Question

Find the equation using the relation if x varies inversely to the square of y and when x=3 we get y=20.

Answer 1

Hint: We will start with the x-y proportionality relationship. The proportionality will then be removed by using a constant. Then, to get the value of the constant, we'll substitute the given values. Then we will find the equation.

Complete step by step answer:
We know that x changes inversely as y squared. This indicates that the inverse of y2 is proportional to x. We may write it mathematically as
$x \propto \dfrac{1}{{{y^2}}}$---(1)
we can now eliminate the sign of proportionality from the relationship (1) using a constant. Let's take the proportionality constant k. Thus,
$x = \dfrac{k}{{{y^2}}}$ ---(2)
We will now find the value of the constant k by substituting the value x=3 and y=20.
When we have substituted the values, we get
$3 = \dfrac{k}{{{{20}^2}}}$
We know that square of 20 is 400
$3 = \dfrac{k}{{400}}$
We have multiplied both side by 400
$k = 1200$
Now, we will substitute the value of k in equation 2 to find the equation.
Hence, the relation x varies inversely to the square of y is $x = \dfrac{{1200}}{{{y^2}}}$ .

Note:
 Direct proportionality and inverse proportionality are the two forms of proportionality. If both variables change in the same proportion, they are said to be directly proportional. For example, if one rises, the other increases as well. When two variables are inversely proportional, they vary in opposing directions, i.e., if one grows, the other decreases, and vice versa.