Question

The variable z is inversely proportional to x. When x is 19, z has the value 0.10526315789474. What is the value of z when x= 28? Round to at least the thousandths place if needed.

Answer 1

When two variables are inversely proportional the relation between them can be written as:

$z=\frac{k}{x}$

Here, k is the constant of proportionality and is always equal to the product of the two variables. So using the given values of z and x, we can find k first.

$k=zx\\ \\ k=0.10526315789474(19)\\ \\ k=2$

The constant of proportionality for the given inverse proportion comes out to be 2. Using the value of k in the equation, we get:

$z=\frac{2}{x}$

We have to find the value of z when x=28. So replacing x by 28, we get:

$z=\frac{2}{28}\\ \\ z=0.07142857143$

Thus, rounding of to nearest thousand the value of z comes out to be 0.071 if x is equal to 28.