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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.

Overarch 2

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

Cushion Ball

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

Population Dynamics - Part 5

Age 16 to 18
Challenge Level

Red dot is when the populations of sharks and fish will remain unchanged.

the equilibrium points are $x=y=0$  and  $x=2, y=0.5$

Other factors

  • The predators only get food by eating the prey
  • The environment does not change to favour one species and genetic evolution is slow