Equating these two expressions yields a formula for the diffusivity:

Substituting this into the definition of the derivative via a difference quotient and taking limits means that the higher order terms – and higher – become negligible, and yields the formula interpreted as

Substituting into the above formula for | F < sub > h </ sub >| yields a horizontal force to be:

There is no known useful formula that yields all of the prime numbers and no composites.

Formally applying the Taylor series with respect to h, yields the formula

Bayes ' formula then yields

* If 4a < sub > 0 </ sub > = −, the above formula yields ũ < sup > 2 </ sup > = 0.

* If 4a < sub > 0 </ sub > > −, the above formula yields ũ < sup > 2 </ sup > > 0.

* If 4a < sub > 0 </ sub > < −, the above formula yields ũ < sup > 2 </ sup > < 0.

Dividing a value of 10 < sup > 7 </ sup > kbit / s ( i. e. 10 Gbit / s ) by the interface bandwidth statement value yields a result that is used in the weighted formula.

One simple example of a co-NP-complete problem is tautology, the problem of determining whether a given Boolean formula is a tautology ; that is, whether every possible assignment of true / false values to variables yields a true statement.

The Golden Ratio is an irrational number approximating 1. 6180 < ref > The golden ratio can be derived by the quadratic formula, by starting with the first number as 1, then solving for 2nd number x, where the ratios = x / 1 or ( multiplying by x ) yields: = x < sup > 2 </ sup >, or thus a quadratic equation: x < sup > 2 </ sup > − x − 1

* XPS is widely used to generate empirical formula because it readily yields excellent quantitative accuracy from homogeneous solid state materials

The formula is obviously more complicated than Swadesh's original one, but, as shown in Starostin's work, yields more credible results than the former ( and more or less agrees with all the cases of language separation that can be confirmed by historical knowledge ).

* Calcium sulfide with strontium sulfide with bismuth as activator, ( Ca, Sr ) S: Bi, yields blue light with glow times up to 12 hours, red and orange are modifications of the zinc sulfide formula.

Since the derivative of ln x is 1 / x, we make ( ln x ) part of u ; since the antiderivative of 1 / x < sup > 2 </ sup > is − 1 / x, we make ( 1 / x < sup > 2 </ sup >) part of v. The formula now yields:

where we use Big-O notation, combining the equations above yields the approximation formula in its logarithmic form:

Further, combining these formulas with Heron's area formula yields the result that

Only the component of the displacement along the line of sight to the Earth is known, which yields a value for the formula m sin i, where m is the mass of the planet and i is the orbital inclination.

First order perturbation theory with these fine-structure corrections yields the following formula for the Hydrogen atom in the Paschen-Back limit:

The two are separated by an arrow symbol (, usually read as " yields ") and each individual substance's chemical formula is separated from others by a plus sign.

This yields as a special case the well-known formula for the area of a triangle, by considering a triangle as a degenerate trapezoid in which one of the parallel sides has shrunk to a point.

Applying the above formula to the 25-meter-diameter antennas often used in radio telescope arrays and satellite ground antennas at a wavelength of 21 cm ( 1. 42 GHz, a common radio astronomy frequency ), yields an approximate maximum gain of 140, 000 times or about 50 dBi ( decibels above the isotropic level ).

The above formula usually yields a negative value, due to the inverse nature of the relationship between price and quantity demanded, as described by the " law of demand ".

Provided that the temperature is measured in the thermodynamic absolute scale, the relation is expressed in the formula

At standard temperature and pressure, hydrogen is a colorless, odorless, tasteless, non-toxic, nonmetallic, highly combustible diatomic gas with the molecular formula H < sub > 2 </ sub >.

A mineral is a naturally occurring substance that is solid and stable at room temperature, representable by a chemical formula, usually abiogenic, and has an ordered atomic structure.

At standard temperature and pressure, two atoms of the element bind to form dioxygen, a very pale blue, odorless, tasteless diatomic gas with the formula.

At standard temperature and pressure, oxygen is a very pale blue, odorless gas with the molecular formula, in which the two oxygen atoms are chemically bonded to each other with a spin triplet electron configuration.

The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of the reaction rate constant, and therefore, rate of a chemical reaction.

As an example, interpret a rule as IF ( temperature is " cold ") THEN ( heater is " high ") by the first order formula Cold ( x )→ High ( y ) and assume that r is an input such that Cold ( r ) is false.

Otto Nordenskiöld theorized that winter conditions also play a role: His formula is W = 9 − 0. 1 C, where W is the average temperature in the warmest month and C the average of the coldest month, both in degrees Celsius ( this would mean, for example, that if a particular location had an average temperature of in its coldest month, the warmest month would need to average or higher for trees to be able to survive there ).

* 1926-Sir Arthur Eddington estimates the non-thermal radiation of starlight in the galaxy ".. by the formula E = σT < sup > 4 </ sup > the effective temperature corresponding to this density is 3. 18º absolute .. black body "

At high temperatures ( T > Θ ) the mean free path and therefore λ < sub > L </ sub > has a temperature dependence T < sup >− 1 </ sup >, to which one arrives from formula by making the following approximation < math >

This form of the ideal gas law is very useful because it links pressure, density, and temperature in a unique formula independent of the quantity of the considered gas.

In another department of physical chemistry, he investigated the expansion of liquids with heat, and devised a formula similar to Gay-Lussac's law of the uniformity of the expansion of gases, while in 1861 he anticipated Thomas Andrews ' conception of the critical temperature of gases by defining the absolute boiling-point of a substance as the temperature at which cohesion and heat of vaporization become equal to zero and the liquid changes to vapor, irrespective of the pressure and volume.

The quantity of gas is determined by Meisner and Kim formula with using the moisture content, volatile content, volume of gas adsorbed on wet coal, fixed carbon, thickness of coal and temperature.

where the temperature offset of 6 kelvins provides the formula with a better fit to reality at lower temperatures.

Using the simple formula, the percent change of the average amount of each parameter, considered independently, to cause a one degree Celsius change in steady-state average earth temperature ( i. e., the climate sensitivity ) is as follows:

Chemical activities should be used to define chemical potentials, where the chemical potential depends on the temperature T, pressure p and the activity a < sub > i </ sub > according to the formula:

This chemical reaction is believed to be a time, temperature and pressure dependent process which creates liquid and / or gaseous hydrocarbon Hc from primary kerogen X and can be summarised using the formula:

Palmer also developed a formula for standardizing drought calculations for each individual location based on the variability of precipitation and temperature at that location.

As detailed in proxy ( climate ), borehole temperature measurements at a series of different depths can be effectively " inverted " ( a mathematical formula to solve a matrix equation ) to help estimate historic surface temperatures.

He derived a formula for calculating the mass and size that a cloud would have to reach as a function of its density and temperature before gravitational contraction would begin.

The relationship between the temperature and the pressure of a gas is estimated by using the formula PV = nRT.

If the Seebeck coefficients are effectively constant for the measured temperature range, the above formula can be approximated as: