Math CentralQuandaries & Queries


Question from Nazrul, a teacher:

If x is proportional to y and y is proportional to z , how can I prove that (x^2+y^2)^3/2 is proportional to z^3


To say that p is proportional to q means that there is a constant so that p is the constant times q.

  • If x is proportional to y then there is a constant (I am going to call it C) so that x = Cy

  • If y is proportional to z there is a constant (this one I'll call K) so that y = Kz.

Use these two facts to eliminate x and y from the expression (x2+y2)3/2, and express it in terms of z. Is the result proportional to z3?


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