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If \(f : x → 2 tan x\) and \(g : x → √(x^2 + 8), find ( g o f )(45^o)\)
An exponential sequence (G.P.) is given by 8√2, 16√2, 32√2, ... . Find the n\(^{th}\) term of the sequence
Solve 6 sin 2θ tan θ = 4, where 0º < θ < 90º
Given that r = (10 N , 200º) and n = (16 N , 020º), find (3r - 2n).
\(Simplify: \frac{log √27 - log √8}{log 3 - log 2}\)
The table shows the mark obtained by students in a test.
| Marks | 1 | 2 | 3 | 4 | 5 |
| Frequency | 2 | k | 1 | 1 | 2 |
If the mean mark is 3, find the value of k.
Express \(\frac{3}{3 - √6}\) in the form \(x + m√y\)
\(Differentiate f (x) = \frac{1}{(1 - x^2)^5}\) with respect to \(x\).
Consider the statements:
x: The school bus arrived late
y: The student walked down to school
Which of the following can be represented by y ⇒ x?
Given that P = {x : 2 ≤ x ≤ 8} and Q = {x : 4 < x ≤ 12} are subsets of the universal set μ = {x : x ∈ R}, find (P ⋂ Q\(^1\)).
Find the fifth term in the binomial expansion of \((q + x)^7\).
A particle began to move at \(27 ms^{-1}\) along a straight line with constant retardation of \(9 ms^{-2}\). Calculate the time it took the particle to come to a stop.
Given that M is the midpoint of T (2, 4) and Q (-8, 6), find the length of MQ .
Find the radius of the circle \(2x^2 + 2y^2 - 4x + 5y + 1 = 0\)
The table shows the operation * on the set {x, y, z, w}.
| * | X | Y | Z | W |
| X | Y | Z | X | W |
| Y | Z | W | Y | X |
| Z | X | Y | Z | W |
| W | W | X | W | Z |
Find the identity of the element.
If\((\frac{1}{9})^{2x-1} = (\frac{1}{81})^{2-3x}\)find the value of x
Given that \(sin x = \frac{4}{5}\) and \(cos y = \frac{12}{13}\), where x is an obtuse angle and y is an acute angle, find the value of sin (x - y).
Evaluate \(\int^1_0 x(x^2-2)^2 dx\)
The distance S metres moved by a body in t seconds is given by \(S = 5t^3 - \frac{19}{2} t^2 + 6t - 4\). Calculate the acceleration of the body after 2 seconds
Find the equation of the normal to the curve y = \(3x^2 + 2\) at point (1, 5).