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

Answer:

y = 1/20 when x = 10

Explanation:

We know that x and y vary inversely and $y=\frac{1}{6}$ 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 $k$:

$\frac{1}{6} =\frac{k}{3}$

$k=\frac{1}{6}*3$

$k=\frac{1}{2}$

Now finding the missing value $y$:

$y=\frac{\frac{1}{2}}{10}$

$y = \frac{1}{2} * \frac{1}{10}$

$y = \frac{1}{20}$

Therefore, the missing value is $(10, \frac{1}{20} )$.

Answer 2

Answer:

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

i.e $x \propto \frac{1}{y}$

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;

$3 \cdot \frac{1}{6} = k$

$\frac{1}{2} = k$

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

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

$10y = \frac{1}{2}$

Divide both sides by 10 we get;

$y = \frac{1}{20}$

therefore, a function that models the inverse variation is; $xy = \frac{1}{2}$ and value of  $y = \frac{1}{20}$ when x = 10.