Suppose that g (x) varies inversely with (x) and g (x) = 0.2 when x=0.1. What is g (x) when x=1.6?

0.0125 "Varies Inversely" means that when one of the items is multiplied by a constant, the other item is divided by the same constant. Or in mathematical notation. xy = k So let's calculate k. xg (x) = k 0.1 * 0.2 = k 0.02 = k

Therefore

g (x) = 0.02/x

Let's plug in the value 1.6:

g (1.6) = 0.02/1.6

g (1.6) = 0.0125

So our answer is 0.0125

Since g (x) varies with x, therefore:

g (x) = k/x where k is a constant.

So, first we need to get k. We are given that g (x) = 0.2 when x = 0.1

Substitute with these values to get k as follows:

g (x) = k/x

0.2 = k/0.1

k = 0.2*0.1 = 0.02

Now, the equation became:

g (x) = 0.02 / x

We need to get the g (x) when x = 1.6

Therefore, we will substitute with x in the equation and calculate the corresponding g as follows:

g (x) = 0.02 / 1.6

g (x) = 0.0125