A quantity p varies jointly with r and s. Which expression represents the constant of variation, k?
prs, p/rs, rs/p, p + r + s

Solution:

The statement that p varies jointly with r and s can be written as follows:

p ∝ rs

Which implies that p varies directly or jointly with r and s.

Replacing the proportionality sign with equal to sign we get:

p = k.r.s

Where k is the proportionality constant or the constant of variation

k = p/rs

Therefore, the expression which represents the constant of variation k is p/rs.

For example loudness (L) of the sound is directly proportional to the square of the amplitude (A) of the sound waves.

Mathematically this shall be expressed as:

L ∝ (A)² --- (1)

To convert the above proportionality into equality the right hand side(RHS) of the above expression will be multiplied by a constant C to obtain the expression below:

L = CA²

The value of the constant is then calculated as :

C = L/A²

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A quantity p varies jointly with r and s. Which expression represents the constant of variation, k?

Summary:

A quantity p varies jointly with r and s, then the expression which represents the constant of variation k is p/rs.