Quote from Google
"If a number is being divided by 9, add each of the digits to each other until you are left with one number (e.g., 1164 becomes 12 which in turn becomes 3), which is the remainder."
n (mod9) = S(n) (mod 9) = S(S(n)) (mod 9) for all integer n
n = S(n) + S(S(n)) (mod 9)
n (mod9) = n (mod9) +n (mod9)
n must be a muliple of 9
How many multiples of 9 are there between 100 and 999?
111-10 = 101
If anyone thinks I have made a logic error please let me know, with your reasons of course.
This is not really a trig question. It is an understanding question.
dH/dt will be 0 when the tangent to the circle is horizontal. That is at the top and bottom. (say 12oclock and 6oclock)
If is starts horizontal to the axis that is at 3oclock or 9 oclock.
So it must travel a quarter of a rotation to get to the top or the bottom,
45/4 = 11.25 seconds then again at 11.25+22.5k seconds (where k is a positive integer)