F.4 maths Variations

(a)
y varies inversely as x^n
Let yx^n=k (where k is a constant)
When x=8, y=9; when x=27, y=6
So
9(8^n)=k...(1)
6(27^n)=k...(2)
(1)/(2):
(3/2)(2/3)^3n=1
(2/3)^(3n)=2/3
3n=1
n=1/3
(b)
yx^(1/3)=k
n=1/3, so yx^(1/3)=k
ALSO
9(8^1/3)=k...(3)
That is
k=18
The expression of y in terms of x is
yx^(1/3)=18
(c)
when y=3
3x^(1/3)=18
x^(1/3)=6
x=6^3
x=216