ElectricPavlov

Rom's answer is correct.....he did not include numbers   60-99 in his calulations.....

Rational numbers can be expressed as a fraction composed of integers (but no '0' denominator)

so   3/4     1/2      2/5    are examples

between 3 and 4     you could have    (improper fractions)   13/4   (3 1/4)    or    7/2  (3 1/2)   as two examples.....

\(\sqrt{2}\)= 1.414213562373095        so it is a little bit shy of 1/2 the way from 1 to 2 on the number line....

Strong work as always, Heureka......but after you found  'r'   and  'r_b'     , why not just add them together to find the distance  'x' between the circle centers?

Maximum displacement is at the peak and at the valley floor   +- 14 cm      I suppose maximum would be + 14 cm

1.5 to 4.5 is one cycle as described   = 3 sec

Period = 3 sec      Freq = 1/per =   1/3 hz    Indicates the number of cycles per second

From 6 to 7.5 the weight is moving up from resting position to its peak.....then it begins moving downward back to the resting position at t = 7.5

27 out of 60 ....    27/60 x 100% =

532 oout of 580     is   .....

START this way:

Multiply FIRST equation by  -2

   then add to equation 3 

      this will allow you to solve for z...........continue on your own and see if you can find x and y

I 'guess' this will work:

\( \sum_{1}^{20}\) (n-1)*7 - (n-2)    = 1160        Still rather clumsy....your answer is more elegant and 'math-y' 

Crafty guesswork......trying to figure out a sigma notation for that mess-guess ! 

             1

+7-0      8

+2*7-1   21

+3*7 -2  40

+4*7-3   65

+5*7-4  96

+6*7 - 5  133

+7*7 -6  176

+8*7 - 7 225

+9*7 -8  280

+10*7 -9  341

+11*7 -10   408     ??

Oops.....I thought it said 12th

20th would be

12*7 -11

13*7 -12

14*7 -13

15*7-14

16*7 -15

17*7 -16

18*7 -17

19*7 - 18   =   1160    ??