Suppose that x and y vary inversely and that y=1/6 when x = 3. Write a function that models the inverse variation and find y when x = 10.

y = C/x

Solve for C with the given information.

1/6 = C/3
C = 1/2
y = 1/(2x)
If x = 10, y = 1/20

To write the function that models the inverse variation, we can use the equation:

y = k/x

where k is the constant of variation.

Given that y = 1/6 when x = 3, we can substitute these values into the equation to find k:

1/6 = k/3

To solve for k, we can cross-multiply:

k = (1/6) * 3

k = 1/2

So, the equation that models the inverse variation is:

y = (1/2)/x

To find y when x = 10, we substitute the value of x into the equation:

y = (1/2)/10

Simplifying, we get:

y = 1/20

Therefore, when x = 10, y = 1/20.

To write a function that models inverse variation, we can use the formula:

y = k/x

where k is the constant of variation. In this case, we are given that y = 1/6 when x = 3. We can use this information to find the value of k.

Substituting the given values into the formula:

1/6 = k/3

To solve for k, we can cross multiply:

k = 1/6 * 3
k = 1/2

So the function that models the inverse variation is:

y = (1/2)/x

To find y when x = 10, we can substitute x = 10 into the function:

y = (1/2)/10
y = 1/20

Therefore, when x = 10, y = 1/20.