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 explanatio…

Question

asked Sep 6, 2020 3.9k views

1 Answer

Jeremy Blalock · Answer 1 · 2020-09-11T17:09:24+0000

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