you mean the 1/2 sin^2?
#help-41
quick ridge
high stag
Wouldn't du be cos(theta) d(theta) there?
high stag
Oh which is the same thing as sin(theta) my bad
high stag
Sorry I'm still trying to process how they replaced cos(theta) d(theta) with sin d(sin theta), isn't cos(theta) d(theta) just equal to sin(theta)?
quick ridge
no
it’s the derivative of sin theta
du
$\int \sin x \mathcolorred{\cos x , dx}$
if it helps, seriously just let u = sinx
du = cosx dx
high stag
Okay I'll write that out one second
I GET IT
Awesome thank you
Okay now the half thing
quick ridge
Awesome thank you
you’re welcome
amber waspBOT
amber waspBOT
Available help channel!
ancient spoke
alright
ancient spoke
how do you solve this one...? I don't know where and how to begin... (this is the complete question)
sterile swan
!status
amber waspBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
yup
ancient spoke
so you've basically done ( number of outcomes ^ number of trails)??
for like a coin toss it would be 2^2 if there were two coins? and 2^3 if there were three coins?
ancient spoke
how did you get the answer?
ancient spoke
yup
thick canyon
so
chance of all of them having are
15% x 15% x 15%
and chance that one of them doesn't have is 85%
so chance of all of them not having are
85% x 85% x 85%
ancient spoke
chance of all of them having are
right right
ancient spoke
85% x 85% x 85%
ohhhk
but how do we know if 15% is for one child or all three children since they haven't specified how many children
amber waspBOT
@ancient spoke Has your question been resolved?
ancient spoke
.close
amber waspBOT
amber waspBOT
Available help channel!
civic spindle
well,. either way, nobody is going to help me here obviously
people dont exist
so ill pursue it myself
pallid canopy
can you complain somewhere else
vocal isle
Hi
pallid canopy
help channels are for people who are working on problems
unborn plaza
just curious what you're working on
vocal isle
What is there to help you?
civic spindle
oh on this
amber waspBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
vocal isle
Finding a number that contains factors that may generate a perfect square may be extremely difficult; however, there was a method proposed titled the "(x+a/2)^2 formula"
civic spindle
i mean youre not gonna care but like we can try
civic spindle
Finding a number that contains factors that may generate a perfect square may be...
correct
vocal isle
I thought you blocked me yesterday.
unborn plaza
what does it mean for a factor to generate a perfect square?
civic spindle
what does it mean for a factor to generate a perfect square?
do you understand or are you actually curious
unborn plaza
i don't understand
civic spindle
I thought you blocked me yesterday.
civic spindle
i mean youre not gonna care but like we can try
vocal isle
Me neither understands.
civic spindle
well thats because we speak different languages, english doesnt exist either so
but i can still try either way
vocal isle
ok
civic spindle
what does it mean for a factor to generate a perfect square?
so 4x4 = 16
thats a perfect square because both factors are the same
unborn plaza
every number generates a perfect square
civic spindle
nope
it has to be of a specefic number
bc you want to recreate it
thats the goal of the formula
i really dont understand why you people come acting like you are going to help when you obviously arent
its pathetic really
wasting my time
smh
i will continue with what i was doing
--------------------------
now that the buffoons are gone ill continue
7 The question of why exactly dividing a number by two and powering it generates a number with two factors
pallid canopy
i really dont understand why you people come acting like you are going to help w...
can you stop being rude
amber waspBOT
Helpers are just people volunteering their time to help you. Be polite and patient.
civic spindle
? im not being rude, im telling it like it is
unborn plaza
do you need/want help with something?
civic spindle
dont act like youre here to help lmfao
pallid canopy
? im not being rude, im telling it like it is
you can tell it like it is AND not be rude
try it some time
pallid canopy
<@&268886789983436800> can you help him
civic spindle
you wouldnt get it im not gonna bother explaining it to you cuz you arent here to help you just pretend like you are
civic spindle
`7` ```
The question of why exactly dividing a number by two and powering it gen...
continuing off of this
zenith heron
Bro ur not paying these helpers so stop acting rude
severe scroll
what is happening
civic spindle
all yall blocked cuz you arent here to help and are wasting my time
besides smay and axe
cuz axe was chill
civic spindle
what is happening
a bunch of ppl are spamming basically
zenith heron
riemann was chill and just telling you to be polite
fierce edge
civic spindle
ive noticed this repeatedly they come into the help channels and dont actually help and talk bout useless matters or just leave the second i ask for a rephrasing
severe scroll
okay, can we all keep it on-topic? i am gonna purge all the off-topic conversation now.
pallid canopy
what is happening
just a whiner whining about people helping and telling him to behave but continues to be unpleasant
civic spindle
okay, can we all keep it on-topic? i am gonna purge all the off-topic conversati...
fr
please do that
cuz they are making it so hard with the spam
scenic dagger
just a whiner whining about people helping and telling him to behave but continu...
This is not helpful to say
scenic dagger
cuz they are making it so hard with the spam
The helpers are volunteers. You should be polite too fwiw.
civic spindle
I know its just after the 50th time
you start to lose control
because you can only be pushed to the limit so many times
severe scroll
it didn't happen 50 times, and part of using the help channels requires you to be polite.
civic spindle
can we move on?
severe scroll
i'm gonna purge the off-topic stuff now if that's okay
scenic dagger
because you can only be pushed to the limit so many times
Nothing here is this serious. Being upset doesn't remove you of the obligation of being respectful to others here.
civic spindle
it didn't happen 50 times, and part of using the help channels requires you to b...
im polite but when i ask 50 times to different people to help me and they give one answer and refuse to rephrase and act like im goofy for not understanding it becomes infuriating because you feel like everyone is only in their own little world and cant understand anyone whos at a lower level and ditches you the moment you wont get it once
and dont forget what i experienced many times before
there were people who literally would come here just to troll and overtime the meaninglessness will get to you
i dont expect you to understand but you arent wrong either
so just move on
scenic dagger
There are a broad range of users
In terms of maturity, interest, mathematical ability and so on.
If somebody is trolling, by all means ping mods. But you do need to be respectful of other users here either way.
civic spindle
people need to learn to move on sometimes rather than talking about peoples imperfections unless they want to actually discuss the problem or reason why someone is annoyed
civic spindle
you do understand what I said though right? Im mad because every time I ask it feels like people are in their own little world of extremely complex semantics and cant simplify it for the life of them typing 5 paragraph essays for me to understand without any willingness to simplify
and that happens 1/2 of the time
vocal isle
Q.1 Powering to what?
Q.2 What if it is odd?
Q.3 Where did you learn this statement?
civic spindle
Q.1 Powering to what?
Q.2 What if it is odd?
Q.3 Where did you _learn_ this stat...
completing the square, many people have mentioned it prior ill show you one example
vocal isle
Ok
civic spindle
also dont act like you were innocent either you know damn well how you acted yesterday when i tried to ask but was confused on how to phrase it
scenic dagger
also dont act like you were innocent either you know damn well how you acted yes...
I get you are upset
civic spindle
this
scenic dagger
But I'm also not asking you to be polite/respectful here.
civic spindle
scenic dagger
I'm telling you you need to do that.
civic spindle
But I'm also not asking you to be polite/respectful here.
i can up until a point
scenic dagger
You can up until the point where I stop warning you and just mute/ban
civic spindle
you also need to understand there comes a time where i actually straight up cannot anymore because i push myself to the limit mentally at some point after hours of trying and getting nowhere
i mean you cant actually do that but sure
you only say that because you dont understand
scenic dagger
The same expectation I'm asking of you here would exist literally anywhere else in your life.
This is not unreasonable.
civic spindle
in life people dont just dissapear the second you ask for further explanation assume you are a troll whenever you want to ask or sometimes act absolutely insane
and if they do they have a good reason or context
scenic dagger
If you cannot control yourself, that's a sign you should take a break.
civic spindle
incorrect, I must eternally pursue this goal.
scenic dagger
That makes very little sense.
civic spindle
I am nearest to my "ideal state" as of recent additions to metastrategisms ive developed.
civic spindle
That makes very little sense.
you do it every single day dont lie
this conversation is pointless semantics
scenic dagger
I don't even care what you mean by that. Point being. Be polite and respectful to other users here.
civic spindle
i am telling you i nor anyone else is always respectful and every now and then it is an observable truth of reality that people will hit their limit with certain people even if they adjust in many situations and insult someone after being judged themselves.
scenic dagger
Then ping mods and disengage.
civic spindle
which that user had done prior immediately assuming I was a troll and refusing to add anything to the conversation
i cannot disengage they are literally in the channel i go to ask for help and last time i had 3-4 people all being toxic simutaneously and the mods didnt do sh##
the mods were about as useful as a potato in that situation
scenic dagger
I am totally for muting/banning users on your behalf if necessary provided some actual rule breaking is happening.
vocal isle
I was just joking
scenic dagger
You should probably leave this user alone as well
civic spindle
I was just joking
you didnt actually help bro you cant say that
that isnt a joke
unbelievable
scenic dagger
Joking at somebodies problem while they are actually looking for help is pretty shitty.
civic spindle
im out
civic spindle
Joking at somebodies problem while they are actually looking for help is pretty ...
look ill try to do what you said but sometimes people hit their limit especially on a stressful topic as math after the 10th failure
scenic dagger
Okay, just try your best next time. If people are trolling or being actively disrespectful you can ping mods or dm modmail.
last totem
Part 1:
okay this is a really complex problem and i have asked for help almost anywhere on the internet, so keep that in mind maybe it can't be cracked the way i am trying to do it, so please think out of the box.
Setup:
let's set the stage with an example, there are 4 people standing on the north pole inside the same point (don't think about how that is possible it just is), they are all looking in the exact same direction, and now imagine that they are all moving in 4 different directions, the first one moves in the same direction they were looking, the second and third moves sideways to the direction they were all looking in opposite directions, and the fourth runs backwards to the direction they were all facing, now imagine that they have reached the south pole all standing only just a few meters from each other, the directions that they are facing are different now.
the first one will look inwards to the south pole
the second and third will look perpendicular to the south pole kind of at the first guy
and the last will look outwards of the south pole
vagrant saffron
What’s the question?
last totem
be patient
vagrant saffron
oh sorry
last totem
Part 2:
Wtf is the problem dude:
well i am making a game in godot where you are a guy wandering around a planet, i want the players feet to always be on the ground, this isn't a problem
the way i am doing it is with quaternions, i first calculate the angle between the players position vector and the north pole position vector, then i find the orthogonal vector to the players position vector (the one on the equator) and then i define the players rotation as the rotation around this vector by the angle from before. This rotation has the players feet on the ground, But you might already know the problem, when going around the south pole without moving the camera left or right the game will spin the player like what was described in Part 1. I need another way to calculate this rotation that will keep the looking direction.
The code:
#first i define the players position vector by subtracting their position with the planets position and then i normalize it of course
var positionVector = ($".".position-$"../Planet".position).normalized()
#then i find v by using the cross product between the vector pointing directly up (north poles position vector) and the players position vector
var v = acos(positionVector.x * Vector3.UP.x + positionVector.y * Vector3.UP.y + positionVector.z * Vector3.UP.z)
#then i find the orthogonal vector by switching x and z and making y 0 this will find the one at the equator and then i normalize it of course
var orthogonalVector = Vector3(-positionVector.z, 0, positionVector.x).normalized()
#then i have a failsafe if the vector is just zero
if orthogonalVector == Vector3.ZERO:
orthogonalVector = Vector3(1, 0, 0)
#then i turn the player with this rotation where i rotate them around the orthogonal axis from the north pole by the angle v
$".".quaternion = Quaternion(positionVector, lookDegrees)*Quaternion(-orthogonalVector, v)
I am sorry i know this isn't a programming server, but it is basically 100% a math problem.
i have a video
i am not moving the camera
and you can notice i am looking the same directions as the 4 people from earlier
vagrant saffron
Would it be easier to just make the player static, then move the sphere below the player
last totem
Would it be easier to just make the player static, then move the sphere below th...
yeah, but that is not really what i want to do, because it will have a lot of limitations, like npcs having to move also and other stuff
vagrant saffron
So it works, but when you get to the equator it like spins you around?
last totem
So it works, but when you get to the equator it like spins you around?
the south pole
vagrant saffron
the south pole
got it
does it still happen if you switch where the players start?
last totem
rn, it is only me playing, basically i just need a way to describe a rotation that rotates the player so that their feet are on the ground while maintaining there looking direction when at the south pole
idk if it is possible
the 4 player example is just an explanation of why it is happening
vagrant saffron
rn, it is only me playing, basically i just need a way to describe a rotation th...
in theory. I was trying to see if it was because that’s where you spawned in, or if it’s because that’s where you start the vector
last totem
in theory. I was trying to see if it was because that’s where you spawned in, or...
yeah i start the rotation at the north pole, the problem is that no matter where you start the rotation the opposite side is going to be a problem
so i need an entirely different way to approach it
vagrant saffron
yeah i start the rotation at the north pole, the problem is that no matter where...
It’s probably stupid but what happens if you place the rotation in the center
last totem
It’s probably stupid but what happens if you place the rotation in the center
okay let me explain it a bit better, the way it works right know is that i define an axis to rotate around, this axis the the one placed at the equator and the one perpendicular to the players up direction, then i define the amount of rotation to be the angle from the north pole to the player. I also have a hard time visualizing this so don't feel bad.
so imagine i spear hook the earth at the equator and then i turn it by turning the spear but instead of the rotation being applied to the earth it is being applied to the player
so to define this rotation i take the axis perpendicular to the player at the equator, and then i turn from the north pole down to the players position by finding the angle between.
vagrant saffron
and it glitches out when you get to the opposite pole of the one it is anchored too?
last totem
yes like this example if i move around the pole i spin exactly like this
vagrant saffron
yes like this example if i move around the pole i spin exactly like this
Is the game getting confused because you have zero distance?
like it’s calculating an angle of nothing
ok wait i just did some research
Problem to rotate player on a sphere/planet by mouse click - Unity Engine - Unity Discussions
https://discussions.unity.com/t/problem-to-rotate-player-on-a-sphere-planet-by-mouse-click/841186
i’m not sure if it will help
amber waspBOT
@last totem Has your question been resolved?
last totem
<@321019970664398851> Has your question been resolved?
don't know yet
amber waspBOT
vagrant saffron
.reopen
amber waspBOT
Available help channel!
vagrant saffron
@last totem did you get it?
amber waspBOT
<@321019970664398851> did you get it?
last totem
<@321019970664398851> did you get it?
no, but what other people are saying is either to rotate the globe instead of the player, or find the rotation needed between the last frame and current frame
vagrant saffron
no, but what other people are saying is either to rotate the globe instead of th...
progress
amber waspBOT
Available help channel!
compact wagon
amber waspBOT
silver maple
What do you mean?
compact wagon
like idk where to start
silver maple
like idk where to start
I think a subsitution of $u=2\ln(x)$ suffices here.
grizzled pagodaBOT
;(
silver maple
Since $\ln(x^2)=2\ln(x)$.
grizzled pagodaBOT
;(
compact wagon
wait so by using the log properties
solar gust
Yes
silver maple
So this would become $\int\frac{dx}{x(2\ln(x))^5}$.
solar gust
But the 5 can't go down
grizzled pagodaBOT
;(
solar gust
wait why not the 5
Its not in the ln
grizzled pagodaBOT
;(
silver maple
I think this is pretty easily computable now.
full sand
whenever you multiply with 1/derivative of what you want to substitute then a subsitution is good
compact wagon
.close
amber waspBOT
amber waspBOT
Available help channel!
round mirage
from top to bottom is it deba
amber waspBOT
from top to bottom is it deba
sterile swan
!status
amber waspBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@round mirage Has your question been resolved?
amber waspBOT
amber waspBOT
Available help channel!
shy sage
Why - 3 < x < 3 and x ≠ 0 could be written as 0 < | x | < 3?
lime jasper
Why is this
amber waspBOT
Why is this
wet breach
Because that's the definition of absolute value.
If the number doesn't have a negative sign, leave it alone. If the number has a negative sign, get rid of it.
And absolute value means to get rid of a negative sign if it has one.
So, that definition does exactly that.
Numbers have a negative sign if they're less than zero.
And taking the negative of a negative gives you a positive.
zenith heron
Mathematically speaking, you can think of that the absolute value of x is equal to the square root of x²
amber waspBOT
@lime jasper Has your question been resolved?
lime jasper
How to piece wise this
amber waspBOT
How to piece wise this
sterile nymph
You have three regions, one where both are negative, one where both are positive, and one where one is positive and the other negative
Can you tell me these regions?
lime jasper
You have three regions, one where both are negative, one where both are positive...
How do you determine that
split sail
By finding the critical points if I am not wrong
sterile nymph
You have two lines
lime jasper
By finding the critical points if I am not wrong
What are those
sterile nymph
All lines (which do not have zero or undefined slope) will have two regions of x values, one where it is positive and the other where it is negative
split sail
critical points are basically where the expressions inside the absolute values change sign
so like
x - 3 = 0 --> when x = 3
x - 1 = 0 --> when x = 1
then this must mean that 1 and 3 are the critical points
These points divide the number line into three intervals like how Omnipotent Entity was mentioning
x < 1
1 <= x < 3
x >= 3
Now that you have the intervals
now for each interval
you need to find the corresponding function
I'll do one
and then you can try to find the other ones
- interval 1: x < 1
--> (x - 3) < 0 therefore --> -(x - 3)
--> (x - 1) < 0 therefore --> - (x - 1)
therefore our function for x < 1 becomes y = -(x - 1) - (x - 3) = -2x + 4
Try to do this for the other intervals as well
and voila! you have your piecewise function
you can ping me if you have any further doubts
lime jasper
1. interval 1: x < 1
--> (x - 3) < 0 therefore --> -(x - 3)
--> (x - 1) < 0 ther...
How come u get (x-3) < 0 and (x-1) < 0
split sail
How come u get (x-3) < 0 and (x-1) < 0
try thinking about this
if you have value of x that are less than 1 (which is true for the first interval, aka x < 1)
--> (x - 3) would ALWAYS evaluate to a negative value
--> (x - 1) would ALWAYS evaluate to a negative value
therefore you would have (x - 3) < 0 and (x - 1) < 0
Does this make any sense?
lime jasper
Oh yeah
keen pawn
I'm trying to show that this limit doesn't exist. How does this structure( which is what I'm Concerned about) look
\
$\lim_{(x,y) \to (x,0)} \frac{y^4}{x^4+3y^4} = 0$
\
\
$\lim_{(x,y) \to (0,x)} \frac{y^4}{x^4+3y^4}= \frac{1}{3}$.
\
\
As the limits along two different paths are different, the limit doesn't exist at (0,0)
grizzled pagodaBOT
What a wonderful world!
compact yarrow
Did you mean (0, y) for your second limit?
keen pawn
yes
compact yarrow
I think my concern with this is that you're not exactly showing the same thing they're asking you to
Like they want the limit of (x,y) -> (0,0), and you're writing (x,y) -> (x,0) and only then sorta implicitly taking the limit as x -> 0
compact yarrow
Probably something like "path 1: along the line y=0 (then do the limit)... path 2: along the line x=0 (etc.)"
It's been like 5 years since I did multivar so my presentation may not be pristine
amber waspBOT
amber waspBOT
Available help channel!
fierce edge
a set contains 5 consecutive even integers
amber waspBOT
a set contains 5 consecutive even integers
fierce edge
is it always true that this set has standard deviation > 2
how do you do this without actually using the formula
here’s my idea:
let 5 even integers be 2n, 2n + 2, 2n +4, 2n + 6, and 2n + 8
you can shift it all down by 2n without changing sd
now our problem has reduced to finding the sd of (0,2,4,6,8)
now i can shift it down by the mean again without changing sd
so now i have (-4, -2, 0, 2, 4)
this is now under “0 mean”
is there some way to instantly go “oh yeah this tuple has standard deviation greater than 2”
noble niche
a set contains 5 consecutive even integers
what is the questin asking?
noble niche
oh
grim forge
so now i have (-4, -2, 0, 2, 4)
Well all there's deviation equal to 2 and more than 2
So the standard deviation should be logically greater than 2
grim forge
here’s my idea:
let 5 even integers be 2n, 2n + 2, 2n +4, 2n + 6, and 2n + 8
The mean of this whole tuple is 2n+4
And we can see the deviation of all the elements of the tuple(excluding 2n+4) is greater than or equal to 2
So the sd>2
@fierce edge
fierce edge
Well all there's deviation equal to 2 and more than 2
that’s just using the formula though
since you’re talking about squared deviations
grim forge
I mean technically I didn't use the formula
I didn't calculate the sd
I just observed that the deviation of all data in the tuple is greater than or equal to 2
It's like how just by observation you can tell (2,2,2,3) has a mean greater than 2
@fierce edge
fierce edge
I just observed that the deviation of all data in the tuple is greater than or e...
that doesn’t make much sense to me 😭
i reduced the problem down to (-4,-2,0,2,4)
now i need to bound it
grim forge
that doesn’t make much sense to me 😭
I mean like the sd is really the average of all the deviations right?
fierce edge
yeah but if we’re going that route then i made my problem super easy to use the formula with
it’s just sqrt(2(2^2 + 4^2)/5)
grim forge
Do you have to give an explanation in your solution?
Or is it just a true false type qn @fierce edge
fierce edge
Do you have to give an explanation in your solution?
yes ofc
fierce edge
Or is it just a true false type qn <@1266602198020919368>
no even then i wouldn’t be guessing
grim forge
no even then i wouldn’t be guessing
What's the smallest difference between two unique even numbers?
Welp nvm
Maybe I'm wilding😭
sterile nymph
I mean, if there is a way of glancing at a set of values, even highly symmetric ones, and just knowing the variance and/or stdev apriori, I'm not aware of it
Fortunately, the formula is pretty easy to calculate, and you get down to 2 sqrt (2) which is clearly larger than 2.
fierce edge
I mean, if there is a way of glancing at a set of values, even highly symmetric ...
not knowing but guesstimating?
fierce edge
Fortunately, the formula is pretty easy to calculate, and you get down to 2 sqrt...
yeah i guess the way i manipulated it and got it down to (-4,-2,0,2,4) makes it pretty easy to compute the population mean ig
i was curious if we could proceed further with manipulation
bc till now i didn’t use the formula
i just need a heuristic approach
not a full blown proof
grim forge
Yea mb I was wilding
fierce edge
it’s cuz we haven’t learn the sd formula so using it would be weird
i mean ik how to use it but that’s besides the point
bc this question is apparently for people only with the knowledge of “standard deviation measures dispersion from mean” rather than how
fierce edge
Yea mb I was wilding
no worries-
sterile nymph
I mean, someone with that level of knowledge would likely compute the mean absolute deviation instead
Which is 12/5, which is still larger than 2, but not really comparing apples to oranges
sterile nymph
The MAD?
sterile nymph
but then they’d have to know that
If they didn't know what a standard deviation is, they'd guess and what they guess would probably be the mean absolute deviation
fierce edge
If they didn't know what a standard deviation is, they'd guess and what they gue...
yes correct
2 + 2 + 4 + 4 =12
12/5
hmmm
okay that’s their own definition ig 😭
sterile nymph
Right, and that's related, somewhat, to the standard deviation, but I do not know if it can be both larger and smaller.
So it's difficult to say that "this is a lower bound"
fierce edge
they usually square it to make the whole thing more conspicuous right?
so maybe it works idk most of the time
sterile nymph
The square is because the standard deviation is the 2nd moment of the distribution.
fierce edge
oh
fierce edge
The square is because the standard deviation is the 2nd moment of the distributi...
okay anyway i guess just use the formula
😭😭
thanks-
fierce edge
yeah it’s just that 😭the question apparently doesn’t require it
cuz the formula isn’t taught
but yep i’ve used it before
u just use the variance formula
sterile nymph
Hmmm
fierce edge
E( (x - mu)^2) and then just replace the mean formula with (x - mu)^2
and then sqrt for standard deviation
also just Var(X) = E(x^2) - 0
sterile nymph
Well, I suppose the standard deviation kinda sorta represents how far away things are on average, and clearly between 0, 2, 2, 4, 4 we are different more than 2 on average?
Just like
fierce edge
Well, I suppose the standard deviation kinda sorta represents how far away thing...
😭i guess yeah
sterile nymph
also just Var(X) = E(x^2) - 0
Only if mu=0 ofc
fierce edge
Only if mu=0 ofc
yes, which i had
cuz shifting my units down
doesn’t affect variance
fierce edge
Well, I suppose the standard deviation kinda sorta represents how far away thing...
okay so this is just heuristics i can use maybe
perhaps this is what they’re going for
amber waspBOT
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bronze basalt
what is the proof of this theorem (idk its name):
if AB = CD and (AB) and (CD) are not parallels
then, there exist only one rotation that transform AB into CD
amber waspBOT
what is the proof of this theorem (idk its name):
if AB = CD and (AB) and (CD) a...
@bronze basalt Has your question been resolved?
bronze basalt
<@&286206848099549185>
bronze basalt
what is the proof of this theorem (idk its name):
if AB = CD and (AB) and (CD) a...
please any idea? or any wiki link
eternal venture
this isn't true for anything more than 2 dimensions
bronze basalt
I am talking about 2D
eternal venture
then I guess the proof depends on how you define "rotation"
if you define it by specifying what happens when you rotate something by an angle theta, you can get some formula to compute the angle between two things
bronze basalt
R(I, theta) (A) = A' <=> IA = IA' and (IA, IA') ≡ theta [2pi]
eternal venture
if you define it as a length preserving orthogonal linear transformation with determinant 1
well I guess you can just grind out the algebra
eternal venture
R(I, theta) (A) = A' <=> IA = IA' and (IA, IA') ≡ theta [2pi]
I don't understand your notation here
bronze basalt
the image of A is A' by the rotation R of center I and angle theta means the distance IA equal to IA' and the angle between the vectors AI and AI' is theta [mod 2 pi]
eternal venture
I don't get how that defines what a rotation is
bronze basalt
like that .. hold on
eternal venture
are you just saying that rotations are all things that preserve length? I don't think that's true
the part where you talk about angles doesn't really say anything other than angles exist
eternal venture
why is there pi/2
eternal venture
I'm pretty sure I know what a rotation is
I'm asking you how you define what a rotation is
like how do you characterize all rotations
bronze basalt
I'm asking you how you *define* what a rotation is
I didn't understand what you mean
eternal venture
because that affects how you prove it
bronze basalt
I'm asking you how you *define* what a rotation is
give me an exemple so I can understand
eternal venture
I just gave you two different ways to define rotation
bronze basalt
hold on
we call rotation of center O and angle theta, the application of the plane in itself which fixes the point O and which at all points M of the plane distinct from O, associates the point M' such that OM = OM' and ( OM, OM') = theta [2 pi]
this is the definition I have
you got it?
@eternal venture
bronze basalt
what is the proof of this theorem (idk its name):
if AB = CD and (AB) and (CD) a...
<@&286206848099549185>
no
its the same
or no
it is not
incorrect
theta is not -theta
nope
it is clear
the rotation will be the center I where I is the intersection of the two medians (AC and BD)
and the angle of the rotation will be (AB, CD) [2pi]
bronze basalt
the rotation will be the center I where I is the intersection of the two medians...
but this is an explaination not a proof
counterclock wise is defined as positive angle and clockwise is defined as negative angle
<@&286206848099549185>
bronze basalt
what is the proof of this theorem (idk its name):
if AB = CD and (AB) and (CD) a...
<@&286206848099549185>
bronze basalt
what is the proof of this theorem (idk its name):
if AB = CD and (AB) and (CD) a...
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
pls help
amber waspBOT
@bronze basalt Has your question been resolved?
night snow
amber waspBOT
sterile swan
supple locust
What does onto mean?
night snow
codom=range
supple locust
Yes
sterile swan
What does onto mean?
surjective
outer hull
What does onto mean?
surjective
sterile swan
one-to-one = injective
onto = surjective
sterile swan
ah, mb
outer hull
ah, mb
supple locust
codom=range
So we must show that everything in R is f(x) for some x
night snow
yea
the denominator has no roots, so it can nvr be 0 in R
w8 bro i just got something
supple locust
That doesn’t discount roots, that would give an asymptote
night snow
oh
its not onto
since
cuz i wont get a negative value
a big negative value
i basically mean x^2 will overpower the -ve values of x
supple locust
I think to make an argument like this precise we should simplify some things
Because we have x^2 on numerator and denominator we can do polynomial division
And get a remainder
silver maple
is it alright if i suggest something?
supple locust
Yeah sure
silver maple
for f to have a codomain in R, you must have one of two requirements: either a vertical asympotote, or lim as x->infinty of f has to be infinity
if neither of these conditions is satisfied, the codomain is restricted
so try calculating those to test the "onto" part
supple locust
Yeah, we should see this after polynomial division
night snow
ic
night snow
the denominator has no roots, so it can nvr be 0 in R
like what i meant to say is that if i keep any value of x from R, we wont get a something/0 form
suppose in the Dr it had (x-1)(x-6), so we wud directly be able to tell that it is an into fn ryt
supple locust
like what i meant to say is that if i keep any value of x from R, we wont get a ...
So this is saying that the function “makes sense” for all x, there are no points where the function is not defined
night snow
ye thats what i meant
night snow
Yeah, we should see this after polynomial division
so ill do that long division bs ryt
winged panther
y = E => x²(y - 1) - (4y + 2)x + (9y + 15) = 0
As x is in R, we must have real roots => ?
supple locust
so ill do that long division bs ryt
You actually can see it without necessarily computing
night snow
ye i get the reminder as 6x -24
winged panther
>>> y = E => x²(y - 1) - (4y + 2)x + (9y + 15) = 0
As x is in R, we must have re...
Is the standard method to find range of rational functions ^^"
night snow
gets large ??
night snow
Is the standard method to find range of rational functions ^^"
ahh ye i just remembered
supple locust
As in it will be bounded as the x^2 in the denominator doninates
It goes to 0 at both sides
winged panther
D ≥ 0 would give you a negative coefficient of y² ≥ 0 immediately suggesting it's not surjective
night snow
D ≥ 0 would give you a negative coefficient of y² ≥ 0 immediately suggesting it'...
lemme try and see what i get
im getting 5y^2 + 10y - 16 < or eq to 0
winged panther
✓ which suggests y falls in an interval implying that range of E is not R
winged panther
HuH?
winged panther
im getting 5y^2 + 10y - 16 < or eq to 0
Y is the value of the expression E. Simply solving this inequality in y would give you that
winged panther
im getting 5y^2 + 10y - 16 < or eq to 0
This is wrong btw
night snow
Y is the value of the expression E. Simply solving this inequality in y would gi...
i forgot how to solve iequality 😭
night snow
This is wrong btw
i got -5y^2 -10y + 16>=0
winged panther
,w Simplify (2y + 1)² - (y - 1)(9y + 15)
grizzled pagodaBOT
winged panther
Should be 2 in place of 10
winged panther
Welp anyways, -2 ≤ y ≤ 8/5 is what you get
Alternatively, you could write:
f - 1 = 6(x - 4)/(x² - 4x + 9)= 6/[(x - 4) + 9/(x - 4) + 4] and you can use this to find max f is 16/10
So f isn't really covering R
night snow
Alternatively, you could write:
> f - 1 = 6(x - 4)/(x² - 4x + 9)= 6/[(x - 4) + ...
what did u do here?
winged panther
Write down each step on a piece of paper and you'll understand
night snow
alr
6/[(x - 4) + 9/(x - 4) + 4]
u basically brought the x-4 down right
wont u get 6/ [ x + (9/x-4)]?
winged panther
Yes
To be able to use AM-GM, I did a lil manipulation and found the minimum of denom
night snow
oh
i also had a doubt in the one one part
in this question , we can simplify it to (x+5)(x-3)
so for 2 value of x we get f = 0
so its not one one
but
what if the numerator had no real roots
then wud it always be one one
amber waspBOT
@night snow Has your question been resolved?
vocal isle
If a sphere is in equilibrium and is not moving in a liquid of two liquids where a liquid of lower density than the other floats on top of the other one and the sphere's m/n volume is in the upper liquid and 1-m/n part in the lower liquid, how can we find it's density in terms of the m/n and the densities of the liquids?
I understand that we have to equate the weight of the sphere by the resultant force (which is 0) of the two liquids, but I fail to understand how the upper liquid is exerting any buoyant force on the sphere that is beneath it.
Is the weight of the liquid exerting the buoyant force?
How can it even exert a buoyant force from above?
vestal hatch
It's just a model for what's happening
The buoyancy force is caused by atoms colliding with the bottom of the ball imparting more force than those colliding with the top
unkempt holly
If a sphere is in equilibrium and is not moving in a liquid of two liquids where...
Archimedes' thrust?
vestal hatch
The reason why putting liquid on top increases the buoyancy is because it increases the pressure of the liquid on the bottom
amber waspBOT
vocal isle
Archimedes' thrust?
No way bro calls it Archimedes' 'thrust'.
unkempt holly
No way bro calls it Archimedes' 'thrust'.
sorry cuh
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Available help channel!
viscid cobalt
amber waspBOT
sterile swan
!status
amber waspBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
I got everything except
the plus 90
idk why they add 90
where did this come frommmmm
heuosfhuosehfousfg
hollow plaza
you solved the integral?
viscid cobalt
yeah
i got the -455/12
its lit just the 90
i dont get
oh
Im guessing they formed some sort of triangle
from here
down to here
that would explain why the length is 23+13
why its multiplied by 5
and by a half
how did they know the integration stops there tho?
I mean as in
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amber waspBOT
viscid cobalt
.reopen
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✅
hollow plaza
why your using graph solving the integral?
viscid cobalt
like i guess my question should be
no i solved the integral on paper
Im just trying to comprehend
graphically
this question
hollow plaza
use desmos
sand cargo
The added stuff is a trapezium
hollow plaza
and you will see
sand cargo
The integral is the unshaded part
viscid cobalt
yeah i get that
sand cargo
Form a line from P ti the x-axis
viscid cobalt
Form a line from P ti the x-axis
just a straight line upwards?
sand cargo
yes because it is the interval
hollow plaza
lol
crystal mantle
doesnt that form a triangle
if you have enough engineering degrees yes it is
sand cargo
viscid cobalt
oh right
crystal mantle
but it's very impractical to consider that a triangle considering you'll leave so much area uncalculated, so just stick to your curves
sand cargo
but it's very impractical to consider that a triangle considering you'll leave s...
wait how do you get a triangle or is this sarcastic
crystal mantle
you don't
sand cargo
🙏🏻
crystal mantle
but if you believe hard enough you can try 🌈
sand cargo
There's another way if you want to use a triangle
viscid cobalt
in the trapezium
sand cargo
You shift the curve upwards
viscid cobalt
yeahhhhhh
sand cargo
you use the 2 parallel sides, divide by 2
Then multiply by the distance between the 2 parallel lines
viscid cobalt
yeah must be -23
or i guess i'll use positive 23
(23 + 13))(5/2)
= 90
sweet
thanksss
sand cargo
or i guess i'll use positive 23
Yes because distance has a modulus ie always positive
viscid cobalt
.close
amber waspBOT
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ripe spruce
what does it mean when i say that the reals have no nontrivial field extention of odd degree. this was a statement my professor spammed after proving the following lemma:
for every polynomial of odd degree in the polynomial ring over the reals that polynomial has a root over the reals
indigo cloud
what do you know about field extensions
ripe spruce
what do you know about field extensions
i know what a field extention is
i know algebraic, normal , and seprable field extentions
i wouldnt say i have alot of deeper knowledge about the topics
i know what is the degree of a field extention which is basically the dimension of extended field as a vectorspace over the smaller field
to make my question more concrete, i dont understand what he means by nontrivial field extention
indigo cloud
not R as a field extension over itself
which of course would have degree 1 which is odd
ripe spruce
omg hahah that makes sense
so you are saying the trivial field extention is just extending the field by itslef
okay i guess here was my confusion thanks for the help
.close
amber waspBOT
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Available help channel!
empty kayak
Don't know how to solve this
amber waspBOT
Don't know how to solve this
somber lance
Don't know how to solve this
Definite integral calculates area under a curve
amber waspBOT
@empty kayak Has your question been resolved?
formal dome
Definite integral calculates area under a curve
*signed area between curve and X axis
somber lance
@empty kayak that should give u hint already
amber waspBOT
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amber waspBOT
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Available help channel!
keen pawn
$\pdv{z}{x} = f'(x-y)$
\
$\pdv{z}{y} = -f'(x-y)$
\
$\pdv{z}{x}+ \pdv{z}{y} = f'(x-y)-f'(x-y) =0$
grizzled pagodaBOT
What a wonderful world!
keen pawn
Is this fine?
amber waspBOT
@keen pawn Has your question been resolved?
keen pawn
<@&286206848099549185>
lost briar
Is this fine?
yes, I don't know if you need to show more explicitly by substituting u=x-y and stating that f' is df/du but it is correct.
keen pawn
yes, I don't know if you need to show more explicitly by substituting u=x-y and ...
Thanks!
.close
amber waspBOT
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Available help channel!
split sail
How do we graph |x|-|y|=2?
amber waspBOT
How do we graph |x|-|y|=2?
fervent acorn
yes
fervent acorn
yea
amber waspBOT
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Available help channel!
meager gale
amber waspBOT
meager gale
vey confused on how to do this. dont know where to start, dont know what its really asking me to do
ig smth like this? but what do i do with this
amber waspBOT
@meager gale Has your question been resolved?
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split sail
amber waspBOT
split sail
What numbers can “a” be here
raw stirrup
You can try and simplify.
split sail
when is something equal to its absolute value?
when its the same distance away from 0?
i think
vestal hatch
it's not a sufficient answer
uneven hedge
It is because the left hand side is exactly |2a+1|
raw stirrup
so a can be any positive number?
No, a cannot be negative.
vestal hatch
It is because the left hand side is exactly |2a+1|
this is a non-sequitir
raw stirrup
that doesn't make any sense
Try plugging a negative value into a.
uneven hedge
$\sqrt{a^2} = |a|$
grizzled pagodaBOT
hiidostuff
vestal hatch
ok, i'll try a = -0.25
uneven hedge
You get the equation |2a + 1| = 2a + 1
split sail
No, a cannot be negative.
wait what if a=-1/2
uneven hedge
So 2a + 1 must be nonnegative
raw stirrup
It's 2a + 1 that cannot be
Right.
uneven hedge
Right.
From that, you can get what a must be greater or equal to
Just rearrange $2a + 1 \ge 0$
grizzled pagodaBOT
hiidostuff
split sail
It's 2a + 1 that cannot be
im lost🥲
raw stirrup
From that, you can get what a must be greater or equal to
2a + 1 ≥ 0
2a ≥ 1
a ≥ 1/2
Interesting-
proven vapor
2a + 1 ≥ 0
2a ≥ 1
a ≥ 1/2
Interesting-
no, 2a >= -1
uneven hedge
Yeah its ok
raw stirrup
Ok,
2a ≥ -1,
a ≥ -1/2.
split sail
yea ofc |2a+1| can not equal negative so 2a+1 can not be negative
1+2a>= 0
2a>=-1
a>=-1/2
right?
raw stirrup
1+2a>= 0
2a>=-1
a>=-1/2
2a ≥ -1, not 2a ≤ -1.
uneven hedge
1+2a>= 0
2a>=-1
a>=-1/2
You don't have to swap the inequality when subtracting
It's only when making transformations that invert comparison
split sail
You don't have to swap the inequality when subtracting
ohh
split sail
You don't have to swap the inequality when subtracting
when do we have to? cuz i remember something
raw stirrup
when do we have to? cuz i remember something
Multiplying and dividing by negative numbers.
uneven hedge
when do we have to? cuz i remember something
As i said, it's when doing transformations that invert comparison
Which like omega just said, involve multiplication by negatives
Also raising to the power of a negative
split sail
As i said, it's when doing transformations that invert comparison
can you tell an example
a simple one
uneven hedge
can you tell an example
Multiplying by a negative number
The way u can think about it is: "if I were to do this operation on the entire number line, would it flip around 0?"
split sail
Multiplying by a negative number
2>-1x /*-1
x>-2?
raw stirrup
Also raising to the power of a negative
I didn't know that one. You learn something new everyday, I guess.
uneven hedge
If so, then you gotta change your inequality
uneven hedge
I didn't know *that* one. You learn something new everyday, I guess.
If a > b, then 1/a < 1/b
split sail
2>-1x /*-1
x>-2?
is this correct?
uneven hedge
2>-1x /*-1
x>-2?
Yes
split sail
got it
uneven hedge
When doing inequality stuff it's a lot more understandable when looking at how it changes the space that the numbers you're working with live on
proven vapor
If a > b, then 1/a < 1/b
not true, 2 > -2 and 1/2 > -1/2
split sail
also when we eliminate the root, why don’t we just make 2a^2 from 4a^2? Why do we have to root both the number and the letter? Aren’t they united?
uneven hedge
not true, 2 > -2 and 1/2 > -1/2
Sure then ig they have to be the same sign
raw stirrup
not true, 2 > -2 and 1/2 > -1/2
I think if |a| > |b|, then 1/a < 1/b.
uneven hedge
But to be fair
proven vapor
I think if |a| > |b|, then 1/a < 1/b.
you mean 1/|a| < 1/|b|
uneven hedge
That's bc ur inverting the inequality twice there
raw stirrup
you mean 1/|a| < 1/|b|
Yeah. Right.
proven vapor
That's bc ur inverting the inequality twice there
I am not inverting anything
uneven hedge
I am not inverting anything
You are but twice so it cancels
proven vapor
it's just the way the function f(x)=1/x behaves
uneven hedge
Bc opposite signs and transforming to reciprocal
raw stirrup
also when we eliminate the root, why don’t we just make 2a^2 from 4a^2? Why do w...
4a²
= 4 * a²
= 2² * a²
√(4a²)
= √(2² * a²)
= √(2²) * √(a²)
= 2a.
uneven hedge
4a²
= 4 * a²
= 2² * a²
√(4a²)
= √(2² * a²)
= √(2²) * √(a²)
= 2a.
Erm 2|a|
raw stirrup
Erm 2|a|
Yes. Right.
Since Atilla's question has been answered, can someone close the channel?
amber waspBOT
@split sail Has your question been resolved?
split sail
4a²
= 4 * a²
= 2² * a²
√(4a²)
= √(2² * a²)
= √(2²) * √(a²)
= 2a.
ah ok
raw stirrup
?
edgy junco
k
oak galleon
is limit of this expression for n to infty equal to 1?
amber waspBOT
is limit of this expression for n to infty equal to 1?
oak galleon
radiant lynx
yes, the exponential dominates both parts of the fraction
amber waspBOT
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Available help channel!
fading cliff
Can someone explain why cos(π/2+x)=-sin(x)? As in why is that the case?
We learn these as defined rules but I want to learn why this one is true
fading cliff
<@&286206848099549185>
raven rune
i explained it awfully so i deleted it, and im not sure my intuition is rigorous but here
to go from red (cosx) to black (-sinx) we must translate the red left by pi/2
which gives you cos(x + pi/2)
if you put this in desmos you can play arouind w the slider and kind oif see how it works
little dagger
this works too or you can also use cos(a+b) = cosacosb - sinasinb
to simplify and get -sinx
amber waspBOT
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compact wagon
amber waspBOT
compact wagon
why would this be wrong
prisma ember
why is the 3theta in an absolute value
prisma ember
yeah that should work
compact wagon
.close
amber waspBOT
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Available help channel!
split sail
amber waspBOT
split sail
chatgpt is saying the answer is e
sterile swan
!nogpt
amber waspBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
sterile swan
!show
amber waspBOT
Show your work, and if possible, explain where you are stuck.
rain arch
@split sail
amber waspBOT
rain arch
what r u on about
sterile swan
<@456226577798135808>
!nogpt
amber waspBOT
<@456226577798135808>
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
split sail
rain arch
cuz u gave it the image?
split sail
yea sending a picture differs from writing it?
rain arch
yea sending a picture differs from writing it?
ofc
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shell talon
amber waspBOT
grizzled pagodaBOT
;(
silver maple
dividing the numerator and denominator by $a^2$ yields $\int\frac{1}{a^2}\cdot\frac{1}{1+\qty(\frac{u}{a})^2}du$
grizzled pagodaBOT
;(
silver maple
now let $v=\frac{u}{a}$; thus $dv=\frac{1}{a}du\implies du=a dv$ and thus we have $\int\frac{1}{a^2}\frac{1}{1+v^2}\cdot adv$
grizzled pagodaBOT
;(
silver maple
which simplifies to $\frac{1}{a}\int\frac{1}{1+v^2}dv$
grizzled pagodaBOT
;(
silver maple
can you finish the rest?
shell talon
Isn't it complete?
silver maple
Isn't it complete?
integrate it and sub u back in
shell talon
Okay
silver maple
ok
amber waspBOT
@shell talon Has your question been resolved?
trail panther
Where are they pulling these GCFs from?
For more context the first photo is about dividing fractions and the second is about multiplying mixed numbers
Im in 7th grade so this might look like a dumb question to yall 😭✋
pallid canopy
factor 6 and 9 separately
trail panther
factor 6 and 9 separately
okie but what abt the -15 on the second photo? Why isnt it 5 instead of 3
pallid canopy
15 = 5 * 3
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placid vector
Can anyone help me?
amber waspBOT
Can anyone help me?
patent raptor
Can anyone help me?
,rcw
grizzled pagodaBOT
patent raptor
what's the objective?
placid vector
Yeah?
late peak
welcome
placid vector
The other one can be
2(square root of 3/2 Sinx + 1/2 cosx) =square root of 2
Yeah tysm
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simple drum
U is the row space of A and C is the column space of A how to find dimUnC and a basis for UnC ?
amber waspBOT
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amber waspBOT
@simple drum Has your question been resolved?
simple drum
<@&286206848099549185>