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 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, we can rewrite these in terms of the traces of the powers.

Using standard trigonometric identities, this equation can be converted to the following form:

Using this form we can use trigonometric identities to compute the probability of observing ω after r iterations mentioned in the previous section,

Using the trigonometric identities tan α

Using the technique outlined above, an identity relating and its two contiguous functions can be given, six identities relating and any two of its four contiguous functions, and fifteen identities relating and any two of its six contiguous functions have been found.

Using the mathematical identities

Using the identities for complementary angles, this becomes:

Using the following two trigonometric identities:

Using the q-expansions of the Eisenstein series given above, they may be restated as identities involving the sums of powers of divisors:

Using this, he found the secret identities of both Green Lantern and the Flash.

Using this identity, he collaborated for a time with his old foe Delilah while searching for information about new villain the Black Tarantula, battling Roughouse and Bloodscream in her company ( although the final fight featured him using all four of his new identities to put them off-guard, decreasing speculation that the new heroes were the same person ).

Using the identities " IndieNH " or " IndyNH ," the aide argued that Democrats might be wasting their time and money supporting Hodes, because Bass was " unbeatable.

Using the identities above, we substitute arctan ( 1 ) for π / 4 and then expand the result.

Using inputs such as input voltage, output voltage, output current, frequency, ambient temperature, and inductance these calculators can predict the losses of the inductors core and AC / DC based on the operating condition of the circuit being used.

Using vibration monitoring, it can be observed that each tap change operation generates a signal that contains information about the condition of the tap changer contacts and the drive mechanisms.

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

Using MRI scans, Dr. Murray Stein, of the University of California, San Diego, found that when people with the disorder are shown pictures of angry faces, their amygdala-the brain's fear center-lights up with more activity than it does in people without the condition.

Using a variety of scientific techniques, archaeologists have come to the conclusion that the trees used in the construction of the monument had all been felled in the same year, 2049 BC, whilst the condition of the sapwood indicated that it had been cut down in spring or early summer.

Using forcing it is easy to see that the condition that x is uncountable cannot be removed.

Using don't cares can simplify decision tables, especially when a given condition has little influence on the actions to be performed.

# Using beyond allocated memory ( buffer overflow ): If an array is used in a loop, with incorrect terminating condition, memory beyond the array bounds may be manipulated.

Using the same carrier frequency for uplink and downlink also means that the channel condition is the same on both directions, and the base station can deduce the downlink channel information from uplink channel estimates, which is helpful to the application of beamforming techniques.

Using the aggregate price index the equilibrium condition becomes

Using robotics, real-time computer graphics, film projections, positional sound, internet links, cell phone interfaces, video and ultrasonic sensors, LED screens and other devices, his installations seek to interrupt the increasingly homogenized urban condition by providing critical platforms for participation.

Using a sunbed without goggles may lead to a condition known as arc eye.

Using Figure 5 the frequency ( denoted by f < sub > 0 dB </ sub >) is found where the loop gain βA < sub > 0 </ sub > satisfies the unity gain or 0 dB condition, as defined by:

Using the initial condition

Using this integrability condition, it is possible to define the exponential map of the Lie algebra and in this way obtain, locally, a group action on P.

Using its own observations, Zirkle was the first to propose that " some (…) susbstance, necessary for the cell to proceed to anaphase, appears some minutes after C ( moment of the arrival of the last chromosome to the metaphase plate ), or after a drastic change in the cytoplasmic condition, just at C or immediately after C ", suggesting that this function is located on kinetochores unattached to the mitotic spindle.

Using the framework of Fourier optics, we may easily explain the significance of the Abbe sine condition.

Using it, Leksell and his collaborators stand also among the pioneers in the surgical approach to the treatment of Parkinson's Disease, a degenerative condition of the motor system of the brain, by precisely lesioning a small structure in the basal ganglia, by means of an operation called pallidotomy.

Using a gag on somebody who is ill, or affected by some condition such as the common cold, catarrh, the flu, or common allergies ( including sensitivities to cologne or perfume ) is also quite dangerous, as most gags make it difficult or impossible to breathe through the mouth.

Using MedcomSoft Record, healthcare providers can track the progression of a condition or disease and easily and securely exchange detailed patient clinical information to ensure appropriate continuity of care.

Using the effects of an isometric contraction followed by a sudden relaxation ( post-isometric relaxation ) can normalise the strained condition.

Using the Routh – Hurwitz theorem, we can replace the condition on p and q by a condition on the generalized Sturm chain, which will give in turn a condition on the coefficients of ƒ.