A skier is skiing down a slope on the mountain. Is the mechanical energy conserved? Why or why not?

The mechanical energy isn't conserved. Some energy is lost to friction.

The reality is that the mechanical energy is supposed to dissapear in this case. The mechanical energy is replaced with the knietic energy. If starting from rest, the mechanical energy of the skier is entirely in the form of potential energy. As the skier begins the descent down the hill, potential energy is lost and kinetic energy is gained.