Question

Write an equation describing the relationship of the given variables Y varies directly as the cube of x when x =2, y= 104

Answer 1

Given:

y varies directly as the cube of x when x =2, y= 104

Aim:

We need to find the equation for the given statement.

Step-by-step explanation:

y varies directly as the cube of x means that y is proportional to the cube of x.

It can be written as follows.

`y\propto x^3`

Or

`y=cx^3`

where c is some constant.

Substitute x=2 and y =104 in the equation to find the value of c.

`104=c(2)^3`

`104=8c`

Divide both sides by 8, we get

`(104)/(8)=(8c)/(8)`
`c=13`

Substitute c=13 in the equation.

`y=13x^3`

Final answer:

`y=13x^3`