Write an equation that expresses the following relationship. y varies directly as x and inversely as the square of z.

Solution:

We will use the concept of direct proportion and indirect proportion to write the required equation.

It is given that y varies directly as x and inversely as the square of z. 

So, directly proportional means that when x increases y should increase, and when x decreases y should also decrease in the same ratio

Hence we can write, y ∝ x ----- ( 1)

Also indirectly proportional that when z  increases then y should decrease and when z decreases then y should increase. Here it is given that y is inversely proportional to the square of z.

Hence, y ∝ 1/z² .----- (2)

On combining equation 1 and 2 we get,

y ∝ x / z²

A constant k comes on the removal of the proportionality sign 

Therefore required equation = kx / z²    

Hence,The equation y = (kx/z²) expresses the relationship, y varies directly as x and inversely as the square of z.

Write an equation that expresses the following relationship. y varies directly as x and inversely as the square of z.

Summary:

Equation y = (k x / z²) expresses the relationship, y varies directly as x and inversely as the square of z