Whakaoti i te P(t)=(98-14t^1/3)dt

$$P ( t ) = ( 98 - 14 t ^ { 1 / 3 } ) d t$$

Whakaoti mō P

$$\left\{\begin{matrix}\\P=14\left(-\sqrt[3]{t}+7\right)d\text{, }&\text{unconditionally}\\P\in \mathrm{R}\text{, }&t=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 98-14t^{\frac{1}{3}} ki te d.

$$Pt=\left(98d-14t^{\frac{1}{3}}d\right)t$$

Whakamahia te āhuatanga tohatoha hei whakarea te 98d-14t^{\frac{1}{3}}d ki te t.

$$Pt=98dt-14t^{\frac{1}{3}}dt$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te \frac{1}{3} me te 1 kia riro ai te \frac{4}{3}.

$$Pt=98dt-14t^{\frac{4}{3}}d$$

He hanga arowhānui tō te whārite.

$$tP=98dt-14dt^{\frac{4}{3}}$$

Whakawehea ngā taha e rua ki te t.

$$\frac{tP}{t}=\frac{14\left(-\sqrt[3]{t}+7\right)dt}{t}$$

Mā te whakawehe ki te t ka wetekia te whakareanga ki te t.

$$P=\frac{14\left(-\sqrt[3]{t}+7\right)dt}{t}$$

Whakawehe 14td\left(7-\sqrt[3]{t}\right) ki te t.

$$P=14\left(-\sqrt[3]{t}+7\right)d$$

Whakaoti mō d

$$\left\{\begin{matrix}d=\frac{P}{14\left(-\sqrt[3]{t}+7\right)}\text{, }&t\neq 343\\d\in \mathrm{R}\text{, }&t=0\text{ or }\left(P=0\text{ and }t=343\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 98-14t^{\frac{1}{3}} ki te d.

$$Pt=\left(98d-14t^{\frac{1}{3}}d\right)t$$

Whakamahia te āhuatanga tohatoha hei whakarea te 98d-14t^{\frac{1}{3}}d ki te t.

$$Pt=98dt-14t^{\frac{1}{3}}dt$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te \frac{1}{3} me te 1 kia riro ai te \frac{4}{3}.

$$Pt=98dt-14t^{\frac{4}{3}}d$$

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

$$98dt-14t^{\frac{4}{3}}d=Pt$$

Pahekotia ngā kīanga tau katoa e whai ana i te d.

$$\left(98t-14t^{\frac{4}{3}}\right)d=Pt$$

Whakawehea ngā taha e rua ki te 98t-14t^{\frac{4}{3}}.

$$\frac{\left(98t-14t^{\frac{4}{3}}\right)d}{98t-14t^{\frac{4}{3}}}=\frac{Pt}{98t-14t^{\frac{4}{3}}}$$

Mā te whakawehe ki te 98t-14t^{\frac{4}{3}} ka wetekia te whakareanga ki te 98t-14t^{\frac{4}{3}}.

$$d=\frac{Pt}{98t-14t^{\frac{4}{3}}}$$

Whakawehe Pt ki te 98t-14t^{\frac{4}{3}}.

$$d=\frac{P}{14\left(-\sqrt[3]{t}+7\right)}$$