Question

Q varies inversely as the square of p, and Q = 36 when p = 7. Find Q when p = 6.

A. Q = 176
B. Q = 6
C. Q = 49
D. Q = 42

Please no guesses and I'd like to see an explanation if possible because I'm reviewing for a final.

Answer 1

For this case we have that by definition, a direct variation is represented as:

$y = kx$

While an inverse variation is represented as:

$y = \frac {k} {x}$

If we have that Q varies inversely as the square of p means that:

$Q = \frac {k} {p ^ 2}$

Substituting the values and clearing the proportionality constant we have:

$36 = \frac {k} {7 ^ 2}\\36 = \frac {k} {49}\\k = 36 * 49\\k = 1764$

Now we must find the value of Q when $p = 6$:

$Q = \frac {k} {6 ^ 2}\\Q = \frac {1764} {36}\\Q = 49$

Answer:

Option C