Answer:
see attached
Explanation:
You want the values that complete the table when y is inversely proportional to the cube of x.
Relation
A proportional relation has the form ...
y = kx
where k is the constant of proportionality.
If y is inversely proportional to x, that is the same as saying y is proportional to the inverse of x:
y = k(1/x)
Here, y is proportional to the inverse of the cube of x:
y = k/x³
The value of k can be found as ...
k = x³·y = (10³)(0.6) = 600
So the relation to use with the table is ...
y = 600/x³
Missing y
The y-value can be found using the equation ...
y = 600/x³
y = 600/5³ = 600/125 = 24/5
y = 4.8
Missing x
Solving the proportion for x gives ...
x³ = k/y
x = ∛(k/y) = ∛(600/75) = ∛8
x = 2
Table
Now, we can fill the table as in the attachment.