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受欢迎的代数 >

8=60t-1800+(1800)/(e^{t/(30))}

解答

8 = 60 t - 1800 + \frac{1800}{e ^{\frac{t}{30}}}

解答

t = 30 W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}, t = 30 W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

+1

十进制

t = - 2.78467 \dots, t = 2.87357 \dots

求解步骤

8 = 60 t - 1800 + \frac{1800}{e ^{\frac{t}{30}}}

将

8 = 60 t - 1800 + \frac{1800}{e ^{\frac{t}{30}}}

调整为朗伯形式:

1800 = (- 60 t + 1808) e^{\frac{t}{30}}

用

\frac{1}{30} t - \frac{226}{225} = u

和

t = 30 u + \frac{452}{15}

改写方程式

1800 = (- 60 (30 u + \frac{452}{15}) + 1808) e^{\frac{( 30 u + \frac{452}{15} )}{30}}

化简

1800 = - 1800 e^{\frac{225 u + 226}{225}} u

改写

1800 = - 1800 e^{\frac{225 u + 226}{225}} u

为朗伯形式:

e^{u} u = - \frac{1}{e ^{\frac{226}{225}}}

解

e^{u} u = - \frac{1}{e ^{\frac{226}{225}}} : u = W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}), u = W_{0} (- \frac{1}{e ^{\frac{226}{225}}})

u = W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}), u = W_{0} (- \frac{1}{e ^{\frac{226}{225}}})

代回

u = \frac{1}{30} t - \frac{226}{225}

，求解

t

解

\frac{1}{30} t - \frac{226}{225} = W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) : t = 30 W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

解

\frac{1}{30} t - \frac{226}{225} = W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) : t = 30 W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

t = 30 W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}, t = 30 W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

验证解:

t = 30 W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

真

, t = 30 W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

真

解为

t = 30 W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}, t = 30 W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

验证解:

t = 30 W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

真

, t = 30 W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

真

解为

t = 30 W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}, t = 30 W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

作图

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