Two fifth graders play on a seesaw. One fifth grader weighs 75 lb and the other weighs 90 lb. In order to balance the seesaw so both can ride, how far from the center pole does the 90 lb fifth graders fifth grader have to be if the 75 lb fifth grader is 6 ft from the center?

5ft from the centre pole

Explanation:

Check the attachment for diagrammatic representation.

Applying the principle of moment which states that the sum of clockwise moment is equal to the sum of anticlockwise moment.

Moment = Force × perpendicular distance

For the clockwise moment:

Moment = 75×6

Moment = 450lb.ft

For anticlockwise moment:

Moment of 90lb weight = 90 × x

= 90xlb.ft

Equating both moments

450 = 90x

x = 450/90

x = 5ft

This means that the 90lb graded needs to be placed 5ft from the center pole to balance the seesaw

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 .