Find a numerical value for rhoearth, the average density of the earth in kilograms per cubic meter. use 6378km for the radius of the earth, g=6.67×10−11m3/(kg⋅s2), and a value of g at the surface of 9.80m/s2. express your answer to three significant figures.

According to the information provided to define an average density, it is necessary to use the concepts related to mass calculation based on gravitational constants and radius, as well as the calculation of the volume of a sphere.

By definition we know that the mass of a body in this case of the earth is given as a function of

Where,

g= gravitational acceleration

G = Universal gravitational constant

r = radius (earth at this case)

All of this values we have,

Replacing at this equation we have that

The Volume of a Sphere is equal to

Therefore using the relation between mass, volume and density we have that

im sorry i dont know

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 .