Plugging $x=2$ into the expression for $f(x)$, we find $f(2)=c(2^3)-9(2)+3=8c-18+3=8c-15$. Since we know that $f(2)=9$, \begin{align*} f(2)&= 9
\\\Rightarrow\qquad8c-15&=9
\\\Rightarrow\qquad8c&=24
\\\Rightarrow\qquad c&=\boxed{3}
\end{align*}
Given $f(x)=cx^3-9x+3$ and $f(2)=9$, find the value of $c$.
{'answer': '3', 'subject': 'Algebra', 'level': 3, 'unique_id': 'test/algebra/148.json'}