Simplify these expressions: (a) cos(πt)(δ(t) + δ(t − 1)) (b) Z [infinity] −[infinity] cos(πt)(δ(t) + δ(t − 1))dt (c) Z [infinity] −[infinity] f(t + 1)δ(t − 2) dt (d) Z [infinity] −[infinity] e jωT δ(t) dt (e) Z [infinity] −[infinity] f(τ )δ(t − 1)δ(t − τ )dτ

Amass of 1.5 kg of air at 120 kpa and 24°c is contained in a gas-tight, frictionless piston-cylinder device. the air is now compressed to a final pressure of 720 kpa. during the process, heat is transferred from the air such that the temperature inside the cylinder remains constant. calculate the boundary work input during this process.

Determine whether or not it is possible to compress air adiabatically from k to 140 kpa and 400 k. what is the entropy change during this process?

Which of the following components of a pid controlled accumulates the error over time and responds to system error after the error has been accumulated? a)- proportional b)- derivative c)- integral d)- on/off.