Answer: the correct option is (B) x = 6.
Step-by-step explanation: Given that x varies inversely as v and x = 48 when v = 8.
We are to find the value of x when v = 64.
Since x varies inversely as v, so we have
[tex]x\propto\dfrac{1}{v}\\\\\\\Rightarrow x=k\dfrac{1}{v}~~~~~~~~~~~~~~~~~~[\textup{where k is the constant of proportionality}][/tex]
When x = 48 and v = 8, then, we get
[tex]48=\dfrac{k}{8}\\\\\Rightarrow k=48\times8\\\\\Rightarrow k=384.[/tex]
So,
[tex]x=\dfrac{384}{v}~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Therefore, when v = 64, then from equation (i), we get
[tex]x=\dfrac{384}{64}=6.[/tex]
Thus, the required value of x is 6.
Option (B) is CORRECT.
