The value of y when x= 3 is 108.
Two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called coefficient of proportionality.
When the value of one quantity increases with respect to decrease in other or vice-versa, then they are said to be inversely proportional.
According to the given question
y varies inversely as [tex]x^{2}[/tex].
⇒ [tex]y = \frac{k}{x^{2} }...(i)[/tex]
where, k is the coefficient of proportionality.
Given, y = 3 when x = 18
⇒ [tex]3 = \frac{k}{324}[/tex]
⇒ k = 3 × 324 =972
Therefore, for the value of y when x = 3
⇒ y = [tex]\frac{972}{(3)^{2} }[/tex] (substitute x =3 and k = 972 in equation (i))
⇒ y = [tex]\frac{972}{9} = 108[/tex]
Hence, the value of y when x = 3 for the expression [tex]y=\frac{972}{x^{2} }[/tex] is 108.
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