Question

Suppose that x and y vary inversely and that x=10 when y=8. write the function that models the inverse variation. find y when x=5

Answer 1

As the variables vary inversely, we have the following relationship:

`y = k / x`
From here, we must find the value of the constant k.
For this, we use the following data:
x = 10 when y = 8
Substituting values we have:

`8 = k / 10`
From here, we clear the value of k:

`k = (8) * (10) k = 80`
Substituting the value of k we have that the function is:

`y = 80 / x`
Then, for x = 5 we have:

`y = 80/5 y = 16`
Answer:
The function that models the inverse variation is:

`y = 80 / x`
when x = 5:

`y = 16`