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Young Ninja Group (ages 3-5)

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Frank Titskey
Frank Titskey

3 : The Balance Distinguishes Not Between Gold ... 2021


Why $\lceil\log_3k\rceil$? Each use of the balance scales actually compares three different groups of coins: the one on the left scale, the one on the right scale, and the one not on the scale at all. If one of the two groups on the scale is heavier, then the gold coin is in that group; if neither, then the gold coin is in the group not on the scale. Thus, each weighing can distinguish between 3 states, and $n$ weighings can distinguish between $3^n$ states. We need an integer solution to $3^n\ge k$, thus $n\ge\log_3k$, thus $n=\lceil\log_3k\rceil$.




3 : The Balance Distinguishes Not Between Gold ...



Now if you have only a two-pan balance that does not give a reading, it is no longerpossible to determine where the gold coins are in one weighing.It will take multiple weighings, as in the solutions to this problemand this problem.


Body water balance represents the net difference between fluid intake and loss. Normal body water turnover in a sedentary adult is from 1 to 3 L/day, the range accountable primarily to differences in insensible water loss, or the evaporation of moisture from the skin (Sawka et al., 2005). Large variations in fluid intake are controlled by the kidneys, which can produce more or less urine, depending on changes in body fluid volumes. Water loss in air exhaled from the lungs is often ignored with respect to water balance because it is usually offset by water production occurring during aerobic metabolism (Sawka et al., 2005). Over the course of a day, humans usually regulate daily bodywater balance remarkably well as a result of thirst and hunger drives coupledwith free access to food and beverage. This is accomplished by physiological responses to changes in body water volume and to changes in concentrations of dissolved substances in body fluids, as well as by non-regulatory social-behavioral factors, such as drinking fluids at meetings and parties (Sawka et al., 2005).


Population estimates of fluid needs are based on qualitative and quantitative data (Sawka et al., 2005). Fluid intake surveys provide qualitative data, whereas water balance studies and biochemical assessments offer quantitative support for the adequacy of reported intakes. The combination of total body water and plasma osmolality provides the "gold standard" for hydration assessment.


Urine Concentration. Urinalysis is a frequently used clinical measure to distinguish between normal and pathological conditions. Urinary markers for dehydration include a reduced urine volume, a high urine specific gravity (USG), a high urine osmolality (UOsm), and a dark urine color (UCol). Urine is a solution of water and various other substances, and the concentration of those substances increases with a reduction in urine volume, which is associated with dehydration. Urine output is roughly 1 to 2 liters per day but can be increased 10-fold when consuming large volumes of fluid (Sawka et al.,2005). This large capacity to vary urine output represents the primary avenue to regulate net body water balance across a broad range of fluid intake volumes and fluid losses from other avenues. Although it is impractical to measure urine volume on a daily basis, the quantitative (USG, UOsm) or qualitative (UCol) assessment of its concentration is far simpler. As a screening tool to differentiate euhydration from dehydration, urine concentration as indicated by USG, UOsm, or UCol is a reliable assessment technique (Armstrong et al., 1994; Bartok et al.,2004; Shirreffs & Maughan, 1998) with reasonably definable thresholds.


Interestingly, such a technique was previously mentioned by the group of Moskovits in 1994 in the context of photoemission measurements46, although it was, in that case, rather used to discriminate between one-photon and two-photon processes. To our knowledge, this procedure has not yet been used to discriminate photothermal from photochemical effects in plasmon-assisted chemical reactions. For instance, it could have been relevant to studies such as ref. 9 by measuring the rate enhancement of H2 dissociation on gold nanoparticles as a function of the illumination area.


Article I describes the design of the legislative branch of US Government -- the Congress. Important ideas include the separation of powers between branches of government (checks and balances), the election of Senators and Representatives, the process by which laws are made, and the powers that Congress has. Learn more...


"Fool's gold" is a common nickname for pyrite. Pyrite received that nickname because it is worth virtually nothing, but has an appearance that "fools" people into believing that it is gold. With a little practice, there are many easy tests that anyone can use to quickly tell the difference between pyrite and gold.


The nickname "fool's gold" has long been used by gold buyers and prospectors, who were amused by excited people who thought they had found gold. These people did not know how to tell the difference between pyrite and gold, and their ignorance caused them to look foolish.


Here are a few simple tests that almost anyone can use to tell the difference between pyrite and gold. They can usually be done successfully by inexperienced people. However, wise people obtain a couple small pieces of pyrite and a couple small pieces of gold and use them to gain valuable experience.


The Gold Standard was a system under which nearly all countries fixed the value of their currencies in terms of a specified amount of gold, or linked their currency to that of a country which did so. Domestic currencies were freely convertible into gold at the fixed price and there was no restriction on the import or export of gold. Gold coins circulated as domestic currency alongside coins of other metals and notes, with the composition varying by country. As each currency was fixed in terms of gold, exchange rates between participating currencies were also fixed.


The use of such methods meant that any correction of an economic imbalance would be accelerated and normally it would not be necessary to wait for the point at which substantial quantities of gold needed to be transported from one country to another.


Penman-Monteith equationIn 1948, Penman combined the energy balance with the mass transfer method and derived an equation to compute the evaporation from an open water surface from standard climatological records of sunshine, temperature, humidity and wind speed. This so-called combination method was further developed by many researchers and extended to cropped surfaces by introducing resistance factors.The resistance nomenclature distinguishes between aerodynamic resistance and surface resistance factors (Figure 7). The surface resistance parameters are often combined into one parameter, the 'bulk' surface resistance parameter which operates in series with the aerodynamic resistance. The surface resistance, rs, describes the resistance of vapour flow through stomata openings, total leaf area and soil surface. The aerodynamic resistance, ra, describes the resistance from the vegetation upward and involves friction from air flowing over vegetative surfaces. Although the exchange process in a vegetation layer is too complex to be fully described by the two resistance factors, good correlations can be obtained between measured and calculated evapotranspiration rates, especially for a uniform grass reference surface.FIGURE 7. Simplified representation of the (bulk) surface and aerodynamic resistances for water vapour flowThe Penman-Monteith form of the combination equation is: (3)where Rn is the net radiation, G is the soil heat flux, (es - ea) represents the vapour pressure deficit of the air, r a is the mean air density at constant pressure, cp is the specific heat of the air, D represents the slope of the saturation vapour pressure temperature relationship, g is the psychrometric constant, and rs and ra are the (bulk) surface and aerodynamic resistances. The parameters of the equation are defined in Chapter 3.The Penman-Monteith approach as formulated above includes all parameters that govern energy exchange and corresponding latent heat flux (evapotranspiration) from uniform expanses of vegetation. Most of the parameters are measured or can be readily calculated from weather data. The equation can be utilized for the direct calculation of any crop evapotranspiration as the surface and aerodynamic resistances are crop specific.Aerodynamic resistance (ra)The transfer of heat and water vapour from the evaporating surface into the air above the canopy is determined by the aerodynamic resistance: (4)wherera aerodynamic resistance [s m-1],zm height of wind measurements [m],zh height of humidity measurements [m],d zero plane displacement height [m],zom roughness length governing momentum transfer [m],zoh roughness length governing transfer of heat and vapour [m],k von Karman's constant, 0.41 [-],uz wind speed at height z [m s-1].The equation is restricted for neutral stability conditions, i.e., where temperature, atmospheric pressure, and wind velocity distributions follow nearly adiabatic conditions (no heat exchange). The application of the equation for short time periods (hourly or less) may require the inclusion of corrections for stability. However, when predicting ETo in the well-watered reference surface, heat exchanged is small, and therefore stability correction is normally not required.Many studies have explored the nature of the wind regime in plant canopies. Zero displacement heights and roughness lengths have to be considered when the surface is covered by vegetation. The factors depend upon the crop height and architecture. Several empirical equations for the estimate of d, zom and zoh have been developed. The derivation of the aerodynamic resistance for the grass reference surface is presented in Box 4.(Bulk) surface resistance (rs)The 'bulk' surface resistance describes the resistance of vapour flow through the transpiring crop and evaporating soil surface. Where the vegetation does not completely cover the soil, the resistance factor should indeed include the effects of the evaporation from the soil surface. If the crop is not transpiring at a potential rate, the resistance depends also on the water status of the vegetation. An acceptable approximation to a much more complex relation of the surface resistance of dense full cover vegetation is: BOX 4. The aerodynamic resistance for a grass reference surface For a wide range of crops the zero plane displacement height, d [m], and the roughness length governing momentum transfer, zom [m], can be estimated from the crop height h [m] by the following equations: d = 2/3 h zom = 0.123 h 041b061a72


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