# V varies inversely with T and V = 18 when T = 3. Which equation shows this relationship?

Apr 1, 2016

$V = \frac{k}{T}$

Or the other way round is just as true

$T = \frac{k}{V}$

#### Explanation:

The question is stating that $V$ has some relationship to $\frac{1}{T}$

Let $k$ be some constant.

Then $V = k \times \frac{1}{T}$...............................(1)

We are told that when T=3 ; V=18

Substitute these values into equation (1) giving

$18 = k \times \frac{1}{3}$

Multiply both sides by 3 giving

$3 \times 18 = k \times \frac{3}{3}$

But 3/3 = 1

$54 = k$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So the relationship becomes.

$V = \frac{k}{T}$

Or the other way round is just as true

$T = \frac{k}{V}$