Question

What is the relation between the variables in the equation x^4/y=7?

a) x^4 varies inversely as y

b) x^4 varies directly as y

c) y varies directly as x^4

d) y varies inversely as x^4

Answer 1

Choice b is correct answer.

Explanation:

We have given an equation.

x⁴ / y = 7

Multiplying y to both sides of above equation, we have

y(x⁴ / y) = y(7)

x⁴ = 7y

Above equation can be written as :

x⁴ = ky where k = 7.

x⁴ ∝ y

hence, x⁴ varies directly as y.

hence, choice b is the answer.

Answer 2

b) x^4 varies directly as y

is the right answer

Explanation:

Given that x and y are related by the equation

`(x^4)/(y) =7`

This can be rewritten as

`x^4=7y`

If x^4 =z is substituted we have

z=7y

i.e. Z directly varies as y and constant of proportionality is 7.

Hence we can write

x^4 varies directly as y

Option b is right