In triangle XYZ, |XY| = 10cm, |YZ| = 9 cm and |XZ| = 7 cm. If XZY = \(\alpha\), find the value of cos \(\alpha\).

If y\(^2\) + 2xy - 8 = 0, find \(\frac{dy}{dx}\)

The mean of four numbers is 5 and the mean of another three numbers is 12. Find the mean of the seven numbers.

Find, correct to the nearest degree, the acute angle between 3x - y - 5 = 0, and 7x - y - 3 = 0

The gradient of a curve is given by 3x\(^2\) - 8x + 2. If the curve passes through P(0, 4), find the equation of the curve.