G8.1 If $y$ is the greatest value of $\frac{14}{5+3 \sin \theta}$, find $y$.
G8.2 In the figure, $100 \cos \alpha=k$. Find $k$.
G8.3 When $3 x^{2}+4 x+a$ is divided by $x+2$, the remainder is 5 . Find $a$.
G8.4 The solution for $3 t^{2}-5 t-2<0$ is $-\frac{1}{3}<t<m$. Find $m$.
$\begin{array}{l}2 \leq 5+3 \sin \theta \leq 8 \\ \frac{14}{8} \leq \frac{14}{5+3 \sin \theta} \leq \frac{14}{2} \\ \Rightarrow y=7 \\ \text { Hypotenuse }=25 \\ k=-100 \cos \left(\alpha-180^{\circ}\right) \\ =-100 \cdot \frac{24}{25}=-96 \\ 3(-2)^{2}+4(-2)+a=5 \\ a=1 \\ (3 t+1)(t-2)<0 \\ \Rightarrow-\frac{1}{3}<t<2 \\ \Rightarrow m=2\end{array}$