Aball is dropped from a height of 12 feet returns to a height that is 1/2 of the height from which it fell. the ball continue to bounce half the height of the previous bounce each time. how far will the ball have traveled when it hits the ground the fifth time

Step-by-step explanation:

I'm not sure if you're asking the total amount of feet it will have traveled in 5 bounces, or if you're asking how far the ball will travel on its 5th bounce.  I think it's the latter you want answered, so here goes.

This is an exponential equation, of the form

 where a is the initial height and b is the decay factor.  Our initial height is 12 feet, and since it comes up 1/2 of its previous height each time it bounces, b = 1/2.  Our equation, then, is

If you want to find out how far it drops on the fifth bounce, sub in a 5 for x and solve for y:

which gives you a height of .375 feet which is 3/8 of a foot.

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.