If the derivative property of phasors is the multiplication of the phasor by jω, the integral property of phasors is division of the phasor by jω. Use phasors and these properties to find the sinusoids in each of the following:

(A) v2 (t) = (1/100) dvi(t)/dt + 20v1(t) and v1(t) = (a) vz(t) = 10 cos(100t + 90°) V
(B) i2(t) = 10 ∫[ i1(t)dt – 3i1(t)] and i1(t) = -4 cos(5t) A

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]