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

Using Newton's second law, the force exerted by body 2 on body 1 is

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 European standards, they condemned the Indians for living in a " wilderness ", for worshipping false gods or no God at all, and for having no written laws, standing armies, forts, or churches.

Using the laws of mass action, it can predict the future, but only on a large scale ; it is error-prone on a small scale.

Using voter intimidation, white Democrats took control of the state legislature by the end of the century ; they passed state electoral laws and a new constitution that essentially disfranchised most blacks, a situation that lasted until the federal legislation of the 1965 Voting Rights Act.

Using this, and other examples, the movie explores and wrestles with issues of personal conscience, responsibility in the face of unjust laws and personal behavior in the face of widespread societal immorality.

Using the authorization granted to him by Congress, on 13 November 2001, President Bush issued a Presidential Military Order: " Detention, Treatment, and Trial of Certain Non-Citizens in the War Against Terrorism " which allowed " individuals ... to be detained, and, when tried, to be tried for violations of the laws of war and other applicable laws by military tribunals ", where such individuals are a member of the organization known as al Qa ' ida ; or has conspired or committed acts of international terrorism, or have as their aim to cause, injury to or adverse effects on the United States, its citizens, national security, foreign policy, or economy.

Using her position as a bully pulpit, Mrs. Obama has pushed the industry to cut back on sugars and salts found in many convenience foods, encouraging self regulation over government intervention through laws and regulations.

Using California's community property laws, they get the distribution and final-cut rights by persuading Sally to sign them over.

Using these lobes, Solarians manipulated their environment with powers akin to telekinesis, and provided for the energy needs of their entire estates, including power for all of the estate's robots, drawing energy from the various spontaneous thermal energy transfers of the planet in apparently complete compliance with the known laws of thermodynamics.

Using her accountancy knowledge to trace the proceeds of illegal activity, she used street names or pseudonyms for underworld figures to avoid Irish libel laws.

Using those as a base, several Spanish jurists started writing the so called " summaries ", which were extracts of a new law or a mixture of several laws about the same theme.

Using rapid oral fluid drug tests in the workplace is a violation of many state and federal laws.

Using the three laws of physics, switch flipping, rocket turrets, and the " helping hand " to knock out guards, the player battles through 45 levels to capture the evil Dr. Craven.

Using classic physical laws we would expect the single picture of the beam on the plate.

Using this argument Ritter contended, e. g., that Frederick the Great's invasion of Silesia in 1740 was a necessary act to allow the Prussian state to live, regardless of international laws against aggression.

Using the physical laws expected to hold in the currently known cosmologies, the initial distribution of matter is allowed to evolve, and the formation of galaxies and black holes in the simulation are recorded.

Using the laws of the Actor model, Hewitt and Baker proved that any Actor that behaves like a function is continuous in the sense defined by Dana Scott ( see denotational semantics ).

Using this physical explanation of electromagnetic motion, Ampère developed a physical account of electromagnetic phenomena that was both empirically demonstrable and mathematically predictive.

Using these coordinates, the motion along the path is viewed as a succession of circular paths of ever-changing center, and at each position s constitutes non-uniform circular motion at that position with radius ρ.

Using high quality film ( good enough to be transferred from television kinescope directly onto 35mm motion picture stock ), new sound recording techniques and having a remarkable cast, the T. A. M. I.

Using a common-view measurement method based on the received signals from radio station WWV, they determined the orbital motion of the Moon about the Earth, from which the apparent motion of the Sun could be inferred, in terms of time as measured by an atomic clock.

Using Starsha's blueprints, they equip the new ship with a space warp drive, called the " wave motion engine ", and a new, incredibly powerful weapon at the bow called the " Wave Motion Gun ".

Using his trademark extreme slow motion, Viola's pieces used actors to portray the metaphorical story behind Wagner's story, seeing for example the first act as an extended ritual of purification in which the characters disrobe and wash themselves before finally plunging headlong into water together ( in Wagner's story, the two characters maintain the facade of being indifferent to each other ( necessary because Isolde is betrothed to Tristan's uncle ) before, mistakenly believing they are going to die anyway, and reveal their true feelings ).

Using motion compensation, a video stream will contain some full ( reference ) frames ; then the only information stored for the frames in between would be the information needed to transform the previous frame into the next frame.

Using the zoom function seems to contribute to motion sickness as well as zooming is not a normal function of the eye.

* Using a faster " flick " motion, the rider can spin the board multiple revolutions before landing.

Using the ailerons to roll an aircraft to the right produces a yawing motion to the left.

Using more efficient video encodings such as MPEG-4 will help promote a lower bit rate, while significant amounts of motion or white noise will require a higher bit rate to encode without visible artifacts.

Using Lagrangian mechanics, it may be shown that the motion of a pendulum can be described by the dimensionless nonlinear equation

Using the cuffing method, players are also afforded the opportunity of performing the windmill motion towards the front ( counterclockwise ), a technique exploited by French athlete Kadour Ziani when he pioneered his trademark double-windmill ( see below ).

Using editing, multiple exposures, jump cutting, superimposition, slow-motion and other camera techniques to her fullest advantage, Deren creates continued motion through discontinued space, while abandoning the established notions of physical space and time, with the ability to turn her vision into a stream of consciousness.

Using his newly-developed electromagnetic principle, Henry in 1831 created one of the first machines to use electromagnetism for motion.

Using this sub-microsecond flash, the bullet can be imaged without motion blur to study external ballistics.

* Pricing options on film revenue, Don Chance, Eric Hillebrand and Jimmy Hilliard ; Using real options to make decisions in the motion picture industry, S. Young, J. Gong, and W. Van der Stede

Using scale analysis, it can be shown that the above equations of motion reduce within the boundary layer to become

Using a certain computer in the Vault will result in the water purification chip being irreparably damaged, thus setting in motion the events of the previous game, that eventually result in the Vault Dweller being exiled and establishing the player character's tribe.

Using pulleys in mechanical toys also allows to change the angle, the speed and the direction of the motion.

Using the 850 and 700 hPa pressure surfaces, one can determine when and where warm advection ( coincident with upward vertical motion ) and cold advection ( coincident with downward vertical motion ) is occurring within the lower portions of the troposphere.