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?