## Albert0898 one year ago 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.

1. amistre64

what sequence do you think we should apply?

2. Albert0898

Infinite Geometric?

3. amistre64

sounds good to me, and how to apply it?

4. Albert0898

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

5. Albert0898

r = .75 a = first term = 10

6. Albert0898

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

7. amistre64

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?

8. Albert0898

Yes

9. Albert0898

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

10. amistre64

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

11. amistre64

so 40/3 sounds fair

12. Albert0898

How did you get that though, 40/3?

13. amistre64

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

14. Albert0898

Ah

15. Albert0898

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

16. amistre64

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

17. Albert0898

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

18. amistre64

accursed exams!! good luck :)

19. Albert0898

Thank you! :D