What is e^{-2t}cos(5t)e^{-st} ?

The solution to e^{-2t}cos(5t)e^{-st} is e^{-2t-ts}cos(5t)

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simplify e^{-2t}cos(5t)e^{-st}

simplify

e^{- 2 t} cos (5 t) e^{- s t}

e^{- 2 t - t s} cos (5 t)

Solution steps

e^{- 2 t} cos (5 t) e^{- s t}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{- 2 t} e^{- s t} = e^{- 2 t - t s}

= cos (5 t) e^{- 2 t - s t}

1.0672 \cdot 10 \cdot (4 π \cdot 1 0^{- 7})

\frac{1}{2} (3) (33)

e^{- 2 (1.5)}

1.23 \cdot 1 0^{- 2}

1.23 \cdot 1 0^{- 3}

What is e^{-2t}cos(5t)e^{-st} ?
The solution to e^{-2t}cos(5t)e^{-st} is e^{-2t-ts}cos(5t)