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{...

Simplify; \(\frac{\sqrt{5} + 3}{4 - \sqrt{10}}\)

If cos x = -0.7133, find the values of x between 0\(^o\) and 360\(^o\)

Find the inverse of \(\begin{pmatrix} 3 & 5 \\ 1 & 2 \end{pmatrix}\)  

If \(\int^3_0(px^2 + 16)dx\) = 129. Find the value of p.

Given that X : R \(\to\) R is defined by x = \(\frac{y + 1}{5 - y}\) , y \(\in\) R, find the domain of x.

Differentiate \(\frac{x}{x + 1}\) with respect to x.

If \(\begin{pmatrix} p+q & 1\\ 0 & p-q \end {pmatrix}\) = \(\begin{pmatrix} 2 & 1 \\ 0 & 8 \end{pmatrix}\) Find the values of p and q  

If \(\frac{6x + k}{2x^2 + 7x - 15}\) = \(\frac{4}{x + 5} - \frac{2}{2x - 3}\). Find the value of k.