Mathematical Modelling and Analysis
Added on 2019-09-26
4 Pages736 Words492 Views
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P2 - Arithmetic Progressions1. A nurse is paid a salary of £21500 per annum and receives annual increments of £1075. Determine her salary in the 6th year and calculate the total she will have received in the first 15 years.P3 - Geometric Progressions2.A drilling machine is to have 7 speeds ranging from 75 rev/min to 850 rev/min. If the speeds form a geometric progression determine their values, each correct to the nearest whole number.P4 - Complex NumbersEnter your surname to find your personal values for Z1, Z2, Z3 and frequency. ~(See sheet for values)3.For your personal numbers (Z1, Z2, Z3), calculate the following, using the rectangular (Cartesian) form. Show your working and give your answers inrectangular form.a) Z1Z2 b) Z1Z2 / Z34.Using the polar form of Z1, Z2, Z3, determine in polar form, with angles stated in radians: a) Z1Z2 b) Z1Z2 / Z3P5 - Ungrouped Data For this part of assignment (Statistical Techniques) open the personaldata: ~(See sheet for values)5.The values of capacitances, in microfarads, of ten capacitors selected at random from a large batch of similar capacitors are given in the personal
data generator file. Determine the mean, the standard deviation from the mean and the variance for these results correct to 3 decimal places.P6 - Grouped Data6.The values of resistance for a number of resistors are shown in the frequency distribution table in the personal data generator file. Determine the estimated mean, the standard deviation from the estimated mean and the variance for these resistors, correct to 4 significant figures.------Simultaneous equations – both of these questions should be solved by plotting 2 straight lines on a graph. ~(See sheet for values)P11.The law connecting friction F and load L for an experiment is of the form F = aL + b, where a and b are constants. When F = 12.0N, L = 7.0N and when F = 8.0N, L = 1.5N. Find the values of ‘a’ and ‘b’ by plotting a graph of ‘b’ against ‘a’. Reduction to straight line form – this question should be solved by plotting the data from the personal data generator on a graph with logarithmic axes-----------Enter your surname to find your individual data sets for P7, P8 See SheetP7 Trigonometrical Graphs2.An A.C. voltage is given by the expression V = V0 sin(2ft + Φ0) where V is the voltage at time t in Volts, f is frequency in Hz (or cycles per second) and Φ0 is phase angle in radians. Plot instantaneous voltage V against time over 1 complete cycle. Use
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