Differentiate \(x^{2} + xy - 5 = 0\).
The fourth term of an exponential sequence is 192 and its ninth term is 6. Find the common ratio of the sequence.
Find the range of values of x for which \(x^{2} + 4x + 5\) is less than \(3x^{2} - x + 2\)
Given that \(\frac{\mathrm d y}{\mathrm d x} = \sqrt{x}\), find y.
Given that \(P = \begin{pmatrix} y - 2 & y - 1 \\ y - 4 & y + 2 \end{pmatrix}\) and |P| = -23, find the value of y.
