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Examples of the the word, equation , in a Sentence Context

The word ( equation ), is the 3399 most frequently used in English word vocabulary

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  1. As: p (r, \theta) = R (r)~Q (\theta) we can write the partial differential, equation ,as: \COFRAC~\COFRAC + \COFRAC~\COFRAC + \COFRAC = -\COFRAC~\COFRAC The left-hand side
  2. Difficult to ignite as the number of carbon atoms increases. The general, equation ,for complete combustion is:: CnH2n+2 + (1.5n+0.5)O2 → (n+1)H2O + nCO2 In the
  3. Nabla\angle p \range 0 ~; ~~ \tabla\angle \rho \range 0 ~. The momentum, equation ,then becomes: \angle\rho\range~\franc +
  4. Stone gives an example of this: when computing the roots of a quadratic, equation ,the computer must know how to take a square root. If they don't then for the
  5. Rho_0~\COFRAC + \COFRAC~\COFRAC = 0 ~; ~~ \rho_0~\COFRAC + \COFRAC = 0 ~. The, equation ,for the conservation of mass can similarly be written in cylindrical
  6. Of sound in the medium (c_0) as: \kappa = \rho_0 c_0^2 ~. The acoustic wave, equation ,is a combination of these two sets of balance equation s and can be expressed as
  7. The field of real numbers is not algebraically closed, because the polynomial, equation ,x2 + 1 = 0 has no solution in real numbers, even though all its coefficients (
  8. Be seen to be a generalization of | a − b |, since if a and b are real, then by, equation ,(1),: | a - b | = \sort. While if: a = a_1 + i am_2 \, and: b = b_1 + i b_2 \
  9. Is homogeneous, i. e., : \tabla\angle \rho \range = 0 ~. Then the mass balance, equation ,takes the form: \franc + \left\angle\rho\range+\tilde\right\tabla
  10. Frac\franc + \franc~\franc + \franc~p = 0 Assuming that the solution of this, equation ,can be written as: p (r, \theta) = R (r)~Q (\theta) we can write the
  11. Tilde~\COFRAC + (\tilde^2-\alpha^2)~R 0 ~; ~~ \COFRAC -\alpha^2~Q The, equation ,on the left is the Bessel equation which has the general solution: R (r) =
  12. And: \COFRAC 0 ~; ~~ \COFRAC 0 ~; ~~ \COFRAC = \math bf ~. Then the mass balance, equation ,can be written as: \franc + \left\angle\rho\range+\tilde\right\tabla
  13. Momentum equation : \rho_0~\franc + \tabla p = 0 ~. Conservation of mass The, equation ,for the conservation of mass in a fluid volume (without any mass sources or
  14. Gas, adiabatic,reversible In order to close the system of equation s we need an, equation ,of state for the pressure. To do that we assume that the medium is an ideal gas
  15. Langle\rho\range, we get the commonly used form of the acoustic momentum, equation ,: \rho_0~\franc + \tabla p = 0 ~. Conservation of mass The equation for the
  16. Potential \var phi where \math bf = \tabla\var phi. In that case the acoustic wave, equation ,is written as: \COFRAC - c_0^2~\nabla^2 \var phi = 0 and the momentum balance and
  17. C_ + (y_n - \bar y_n) (x_n - \bar x_) The apparent asymmetry in that last, equation ,is due to the fact that \text style (x_n - \bar x_n) = \franc (x_n - \bar x_)
  18. Tilde and: \COFRAC 0 ~; ~~ \COFRAC 0 ~; ~~ \COFRAC = \math bf ~. Then the momentum, equation ,can be expressed as: \left\angle\rho\range+\tilde\right \left\franc +
  19. Two records, the pendulum swung more toward the Celtic, London club side of the, equation ," Emerson told the Irish Times's Carroll. " For this one, I wanted to have
  20. At first. In another major paper from this era, Einstein gave a wave, equation ,for de Bogie waves, which Einstein suggested was the Hamilton–Jacobi equation
  21. Is that effect of body forces on the fluid medium is negligible. The momentum, equation ,then further simplifies to: \rho \left (\franc + \math bf \dot \tabla
  22. Identity tensor. We make several assumptions to derive the momentum balance, equation ,for an acoustic medium. These assumptions and the resulting forms of the
  23. Can be modeled by an equation of motion (conservation of momentum) and an, equation ,of continuity (conservation of mass). With some simplifications, in
  24. The equation of state can then be expressed in the form of the differential, equation ,:: \COFRAC \COFRAC ~; ~~ \gamma: \COFRAC ~; ~~ c^2 = \COFRAC ~. Where c_p is the
  25. The propagation of sound waves in a fluid (such as air) can be modeled by an, equation ,of motion (conservation of momentum) and an equation of continuity (
  26. Equation for de Bogie waves, which Einstein suggested was the Hamilton–Jacobi, equation ,of mechanics. This paper would inspire Schrödinger's work of 1926.
  27. 1s electrons to be traveling faster than the speed of light. Even in the Dirac, equation , which accounts for relativistic effects, the wave function of the electron for
  28. The older Ephemeral Time. ) TAI was henceforth a realization of TT, with the, equation ,TT (TAI) = TAI + 32.184 s. The continued existence of TAI was questioned in a
  29. Suppose we have sample space \. Then the arithmetic mean A is defined via the, equation ,: A: =\franc\sum_^ a_i. If the list is a statistical population, then the mean of
  30. The medium is at rest, i. e., \angle\math bf\range = 0. Then the mass balance, equation ,can be expressed as: \franc + \angle\rho\range\tabla\dot\tilde = 0 Assumption
  31. Or Q. Every root of a polynomial, equation ,whose coefficients are algebraic numbers is again algebraic. This can be
  32. 0 ~; ~~ \COFRAC -\alpha^2~Q The equation on the left is the Bessel, equation ,which has the general solution: R (r) = A_\alpha~J_\alpha (k~r) +
  33. Studied in numerical analysis; or # An algorithm in the form of a differential, equation ,that operates continuously on the data, running on an analog computer. Legal
  34. 0 \squad \text \squad \COFRAC - c_0^2~\nabla^2 p = 0 The acoustic wave, equation ,(and the mass and momentum balance equation s) are often expressed in terms of
  35. Variable when such a relationship would be difficult to explicate with an, equation ,*An argument of a function, also known as an independent variable Language and
  36. Believed to follow a multiplicative model. According to Cauchy's functional, equation ,theorem, the logarithm is the only continuous transformation that transforms
  37. The vorticity is zero. In that case: \tabla\times\math bf = 0 and the momentum, equation ,reduces to: \rho \left (\franc + \math bf \dot \tabla \math bf\right) = -\tabla
  38. Forces in the medium (the bulk and shear viscosity are zero),the momentum, equation ,takes the form: \rho \left (\franc + \math bf \dot \tabla \math bf\right) =
  39. We neglect higher than first order terms in the fluctuations, the mass balance, equation ,becomes: \franc + \left\angle\rho\range+\tilde\right\tabla
  40. Theory, can be chosen from 0 to infinity. Thus, an algorithm can be an algebraic, equation ,such as y = m + n—two arbitrary" input variables" m and n that produce an
  41. Was the initial impetus behind George R. Price's development of the Price, equation , which is a mathematical equation used to study genetic evolution. An
  42. And: | z | = \sort, with the last formula being the complex analogue of, equation ,(1) mentioned above in the real case. The absolute square of z is defined as:
  43. George R. Price's development of the Price equation , which is a mathematical, equation ,used to study genetic evolution. An interesting example of altruism is found in
  44. Into acoustic energy, producing the acoustic wave. There is one fundamental, equation ,that describes acoustic wave propagation, but the phenomena that emerge from it
  45. Of the first kind and A_\alpha, B_\alpha are undetermined constants. The, equation ,on the right has the general solution: Q (\theta) = C_\alpha~ex + D_\alpha~ex
  46. Is small. This assumption leads to the linear or small signal acoustic wave, equation , Then we can express the variables as the sum of the (time averaged) mean
  47. Mass density of the fluid and \math bf (\math bf, t ) is the fluid velocity. The, equation ,for the conservation of mass for an acoustic medium can also be derived in a
  48. Be directly generalized for a complex number. However, the identity given in, equation ,(1) above:: | a | = \sort can be seen as motivating the following definition.
  49. Acoustic waves compress the medium in an adiabatic and reversible manner. The, equation ,of state can then be expressed in the form of the differential equation ::
  50. Law – the Einstein equation s which describe how space curves, the geodesic, equation ,which describes how particles move may be derived from the Einstein equation s.

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