Write an equation for the relationship
z varies jointly with x and the square of y, and inversely with r and s.
z = k x y^2/ (r s)
where k is a constant
The equation for the relationship described would be:
z = k * (x * y^2) / (r * s)
where z represents the dependent variable, x represents one of the independent variables, y represents another independent variable squared, and r and s represent the two inversely proportional variables. k represents the constant of variation.
To write an equation for the relationship described, we can combine the concepts of direct variation and inverse variation.
Direct variation means that as one variable increases, the other variable also increases, while inverse variation means that as one variable increases, the other variable decreases.
Let's break down the given information:
1. "z varies jointly with x and the square of y" means that z is directly proportional to both x and the square of y. This can be written as z ∝ x * y^2.
2. "z varies inversely with r and s" means that z is inversely proportional to both r and s. This can be written as z ∝ 1/(r * s).
Combining these two variations, we can write the equation as:
z = k * (x * y^2) / (r * s)
Here, k represents the constant of proportionality which accounts for the specific relationship between the variables.