Q.2.Two sinusoidal waves combining in a medium are described by the wave functions y1 = (0.3m ) cos (2πx +40πt) y2=( 0.3 m) sin (2πx +40πt ) (i). What will be the resultant displacement wave function expression and what type of the resultant wave will be generated by it. [3] (ii). What will be the amplitude, frequency and the speed of the resultant wave? [3] (iii).Find the transverse velocity and transverse acceleration at x= 0.25m, and t= 2sec?

The probability that a student correctly answers on the first try (the event A) is P(A) = 0.3. If the student answers incorrectly on the first try, the student is allowed a second try to correctly answer the question (the event B). The probability that the student answers correctly on the second try given that he answered incorrectly on the first try is 0.4. Find the probability that the student answers the question on the first or second try.

a) 0.88

b) 0.12

c) 0.70

d) 0.42

e) 0.58

1. An investor holds a portfolio which is expected to yield a rate of return of 18% with a standard deviation of 2.5%. The investor is considering buying a new share (investment being 5% of the total investment in the new portfolio). The share has the following distribution of return:

The correction coefficient between the new portfolio and the new security is 0.3; calculate the portfolio return and standard deviation of the portfolio.                                       [10 marks]

Data for the mean mass of various animal species and their corresponding metabolic rate is provided below. It is believed that the data follows the power model. i.e. ?????????? = ? (????)? where α and β are the regression coefficients.

Show by hand with pen and paper the linearisation of this nonlinear model.

A piston–cylinder device contains steam that undergoes a reversible thermodynamic cycle. Initially the steam is at 400 kPa and 350oC with a volume of 0.3 m3. The steam is first expanded isothermally to 150 kPa, then compressed adiabatically to the initial pressure, and finally compressed at the constant pressure to the initial state. Determine (a) the net work and heat transfer for the cycle after you calculate the work and heat interaction for each process and (b) show the cyclic process on a PV diagram

1. A 4 kg mass is resting on a ramp inclined at an angle of 30 degrees with respect to the horizontal. A string is attached to the 4 kg mass and passes over a frictionless pulley and is connected to a 5 kg mass hanging over the side. If the coefficient of friction between the ramp and the 4 kg mass if 0.3 find; A) The acceleration of both masses B) The tension in the string C) Find the speed of both blocks after they move a distance of 2 meters.

1. Describe the meaning of the molecular equation between the NaOH and HCl solutions on the microscopic and macroscopic scales.
2. Provide a detailed description for titrating the calculated volume of HCl solution with the 0.3 M NaOH solution. Make sure to describe what equipment you would use, how it is used and which characteristics of the equipment make them suitable for this purpose.
3. Consider the properties of HCl solutions. Identify reasons why it needs to be titrated to determine its actual concentration.

A team of USGS scientists detected a plume of the soil fumigant 1,2-dichloro-propane (DCP) in the groundwater flowing away from a field. The aquifer solids have an fOC (organic carbon content) of 0.6%, a solid density of 2.66, and a porosity of 0.3. If DCP partitions fast between OC and water, and if partitioning into OC is the main process that slows down DCP transport estimate the retardation factor Rf. log KOC [L/kg] = 2.28 for DCP.

4. Consider a reheat–regenerative vapor power cycle with two feedwater heaters, a closed feedwater heater and an open feedwater heater. Steam enters the first turbine at 12.0 MPa, 520C and expands to 0.6 MPa. The steam is reheated to 440C before entering the second turbine, where it expands to the condenser pressure of 0.006 MPa. Steam is extracted from the first turbine at 2 MPa and fed to the closed feedwater heater. Feedwater leaves the closed heater at 200C and 8.0 MPa, and condensate exits as saturated liquid at 2 MPa. The condensate is trapped into the open feedwater heater. Steam extracted from the second turbine at 0.4 MPa is also fed into the open feedwater heater, which operates at 0.3 MPa. The stream exiting the open feedwater heater is saturated liquid at 0.3 MPa. The net power output of the cycle is 100 MW. There is no stray heat transfer from any component to its surroundings. If the working fluid experiences no irreversibilities as it passes through the turbines, pumps, steam generator, reheater, and condenser, determine (a) the thermal efficiency, (b) the mass flow rate of the steam entering the first turbine, in kg/h. (Turbine and pump isentropic efficiencies 100% & Create a table of all values)

A 95 lb child is being treated with diazepam for muscle relaxation. The recommended dose for the child is 0.2 mg/kg q6-8h prn. Diazepam is available as a 5 mg/5 mL oral solution.
What volume of medication should the child receive per dose?