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

Revision as of 02:35, 11 September 2007

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 $(C)$ .

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 14: / Line 14: @@
 which is choice <math>(C)</math>.
-== See Also ==
+== See also ==
-*[[2006 AMC 10A Problems]]
+{{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]]