A woman exerts a horizontal force of 5 pounds on a box as she pushes it up a ramp that is 6 feet long and inclined at an angle of 30 degrees above the horizontal. Find the work done on the box.

26 lbft

Explanation:

Given that

Force exerted by the woman, F = 5 lb

Length of the ramp, d = 6 ft

angle of inclination, θ = 30° above the horizontal

Work done on the box, W = ?

This is very much a straightforward question..

Work done, W = F * d, where the force takes the factor of the Angie if inclination. So that,

W = Fcosθ * d

On substituting, we have

W = 5 * cos 30 * 6

W = 5 * 0.866 * 6

W = 30 * 0.866

W = 25.98 lbft

Therefore, the work done on the box is 25.98 or approximately 26 lbft

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 .