Given that y =(\(\frac{pr}{m} - p^2r\))\(^{\frac{-3}{2}}\)
(a) make r the subject;
(b) find the value of r when y = -8, m = 1 and p = 3.
(a) y =(\(\frac{pr}{m} - p^2r\))\(^{\frac{-3}{2}}\)
y = (\(\frac{pr - mrp^2}{m})^\frac{-3}{2}\)
y = [\(\frac{m}{pr - mrp^2}]^\frac{3}{2}\)
\(y^\frac{2}{3} = \frac{m}{r(p - mp^2)}\)
r = \(\frac{m}{y^\frac{2}{3}[p - mp^2]}\)
b) Given y = -8, m = 1 p = 3
r = \(\frac{m}{y^\frac{2}{3}[p - mp^2]}\)
r = \(\frac{1}{(-8)^\frac{2}{3}[ 3 - (1)3^2]}\)
r = \(\frac{1}{(-2)^2[3 - 9]}\)
r = \(\frac{1}{[4][-6]}\) = \(\frac{-1}{24}\)
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