Calculate, correct to one decimal place, the length of the line joining points X(3, 5) and Y(5, 1).

If \(y = 2(2x + \sqrt{x})^{2}\), find \(\frac{\mathrm d y}{\mathrm d x}\).

Calculate, correct to one decimal place, the acute angle between the lines 3x - 4y + 5 = 0 and 2x + 3y - 1 = 0.

Evaluate \(\int_{1}^{2} \frac{4}{x^{3}} \mathrm {d} x\)

If \(\begin{vmatrix} 3 & x \\ 2 & x - 2 \end{vmatrix} = -2\), find the value of x.