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

Afluid flows with a velocity field given by v=(x/t)i.. determine the local and convective accelerations when x=3 and t=1.

A-mn has a cubic structure with a0 0.8931 nm and a density of 7.47 g/cm3. b-mn has a different cubic structure, with a0 0.6326 nm and a density of 7.26 g/cm3. the atomic weight of manganese is 54.938 g/mol and the atomic radius is 0.112 nm. determine the percent volume change that would occur if a-mn transforms to b-mn.

Athin walled concentric tube exchanger is used to cool engine oil from 160°c to 60°c with water that is available at 25°c acting as a coolant. the oil and water flow rates are each at 2 kg/s, and the diameter of the inner tube is 0.5 m and the corresponding value of the overall heat transfer coefficient is 250 w/m2. oc. how long must the heat exchanger be to accomplish the desired cooling? cpwater=4.187 kj/kg-candcpengine el=2.035 kj/kg·°c, oil . 120]