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Express (14N, 240°) as a column vector.
Evaluate \(\frac{\tan 120° + \tan 30°}{\tan 120° - \tan 60°}\)
Find \(\lim\limits_{x \to 3} (\frac{x^{3} + x^{2} - 12x}{x^{2} - 9})\)
Find the distance between the points (2, 5) and (5, 9).
A ball is thrown vertically upwards with a velocity of 15\(ms^{-1}\). Calculate the maximum height reached. \([g = 10ms^{-2}]\)
If the points (-1, t -1), (t, t - 3) and (t - 6, 3) lie on the same straight line, find the values of t.
Find the variance of 1, 2, 0, -3, 5, -2, 4.
In how many ways can 9 people be seated on a bench if only 3 places are available?
A particle accelerates at 12\(ms^{-2}\) and travels a distance of 250m in 6 seconds. Find the initial velocity of the particle.
For what values of m is \(9y^{2} + my + 4\) a perfect square?
The first term of a linear sequence is 9 and the common difference is 7. If the nth term is 380, find the value of n.
Find the equation of a circle with centre (2, -3) and radius 2 units.
The deviations from the mean of a set of numbers are \((k+3)^{2}, (k+7), -2, \text{k and (} k+2)^{2}\), where k is a constant. Find the value of k.
Forces 90N and 120N act in the directions 120° and 240° respectively. Find the resultant of these forces.
If a fair coin is tossed four times, what is the probability of obtaining at least one head?
Find the coefficient of \(x^3\) in the binomial expansion of \((3x + 4)^4\) in ascending powers of x.
Find the angle between \((5i + 3j)\) and \((3i - 5j)\).
Given that \(AB = \begin{pmatrix} 4 \\ 3 \end{pmatrix}\) and \(AC = \begin{pmatrix} 2 \\ -3 \end{pmatrix}\), find |BC|.
Integrate \((x - \frac{1}{x})^{2}\) with respect to x.
If \(Px^{2} + (P+1)x + P = 0\) has equal roots, find the values of P.