Question

Necesito despejar las siguientes ecuaciones

I) 1/p = 1/f + 1/g Despejar F

II) R= R1.R2/ R1+R2 Despejar R1

III) S = a- rl/1-r Despejar r

IV) I = nE/R+ nr Despejar n

V) v=$\pi$ R^2 h - $\pi$ r ^2h Despejar h

Answer 1

$\frac{1}{p} = \frac{1}{f} + \frac{1}{g}\\ \frac{1}{p} -\frac{1}{g}= \frac{1}{f} \\ \frac{g-p}{pg} = \frac{1}{f}\\f= \frac{pg}{g-p}$

$R= \frac{R1*R2}{R1+R2} \\R(R1+R2)=R1R2\\RR1+RR2=R1R2\\RR1-R1R2=-RR2\\R1(R-R2)=-RR2\\ R1=-\frac{RR2}{R-R2} \\si.meto.signo\\R1=\frac{RR2}{R2-R}$

$S=a- \frac{rl}{1-r}\\S-a= - \frac{rl}{1-r}\\S-a= \frac{rl}{r-1}\\(S-a)(r-1)=rl\\Sr-S-ar+a=rl\\Sr-ar-rl=S-a\\r(S-a-l)=S-a\\r= \frac{S-a}{S-a-l}$

$I= \frac{nE}{R}+nr\\ I= \frac{nE+nrE}{R}\\ IR=nE+nrE\\IR=n(E+rE)\\ n=\frac{IR}{E+rE}$

v= πR²h -  πr²h
v=h( πR² -  πr²)
h=( πR² -  πr²)/v

espero te sirva :)