The DW Math Thread

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  • Rammy - Dreamweaver
    Rammy - Dreamweaver Posts: 6 Arc User
    edited March 2012
    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.

    Not anything divided by 0 is infinity. Or anything infinity at a power of something is infinity.

    Don't forget about the indeterminate forms of limits:

    0 / 0
    ∞ / ∞
    ∞ x 0
    ∞ ^ 0

    I think they're more but really forgot them. But in the case of ∞ / 0 it is basically ∞ x 1 / 0 which is ∞ x ∞. You can't get an accurate answer unless you calculate the limit of it like:

    lim when n -> ∞ of n / 0. In this case you can affirm it is ∞ :3
    Love the bunnies !
    [SIGPIC][/SIGPIC]
  • ColdAsLife - Dreamweaver
    ColdAsLife - Dreamweaver Posts: 432 Arc User
    edited March 2012
    And after all this time, the thread is still alive. What have I done b:shocked
    ColdAsLife, 90, Proud Sage Archer
    ArchRaziel, 5x, Cleric
    XBushidoX, xbushidox.guildportal.com
    Rectitude, Courage, Benelovence, Respect, Honesty, Honor, Loyalty.
    [SIGPIC][/SIGPIC]
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited March 2012
    And after all this time, the thread is still alive. What have I done b:shocked

    I miss ya, bud. Thanks for letting me do it :3
    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
  • Sneaker - Dreamweaver
    Sneaker - Dreamweaver Posts: 125 Arc User
    edited March 2012
    wow finally a thread worth reading,

    tysm Decus

    b:cute
    Sneaker 105 sage sin

    "Memory is the guardian of all things"

    Cicero
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited March 2012
    wow finally a thread worth reading,

    tysm Decus

    b:cute

    I aim to please. I hope you enjoy it.
    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
    0 / 0
    ∞ / ∞
    ∞ x 0
    ∞ ^ 0
    ∞ ^ ∞
    ∞ * 0
    0 ∞ 0
    ∞ / 0
    0 / ∞
    0 0 0 ∞ ∞ 0 ∞ 0 0 ∞ 0 ∞ 0 ∞ ∞ ∞ 0 0 ∞ 0 ∞ ∞∞∞∞∞∞∞∞∞∞∞∞∞...


    lol i have no idea what you mean by indeterminate form of limits. a nab like me should better stay off this thread and learn/observe more
    the loser fail nab cleric from dreamweaver who quit pwi, but still wanders the forums.
  • nfgdjksnbsd
    nfgdjksnbsd Posts: 13 Arc User
    edited April 2012
    Solve:

    ln(z) = z

    in terms of a and b where z = a + bi

    and

    cosh(x) = cos(x)
    (x =/= 0)
    find x.
  • Elanxu - Dreamweaver
    Elanxu - Dreamweaver Posts: 521 Arc User
    edited April 2012
    Solve:

    ln(z) = z

    in terms of a and b where z = a + bi

    and

    cosh(x) = cos(x)
    (x =/= 0)
    find x.

    for the first one, z=0.318132 - 1.33724i

    i used a calculator :D
    the loser fail nab cleric from dreamweaver who quit pwi, but still wanders the forums.
  • nfgdjksnbsd
    nfgdjksnbsd Posts: 13 Arc User
    edited April 2012
    for the first one, z=0.318132 - 1.33724i

    i used a calculator :D

    i said in terms of a and b, didnt want a numerical value :P
  • Elanxu - Dreamweaver
    Elanxu - Dreamweaver Posts: 521 Arc User
    edited April 2012
    i said in terms of a and b, didnt want a numerical value :P

    then a=0.318 and b=-1.34 right?
    the loser fail nab cleric from dreamweaver who quit pwi, but still wanders the forums.
  • Laterra - Dreamweaver
    Laterra - Dreamweaver Posts: 7 Arc User
    edited April 2012
    Bonus!
    (You get cookies for solving it. I stumbled on this problem and could not RESIST posting it!)

    A calculator is broken so that the only keys that still work are the sin, cos, tan, arcsin, arccos, and arctan buttons. The display initially shows 0. Given any positive rational number q, show that pressing some finite sequence of buttons will yield q. Assume that the calculator does real number calculations with infinite precision. All functions are in terms of radians.
    I was on an overnight train last night and couldn't sleep, and I found myself pondering over this question instead...

    Pressing any finite sequence of buttons on a calculator (all possible combinations) yields a finite set of numbers. The rational numbers Q form a countable infinite set. So for any calculater generated set there exist elements in Q that are not in that set (i.e. you would have to press more buttons to get it). So no, you cannot get any q by pressing a finite sequence of buttons.
  • nfgdjksnbsd
    nfgdjksnbsd Posts: 13 Arc User
    edited April 2012
    then a=0.318 and b=-1.34 right?

    as in a = (e^b)(b-a) b= (e^a)(a-b)

    ==> z = (e^b)(b-a) + i(e^a)(a-b)


    that is not the answer btw
  • Elanxu - Dreamweaver
    Elanxu - Dreamweaver Posts: 521 Arc User
    edited April 2012
    as in a = (e^b)(b-a) b= (e^a)(a-b)

    ==> z = (e^b)(b-a) + i(e^a)(a-b)


    that is not the answer btw

    b:surrender
    the loser fail nab cleric from dreamweaver who quit pwi, but still wanders the forums.
  • Notso - Raging Tide
    Notso - Raging Tide Posts: 41 Arc User
    edited April 2012
    I am good at maths but I can't read it unless it's on paper! None of this ^ business for powers and * for multiplyb:surrenderb:infuriatedb:avoid
  • Elanxu - Dreamweaver
    Elanxu - Dreamweaver Posts: 521 Arc User
    edited April 2012
    I am good at maths but I can't read it unless it's on paper! None of this ^ business for powers and * for multiplyb:surrenderb:infuriatedb:avoid

    *busts out my scanner* pdf format of RL paper FTW
    the loser fail nab cleric from dreamweaver who quit pwi, but still wanders the forums.
  • Mitachi - Dreamweaver
    Mitachi - Dreamweaver Posts: 1,201 Arc User
    edited April 2012
    yeah and we cant use x either cause it could be ex or multiply
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited April 2012
    yeah and we cant use x either cause it could be ex or multiply

    That's why you should always either use parentheses or dots. The way I see it, I only ever use an x for multiplication working with cross products :3
    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 April 2012
    That's why you should always either use parentheses or dots. The way I see it, I only ever use an x for multiplication working with cross products :3

    Ahh yes forgot about the good ole dots i always use them lol how could i forgetb:surrender
  • Darren_Kris - Lothranis
    Darren_Kris - Lothranis Posts: 7 Arc User
    edited April 2012
    Solve:

    ln(z) = z

    in terms of a and b where z = a + bi

    and

    cosh(x) = cos(x)
    (x =/= 0)
    find x.

    how about this,
    ln(z) = z
    e^[ln(z)] = e^z
    z = e^z
    z = e^(a + ib)
    z = (e^a)(e^ib)
    z = (e^a)(cos b + isin b)
    ==> a = (e^a)(cos b) , b = (e^a)(sin b)

    I couldn't do the other 1 b:cry
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited May 2012
    New stuff! Yay!

    Two are harder this time, though you can brute-force one of them (but that's not fun) :D


    0000

    Say you painted a block of wood that's a x b x c cm (where a <or= b <or= c and a,b,c are all whole numbers). After that, you then cut it up into 1 cm cubes and found that half of the cubes have paint on them and half do not. What are all possible values of a, b, and c?


    1000

    At their traditional poker game, Clifton and Lawrence agree on the stakes for each hand: The loser pays 1/3 of the money he has remaining, to the winner.

    After a while, Lawrence gives up: "You now have exactly three times the cash I have, you've won the last few hands, and I've lost just about four bucks!"
    "But you won every hand before that," Clifton replied, "in fact you've won the same
    number of hands I have!"

    How many hands were played, how much money did they each start with, and how much do they have now?


    0100

    The numbers 480608, 508811, and 723217, when divided by a certain natural number greater than 1 , all yield the same remainder. What is that divisor and that remainder?
    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
  • WackyTaffy - Dreamweaver
    WackyTaffy - Dreamweaver Posts: 26 Arc User
    edited May 2012
    the last one is divide by 79 and get a remainder of 51. And no I didn't use brute force...
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited May 2012
    Show work, Wacfy! b:thanks
    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 May 2012
    Show work, Wacfy! b:thanks

    Lol I found the answer for this one, because i used brute forceb:shutup
  • WackyTaffy - Dreamweaver
    WackyTaffy - Dreamweaver Posts: 26 Arc User
    edited May 2012
    Show work, Wacfy! b:thanks

    The difference between the numbers GCD is 79 thus they'd all have the same remainder if divided by 79.
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited May 2012
    The difference between the numbers GCD is 79 thus they'd all have the same remainder if divided by 79.

    So you said you were going to do the other problems. Why haven't you? 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
  • Xarathox - Dreamweaver
    Xarathox - Dreamweaver Posts: 1,657 Arc User
    edited May 2012
    I see you're still at it, Dec.

    p.s. you're still an old man.
    Some people risk to employ me

    Some people live to destroy me

    Either way they die
  • Yorkin - Dreamweaver
    Yorkin - Dreamweaver Posts: 271 Arc User
    edited May 2012
    I see you're still at it, Dec.

    p.s. you're still an old man.

    Persistence is a mathematician's greatest virtue.

    (Ofc, he's old... he's a Elf, in Heaven Tear's name xD)
    [SIGPIC][/SIGPIC]

    A small tribute to elven mathematician from a human physicist. b:pleased

    Yorkin - The Retired Wizard
  • WackyTaffy - Dreamweaver
    WackyTaffy - Dreamweaver Posts: 26 Arc User
    edited May 2012
    So you said you were going to do the other problems. Why haven't you? b:angry

    I never figured out how to do the first one without brute force. And the last one looked too easy so I didn't bother.
  • WackyTaffy - Dreamweaver
    WackyTaffy - Dreamweaver Posts: 26 Arc User
    edited May 2012
    So, decus said to go ahead and just solve it...


    0000

    Say you painted a block of wood that's a x b x c cm (where a <or= b <or= c and a,b,c are all whole numbers). After that, you then cut it up into 1 cm cubes and found that half of the cubes have paint on them and half do not. What are all possible values of a, b, and c?



    so seeing as how no one else is answering this. (a * b * c) = the number of cubes. that number divided by 2 equals the number of painted and not painted cubes. The number of not painted cubes is equal to (a - 2) * (b - 2) * (c -2). Because if you subtract 2 you get the inside area of the block. So,
    (a * b * c) / 2 = (a-2)*(b-2)*(c-2)

    From here it is a simple matter of brute force to solve it. Or you could try to solve it mathematically and fill out 3 pages of math instead. It's easy enough to see that a can't be 1 or 2 because there is no inner area of cubes that don't get painted. The inner area when a is 3 is always going to be smaller than the out area so that is also impossible. So, we'll start with a is 4. Like wise we can see that a can't be 10 or greater because the smallest the inner area can be at the time will be great than the out area:
    a = 10, b = 10, c = 10.
    (a * b * c) / 2 = (a-2)*(b-2)*(c-2)
    500 < 512
    Any increases in b or c will only make the inner area even larger than the outer area.

    Anyways on to the code for the brute force phase:
    long a = 3, b = 3, c = 3;
    //Randomly used 1000 as the cut cause I don't want it to take forever.
    for(a = 3; a < 1000; a++)
    for(b = a; b < 1000; b++)
    for( c = b; c < 1000; c++)
    {
    if( (a*b*c) == ((a-2)*(b-2)*(c-2)*2))
    cout << a << ":" << b << ":" << c << endl;
    }
    Answers:
    a b c
    5 13 132
    5 14 72
    5 15 52
    5 16 42
    5 17 36
    5 18 32
    5 20 27
    5 22 24
    6 9 56
    6 10 32
    6 11 24
    6 12 20
    6 14 16
    7 7 100
    7 8 30
    7 9 20
    7 10 16
    8 8 18
    8 9 14
    8 10 12


    yea that's a lot of answers
    *edited apparently it removes spacing from code ... oh well*
  • Sneaker - Dreamweaver
    Sneaker - Dreamweaver Posts: 125 Arc User
    edited June 2012
    not sure where to post this decus :((
    but i cant find my toons nothing shows up on log in screen :((

    missing my 105 wiz my 104 bm my 104 sin :((

    sorry for posting here dont know how to start a new thread :((
    Sneaker 105 sage sin

    "Memory is the guardian of all things"

    Cicero
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