If \(X\) and \(Y\) are two independent events such that \(P (X) = \frac{1}{8}\) and \(P (X ⋃ Y) = \frac{5}{8}\), find \(P (Y)\).

Find the radius of the circle \(2x^2 + 2y^2 - 4x + 5y + 1 = 0\)

The distance S metres moved by a body in t seconds is given by \(S = 5t^3 - \frac{19}{2} t^2 + 6t - 4\). Calculate the acceleration of the body after 2 seconds

If\((\frac{1}{9})^{2x-1} = (\frac{1}{81})^{2-3x}\)find the value of x

Given that \(sin x = \frac{4}{5}\) and \(cos y = \frac{12}{13}\), where x is an obtuse angle and y is an acute angle, find the value of sin (x - y).

Evaluate \(\int^1_0 x(x^2-2)^2 dx\)

Find the equation of the normal to the curve y = \(3x^2 + 2\) at point (1, 5).

Calculate, correct to one decimal place, the angle between 5 i + 12 j and -2 i + 3 j

The table shows the operation * on the set {x, y, z, w}. * X Y Z W X Y Z X W Y Z W Y X Z X Y Z W W W X W Z Find the identity of the element.