Question

Write an equation describing the relationship of the given variables.

y varies directly as the fourth power of x and when x=3, y=243.

Answer 1

y = 3
`x^{4`

Explanation:

given y varies directly as
`x^(4)` then the equation relating them is

y = k
`x^(4)` ← k is the constant of variation

to find k use the condition when x = 3 , y = 243 , then

243 = k ×
`3^(4)` = 81k ( divide both sides by 81 )

3 = k

y = 3
`x^(4)` ← equation of variation