The minute hand of a clock is 6 inches long. how far does the tip of the minute hand move in 15 minutes? how far does it move in 25 minutes? round answers to two decimal places.

We can think that the tip of the minute hand moves in a circle of radius R = 6in.

We will find that for each case, 15 minutes and 25 minutes, the distance traveled is 9.42 in and 15.7 in correspondingly.

Remember that the length of an arc is defined by an angle θ in a circle of radius R is given by:

L = (θ/360°)×2×pi×R

where pi = 3.14

Here, we know that R = 6in.

Now we want to find how much does the tip of the minute hand moves in 15 minutes.

Then we need to find the angle θ that the tip moves in these 15 minutes.

Remember that a complete rotation in the clock has 60 minutes.

This means that there is an equivalence:

60 min = 360°

1 = (360°/60 min)

with this we can rewrite:

15 min = (15 min)×(360°/60 min) = 90°

Then, in 15 minutes, the tip of the minute hand moves:

L = (90°/360°)×2×3.14×6in = 9.42 in

For the case of 25 minutes the procedure is the same:

25 min =  (25 min)×(360°/60 min) = 150°

Then, in 25 minutes, the tip of the minute hand moves:

L = (150°/360°)×2×3.14×6in = 15.7 in

If you want to learn more, you can read:

link

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.

215.92 dollars is the answer