Apassenger rides on a train that is moving at 100.0 km/h eastward. the passenger walks toward the front of the train at a speed of 3 km/h relative to the train. whilst walking, he throws a ball at 10 km/h toward the back of the train. what is the velocity of the ball relative to the ground?

velocity of train = 100 km/h (east)

Velocity of person walking in forward direction = 3 km/h (with respect to train)

now we can find the velocity of person with respect to ground as follows

now he throw a ball backwards with speed 10 km/h with respect to him

so here we will have

Towards East

so with respect to ground the ball speed is 93 km/h towards East

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 .