Question

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.

Answer 1

y = 1/20 when x = 10

Explanation:

We know that x and y vary inversely and
`y=(1)/(6)` when
`x=3`.

So we can write the function of an inverse variation as:

`y` ∝
`\frac{1} {x}`

`y = \frac {k} {x}`

Finding the constant
`k`:

`(1)/(6) =(k)/(3)`

`k=(1)/(6)*3`

`k=(1)/(2)`

Now finding the missing value
`y`:

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

`y = (1)/(2) * (1)/(10)`

`y = (1)/(20)`

Therefore, the missing value is
`(10, (1)/(20) )`.

Answer 2

The Inverse variation states a relationship between the two variable in which the product is constant.

i.e
`x \propto (1)/(y)`

then the equation is of the form:
`xy = k` 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;

`3 \cdot (1)/(6) = k`

`(1)/(2) = k`

Now, find the value of y when x = 10.

Substitute the given values of x=10 and k = 1/2, in [1] we have;

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

Divide both sides by 10 we get;

`y = (1)/(20)`

therefore, a function that models the inverse variation is;
`xy = (1)/(2)` and value of
`y = (1)/(20)` when x = 10.