If y varies directly as x3 and y = 41 when x = 2, find y if x = 6. (Round off your answer to the nearest hundredth.)
If y varies directly as x^3, it means that y can be expressed as y = kx^3, where k is the constant of variation.
To find the value of k, we can use the given values of y and x. When y = 41 and x = 2, we have:
41 = k(2^3)
41 = 8k
k = 41/8
Now that we have the value of k, we can use it to find y when x = 6:
y = (41/8)(6^3)
y = (41/8)(216)
y ≈ 1102.25
Therefore, when x = 6, y ≈ 1102.25.