Whakaoti i te b/8=frac{sqrt{100-x^2}}{40/3-x}

$$\frac { b } { 8 } = \frac { \sqrt { 100 - x ^ { 2 } } } { \frac { 40 } { 3 } - x }$$

Whakaoti mō b (complex solution)

$$b=\frac{24\sqrt{100-x^{2}}}{40-3x}$$

$$x\neq \frac{40}{3}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

He hanga arowhānui tō te whārite.

$$\frac{1}{8}b=\frac{\sqrt{100-x^{2}}}{\frac{40}{3}-x}$$

Me whakarea ngā taha e rua ki te 8.

$$\frac{\frac{1}{8}b}{\frac{1}{8}}=\frac{3\sqrt{100-x^{2}}}{\frac{1}{8}\left(40-3x\right)}$$

Mā te whakawehe ki te \frac{1}{8} ka wetekia te whakareanga ki te \frac{1}{8}.

$$b=\frac{3\sqrt{100-x^{2}}}{\frac{1}{8}\left(40-3x\right)}$$

Whakawehe \frac{3\sqrt{-x^{2}+100}}{40-3x} ki te \frac{1}{8} mā te whakarea \frac{3\sqrt{-x^{2}+100}}{40-3x} ki te tau huripoki o \frac{1}{8}.

$$b=\frac{24\sqrt{100-x^{2}}}{40-3x}$$

Whakaoti mō b

$$b=\frac{24\sqrt{100-x^{2}}}{40-3x}$$

$$|x|\leq 10$$

Ngā Upane mō te Whakaoti Whārite Rārangi

He hanga arowhānui tō te whārite.

$$\frac{1}{8}b=\frac{\sqrt{100-x^{2}}}{\frac{40}{3}-x}$$

Me whakarea ngā taha e rua ki te 8.

$$\frac{\frac{1}{8}b}{\frac{1}{8}}=\frac{3\sqrt{100-x^{2}}}{\frac{1}{8}\left(40-3x\right)}$$

Mā te whakawehe ki te \frac{1}{8} ka wetekia te whakareanga ki te \frac{1}{8}.

$$b=\frac{3\sqrt{100-x^{2}}}{\frac{1}{8}\left(40-3x\right)}$$

Whakawehe \frac{3\sqrt{100-x^{2}}}{40-3x} ki te \frac{1}{8} mā te whakarea \frac{3\sqrt{100-x^{2}}}{40-3x} ki te tau huripoki o \frac{1}{8}.

$$b=\frac{24\sqrt{100-x^{2}}}{40-3x}$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}x=-\frac{40\left(-b^{2}+2\sqrt{576-7b^{2}}\right)}{3\left(b^{2}+64\right)}\text{; }x=\frac{40\left(b^{2}+2\sqrt{576-7b^{2}}\right)}{3\left(b^{2}+64\right)}\text{, }&b=0\text{ or }\left(b\neq -8i\text{ and }b\neq 8i\text{ and }arg(-\frac{bx}{8}+\frac{5b}{3})<\pi \right)\\x=\frac{20\left(b^{2}-36\right)}{3b^{2}}\text{, }&\left(b=-8i\text{ and }arg(\frac{40}{3}i-ix)\geq \pi \right)\text{ or }\left(b=8i\text{ and }arg(\frac{40}{3}i-ix)<\pi \right)\end{matrix}\right.$$

Whakaoti mō x

$$x=-\frac{40\left(-b^{2}+2\sqrt{576-7b^{2}}\right)}{3\left(b^{2}+64\right)}$$

$$x=\frac{40\left(b^{2}+2\sqrt{576-7b^{2}}\right)}{3\left(b^{2}+64\right)}\text{, }b\geq 0\text{ and }b\leq \frac{24\sqrt{7}}{7}$$