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Simplify \((216)^{-\frac{2}{3}} \times (0.16)^{-\frac{3}{2}}\)
The derivative of a function f with respect to x is given by \(f'(x) = 3x^{2} - \frac{4}{x^{5}}\). If \(f(1) = 4\), find f(x).
The roots of a quadratic equation are -3 and 1. Find its equation.
p and q are statements such that \(p \implies q\). Which of the following is a valid conclusion from the implication?
The first term of a geometric progression is 350. If the sum to infinity is 250, find the common ratio.
An arc of length 10.8 cm subtends an angle of 1.2 radians at the centre of a circle. Calculate the radius of the circle.
The gradient of point P on the curve \(y = 3x^{2} - x + 3\) is 5. Find the coordinates of P.
Given that \(2^{x} = 0.125\), find the value of x.
The roots of the quadratic equation \(2x^{2} - 5x + m = 0\) are \(\alpha\) and \(\beta\), where m is a constant. Find \(\alpha^{2} + \beta^{2}\) in terms of m.
Express \(\frac{2}{3 - \sqrt{7}} \text{ in the form} a + \sqrt{b}\), where a and b are integers.
Which of the following binary operations is not commutative?
Find the coefficient of \(x^{4}\) in the binomial expansion of \((2 + x)^{6}\).
Given \(\sin \theta = \frac{\sqrt{3}}{2}, 0° \leq \theta \leq 90°\), find \(\tan 2\theta\) in surd form.
The coordinates of the centre of a circle is (-2, 3). If its area is \(25\pi cm^{2}\), find its equation.
If (x + 3) is a factor of the polynomial \(x^{3} + 3x^{2} + nx - 12\), where n is a constant, find the value of n.
Solve \(x^{2} - 2x - 8 > 0\).
In the diagram above, forces P, Q and 50N are acting on a body at M. If the system is in equilibrium, calculate, in terms of \(\theta\), the magnitude of P.
The distance between P(x, 7) and Q(6, 19) is 13 units. Find the values of x.
If \(y = x^{2} - 6x + 11\) is written in the form \(y = a(x - h)^{2} + k\), find the value of \((a + h + k)\).
The initial and final velocities of an object of mass 5 kg are \(u = \begin{pmatrix} 1 \\ 3 \end{pmatrix}\) and \(v = \begin{pmatrix} 4 \\ 7 \end{pmatrix}\) respectively. Find the magnitude of its change in momentum.