If \( x=4 \) and \( y=-2 \), determine the value of \( -2(x+y)^{3} \) Factorise completely: i. \( 16 x^{4}-1 \) ii. \( 3 a^{2}-24 a+45 \) Write down the restriction(s) and solve for \( x: \frac{5}{6}-\frac{3}{2 x}=\frac{3}{x}-\frac{2}{3} \)

Solve each system of equations by elimination. \[ \begin{aligned} x-5 y & =26 \\ -7 x+5 y & =-2\end{aligned} \]

Evaluate the expression \( \sin ^{-1}\left(\cos \left(\frac{7 \pi}{6}\right)\right) \) . Give your answer as an exact value

Formula for standard error of the mean: \( \sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}} \) \( Z=\frac{\hat{x}-\mu}{\sigma_{x}} \) - Population mean \( =500 \) - Population standard deviation \( =100 \) - School sample mean \( =488 \) - Sample size \( =144 \)

Calculate the area of the shaded port. 30 km

3.3 Show that: \[ \sqrt{1-\frac{\tan ^{2} \theta}{1+\tan ^{2} \theta}}=\cos \theta \] Hence or otherwise solve the equation \[ \sqrt{1-\frac{\tan ^{2} \theta}{1+\tan ^{2} \theta}}=0,60181 \] Where \( 0^{\circ} \leq \theta \leq 360^{\circ} \)