...differential at the turning point(s). • If f ''(x) > 0, you have a minimum point. • If f ''(x) < 0, you have a maximum point. • If f ''(x) = 0, you may have a point of inflection. 1. Multi Variables Optimisation 1.0 Differentiation Many relationships involve more than two variables. E.g. Demand for a good is a function of its price, advertising, price of other goods, etc E.g. y = f(x1, x2, …, xn) Interested in impact of change in one/all of the variables on y Since there are more than just 1 variable, we distinguish between partial derivative and total derivative Partial: change in y when only 1 of the x’s is changing. The partial derivative of y with respect to xi is denoted as δy/δxi or yxi or δf/δxi or fxi and is found by differentiating y with respect to xi holding all the other variables constant. Total: change in y when all x’s are changing at the same time. It is denoted as dz/dxi. Note difference between δ (partial derivative) & d (total...
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...reach an altitude of 10000 feet or more, people physiologically fall into hypoxia. The amount of air depends on the change of an altitude. And partial oxygen pressure drop due to total air pressure drop on high altitude. Human’s body have not enough oxygen, anemia condition is caused and it is caused by deteriorate body’s function. In other words increased height means less air density, therefore lower mass of oxygen available in each breath. Also lower partial pressure reduces ability of oxygen to permeate lung tissue. In an aircraft has a pressurized system to adjust pressure and maintain a constant partial pressure of the cabin environment. Virtually a plane is flying at an altitude of 30000 feet over; the altitude of cabin is a mere 6000-8000 feet will be maintained due to the pressurized system. With this the physical effect of the air make the maximum reduces and prevents a bad affect the human body. To sum up hypoxia is caused by lack of oxygen in the air (hypoxic hypoxia), partial pressure of oxygen too low and inability of blood to carry oxygen (anemic hypoxia) due to medical condition (anemia) or to carbon monoxide poisoning. Definition Hypoxia is one of the disorders of respiratory function. It’s a condition which is hard to breathe away of dropping pressure of oxygen in our body. In other words Hypoxia signifies that the partial pressure of oxygen is less than 60mmHg or arterial oxygen-saturation is less than 90%. The primary role of cardiopulmonary is that deliver...
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...uses a mixture of 12% oxygen by volume, would this be a breathable mixture on the surface? Explain your answer. Assumptions * Density (p) of fluid in question is 1025 kg/m3, as is that of sea water. * A single atmosphere of pressure is equal to 101.325 kPa. * Acceleration due to gravity (g) is 9.8 m/s2. Solutions I. Given molar fraction of O2 (Yi) as 36%, and partial pressure (PPO2) of 1.6 bar maximum, we can calculate a maximum pressure (Ptotal ) from Daltons law of partial pressures as, PPO2Yi =Ptotal 1.60.36 =4.44 atm Removing the single atmosphere of pressure at the surface we get, Pdepth= Ptotal - Patm Pdepth=3.44 Converting this pressure to pascals and then to a depth (h) in metres, Pdepth (Pa)p ×g=h 3.44 ×101.3251025×9.8=34.7 m II. No. Gas suitable for consumption at the surface is made up of oxygen and a mixture of inert gases, the function of which is to dilute the oxygen to an adequate concentration for human consumption. At sea level, or surface pressure, the partial pressure of oxygen in a 12% molar fraction mixture is simply 0.12 x 1atm of pressure, this partial pressure of 0.12 is far below the normal value of 0.21 and well into the range that will cause impaired activity, immediate exhaustion, and possibly health problems. References 1. Michael Ange 2008, SCUBA Diving. Available from: http://www.scubadiving.com/training/basic-skills/practical-guide-nitrox. [6 April 2016] 2. Jonathan G. Fairman 1996, NASA. Available from:https://www...
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...Acta mater. 48 (2000) 4709–4714 www.elsevier.com/locate/actamat GADOLINIA-DOPED CERIA AND YTTRIA STABILIZED ZIRCONIA INTERFACES: REGARDING THEIR APPLICATION FOR SOFC TECHNOLOGY A. TSOGA1*, A. GUPTA1, A. NAOUMIDIS1 and P. NIKOLOPOULOS2 Institut fur Werkstoffe und Verfahren der Energietechnik (IWV1), Forschungszentrum Julich, D-52425 ¨ ¨ Julich, Germany and 2Chemical Engineering Department, University of Patras, GR 265 00 Patras, Greece ¨ 1 Abstract—For solid oxide fuel cells (SOFCs) operating at intermediate temperatures the adjacency of the state-of-the-art yttria-stabilized zirconia (YSZ) electrolyte with ceria-based materials to both anodic and cathodic sides is regarded as crucial for the effectiveness of the cell. Solid-state reaction, however, and interdiffusion phenomena between YSZ and ceria-based materials can cause degradation of the electrolyte. When a gadolinia-doped-ceria (GDC) layer is used to protect YSZ against interaction with Co-containing cathodes, an unfavorable solid state reaction at the YSZ–GDC interface can be efficiently suppressed when a thin ( 1 µm thick) interlayer with nominal composition of Ce0.43Zr0.43Gd0.10Y0.04O1.93 is incorporated at the interface. When ceria is to be employed at the electrolyte–anode interface to reduce polarization losses, use of a ceria–40% vol Ni cermet is recommended, since suppression of the reactivity between YSZ and ceria can also be achieved in the presence of Ni. © 2000 Acta Metallurgica Inc. Published by Elsevier...
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...1. Solve the inequality 12x + 11 > 3x - 1 2. Find the gradient of the curve with equation: 3. The sequence of values given by the Iterative formula 2x2 - 4xy + 31 = 9 at the point (2,1) + 1 = 2. (xn +_1_ ) 2 3 Xn with initial value x I = 1 converges to a. Xn (i) Use this formula to find a correct to 2 d.p, showing the result of each iteration. (ii) State an equation satisfied by a, and hence fmd the exact value of a. 4. Express sine -J3 cose =.fi in the form Rsin(e - a) where R > 0 and 0 < a < 1! 2 giving the exact value of a. Hence show that one solution of the equation sine - J3 cose = J2 is e = 7n and find 12 '1 l Cj 100 . 5.(i) 3x - 1 2. Find the gradient of the curve with equation: 3. The sequence of values given by the Iterative formula 2x2 - 4xy + 31 = 9 at the point (2,1) + 1 = 2. (xn +_1_ ) 3 xn2 with initial value Xl = 1 converges to a. Xn (i) Use this formula to find a correct to 2 d.p, showing the result of each iteration. (ii) State an equation satisfied by 4. Express sine -.J3 cose = Ct, Ji and hence fmd the exact value of a. in the form Rsin(e - a) where R > 0 and 0 < a < 1! 2 giving the exact value of a. Hence show that one solution of the equation sine '1 -.J3 cose = Ji is e = 7n and find 12 ® lljlOO' Wl ( 5.(i) Show that 10glO(x+ 5) = 2 - 10glOx may be written...
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... 2. Nitrogen gas contained in a 1.85 L vessel exerts a pressure of 1.00 atm at 0 oC. Determine the required change in temperature to increase the pressure of nitrogen gas to 1.65 atm after it has been transferred to a 1.50 L vessel. (92.297) 3. An empty tank of 3 dm3 has a mass of 897.3 g. It is filled with propane gas, C3H8, at 25 o C to a pressure of 3.30 atm. Calculate the mass of the tank after it is filled. (Assuming that the expansion of the tank from an increase in temperature is negligible) (915.141 g) 4. A mixture of noble gases contains 4.46 moles of Neon and 0.74 moles of Krypton and y mole of Xenon at a pressure of 2 atm. (a) Determine y mole of Xenon if the partial pressure of Neon is 1.214 atm. (2.148 moles) (b) Determine the partial pressure of Krypton. [Sep 2014] (0.2 atm) 5. Calculate the number of moles of sulfur dioxide gas, SO2, transported in a 2 L container at s.t.p. (0.089 mole) 6. Water has a vapour pressure of 24 mm Hg at 25 °C and 182 mm Hg at 67 °C. Calculate the heat of vaporization. [Sep 2011] (40.685 kJ mole-1)...
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...Hydrostatic vs Osmotic Pressure Hydrostatic pressure is the pressure going outward from the capillary. Hydrostatic Pressure forces the fluid from capillary to move outward into the interstitial space. Osmotic pressure is the water trying to move from interstitial space into the capillary Hydrostatic pressure will be greater in the arterial side as opposed to the venule side. Osmotic Pressure is constant throughout the capillary. Because the hydrostatic pressure drops across the capillary, at the artery side fluid is pushed into the interstitial space whereas in the venule side, fluid is pushed into the vessel. If you have high blood pressure, it can cause build up of fluid in interstitial space (due to high hydrostatic pressure) and cause edema. Also, if fluid is not taken in by lymphatic vessels, it can also cause edema. Water that is lost from fluid due to hydrostatic pressure eventually goes into lymph vessels and is put back into the vessels. Note: Capillary walls are made up of endothelial cells Sodium Potassium ATPase: Pumps 3 Na ions out and 2 K ions in. Ketone Bodies: Ketone bodies are produced when AcetylcoA exceeds krebs cycles capacity. So, when you are starving, ketone bodies are used primarily rather than glucose. Glucose is preserved for brain. Brain, heart, muscle can use ketone bodies. Liver cannot use ketone bodies. Insulin: Insulin helps glucose intake by cells normally. Unsaturated fat is easy to burn off because they produce...
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...5.4 | 75 | 5.6 | 5.4 | 70 | 5.4 | 5.2 | 65 | 5.4 | 5.2 | 60 | 5.3 | 5.1 | 55 | 5.2 | 5.0 | 50 | 5.1 | 4.9 | 5 | 4.8 | 4.6 | Calculations: Any calculations should be included here if they are unrelated to answering questions from the laboratory report. Laboratory questions: 1. Calculate the number of moles of trapped air (using data from temperature < 5 degrees Celsius). nair = Patm * Vfinal / R * Tfinal nair = moles of air trapped (unknown) Patm = barometric pressure Vfinal = volume final R= 0.0821 liter atm / mol K Tfinal = temperature final nair = 0.96737 atm * 0.0048 L = 2.03 x 10-4 moles 0.0821 liter atm / mol K* 278.15 K 2. Calculate the partial pressure of air in the gas-water vapor mixture for each temperature. Pair = nair*R*T / V 80 ºC: Pair = 2.03 x 10-4 moles * 0.0821 liter atm/mol K * 353.15 K = 1.051 atm 0.0056 L 75ºC: Pair = 2.03 x 10-4 moles * 0.0821 liter atm/mol K *348.15 K = 1.036 atm 0.0056 L 70ºC: Pair = 2.03 x 10-4 moles * 0.0821 liter atm/mol K *343.15 K = 1.059 atm...
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...Test 2 – AF202 Prep |Basic Anatomy Gas Laws | |Part 61 Certification Pilots, Flight Instructors and Ground Instructors | |.14—Refusal to submit to a drug or alcohol test | |.15—Offenses involving alcohol or drugs | |.16—Refusal to submit to an alcohol test or to furnish test results | |.23—Medical certificates: Requirement and duration | |.31g—Additional training required for operating pressurized aircraft capable of operating at high altitudes | |.53—Prohibition on operations during medical deficiency | |Part 67 Medical Standards & Certification | |Part 91 ...
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...Oxygen transfer Abstract (193 words) This practical was carried out with the aim of determining the KLa value for oxygen transfer as well as examining the relationship between KLa and other fermenter variables like speed of the impeller and air flow rate, thereby calculating the values α and β in the KLa correlation: KLa = K[Pg/V]α (Vs)β KLa is the volumetric liquid phase mass transfer coefficient indicative of the mass transfer of oxygen dissolved in the liquid to the cell. It is calculated using the dynamic method which is usually used for vessels which are less than 1m in height because there is nitrogen gas hold-up in the vessel when air is reintroduced and the measurement of concentration of oxygen in the liquid does not reflect the kinetics of simple oxygen transfer until a hold-up of air in established. The measured parameters included gassed power (Pg), impeller speed, flow rate (indirectly superficial gas velocity) and DOT%. It was seen that as the power input was increased, the KLa increased for the same flow rate and that this increase was greater than increase in the flow rate of the gas, which shows confirms the results described in the literature. Introduction (326 words) Cells in aerobic cultures require oxygen for metabolism and growth. The rate of oxygen transfer from aerated liquid to the cell is especially important at high cell densities, when cell growth is likely to be limited by the availability of oxygen in the medium. The solubility of oxygen...
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...sketch the domain of g(x, y) = ln(4 − x2 − y 2 ). 11 Homework 12: Multivariable Functions II: Limits and Continuity Name Due on Tuesday, in class. Submit your solutions (work and answers) on this page only! (1) Find lim(x,y)→(1,3) xy . x2 +y 2 (2) Find lim (x,y)→(1,1) x=y x2 −y 2 x−y (hint: factor) (3) Find lim (x,y)→(2,0) 2x−y=4 √ 2x−y−2 2x−y−4 (hint: conjugate) (4) Show that lim(x,y)→(0,0) and C3 {y = x2 }. 2x4 −3y 2 x4 +y 2 does not exist by finding the limit along the three paths: C1 {x = 0}, C2 {y = 0} (5) Show that lim(x,y)→(0,0) cos 2x4 y x4 +y 4 =1 12 Homework 13: Multivariable Functions III: Partial Derivatives Name Due at the beginning of our next class period. Submit your solutions (work and answers) on this page only! (1) Compute all first and second order partial derivatives of f (x, y) = x3 y 4 + ln( x ). y (2) Find the equation of the tangent plane to the graph of the function z = f (x, y) = exp(1 − x2 + y 2 ) at (x, y) = (0, 0). Convert to normal form. (3) Find the equation of the tangent plane to the surface r(u, v) = u3 −v 3 , u+v +1, u2 at (u, v) = (2, 1). Convert to normal form. (4) Suppose that fx (x, y) = 6xy + y 2 and fy (x, y) = 3x2 + 2xy. Compute fxy and fyx to determine if there is a function f (x, y) with these first derivatives. If so, integrate to find such a function. (5) Show that the function u(x, y) = ln( x2 + y 2 ) is Harmonic (i.e., it satisfies Laplaces equation uxx + uyy...
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...Market Equilibration Process Vonda Herrin ECO/561 October 8, 2013 Emmanuel Welbeck Market Equilibration Process Having equilibrium in the market is the same as having equilibrium in our daily activities. Economic equilibrium is “a condition or state in which economic forces are balanced. It can also be defined “as the point where supply equals demand for a product – the equilibrium price is where the hypothetical supply and demand curves intersect” (Investopedia, 2013). It is important to understand supply and demand of a product in order to find equilibrium. In today’s market, consumers are usually weary about purchases of large items due to the fact there are many competitors competing for the same potential customers. Could you live without the internet, cell phone, microwave, television, or any other electric technologies? Law of Demand and Supply The world today have grown to rely heavily on technology, especially the cellular phones, in their daily activities. “The average U.S. household today owns at least 23 consumer electronic products” (Get Energy Active, 2011). As the technology in cell phones changes, consumers are eager to purchase the latest styles whether for practical uses or to be consider part of the “in crowd”. Suppliers uses this information in researching and to appropriately distribute the products and services by applying the laws of demand and supply. The law of demand is when “supply is held constant, an increase in demand leads to...
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...CAE 3 a) As we have to find the market equilibrium we must equal both functions. P=500-0’1QD P=500-0’1QD P=50+0’05QS 500=0’1QD 500-0’1Q=50+0’05Q Q= 500/0’1 -3/20Q= -450 QD=5000 Q=-450/(-3/20); QE=3000 P=500-0’1·3000 PE=200 (Graphically represented in the end) b) ԐPD=-(P/Q)· Variation ԐPD=-200/3000· (-10) ԐPD=2/3 ԐPS=-(P/Q)· Variation ԐPS=-200/3000· (-20) ԐPS=4/3 c) The first situation the government proposes is to fix a Price floor of 100€. Todos los derechos reservados Unybook Worldwide S.L. © unybook.com P=500-0’1QD P=50+0’05QS 100=500-0’1QD 100=50+0’05QS -400/-0’1=QD 50/0’05=QS QD=4000 QS=1000 QD-QS=4000-1000=3000 so it’s a shortage. The next situation the government proposes is to fix a Price floor of 300€. P=500-0’1QD P=50+0’05QS 300=500-0’1QD 300=50+0’05QS -200/-0’1=QD 250/0’05=QS QD=2000 QS=5000 QD-QS=2000-5000=-3000 so it’s a surplus. The next situation the government proposes is to fix a Price ceiling of 100€. P=500-0’1QD P=50+0’05QS 100=500-0’1QD 100=50+0’05QS -400/-0’1=QD 50/0’05=QS QD=4000 QS=1000 QD-QS=4000-1000=3000 so it’s a surplus. The next situation the government proposes is to fix a Price ceiling of 300€. P=500-0’1QD P=50+0’05QS 300=500-0’1QD 300=50+0’05QS -200/-0’1=QD 250/0’05=QS QD=2000 QS=5000 QD-QS=2000-5000=-3000 so it’s a shortage. Todos los derechos reservados Unybook Worldwide S.L. © unybook.com ...
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...alpha/2, 0, 1) hatmu=mean(t1); hatmu=mean(t2) s=std(t1); s=std(t2) n=length (t1); n=length (t2) margin=z*s/sqrt(8) MATLAB Answers alpha=0.02 z=2.3263 margin(t1)=0.6741; margin(t2)=0.2931 C3: MATLAB Codes syms l s b T1 T2 l=0.0496; s=1.00; b=10; T1=0.0386988; T2=0.0220925; g=((l^2)/(2*s*sind(b)))*((1/T2^2)-(1/T1^2)) MATLAB Answers g=9.7835 C4: MATLAB Codes for Partial Derivatives g=((l^2)/(2*s*sin(b)))*((1/T2^2)-(1/T1^2)) gl=diff(g,l) gs=diff(g,s) gb=diff(g,b) gT1=diff(g,T1) gT2=diff(g,T2) MATLAB Answers for Partial Derivatives gl=-(l*(1/T1^2 - 1/T2^2))/(s*sin(b)) gs=(l^2*(1/T1^2 - 1/T2^2))/(2*s^2*sin(b)) gb=(l^2*cos(b)*(1/T1^2 - 1/T2^2))/(2*s*sin(b)^2) gT1=l^2/(T1^3*s*sin(b)) gT2=-l^2/(T2^3*s*sin(b)) MATLAB Codes for Partial Derivative Values gl0=subs(gl,[l s b T1 T2],[l0 s0 b0 T10 T20]) gs0=subs(gs,[l s b T1 T2],[l0 s0 b0 T10 T20]) gb0=subs(gb,[l s b T1 T2],[l0 s0 b0 T10 T20]) gT10=subs(gT1,[l s b T1 T2],[l0 s0 b0 T10 T20]) gT20=subs(gT2,[l s b T1 T2],[l0 s0 b0 T10 T20]) MATLAB Answers for Partial Derivative Values gl0= -125.9202 gs0= 3.1228 gb0= 4.8165 gT10= -78.0288 gT20= 419.3851 MATLAB Codes for Finding Uncertainties for g g=9.7835; gl0= -125.9202; gs0= 3.1228; gb0= 4.8165; gT10= -78.0288; gT20= 419.3851 Wl=0.0005; Ws=0.002; Wb=0.3; WT1=0.6741; WT2=0.2931 Wg=sqrt((gl0*Wl)^2+(gs0*Ws)^2+(gb0*Wb)^2+(gT10*WT1)^2+(gT20*WT2)^2) fprintf('The value of g...
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...allocation, etc. II. Data Set Description and Methods Used This paper will be conducting a time series analysis on U.S. Natural Gas prices from January 2002 through December 2012. Prices were collected by the Energy Information Administration on a monthly basis, and the prices are measured in dollars per thousand cubic feet. The raw data set is much more extensive, and measures data such as wellhead price, import and export price, etc. I chose to neglect this in my data set for simplicity sake and because it is more applicable to look at prices directly affecting everyday individual consumers. The methods used in the time series analysis of U.S. Natural Gas Prices include non-seasonal differencing, exploring autocorrelation and partial autocorrelation functions, ARIMA modeling, conducting diagnostics on modeling by looking at residual normality [QQ plot, Shapiro Test], Box-Pierce...
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