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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.

User Omer Sagi
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1 Answer

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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

User Jeremy Blalock
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