4. In a long distance race, the athletes were expected to take four rounds of the track such that the line of finish was same as the line of start. Suppose the length of the track was 200m. What is the total distance to be covered by the athletes? What is the displacement of the athletics when they touch the finish line?

The total distance to be covered by the athletes is 800 m

The displacement of the athletes when they touch the finish line is zero.

Explanation:

Given;

Length of the track, L = 200m

the Length of the track for a single round = 200 m

(a) Distance is a scalar quantity which has only magnitude;

If the athletes were expected to take four rounds of the track, then the total distance = 4 x 200 m = 800 m

(b) Also, if  the line of finish was same as the line of start, then displacement of the athletes when they touch the finish line is zero (0 meters). This is because displacement has both magnitude and direction. Once the athlete returns to his starting point, his displacement at that point is zero.

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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 .