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Ball Bearings

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Far Horizon

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Air Routes

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

What's That Graph?

Age 14 to 18
Challenge Level
A 'temperature-time' graph has temperature on the vertical (y) axis and time on the horizontal (x) axis.
What would the temperature be after a short time has passed?
What would happen to the temperature as time passes?
A 'height-distance' graph has height on the vertical axis and distance on the horizontal axis...