The DW Math Thread

Alias - Dreamweaver

*Erects certain Tantric shields against your filthy math*

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

Decus - Dreamweaver

Alias - Dreamweaver wrote: »

*Erects certain Tantric shields against your filthy math*

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

Absolutely, since physics is just applied math

Alias - Dreamweaver

Decus - Dreamweaver wrote: »

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

Teppeii - Dreamweaver wrote: »

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


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

Teppeii - Dreamweaver

Decus - Dreamweaver wrote: »

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


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

Appreciate the tidbit.b:cute

Tearle - Dreamweaver

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

Tearle - Dreamweaver wrote: »

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!

Alias - Dreamweaver

Tearle - Dreamweaver wrote: »

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

Tearle - Dreamweaver

Alias - Dreamweaver wrote: »

Listen to your doctor.
And Ds O.o lalala typing where no one can see me

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

Tearle - Dreamweaver wrote: »

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!

MageFizban - Lost City

http://24.media.tumblr.com/tumblr_lgn770obQL1qexm91o1_500.jpg

Decus - Dreamweaver

Fiz I gave plenty of problems for the past week, why haven't you solved any >:(

MageFizban - Lost City

Decus - Dreamweaver wrote: »

Fiz I gave plenty of problems for the past week, why haven't you solved any >:(

End of semester. Busy.

Teppeii - Dreamweaver

I know not your speak of fluents and fluxions

But seriously, answer plox.

Decus - Dreamweaver

Teppeii - Dreamweaver wrote: »

I know not your speak of fluents and fluxions

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.

Decus - Dreamweaver

Decus - Dreamweaver wrote: »

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!

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

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

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

ColdSnow - Dreamweaver

Decus - Dreamweaver wrote: »

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"

Decus - Dreamweaver

ColdSnow - Dreamweaver wrote: »

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"

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

Cheze - Lost City

ColdSnow - Dreamweaver wrote: »

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"

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

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)

Yorkin - Dreamweaver

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

Decus - Dreamweaver

Cheze - Lost City wrote: »

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...

Cheze - Lost City wrote: »

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

lizrau

@Rune, answer would be 90169.81908.

Runemine - Dreamweaver

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)

Prophete - Dreamweaver

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

1+1=3 >:o

ColdAsLife - Dreamweaver

I allowed the existence of a math thread ... I ruined the forums -insert drama face here-

Decus - Dreamweaver

lizrau wrote: »

@Rune, answer would be 90169.81908.

Runemine - Dreamweaver wrote: »

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.

Namari - Dreamweaver

*head explodes*

Clean up on aisle 7. o.o

MageFizban - Lost City

Yeah, math competition-like questions would be more fun than integrate f(x) =blahbah