Question

Write an equation describing the relationship of the given variables.

y varies inversely as the cube root of x and when x=64 , y=2.

Answer 1

`y = 8x^(-1/3)`

Explanation:

If y varies inversely as the cube root of x, we can write this relationship mathematically as:

y = k / (x^(1/3))

where k is a constant of proportionality. To solve for k, we can use the given information that when x=64, y=2:

2 = k / (64^(1/3))

Simplifying, we have:

2 = k / 4

Multiplying both sides by 4, we get:

k = 8

Therefore, the equation describing the relationship between x and y is:

y = 8 / (x^(1/3))

or equivalently:

y = 8x^(-1/3)