The tangent to the curve \(y = 4x^{3} + kx^{2} - 6x + 4\) at the point P(1, m) is parallel to the x- axis, where k and m are constants. Determine the coordinates of P.

Given that \(\log_{2} y^{\frac{1}{2}} = \log_{5} 125\), find the value of y.

Two vectors m and n are defined by \(m = 3i + 4j\) and \(n = 2i - j\). Find the angle between m and n.

Find the area of the circle whose equation is given as \(x^{2} + y^{2} - 4x + 8y + 11 = 0\).

Two bodies of masses 8 kg and 5 kg travelling in the same direction with speeds x m/s and 2 m/s respectively collide. If after collision, they move together with a speed of 3.85 m/s, find, correct to the nearest whole number, the value of x.