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Provided that you have access to the appropriate financial data, calculating the earnings available for common stockholders is relatively simple. The calculation involves first finding the amount of dividends paid, and then finding the amount paid per share. Using the number of common shares outstanding, you can then find the total available to common stockholders.
An atom contains positively charged protons, negatively charged electrons and neutrally charged neutrons. To remain neutrally charged, atoms need an equal number of protons and electrons. The number of protons/neutrons is the atomic number. The atomic weight of each element appears on the periodic table. The atomic weight rounded to the nearest whole number is called the mass number. The mass number is the number of protons plus the number of neutrons. Isotopes are versions of an element with different numbers of neutrons. That leaves the atomic number the same but changes the atomic mass numbers.
A cannonball attached to a parachute falls much more slowly than a cannonball alone, but the difference has nothing to do with weight. It stems from air resistance. On the moon, both a feather and a pencil would fall at the same speed. If you need to estimate the force of air resistance, you can do so by using a simple equation, as long as you have the cross-sectional area of your object so you can use it in this equation.
When running an experiment or conducting a survey, you need to collect data to draw conclusions from your work. The data you collect can fall into one of two types, discrete or continuous. It is useful to know what type the data is so you can best analyze and present it.
The cross-section of a pipe is the circle. The pipe circumference or perimeter refers to the length around such a circle. The circumference is an important characteristic that allows you to calculate other values, for example the amount of water passing through the pipe. To get the required circumference, you either calculate it from the diameter of the pipe or measure it directly.
If it was not for hydrostatic equilibrium, stars would simply collapse or explode. Instead, they achieve stability through a natural balance of forces. A star's mass determines how much force is required to achieve this stellar balance. Furthermore, mass and hydrostatic equilibrium also affect the star's luminosity and lifespan.
We are all used to the effects of normal gravity; we've lived with it since we were born. Scientists refer to our gravity as a force of 1 g, or 1 G-force. The Newton is, according to Professor Russ Rowlett of the University of North Carolina, the force that accelerates a mass of one kilogram at the rate of one meter per second per second. To convert Newtons to G-force you must know both the mass of the object and its acceleration.
In a dehydration reaction, a molecule of water or the equivalent is removed from a reactant during the course of the reaction. One example is the reaction of concentrated sulfuric acid with an alcohol like ethanol. The concentration of water has an important effect on dehydration reactions, because in a more dilute solution, the reverse process takes place.
A cation is a positively charged ion of a metallic element that is formed during a chemical bonding process known as ionic bonding. An ion (or particle) becomes positively charged when it loses electrons. These metallic elements are able to gain or lose electrons easily because they holds their outer electrons loosely.
Chemists use the term "ion" to refer to a chemical species which has an electrical charge; either positive or negative. Ions are formed when certain elements which differ in their attraction for electrons combine and in the process take on opposite charges. They are very common and are encountered often in daily life. Scientists name some ions anions and their counterpart cations based on their charge.
The technical definition of linear impulse is the integral of a force with respect to time. This is equivalent to the magnitude of the change in momentum of an object over a period of time when a force is applied to the object. In symbols, I = m"v, where I is the impulse, m is the mass of the object and "v is the change in velocity over a period of time. This means that a small applied force produces the same impulse over a long period of time as a large force produces in a brief period of time.
Chemists use the term "ion" to refer to a chemical species with an electrical charge. These charged chemicals are very important in daily life on Earth and are also very prevalent. You encounter them in the water you drink and the food you eat, and they also play many important roles in the metabolisms of all living things.
Many of the substances dealt with in chemistry, as in life, are not pure --- rather they are dissolved in water. This makes knowing how concentrated a solute (solid) is in a solvent (the liquid it is dissolved in, usually water) crucial in interpreting an experiment's results. A substance's concentration, also called its molarity, is measured in moles per liter, expressed as either mol/L or mol L^-1. It can be found using a simple mathematical formula.
Testing for nitrate anions in solutions is more difficult than for other types of anions, because even after precipitation, nitrates remain water soluble. Sulfates give off a barium precipitate when tested for anions in the same solution, for example -- and barium settles nicely to the bottom instead of dissolving back into the water. However, by adding iron (II) sulfate and sulfuric acid to an aqueous nitrate solution, you can determine whether nitrate anions are present.
Isotopes of an element are atoms that have a varying number of neutrons. While atoms of the same element must have the same number of protons in order to be classified as the same element, the number of neutrons are allowed to change. The relative abundance of an isotope is the percentage of the atoms of a particular element that are of a certain isotope. An isotope of an element is designated by a number following the name of the element. For instance, the element carbon always has six protons. Carbon isotopes such as carbon-12 and carbon-14 have a different…
A derivative is a concept from calculus that describes the rate of change of a curve. This concept can be extended to two (or more) dimensions through the use of a partial derivative. Partial derivatives allow one to determine the rate of change of surfaces. These three-dimensional surfaces can also be described using a two-dimensional representation known as a contour map, which estimates the elevation of point of the surface using lines. Contour maps can be used to estimate the partial derivative of a function using a few short steps.
Many living organisms are able to maintain balance and movement. Although a body may face forces such as gravity daily, the body is able to sustain balance through the use of internal organs. The theory of equilibrium explains how the body is able to balance while being influenced by outside forces.
When a chemical reaction between two or more gases has reached equilibrium, the partial pressures of the gases cease to change, because both the forward and reverse reactions are now running at the same rate. The equilibrium constant expression relates the partial pressures of the reactant and product gases to a constant called K (or sometimes Kp), which is specific for the reaction in question at a given temperature.
Factorial statistical analysis refers to analysis in which a quantitative dependent variable is compared to one or more categorical independent variables (analysis of variance, or ANOVA) and possibly one or more quantitative independent variables as well (analysis of covariance, or ANCOVA). The dependent variable is one that you think is affected by or related to the independent variables; for example, you might investigate the relationship, in American adults, between income (dependent variable) and sex, ethnic/racial group and state of residence (independent variables). Categorical independent variables are also known as "factors; factorial designs are classified based on the number of factors…
The idea of tension in physics refers to the amount of pulling force being applied to a rope, cable or other similar object. Tension is measured in newtons and always indicates the degree of force parallel to the rope. Two possibilities exist in rope tension problems. The first is when the acceleration of the objects being held by the rope equals zero, in which case tension simply equals the amount of force being exerted on the rope. The other possibility is when the system of objects is accelerating and the net force must be considered. Also, the rope is considered…
Surf's up! You don't have to be a board or body surfer to love waves. When it's a hot summer day, waves are fun to splash and romp in at beaches. Waves also represent a physical phenomenon: the transfer of energy through a medium, in this case, water. Though the water in a wave seems to be traveling along with the wave, the energy of the wave itself is what travels. The water in the wave keeps its general position in relation to the ocean or lake bed, only rising and falling as the wave passes.
Hydrostatic equilibrium refers to the balance of forces keeping gasses and liquids stable. The atmosphere around the Earth, for example, is in hydrostatic equilibrium --- if it weren't, then the air would collapse down into a tiny layer just above the surface, or it would spread much farther away from the surface. Either situation would not be good for life on Earth. The forces balancing each other are the force of gravity pulling down and pressure pushing back. For planets mostly composed of gasses --- or for stars --- hydrostatic equilibrium completely defines their structure.
In basketball, you can evaluate a player by his hang time. Hang time is how long a player is in the air. To calculate this, you need to use a physics equation for falling bodies. A falling-body equation looks at the time it takes for an object to fall. Remember that when falling, the only thing that matters is distance and gravity. The mass of an object does not matter. After you know how long it takes for the object to fall, doubling the amount gives you an approximate estimate of hang time.
The statistical test you choose depends on the type of data and your research objective. Data can be either continuous, binomial or ranked. Continuous data is measured on a scale with a full range of values. Examples include temperature, height and weight. Binomial data has only two values, typically yes and no, favor and disfavor or win and lose. Positions in a race are ranked data. Once you have figured out what type of data you have, determine your research questions, which might include describing data, comparing data, testing association and predicting outcome.
Discrete data is data that can only take on a limited number of values. These may be ordinal or nominal. Ordinal data has an order. For example, if you ask people "How much do you support the president?" and the possible answers are "none," "a little," "some" and "a lot," then the data is discrete (only four possible answers) but has an order. Nominal data has no such order. For example, if you ask people about their hair color and the choices are "blonde," "brown," "red," "white," "bald" and "other" then the possibly answers have no order.
You can learn to determine the magnitude of the average net force for physics calculations involving an impulse. An impulse results when a force, which may vary in magnitude during application, acts on an object over a time interval; for example, when a baseball bat collides with a ball. The magnitude, or measure without regard to direction, of the average force applied to the ball by the bat is related to the change in velocity of the ball, its mass and the duration of contact. Common units for force include newtons and pounds.
Unlike molarity, which gives you moles of solute per liter of solution, osmolarity gives you moles of solute particles per liter of solution. For a compound like sugar or benzene, there is no difference, because these compounds don't split up into separate particles when they dissolve. Ionic compounds like sodium or cesium chloride, however, do split up into separate particles, so the osmolarity and the molarity for these kinds of compounds will not be the same.
ANOVA stands for Analysis of Variance. ANCOVA stands for Analysis of Covariance. Despite these names, both are statistical methods of comparing means of groups of subjects on some numerical variable. Adding to the potential for confusion, both of these techniques are part of what is known as the general linear model, which also includes regression.
Calculating concentrations at equilibrium is an important skill for your success in general or introductory chemistry. Fortunately, it's not typically too difficult -- as long as you remember your algebra and know how to set up the equilibrium constant equation, you can usually solve it without too much trouble. Remember, however, that the equilibrium constant will change if the temperature changes, so you should always make sure the equilibrium constant you are using is valid for the temperature in question.
"Est modus in rebus" (Things have their due measure), wrote the Roman lyric poet Horace (65-8 B.C.). In other words, scientists do not measure the capacity of the Atlantic Ocean in teaspoons or cite the distance to the moon in millimeters. Very small entities demand very small units and very large ones require very large units. The micron, or micrometer, is a unit of length measurement. It is also used informally as a unit of pressure.
Scientists commonly model periodic relationships on a sine function. For example, in the 1970s a Massachusetts Institute of Technology master's student modeled the oscillating relationship between lynx and arctic hare populations, finding that as hare density increased, lynx deaths decreased, and as hare density decreased with the subsequent decrease in lynx deaths, lynx deaths increased. The period of the modeling function for this relationship was approximately 10 years. You can figure out the period of a sine function easily.
Comparing groups is a very common statistical activity. The proper method depends on whether you have two or more than two groups, and what type of variable you want to compare, such as nominal, ordinal, interval or ratio scale.
A beam of laser light remains pencil-thin for long distances due to its high concentration and purity. Different kinds of lasers have a range of energy levels to suit delicate tasks such as eye surgery or heavy-duty applications like cutting steel. The effects of laser light also include curing soft resins into hard plastics, acting as delicate tweezers and producing impulses in electronic detectors.
When on Earth, your mass and your weight are always equal to each other. However, when you leave the Earth, your mass will remain constant but your weight will change. Your weight changes due to gravity. The difference between your weight on Earth and your weight on another planet, can be shown as a change in weight.
Learn to calculate the normal force between two blocks to help solve physics problems. Many physics problems require finding the normal force, including the determination of friction. When an object rests upon another, the top object's weight must be balanced by a reaction force according to Newton's Third Law. The reaction force is the normal force and equals the top object's weight, as long as it does not crash through the bottom object. The normal force points away, perpendicularly, from the surface to which weight is applied.
Statistical tests are used by scientists to interpret large amounts of data gathered from experiments. There are no hard and fast rules when choosing an appropriate statistical analysis tool. Most data can be legitimately analyzed in a number of ways. Once a test has been chosen, most are usually performed using the SAS, Stata and SPSS computer programs.
Ounces and pounds are ancient units of measurement, dating to at least the 11th century. Their weight values and the relationship between them has varied, but today the weights and the relationship are fixed. The word "pound" originates in the Latin word "pondus," meaning weight, but the pound symbol, "lb." is from another Latin word "libra," meaning "pound." The ounce originated from "uncia," which is Latin for twelfth. The symbol "oz." is an abbreviation of the medieval Italian word for ounce -- onza.
Generated by wind or other forces, water waves are everywhere -- in oceans, rivers, ponds, lakes, rain puddles, bathtubs, sinks and even your morning cup of coffee. Yet you may not have the words to describe these fascinating natural phenomena that are so much a part of our lives. Although you can learn a lot from scientists, especially oceanographers and physicists, you do not need to be or become one in order to learn the language of water waves.
Learn to calculate the pulling tension in a cable to prevent an accident. Crane and pulley systems use an upward force on a cable to raise objects. This creates a tension in the cable that should not exceed the tensile strength of the cable in pounds. Exceeding the tensile strength may cause the cable to snap or deform. When the crane lifts the cable the tension increases while lowering the cable decreases the tension. (See References 1) An accelerometer may be employed to measure the cable's acceleration when it's lifted or lowered. Also, increasing the weight attached to the cable…
Scientists, sociologists, pollsters and many others use statistical analysis to obtain the information they need. Statistics can be a powerful tool and it can provide useful answers. However, there are some drawbacks. When you perform a statistical test, you are usually testing a sample taken from a population, then using your sample data to make conclusions about that population. For example, a telephone survey might poll 1,000 people to find out what everyone in the country is thinking about a certain political party. Many of the disadvantages of statistics stem from the use of samples.
The foot-pound and the inch-pound are two of many different units used to measure work and torque. These two customary units are equal to the force of 1 lb. acting through the distance of one foot and 1 lb. acting through the distance of one inch. Because both units are based on the pound and a customary unit of length, converting one to the other is a straightforward process.
Statistical data analysis covers a huge range of techniques (such as various types of regression, factor analysis, t-tests, analysis of variance, multi-level models, and many others), and can work with a range of types of data (nominal, ordinal, interval or ratio variables, date variables, count variable and others) that were collected in a variety of ways (observational data, quasi-experimental data, or experimental data). Nevertheless, there are some general procedures that apply to many, if not all, of these analyses.
Living in a consistent gravity field, humans have naturally used weight, the force of gravity acting on an object, as a convenient measure of mass. The Imperial unit of mass, the pound, is based on the old Roman libra, which is why it is abbreviated "lb.," but the pound is also used as a unit of force, which can be confusing. Yet it was only after Sir Isaac Newton articulated his famous law, F = ma (force equals mass times acceleration) that it really became important to distinguish between the two.
Aside from the sun, moon, planets and hundreds of man-made satellites, there are thousands of objects within one light year of Earth. NASA, in conjunction with astronomical observatories around the world, searches for and tracks these objects in order to provide an early detection system in case one of these near-Earth objects might be on a collision course with our planet.
Waves represent a disturbance or variation that transfers energy through a medium, from one point to another. There are two types of waves: transverse and longitudinal. By nature, transverse waves have high and low points. These high and low points represent the two parts of a transverse wave, called the crest and trough. Furthermore, there are three properties used to describe these wave parts, called amplitude, wavelength and frequency.
"Mass" refers to the actual amount of matter that makes up an object. Weight, by contrast, is a measure of force, which equals the mass of an object multiplied by its acceleration due to gravity. This is sometimes confusing, because the pound can measure either mass or weight, whereas the kilogram is solely a unit of mass. In order to calculate the difference in weight between objects on Earth and the moon, you must first convert kilograms to newtons, which are the unit of force under the International System of Units.
Random effects and fixed effects are terms used in statistical modeling. The contrast between them causes a lot of confusion. Random and fixed effects originate in the data sampling plan and analysis plan and must be dealt with differently in statistical analysis. Sometimes, a statistical model includes both random and fixed effects; this requires a type of model that has many names, including mixed model and hierarchical model.
As per Isaac Newton's Second Law of Motion, the rate of change of momentum is proportional to the imposed force and goes in the direction of the force. It can be expressed as F = mg, where F= force (weight), m = mass and g = acceleration of gravity. The value of "g" is 9.81 meters per second per second. This formula can be used to convert the mass into newtons.
An electric dipole is a configuration of two equal but opposite electrical charges separated by a distance. A dipole moment is the vector sum of a system of point charges around a single point. Often a dipole moment is calculated for a pair of charges, though a dipole moment can be calculated for systems of three or more charges. The dipole moment does not depend on the coordinate system since it is an inherent property of a dipole.
When reading about statistical analysis of data, you will often see words such as "statistically significant" or just "significant". Sometimes you will also see a phrase such as "p < 0.05". What do these mean? How are they determined? Are they important? Is a result that is statistically significant necessarily replicable or important?
An ion is an atom or molecule that carries an electrical charge. Cations are positively-charged ions created by the loss of electrons. Anions are negatively-charged ions created by the gain of electrons. In chemical reactions, all ions exhibit their own unique, characteristic behaviors.
Mass is the most basic unit of measurement. Mass and weight are often confused, although the two are not quite the same; an object's weight is the force exerted on it by gravity. In space, an object is weightless, but it still has the same mass. Acceleration due to gravity is constant for objects near Earth's surface; however, mass is directly proportional to weight, and a scale will give you the mass of an object based on how much it weighs.
Any object within the earth's gravitational field is subject to its gravitational force, and the object's weight is a measure of that force. The unit for gravitational force is the newton, named after Sir Isaac Newton. He first explained the mathematical equivalence between force and the product of an object's mass and the acceleration the force produces. In the British system of units, weight is measured in pounds, and because weight is a measure of force, pounds and newtons are units for the same thing. Convert from one to the other by multiplying by a constant.
Polygons are geometric figures created by intersecting straight line segments, or sides. Common examples are triangles and pentagons. You can find the length of a side assuming you know either the apothem or the radius for the polygon. The apothem is the distance from the polygon's center to the midpoint of a side. A radius is similar but goes from the center to a vertex, or connecting corner, of two sides. These calculations only work for regular polygons. Irregular polygons, by their vary nature, can have sides that vary widely in length to each other.
Force is "push or pull" on an object exerted by another object, either through direct contact, such as normal force, or by action-at-a-distance, such as gravity. The metric unit of force is the newton, or N. A newton is the force required to accelerate a mass of 1 kilogram at 1 meter per second per second. The English unit of force is the poundal, or pdl. This is the force required to accelerate a mass of 1 pound at 1 foot per second per second.
All specialized occupations have their own language, and physics is no different. It's not only a matter of making up new terms, but also assigning special meanings to common words. "Mass" and "weight" are good examples. In common usage, they mean the same thing. In physics, they have quite different meanings. Mass is an intrinsic property of all physical objects, while "weight" is a measure of gravitational force --- how strongly one object (the Earth, for example) pulls on another. So, although you can say that a pound equals 0.454 kilograms, the real equivalence is between pounds and "newtons," another…
Chemists use the mole concept to perform chemical calculations and express concentration. Technically, a mole represents 6.022 x 10^23 atoms or formula units of a substance, which corresponds to the number of atoms or formula units necessary to form an amount of substance in grams equal to its formula weight. The formula weight is determined by adding together the atomic masses, as found on the periodic table of the elements, for all of the atoms in the compound's chemical formula. The mole concept also allows chemists to determine the relative amounts of substances from balanced chemical equations. Ionic substances comprise…
The head of a fluid is an important concept in fluid mechanics which relates the energy stored in a fluid to the height of a static (stationary) column of fluid. The velocity head is a particular type of head that refers to the energy in a fluid due to the motion of a fluid, which is expressed as kinetic energy. In engineering applications, the velocity head is an important concept and can be calculated in only a few steps.
Imagine you grasp one end of a string held taut at its other end -- attached to a post, let's say -- and then imagine that you pluck your end of the string. The speed of the resulting wave can be calculated using some basic physics. The tension force does work on the string, transferring energy along the string in one direction. This wave transfers energy but not mass. Here's how to calculate its speed.
Newton's Three Laws of Motion provide the basis for understanding the source of movement for many macroscopic objects. One important implication of these laws is that any changes in motion of an object is caused by a force (such as a push or pull). These interactions where two (or more) bodies are in contact are called contact forces. Contact forces are ubiquitous and are the cause of most everyday interactions that are explained by Newton's Laws.
Ionic strength measures the concentration of ions of a dissolved salt in solution. It can significantly affect the properties of a solution, so it's an important consideration in chemistry and physics. Calculating ionic strength is fairly straightforward, even in cases where multiple salts have been dissolved; it is important to note, however, that we can calculate it in terms of molarity (moles of solute per liter of solvent) or molality (moles of solute per kilogram of solvent). Whether molarity or molality is preferable depends on the type of experiment and the problem you want to solve.
In any type of research, statistical analysis is essential to properly represent your data results. Statistics is a part of the research process that answers questions through data. To perform statistical analysis, you must properly collect and organize data. Depending on your data set and the questions you need to answer, there are several types of statistical data analysis to choose from.
The vertical tangent to a curve occurs at a point where the slope is undefined (infinite). This can also be explained in terms of calculus when the derivative at a point is undefined. There are many ways to find these problematic points ranging from simple graph observation to advanced calculus and beyond, spanning multiple coordinate systems. The method used depends on the skill level and the mathematic application. The first step to any method is to analyze the given information and find any values that may cause an undefined slope.
Calculate the velocity of an object after an applied impulse to determine how fast it is moving post-collision. An impulse is a push or pull, or force, acting over a given amount of time. One example is a moving car striking a parked car. If the time over which the impulse occurs is extended, the damage may be minimized by decreasing the impulse. An example would could be a boxer rolling with a punch that hits him. The impulse changes the velocity of the object it affects. The new velocity depends on the magnitude of the impulse, the initial velocity…
Learn to determine the force between two touching objects to be able to complete physics problems. According to Isaac Newton's third law of motion, forces in nature exist in pairs. Specifically, when an object applies a force to another object, an equal force directed in the opposite direction appears. An example is a book sitting on a table. The book exerts a force downward on the table equal to its weight. The table exerts a reaction force, called normal force, back on the book equal to the book's weight.
Consider calculating the tensile force, also called tension, on a cable system to avoid an accident. Weights hung from a cable or rope produce a tensile force which should not exceed the tension rating of the cable. If the tension rating is passed the cable may snap, causing injury or property damage. The tension in the cable depends on the weight hanging from it and the acceleration of the cable. A downward accelerating cable reduces tension, but an upward acceleration increases tension. Forces and weights are measured in newtons in science and in pounds in standard units.
A jib crane consists of a hoist mounted on a horizontal beam that extends well beyond, or is cantilevered from, a vertical support. The beam pivots around the support to provide the horizontal sweep of the crane.
Statistics is the branch of mathematics that deals with organizing data to provide useful summaries. Many statistical techniques are used to analyze data, but learning just a few of the basic and most widely used approaches will allow you to produce meaningful data analysis. These techniques fall into two general categories, descriptive and inferential. They can serve many purposes: to summarize the data in a simple manner, to organize it so it's easier to understand and to use the data to test theories about a larger population.
Nozzles are mechanical devices which are used to control the flow or characteristics of fluids. Nozzles can come in many different shapes and forms; for example, nozzles can be used to increase thrust on a rocket, or to control the amount of fluid released from a pipe in a given amount of time. There can be many forces and moments that nozzles are subject to; however, the principles of calculating these forces and moments can be relatively straightforward.
The concept of moles helps you determine the volume and concentration of a substance. One mole of a substance has a mass in grams that is equal to its molecular mass, which is the number that usually appears at the top of each element box in the periodic table. For example, one mole of carbon atoms has a mass of 12 grams. If you know the volume of a gas, you can determine its number of moles.
Determine the load on a boom to prevent hoisting too much weight. Not only will this keep you safe, but it may also prevent mechanical failure. A load equals the tension placed in the boom's lifting cable. Applying Newton's second law of motion shows that if the boom cable accelerates upward, more tension is placed on the cable. Conversely, if the object held by the boom accelerates downward, the boom experiences less tension. Perform calculations with Newton's laws in metric units, then convert to standard units at the end to avoid errors.
When you do not have an explicit formula for a function with two variables, you can still estimate the partial derivatives of the function by using a contour diagram. Regular derivatives measure the rate of change of the function, or the slope of the tangent line at point x. Partial derivatives help you tackle functions with more than one variable, by finding the regular derivative of the function while keeping one variable constant. This way, you will be able to see how fast the function is changing in either the x or y direction. Estimate partial derivatives numerically using level…
Data collected in scientific research studies must be statistically analyzed before drawing conclusions about results. Generally, you have to demonstrate that there is less than a five percent probability the results you found were due to chance. Writing up statistical analyses requires reporting the statistical tests used, the variables examined and, finally, the results.
A buffer solution is a solution that is able to resist pH change after the addition of acid or base. Buffers are made by mixing large amounts of weak acids or bases together along with its conjugate. These solutions are important for many chemical applications, especially applications that are sensitive to pH changes such as biological systems. Typically, it is more important to determine the ionic strength of a buffer solution rather than the buffer's concentration. Determining ionic strength accurately defines pH of solutions by estimating concentrations of all ions in the solution.
"Mass" is a measure of how much matter an object has. "Weight" is a measure of the amount of force brought to bear on an object by gravitational attraction. Gravitational force changes based on location. For example, the gravitational force on the Moon is 0.165 of that here on Earth. Weight changes based on location in direct correlation to the measure of gravitational force at the location. Mass does not change with location. To find an object's mass using its weight, the formula is Mass equals Weight divided by the Acceleration of Gravity (M = W/G).
Statistical analysis is a quantitative method to find probabilities between sets or results of data. This data can come from the natural or social sciences. Statistical analysis helps elaborate on trends or patterns found within the research of a topic. For example, if a medical doctor needed to test the probable effectiveness of a drug, she would utilize statistics to see if the drug worked a certain number of times for a certain population. Then, she would analyze the results to see if the drug results have a relative or probable accuracy.
Ocean waves are the rising and falling movement, known as undulation, of the sea surface and can travel thousands of miles before making landfall. Waves on the ocean are usually caused by winds, and a general rule is that stronger winds result in bigger waves, but they can also be generated by activity above or below the surface of the sea. Your classroom can be an easy venue to better understand ocean waves and how they are made.
Calculating the bending moment is a crucial part of structural engineering, particularly in the construction of bridges. Calculating the bending moment in the metric system is no different from that in the imperial system, and involves working out the forces exerted on a given point a known distance away from the pivot point. Calculating this is a simple process, and does require a great deal of technical expertise or technical equipment, yet will provide a great deal of useful information.
Arctg is an abbreviation for "arctangent," which is an inverse trigonometric function. The arctg function calculates an angle from a tangent, or "tan," value, expressing the angle in either degree or radian units. Computing arctg values is a common type of trigonometric problem or math class assignment, and you can use a calculator or available online tools to calculate this function.
Adding chlorine to your pool helps to kill unwanted germs and gets rid of algae. But too much chlorine can be a dangerous, and even deadly, thing. If you feel that there's too much chlorine in your pool, you should stay out of it until you lower the level. You can reduce the amount of chlorine in your pool, but first you'll have to see just how much you have to get rid of.
A polygon is a figure with three or more sides, such as a square or triangle. A regular polygon has all sides of the same length, and all adjacent sides intersect at the same angle. A regular hexagon has six equal sides. The apothem of a regular polygon is a line drawn from its center that intersects a side at a right angle. The term also refers to the length of that line. If you know the length of a side, you can compute the apothem of a hexagon with a simple formula.
Ionic strength is the total ion concentration in solution. Knowing ionic strength is important to chemists because ions have an electrical charge that attract or repel against each other. This attraction and repulsion causes ions to behave in certain ways. Basically ionic strength represents interactions between the ions in water and the ions of a solution. Although ionic strength has been looked at for over the past 100 years, it is still not fully understood. Ionic strength is calculated by using a mathematical formula proposed in 1923 by Peter Debye and Erich Huckel.
The atoms in a molecule bond by sharing electrons. Theoretically, the atoms share electrons equally, so the positive electrical charge in one atom balances the negative electrical charge in another atom. In practice, however, electron sharing is imperfect, as atoms bonded to each other do not overlap perfectly. Thus, the electron carries a slight electric charge as it travels from one atom to another in a bonded pair. The charge gets bigger as the distance between the bonded atoms increases. This charge is known as a dipole moment, and the substance made up of these types of pairs is considered…
Akaike's Information Criterion (AIC) is a statistical measure of the likelihood of a model, penalized for the complexity of the model. It is useful when comparing two or more statistical models for data. All of the models must have the same dependent variable. The formula for AIC is 2k - 2 ln(L), where "k" is the number of parameters in the model and "L" is the likelihood of the model. A smaller AIC indicates a better-fitting model.
The kinetic rotational energy K of a rigid body can be found by taking the product of its moment of inertia I and its rotational velocity w squared multiplied by ½, as follows: K= 1/2 I*w^2 . Inertia is a property that indicates how much resistance a body exerts when a force tries to accelerate it from rest, or change its motion if it is moving at a constant velocity. Kinetic energy is the energy a body possesses due to its motion and is a measure of how much work that has been done on it to increase its velocity.
Arc flashes happen when electricity suddenly arcs between two conductors. They are extremely dangerous, and some of the causes are dirty or damaged equipment, or employee proximity to live wires. The purpose of an arc flash analysis is to protect workers from possibly being injured during such incidents. The analysis helps determine the appropriate clothing and equipment needed to protect workers from arc flashes.
Tension is the magnitude of pulling force exerted on a string. If you hold a length of string tight between your hands, any force that you exert on one end of the string is transmitted through the entire length of string to the other hand. The force transmitted by the string is called the tension in the string. This concept of tension is very important when you use a stringed instrument. The tune carried by a string is proportional to the speed that sound travels in the string, and that speed in turn depends on how tense and heavy the…
A triangle wave is a type of sinusoidal wave that has no curves; it has peaks just like a sine wave, but between each peak is a straight line. While one would think this would be easier to plot than a normal sine wave, it is in fact much harder. The current conventions that most systems use to plot a wave are based on the normal sine wave and converting that to a triangle wave can be rather tricky.
Chemical equilibrium refers to a state in which the products of a reaction are being converted back to reactants at the same rate that the reactants are being converted to products. You can calculate the equilibrium constant, K, using a formula. You can then use this constant to calculate the concentration of a particular reactant at equilibrium.
When a salt, known as the “solute,\" is dissolved in a solvent, it undergoes a process in which the positive and negative ions of the salt separate. This process is called “dissociation.” The concentrations of the ions depend on the ratio in which they were present in the salt before dissolution and on the amount of solvent in which they have been dissolved. The concentrations are mostly commonly expressed in units of molarity, or moles per liter.
The Fahrenheit scale is commonly used in the United States to express temperature. Water freezes at 32 degrees and boils at 212 degrees on this scale. Many other countries have adopted the Celsius scale, in which water freezes at 0 degrees and boils at 100 degrees. You can insert a temperature conversion formula into the Microsoft Excel spreadsheet, or simply compute Fahrenheit degrees on a calculator.
You can easily measure the height of a flagpole without having to climb it by using the rule of similar triangles. The idea is that if two triangles have the same three angles, then the ratio between the sides' lengths is the same between triangles as well. For example, if two triangles have angles 45, 45 and 90 degrees, then the two sides other than the hypotenuse are equal in each triangle.
The circumference of a circle is the length of the line that goes around it. You may need to find the circumference of a circle to solve a math or geometry problem, or for a real-life task such as finding the length of fencing to put around a circular garden. Pi is the ratio of the circumference of a circle to its diameter. Pi has the same value for all circles, approximately 3.14159265 (the digits actually go on without repetition). If you know the diameter or radius of a circle, you can use pi to find its circumference.
Isotope is a chemistry term used to describe the elements of the periodic table. Specifically, it describes the difference between two atoms that have the same number of protons but a different number of neutrons. When this occurs, the two are said to be isotopes of one another. Isotope abundance is an expression of how frequently the various isotope arrangements of a given element actually occur.
Coils are inductors--they resist the flow of alternating current. This inductance is accomplished by magnetically shifting the relationship between the voltage (how much electromagnetic force is being applied) and the current (how many electrons are flowing). Usually voltage and current are in phase--both high at the same time, both low at the same time. Coils change that, and the stronger the coil (the more henrys, or units of inductance), the bigger the phase shift.
When applying statistical modeling to a set of data, the "normal distribution" refers to a bell-shaped probability function that is centered around the mean value of the sample. Once constructed, this function allows researchers to evaluate the significance of individual points or values through the use of Fourier Transforms and other operations from higher mathematics. To derive the normal distribution function, you must first calculate the mean and standard deviation for the data sample.
Oxygen is a prevalent gas in the Earth’s atmosphere that is essential for living organisms. Chemically, this gas consists of two oxygen atoms denoted with the formula “O2.” The quantity of the oxygen gas can be measured in moles that serve as a specific unit in chemistry to express the amount of substance. You can straightforwardly compute moles if the mass of an oxygen sample is known. The other method relies on the ideal gas law that allows you to calculate oxygen moles if the volume of the gas under certain pressure/temperature conditions is given.
Electrical watts measure the flow of electrical energy in a circuit. Electrical energy is measured in Joules. Watts measures how many Joules are flowing through the electrical circuit over a given amount of time. To determine watts, you must multiply the volts by the amperes. To determine the number of volts and amperes, use a multimeter that measures these quantities. Insert the numbers in your formula and you can calculate watts of electrical use.
According to Wolfram's Math World, the first known solution to the quadratic equation, x^2+bx+c=0, was discovered around 2000 B.C. However, the general solution to the cubic equation z^3+a_2*z^2+a_1*z+a_0=0 (where * stands for multiplication, the caret ^ stands for exponentiation and a_1 and a_2 are coefficients) was not discovered until the 1500s. This gives some indication of the difference in complexity of the two problems. To solve the cubic equation takes several steps, but it is not beyond the capability of anyone who can learn and use the solution to the quadratic equation.
The gamma function ?(p) is an integral function of a parameter, p. It has the property that, if p is an integer, then ?(p)=(p-1)!. Here, the exclamation point indicates a factorial. For example, ?(4)=3x2x1=6. The gamma function also has values for non-integer parameters. ?(p) is defined as the integral of x from 0 to infinity of an argument, where the argument is the product of x raised to the (p-1) power and e raised to the -x power. “e” is the base of the natural logarithm. The gamma function plays an instrumental role in the gamma distribution of statistical fame,…
Rotational inertia, also called the “moment of inertia,” describes how the mass of a body is distributed about an axis of rotation. Moment of inertia is usually denoted with a capital L. As shown in Halliday and Resnick’s introductory textbook “Fundamentals of Physics,” the rotational kinetic energy, K, of a body is a function of its moment of inertia: K=(1/2)I?^2, where ? is its rate of rotation and the caret ^ indicates exponentiation. L can be found either by summing over individual masses m_i, based on their distances r_i from the axis of choice, or a continuous mass can be…
V-belts are a type of drive belt that is used to transfer power from one shaft to another via pulleys. The pulleys used with V-belts have a V-shaped groove that allows the belt to seat itself within the groove, preventing the belt from sliding off of the pulley and providing additional torque when stretched. V-belts are made from rubber, but can also be reinforced with steel or polyester fibers. When V-belts wear out, they need to be replaced so they don't break. Calculating the necessary V-belt length for replacement belts can be tricky if the pulleys are different sizes.
Given three points, you can find the center of a circle that passes through all three. Once you've located the circle's center, you can easily find the circle's radius, which is just the distance between the center and any one of the three points through which the circle passes. This is a common problem that comes up in geometry and technical drawing classes.
In a year, the earth completes one orbit around the sun. Equinox is the two times of the year when the sun crosses the plane of the earth's equator and when the length of day and night is just about equal in all parts of the world. There are two types of equinoxes that occur each year: the vernal equinox and the autumnal equinox. The vernal equinox occurs during spring, and is believed by many cultures and religions to be the time of rebirth. One of the most popular festivals associated with this is the Easter holiday.
A golf handicap allows golfers of different skill levels to compete on a more equal playing field. Determining your handicap is essential to the game, and gives players a goal in improving their game.
The structure of soil determines its suitability for agriculture, road subsurface or building foundation. Soil has four constituent parts. Sand is any soil particle larger than 0.06 millimeters (0.002 inches). Silt is any soil particle from 0.002--0.06 millimeters. Clay is any soil particle below 0.002 millimeters, including colloidal clay so small it does not settle out of suspension in water. Humus is colloidal decayed organic matter. The percentage distribution of those parts determines soil structure.
One may want to solve for a variable in an exponent to determine, for example, how much time must pass before an investment is doubled in value. Specifically, if the value of an account is principal---(1+interest)^years, then the equation to determine the time to doubling is principal---(1+interest)^n = 2---principal, or (1+interest)^n = 2. One then needs to solve for the exponent n, for a given interest rate.
One aspect of chemistry examines the interactions of elements and molecules in formulas. Calculating formula mass only requires simple addition of masses. Most of the mistakes made when determining the mass of a chemistry formula occur if students lose track of the number of individual elements or they ascribe the incorrect atomic weight to the elements.
Analysis of covariance (ANCOVA) is a more sophisticated form of analysis of variance. It accounts for a shared variable between populations that may be explaining variation. For example, three groups may receive three treatments. Variations between group survivals may be driven by age differences; therefore, controlling for the effect of age by including it as a variable could improve the model's explanatory power.
Random number generators (RNGs) are important for accurate computer simulations of scientific experiments based on random numbers. These are called Monte Carlo simulations. Random numbers are also useful for data encryption. Methods of RNG vary from selecting a digit from an irrational number to using random atmospheric noise.
The derivative of a function, or curve, at a particular point is its slope or steepness or rise-over-run, which is also its rate of change. It is also the slope of a line touching and parallel to the curve (i.e. the slope of a tangent line). The derivative is therefore a generalization of the concept of slope from a line to a curve, and the derivative of a line has the same value at every point along the line.
In geometry, concentricity is the quality of imbedded circles having the same center. In industry, concentricity is a measure of constancy of tube or pipe wall thickness. Such constancy is desirable for different reasons in different situations. Evenness of wall thickness is desirable for integrity if pressure will be applied to the tubing. If the tubing needs to be spun, variation in wall thickness can cause shimmy. The formula for calculating concentricity is simple. The difficult part is making sure the survey of the varying thickness of the piping wall is comprehensive enough.
A cylinder has the shape of a typical can of soup, container of uncooked oatmeal or a can of Pringles potato chips. The volume is basically the capacity of this solid object with circular ends. Sometimes it is necessary to determine how many gallons can be held by a cylinder; for example, determining how many gallons of punch can fit in a large pot. Use a straightforward series of steps to make the calculation.
Mass can be measured on a digital scale. If the scale measures in kilograms, the mass of the weighed object can be read directly. If the scale measures in pounds, a simple equation can be used to convert to mass.
Calculus can be used to find a range of formulas for volume and area, but the ancient Greeks knew formulas for volume without using it at all. They found formulas for the volume of the sphere, cone, pyramid and even for objects with more than four sides.
Micron is a unit of length used to conveniently express a size of very small objects (e.g., crystal dimensions in crystallography). Micron is equal to one millionth of the meter or 1E-6 meter (1E-6 denotes "ten in power -6"). Microns can also refer to a unit of pressure that is equal to the micrometer of mercury (umHg). As an example, we will calculate 0.0000086 meters in microns and the pressure of 200 Pa in microns.
Angstrom is a unit of length named after the Swedish scientist A.J. Angstrom. Despite being not the part of the International System of Units (SI), angstrom is regularly used in crystallography and spectroscopy. Angstrom is equal to 1E-10 meter (1E-10 refers "ten in power -10"). As an example, consider two common types of calculations: from meters and nanometers to angstroms.
Ocean swells are characteristically smooth, without the peaks and breakers of a wave. They might appear to be gently rolling across the seascape like watery creatures lumbering peacefully toward an unknown destination, possibly imparting a gentle rocking motion to the vessels they encounter on the journey. They may even possibly leave a boat's occupants in a temporary state of zero gravity, if their period is short enough and if they are occur in concert with waves.
