Afloor polisher has a rotating disk that has a 19-cm radius. the disk rotates at a constant angular velocity of 1.6 rev/s and is covered with a soft material that does the polishing. an operator holds the polisher in one place for 43 s, in order to buff an especially scuffed area of the floor. how far (in meters) does a spot on the outer edge of the disk move during this time?

Arc length(S) = 82.14m

Step-by-step explanation:

Given: Radius=19cm= 0.19m , angular velocity =1.6 rad/s , time = 43secs

As the disk is rotating,angular displacement=s/r

Where r=radius and s=arc length

The rate of change of the angular displacement represents the angular velocity .w=angular displacement/ time

w=(1.6)(2×3.142)

w=10.054 rad/s

Angular displacement =at

Angular displacement =10.054 ×43=432.32rad

S=angular displacement × radius

S= 432.32 ×0.19

S= 82.14m

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.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1