$P$ is inversely proportional to $y$. When $P=15,y=0.2$. Find $P$ when $y=1.5$.

$M$ varies directly as the square of $c$. When $M=12.6, c=3$. When $M=17.15$, find $c$, where $c>0$.

$p$ is inversely proportional to the square of $q$. Find the missing values in this table:

$\begin{array}{|cccc|}\hline p& 100& & 1\\ q& & 0.4& 2\\ \hline\end{array}$

Write down the function connecting $x$ and $y$ for the given table of values:

$\begin{array}{|ccccc|}\hline x& -1& 3& 5& 8\\ y& 0.25& 2.25& 6.25& 16\\ \hline\end{array}$

Write down the function connecting $x$ and $y$ for the given table of values:

$\begin{array}{|ccccc|}\hline x& -2& -1& 0.5& 4\\ y& 2.5& 5& -10& -1.25\\ \hline\end{array}$

A supermarket sells $300\mathrm{ml}$ bottles of ketchup for $\pounds 1.30$ a bottle. Explain why total cost of ketchup is in direct proportion to the number of bottles of ketchup bought.

A supermarket sells $300\mathrm{ml}$ bottles of ketchup for $\pounds 1.30$ a bottle. In a special offer, if you buy two bottles you get one free. Is the total cost still in direct proportion to the number of bottles bought? Justify your answer.

The force needed to break a board varies inversely with the length of the board. It takes a force of $120$ Newtons to break a board $60 \mathrm{cm}$ long. Find the force needed to break a board $20 \mathrm{cm}$ long.

The number of tennis balls you can pack in a box varies inversely with the volume of the balls. Write down the variation function that expresses the relationship between the number of balls that can fit in a box and the radius of the balls.