For this case we have that by definition, a direct variation is represented as:
[tex]y = kx[/tex]
While an inverse variation is represented as:
[tex]y = \frac {k} {x}[/tex]
If we have that Q varies inversely as the square of p means that:
[tex]Q = \frac {k} {p ^ 2}[/tex]
Substituting the values and clearing the proportionality constant we have:
[tex]36 = \frac {k} {7 ^ 2}\\36 = \frac {k} {49}\\k = 36 * 49\\k = 1764[/tex]
Now we must find the value of Q when [tex]p = 6[/tex]:
[tex]Q = \frac {k} {6 ^ 2}\\Q = \frac {1764} {36}\\Q = 49[/tex]
Answer:
Option C
