Ascanning tunneling microscope is used to measure small changes in height of a surface by detecting changes in the tunneling current between the tip and the surface. the current is proportional to the tunneling coefficient (ie. i = const * t) which follows the general equation for tunneling through a square well , with c dependent on the molecule and l is the distance. the transmission coefficient at one point is t = 0.01, what is the relative current if the distance is increased from l to 5l? we are interested in i(5l)/i(l). (note: there may be more information provided than you need to solve the problem.)

which piece of furniture will have the most inertia and give the furniture movers the most difficulty in moving?  

answer

a 75kg dining table

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 .

god i hope this !