Question

y varies inversely with the square of x, given that$y = \dfrac{1}{3}$ when $x = - 2$, express y in terms of x?

Answer 1

In the given question, we are required to find the value of a dependent variable such that the value of the independent variable is given to us. Here, in the given problem, we have y as the dependent variable and x as the dependent variable. There are mainly two types of relations between any two given variables: direct relation or direct proportion and inverse relation or inverse proportion.

Complete step by step solution:
In the given problem, we are required to express y in terms of x. A relation between both variables x and y is given to us and we are also told that y varies inversely with the square of x. So, we can deduce an inverse square proportionality from the above given statements.
So, $y \propto \dfrac{1}{{{x^2}}}$.
So, we can write $y = k\dfrac{1}{{{x^2}}}$, where ‘k’ is a constant of proportionality.
Substituting the given values of y and x in above relation, to get the value of ‘k’.
$\dfrac{1}{3} = k\dfrac{1}{{{{( - 2)}^2}}}$
$\Rightarrow k = \dfrac{4}{3}$
Thus, substituting the value of k and expressing y in terms of x, we get,
$y = \dfrac{4}{3}\left( {\dfrac{1}{{{x^2}}}} \right)$
$\Rightarrow y = \dfrac{4}{{3{x^2}}}$

Note: In the question, we need to express a variable in terms of another variable with the help of a relation given to us. Such a variable whose value depends on another variable is called dependent variable and the variable whose value does not depend on any other parameter is called independent variable.