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Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?

Good Approximations

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.

Target Six

Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.


Age 16 to 18
Challenge Level
If you are stuck on this, don't worry! It's not meant to be easy! If you're having problems with the graph, try calculating the value of p for some values of s and plotting points. This will help you to work out the general shape of the graph.
When working out what optimal egg size is, try defining the function that you are attempting to maximise - the payout. In this case this is the expected number of chicks that will hatch, which is equal to the number of eggs multiplied by the probability that each egg has of survival. What is the total number of eggs equal to? How might you go about working out what the maximum of a function is? Once you've defined your function it might help to sketch a graph of it.