[latex]b) P=dfrac{a+b}{2}cdot h |cdot2\\(a+b)h=2P |:h\\a+b=dfrac{2P}{h} |-a\\oxed{b=dfrac{2P}{h}-a}[/latex] [latex]c) V=dfrac{1}{3}pi r^2h |cdot3\\pi r^2h=3V |:pi r^2\\oxed{h=dfrac{3V}{pi r^2}}[/latex] [latex]d) V=dfrac{4}{3}pi r^3 |cdotdfrac{3}{4}\\pi r^3=dfrac{3V}{4} |:pi\\r^3=dfrac{3V}{4pi}\\oxed{r=sqrt[3]{frac{3V}{4pi}}}[/latex] [latex]f) F=mg-momega^2R\\m(g-omega^2R)=F |:(g-omega^2R)\\oxed{m=dfrac{F}{g-omega^2R}}[/latex] [latex]g) W=GMmleft(dfrac{1}{r}-dfrac{1}{R} ight) |:GMm\\dfrac{1}{r}-dfrac{1}{R}=dfrac{W}{GMm} |+dfrac{1}{R}\\dfrac{1}{r}=dfrac{W}{GMm}+dfrac{1}{R}\\dfrac{1}{r}=dfrac{WR}{GMmR}+dfrac{GMm}{GMmR}\\dfrac{1}{r}=dfrac{WR+GMmR}{GMmR}\\oxed{r=dfrac{GMmR}{WR+GMmR}}[/latex]
