What is e^{-20t}(5cos(40t)+5/2 sin(40t)) ?

The solution to e^{-20t}(5cos(40t)+5/2 sin(40t)) is (5cos(40t)+5/2 sin(40t))/(e^{20t)}

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simplify e^{-20t}(5cos(40t)+5/2 sin(40t))

simplify

e^{- 20 t} (5 cos (40 t) + \frac{5}{2} sin (40 t))

\frac{5 cos ( 40 t ) + \frac{5}{2} sin ( 40 t )}{e ^{20 t}}

Solution steps

e^{- 20 t} (5 cos (40 t) + \frac{5}{2} sin (40 t))

Apply exponent rule:

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

= \frac{1}{e ^{20 t}} (5 cos (40 t) + \frac{5}{2} sin (40 t))

Multiply fractions:

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

= \frac{1 \cdot ( 5 cos ( 40 t ) + \frac{5}{2} sin ( 40 t ) )}{e ^{20 t}}

1 \cdot (5 cos (40 t) + \frac{5}{2} sin (40 t)) = 5 cos (40 t) + \frac{5}{2} sin (40 t)

= \frac{5 cos ( 40 t ) + \frac{5}{2} sin ( 40 t )}{e ^{20 t}}

60 e^{- 3}

(9 x^{2}) (4 x^{2})

\frac{1}{0.86} \cdot e^{- (\frac{1}{0.86} + 1)}

(e^{\frac{- x}{a}})^{2}

What is e^{-20t}(5cos(40t)+5/2 sin(40t)) ?
The solution to e^{-20t}(5cos(40t)+5/2 sin(40t)) is (5cos(40t)+5/2 sin(40t))/(e^{20t)}