A fan is running at 10 revolutions per second. After it is turned off, it's speed decreases at a rate of 75% per second. Determine the number of revolutions completed by the fan after it is turned off.

Question

amistre64 · Answer

what sequence do you think we should apply?

albert0898 · Answer

Infinite Geometric?

amistre64 · Answer

sounds good to me, and how to apply it?

albert0898 · Answer

$$S \infty = \frac{ a }{ 1 - r }$$

albert0898 · Answer

r = .75
a = first term = 10

albert0898 · Answer

I was wondering it that was the correct approach and answer? Or do I use a different formula?

amistre64 · Answer

i dont think r=.75, i could be mistaken tho

if it decreases at a rate of k, then it retains 1-k of its speed, right?

albert0898 · Answer

Yes

albert0898 · Answer

So if it decreases .75, then it retains .25

amistre64 · Answer

10 + 10(.25) + 10(.25)(.25) + ...

amistre64 · Answer

so 40/3 sounds fair

albert0898 · Answer

How did you get that though, 40/3?

amistre64 · Answer

10/(1-.25) = 10/(3/4) = 10*4/3

albert0898 · Answer

Ah

albert0898 · Answer

R is the common ratio, so r = .25?

amistre64 · Answer

i would say so.  we want to determine how much of the rotations we are retaining. in order to count them.

albert0898 · Answer

This type of problem just happened to be the one I got incorrect on my exam.

 Thank you for your help!

amistre64 · Answer

accursed exams!!  good luck :)

albert0898 · Answer

Thank you! :D