Question

select the correct answer. the variable m varies inversely as the fourth power of n. if k is the constant of variation, which equation represents this situation? \\( mn^4 = k \\) \\( mn = k^4 \\) \\( \frac{m}{n} = k^4 \\) \\( \frac{m}{n^4} = k \\)

Explanation:

Step1: Recall inverse variation formula

Inverse variation between two variables \( x \) and \( y \) is given by \( xy = k \) (or \( y=\frac{k}{x} \)) where \( k \) is the constant of variation. For a variable varying inversely as a power of another, if \( m \) varies inversely as \( n^4 \), we start with the basic inverse variation form.

Step2: Apply to \( m \) and \( n^4 \)

If \( m \) varies inversely as \( n^4 \), then using the inverse variation formula, we can write \( m\times n^4=k \) (since in inverse variation, the product of the variable and the quantity it varies inversely with is constant).

Answer:

\( mn^4 = k \) (the first option)