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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 speed at which a bicycle travels depends on three independent factors:
l        The first is the speed at which the cyclist pedals to turn the front gear (measured in rotations per minute)
l        The second is the gear ratio from the front gear to the rear wheel (a ratio between the number of teeth on the front gear compared to the number of teeth on the rear gear)
l        The third is the size of the rear wheel (measured as the diameter of the wheel)
a)        Develop a formula that predicts the velocity in km/h for a bicyclist.
b)        How fast will a cyclist travel (in km/h) who is pedalling at 50rmp with a 42-toothed gear on the front, a 14-toothed gear on the back, and a tire with a diameter of 26 inches?
c)        In what ways can a cyclist pedal more slowly but maintain the same speed?








A weight is attached to a spring and is suspended from a ceiling so that it lies 30 cm from the ceiling when it is at rest. The spring is stretched so that the weight is 38 cm from the ceiling and is then released. It bounces up and down for a while. Each time is comes to bottom of its bounce, the length of the stretch is 75% of the previous stretch.
a)  The period of each oscillation (bounce) of the weight is 1/2 second. Write an equation that represents the distance from the weight to the ceiling.
b)        Draw a graph of the function.
c)        Without doing any calculations, state the distance of the spring from the ceiling after 1 minute.


75.        Graph y=(1.1)x + sinx over the following intervals with an appropriate scale for y:
Why does the sine curve seem to disappear?