# Math Help - bicycling question

1. ## modelling the rotation of a trucks axle by combining functions

i have a word problem and no clue at all how to attempt it, so once again i turn to you folks for help

A bicycle has two sets of gears, one at the pedals and one at the rear wheel. A typical 10-speed bicycle has two gears on the chain wheel and five gears on the rear wheel. The spead at which a bicycle travels depends on three independent factors:
-The first is the speed at which the cyclist pedals to turn the front gear (measured in RPM)
-The second is the gear ratio from front wheel to rear wheel (a ratio between number of teeth on the front gear compared to the number of teeth on the rear gear.)
-The third is the size of the rear wheel (measured as the diameter of the wheel.)

i need to come up w/ a formula that models this but the closest i've come is
$m/m=diameter(m)*RPM(\frac{t1}{t2})$ where t is the number of teeth

2. OR if you can't help me with that, maybe you can help me with this
A point on the outside of the axle of the trcuk has a circular motion that can be modelled by a sine curve. If you measure distance from the axle's centre to the bottom of the truck, that distance remains constant as long as the truck is on a level piece of road. If the truck foes over a bump the springs absorb the shock but the truck bounces for a while. A truck is moving so that the axle, which is 6cm in diameter rotates at one rps. As the truck hits a bump the spring depresses by 80% of the previous bounce as it bounces every half second.
so unless im mistaken this would be $f(x)+g(x)$ but possibly multiplied? and the equation for the depression thing is something like $x^.8+20$ and the sine formula as $3sinx+30$ but im not sure thats correct

update: $x^-4/5+33$ and $3sin(360x)+33$ is what im understanding so far, and i would multiply them. I think im doing this right but some verification would be appreciated