Question

The square of y varies directly as the cube of x. When x = 4, y = 2. Which equation can be used to find other combinations of x and y?

a. y^2 = 1/16 x^3
b. y = x^(1/2)
c. xy = 8
d. x^3 * y^2 = 128

Answer 1

The relationship between x and y is given by the equation y^2 = (1/16)x^3, which is derived from the given values x = 4 and y = 2.

Step-by-step explanation:

The question states that the square of y varies directly as the cube of x. This means we can write the equation as y^2 = kx^3, where k is the constant of variation. To find k, we use the given values of x = 4 and y = 2. Substituting these values into the equation, we get 2^2 = k(4^3), which simplifies to 4 = 64k. Therefore, k is 1/16. The equation representing the relationship is y^2 = (1/16)x^3.