Questions asked by Tom

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• How you determine the parametric equation of a line with the cartesian equation #ax+by+cz + d = 0 ; a'x+b'y+c'z + e = 0# and vice versa ?
  
• How do i determine the distance between #x^2+y^2-z^2=1# and the point #P(1,3,1)# ?
  
• Given the following system #x^2+y^2-z^2+w^2=2 ; x+2y+z^2-3w^2=1# how do I show that if the couple of solution #(x_0,y_0,z_0,w_0)# satisfy #z_0*w_0 != 0# I can find solution for #z# and #w# depending to #x# and #y# ?
  
• I do find a polynomial such as #P(-3) = 0# #P(4) = 0# and #P'(-sqrt(3)) = 0# #P'(e) = 0# ?
  
• How do i find a function such as #f(a)f(b)f(c) = f(sqrt(a^2+b^2+c^2))f^2(0)# ?
  
• How can i find a plane #P# with #A(0,-1,1) in P#, #B(-1,2,3) in P# and parallel to the y axis ?
  
• How i calculate the value of the sum #2^(n+3)/(n!)# ?
  
• How do you demonstrate that, if #(df)/(dr)= (dg)/(dy)#, then #(df)/(dr)= (dg)/(dy) = K # where K is a constant ?
  
• Why when i add #NaOH# to 1 it give 2 and not 3 ?
  
• I put sugar on strawberry after few time they becom softened and juicy why ?
  
• #(dL)/L = \alphadT + 1/(sE_T)df \rightarrow ln(L/L_0) = \alpha\DeltaT + f/(sE_T)# Is that mathematically correct ?
  
• Solving this electronic problem with impedance ?