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. y² = 1/16 x³
B. y = 1/2x
C. xy = 8
D. x³y² = 128

Answer 1

The equation that can be used to find other combinations of x and y, given that the square of y varies directly as the cube of x, and when x=4, y=2, is A. y² = 1/16 x³.

Step-by-step explanation:

The equation describing the relationship where the square of y varies directly as the cube of x can be determined using the provided conditions: when x=4, y=2. This relationship can be expressed as y² = kx³, where k is the constant of variation. To find the value of k, we substitute the given values:

• 2² = k·(4)³
• 4 = k·(64)
• k = 4/64
• k = 1/16

We now have the equation y² = (1/16)x³. This matches option A. Thus, A. y² = 1/16 x³ is the equation that can be used to find other combinations of x and y.