What is inverse oflaplace ((85))/((18s+90)) ?

The answer to inverse oflaplace ((85))/((18s+90)) is 85/18 e^{-5t}

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inverse oflaplace ((85))/((18s+90))

inverse laplace

\frac{( 85 )}{( 18 s + 90 )}

\frac{85}{18} e^{- 5 t}

Solution steps

L^{- 1} {\frac{( 85 )}{( 18 s + 90 )}}

= L^{- 1} {\frac{85}{18} \cdot \frac{1}{s + 5}}

Use the constant multiplication property of Inverse Laplace Transform:

For function

f (t)

and constant

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

= \frac{85}{18} L^{- 1} {\frac{1}{s + 5}}

Use Inverse Laplace Transform table:

L^{- 1} {\frac{1}{s - a}} = e^{a t}

L^{- 1} {\frac{1}{s + 5}} = e^{- 5 t}

= \frac{85}{18} e^{- 5 t}

What is inverse oflaplace ((85))/((18s+90)) ?
The answer to inverse oflaplace ((85))/((18s+90)) is 85/18 e^{-5t}