y varies directly as the cube root of x. If x=27, then y=2. What is the answer?

Question

It's about variation.

Thanks!

Answer 1

One solution is y = x^(1/3) - 1

Another is y = (2/3)* x^(1/3)

Answer 2

As the cube root of 27 is 3 , I assume that the answer is the cube root minus 1

Answer 3

y varies directly as x^(1/3) means that
y = k * x^(1/3) for some constant k.

Plugging in x = 27 and y = 2 gives :
2 = k * 27^(1/3)
2 = k * 3
k = 2/3

The equation is therefore : y = (2/3) * x^(1/3)

Answer 4

You only have one equation so you can't have a unique solution

The cuberoot of x is 3 but you can perform a whole variety of function to make it 2

Subtract 1
Multiply by 2/3
Divide by 3 and add 1

y = [x^(1/3)] - 1
y = 2/3[x^(1/3)]
y = [x^(1/3)]/3 + 1

Are all valid

edit: Since it is variation the second one is best, with k = 2/3

Answer 5

y = k(cube root of x)
cube root of 21 is 3
2 = k3
the constant is 3/2 = 1.5

Answer 6

The equations are as follows:
y = k * qrt(x), or
y^3 = k1 * x ..........1)
Substitute your numbers in 1) above to obtain k1
2*2*2 = k1 * 27
or k1 = 8/27
Now rewrite 1) with value for k1
y^3 = 8/27 * x
or y = 2/3 * qrt (x)

Answer 7

Do you mean find an equation ?
If yes , one of the solutions is :
x^(1/3)-1= y;
But because you ask "direct variation" it is rather a term used for linear equations :
y= x^(1/3)*(2/3)