Grass height varies inversely with the number of cows squared. If the grass is 6 inches when there are 40 cows, how tall is it when there are 80 cows?

Answer 1

The phrase y varies inversely with x means we can model the equation as y = k / x, where k is some constant.

Here we have that height varies directly with the number of cows squared. So height = k / (number of cows)².

In addition, we know that the grass is 6 in when there are 40 cows. This means that 6 = k / 40². We can then solve for k. Thus, k = 6 * 1600 = 9600.

The final equation we get is height = 9600 / (number of cows)².

We can then find the height of the grass when there are 80 cows using the equation and substituting 80 for the number of cows.