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Find the inverse of \(\begin{pmatrix} 3 & 5 \\ 1 & 2 \end{pmatrix}\)
A binary operation * is defined on the set of real number, R, by x*y = x\(^2\) - y\(^2\) + xy, where x, \(\in\) R. Evaluate (\(\sqrt{3}\))*(\(\sqrt{2}\))
\({\color{red}2x} \times 3\)
Evaluate: \(^{lim}_{x \to 1} \begin{pmatrix} \frac{1 - x}{x^2 - 3x + 2} \end {pmatrix}\)
A uniform beam, PQ. is 100 m long and weighs 35 N. It is placed on a support at a point 40 cm from P. If weights of 54 N and FN are attached at P and Q respectively in order to keep it in a horizontal position, calculate, correct to the nearest whole number, the value of F.
Given that X and Y are independent events such that P(X) = 0.5, P(Y) = m and P(X U Y) = 0.75, find the value of m.
The probabilities that John and Jane will pass an examination are 0.9 and 0.7 respectively. Find the probability that at least one of them will pass the examination.
How many numbers greater than 200 can be formed from the digits 1,2,3,4, 5 if no digit is to be repeated in any particular number?
Find the area between line y = x + 1 and the x-axis from x = -2 to x = 0.
Find correct to the nearest degree,5 the angle between p = 12i - 5j and q = 4i +3j
Which of the following vectors is perpendicular to \(\begin{pmatrix} -1 & 3 \end{pmatrix}\)?
If y = (5 - x)\(^{-3}\), and \(\frac{dy}{dx}\)
The function f : x \(\to\) x\(^2\) + px + q has turning point when x = -3 and remainder of -6 when divided by (x + 2). Find the value of q.
Evaluate \(\int^9_0 \sqrt{x} dx\)
Find the coordinates of the centre of the circle 3x\(^2\) + 3y\(^2\) - 6x + 9y - 5 = 0
Find the coefficient of the third term in the binomial expansion of [2x + \(\frac{3y}{4}\)]\(^3\) in descending powers of x.
Given that P and Q are non-empty subsets of the universal set, U. Find P \(\cap\) (Q U Q`).
Solve, correct to three significant figures, (0.3)\(^x\) = (0,5)\(^8\)
A 35 N force acts on a body of mass 5 kg for 2 seconds. Calculate the change in momentum of the body.
Which of these inequalities is represented by the shaded portion of the graph?
Find the constant term in the binomial expansion of (2x\(^2\) + \(\frac{1}{x^2}\))\(^4\)