Answer:
p = 18
Explanation:
General inverse variation equation:
The general inverse variation equation is given by:
y = kx, where
- y varies inversely as x,
- and k is the constant of proportionality.
Since p is inversely proportional to the square of q, we can represent this with the equation p = k/q^2
Finding k (the constant of proportionality):
We can first find k by substituting 8 for p and 3 for q in p = k/q^2:
8 = k/(3^2)
(8 = k/9) * 9
72 = k
Thus, the constant of proportionality (k) is 72.
This means the equation we'll use for the last step is given by:
p = 72/q^2
Finding p when q is 2:
Now we can find p when q is 2 by substituting 2 for q in p = 72/q^2:
p = 72/(2^2)
p = 72/4
p = 18
Thus, p = 18 when q = 2.