Use the following situation to answer the question.
The number of letters (n) which can be typed on a sheet of paper varies inversely as the square of the size (s) of the letters used.
What is the relationship connecting n and s?
ns = k, a constant value.
or, it is often written as
n = k/s
direct variation is
n = ks
The relationship connecting the number of letters (n) and the size of the letters used (s) is an inverse relationship. More specifically, it is an inverse square relationship. This means that as the size of the letters increases, the number of letters that can be typed on a sheet of paper decreases. On the other hand, as the size of the letters decreases, the number of letters that can be typed on a sheet of paper increases.
To better understand this relationship, we need to look at the concept of inverse variation. Inverse variation occurs when two variables change in opposite ways. In this case, as the size of the letters increases, the area taken up by each letter also increases. Therefore, fewer letters can fit on a sheet of paper. Conversely, as the size of the letters decreases, the area taken up by each letter decreases, allowing more letters to fit on a sheet of paper.
The inverse square relationship means that the number of letters (n) is inversely proportional to the square of the size of the letters (s^2). Mathematically, this relationship can be expressed as:
n = k / s^2
where n is the number of letters, s is the size of the letters, and k is the constant of variation.
By understanding this relationship, we can analyze how changes in the size of the letters will affect the number of letters that can be typed on a sheet of paper.