The electrostatic potential satisfies Laplace’s equation in any region free of charges. Also the heat equation (Sec. 12.5) reduces to Laplace’s equation if the temperature u is time-independent ("steady-state case"). Using (20), find the potential (equivalently: the steady-state temperature) in the disk if the boundary values are (sketch them, to see what is going on)

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.

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 .

answer(20) psi;