Question

If $c\propto \frac{1}{d}$, complete the following table:

$c$	$15$	.....	$12$	.....
$d$	$4$	$10$	.....	$30$

Answer 1

$c$	$15$	$6$	$12$	$2$
$d$	$4$	$10$	$5$	$30$

Given proportion is $c\propto \frac{1}{d}$
$\therefore c=k\frac{1}{d}$ (where $k$ is a constant of variation)
$k=cd$ ...(1)
Substituting $c=15$ and $d=4$ in equation (1)
$k=15\times 4=60$
(a) When $d=10$, $k=60$, $c=$?
$c=\frac{k}{d}=\frac{60}{10}=6$
(b) When $c=12$, $k=60$, $d=$?
$d=\frac{k}{c}=\frac{60}{12}=5$
(c) When $d=30$, $k=60$, $c=$?
$c=\frac{k}{d}=\frac{60}{30}=2$