... also passes through the center ofthe circle, so the intersection of 2’ and will be the center ofthe circle The slope of is Hence, by Theorem 3.2, the slope of A is - So A has the slope-intercept ... from the other two vertices 23 Prove analytically that the sum ofthe squares ofthe four sides of a parallelogram is equal to the sum ofthe squares ofthe diagonals 24 Prove analytically that the ... principles, and theorems These are followed by the solved problems that form the core ofthe book They give step-by-step practice in applying the principles and provide derivations of some ofthe theorems...
... action and lobbying but also involves understanding the attitudes and positions of key decision-makers and stakeholders and informing them of information and arguments to persuade them ofthe educational, ... type of text, the writer’s understanding ofthe readers for whom the text is intended The writer’s understanding ofthe readers’ beliefs, values and understandings can have an influence on how the ... in the second edition as well as revisions of many ofthe entries in the second edition Each term has been selected on the basis of its importance within an area and reflects the fact that the...
... Each of these areas affects the others in the ongoing process of improving the way we meet the needs of children Possibly the most important use of these standards will be to raise the level of understanding ... relationships (6) The well-being ofthe children, the confidence ofthe parents/guardians of children in the facility’s care, andthe high morale and consistent professional growth ofthe staff depend ... health and safety in early care and education programs The increased use ofthe standards both in practical onsite applications and in research documents the value ofthe standards and validates the...
... appreciation ofthe clinical and public health importance ofinfantand child nutrition In the earliest part ofthe last century, and well before, nutrition was a prominent and vital part of caring for infants ... position when the lower margin ofthe orbit andthe upper margin ofthe auditory meatus are in line The second person holds theinfant s knees flat to the table and heels flat against the movable ... over the center ofthe triceps muscle on the back ofthe arm (measured and marked beforehand) The anthropometrist lifts the skinfold with the thumb and index finger, approximately cm above the...
... triangles: the square ofthe hypotenuse equals the sum ofthe squares ofthe other two sides (Figure 1.1) The “sum” is of course the sum of areas andthe area of a square of side l is l2 , which ... roots and strong interconnections The major themes are the concepts of number and space: their initial separation in Greek mathematics, their union in the geometry of Fermat and Descartes, andthe ... Subtracting these four triangles from the large square leaves, on the one hand (Figure 1.7, left), the sum ofthe squares on the two sides ofthe triangle On the other hand (right), it also leaves the...
... member ofthe Board of Directors ofthe Southern Illinois University Credit Union Aswath Damodaran is a professor of finance at the Stern School of Business at New York University, and teaches the ... Gruber, PhD, is the past president ofthe American Finance Association, andthe author of more than seven books and 75 articles The sixth editionof his book, Modern Portfolio Theory and Investment ... Schiff Professor of Finance and Chair ofthe Department of Finance at the Stern School of Business at New York University He holds positions on the Board of Academic Consultants ofthe Federal...
... P, andthe palm is facing in the direction of a vector Q, then the thumb points along the direction ofthe cross product P × Q The unit vectors i, j, and k, which point in the directions ofthe ... (3.5) k =1 Another way of looking at this is that the ( i, j ) entry of FG is equal to the dot product ofthe i-th row of F andthe j-th column of G There is an n × n matrix called the identity ... 2.1 The triangle inequality states that P + Q ≤ P + Q Geometrically, this follows from the fact that the length of one side of a triangle can be no longer than the sum ofthe lengths ofthe other...
... universe The heat flows that result from the cooling ofthe sun are the primary processes that we experience naturally The conductive cooling of Earth’s center andthe radiative cooling ofthe other ... does the entropy ofthe universe increase? We turn to this question next Entropy production The entropy increase ofthe universe as the result of a process is the sum ofthe entropy changes of ... average over the surface ofthe body Without the bar, h denotes the “local” value ofthe heat transfer coefficient at a point on the surface The units of h and h are W/m2 K or J/s·m2·K The conversion...
... r is the radius ofthe fin From the figure we see that the actual heat flux into the fin, Qactual , andthe actual root temperature are both reduced when the Biot number, hr /k, is large andthe fin ... Neglect the tip convection from the fin in Example 4.8 and suppose that it is embedded in a wall ofthe same material Calculate the error in Q andthe actual temperature ofthe root if the wall ... both sides of it by q h(T1 − T2 )/˙δ The result is h(T − T1 ) = Bi ξ − ξ + ˙ qL 2 (4.26) The result is plotted on the right-hand side of Fig 4.5 The following features ofthe graph are of interest:...
... than 0.5% ofthe difference between the pipe wall temperature andthe temperature of fluid flowing in a pipe? The well consists of a tube with the end closed It has a cm O.D and a 1.88 cm I.D The material ... for the simplest case and then look at the results of such calculations in other situations A simple slab, shown in Fig 5.6, is initially at a temperature Ti The temperature ofthe surface ofthe ... including both convection and radiation If the thermocouple reads Ttc = 40◦ C, estimate the actual temperature Ts ofthe surface and suggest a better arrangement ofthe wires 4.44 The resistor leads...
... /hA, and that t is measured from the time of immersion The Biot number ofthe body is small Find the temperature response ofthe body Plot the response andthe bath temperature as a function of ... Problems 253 There is a heat transfer coefficient, hm , on the inside ofthe thin metal container ofthe mercury and another one, hc , between the copper block andthe mercury The container is then suddenly ... temperature of T = 102◦ C The top is suddenly opened to the air at atm pressure Plot the decrease ofthe height of water in the tube by evaporation as a function of time until the bottom ofthe tube...
... room at 20◦ C, find: the temperature in the center ofthe butter tub, the temperature around the edge ofthe top surface ofthe butter, andthe total energy (in J) absorbed by the butter tub 5.51 ... behavior depends strongly on the amount of turbulence in the flow over the plate, the precise shape ofthe leading edge, the roughness ofthe wall, andthe presence of acoustic or structural vibrations ... is ofthe order of magnitude of to 10 • For liquid metals, Pr is ofthe order of magnitude of 10−2 or less • If the molecular structureof a liquid is very complex, Pr might reach values on the...
... into a mixing cup, the enthalpy ofthe mixed fluid in the cup would equal the average enthalpy ofthe fluid flowing through the cross section, andthe temperature ofthe fluid in the cup would be Tb ... 7.2 The thermal developmentof flows in tubes with a uniform wall heat flux and with a uniform wall temperature (the entrance region) Figures 7.2 and 7.3 show thedevelopmentof two flows and their ... bulk, enthalpy and temperature, hb and Tb The enthalpy is of interest because we use it in writing the First Law of Thermodynamics when calculating the inflow of thermal energy and flow work to...
... vertical isothermal surfaces These data were organized by Churchill and Chu [8.3] and they span 13 orders of magnitude ofthe Rayleigh number The correlation of these data in the coordinates of Fig ... around the periphery ofthe large tube The Freon enters at 15 C and is fully developed over almost the entire length The average speeds are 30 m/s for the air and 0.5 m/s for the Freon Determine the ... that soldering provides perfect thermal contact between the entire surface ofthe small tubes andthe surface ofthe large tube Criticize the heat exchanger design and propose some design improvement...
... (i.e., the component of gravity normal to the plate) and that the larger value ofthe heat ow be taken Stable Cases: For the upper side of cold plates andthe lower side of hot plates, the ow ... consists of two cones joined at their bases The diameter is 10 cm andthe overall length ofthe joined cones is 25 cm The axis ofthe body is vertical, andthe body is kept at 27 C in C air What is the ... section, k, à, cp , and Pr refer to properties ofthe liquid, rather than the vapor Film condensation Đ8.5 429 exceptions to this.) The same is true ofthe role ofthe Prandtl number Therefore, during...
... the tank Plot the temperature ofthe base as a function of time on the basis of Fig 9.2 if the bottom ofthe base is insulated In your graph, indicate the regimes of boiling and note the temperature ... (2) depends on the following influences: • T1 and T2 • The areas of (1) and (2), A1 and A2 • The shape, orientation, and spacing of (1) and (2) • The radiative properties ofthe surfaces • Additional ... introduction of a non-condensible gas in the pipe This gas will collect at the condenser, limiting the area ofthe condenser that vapor can reach By varying the amount of gas, the thermal resistance of the...
... Only 45% ofthe sun’s energy actually reaches the earth’s surface The mean energy received is about 235 W/m2 if averaged over the surface andthe year The lower left-hand portion ofthe figure ... temperature ofthe roof if it is painted with either white acrylic paint or a non-selective black paint having ε = 0.9 Solution Heat loss from the roof to the inside ofthe barn will lower the roof temperature ... to the rising concentrations of these gases, the surface temperature ofthe earth has risen significantly Over the course ofthe twentieth century, a rise of 0.6–0.7 K occurred, with 0.4–0.5 K of...
... its thermal conductivity Accordingly, we now consider the calculation of µ and k for mixtures of gases Two ofthe most important results ofthe kinetic theory of gases are the predictions of µ and ... to fix the constant andthe two mole fluxes, N1,s and Ns To this, we apply the boundary conditions at either end ofthe layer The first boundary condition is the mole fraction of species at the bottom ... 11.16, and in some ofthe end -of- chapter problems Transport properties of mixtures §11.4 Figure 11.6 potential 615 The Lennard-Jones in the bulk properties ofthe gas The Chapman-Enskog kinetic theory...