Solve the question
An assistant to Stacy gave her the PW values for four alternatives they are comparing for the devel- opment of a remote control vibration control sys- tem for offshore platform application. The results in the table use a MARR of 14% per year. Deter- mine which alternative(s) should be selected (a) if the alternatives are exclusive, and (b) if the projects are independent. K Life n, years 3 12 6 PW over a years, $ 16/08 31.12 -257.46 140.46 PW over 6 years, $ 26.94 15.78 -653.29 140.46 PW over 12 years, $ 39.21 60.45 -257.46 204.46 Future Worth ComparisonA plane layer of coal of thickness & = I'm experiences uniform volumetric generation at a mic of q = 20 W/m due to slow oxidation of the coal particles. Averaged over a daily period, the top surface of the layer trans- fers heat by convection to ambient air for which h =3 W/m'-K and T. = 25 C, while receiving solar irradiation in the amount G, = 400 Wm'. Irradiation from the atmosphere may be neglected. The solar absorptivity and emissivity of the surface are each = =095. Ambient air TA (a) Write the steady-state form of the heat diffusion equation for the layer of coal. Verify that this equa- tion is satisfied by a temperature distribution of the form m=I From this distribution, what can you say about condi- tions at the bottom surface (x = Q? Sketch the temper- ature distribution and label key features. (b) Obmin an expression for the rate of heat transfer by conduction per unit area at .= L. Applying am energy balance to a control surface about the top surface of the layer, obtain an expression for Evaluate T, and TQU) for the prescribed conditions. (cl Daily average values of Gy and & depend on & num- ber of factors, such as time of year, cloud cover, and wind conditions. For A = $ Win' - K, compute and plot 7, and TOO) as a function of G, for 50 8 G 5 500 Wim'. For G. = 400 W/m , compute and plot 7, and 710) as a function of h for 5 5 Am 50 Win-KMeasurements of scientific systems are always subject to variation, some more than others. There are many structures for measurement error, and statisticians spend a great deal of time modeling these errors. Suppose the measurement error X of a certain physical quantity is decided by the density function f(x) = [*(3-r'), -15251, elsewhere. (a) Determine * that renders f(x) a valid density function.(b) Find the probability that a random error in measurement is less than 1/2.(c) For this particular measurement, it is undesirable if the magnitude of the error (ie., (x]) exceeds 0.8. What is the probability that this occurs? Five independent coin tosses result in HHHHH. It turns out that if the coin is fair the probability of this outcome is (1/2)5 = 0.03125. Does this produce strong evidence that the coin is not fair? Comment and use the concept of P-value discussed inSection 1.1.For Exercise 1.6 on page 13, compute the sample standard deviation in tensile strength for the samples separately for the two temperatures. Does it appear as if an increase in temperature influences the variability in tensile strength? Explain. Reference: Exercise 1.6: The tensile strength of silicone rubber is thought to be a function of curing temperature. A study was carried out in which samples of 12 specimens of the rubber were prepared using curing temperatures of 20 C and 45 C. The data below show the tensile strength values in megapascals. 20 C: 2.07 2.14 2.22 2.03 2.21 2.03 2.05 2.18 2.09 2.14 2.11 2.02 45"C: 2.52 2.15 2.49 2.03 2.37 2.05 1.09 2.42 2.08 2.42 2.29 2.01 (a) Show a dot plot of the data with both low and high temperature tensile strength values. (b) Compute sample mean tensile strength for both samples. (c) Does it appear as if curing temperature has an influence on tensile strength, based on the plot? Comment further. (d) Does anything else appear to be influenced by an increase in curing temperature? Explain
