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  • Algebra help.

    So, Im stuck. Help me with these questions.

    Prove that the arithmetic mean of two numbers is not less than their geometric mean. hence, show that if teh sum of four positive numbers is 1, their product is not more than 4^-4

    If a:b = c: d prove that a+c:a+b+c+d = a:a+b

    if a and g are the arithmetic and geometric means respectively of 'n' and 'm, and k^2 is the arithemetic mean of m^2 and n^2, prove that a^2 is the arithmetic mean of g^2 and k^2

    Any helps appreciated.
    Sam Rudge
    A 5D3, some Canon lenses, the Sigma L and a flash

  • #2
    47!

    Comment


    • #3
      Ok, this I think is the answer for the one you asked me on MSN. The question asked for values of x which arose as a result of different values of k, so here are the 4 values of k and their corresponding x values.



      PHP Code:
      1. If k=0then -inf<x<inf 


      PHP Code:
      2. If k=xthen -inf<x<inf 


      PHP Code:
      3. If k>0then:

                  
      a) if x>kthen x>0

                  b
      ) if x<kthen x has no real values 


      PHP Code:
      4. If k<0then:

                  
      a) if x>kthen -inf<x<inf

                  b
      ) if x<kthen x has no real values 
      I had to put this in the code boxes because for some reason the VB code was deleting certain things I had written.

      Ok, this is the answer for the second one you posted up there:

      PHP Code:
       a/c/dCross multiplyingwe getad=bcLet this be equality #1.
       
      You need to prove that (a+c)/(a+b+c+d) = a/(a+b)
       
      So nowcross multiplying this equalitywe get:
       
      aa+ab+ac+bc=aa+ab+ac+ad
       
      Cancelling like terms from both sides
      we are left with:
       
      bc ad
       
      But bc 
      and ad are equal as shown in equality #1 earlier, therefore:
       
      (a+c)/(a+b+c+d) = a/(a+c
      Hope that wasn't too complicated.
      "The Director also sets the record straight on what would happen if oxygen masks were to drop from the ceiling: The passengers freak out with abandon, instead of continuing to chat amiably, as though lunch were being served, like they do on those in-flight safety videos."

      -- The LA Times, in a review of 'Flightplan'

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      • #4
        Sounds to me like your being taught something you don't need to be

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        • #5
          Yeah, the accelerated class sucks at times.
          Sam Rudge
          A 5D3, some Canon lenses, the Sigma L and a flash

          Comment


          • #6
            Originally posted by Simpleboy
            Yeah, the accelerated class sucks at times.
            I was going to post, but I was in the Decelerated class.
            My Flickr Pictures! Click Me!

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