Question

Write an equation that expresses the following relationship.

u varies directly with the square of p and inversely with d

In your equation, use k as the constant of proportionality.

Answer 1

Given:

u varies directly with the square of p and inversely with d.

To find:

The equation for the given situation.

Solution:

If y is directly proportional to x, then

`y\propto x`

If y is inversely proportional to x, then

`y\propto (1)/(x)`

It is given that u varies directly with the square of p and inversely with d. So,

`u\propto (p^2)/(d)`

It can be written as:

`u=k(p^2)/(d)`

Where, k is the constant of proportionality.

Therefore, the required equation is
`u=(kp^2)/(d)`.