To express the relationship where y varies directly as x and inversely as the square of z, we can use a mathematical equation. This can be represented as:
y = k * (x / z²)
In this equation:
- y is the dependent variable that we want to determine.
- x is the variable that y directly varies with.
- z is the variable that y inversely varies with, specifically as the square of z.
- k is a constant of proportionality that helps define the relationship between these variables.
Essentially, as x increases, y will also increase, but as z increases, y will decrease significantly because it is inversely proportional to the square of z. This means that if z doubles, the value of y will decrease by a factor of four, which emphasizes the strength of the inverse relationship.