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need some help from fellow math geeks

Discussion in 'Members' Lounge' started by GSRCRXsi, Jan 23, 2004.

  1. GSRCRXsi

    GSRCRXsi Super Moderator Moderator VIP

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    ok i need a little help for my multivariable calc class. we have this assignment, and i cant figure out this one problem for the life of me. we are doing vectors.

    the problem:

    write c in the form ra + sb, where r and s are scalars.

    a = 3i + 2j, b = 8i + 5j, c = 7i + 9j

    now basically i have to set
    c = ra + sb
    or
    7i + 9j = r(3i + 2j) + s(8i + 5j)
    and find the actual value of r and s but i just dont know how to go about it, ive been trying to do it with trial and error but nothing has worked so far. is there a special way i should go about this or manipulate it to make it work?. anyone have any tips?
     
  2. TurboMirage

    TurboMirage YEEAAAHHH VIP

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    "damnit jim im a doctor not a math teacher!!"
     
  3. GSRCRXsi

    GSRCRXsi Super Moderator Moderator VIP

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    ok this is what i have so far....

    i distributed the r and s: (r3i + r2j) + (s8i + s5j)

    combine like terms: (r3i + s8i) + (r2j + s5j)

    pull out the coefficients: (3r + 8s)i + (2r + 5s)j

    now (3r + 8s) has to = 7, because i need 7i for the i component
    and
    (2r + 5s) has to = 9 becasue i need 9j for the j component

    now i did some algebra:

    7 = 3r + 8s 7 = 2r + 5s - 2

    3r + 8s = 2r + 5s -2
    3r - 2r = 5s - 8s - 2
    r= -3s - 2

    plug the r substitution back into the equation:

    3(-3s - 2) + 8s = 2(-3s - 2) + 5s - 2
    -9s -6 +8s = -6s -4 + 5s -2
    -s - 6 = -s - 6
    s=s

    now i just proved that s=s, WTF??? thats not what i need, i need to find the numerical answer. what am i doing wrong?
     
  4. TommyTheCat

    TommyTheCat Gonzo Scientist

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    using, find c = ra +sb
    a = 3i + 2j, b = 8i + 5j, c = 7i + 9j

    By substitution, we find that c = 7i + 9j = r(3i + 2j) + s(8i + 5j)

    Now, let us simplify by concentrating on only one of the vectors.

    7i = r(3i) + s(8i) and 9j = r(2j) + s(5j), ignore the vector components now:

    7 = 3r + 8s
    9 = 2r + 5s

    Let's use the j vector comp. equa. and solve for s.

    9 = 2r + 5s
    9 - 2r = 5s
    (9 - 2r) / 5 = s

    Now put this s value defined by r into the other equa.

    7 = 3r + 8(9 - 2r) / 5

    By out algebra, we simplify and get:

    r = 37

    Plus this value into either equa. to find s:

    7 = 3r + 8s
    7 = 3(37) + 8(s)
    s = -13

    Any questions?
     
  5. TommyTheCat

    TommyTheCat Gonzo Scientist

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    When you did this:

    7 = 3r + 8s 7 = 2r + 5s - 2

    3r + 8s = 2r + 5s -2
    3r - 2r = 5s - 8s - 2
    r= -3s - 2

    You were ignoring the i and j parts. They are really still there. So you did this:

    7i = 3ir + 8is 7j = 2jr + 5js - 2

    and 7i =/= 7j
    you cant take that step, you have to solve within the respective systems.
     
  6. Def_Jam

    Def_Jam Senior Member

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    :blink:

    I knew I should have sleep less in highschool and went to collage afterward.
     
  7. Gen2Teg

    Gen2Teg Senior Member

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    that hurteded my head :huh:
     
  8. randerson165

    randerson165 Senior Member

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    :hmm: Thats some crazy math there. Makes me wanna go back to school and learn.
     
  9. TommyTheCat

    TommyTheCat Gonzo Scientist

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    It's really not that hard when you learn how to ignore some things. I'm only starting CalcII with vector stuff (all the i and j junk) and we're not doing multivariables (CalcIII). This is pure algebra work here, separating variables from numbers/scalars and finding values for the variables.

    But, GSRCRXsi, just wondering if you got it.
     
  10. GSRCRXsi

    GSRCRXsi Super Moderator Moderator VIP

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    yea i got it tommy, thanks. i was trying to set the 2 equations equal to each other when i shoulda done each one seperate, i always mess up little details like that, lol. too bad i turned in the assignment before i got your explaination. i just left it as c = 7i + 9j = r(3i + 2j) + s(8i + 5j), lol. whatever, its not that important, i jus wanted to make sure I understood what was happening. i had calcII last semester and we touched on vectors at the very end. the vector stuff is somewhat review, and then we are going on from that. we are getting into dot products and all kinds of fun shit now :) . and i will need ANOTHER semester of math as well calc IV baby, and im only a damn freshman, lol. all the people in my calc 3 class are upper classmen, except me and 1 other kid.

    now i did some of this stuff in highschool too, jus wondering tommy, what year are you in in college (if in college) and whats your major?

    thanks again for the help tommy, and to everyone else, dont you wish you knew what was going on? :p :lol:
     
  11. CRX-YEM

    CRX-YEM Super Moderator Moderator VIP

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    Differential Equations (aka Calc IV), I've got to take that class as well.
    Calc III is way easier than Calc II
     
  12. GSRCRXsi

    GSRCRXsi Super Moderator Moderator VIP

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    yea calc 2 has so much crammed into it
     
  13. B16

    B16 Super Moderator VIP

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    i went through calc II, barely made it :(
     
  14. Tonyd0821

    Tonyd0821 Banned

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    :sleep:
     
  15. GSRCRXsi

    GSRCRXsi Super Moderator Moderator VIP

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    come on tony, its that that bad :)
     
  16. MaaseyRacer

    MaaseyRacer Senior Member

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    I am starting calc one on monday and you guys now have me scared as I understood nothing of the above. :(
     
  17. GSRCRXsi

    GSRCRXsi Super Moderator Moderator VIP

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    dont worry dude, thats calc 2/3 shit, calc 1 is stupid easy. just limits taking derivatives and shit, its easy, i swear, lol.
     
  18. CRX-YEM

    CRX-YEM Super Moderator Moderator VIP

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    yeah if you can multiply and divide
    you can easily do calc 1 it's cake
     
  19. jiahanhao

    jiahanhao Senior Member

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    i miss calc...

    calc >>>> combinatorics and optimization

    i could sing an ode to O.D.E's...
     
  20. jamesA

    jamesA Well known pissed off telephone guy VIP

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    I could understand the Algebra part...but thats about it. :blink:
     
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