X varies inversely as the square of y.


The value of x when y is 6.



Inverse variation, also known as inverse proportion, is a relationship between two variables where an increase in one variable leads to a decrease in the other variable, and vice versa. Mathematically, if two variables x and y vary inversely, their relationship can be represented as:

x = k/y

Where k is the constant of variation.


We are given that x varies inversely as the square of y. This can be represented as:

x = k/y^2

To find the value of k, we can use the given values of x and y when they are in a direct variation. We are given that when y = 2, x = 1. Substituting these values into the equation, we get:

1 = k/2^2
1 = k/4
k = 4


Now that we have the value of k, we can substitute it back into the equation:

x = 4/y^2

To find the value of x when y = 6, we substitute y = 6 into the equation:

x = 4/6^2
x = 4/36
x = 1/9

So, when y is 6, the value of x is 1/9.