Make s the subject of the relation: P = S + \(\frac{sm^2}{nr}\)
Answer Details
To make s the subject of the relation P = S + \(\frac{sm^2}{nr}\), we need to isolate s on one side of the equation.
First, we can start by moving the \(\frac{sm^2}{nr}\) term to the other side of the equation by subtracting it from both sides:
P - \(\frac{sm^2}{nr}\) = S
Next, we can solve for s by multiplying both sides of the equation by \(\frac{nr}{m^2}\):
s = \(\frac{nr}{m^2}\)(P - \(\frac{sm^2}{nr}\))
Simplifying the right-hand side, we get:
s = \(\frac{nrp}{m^2}\) - \(\frac{s}{m}\)
To isolate s, we can add \(\frac{s}{m}\) to both sides of the equation:
s + \(\frac{sm}{m^2}\) = \(\frac{nrp}{m^2}\)
Simplifying the left-hand side, we get:
s(\(\frac{m + 1}{m^2}\)) = \(\frac{nrp}{m^2}\)
Finally, we can solve for s by dividing both sides of the equation by \(\frac{m+1}{m^2}\):
s = \(\frac{nrp}{nr + m^2}\)
Therefore, the answer is s = \(\frac{nrp}{nr + m^2}\).