Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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

m (→‎Solution)
m (added category and link to previous and next problem)
Line 16: Line 16:
 
== See Also ==
 
== See Also ==
 
*[[2006 AMC 10A Problems]]
 
*[[2006 AMC 10A Problems]]
 +
 +
*[[2006 AMC 10A Problems/Problem 1|Previous Problem]]
 +
 +
*[[2006 AMC 10A Problems/Problem 3|Next Problem]]
 +
 +
[[Category:Introductory Algebra Problems]]

Revision as of 15:36, 4 August 2006

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2006_AMC_10A_Problems/Problem_2&oldid=9227"