Using Horner's method in combination with Newton's method, it is possible to approximate the real roots of a polynomial.

Using Newton's laws of motion this leads to the system of equations

Using Newton's law of universal gravitation, proving Kepler's Laws for the case of a circular orbit is simple.

Using Newton's second law, these forces ( referenced in the equations above as the accelerations due to these forces ) may be summed to produce an equation of motion that describes this system.

Using Newton's notation, we can write:

Using Newton's laws of motion, numerous 18th-century mathematicians solved many frictionless ( zero-viscosity ) flow problems.

Using these accelerations a comparison of Newton's second law as formulated in the frames identifies the fictitious forces.

Using Newton's second law of motion, we obtain:

Using Nurse Ratched from One Flew Over the Cuckoo's Nest as a starting point, Manson's character was created from a mix of 1950s European nurse in costume, and evoking Helmut Newton's " strong yet vulnerable " photography subjects in her make-up.

Using Newton's identities, this condition can be re-expressed in terms of the traces of the powers of the Einstein tensor as

Using Newton's identities, we can rewrite these in terms of the traces of the powers.

Using the Greek stadium of 185 to 190 meters, the former translation comes to a far too low 755, 000 km whereas the second translation comes to 148. 7 to 152. 8 million km ( accurate within 2 %).

Using the thoroughbred racing convention of one length equaling one-fifth of a second to calculate Sham ’ s time, he also finished in under two minutes.

Using local downtown musicians the first music stream was " Big Wheel " by Karthik Swaminathan and the second being " When We Were Poor " by Karthik Swaminathan with Marc Ribot and Christine Bard.

Using a uniqueness theorem and showing that a potential satisfies Laplace's equation ( second derivative of V should be zero i. e. in free space ) and the potential has the correct values at the boundaries, the potential is then uniquely defined.

Using a homemade chronograph these were clocked at per second.

Using the second definition of depression, most economists refer to the Great Depression, as the period between 1929 and 1941.

But ( 0, 1 ) clearly cannot be written as a union of the elements of S. Using the alternate definition, the second property fails, since no base element can " fit " inside this intersection.

Using these techniques, Seldon foresees the imminent fall of the Galactic Empire, which encompasses the entire Milky Way, and a dark age lasting thirty thousand years before a second great empire arises.

Using a simple 15 stage divide-by-two circuit, this is turned into a 1 pulse per second signal responsible for the watch's keeping of time .</ ref >

where the reference variables may be functions of the number of particles N. Using the definition of the heat capacity at constant volume for the first differential and the appropriate Maxwell relation for the second we have:

; Inquilinism: Using a second organism for housing.

Using falling factorials, we can also characterize the Stirling numbers of the second kind by

Using Kuratowski's representation for an ordered pair, the second definition above can be reformulated in terms of pure set theory:

Using the formula for the second derivative of the inverse function,

Using control points ( automatically or manually entered ), the computer performs transformations on one image to make major features align with a second image.

Using low-earth orbiting satellites small antennas could be used to provide uplinks of as much as 100 Mbit / second and downlinks of up to 720 Mbit / second.

Using the normal-mode and streamfunction representations, this condition is, the second interfacial condition.

Using this shutter, in 1 second of video ( 60 fields equaling 30 frames ), 48 television fields ( totaling to 24 frames of video ) would be captured on 24 frames of film, and 12 additional fields would be omitted as the shutter closed and the film advanced.

Using the Barton / Hall method of combining 1 Henry VI with the first half of 2 Henry VI, and the second half of 2 Henry VI with 3 Henry VI, the plays were renamed Henry VI: Revenge in France and Henry VI: Revolt in England.

Using the Barton / Hall method of combining 1 Henry VI with the first half of 2 Henry VI, and the second half of 2 Henry VI with 3 Henry VI, the plays were renamed Henry VI: Revenge in France and Henry VI: Revolt in England.

Using the Barton / Hall method of combining 1 Henry VI with the first half of 2 Henry VI, and the second half of 2 Henry VI with 3 Henry VI, the plays were renamed Henry VI: Revenge in France and Henry VI: Revolt in England.

Using the second to the exclusion of the first may be considered offensive to some in that it excludes francophones born in or with ethnic origins from other countries, such as Haiti, Vietnam or Tunisia, from the Franco-Ontarian community.

Using the first to the exclusion of the second obscures the very real ethno-cultural distinctions that exist between Franco-Ontarians, Québécois, Acadians, Métis and other Canadian francophone communities, and the pressures toward assimilation into the anglophone majority that the community faces.

Using the ideal gas law and assuming a constant molar quantity ( as often happens in practical cases ),

Using F for the drag force, ρ for the density, S for the area of the flat plate, V for the flow velocity, and θ for the inclination angle, his law was expressed as

" Using this legal principle, many judges in Britain and the United States had voided, as an infringement of an individual's property rights, legislation that regulated common law bargains made in the marketplace between employers and their workers.

" Freedom of contract is a qualified and not an absolute right ...," Hughes declared in upholding an Iowa law that voided contracts limiting the legal rights of railroad workers: The state may " interfere where the parties do not stand upon an equality ...." Using similar reasoning, the associate justice upheld a California law that mandated a forty-eight-hour work-week for women in various industries and allowed a federal statute to override a contract between an interstate railroad and its employees.

* Using cases as repositories of evidence about the " unwritten law ";

Using this approach to justify the electromotive force equation ( the precursor of the Lorentz force equation ), he derived a wave equation from a set of eight equations which appeared in the paper and which included the electromative force equation and Ampère's circuital law.

Using this setup, he discovered the direct proportionality between the intensity of light and the induced photo electric current ( the first law of photoeffect or Stoletov's law ).

Using the fact that and Snell's law, one finally obtains

) Using the customary international law principle of a nation's right to protect its natural resources, President Truman in 1945 extended United States control to all the natural resources of its continental shelf.

Using Raoult ’ s law as the definition of an ideal solution, it is possible to deduce that the chemical potential of each component is given by

Using Snell's law,

Using the well known dependence of the wave number on the refractive index of the medium, we derive Snell's law immediately.

* Light from the Sun: The effective temperature of the Sun is 5778 K. Using Wien's law, it is often concluded that this corresponds to a peak emission at a wavelength of 2. 90 million nm K / 5778 K = 502 nm.

This application of Ohm's law is illustrated with examples in " How To Analyze Resistive Circuits Using Ohm's Law " on wikiHow.

Using the justification that the Incas had " broken the inviolate law observed by all nations of the world regarding ambassadors " the new Viceroy, Francisco de Toledo, Count of Oropesa, decided to attack and conquer Vilcabamba.

* 357 Magnum: Using a lengthened version of the. 38 Special case loaded to about twice the maximum chamber pressure as the 38 Spc., the 357 Magnum was rapidly accepted by hunters and law enforcement.

Using Kramers ' law for the opacity it is found that

Using the law of sines, we conclude that

Using the ideal gas law to replace with nRT / V, and replacing ρ with nM / V, the equation for an ideal gas becomes:

Using the Jurisdiction and Removal Act of 1875, a law created so black litigants could bypass hostile southern state courts if they were denied justice, Southern Pacific was able to appeal all the way to the U. S. Supreme Court.

Using the wrong Dulong-Petit law he estimated the temperature of the Sun's surface to be around 1800 ° C.