Question

Write an equation that expresses the following relationship.

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

$y\propto \dfrac{1}{x}$

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

$u\propto \dfrac{p^2}{d}$

It can be written as:

$u=k\dfrac{p^2}{d}$

Where, k is the constant of proportionality.

Therefore, the required equation is $u=\dfrac{kp^2}{d}$.