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受欢迎的代数 >

e^{-5.6k}+4k=1

解答

e^{- 5.6 k} + 4 k = 1

解答

k = \frac{4 W _{- 1} ( - \frac{7}{5 e ^{\frac{39.2}{28}}} ) + 5.6}{22.4}, k = \frac{4 W _{0} ( - \frac{7}{5 e ^{\frac{39.2}{28}}} ) + 5.6}{22.4}

+1

十进制

k = 0, k = 0.12775 \dots

求解步骤

e^{- 5.6 k} + 4 k = 1

将

e^{- 5.6 k} + 4 k = 1

调整为朗伯形式:

1 = (1 - 4 k) e^{5.6 k}

用

5.6 k - \frac{5.6}{4} = u

和

k = \frac{5 u + 7}{28}

改写方程式

1 = (1 - 4 (\frac{5 u + 7}{28})) e^{5.6 (\frac{5 u + 7}{28})}

化简

1 = e^{\frac{5.6 ( 5 u + 7 )}{28}} (1 - \frac{5 u + 7}{7})

改写

1 = e^{\frac{5.6 ( 5 u + 7 )}{28}} (1 - \frac{5 u + 7}{7})

为朗伯形式:

e^{u} u = - \frac{7}{5 e ^{\frac{39.2}{28}}}

解

e^{u} u = - \frac{7}{5 e ^{\frac{39.2}{28}}} : u = W_{- 1} (- \frac{7}{5 e ^{\frac{39.2}{28}}}), u = W_{0} (- \frac{7}{5 e ^{\frac{39.2}{28}}})

u = W_{- 1} (- \frac{7}{5 e ^{\frac{39.2}{28}}}), u = W_{0} (- \frac{7}{5 e ^{\frac{39.2}{28}}})

代回

u = 5.6 k - \frac{5.6}{4}

，求解

k

解

5.6 k - \frac{5.6}{4} = W_{- 1} (- \frac{7}{5 e ^{\frac{39.2}{28}}}) : k = \frac{4 W _{- 1} ( - \frac{7}{5 e ^{\frac{39.2}{28}}} ) + 5.6}{22.4}

解

5.6 k - \frac{5.6}{4} = W_{0} (- \frac{7}{5 e ^{\frac{39.2}{28}}}) : k = \frac{4 W _{0} ( - \frac{7}{5 e ^{\frac{39.2}{28}}} ) + 5.6}{22.4}

k = \frac{4 W _{- 1} ( - \frac{7}{5 e ^{\frac{39.2}{28}}} ) + 5.6}{22.4}, k = \frac{4 W _{0} ( - \frac{7}{5 e ^{\frac{39.2}{28}}} ) + 5.6}{22.4}

作图

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