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(1+i)¸= 1 + 2i + i¸= 2i.
If \((x - 5)\) is a factor of \(x^3 - 4x^2 - 11x + 30\), find the remaining factors.
In how many ways can four Mathematicians be selected from six ?
Find the coefficient of the \(6^{th}term\) in the binomial expansion of \((1 - \frac{2x}{3})10\) in ascending powers of \(x\).
If m and ( m + 4) are the roots of \(4x^2 - 4x - 15 = 0\), find the equation whose roots are 2 m and (2 m + 8).
Given that \(p = \begin{bmatrix} x&4\\3&7\end{bmatrix} Q =\begin{bmatrix} x&3\\1&2x\end{bmatrix}\) and the determinant of \(Q\) is three more than that of \(P\) , find the values of \(x\).
The probabilities that Atta and Tunde will hit a target in a shooting contest are \(\frac{1}{6}\) and \({1}{9}\) respectively. Find the probability that only one of them will hit the target.
A function \(f\) is defined by \(f :x→\frac{x + 2}{x - 3},x ≠ 3\).Find the inverse of \(f\) .
If \(X\) and \(Y\) are two independent events such that \(P (X) = \frac{1}{8}\) and \(P (X ⋃ Y) = \frac{5}{8}\), find \(P (Y)\).
Given that \(y^2 + xy = 5,find \frac{dy}{dx}\).
A linear transformation on the oxy plane is defined by \(P : (x, y) → (2x + y, -2y)\). Find \(P^2\)
The velocity of a body of mass 4.56 kg increases from \((10 ms^{-1}, 060^o) to (50 ms ^{-1}, 060^o)\) in 16 seconds . Calculate the magnitude of force acting on it.
Given that \(\frac{3x + 4}{(x - 2)(x + 3)}≡\frac{P}{x + 3}+\frac{Q}{x - 2}\),find the value of Q.
If \(3x^2 + p x + 12 = 0\) has equal roots, find the values of p .
If α and β are the roots of \(7x2 +12x - 4 = 0\),find the value of \(\frac{αβ}{(α + β)^2}\)
Evaluate: \(\int(2x + 1)^3 dx\)
In how many ways can a committee of 3 women and 2 men be chosen from a group of 7 men and 5 women?
Adu's scores in five subjects in an examination are 85, 84, 83, 86 and 87. Calculate the standard deviation.
An exponential sequence (G.P.) is given by \(\frac{9}{2},\frac{3}{4},\frac{1}{8},\)....Find its sum to infinity.
A uniform beam PQ of length 80 cm and weight 60 N rests on a support at X where | PX | = 30 cm. If the body is kept in equilibrium by a mass m kg which is placed at P , calculate the value of m
[Take g = 10 ms\(^{-2}\)]