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.
Hello, Mukilab!
Do you really understand proportionality?
$\displaystyle Q \:=\:\frac{k}{T^3}$ .[1]$\displaystyle Q$ is inversely proportional to the cube of $\displaystyle T$.
Substitute into [1]: .$\displaystyle 12.6 \:=\:\frac{k}{5^3} \quad\Rightarrow\quad k \:=\:1575$When $\displaystyle T=5,\;Q=12.6$
Therefore: .$\displaystyle Q \:=\:\frac{1575}{T^3}$
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.
They did mention it was inversely proportional, right? That means;
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.Originally Posted by Soroban