Express: y varies directly as x and inversely as the square of z.

We will use the concept of direct and indirect proportion to express the above relation.

Let us see how we will use the concept of direct and inverse proportion to express the above relation.

Solution:

Direct proportional means that if one variable y increases, then the other variable x increases, and if y decreases, then x also decreases.

Mathematically, y ∝ x is the representation of direct proportionality.

Inverse proportional means that if one variable y increases, then the other variable x decreases, and if y decreases, then z increases.

Mathematically, y ∝ 1 / z is the representation of inverse proportionality.

Hence, combining the above two equations we get that, y ∝ x / z²

Now, removing the proportionality sign, a constant comes into play and we get that, y = ( k × x ) / z², where k is the constant of proportionality.

Therefore, the required expression is y = ( k × x ) / z², where k is the constant of proportionality.

Express: y varies directly as x and inversely as the square of z.

Summary:

y = ( k × x ) / z², where k is the constant of proportionality.