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​

You are making beer. the first step is filling the glass carboy with the liquid wort. the internal diameter of the carboy is 15 in., and you wish to fill it up to a depth of 2 ft. if your wort is drawn from the kettle using a siphon process that flows at 3 gpm, how long will it take to fill?

Apiston-cylinder device contains 0.1 m3 of liquid water and 0.9 m3 of water vapor in equilibrium at 800 kpa. heat is transferred at constant pressure until the temperature of water reaches 350 °c. determine (a) the quality of water at the initial state (b) the work associated with this process, (c) the heat associated with this process.

Atank with constant volume contains 2.27 kg of a mixture of water phases (liquid-vapor). in the initial state the temperature and the quality are 127 °c and 0.6, respectively. the mixture is heated until the temperature of 160 oc is reached. illustrate the process in a t-v diagram. then, determine (1) the mass of the vapor in kg at the initial state, (2) the final pressure in kpa.