Help: simple equation

Discussion in 'Math' started by gotumal, Jul 1, 2009.

  1. gotumal

    Thread Starter Active Member

    Mar 24, 2008
    99
    0
    Hello reader,

    Here is a simple problem,

    (i2+i3)-(i1+i4) X
    ------------- = ---
    i1+i2+i3+i4 5

    And

    (i2+i4)-(i1+i3) Y
    ------------- = ---
    i1+i2+i3+i4 5

    Also,

    i1+i2+i3+i4 = E

    Can I find out i1, i2, i3 and i4 if I know X, Y and E?
    What is the relation?

    I tried with excel but could not do! :(

    Thanks in advance!
     
  2. Ratch

    New Member

    Mar 20, 2007
    1,068
    3
    gotumal,

    What does --- mean?
    Are X,Y, and E constants?
    What does i1+i2+i3+i4 5 mean?

    It looks like you have 3 equations for at least 4 unknowns.
    What does that tell you?

    Ratch
     
  3. RiJoRI

    Well-Known Member

    Aug 15, 2007
    536
    26
    <deleted>

    --Rich
     
  4. gotumal

    Thread Starter Active Member

    Mar 24, 2008
    99
    0
    The equations were,

    [(i2+i3)-(i1+i4)]/[i1+i2+i3+i4]= X/5

    And

    [(i2+i4)-(i1+i3)]/[i1+i2+i3+i4] = Y/5

    Also,

    i1+i2+i3+i4 = E

    I want to find out i1, i2, i3 and i4 with the values X, Y and E.

    Actually there is a sensor which gives you the co-ordinates (X and Y) of a light spot faliing on it. And i1, i2, i3 and i4 are the four outputs. I was checking if it can be done reversed for my calculations.

    Apart from above relation, there is more info like,

    1. When (X,Y)=(0,0); i1=i2=i3=i4=E/4
    2. When (X,Y)=(5,5),i2=E
    2. When (X,Y)=(-5,5),i4=E
    2. When (X,Y)=(5,-5),i3=E
    2. When (X,Y)=(-5,-5),i1=E

    Can we have another equation since we have four variables?

    X and Y co-ordinates range which I am interested is -5 to +5.
     
  5. someonesdad

    Senior Member

    Jul 7, 2009
    1,585
    141
    You've got three equations in four unknowns. There will be a continuum of solutions.
     
  6. gotumal

    Thread Starter Active Member

    Mar 24, 2008
    99
    0
    Thanks someonesdad. OK, let me put it in other way,

    I have a equation N/D = X/5

    X range -5000 to +5000
    N range -D to D (so the ranage of N/D -1 to +1)
    D range 1000 to 10000

    Now if I want to calculate X in the given range with step size of 1.5 i.e. total no. of results would be 10000/1.5 and not the coninous one,

    Then what should be the mimimum step size of N and D
     
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