Difference between revisions of "2006 AMC 12A Problems/Problem 4"
m (2006 AMC 12A Problem 4 moved to 2006 AMC 12A Problems/Problem 4: subpage) |
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− | + | Define <math>x\otimes y=x^3-y</math>. What is <math>h\otimes (h\otimes h)</math> | |
+ | <center><math> \mathrm{(A) \ } -h\qquad \mathrm{(B) \ } 0\qquad \mathrm{(C) \ } h\qquad \mathrm{(D) \ } 2h\qquad \mathrm{(E) \ } h^3 </math></center> | ||
+ | |||
+ | == Solution== | ||
+ | Plugging our values in the function, we have | ||
+ | |||
+ | <center><math>\displaystyle h^3-h</math></center> | ||
+ | |||
+ | Plugging in the function once more, we have | ||
+ | |||
+ | <center><math>\displaystyle h^3-(h^3-h)=h, | ||
+ | (C)</math></center> | ||
+ | |||
+ | == See also == | ||
+ | |||
+ | * [[2006 AMC 12A Problems]] |
Revision as of 00:24, 10 July 2006
Define . What is
![$\mathrm{(A) \ } -h\qquad \mathrm{(B) \ } 0\qquad \mathrm{(C) \ } h\qquad \mathrm{(D) \ } 2h\qquad \mathrm{(E) \ } h^3$](http://latex.artofproblemsolving.com/3/b/c/3bcdc4ebc622a47d77d1ccf593c31d7ecc819aad.png)
Solution
Plugging our values in the function, we have
![$\displaystyle h^3-h$](http://latex.artofproblemsolving.com/c/e/1/ce1167e0a0c5b51a4385e01e624dbce035d70e39.png)
Plugging in the function once more, we have
![$\displaystyle h^3-(h^3-h)=h, (C)$](http://latex.artofproblemsolving.com/d/1/d/d1d5f5760ef436efef9ca946680769a65de174c4.png)