Cálculo Exemplos

$- 5 e^{- 5 \cdot 0.007} \sin (250 π (0.007)) + 250 π (0.007) + 250 π e^{- 5 \cdot 0.007} \cos (250 π (0.007))$

Etapa 1

Simplifique cada termo.

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Etapa 1.1

Multiplique $- 5$ por $0.007$ .

$- 5 e^{- 0.035} \sin (250 π (0.007)) + 250 π (0.007) + 250 π e^{- 5 \cdot 0.007} \cos (250 π (0.007))$

Etapa 1.2

Reescreva a expressão usando a regra do expoente negativo $b^{- n} = \frac{1}{b^{n}}$ .

$- 5 \frac{1}{e^{0.035}} \sin (250 π (0.007)) + 250 π (0.007) + 250 π e^{- 5 \cdot 0.007} \cos (250 π (0.007))$

Etapa 1.3

Combine $- 5$ e $\frac{1}{e^{0.035}}$ .

$\frac{- 5}{e^{0.035}} \sin (250 π (0.007)) + 250 π (0.007) + 250 π e^{- 5 \cdot 0.007} \cos (250 π (0.007))$

Etapa 1.4

Mova o número negativo para a frente da fração.

$- \frac{5}{e^{0.035}} \sin (250 π (0.007)) + 250 π (0.007) + 250 π e^{- 5 \cdot 0.007} \cos (250 π (0.007))$

Etapa 1.5

Substitua $e$ por uma aproximação.

$- \frac{5}{{2.71828182}^{0.035}} \sin (250 π (0.007)) + 250 π (0.007) + 250 π e^{- 5 \cdot 0.007} \cos (250 π (0.007))$

Etapa 1.6

Eleve $2.71828182$ à potência de $0.035$ .

$- \frac{5}{1.0356197} \sin (250 π (0.007)) + 250 π (0.007) + 250 π e^{- 5 \cdot 0.007} \cos (250 π (0.007))$

Etapa 1.7

Divida $5$ por $1.0356197$ .

$- 1 \cdot 4.82802708 \sin (250 π (0.007)) + 250 π (0.007) + 250 π e^{- 5 \cdot 0.007} \cos (250 π (0.007))$

Etapa 1.8

Multiplique $- 1$ por $4.82802708$ .

$- 4.82802708 \sin (250 π (0.007)) + 250 π (0.007) + 250 π e^{- 5 \cdot 0.007} \cos (250 π (0.007))$

Etapa 1.9

Multiplique $250 π (0.007)$ .

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Etapa 1.9.1

Multiplique $0.007$ por $250$ .

$- 4.82802708 \sin (1.75 π) + 250 π (0.007) + 250 π e^{- 5 \cdot 0.007} \cos (250 π (0.007))$

Etapa 1.9.2

Multiplique $1.75$ por $π$ .

$- 4.82802708 \sin (5.49778714) + 250 π (0.007) + 250 π e^{- 5 \cdot 0.007} \cos (250 π (0.007))$

Etapa 1.10

Multiplique $- 4.82802708$ por $\sin (5.49778714)$ .

$3.41393068 + 250 π (0.007) + 250 π e^{- 5 \cdot 0.007} \cos (250 π (0.007))$

Etapa 1.11

Multiplique $250 π (0.007)$ .

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Etapa 1.11.1

Multiplique $0.007$ por $250$ .

$3.41393068 + 1.75 π + 250 π e^{- 5 \cdot 0.007} \cos (250 π (0.007))$

Etapa 1.11.2

Multiplique $1.75$ por $π$ .

$3.41393068 + 5.49778714 + 250 π e^{- 5 \cdot 0.007} \cos (250 π (0.007))$

Etapa 1.12

Multiplique $- 5$ por $0.007$ .

$3.41393068 + 5.49778714 + 250 π e^{- 0.035} \cos (250 π (0.007))$

Etapa 1.13

Reescreva a expressão usando a regra do expoente negativo $b^{- n} = \frac{1}{b^{n}}$ .

$3.41393068 + 5.49778714 + 250 π \frac{1}{e^{0.035}} \cos (250 π (0.007))$

Etapa 1.14

Multiplique $250 π \frac{1}{e^{0.035}}$ .

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Etapa 1.14.1

Combine $\frac{1}{e^{0.035}}$ e $250$ .

$3.41393068 + 5.49778714 + \frac{250}{e^{0.035}} π \cos (250 π (0.007))$

Etapa 1.14.2

Combine $\frac{250}{e^{0.035}}$ e $π$ .

$3.41393068 + 5.49778714 + \frac{250 π}{e^{0.035}} \cos (250 π (0.007))$

Etapa 1.15

Multiplique $250 π (0.007)$ .

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Etapa 1.15.1

Multiplique $0.007$ por $250$ .

$3.41393068 + 5.49778714 + \frac{250 π}{e^{0.035}} \cos (1.75 π)$

Etapa 1.15.2

Multiplique $1.75$ por $π$ .

$3.41393068 + 5.49778714 + \frac{250 π}{e^{0.035}} \cos (5.49778714)$

Etapa 1.16

Combine $\frac{250 π}{e^{0.035}}$ e $\cos (5.49778714)$ .

$3.41393068 + 5.49778714 + \frac{250 π \cos (5.49778714)}{e^{0.035}}$

Etapa 1.17

Simplifique o numerador.

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Etapa 1.17.1

Avalie $\cos (5.49778714)$ .

$3.41393068 + 5.49778714 + \frac{250 π \frac{\sqrt{2}}{2}}{e^{0.035}}$

Etapa 1.17.2

Combine expoentes.

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Etapa 1.17.2.1

Combine $\frac{\sqrt{2}}{2}$ e $250$ .

$3.41393068 + 5.49778714 + \frac{\frac{\sqrt{2} \cdot 250}{2} π}{e^{0.035}}$

Etapa 1.17.2.2

Combine $\frac{\sqrt{2} \cdot 250}{2}$ e $π$ .

$3.41393068 + 5.49778714 + \frac{\frac{\sqrt{2} \cdot 250 π}{2}}{e^{0.035}}$

Etapa 1.17.3

Cancele o fator comum de $250$ e $2$ .

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Etapa 1.17.3.1

Fatore $2$ de $\sqrt{2} \cdot 250 π$ .

$3.41393068 + 5.49778714 + \frac{\frac{2 (\sqrt{2} \cdot 125 π)}{2}}{e^{0.035}}$

Etapa 1.17.3.2

Cancele os fatores comuns.

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Etapa 1.17.3.2.1

Fatore $2$ de $2$ .

$3.41393068 + 5.49778714 + \frac{\frac{2 (\sqrt{2} \cdot 125 π)}{2 (1)}}{e^{0.035}}$

Etapa 1.17.3.2.2

Cancele o fator comum.

$3.41393068 + 5.49778714 + \frac{\frac{2 (\sqrt{2} \cdot 125 π)}{2 \cdot 1}}{e^{0.035}}$

Etapa 1.17.3.2.3

Reescreva a expressão.

$3.41393068 + 5.49778714 + \frac{\frac{\sqrt{2} \cdot 125 π}{1}}{e^{0.035}}$

Etapa 1.17.3.2.4

Divida $\sqrt{2} \cdot 125 π$ por $1$ .

$3.41393068 + 5.49778714 + \frac{\sqrt{2} \cdot 125 π}{e^{0.035}}$

Etapa 1.17.4

Mova $125$ para a esquerda de $\sqrt{2}$ .

$3.41393068 + 5.49778714 + \frac{125 \sqrt{2} π}{e^{0.035}}$

Etapa 2

Simplifique somando os termos.

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Etapa 2.1

Some $3.41393068$ e $5.49778714$ .

$8.91171783 + \frac{125 \sqrt{2} π}{e^{0.035}}$

Etapa 2.2

Some $8.91171783$ e $\frac{125 \sqrt{2} π}{e^{0.035}}$ .

$545.17069644$