The DW Math Thread

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  • Alias - Dreamweaver
    Alias - Dreamweaver Posts: 478 Arc User
    edited April 2011
    *Erects certain Tantric shields against your filthy math*

    So....you do physics in here too? b:scorn
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited April 2011
    *Erects certain Tantric shields against your filthy math*

    So....you do physics in here too? b:scorn

    Absolutely, since physics is just applied math ;)
    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
  • Alias - Dreamweaver
    Alias - Dreamweaver Posts: 478 Arc User
    edited April 2011
    Absolutely, since physics is just applied math ;)

    o.o!
    Excerrent I think o.o Dont rember **** from physices cus my teacher was a failgoat >.>
    *Gets to wikipediaing*
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited April 2011
    But I already got the other two and checked my work for good measure. I decided not to post any solutions on the chance that I eventually get this one. I keep coming back to it. I really, really wanna figure it v.v

    As a general rule of thumb, always try algebraic manipulations and creative substitutions.

    This case is no exception ;)

    Failing that, try to see if anything relates to anything else in the integrand :D


    That's all the help I'll ever give for the challenge problems.
    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
  • Teppeii - Dreamweaver
    Teppeii - Dreamweaver Posts: 1,206 Arc User
    edited April 2011
    As a general rule of thumb, always try algebraic manipulations and creative substitutions.

    This case is no exception ;)

    Failing that, try to see if anything relates to anything else in the integrand :D


    That's all the help I'll ever give for the challenge problems.

    Appreciate the tidbit.b:cute
    On indefinite hiatus :3
  • Tearle - Dreamweaver
    Tearle - Dreamweaver Posts: 511 Arc User
    edited April 2011
    Ok Decus, i'm tired and not in the right mind and I thought of this question and Teppers won't answer it so I'ma present it to you.

    Ok, i'm in a weird mood and let's say I attack my wall with two different things.
    A sledgehammer, and a spork. Which will do more damage in the long run?
    Let's say for the sake of argument that the spork hits at 1.53 but does half the dph the sledge hammer does, and crits every 7 hits.
    Now the sledgehammer hits at .80 and does double the dps of the spork and crits ever 5 hits.

    Now in my imaginary world crits don't always hit 200% but range from 150%-300%

    Which out DDs which on average?

    I need to take less medicine I think, even if the doc tells me to take full doses.




    -edit- jake called me **** for typing this v___v
  • Dsholder - Dreamweaver
    Dsholder - Dreamweaver Posts: 626 Arc User
    edited April 2011
    Ok Decus, i'm tired and not in the right mind and I thought of this question and Teppers won't answer it so I'ma present it to you.

    Ok, i'm in a weird mood and let's say I attack my wall with two different things.
    A sledgehammer, and a spork. Which will do more damage in the long run?
    Let's say for the sake of argument that the spork hits at 1.53 but does half the dph the sledge hammer does, and crits every 7 hits.
    Now the sledgehammer hits at .80 and does double the dps of the spork and crits ever 5 hits.

    Now in my imaginary world crits don't always hit 200% but range from 150%-300%

    Which out DDs which on average?

    I need to take less medicine I think, even if the doc tells me to take full doses.



    -edit- jake called me **** for typing this v___v

    Your Sledgehammer would out DD your Spork in the Long Run:

    Spork has 5000 DPH, 1.53 APS and a total of 7650 DPS with only 14.2857% Critical Strike:

    Amount of Normal Hits Performed in 1 hour: 4721.1436
    Normal Damage Total: 23,605,718

    Amount of Critical Strikes Performed in 1 hr. Session: 786.8564
    The Damage from Crits in the 1 hr. Session:
    The Spork's Critical Strike Damage @ 150% Rage Damage: 5,901,423
    The Spork's Critical Strike Damage @ 200% Rage Damage: 7,868,564
    The Spork's Critical Strike Damage @ 300% Rage Damage: 11,802,846
    Spork's Total Damage w/ 150% R. Damage in 1 hr + Normal Hits: 29,507,141
    Spork's Total Damage w/ 200% R. Damage in 1 hr + Normal Hits: 31,474,282
    Spork's Total Damage w/ 300% R. Damage in 1 hr + Normal Hits: 35,408,564



    Sledgehammer has 10000 DPH, 0.80 APS, and a total of 8000 DPS with 20% Critical Strike:

    Amount of Normal Hits Performed in 1 hr: 2304
    Normal Damage Total: 23,040,000

    Amount of Critical Strikes Performed in 1 hr. Session: 576
    The Damage from Crits in the 1 hr. Session:
    The Sledgehammer's Critical Strike Damage @ 150% Rage Damage: 8,640,000
    The Sledgehammer's Critical Strike Damage @ 200% Rage Damage: 11,520,000
    The Sledgehammer's Critical Strike Damage @ 300% Rage Damage: 17,280,000
    Sledgehammer's Total Damage w/150% R. Damage in 1 hr + Normal Hits: 31,680,000
    Sledgehammer's Total Damage w/200% R. Damage in 1 hr + Normal Hits: 34,560,000
    Sledgehammer's Total Damage w/300% R. Damage in 1 hr + Normal Hits: 40,320,000

    Evidence has shown that the Sledgehammer would be more effective against the Spork with a time limit of one hour (3600 Seconds).

    Here's Some Formulas:

    Spork Damage Dealt= (1/7 (Total Hits) *(R.Dmg%*DPH) + (6/7(Total Hits) * DPH)

    Sledgehammer Dmg Dealt= (1/5 (Total Hits) *(R.Dmg%*DPH) + (4/5(Total Hits) * DPH)

    DPH Spork = 1/2 ( Sledgehammer's DPH)

    DPH Sledgehammer = 2 (Spork's DPH)

    Total Hits = ( Attack Rate * Time in Seconds )

    After filling in many options I've discovered:
    With 150% Rage Damage: The Sledgehammer does 6.859% more damage than Spork
    With 200% Rage Damage: The Sledgehammer does 8.929% more damage than Spork
    With 300% Rage Damage: The Sledgehammer does 12.181% more damage than Spork
    As Rage Damge increases the damage of Sledgehammer over Spork increases exponentially!
    [SIGPIC]http://a.imageshack.us/img714/9433/testoz.jpg[/SIGPIC]

    If I had a dime for every time I was wrong, I'd be broke.
  • Alias - Dreamweaver
    Alias - Dreamweaver Posts: 478 Arc User
    edited April 2011
    Ok Decus, i'm tired and not in the right mind and I thought of this question and Teppers won't answer it so I'ma present it to you.

    Ok, i'm in a weird mood and let's say I attack my wall with two different things.
    A sledgehammer, and a spork. Which will do more damage in the long run?
    Let's say for the sake of argument that the spork hits at 1.53 but does half the dph the sledge hammer does, and crits every 7 hits.
    Now the sledgehammer hits at .80 and does double the dps of the spork and crits ever 5 hits.

    Now in my imaginary world crits don't always hit 200% but range from 150%-300%

    Which out DDs which on average?

    I need to take less medicine I think, even if the doc tells me to take full doses.




    -edit- jake called me **** for typing this v___v

    Listen to your doctor.
    And Ds O.o lalala typing where no one can see me :D
  • Tearle - Dreamweaver
    Tearle - Dreamweaver Posts: 511 Arc User
    edited April 2011
    Listen to your doctor.
    And Ds O.o lalala typing where no one can see me :D

    I do listen to my doctor but she gives me way too much med to take per dose and I get all looped out ._.
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited April 2011
    Ok Decus, i'm tired and not in the right mind and I thought of this question and Teppers won't answer it so I'ma present it to you.

    Ok, i'm in a weird mood and let's say I attack my wall with two different things.
    A sledgehammer, and a spork. Which will do more damage in the long run?
    Let's say for the sake of argument that the spork hits at 1.53 but does half the dph the sledge hammer does, and crits every 7 hits.
    Now the sledgehammer hits at .80 and does double the dps of the spork and crits ever 5 hits.

    Now in my imaginary world crits don't always hit 200% but range from 150%-300%

    Which out DDs which on average?

    I need to take less medicine I think, even if the doc tells me to take full doses.




    -edit- jake called me **** for typing this v___v

    I am fairly certain Dsholder nailed it, and I am far too tired at the moment to really take a stab at it. The math, from my cursory perusing, checks out. Though I wouldn't say it's exponential as rage damage increases, but I haven't the patience at the moment to really investigate. Either way, you aren't **** for typing it. Tell Tepp-chan that he's **** since he cannot solve the integral ;)

    Feel better!
    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
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited April 2011
    Fiz I gave plenty of problems for the past week, why haven't you solved any >:(
    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
  • MageFizban - Lost City
    MageFizban - Lost City Posts: 1,158 Arc User
    edited April 2011
    Fiz I gave plenty of problems for the past week, why haven't you solved any >:(

    End of semester. Busy.
  • Teppeii - Dreamweaver
    Teppeii - Dreamweaver Posts: 1,206 Arc User
    edited April 2011
    I know not your speak of fluents and fluxions D:

    But seriously, answer plox.
    On indefinite hiatus :3
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited April 2011
    I know not your speak of fluents and fluxions D:

    But seriously, answer plox.

    The first step is to re-write the integral as this by dividing the numerator by x^2 and dividing the quadratic factor in the denominator by x.

    In so doing, we get x^2 as a factor in both the numerator and denominator and they cancel out. Then we just add 2 and subtract 2 in the radical (completing the square, sort of) and we can factor that to get what you see in the previous link.

    Now we use the tricky (for some) substitution x = t + 1/t, which transforms our old integral into this one. After that, the rest is fairly obvious. We use the substitution t = sqrt(2)sec(q) and the integral becomes laughably doable. I am not going to give you the answer, you can do it yourself after I gave you the key to it ;)

    The rest I am not solving for you since you are perfectly capable of doing it ^.^

    Once I get solutions I'll give out a set for this week.
    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
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited May 2011
    I'm putting them up early because I probably won't put them up till Wednesday otherwise:

    New week (not really, but go with it!); new problems! :D

    I'll even throw in a fun algebra problem for the younger readers! So you get the normal two plus a bonus. Cookies to whoever solves the challenging one this week, it's frustratingly annoying :3

    Ein:

    Solve this indefinite integral. No online integrators, calculators, or google-ing! Do your own work! :<
    It's not easy, but it isn't impossible; and far more rewarding if you figure out a creative way to do it.

    Zwei:

    Prove there are no rational numbers x, y such that 2x^2 - 3y^2 = 1
    but that there are infinitely many rational x, y such that 2x^2 - 3y^2 = -1
    As always, show your work D:

    Drei:

    Find all positive real numbers n such that this is an integer. No google-ing necessary, it's pretty easy to do. Just try it!

    Enjoy mathies, and good luck!

    No takers? b:sad
    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
  • ColdSnow - Dreamweaver
    ColdSnow - Dreamweaver Posts: 983 Arc User
    edited May 2011
    No takers? b:sad

    i like math but tbh i hate integral so i dont even want to touch it -runs- xD

    PS: and its "Eins" and not "Ein" :3
    If i m trolling and spamming on forum...then i cant sleep and need a good laugh
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited May 2011
    i like math but tbh i hate integral so i dont even want to touch it -runs- xD

    PS: and its "Eins" and not "Ein" :3

    I totally knew that b:quiet

    I was just testing you b:surrender



    Anyway I gave the procedure for the integral since it is pretty tough, but the other problems are not integrals =)
    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
  • Cheze - Lost City
    Cheze - Lost City Posts: 200 Arc User
    edited May 2011
    i like math but tbh i hate integral so i dont even want to touch it -runs- xD

    PS: and its "Eins" and not "Ein" :3

    same. I don't like math questions that are like "here's a matrix, see if you've learned the plug and chug techniques to calculate this matrix's other stuff" or "here's an integral, see if you've learned the techniques to solve it" or "here's a thingy, see if you've learned approximation algorithms to estimate it"

    not really interested in stuff that just seems pretty much plug and chug of formulas, algorithms like quesitons that appear on tests, but rather problems that are original and that actually requires some amount of creative thinking without requiring lots of prior knowledge in random stuff.

    for example

    Ten identical crates each of dimensions 3ft x 4ft x 6ft. The first crate is placed flat on the floor. Each of the remaining nine crates is placed, in turn, flat on top of the previous crate, and the orientation of each crate is chosen at random. Find the probability that the stack of crates is exactly 41ft tall.
  • Runemine - Dreamweaver
    Runemine - Dreamweaver Posts: 572 Arc User
    edited May 2011
    Whats the square route of 9,832,785,125 Times 10 Divided by 22 Plus 12 Times 2?

    (Had to do at least 1 post here lol)
    101 Blademaster(Pro/Fail 4.0 BM with 11k base HP+G16(+10))
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  • Yorkin - Dreamweaver
    Yorkin - Dreamweaver Posts: 271 Arc User
    edited May 2011
    Damn, Decus, you started an uprising around here. Anyhow, there is lot to be read here so I'll start with that alternating sum of yours :D
    [SIGPIC][/SIGPIC]

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

    Yorkin - The Retired Wizard
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited May 2011
    same. I don't like math questions that are like "here's a matrix, see if you've learned the plug and chug techniques to calculate this matrix's other stuff" or "here's an integral, see if you've learned the techniques to solve it" or "here's a thingy, see if you've learned approximation algorithms to estimate it"

    not really interested in stuff that just seems pretty much plug and chug of formulas, algorithms like quesitons that appear on tests, but rather problems that are original and that actually requires some amount of creative thinking without requiring lots of prior knowledge in random stuff.

    That's unfortunate because I really enjoy solving differential equations and integrals. I don't really see it as memorizing formulas, but that's just me. I rather enjoy not knowing how to integrate a function and playing around with it till it looks like something I can do ore messing with a DE to get something solvable...

    Ten identical crates each of dimensions 3ft x 4ft x 6ft. The first crate is placed flat on the floor. Each of the remaining nine crates is placed, in turn, flat on top of the previous crate, and the orientation of each crate is chosen at random. Find the probability that the stack of crates is exactly 41ft tall.

    I really, really hate probability and never took a formal course (more out of refusal than anything else), but I'll give it a shot!

    You first need to determine how many of each kind of crate you need:

    x + y + z = 10
    3x + 4y + 6z = 41
    x, y, and z >= 0

    Solving these gives you the following acceptable values for (x,y,z): (1,8,1), (2,5,3), (3,2,5), where x,y,z and represent the orientations of 3ft, 4ft and 6 ft respectively.

    The total number of orientations possible is 3^10 (3 orientations possible for each crate and then there are 10 crates).

    We now must find the total number of orientations that yield the values found above.
    Since these are combinations...

    n = number of objects
    m = resultant possibilities:
    m = (n C x) * ((n - x) C y)* ((n - x - y) C z)*....

    So for the first value

    Combinations of 8 in 10 -> 45
    Combinations of 1 in 2 -> 2
    2*45 = 90 possibilities

    For the second one
    Combinations of 5 in 10 -> 252
    Combinations of 3 in 5 -> 10
    10*252 = 2520

    The third one
    Identical numbers so, same 2520 number of possibilities from above.

    So the over all probability is given by:
    (2520+2520+90)/3^10 = 0.086877 ~ 8.7%

    I think this approach is correct. I may have made a few math errors but I don't think so and don't feel like bothering more with it.

    b:surrender
    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
  • lizrau
    lizrau Posts: 0 Arc User
    edited May 2011
    @Rune, answer would be 90169.81908.
    [SIGPIC][/SIGPIC]


    Sig credits to Myra :D
  • Runemine - Dreamweaver
    Runemine - Dreamweaver Posts: 572 Arc User
    edited May 2011
    I came up with 45096.90954206059305 with my scientific calculator

    Can use this to check maybe i input it wrong(Hope i didn't gotta use it for part GED testb:shocked)
    101 Blademaster(Pro/Fail 4.0 BM with 11k base HP+G16(+10))
    100 Seeker(The Vortex Beast)
    86 Assassin(Solo king)
    76 Archer(Squishy Nuker)
    72 Cleric(Horrible healer)
    67 Barb(Buff baby)
    61 Wizard(King Aoe)
    37 Mystic(Fun project)
  • Prophete - Dreamweaver
    Prophete - Dreamweaver Posts: 283 Arc User
    edited May 2011
    Here is one for you Decus:

    Let W=(Wt; t>=0) denote the Brownian Motion.
    1. Calculate E(Ws l Wt), 0<=s<t (expactation of Ws given Wt)
    2. Show that (Wt) is a martingale adapted to the filtration Ft
    3. Prove that exp(Wt)*exp(-t
  • Viscosity - Dreamweaver
    Viscosity - Dreamweaver Posts: 127 Arc User
    edited May 2011
    1+1=3 >:o
  • ColdAsLife - Dreamweaver
    ColdAsLife - Dreamweaver Posts: 432 Arc User
    edited May 2011
    I allowed the existence of a math thread ... I ruined the forums -insert drama face here-
    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 May 2011
    lizrau wrote: »
    @Rune, answer would be 90169.81908.
    I came up with 45096.90954206059305 with my scientific calculator

    The issue lies in whether you are doing all the calculations and then doubling the answer or whether you are doubling 12 and adding it...

    What I mean is:

    [sqrt(9,832,785,125)*10/22 + 12 ] * 2 ~ 90169.8

    sqrt(9,832,785,125)*10/22 + 12*2 ~ 45096.9

    Both of you are correct in calculations, it's just the explanation that's unclear.
    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
  • Namari - Dreamweaver
    Namari - Dreamweaver Posts: 598 Arc User
    edited May 2011
    *head explodes*

    Clean up on aisle 7. o.o
    Censorship is the bane of creativity. Censorship is the bane of personality. Most of all...censorship is the bane of identity.

    My main is Ivy_. I'm better known as Destini. Also known as _Yvi. Yes, I have an identity crisis. b:chuckle

    Looking for a signature for this character. Wanna make me one?
  • MageFizban - Lost City
    MageFizban - Lost City Posts: 1,158 Arc User
    edited May 2011
    Yeah, math competition-like questions would be more fun than integrate f(x) =blahbah
This discussion has been closed.