Find the Laplace transforms
a) \( 3 e^{-4t} \)
\[
F(s) = \mathcal{L}\{ 3 e^{-4t} \} = 3 \mathcal{L}\{ e^{-4t} \}
= 3 \left( \frac{1}{s + 4} \right)
\]
\[
\boxed{ \frac{3}{s + 4} }
\]
b) \( 2t^2 \)
\[
F(s) = 2 \mathcal{L}\{ t^2 \}
= 2 \cdot \frac{2!}{s^{2 + 1}}
\]
\[
\boxed{ \frac{4}{s^3} }
\]
c) \( 4 \cos(5t) \)
\[
F(s) = 4 \mathcal{L}\{ \cos(5t) \}
= 4 \left( \frac{s}{s^2 + 25} \right)
\]
\[
\boxed{ \frac{4s}{s^2 + 25} }
\]