If x varies inversely as $$y^3 - 1$$​ and is equal to 3 when y = 2, find x when y = 4.

Correct option is A

Given:

x varies inversely as y³ - 1
Concept Used:
Inverse variation: If x varies inversely as y, then x$$\times$$​y = k (where k is a constant). In this case, x (y³ - 1) = k
Solution:
Find the constant of variation (k):
x (y³ - 1) = k
3(2³- 1) = k
3 (8 - 1) = k
3 $$\times$$7 = k
k = 21
Find x when y = 4:
x(y³ - 1) = k
x(4³- 1) = 21
x (64-1) = 21

x $$\times$$ 63= 21
x =$$\frac{21}{ 63}= \frac{1}{3}$$