SG. 1 If $2 a t^{2}+12 t+9=0$ has equal roots, find $a$.
SG. 2 If $a x+b y=1$ and $4 x+18 y=3$ are parallel, find $b$.
SG. 3 The $b^{\text {th }}$ prime number is $p$. Find $p$.
SG. 4 If $k=\frac{4 \sin \theta+3 \cos \theta}{2 \sin \theta-\cos \theta}$ and $\tan \theta=3$, find $k$.
$\begin{array}{l}(12)^{2}-4(2 a)(9)=0 \\ \Rightarrow a=2 \\ -\frac{2}{b}=-\frac{4}{18} \\ \Rightarrow b=9 \\ 2,3,5,7,11,13,17,19,23,29, \ldots \\ p=23 \\ k=\frac{(4 \sin \theta+3 \cos \theta) \div \cos \theta}{(2 \sin \theta-\cos \theta) \div \cos \theta} \\ =\frac{4 \tan \theta+3}{2 \tan \theta-1} \\ \quad=\frac{4(3)+3}{2(3)-1}=3\end{array}$