2006 AMC 10A Problems/Problem 2: Difference between revisions

Revision as of 08:14, 28 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 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 $(C)$ .

@@ Line 4: / Line 4: @@
 <math> \mathrm{(A) \ } -h\qquad \mathrm{(B) \ } 0\qquad \mathrm{(C) \ } h\qquad \mathrm{(D) \ } 2h\qquad \mathrm{(E) \ } h^3 </math>
 == Solution ==
-Plugging our values in the function, we have
+Plugging our values into the defined [[operation]], we have
-<center><math>\displaystyle h^3-h</math></center>
+<center><math>\displaystyle h\otimes h = h^3-h</math></center>
-Plugging in the function once more, we have
+Plugging in the [[function]] once more, we have
-<center><math>\displaystyle h^3-(h^3-h)=h,
+<center><math>\displaystyle h\otimes(h\otimes h) = h\otimes (h^3 - h) = h^3-(h^3-h)=h</math></center>
-(C)</math></center>
+which is choice <math>(C)</math>.
 == See Also ==
 *[[2006 AMC 10A Problems]]