Difference between revisions of "2006 AMC 10A Problems/Problem 2"

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which is choice <math>(C)</math>.
 
which is choice <math>(C)</math>.
  
== See Also ==
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== See also ==
*[[2006 AMC 10A Problems]]
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{{AMC10 box|year=2006|ab=A|num-b=1|num-a=3}}
 
 
*[[2006 AMC 10A Problems/Problem 1|Previous Problem]]
 
 
 
*[[2006 AMC 10A Problems/Problem 3|Next Problem]]
 
  
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]

Revision as of 02:35, 11 September 2007

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

Plugging our values into the defined operation, we have

$\displaystyle h\otimes h = h^3-h$

Plugging in the function once more, we have

$\displaystyle h\otimes(h\otimes h) = h\otimes (h^3 - h) = h^3-(h^3-h)=h$

which is choice $(C)$.

See also

2006 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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All AMC 10 Problems and Solutions
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