Translate the statement of variation into an equation; use k as the constant of variation. V...

Question:

Translate the statement of variation into an equation; use {eq}k {/eq} as the constant of variation.

{eq}V \textrm{ varies jointly as } s \textrm{ and the fourth power of } u. {/eq}

Joint Variation:

If a variable {eq}c {/eq} varies jointly with respect to both the variables {eq}a {/eq} and {eq}b {/eq}, then it means that:

$$z= kab$$

where, {eq}k {/eq} is a constant of variation.

Note: It means that {eq}c {/eq} is directly proportional to each of {eq}a {/eq} and {eq}b {/eq} taken one at a time.

The given statement is, "{eq}V \textrm{ varies jointly as } s \textrm{ and the fourth power of } u. {/eq}".

Here, "the fourth power of u" means {eq}u^4 {/eq}.

So the above sentence translates to, "{eq}V \textrm{ varies jointly as } s \textrm{ and } u^4 {/eq}".

Then by the definition of joint variation,

$$\boxed{\mathbf{V = ksu^4}}$$