Substituting into the previous expression for,

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

Substituting the derivative of u < sub > ρ </ sub > into the expression for velocity:

Substituting 0 for h in the difference quotient causes division by zero, so the slope of the tangent line cannot be found directly using this method.

Substituting this into the gain equation and solving for:

Substituting for F, we have P = 2ρQ ( V < sub > i </ sub > − u ) u.

Substituting cos θ < sub > c </ sub > for sin θ < sub > r </ sub > in Snell's law we get:

Substituting the above 2 results ( for E and J respectively ) into the continuum form shown at the beginning of this section:

Substituting for the masses in the equation for the Roche limit, and cancelling out gives

Substituting into the equation for the change in entropy:

Substituting ω for W into the above velocity expression, and replacing matrix multiplication by an equivalent cross product:

Substituting the beverage for the lost elixir, he sprays LeChuck, destroying the ghost pirate.

Substituting for an ill UP colleague, Helms attended the annual NSDAP Parteitag in September 1936.

Substituting into equation ( iii ) and solving for y gives this value of y:

Substituting this into the first differential equation lets us solve for x in terms of θ:

Substituting and, we see that these equations for and are those of a circle rolling along a horizontal line — a cycloid:

Substituting from the expressions for v and v < sub > m </ sub > above gives:

Substituting for V '< sub > in </ sub > in the first expression,

Substituting the value for this example, using 4 processors we get.

Substituting the potential gradient for the electric field

Substituting this in the equation for the area,

Substituting this form for D in the expression for displacement current, it has two components:

* " Substituting A for B " when the intended meaning is " substituting B for A " or " replacing A with B ", i. e. " removing A and putting B in its place.

Substituting p = μ · n < sup >− 1 </ sup > gives g '( t ) = (( μ < sup >− 1 </ sup > − n < sup >− 1 </ sup >)· e < sup >− t </ sup > + n < sup >− 1 </ sup >)< sup >− 1 </ sup > and κ < sub > 1 </ sub > = μ.

Substituting p = ( μ · n < sup >− 1 </ sup >+ 1 )< sup >− 1 </ sup > gives g '( t ) = (( μ < sup >− 1 </ sup >+ n < sup >− 1 </ sup >)· e < sup >− t </ sup >− n < sup >− 1 </ sup >)< sup >− 1 </ sup > and κ < sub > 1 </ sub > = μ.

Substituting any bandwidth h which has the same asymptotic order n < sup >- 1 / 5 </ sup > as h < sub > AMISE </ sub > into the AMISE

Substituting a segment requires placing two or more segments of rail on flat plate that is moved in its entirety to provide straight or curved track.

Substituting on the field for Ian Davis, he injured his shoulder attempting to catch Imran Khan.

Here, the right hand side is clearly not convergent for any non-zero value of t. However, by truncating the series on the right to a finite number of terms, one may obtain a fairly good approximation to the value of for sufficiently small t. Substituting and noting that results in the asymptotic expansion given earlier in this article.

Substituting for Y based on the assumed linear model,

Substituting the hypsometric equation, one gets a form based on temperature,

Substituting the previous formula for voltage ( V ) shows that the electrostatic force can be split up into three contributions, as the total electrostatic force F acting on the tip then has spectral components at the frequencies ω and 2ω.

Substituting the data ( from Wikipedia ) one will get − 0. 7395 ° day < sup >− 1 </ sup >, a value substantially different from zero!

which says that the length of this vector is proportional to the rest mass m. Substituting the operator equivalents of the energy and momentum from the Schrödinger theory, we get an equation describing the propagation of waves, constructed from relativistically invariant objects,

Substituting D from this equation into the previous and solving for Δ < var > t '</ var > gives:

Substituting x ( t ) from above:

Substituting from information theory, an equivalent form of the above definition is:

Substituting cosE as found above into the expression for r, the radial distance from the focal point to the point P, can be found in terms of the true anomaly as well:

Substituting cruise missiles for air attacks, VVS and AV-MF commanders set about to convert their heavy bombers as raketonosets, or missile carriers, which could be launched against approaching enemy fleets and task forces from coastal or island airfields.

Substituting from equations () and () into equation (),

Substituting for from the follower's problem:

Many doctors advise patients who are suffering from SSRI discontinuation syndrome to use fluoxetine as a substitute for their current drug .< ref > Substituting fluoxetine in the final stages of SSRI discontinuation, or post discontinuation, provides a rate of reduction of antidepressant which can minimize or eradicate withdrawal symptoms in the patient.