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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def vertical_velocity(omega, pressure, temperature, mixing=0):
 r"""Calculate w from omega assuming hydrostatic conditions. This function converts vertical velocity with respect to pressure :math:`\left(\omega = \frac{Dp}{Dt}\right)` to that with respect to height :math:`\left(w = \frac{Dz}{Dt}\right)` assuming hydrostatic conditions on the synoptic scale. By Equation 7.33 in [Hobbs2006]_, .. math: \omega \simeq -\rho g w so that .. math w \simeq \frac{- \omega}{\rho g} Density (:math:`\rho`) is calculated using the :func:`density` function, from the given pressure and temperature. If `mixing` is given, the virtual temperature correction is used, otherwise, dry air is assumed. Parameters omega: `pint.Quantity` Vertical velocity in terms of pressure pressure: `pint.Quantity` Total atmospheric pressure temperature: `pint.Quantity` Air temperature mixing: `pint.Quantity`, optional Mixing ratio of air Returns ------- `pint.Quantity` Vertical velocity in terms of height (in meters / second) See Also -------- density, vertical_velocity_pressure """

    rho = density(pressure, temperature, mixing)
    return (omega / (- mpconsts.g * rho)).to('m/s')