# Academic Guidance""Laplace""This questions are important for my master degree.. thanks for helpings

#### romsek

Math Team
You give us questions in a language the bulk of us don't speak and you post it as an image so we can't even cut and paste it into google translate.

You must not want help very badly.

#### skipjack

Forum Staff
It's Turkish. Prove the formula for #1 and obtain the Z-transform or Laplace transform for the rest, noting that "ters" means "inverse".

4.$\$ (2s + 14)/(s² + 4s + 8) = 2(s + 2)/((s + 2)² + 4) + 10/((s + 2)² + 4),
$\ \ \ \$so its inverse Laplace transform is e$^{-2\text{t}}$(2cos(2t) + 5sin(2t)).

• greg1313

#### romsek

Math Team
You can do (3) by inspection.

By definition $X(z) = \sum \limits_{n=-\infty}^\infty~X(n) z^{-n}$

Thus we see
$X(n)=\begin{cases}n &n=5,6,7,8\\0&\text{else}\end{cases}$

• greg1313

#### romsek

Math Team
#2

$Z\left\{f(n-k)\right\} = z^{-k}Z\{f(n)\}$

$Z\{\delta(n)\} = \sum \limits_{n=-\infty}^\infty~\delta(n)z^{-n} = z^{-0} = 1$

$Z\{\sum \limits_{k=1}^4~(k+1) \delta(n-k)\} = \sum \limits_{k=1}^4 (k+1) z^{-k}$

• greg1313