Your pulse rate gives the speed at which blood flows through your body. Suppose your pulse after running is 160 beats per minute (bpm). After 4 min of rest, your pulse is 84 bpm. Find the rate at which your pulse has changed following
exercise

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this

10 down (bang1)

5 up

5down (2)

2.5 up

2.5 down (3)

1.25 up

1.25 down (4)

now add them up : )

hoped i lol