Difference between revisions of "2006 AMC 12A Problems/Problem 4"

Revision as of 23:24, 9 July 2006

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

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

Plugging our values in the function, we have

$\displaystyle h^3-h$

Plugging in the function once more, we have

$\displaystyle h^3-(h^3-h)=h, (C)$

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-#REDIRECT [[2006 AMC 12A Problems\Problem 4]]
+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]]