Exercise 1.3 Determine the following derivatives and simplify if possible
X
1. y(x) = sin Vx
2. y(x) = sin3 V
3. y(x) = sin Vx3
4. y(x) =
V sin3 Vx3
5. y(x) = cos2 V1 – x2 + cos V1 – x2
6. y(x) =
GA
7. y(x) = cot(In Vx) + cot(Vln x) + cot(In x)
8. y(x) = exln x + In(In x) + In () + In[ln (In x)]
х
2
= CSC
+ esc²
X+1​

Ahouse has the following electrical appliance usage (1) single 40w lamp used for 4 hours per day (2) single 60w fan used for 12 hours per day (3) single 200w refrigerator that runs 24 hours per day with compressor run 12 hours and off 12 hours find the solar power inverter size in watt with correction factor of 1.25.

10 kg of co2 is initially contained at 400 kpa and 300 k. the gas constant for carbon dioxide is 189 j/lkg k) and has a specific heat ratio, k, of 1.289. isentropic expansion then occurs until the pressure is 200 kpa. a) determine the initial volume of co2 in m. b) determine the final temperature in k. c) determine the work done by the system during the expansion kl.

Liquid flows at steady state at a rate of 2 lb/'s through a pump, which operates to raise the elevation of the liquid 100 ft from control volume inlet to exit. the liquid specific enthalpy at the inlet is 40.09 btu/lb and at the exit is 40.94 btub. the pump requires 3 btu/s of power to operate. if kinetic energy effects are negligible and gravitational acceleration is 32.174 tt/s, the heat transfer rate associated with this steady state process is most closely 1)-2,02 btu/s from the liquid to the surroundings 2)-3.98 btu/s from the surroundings to the liquid. 3)-4.96 btu/s from the surroundings to the liquid. 4)-1.04 btu/s from the liquid to the surroundings.