簡約 500(1/4)e^{-16(1/4)^2}

解

簡約

500 (\frac{1}{4}) e^{- 16 (\frac{1}{4})^{2}}

\frac{125}{e}

十進法表記

45.98493 \dots

解答ステップ

500 (\frac{1}{4}) e^{- 16 (\frac{1}{4})^{2}}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

= 500 \cdot \frac{1}{4} \cdot \frac{1}{e ^{16 (\frac{1}{4})^{2}}}

\frac{1}{e ^{16 (\frac{1}{4})^{2}}} = \frac{1}{e}

= 500 \cdot \frac{1}{4} \cdot \frac{1}{e}

分数を乗じる:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{1 \cdot 1 \cdot 500}{4 e}

数を乗じる:

1 \cdot 1 \cdot 500 = 500

= \frac{500}{4 e}

数を割る:

\frac{500}{4} = 125

= \frac{125}{e}