Find the directional derivative of the function at the given point in the direction of the vector v. h(r, s, t) = ln(3r + 6s + 9t), (1, 1, 1), v = 12i + 36j + 18

Abanked road comer of radius 146 m is to be constructed. if the comer is designed for vehicles moving with a speed of 20.0 m/s, what should the banking angle be, in units of degrees?

Explain the consequences of this addiction to the brain tissue

As part of an industrial process, air as an ideal gas at 10 bar, 400k expands at steady state through a valve to a pressure of 4 bar. the mass flow rate of air is 0.5 kg/s. the air then passes through a heat exchanger where it is cooled to a temperature of 295k with negligible change in pressure. the valve can be modeled as a throttling process, and kinetic and potential energy effects can be neglected. (a) for a control volume enclosing the valve and heat exchanger and enough of the local surroundings that the heat transfer occurs at the ambient temperature of 295 k, determine the rate of entropy production, in kw/k. (b) if the expansion valve were replaced by an adiabatic turbine operating isentropically, what would be the entropy production? compare the results of parts (a) and (b) and discuss.