Whakaoti i te M=frac{M_{0}}{sqrt{1-v^2/c^2}}

$$M = \frac { M _ { 0 } } { \sqrt { 1 - \frac { v ^ { 2 } } { c ^ { 2 } } } }$$

Whakaoti mō M_0 (complex solution)

$$M_{0}=\sqrt{-\left(\frac{v}{c}\right)^{2}+1}M$$

$$v\neq -c\text{ and }v\neq c\text{ and }c\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{c^{2}}{c^{2}}.

$$M=\frac{M_{0}}{\sqrt{\frac{c^{2}}{c^{2}}-\frac{v^{2}}{c^{2}}}}$$

Tā te mea he rite te tauraro o \frac{c^{2}}{c^{2}} me \frac{v^{2}}{c^{2}}, me tango rāua mā te tango i ō raua taurunga.

$$M=\frac{M_{0}}{\sqrt{\frac{c^{2}-v^{2}}{c^{2}}}}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\frac{M_{0}}{\sqrt{\frac{c^{2}-v^{2}}{c^{2}}}}=M$$

He hanga arowhānui tō te whārite.

$$\frac{1}{\sqrt{\frac{c^{2}-v^{2}}{c^{2}}}}M_{0}=M$$

Whakawehea ngā taha e rua ki te \left(\sqrt{\left(c^{2}-v^{2}\right)c^{-2}}\right)^{-1}.

$$\frac{\frac{1}{\sqrt{\frac{c^{2}-v^{2}}{c^{2}}}}M_{0}\sqrt{\frac{c^{2}-v^{2}}{c^{2}}}}{1}=\frac{M\sqrt{\frac{c^{2}-v^{2}}{c^{2}}}}{1}$$

Mā te whakawehe ki te \left(\sqrt{\left(c^{2}-v^{2}\right)c^{-2}}\right)^{-1} ka wetekia te whakareanga ki te \left(\sqrt{\left(c^{2}-v^{2}\right)c^{-2}}\right)^{-1}.

$$M_{0}=\frac{M\sqrt{\frac{c^{2}-v^{2}}{c^{2}}}}{1}$$

Whakawehe M ki te \left(\sqrt{\left(c^{2}-v^{2}\right)c^{-2}}\right)^{-1}.

$$M_{0}=\sqrt{-\frac{v^{2}}{c^{2}}+1}M$$

Whakaoti mō M_0

$$M_{0}=\frac{M\sqrt{c^{2}-v^{2}}}{|c|}$$

$$\left(v<c\text{ and }v>-c\text{ and }c\neq 0\text{ and }|v|<|c|\right)\text{ or }\left(v<-c\text{ and }v>c\text{ and }c\neq 0\text{ and }|v|<|c|\right)$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{c^{2}}{c^{2}}.

$$M=\frac{M_{0}}{\sqrt{\frac{c^{2}}{c^{2}}-\frac{v^{2}}{c^{2}}}}$$

Tā te mea he rite te tauraro o \frac{c^{2}}{c^{2}} me \frac{v^{2}}{c^{2}}, me tango rāua mā te tango i ō raua taurunga.

$$M=\frac{M_{0}}{\sqrt{\frac{c^{2}-v^{2}}{c^{2}}}}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\frac{M_{0}}{\sqrt{\frac{c^{2}-v^{2}}{c^{2}}}}=M$$

He hanga arowhānui tō te whārite.

$$\frac{1}{\sqrt{\frac{c^{2}-v^{2}}{c^{2}}}}M_{0}=M$$

Whakawehea ngā taha e rua ki te \left(\sqrt{\left(c^{2}-v^{2}\right)c^{-2}}\right)^{-1}.

$$\frac{\frac{1}{\sqrt{\frac{c^{2}-v^{2}}{c^{2}}}}M_{0}\sqrt{\frac{c^{2}-v^{2}}{c^{2}}}}{1}=\frac{M\sqrt{\frac{c^{2}-v^{2}}{c^{2}}}}{1}$$

Mā te whakawehe ki te \left(\sqrt{\left(c^{2}-v^{2}\right)c^{-2}}\right)^{-1} ka wetekia te whakareanga ki te \left(\sqrt{\left(c^{2}-v^{2}\right)c^{-2}}\right)^{-1}.

$$M_{0}=\frac{M\sqrt{\frac{c^{2}-v^{2}}{c^{2}}}}{1}$$

Whakawehe M ki te \left(\sqrt{\left(c^{2}-v^{2}\right)c^{-2}}\right)^{-1}.

$$M_{0}=\frac{M\sqrt{\left(c-v\right)\left(v+c\right)}}{|c|}$$

Whakaoti mō M (complex solution)

$$M=\left(-\left(\frac{v}{c}\right)^{2}+1\right)^{-\frac{1}{2}}M_{0}$$

$$v\neq -c\text{ and }v\neq c\text{ and }c\neq 0$$

Whakaoti mō M

$$M=\frac{M_{0}|c|}{\sqrt{c^{2}-v^{2}}}$$

$$\left(|c|>|v|\text{ and }v<c\text{ and }v>-c\text{ and }c\neq 0\right)\text{ or }\left(|c|>|v|\text{ and }v<-c\text{ and }v>c\text{ and }c\neq 0\right)$$