Assume (unrealistically) that a tv station acts as a point source broadcasting isotropically at 3.2 mw. what is the intensity of the transmitted signal reaching proxima centauri, the star nearest our solar system, 4.3 ly away? (an alien civilization at that distance might be able to watch x files.) a light-year (ly) is the distance light travels in one /m2

Explanation:

The intensity is related to the power and surface area by . We need to calculate the surface area of a sphere of radius r=4.3ly.

Since 4.3ly is the distance light travels in 4.3 years at 299792458m/s, we can obtain it in meters by doing:

So we have:

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 .