Make q the subject of the relation t = \(\sqrt{(\frac{pq}{r} - r^2q)}\)
A
q = \(\frac{rt^2}{p - r^3}\)
B
q = \(\frac{p - r^3}{rt^2}\)
C
q = \(\frac{t^2}{p - r^3}\)
D
q = \(\frac{rt}{p - r^3}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
t = \(\sqrt{(\frac{pq}{r} - r^2q)}\)
Take the square of both sides
t\(^2\) = \(\frac{pq}{r}\) - r\(^2\)q
t\(^2\) = \(\frac{pq - r^3q}{r}\)
cross multiply
rt\(^2\) = pq - r\(^3\)q = q(p - r\(^3\))
q = \(\frac{rt^2}{p - r^3}\)
Source: Myschool Past Questions Archive (Record #71529)