Whakaoti i te 17-1.5=1/2*9.8*t^2

$$17 - 1.5 = \frac { 1 } { 2 } \times 9.8 \times t ^ { 2 }$$

Whakaoti mō t

$$t = \frac{\sqrt{155}}{7} \approx 1.778557085$$

$$t = -\frac{\sqrt{155}}{7} \approx -1.778557085$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 1.5 i te 17, ka 15.5.

$$15.5=\frac{1}{2}\times 9.8t^{2}$$

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

$$15.5=\frac{49}{10}t^{2}$$

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

$$\frac{49}{10}t^{2}=15.5$$

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

$$t^{2}=15.5\times \frac{10}{49}$$

Whakareatia te 15.5 ki te \frac{10}{49}, ka \frac{155}{49}.

$$t^{2}=\frac{155}{49}$$

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

$$t=\frac{\sqrt{155}}{7} t=-\frac{\sqrt{155}}{7}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 1.5 i te 17, ka 15.5.

$$15.5=\frac{1}{2}\times 9.8t^{2}$$

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

$$15.5=\frac{49}{10}t^{2}$$

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

$$\frac{49}{10}t^{2}=15.5$$

Tangohia te 15.5 mai i ngā taha e rua.

$$\frac{49}{10}t^{2}-15.5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{49}{10} mō a, 0 mō b, me -15.5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times \frac{49}{10}\left(-15.5\right)}}{2\times \frac{49}{10}}$$

Pūrua 0.

$$t=\frac{0±\sqrt{-4\times \frac{49}{10}\left(-15.5\right)}}{2\times \frac{49}{10}}$$

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

$$t=\frac{0±\sqrt{-\frac{98}{5}\left(-15.5\right)}}{2\times \frac{49}{10}}$$

Whakareatia -\frac{98}{5} ki te -15.5 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.

$$t=\frac{0±\sqrt{\frac{1519}{5}}}{2\times \frac{49}{10}}$$

Tuhia te pūtakerua o te \frac{1519}{5}.

$$t=\frac{0±\frac{7\sqrt{155}}{5}}{2\times \frac{49}{10}}$$

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

$$t=\frac{0±\frac{7\sqrt{155}}{5}}{\frac{49}{5}}$$

Nā, me whakaoti te whārite t=\frac{0±\frac{7\sqrt{155}}{5}}{\frac{49}{5}} ina he tāpiri te ±.

$$t=\frac{\sqrt{155}}{7}$$

Nā, me whakaoti te whārite t=\frac{0±\frac{7\sqrt{155}}{5}}{\frac{49}{5}} ina he tango te ±.

$$t=-\frac{\sqrt{155}}{7}$$

Kua oti te whārite te whakatau.

$$t=\frac{\sqrt{155}}{7} t=-\frac{\sqrt{155}}{7}$$