Answer: The correct option is (A) 6..
Step-by-step explanation: Given that y varies inversely as the square of x and y = 7.2 when x = 10.
we are to find the value of x when y = 20.
Since y varies inversely as the square of x, so we have
[tex]y\propto \dfrac{1}{x^2}\\\\\\\Rightarrow y=k\times \dfrac{1}{x^2}~~~~~~~~~~~~~~~~\textup{[where k is the proportionality constant]}[/tex]
When y = 7.2 and x = 10, then we get
[tex]y=\dfrac{k}{x^2}\\\\\\\Rightarrow 7.2=\dfrac{k}{10^2}\\\\\Rightarrow k=7.2\times 100\\\\\Rightarrow k=720.[/tex]
So, we get the relation as follows :
[tex]y=\dfrac{720}{x^2}~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
When y = 20, then from equation (i), we get
[tex]20=\dfrac{720}{x^2}\\\\\\\Rightarrow x^2=\dfrac{720}{20}\\\\\Rightarrow x^2=36\\\\\Rightarrow x=\pm 6.[/tex]
Thus, the required value of x is 6 or -6. Since x = -6 is not in the options, so option (A) is CORRECT.
