There is no algorithm which has a runtime of $O(n^2)$ and $\Theta(n^\frac{7}{2})$

Question

How can I proof that there exists no algorithm which has a runtime of $O(n^2)$ and $\theta(n^{\frac{7}{2}})$?

Or is this possible because logically I would say that if a function is $O(n^{\frac{7}{2}})$ then it is also $O(n^2)$.

Answer 1

HINT: $n^{3.5}>n^{2}$ for $n>1$