Whakaoti i te 3+1.2=1/2*9.8r^2

$$3 + 1.2 = \frac { 1 } { 2 } \times 9.8 r ^ { 2 }$$

Whakaoti mō r

$$r=\frac{\sqrt{42}}{7}\approx 0.9258201$$

$$r=-\frac{\sqrt{42}}{7}\approx -0.9258201$$

Ngā Upane mā te Kimi Pūtakerua

Tāpirihia te 3 ki te 1.2, ka 4.2.

$$4.2=\frac{1}{2}\times 9.8r^{2}$$

Whakareatia te \frac{1}{2} ki te 9.8, ka \frac{49}{10}.

$$4.2=\frac{49}{10}r^{2}$$

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

$$\frac{49}{10}r^{2}=4.2$$

Me whakarea ngā taha e rua ki te \frac{10}{49}, te tau utu o \frac{49}{10}.

$$r^{2}=4.2\times \frac{10}{49}$$

Whakareatia te 4.2 ki te \frac{10}{49}, ka \frac{6}{7}.

$$r^{2}=\frac{6}{7}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$r=\frac{\sqrt{42}}{7} r=-\frac{\sqrt{42}}{7}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te 3 ki te 1.2, ka 4.2.

$$4.2=\frac{1}{2}\times 9.8r^{2}$$

Whakareatia te \frac{1}{2} ki te 9.8, ka \frac{49}{10}.

$$4.2=\frac{49}{10}r^{2}$$

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

$$\frac{49}{10}r^{2}=4.2$$

Tangohia te 4.2 mai i ngā taha e rua.

$$\frac{49}{10}r^{2}-4.2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{49}{10} mō a, 0 mō b, me -4.2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times \frac{49}{10}\left(-4.2\right)}}{2\times \frac{49}{10}}$$

Pūrua 0.

$$r=\frac{0±\sqrt{-4\times \frac{49}{10}\left(-4.2\right)}}{2\times \frac{49}{10}}$$

Whakareatia -4 ki te \frac{49}{10}.

$$r=\frac{0±\sqrt{-\frac{98}{5}\left(-4.2\right)}}{2\times \frac{49}{10}}$$

Whakareatia -\frac{98}{5} ki te -4.2 mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$r=\frac{0±\sqrt{\frac{2058}{25}}}{2\times \frac{49}{10}}$$

Tuhia te pūtakerua o te \frac{2058}{25}.

$$r=\frac{0±\frac{7\sqrt{42}}{5}}{2\times \frac{49}{10}}$$

Whakareatia 2 ki te \frac{49}{10}.

$$r=\frac{0±\frac{7\sqrt{42}}{5}}{\frac{49}{5}}$$

Nā, me whakaoti te whārite r=\frac{0±\frac{7\sqrt{42}}{5}}{\frac{49}{5}} ina he tāpiri te ±.

$$r=\frac{\sqrt{42}}{7}$$

Nā, me whakaoti te whārite r=\frac{0±\frac{7\sqrt{42}}{5}}{\frac{49}{5}} ina he tango te ±.

$$r=-\frac{\sqrt{42}}{7}$$

Kua oti te whārite te whakatau.

$$r=\frac{\sqrt{42}}{7} r=-\frac{\sqrt{42}}{7}$$