The J/ψ meson, discovered in 1974, was measured to have an average mass of mav =3100 MeV/c2 (note the use of energy units since E = mc2) and an intrinsic width ∆m=63 keV/c2. By this we mean that the masses of different J/ψ mesons were actually measured to be slightly different from one another. This mass “width” is related to the very short lifetime of the J/ψ before it decays into other particles. Estimate its lifetime using the uncertainty principle.

this could be newton#'s law of cooling. the cooling curve is exponential

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)

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 .