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.

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

$\frac{104}{8}=\frac{8c}{8}$$c=13$

Substitute c=13 in the equation.

$y=13x^3$

Final answer:

$y=13x^3$