Forces 50N and 80N act on a body as shown in the diagram. Find, correct to the nearest whole number, the horizontal component of the resultant force.

If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 6x + 5 = 0\), evaluate \(\frac{\beta}{\alpha} + \frac{\alpha}{\beta}\).

Express \(\log \frac{1}{8} + \log \frac{1}{2}\) in terms of \(\log 2\).

Given that \(a^{\frac{5}{6}} \times a^{\frac{-1}{n}} = 1\), solve for n.

Find the third term in the expansion of \((a - b)^{6}\) in ascending powers of b.

If \(f(x) = x^{2}\) and \(g(x) = \sin x\), find g o f.

Solve: \(\sin \theta = \tan \theta\)

A binary operation * is defined on the set of real numbers, R, by \(x * y = x + y - xy\). If the identity element under the operation * is 0, find the invers...

If \(\sqrt{x} + \sqrt{x + 1} = \sqrt{2x + 1}\), find the possible values of x.