Answer:
The Inverse variation states a relationship between the two variable in which the product is constant.
i.e [tex]x \propto \frac{1}{y}[/tex]
then the equation is of the form: [tex]xy = k[/tex] where k is the constant of variation.
As per the given information: It is given that x and y vary inversely and that y = 1/6 when x = 3.
then, by definition of inverse variation;
xy = k ......[1]
Substitute the given values we have;
[tex]3 \cdot \frac{1}{6} = k[/tex]
[tex]\frac{1}{2} = k[/tex]
Now, find the value of y when x = 10.
Substitute the given values of x=10 and k = 1/2, in [1] we have;
[tex]10y = \frac{1}{2}[/tex]
Divide both sides by 10 we get;
[tex]y = \frac{1}{20}[/tex]
therefore, a function that models the inverse variation is; [tex]xy = \frac{1}{2}[/tex] and value of [tex]y = \frac{1}{20}[/tex] when x = 10.
