h)=h$ . The answer is $\mathrm{(C)}$ .

2006 AMC 12A (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 12 Problems and Solutions

2006 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

@@ Line 1: / Line 1: @@
-{{duplicate|[[2006 AMC 12A Problems|2006 AMC 12A #2]] and [[2006 AMC 10A Problems/Problem 2|2008 AMC 10A #2]]}}
+{{duplicate|[[2006 AMC 12A Problems|2006 AMC 12A #2]] and [[2006 AMC 10A Problems/Problem 2|2006 AMC 10A #2]]}}
 == Problem ==
 Define <math>x\otimes y=x^3-y</math>. What is <math>h\otimes (h\otimes h)</math>?

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Difference between revisions of "2006 AMC 12A Problems/Problem 2"

Revision as of 22:03, 31 May 2009

Problem

Solution

See also