What is 1.1*9.81*e^{(-0.143*50)}*(pi*4^2)/4*sqrt(2*pi/(43.8)*9.81) ?

The solution to 1.1*9.81*e^{(-0.143*50)}*(pi*4^2)/4*sqrt(2*pi/(43.8)*9.81) is 0.12625…

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simplify 1.19.81e^{(-0.14350)}(pi4^2)/4sqrt(2pi/(43.8)9.81)

simplify

1.1 \cdot 9.81 \cdot e^{(- 0.143 \cdot 50)} \cdot \frac{π \cdot 4 ^{2}}{4} \cdot 2 \cdot \frac{π}{43.8} \cdot 9.81

0.12625 \dots

Solution steps

1.1 \cdot 9.81 e^{(- 0.143 \cdot 50)} \frac{π 4 ^{2}}{4} 2 \cdot \frac{π}{43.8} \cdot 9.81

Apply exponent rule:

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

= 1.1 \cdot 9.81 \cdot \frac{4 ^{2} π}{4} \cdot \frac{1}{e ^{50 \cdot 0.143}} 2 \cdot 9.81 \cdot \frac{π}{43.8}

Multiply the numbers:

0.143 \cdot 50 = 7.15

= 1.1 \cdot 9.81 \cdot \frac{4 ^{2} π}{4} \cdot \frac{1}{e ^{7.15}} 2 \cdot 9.81 \cdot \frac{π}{43.8}

\frac{π 4 ^{2}}{4} = 4 π

= 4 \cdot 1.1 \cdot 9.81 π \frac{1}{e ^{7.15}} 2 \cdot 9.81 \cdot \frac{π}{43.8}

2 \cdot \frac{π}{43.8} \cdot 9.81 = 1.40726 \dots

= 4 \cdot 1.1 \cdot 9.81 1.40726 \dots π \frac{1}{e ^{7.15}}

Multiply fractions:

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

= 1.1 \cdot 9.81 \cdot \frac{1 \cdot 4 1.40726 \dots π}{e ^{7.15}}

\frac{1 \cdot 4 π 1.40726 \dots}{e ^{7.15}} = 0.01170 \dots

= 0.01170 \dots \cdot 1.1 \cdot 9.81

Multiply the numbers:

1.1 \cdot 9.81 \cdot 0.01170 \dots = 0.12625 \dots

= 0.12625 \dots

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What is 1.1*9.81*e^{(-0.143*50)}*(pi*4^2)/4*sqrt(2*pi/(43.8)*9.81) ?
The solution to 1.1*9.81*e^{(-0.143*50)}*(pi*4^2)/4*sqrt(2*pi/(43.8)*9.81) is 0.12625…