簡約 (0.25)/(sqrt(pi))(2e^{-(0.25)^2})

解

簡約

\frac{0.25}{π} (2 e^{- (0.25)^{2}})

0.26500 \dots

解答ステップ

\frac{0.25}{π} (2 e^{- (0.25)^{2}})

指数の規則を適用する:

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

= 2 \cdot \frac{0.25}{π} \cdot \frac{1}{e ^{0.2 5^{2}}}

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{0.25 \cdot 1 \cdot 2}{π e ^{0.2 5^{2}}}

数を乗じる:

0.25 \cdot 1 \cdot 2 = 0.5

= \frac{0.5}{π e ^{0.2 5^{2}}}

0.2 5^{2} = 0.0625

= \frac{0.5}{e ^{0.0625} π}

元を10進法形式に変換する

π = 1.77245 \dots

= \frac{0.5}{1.77245 \dots e ^{0.0625}}

e^{0.0625} = 1.06449 \dots

= \frac{0.5}{1.77245 \dots \cdot 1.06449 \dots}

数を乗じる:

1.77245 \dots \cdot 1.06449 \dots = 1.88676 \dots

= \frac{0.5}{1.88676 \dots}

数を割る:

\frac{0.5}{1.88676 \dots} = 0.26500 \dots

= 0.26500 \dots