What is e^{-20x}((7cos(40x))+(7/2 sin(40x))) ?

The solution to e^{-20x}((7cos(40x))+(7/2 sin(40x))) is (7cos(40x)+7/2 sin(40x))/(e^{20x)}

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simplify e^{-20x}((7cos(40x))+(7/2 sin(40x)))

simplify

e^{- 20 x} ((7 cos (40 x)) + (\frac{7}{2} sin (40 x)))

\frac{7 cos ( 40 x ) + \frac{7}{2} sin ( 40 x )}{e ^{20 x}}

Solution steps

e^{- 20 x} ((7 cos (40 x)) + (\frac{7}{2} sin (40 x)))

Apply exponent rule:

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

= \frac{1}{e ^{20 x}} (7 cos (40 x) + \frac{7}{2} sin (40 x))

Multiply fractions:

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

= \frac{1 \cdot ( 7 cos ( 40 x ) + \frac{7}{2} sin ( 40 x ) )}{e ^{20 x}}

1 \cdot (7 cos (40 x) + \frac{7}{2} sin (40 x)) = 7 cos (40 x) + \frac{7}{2} sin (40 x)

= \frac{7 cos ( 40 x ) + \frac{7}{2} sin ( 40 x )}{e ^{20 x}}

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

(1 + 2 z) e^{- 2 z}

\frac{0.025}{19} \cdot 1. 1^{- 5}

d e (s - 6) (s - 1)^{- 3}

What is e^{-20x}((7cos(40x))+(7/2 sin(40x))) ?
The solution to e^{-20x}((7cos(40x))+(7/2 sin(40x))) is (7cos(40x)+7/2 sin(40x))/(e^{20x)}