Answer: The required constant of inverse variation is 37.5 and equation for the inverse variation is \(yx=37.5.\)
Step-by-step explanation: We are given to find the constant of inverse variation and to write an equation for the following inverse variation :
y = 5 when x = 7.5.
Let k denote the constant of inverse variation.
According to the given information, we can write
\(y\propto\dfrac{1}{x}\\\\\\\Rightarrow y=\dfrac{k}{x}~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{k is the constant of inverse variation}]\\\\\Rightarrow yx=k~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
When y = 5, x= 7.5, then from equation (i), we get
\(5\times7.5=k\\\\\Rightarrow k=37.5.\)
Substituting the value of k in equation (i), we arrive at
\(yx=37.5.\)
Thus, the required constant of inverse variation is 37.5 and equation for the inverse variation is \(yx=37.5.\)
