Questions asked by Typo

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• If `log_8(y*(x+2))=z-1/3` and `log_2((x-2)/y)=2z+1`, how to show that `x^2=32^z+4`?
  
• How do I formally express the solution of `x! = x` when I know that `x = 1, 2 {x in NN}`?
  
• Given that there are 2 reactants, doubling the concentration of a reactant doubles the amount of product produced. So, should doubling the volume of a reactant sample also double the amount of product produced?
  
• Why are the hyperbolic functions defined using `e`? Why not some other constant?
  
• There are 40 marbles of radius `x`cm each & 60 marbles of radius `y`cm each. If `x` & `y` vary such that `x + y = 15`, how do I find the (exact) value of `x` & `y` that will make the sums of the volumes a minimum?
  
• How do I prove that `2/(cotxtan2x) -= 1 - tan^2x`?
  
• The position vectors of the points A, B, C of a parallelogram ABCD are a, b, and c respectively. How do I express, in terms of a, b and, the position vector of D?