A small sphere that carries a charge q is whirled in a circle at the end of an insulating string. The angular frequency of rotation is ω. What average current does this rotating charge represent? (Use any variable or symbol stated above as necessary.)

i = qω/2π

Explanation:

Since the charge moves in a circle, its velocity v = rω. where r is the radius of the circle and ω the angular frequency of the charge.

The distance it covers in one cycle is the circle's circumference,d = 2πr.

The time it takes to cover this distance, t = d/v = 2πr/rω = 2π/ω

We know that current i = charge/time = q/t = q/2π/ω = qω/2π

So, the average current, i = qω/2π

answer: 802.3 kilo joules of energy represents 191.75 kilo calorie of energy.

explanation:

energy released during combustion of one mole methane = 802.3 kilo joules

if 1 kilo joule = 0.239006   kilo calorie

then ,802.3 kilo joule will be = 802.30.239006 kilo calorie

802.3 kilo joule = 191.75 kilo calorie

hence, the energy in kilo calorie is 191.75 kilo calorie.

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 .