# Inversely proportional!?!

• Jan 5th 2010, 08:49 AM
Mukilab
Inversely proportional!?!
Q is inversely proportional to the cube of T

When T=5, Q=12.6

$\displaystyle 5^3=125$

It's as if someone added a decimal point and then added a 0.1 although it is never so with maths....thankfully.
• Jan 5th 2010, 09:10 AM
Soroban
Hello, Mukilab!

Do you really understand proportionality?

Quote:

$\displaystyle Q$ is inversely proportional to the cube of $\displaystyle T$.
$\displaystyle Q \:=\:\frac{k}{T^3}$ .[1]

Quote:

When $\displaystyle T=5,\;Q=12.6$
Substitute into [1]: .$\displaystyle 12.6 \:=\:\frac{k}{5^3} \quad\Rightarrow\quad k \:=\:1575$

Therefore: .$\displaystyle Q \:=\:\frac{1575}{T^3}$

• Jan 5th 2010, 10:14 AM
Mukilab
Quote:

Originally Posted by Soroban
Hello, Mukilab!

Do you really understand proportionality?

$\displaystyle Q \:=\:\frac{k}{T^3}$ .[1]

Substitute into [1]: .$\displaystyle 12.6 \:=\:\frac{k}{5^3} \quad\Rightarrow\quad k \:=\:1575$

Therefore: .$\displaystyle Q \:=\:\frac{1575}{T^3}$

No I did not understand proportionality but now I do understand, thank you.
If I only have T, let's say it is 3. How would I calculate Q. Surely I need this k (where did you get it from?)
• Jan 5th 2010, 11:08 AM
dkaksl
Proportionality afaik requires a variable equal to another variable multiplied (or divided) by a constant.

$\displaystyle X=kV$ ; $\displaystyle X$ is proportional to $\displaystyle V$. An inverse proportionality would be $\displaystyle X=\frac{k}{V}$

So the constant $\displaystyle k$ either has to be given, or you need to be able to calculate it from the information you have.
• Jan 5th 2010, 11:14 AM
Mukilab
Quote:

Originally Posted by dkaksl
Proportionality afaik requires a variable equal to another variable multiplied (or divided) by a constant.

$\displaystyle X=kV$ ; $\displaystyle X$ is proportional to $\displaystyle V$. An inverse proportionality would be $\displaystyle X=\frac{k}{V}$

So the constant $\displaystyle k$ either has to be given, or you need to be able to calculate it from the information you have.

The information given is: T is now 3. Work out Q. GCSE paper :/ don't think they made a mistake
• Jan 5th 2010, 11:31 AM
dkaksl
They did mention it was inversely proportional, right? That means;

Quote:

Originally Posted by Soroban
$\displaystyle Q=\frac{k}{T^3}$

even though $\displaystyle k$ isn't written anywhere you know there is a constant to define the relationship between Q and T. You can also call that constant whatever you like. It's basically rule 1 of algebra.