1. ## 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.

2. Hello, Mukilab!

Do you really understand proportionality?

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

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

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

3. 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?)

4. 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.

5. 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

6. They did mention it was inversely proportional, right? That means;

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.
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