Sentence examples for substituting the formula from inspiring English sources

so, substituting the formula (3.4) into the right-hand side of (3.3) gives (3.5).

so, substituting the formula (2.21) into the right-hand side of (2.20), we get that (2.22).

By Poincaré's inequality, we have K ∫ Ω u ε p + r − 2 d x ≤ ∫ Ω | ∇ u ε p + r − 2 p | p d x, where K denotes a positive constant only dependent on | Ω |, N. Substituting the formula above into (2.7), we have ∫ Ω ∂ u ε r ∂ t d x ≤ − K r ( r − 1 ) p p ( p + r − 2 ) p ∫ Ω u ε p + r − 2 d x + r ∫ Ω u ε α + r − 1 ( a − b u ε + c v ε ) d x. (2.8).

Substituting the formula for Z gives the final result : \langle H \rangle = h\nu \frac{e^{-\beta h\nu}}{1 - e^{-\beta h\nu}}.

Substituting the last formula into the solution formula we write tilde{u}_ xi =sigma^{-1}_ xi) (xi+i)^{ae}P bigl((xi -i)^{|ae|}sigma^{-1}_ xi =sigma^{-1}_ xit{lv}}(xi+ibigr).

For example the density of a ball of mass M and radius r can be obtained by substituting the above formula for the volume of a ball for V in the above formula for the density of a solid.

Substituting the above formula into (3.4), we get the following theorem.

By substituting the above formula for W and (18) into (19), the square error function is obtained as, J ( v ) = ( H v - 1 M v T D v - s ) T Ω - 1 ( H v - 1 M v T D v - s ) (20).

Substituting the approximate formula for T(a) into this equation yields an estimate for Y(n) Y(n) \approx \frac{12}{\pi^{2}} \ln 2 \ln n + 0.06.

Solving this equation for s gives Substituting the above formula for s into OR*0 gives a function of k that we denote OR*0 (k).

The 12 hour food intake/fecal output measurements for other insults can be expressed in terms of LPS dose by substituting the amount into the formula for the fitted curves.