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Real(ly) Numbers

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

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How Many Solutions?

Find all the solutions to the this equation.

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After Thought

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

Graphic Biology

Age 16 to 18 Challenge Level:

 



The graph above has several plots representing biological processes. Can you assign as many possible solutions to each of these plots?

Can you model each one as a mathematical function?

What units and labels would be appropriate for each of the axes, considering each plot in turn?