.A millimeter cube of carbon the size of a pencil point contains about 77 coulombs of positive and negative charge. If you could separate all of the positive and negative charges by a distance of one meter the attractive force between them would be about

Explanation:

The magnitude of the electricforce between two charges is given by the formula:

where:

is the Coulomb's constant

are the two charges

r is the separation between the two charges

And the force is:

- Repulsive if the two charges have same sign

- Attractive if the two charges have opposite sign

In this problem, we have:

is the magnitude of the positive charge

is the magnitude of the negative charge

r = 1 m is the distance between the two charges

So, the magnitude of the electrostatic force 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 .