Question

I varies directly as m and I is equal to 5, when m = $\dfrac{2}{3}$. Find I when m = $\dfrac{{16}}{3}$

Answer 1

Hint: To solve this problem first we have to calculate the constant of proportionality. We consider this constant of proportionality as “k”. with the help of the value of k that is the proportionality constant we can find the value of I.

Complete step-by-step answer:
We have given that, I is directly proportional to m. directly proportional means as the value of m varies , the value of I also varies directly. That means if the value of m increases, the value of I also increases. If the value of m decreases the value of also decreases.
 This means, I α m; here α is the symbol of proportionality. We replace α by some constant
I = km………………….(i)
Here, k is that constant and called constant of proportionality.
Firstly we have to calculate the value of k from the given information.
We have given that I = 5 when m = $\dfrac{2}{3}$. We put this value of I and m in equation (i) So that we can calculate the value of k.
Therefore $5 = \dfrac{{k \times 3}}{2}$
$ \to k = \dfrac{{15}}{2}$
This is the value of k.
Now, we have to calculate I when m = $\dfrac{{16}}{3}$.
Since I = km
K already calculates that is $k = \dfrac{{15}}{2}$and m is given that is m $ = \dfrac{{16}}{3}$
So, $I = \dfrac{{15}}{2} \times \dfrac{{16}}{3}$
I = 8 × 5 = 40
So from above calculation value of I =40.

Note: In mathematics, two varying quantities are said to be in a relation of proportionality, if they are multiplicatively connected to a constant that is when either their ratio or their product yields a constant. The value of this constant is called the coefficient of proportionality or proportionality constant.