Question

How do you write the equation if E is inversely proportional to Z and Z=4 when E =6 ?

Answer 1

Hint: In this problem we need to write the equation which represents the relation between the given variables $\text{E}$ and $\text{Z}$. In this problem they have mentioned that the two variables are inversely proportional to each other. Now we will represent this relation mathematically and remove the proportionality symbol by placing an equality symbol and a constant. This will be our first equation. In this equation we will substitute the given values of $\text{E}$ and $\text{Z}$ to calculate the constant value. After getting the constant value we will substitute this in our first equation to get the required result.

Complete step-by-step solution:
Given that, the two variables $\text{E}$ and $\text{Z}$ are inversely proportional to each other. We can write this statement mathematically as
$\Rightarrow \text{E}\propto \dfrac{1}{\text{Z}}$
In the above equation we can observe the proportionality symbol$\left( \propto \right)$. We are going to replace this proportionality symbol with an equality symbol $\left( = \right)$ and a constant let’s say $c$, then the above equation is modified as
$\Rightarrow \text{E}=c\times \dfrac{1}{\text{Z}}....\left( \text{i} \right)$
Now we have the equation which shows the relation between the given variables $\text{E}$ and $\text{Z}$ but in the above equation we have a constant term $c$, we need to calculate this constant value.
For calculating the constant value, we are going to substitute the given values of $\text{E}$ and $\text{Z}$ which are $\text{E}=6$, $\text{Z}=4$ in the equation $\left( \text{i} \right)$, then we will get
$\begin{align}
  & \Rightarrow 6=c\times \dfrac{1}{4} \\
 & \Rightarrow c=6\times 4 \\
 & \Rightarrow c=24 \\
\end{align}$
Substituting the $c$ value in the equation $\left( \text{i} \right)$, then we will get
$\begin{align}
  & \Rightarrow \text{E}=\dfrac{24}{\text{Z}} \\
 & \Rightarrow \text{EZ}=24 \\
\end{align}$
Hence the required equation is $\text{EZ}=24$.

Note: In this problem they have mentioned that both the variables are inversely proportional each other, so we have represented it as $\text{E}\propto \dfrac{1}{\text{Z}}$. If they have mentioned that both the variables are directly proportional to each other then we will represent it as $\text{E}\propto \text{Z}$ and follow the above procedure to get the required result.