You are trying to experimentally determine the electric potential of a conducting sphere, which you know is given by V=kQ/r. You experimentally measured the charge to be Q=3.2042e−19 C and the radius to be r=0.08 m, and also find you have an uncertainty in both of those quantities equal to ΔQ=1.6021e−21 C and Δr=0.005 m respectively. What is the uncertainty in V due to the uncertainty in your measurement of the radius r?

Uncertainty ΔV = 22.601 x 10^-10

ΔV = 2.2601nv or 2.2601 x 10^9V

Explanation:

from V = kQ/r

Uncertainty in V is given by δV = V square root [ (δQ/Q)^2 + (δr/r)^2]

ΔV = V square root [ (ΔQ/Q)^2 + (Δr/r)^2] (2)

Given that ; Q = 3.2042e−19 C, r = 0.08 m, ΔQ = 1.6021e−21 C, Δr = 0.005 m

Plugging the values given into equation (2)

from ΔV =(kQ/r) square root [ (ΔQ/Q)^2 + (Δr/r)^2]

ΔV = 9 x 10^9 x 3.2042e−19 / 0.08 square root [ (1.6021e−21/ 3.2042e−19)^2 + ( 0.005/0.08)^2]

ΔV = 360.47 x 0.06269 x 10^-10

Uncertainty ΔV = 22.601 x 10^-10

ΔV = 2.2601nv or 2.2601 x 10^-9V

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 .