Question

The quantity y varies directly with the square of x and inversely with z. When x is 9 and z is 27, y is 6. What is the constant of variation?

A) 2
B) 9
C) 18
D) 54

Answer 1

The constant of variation for the given relationship, where y varies directly with the square of x and inversely with z, is 2. This is found by substituting the given values into the equation y = k * (x^2) / z and solving for k.

Step-by-step explanation:

The student asked to find the constant of variation for a quantity y that varies directly with the square of x and inversely with z. Given that when x is 9 and z is 27, y is 6, we can set up an equation based on the direct and inverse variation formula:

y = k * (x^2) / z

Here, k represents the constant of variation. With the provided values:

6 = k * (9^2) / 27

6 = k * 81 / 27

6 = k * 3

k = 6 / 3

k = 2

Therefore, the constant of variation is 2, which corresponds to option A.