Problem 4: For a conservative force, esvoedca2beee49af123450c68a7237065a 45ad885a4229cb932c3697d0b27c6328eae ovse 0N86-C1-52-40-A837-22820 If you push a wooden crate across rough ground with a force F over a distance d, what is the potential energy stored in the system due to this force

PE = Fd

Explanation:

Potential energy is the energy possessed by a body by virtue of its position. It is expressed mathematically as:

PE = mgd

m is the mass

g is the acceleration due to gravity

d is the distance

Since Force F is expressed as the product of mass and acceleration due to gravity then, F = mg

Substitute into the formula above:

Recall that: PE = mgd

Since F = mg

PE = Fd

Hence the required expression is PE = Fd

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 .