Whakaoti i te 4/k(1+5/98k)=10

$$\frac { 4 } { k } ( 1 + \frac { 5 } { 98 } k ) = 10$$

Whakaoti mō k

$$k=\frac{49}{120}\approx 0.408333333$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe k ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 98k, arā, te tauraro pātahi he tino iti rawa te kitea o k,98.

$$98\times 4\left(1+\frac{5}{98}k\right)=980k$$

Whakareatia te 98 ki te 4, ka 392.

$$392\left(1+\frac{5}{98}k\right)=980k$$

Whakamahia te āhuatanga tohatoha hei whakarea te 392 ki te 1+\frac{5}{98}k.

$$392+392\times \frac{5}{98}k=980k$$

Tuhia te 392\times \frac{5}{98} hei hautanga kotahi.

$$392+\frac{392\times 5}{98}k=980k$$

Whakareatia te 392 ki te 5, ka 1960.

$$392+\frac{1960}{98}k=980k$$

Whakawehea te 1960 ki te 98, kia riro ko 20.

$$392+20k=980k$$

Tangohia te 980k mai i ngā taha e rua.

$$392+20k-980k=0$$

Pahekotia te 20k me -980k, ka -960k.

$$392-960k=0$$

Tangohia te 392 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-960k=-392$$

Whakawehea ngā taha e rua ki te -960.

$$k=\frac{-392}{-960}$$

Whakahekea te hautanga \frac{-392}{-960} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -8.

$$k=\frac{49}{120}$$