If the lifted index is positive, is the parcel warmer than, the same temperature as, or cooler than its environment?

A positive lifted index means that a parcel of air, if lifted, would be COLDER than the surrounding air at 500mb. The air is, therefore, stable and would resist vertical motion. Large positive values (+8) would normally indicate very stable air.

if the thermos has a vacuum innner, then heat through conv currents and conduction are reduced = vacuum flask

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .