The DW Math Thread

1…5681011…17

Comments

  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited January 2012
    Runemine - Dreamweaver wrote: »
    Yep seen how i screwed that up. Now im doing fractions yay......starting Monday or Tuesday i do decimals.......AHHHHH and 3ish weeks from now i do polinumerals i got no clue how to even spell it......

    Glad I could help. The thread's here if ya need it.



    SOMEONE DO THE CHALLENGES! Cheze! Fiz! Astypoo! Yorkin! b:angry
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • truekossy
    truekossy Posts: 7,021 Arc User
    edited January 2012
    Am I allowed to give the hint that... Number 2 is not only possible but also easily has multiple solutions




    I'm a lazy bum that isnt supposed to be here? b:avoid
  • snufalufaguss
    snufalufaguss Posts: 0 Arc User
    edited January 2012
    If you divide zero by zero does it create a wormhole?
  • Esnemyl - Dreamweaver
    Esnemyl - Dreamweaver Posts: 3,079 Arc User
    edited January 2012
    Lemme at it..
    At first cos(0)=1 and then:

    sin(arctan(1)) = 1/√2
    sin(arctan(1/√2)) = 1/√3
    sin(arctan(1/√3)) = 1/√4 = 1/2 ************************ (A)

    sin(arctan(1/2)) = 1/√5
    sin(arctan(1/√5)) = 1/√6
    sin(arctan(1/√6)) = 1/√7
    sin(arctan(1/√7)) = 1/√8
    sin(arctan(1/√8)) = 1/√9 = 1/3 *********************** (B)

    .....

    If we want rational number with numerator 2, then after (A) take first
    cos(arctan(1/2)) = 2/√5 and then like we do
    sin(arctan(2/√5)) = 2/√9 = 2/3

    If we want rational number with numerator 3, then after (B) take first
    cos(arctan(1/3)) = 3/√10 and then like we do
    sin(arctan(3/√10)) = 3/√19
    sin(arctan(3/√19)) = 3/√28
    sin(arctan(3/√28)) = 3/√37
    sin(arctan(3/√37)) = 3/√46
    sin(arctan(3/√46)) = 3/√55
    sin(arctan(3/√55)) = 3/√64 = 3/8
    and so on... long, but it works?
    [SIGPIC][/SIGPIC]<3 by Silvy
    Reborn ditzy archer with a serious oreo addiction =3

    '...cuz my IQ is just above what is required to function as a human' - tsumaru2
  • krisnda
    krisnda Posts: 4,655 Community Moderator
    edited February 2012
    II.

    Fifteen college teachers (A,B,...,O) must serve on a total of twenty committees (1-20), such that:

    a) Each teacher is on exactly four committees
    b) Each committee has three teachers on it
    c) No two committees have more than one teacher in common

    List (or accurately describe) such a committee structure, or else prove it can't exist.

    First question before I attempt to answer this:

    Do all of the 15 teachers need to be on all 20 committees at the same time?

    Because I was going to say: Put all 15 teachers in each committee (in groups of 3's), until there are no teachers left, so there would only be 5 committees filled at one time. Then they could just rotate to each of the other committees until they went to all 20, however I know this can't be right ><
    unNReyA.jpg

    Get the Forums Enhancement Extension!
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited February 2012
    Krisnda wrote: »
    First question before I attempt to answer this:

    Do all of the 15 teachers need to be on all 20 committees at the same time?

    Because I was going to say: Put all 15 teachers in each committee (in groups of 3's), until there are no teachers left, so there would only be 5 committees filled at one time. Then they could just rotate to each of the other committees until they went to all 20, however I know this can't be right ><

    Well, not quite "the same time," but for the purposes of the problem, yes. Think of it as if you're assigning teachers to different committees on a big sign-up sheet. It has nothing to do with actually meeting, just combinations of teachers.
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Mitachi - Dreamweaver
    Mitachi - Dreamweaver Posts: 1,201 Arc User
    edited February 2012
    We're doing Surds atm but with normal numbers, not with algebra.
    lalalala Pokemon
    [SIGPIC]http://th06.deviantart.net/fs71/200H/f/2011/187/1/b/dragonite_by_silver_noctis-d3l67zm.jpg[/SIGPIC]
  • Escorian - Dreamweaver
    Escorian - Dreamweaver Posts: 2,802 Arc User
    edited February 2012
    Decus - Dreamweaver wrote: »
    II.

    Fifteen college teachers (A,B,...,O) must serve on a total of twenty committees (1-20), such that:

    a) Each teacher is on exactly four committees
    b) Each committee has three teachers on it
    c) No two committees have more than one teacher in common

    List (or accurately describe) such a committee structure, or else prove it can't exist.




    1.ABC
    2.AKE
    3.AFG
    4.BDF
    5.BEL
    6.CDH
    7.CIG
    8.EHI
    9.FHO
    10.IJK
    11.JLM
    12.KLN
    13.KOM
    14.LOD
    15.NBI
    16.NCF
    17.MDG
    18.OEJ
    19.MHA
    20.GNJ


    Like this?
    [SIGPIC][/SIGPIC]
    ty Nowitsawn

    Everything has its beginnings, but it doesn't start at one. It starts long before that... The world is born From zero. The moment zero becomes one is the moment the world springs to life. One becomes 2. 2 becomes 10. 10 becomes 100. taking it all back to one solves nothing. so long as zero remains... One.. Will eventually grow to 100 again.
  • Escorian - Dreamweaver
    Escorian - Dreamweaver Posts: 2,802 Arc User
    edited February 2012
    wtf decus i solve a math problem of yours and your not even gonna comment on it? b:cryb:angry
    [SIGPIC][/SIGPIC]
    ty Nowitsawn

    Everything has its beginnings, but it doesn't start at one. It starts long before that... The world is born From zero. The moment zero becomes one is the moment the world springs to life. One becomes 2. 2 becomes 10. 10 becomes 100. taking it all back to one solves nothing. so long as zero remains... One.. Will eventually grow to 100 again.
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited February 2012
    Escorian - Dreamweaver wrote: »
    wtf decus i solve a math problem of yours and your not even gonna comment on it? b:cryb:angry

    Sorry I haven't the time to verify at the moment. I am out of town on business and living off the occasional free wi-fi I can snag :<

    When I get back home I'll let ya know!
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Escorian - Dreamweaver
    Escorian - Dreamweaver Posts: 2,802 Arc User
    edited February 2012
    Decus - Dreamweaver wrote: »
    Sorry I haven't the time to verify at the moment. I am out of town on business and living off the occasional free wi-fi I can snag :<

    When I get back home I'll let ya know!

    b:chuckle lol my plan worked I got you to reply.
    [SIGPIC][/SIGPIC]
    ty Nowitsawn

    Everything has its beginnings, but it doesn't start at one. It starts long before that... The world is born From zero. The moment zero becomes one is the moment the world springs to life. One becomes 2. 2 becomes 10. 10 becomes 100. taking it all back to one solves nothing. so long as zero remains... One.. Will eventually grow to 100 again.
  • _Perses_ - Lost City
    _Perses_ - Lost City Posts: 1,917 Arc User
    edited February 2012
    Ok....This thread actually makes me interested in math :>....


    That is a weird thought >_>
    Nothing worthwhile to mention here, enjoy the animated signature~

    [SIGPIC][/SIGPIC]
  • Traz - Dreamweaver
    Traz - Dreamweaver Posts: 2,843 Arc User
    edited February 2012
    Decus did you hear valentine's day got canceled?
    BladedZero - Sanctuary
    "Also I don't think actually playing through the game helps your skill either."

    -And we wonder why this game has gone to hell b:cute
  • Arctix - Dreamweaver
    Arctix - Dreamweaver Posts: 124 Arc User
    edited February 2012
    Traz - Dreamweaver wrote: »
    Decus did you hear valentine's day got canceled?

    Isnt Zanryu the one interested in valentine's day?
  • Escorian - Dreamweaver
    Escorian - Dreamweaver Posts: 2,802 Arc User
    edited March 2012
    decus did you ever check the math on the answer i gave you?
    [SIGPIC][/SIGPIC]
    ty Nowitsawn

    Everything has its beginnings, but it doesn't start at one. It starts long before that... The world is born From zero. The moment zero becomes one is the moment the world springs to life. One becomes 2. 2 becomes 10. 10 becomes 100. taking it all back to one solves nothing. so long as zero remains... One.. Will eventually grow to 100 again.
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited March 2012
    Escorian - Dreamweaver wrote: »
    decus did you ever check the math on the answer i gave you?

    Looks legit to me :p

    Nicely done, Esco!

    (Sorry I forgot about this, I've been really busy)
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • krisnda
    krisnda Posts: 4,655 Community Moderator
    edited March 2012
    You forgot about this awesome thread?!

    *shame finger*
    unNReyA.jpg

    Get the Forums Enhancement Extension!
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited March 2012
    Krisnda wrote: »
    You forgot about this awesome thread?!

    *shame finger*

    b:cry I'm sorry!

    I have obligations outside of the internet too ya know, as much as I would rather not b:cry
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Elanxu - Dreamweaver
    Elanxu - Dreamweaver Posts: 521 Arc User
    edited March 2012
    Decus - Dreamweaver wrote: »

    Tell me the sum of all the alternating odd numbers from 1 to 999 (starting with -1).

    Put another way...

    Bonus points if you tell me why this is a neat little series :D

    @...anyways its -999 and i believe its special because each number cancels out the next one, except the last one.

    am i right, or am i write?


    i got a question try not to use a calculator:

    is pi to the e bigger or e to the pi?
    the loser fail nab cleric from dreamweaver who quit pwi, but still wanders the forums.
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited March 2012
    Elanxu - Dreamweaver wrote: »
    @...anyways its -999 and i believe its special because each number cancels out the next one, except the last one.

    am i right, or am i write?


    i got a question try not to use a calculator:

    is pi to the e bigger or e to the pi?



    (Well I got halfway through typing it all out neatly, and then I hit the back button on my mouse, and lost it. Brilliant move, on my part... This isn't as nice to read.)


    I figured I could define a fn and then take partial derivatives to see which change in variable resulted in a larger difference, but then I realized I could just be lazy and use logarithms...

    I'll propose: e^pi > pi^e (because e^pi is transcendental, I like to think it's cooler than pi^e) (1)

    To test it:

    ln(e^pi) > ln(pi^e)
    pi > e*ln pi
    pi/(ln pi)> e (divide by ln pi) (2)

    So, let's define some fn, f(x), where f(x) = x/(ln x) and then we'll take the first derivative of f to find the critical points...

    f'(x) = (log(x) - 1)/(log(x)^2) (we use the quotient rule to get that)

    now f'(x) = 0 when log(x) -1 = 0
    log x = 1
    x = 10

    so f(10) is a critical point...

    Now, f'(x) is also undefined at x = 1 (since log 1 = 0), so let's consider the interval (1,10]. Keeping in mind that log 10 = 1, then f'(x) < 0 on that interval. Similar intuition tells us that f'(x) is increasing on the interval [10,inf). (Not that we really care about that second interval, but I like to be thorough.)

    Thus x = 10 is the minimum value of f(x) and, since e < pi, then f(e) < f(pi)...

    Since f(e) = e, then e < f(pi), which verifies (2) and proves (1). QED.
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Elanxu - Dreamweaver
    Elanxu - Dreamweaver Posts: 521 Arc User
    edited March 2012
    Decus - Dreamweaver wrote: »
    (Well I got halfway through typing it all out neatly, and then I hit the back button on my mouse, and lost it. Brilliant move, on my part... This isn't as nice to read.)


    I figured I could define a fn and then take partial derivatives to see which change in variable resulted in a larger difference, but then I realized I could just be lazy and use logarithms...

    I'll propose: e^pi > pi^e (because e^pi is transcendental, I like to think it's cooler than pi^e) (1)

    To test it:

    ln(e^pi) > ln(pi^e)
    pi > e*ln pi
    pi/(ln pi)> e (divide by ln pi) (2)

    So, let's define some fn, f(x), where f(x) = x/(ln x) and then we'll take the first derivative of f to find the critical points...

    f'(x) = (log(x) - 1)/(log(x)^2) (we use the quotient rule to get that)

    now f'(x) = 0 when log(x) -1 = 0
    log x = 1
    x = 10

    so f(10) is a critical point...

    Now, f'(x) is also undefined at x = 1 (since log 1 = 0), so let's consider the interval (1,10]. Keeping in mind that log 10 = 1, then f'(x) < 0 on that interval. Similar intuition tells us that f'(x) is increasing on the interval [10,inf). (Not that we really care about that second interval, but I like to be thorough.)

    Thus x = 10 is the minimum value of f(x) and, since e < pi, then f(e) < f(pi)...

    Since f(e) = e, then e < f(pi), which verifies (2) and proves (1). QED.

    you gave a simple easy question a complicated and in depth answer that answers every question in the universe. great job man.
    the loser fail nab cleric from dreamweaver who quit pwi, but still wanders the forums.
  • _Perses_ - Lost City
    _Perses_ - Lost City Posts: 1,917 Arc User
    edited March 2012
    Calculator allowed:


    ∞/0
    Nothing worthwhile to mention here, enjoy the animated signature~

    [SIGPIC][/SIGPIC]
  • Mitachi - Dreamweaver
    Mitachi - Dreamweaver Posts: 1,201 Arc User
    edited March 2012
    WTB high school math question
    lalalala Pokemon
    [SIGPIC]http://th06.deviantart.net/fs71/200H/f/2011/187/1/b/dragonite_by_silver_noctis-d3l67zm.jpg[/SIGPIC]
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited March 2012
    Elanxu - Dreamweaver wrote: »
    you gave a simple easy question a complicated and in depth answer that answers every question in the universe. great job man.

    Tell me how you would answer it, then. I'm curious as to ways to simplify it. I chose the path of least resistance. I apologize if it was not elegant.
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Elanxu - Dreamweaver
    Elanxu - Dreamweaver Posts: 521 Arc User
    edited March 2012
    Decus - Dreamweaver wrote: »
    Tell me how you would answer it, then. I'm curious as to ways to simplify it. I chose the path of least resistance. I apologize if it was not elegant.

    lol idk how i woulda answered it. and nonono it was very elegant and descriptive b:victory i like the amount of detail you shoved into one thread it was kinda amusing too
    the loser fail nab cleric from dreamweaver who quit pwi, but still wanders the forums.
  • Laterra - Dreamweaver
    Laterra - Dreamweaver Posts: 7 Arc User
    edited March 2012
    Decus - Dreamweaver wrote: »
    Tell me the sum of all the alternating odd numbers from 1 to 999 (starting with -1).

    Put another way...
    Should be sum for n=1..500 if you want to add numbers up to 999 b:quiet
    So it actually adds up to 500. This is easy enough to prove by induction, but too lazy to type that atm...
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited March 2012
    Laterra - Dreamweaver wrote: »
    Should be sum for n=1..500 if you want to add numbers up to 999 b:quiet
    So it actually adds up to 500. This is easy enough to prove by induction, but too lazy to type that atm...

    This was already answered way back on page 1 by Cheze. Why does no one do the current problems? D:
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Laterra - Dreamweaver
    Laterra - Dreamweaver Posts: 7 Arc User
    edited March 2012
    Decus - Dreamweaver wrote: »
    This was already answered way back on page 1 by Cheze. Why does no one do the current problems? D:
    I only just started looking at this thread, sorry about that. That said, I wouldn't have posted if I hadn't reckoned the answer Cheze gave is incorrect (which I still believe btw).
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited March 2012
    Laterra - Dreamweaver wrote: »
    I only just started looking at this thread, sorry about that. That said, I wouldn't have posted if I hadn't reckoned the answer Cheze gave is incorrect (which I still believe btw).

    Gosh you're absolutely right! It's been so long since I posted that. Thanks for pointing out that the question posted did not match the series... (or vice versa) ~_~

    I am surprised no one caught that :(

    I suppose, it's better to have asked for the odd numbers up to 1997 b:chuckle I edited the original post to give credit where credit is due :)
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Elanxu - Dreamweaver
    Elanxu - Dreamweaver Posts: 521 Arc User
    edited March 2012
    _Perses_ - Lost City wrote: »
    Calculator allowed:


    ∞/0

    eh, anything divided by 0 is infinity, so infinity/0 is something along the lines of infinity, or infitity squared, which is basically infinity, because infinity is infinity theres no way of changing the fact that infinity is infinity. i just used infinity in the last sentence like 15 times.

    infinity.
    the loser fail nab cleric from dreamweaver who quit pwi, but still wanders the forums.
This discussion has been closed.

Categories