Resolver v=1/3pir^2h

$$v = \frac { 1 } { 3 } \pi r ^ { 2 } h$$

Ebatzi: h (complex solution)

$$\left\{\begin{matrix}h=\frac{3v}{\pi r^{2}}\text{, }&r\neq 0\\h\in \mathrm{C}\text{, }&v=0\text{ and }r=0\end{matrix}\right.$$

Ekuazio lineala ebazteko urratsak

Trukatu aldeak, aldagaiak ezkerraldean egon daitezen.

$$\frac{1}{3}\pi r^{2}h=v$$

Modu arruntean dago ekuazioa.

$$\frac{\pi r^{2}}{3}h=v$$

Zatitu ekuazioaren bi aldeak \frac{1}{3}\pi r^{2} balioarekin.

$$\frac{3\times \frac{\pi r^{2}}{3}h}{\pi r^{2}}=\frac{3v}{\pi r^{2}}$$

\frac{1}{3}\pi r^{2} balioarekin zatituz gero, \frac{1}{3}\pi r^{2} balioarekiko biderketa desegiten da.

$$h=\frac{3v}{\pi r^{2}}$$

Ebatzi: h

$$\left\{\begin{matrix}h=\frac{3v}{\pi r^{2}}\text{, }&r\neq 0\\h\in \mathrm{R}\text{, }&v=0\text{ and }r=0\end{matrix}\right.$$

Ekuazio lineala ebazteko urratsak

Trukatu aldeak, aldagaiak ezkerraldean egon daitezen.

$$\frac{1}{3}\pi r^{2}h=v$$

Modu arruntean dago ekuazioa.

$$\frac{\pi r^{2}}{3}h=v$$

Zatitu ekuazioaren bi aldeak \frac{1}{3}\pi r^{2} balioarekin.

$$\frac{3\times \frac{\pi r^{2}}{3}h}{\pi r^{2}}=\frac{3v}{\pi r^{2}}$$

\frac{1}{3}\pi r^{2} balioarekin zatituz gero, \frac{1}{3}\pi r^{2} balioarekiko biderketa desegiten da.

$$h=\frac{3v}{\pi r^{2}}$$

Ebatzi: r (complex solution)

$$\left\{\begin{matrix}r=-\left(\pi h\right)^{-\frac{1}{2}}\sqrt{3v}\text{; }r=\left(\pi h\right)^{-\frac{1}{2}}\sqrt{3v}\text{, }&h\neq 0\\r\in \mathrm{C}\text{, }&v=0\text{ and }h=0\end{matrix}\right.$$

Ebatzi: r

$$\left\{\begin{matrix}r=\sqrt{\frac{3v}{\pi h}}\text{; }r=-\sqrt{\frac{3v}{\pi h}}\text{, }&\left(v\geq 0\text{ and }h>0\right)\text{ or }\left(v\leq 0\text{ and }h<0\right)\\r\in \mathrm{R}\text{, }&v=0\text{ and }h=0\end{matrix}\right.$$