The first statement should be;
y is inversely proportional to a³.
Answer:
y = 0.64/x³
Step-by-step explanation:
y is inversely proportional to a³. This is;
y ∝ 1/a³
Thus, y = k(1/a³).
Where k is the constant of proportionality.
When y = 10, a = 2.
Thus; 10 = k(1/2³)
10 = k/8
k = 80.
Thus; y = 80(1/a³) - - -(1)
Also, a is directly proportional to x. Thus;
x ∝ a
So, x = ka
when x = 4, a = 20
Thus;
4 = 20k
k = 4/20
k = 1/5
Thus;
x = a/5
a = 5x
Put 5x for a in eq 1 to get;
y = 80(1/(5x)³)
y = (80/125) × 1/x³
y = 0.64/x³
