Solve \(9^{2x + 1} = 81^{3x + 2}\)
The inverse of a function is given by \(f^{-1} : x \to \frac{x + 1}{4}\).
If \(\begin{pmatrix} 3 & 2 \\ 7 & x \end{pmatrix} \begin{pmatrix} 2 \\ 3 \end{pmatrix} = \begin{pmatrix} 12 \\ 29 \end{pmatrix} \), find x.
The fourth term of a geometric sequence is 2 and the sixth term is 8. Find the common ratio.
What percentage increase in the radius of a sphere will cause its volume to increase by 45%?
