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Find the area of the circle whose equation is given as \(x^{2} + y^{2} - 4x + 8y + 11 = 0\).
Two vectors m and n are defined by \(m = 3i + 4j\) and \(n = 2i - j\). Find the angle between m and n.
Given that \(\log_{2} y^{\frac{1}{2}} = \log_{5} 125\), find the value of y.
The tangent to the curve \(y = 4x^{3} + kx^{2} - 6x + 4\) at the point P(1, m) is parallel to the x- axis, where k and m are constants. Determine the coordinates of P.
The tangent to the curve \(y = 4x^{3} + kx^{2} - 6x + 4\) at the point P(1, m) is parallel to the x- axis, where k and m are constants. Find the value of k.
Find the fourth term of the binomial expansion of \((x - k)^{5}\) in descending powers of x.
The binary operation * is defined on the set of R, of real numbers by \(x * y = 3x + 3y - xy, \forall x, y \in R\). Determine, in terms of x, the identity element of the operation.
Simplify \(\frac{\tan 80° - \tan 20°}{1 + \tan 80° \tan 20°}\)
Simplify \(\frac{\sqrt{3}}{\sqrt{3} - 1} + \frac{\sqrt{3}}{\sqrt{3} +1}\)
The gradient of the line passing through the points P(4, 5) and Q(x, 9) is \(\frac{1}{2}\). Find the value of x.
Two functions f and g are defined on the set R of real numbers by \(f : x \to 2x - 1\) and \(g : x \to x^{2} + 1\). Find the value of \(f^{-1} \circ g(3)\).
The sum of the first three terms of an Arithmetic Progression (A.P) is 18. If the first term is 4, find their product.
Which of the following is the same as \(\sin (270 + x)°\)?
Given that \(\alpha\) and \(\beta\) are the roots of an equation such that \(\alpha + \beta = 3\) and \(\alpha \beta = 2\), find the equation.
Given that the straight lines \(kx - 5y + 6 = 0\) and \(mx + ny - 1 = 0\) are parallel, find a relationship connecting the constants m, n and k.
ABCD is a square. Forces of magnitude 14N, 4N, 2N and \(2\sqrt{2} N\) act along the sides AB, BC, CD and DA respectively. Find in Newtons, the magnitude of the resultant of the forces.
Two forces, each of magnitude 16 N, are inclined to each other at an angle of 60°. Calculate the magnitude of their resultant.
A particle is projected vertically upwards from a height 45 metres above the ground with a velocity of 40 m/s. How long does it take it to hit the ground? [Take g = \(10 ms^{-2}\)].
Calculate, correct to one decimal place, the angle between 5i + 12j and -2i + 3j.
A lift moving upwards with a uniform acceleration of 5\(ms^{-2}\) carries a body of mass p kg. If the reaction on the floor is 480 N, find the value of p. [Take g = \(10 ms^{-2}\)].