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The third of geometric progression (G.P) is 10 and the sixth term is 80. Find the common ratio.
Given that \(P = {x : \text{x is a factor of 6}}\) is the domain of \(g(x) = x^{2} + 3x - 5\), find the range of x.
If \(\begin{vmatrix} 3 & x \\ 2 & x - 2 \end{vmatrix} = -2\), find the value of x.
Evaluate \(\int_{1}^{2} \frac{4}{x^{3}} \mathrm {d} x\)
Calculate, correct to one decimal place, the acute angle between the lines 3x - 4y + 5 = 0 and 2x + 3y - 1 = 0.
If \(y = 2(2x + \sqrt{x})^{2}\), find \(\frac{\mathrm d y}{\mathrm d x}\).
Calculate, correct to one decimal place, the length of the line joining points X(3, 5) and Y(5, 1).
For what values of x is \(\frac{x^{2} - 9x + 18}{x^{2} + 2x - 35}\) undefined?
If \(\sin x = -\sin 70°, 0° < x < 360°\), determine the two possible values of x.
If (x - 3) is a factor of \(2x^{2} - 2x + p\), find the value of constant p.
The roots of a quadratic equation are \((3 - \sqrt{3})\) and \((3 + \sqrt{3})\). Find its equation.
The coefficient of the 7th term in the binomial expansion of \((2 - \frac{x}{3})^{10}\) in ascending powers of x is
Simplify \(\frac{\log_{5} 8}{\log_{5} \sqrt{8}}\).
If \(16^{3x} = \frac{1}{4}(32^{x - 1})\), find the value of x.
If \(\frac{5}{\sqrt{2}} - \frac{\sqrt{8}}{8} = m\sqrt{2}\), where m is a constant. Find m.
Find the value of \(\cos(60° + 45°)\) leaving your answer in surd form.
Find the domain of \(f(x) = \frac{x}{3 - x}, x \in R\), the set of real numbers.
In the diagram, a ladder PS leaning against a vertical wall PR makes angle x° with the horizontal floor. The ladder slides down to a point QT such that angle QTR = 30° and SNT = y°. Find an expression for tan y.
In the diagram, a ladder PS leaning against a vertical wall PR makes angle x° with the horizontal floor. The ladder slides down to a point QT such that angle QTR = 30° and SNT = y°. Find the relation between x and y.
A body is acted upon by forces \(F_{1} = (10 N, 090°)\) and \(F_{2} = (6 N, 180°)\). Find the magnitude of the resultant force.