"no acceleration'
#help-42
marsh blade
crystal forge
if there is no acceleration, what would happen to the velocity graph? remember what we said before that we can think of acceleration as the slope of the velocity graph (which we are looking at)
so betwen B and C what would be the acceleration?
crystal forge
the velocity at B is around 40 isnt it? and at C it's around 15...is that constant?
between B and C the acceleration is negative (the velocity is decreasing)
if there were no acceleration the graph of the velocity would appear flat (i.e. slope of 0)
marsh blade
if there were no acceleration the graph of the velocity would appear flat (i.e. ...
is this correct to?
nvm its no acceleration
velocity is +
crystal forge
well think about what is happening, they jump at t = 0 and their velocity is increasing really fast right? until it sort of "peters off" because they are probably reaching terminal velocity (the velocity increasing from gravity's acceleration balances out with the velocity decreasing from air resistance). we can see how their veloicity increasing tapers off between A and B
crystal forge
is this correct to?
again, no velocity would be the velocity graph having a y of 0, over there the velocity is constant i.e. its around y = 8 or whatever for a short period that means there is ** no acceleration **
crystal forge
then suddenly at point B their velocity decreases from a very high value to suddenly much lower, over a very short period of time...what do you think would cause your velocity to suddenly decrease quickly while you are falling?
marsh blade
I guess its point B where parachute is opened due to difference in acceleration
crystal forge
because i have a quesiton on it
i've already talked about this, i suggest to read what i said : )
marsh blade
(the velocity increasing from gravity's acceleration balances out with the velocity decreasing from air resistance)
that is what you said
but i dont know how to apply it on this graph
i say i guess 40?
because it appears there is no acceleration at this point
crystal forge
that's BEFORE the parachute is opened, but where does the balance point seem to lie afterwards? the air resistance is much higher now
the parachute slows down the person a lot, but not all the way to 0, where does it balance out?
marsh blade
at 5s?
crystal forge
5s?
crystal forge
right, at point D
cobalt basalt
How do you do this?
calm coralBOT
How do you do this?
bitter maple
How do you do this?
Find the radius of the circle first
The radius of the circle can be found using this formula
For any inscribed triangle in a circle
The radius of the circle is
ABC/(4∆abc)
A is the length of side a
B is the length of side b
C is the length of side c
Divided by the area times 4
calm coralBOT
@cobalt basalt Has your question been resolved?
forest stag
The answer I got is (0.08, 0.34) but the correct answer given is (16.7, 27.0). Help
ancient grotto
The answer I got is (0.08, 0.34) but the correct answer given is (16.7, 27.0). H...
yeah because a "confidence limit" involves the mean.
or, here, the sample given.
so, its going to be (14-ak, 14+ak), where a and k are constants to be determined.
forest stag
I don't understand, this is what i did:/
calm coralBOT
@forest stag Has your question been resolved?
calm coralBOT
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pine hedge
i went through an example and i don’t understand how the program went from x^2 - 7x - 30 = 0 to (x + 3)(x - 10) = 0.
for the question i have to do, i need to factor x^2 - 3x - 40 = 0 and im not sure quite how to do that
finite oasis
i went through an example and i don’t understand how the program went from x^2 -...
So, just to be clear, is your current issue
i don’t understand how the program went from x^2 - 7x - 30 = 0 to (x + 3)(x - 10) = 0.
or
i need to factor x^2 - 3x - 40 = 0 and im not sure quite how to do that
pine hedge
moreso the first part
finite oasis
Okay, let's talk about that first then
pine hedge
i largely don’t understand the factoring and need help with it. i provided both so either could be used in case one was easier haha
finite oasis
do you know the common mnemonic for factoring quadratics like that?
"Find two numbers that multiply into -30, and add to -7"
pine hedge
like common denominators?
pine hedge
"Find two numbers that multiply into -30, and add to -7"
i don’t think i’ve ever heard of this before
finite oasis
i largely don’t understand the factoring and need help with it. i provided both ...
Alright, either would be fine. You just need to understand the method to do it i suppose
finite oasis
"Find two numbers that multiply into -30, and add to -7"
but yeah this is the best way to go about it I think
give it a think
can you think of two numbers that satisfy that
to thin it down, guess two numbers that multiply into -30 first
any two numbers work
pine hedge
six and five doesn’t, does it?
finite oasis
Close! thats 30
pine hedge
-5?
pine hedge
no it’s -1
finite oasis
1 actually
pine hedge
oh oops
finite oasis
but yeah, incorrect either way
so this guess was incorrect
think of two other numbers that multiply into -30
pine hedge
15 and -2? or -15 and 2?
pine hedge
it can’t be -1 x 30 or 30 x -1
pine hedge
is it a decimal? i can’t think of any others that make 30
finite oasis
it is not fractional/in decimal, no
pine hedge
oh 3 and 10, i have it written, duh
finite oasis
there is one obvious one you missed
finite oasis
yes exactly, so it should be (x-10)(x+3)
ok now
do the same thing but for x^2 + 4x - 21
what is your first step?
pine hedge
something that multiplies to -21?
pine hedge
(x - 3) (x + 7)
finite oasis
yeah good job! u got the hang of it
now for your second question
do the same for x^2 - 3x - 40 = 0
pine hedge
-8 and 5?
finite oasis
super close
oh wait
no i was the one who messed up this time haha
yeah it is that
finite oasis
affirmative
pseudo wedge
so then its (x + 8) (x - 5)?
No
pine hedge
wait what’s a root-
pseudo wedge
wait what’s a root-
A value of x where the expression equals 0
finite oasis
No, don't conflate things. What he meant to say is that the roots are x_1 = 8 and x_2 = -5 but you write the quadratic as (x-8)(x+5) = 0
its basically solving x-8 = 0 and x+5 = 0
finite oasis
yes
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noble crown
calm coralBOT
noble crown
how
swift dragon
!status
calm coralBOT
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
clear delta
we want to get a sense of where you are in terms of progress on this problem
noble crown
we want to get a sense of where you are in terms of progress on this problem
Its not possible to interact with the bot
and set your status
it just gives u a bunch of questions
noble crown
oh
i guess
do you have an idea on how to solve it?
initially it seemed pretty easy
im used to dealing with circles
I was taught that the equation for the circle is
$(x-a)^2$ + $(y-b)^2$ = $r^2$
potent lotusBOT
kronium_
noble crown
wait
I THINK I GET HOW TO DO IT
$x^2$ - $2ax$ + $y^2$ - $2by$ + $(a^2 + b^2 - r^2) $ = $0$
potent lotusBOT
kronium_
potent lotusBOT
kronium_
noble crown
$b$ = 2.5
potent lotusBOT
kronium_
noble crown
$3^2 + 2.5^2 = 9 + 6.25 = 15.25$
potent lotusBOT
kronium_
noble crown
so $r^2$ = 6.25,
Therefore 'r' must equal 2.5
potent lotusBOT
kronium_
noble crown
$coordinates$ of the original of the circle must be [3, 2.5]
& since r = 2.5, which equals to the height, circle be tangent to the x axis cuz when its directly down it just touches the x axis
potent lotusBOT
kronium_
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
noble crown
$e^{ix}$ = $cosx$ + $i$$sinx$
potent lotusBOT
kronium_
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eternal tiger
Can someone explain the second order conditions in lagrange multipliers method
leaden thunder
an example of what problem you're working on or screenshot/picture of what you're reading would be best
eternal tiger
I'm thinking about the utility function maximisation problem
In Economics
Under the budget constraint
leaden thunder
a specific, concrete problem
eternal tiger
Um, concretely speaking, I'm wondering why the bordered hessian being negative semi definite leads us to the maximas instead of the other stationary points, and also I'm wondering what the bordered hessian represents as opposed to say the hessian matrix of the lagrangian (L)
eternal tiger
No I'm just trying to figure out the reasoning here
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raven crest
Can someone please help me on this question
calm coralBOT
Can someone please help me on this question
abstract wave
!status
calm coralBOT
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
So far, I know that triangle ADM has side lengths 6, 8, 10, with the height being 8 and the other leg being 6
and the hypotenuse is 10
so side length AB and DC are both equal to 112/8=14
idk what to do next
flat gorge
wait what?
raven crest
i tried creating more triangles but couldn't really go anywhere
flat gorge
what value did you get for AM? Also how?
raven crest
i got 8
since AD is 10, i just used the pythagorean triple (3,4,5) to find the other side lengths
flat gorge
it's not mentioned AM and DM have integer lengths
raven crest
it never said it doesn't have integer lengths
flat gorge
Exactly, so pythagorean triplets don't give you AM or DM just from knowing AD
raven crest
then how am i supposed to calculate it?
abstract wave
you can't assume something about anything unless specifically written in the question or proven by you
flat gorge
Use that ABCD and EFGH are congruent => [EFGH] = 112 and FG = EH = AD = 10
should know EN at a glance
raven crest
11.2?
crude atlas
en is 5
abstract wave
is EN the height of the entire paralleogram?
yes
raven crest
bruh
that's what i said last time and someone said it was wrong
thanks for helping
.close
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lavish nova
I started from here, how would I factor this
calm coralBOT
I started from here, how would I factor this
ancient grotto
I started from here, how would I factor this
to be completely honest, using the rational root theorem is your best bet here
this isn't "nicely" factorable
viral patrol
One root is 7/2 it
ancient grotto
One root is 7/2 it
!noans
calm coralBOT
One root is 7/2 it
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
lavish nova
to be completely honest, using the rational root theorem is your best bet here
Is brute forcing the only viable method here?
lavish nova
One root is 7/2 it
How did u get that
viral patrol
How did u get that
Hit and trial checked a few
viral patrol
Is brute forcing the only viable method here?
Yeah
lavish nova
Hit and trial checked a few
I don’t see how u landed on 7/2 tho
ancient grotto
Check for integers first
*rationals
viral patrol
N this case that is 1575
calm coralBOT
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Available help channel!
onyx solar
Solve the equationsystem
8x+2y=4
4x+7y=6
calm coralBOT
Solve the equationsystem
8x+2y=4
4x+7y=6
onyx solar
Bear with me I'm new to this stuff
onyx solar
I'm new to substitution
I'm not familiar with how to solve when there are 2 constants
onyx solar
I'm new to substitution
But yes I know
viral patrol
Ok I can guide you
onyx solar
That'd be very much appreciated
potent lotusBOT
Chris
viral patrol
You can write
onyx solar
-2y on both sides?
potent lotusBOT
Chris
onyx solar
divide by 8?
onyx solar
lol
potent lotusBOT
Chris
viral patrol
Yeah try resolving it
onyx solar
uh ok
onyx solar
Wait do I divide by 8 first
potent lotusBOT
Chris
viral patrol
Got it?
onyx solar
one sec
mellow yew
a
dreamy lance
Oh I see you moved
mellow yew
dreamy lance
Okay, so lets say we restrict b and c to real numbers to be safe.
Notice how going from the first line to the second the only real justification that is required is because bx=2(b/2)x
Most of the justifications for each line are roughly along these lines.
dreamy lance
Simple statements that hold immediately by rules of algebra.
mellow yew
you want me to write my proof in mathematical or grammatical form?
dreamy lance
Try and limit yourself to at most a sentence per line.
mellow yew
dreamy lance
So for example "line 2 follows from line 1 because b=2(b/2)" would be a reasonable way to justify line 1 to line 2
dreamy lance
"Line 3 follows from line 2 because blah blah"
There are multiple levels of formalism we could do here. But this level is most relevant imo
How come I can go from line 2 to line 3?
mellow yew
https://cdn.discordapp.com/attachments/905286165316403271/1330345829243944960/20...
1we want to complete the square so given any value we can easily solve
2 because (10/2)^2 = 25's factors add to 10 and multiply to itself (proves any number divided by 2
squared grants number whos factors add & multiply to itself)
3 same as line 2
4 (x+b/2)^2 = line3 since both individual parts of square are equal solving for one solves for X
5 sqrt the right and left sides to maintain equality
6 you subtract everything affecting X to isolate X
mellow yew
How come I can go from line 2 to line 3?
drifting seal
doot if you dont mind can you check modmail
dreamy lance
I don't understand your numbering here but also my picture never mentions specific values for b and c so the numbers 10 and 25 don't really pop up.
mellow yew
I don't understand your numbering here but also my picture never mentions specif...
they dont, I stated I was proving the rule
i will clarify
reread
dreamy lance
i will clarify
I agree with what you said at the first line. We are trying to complete the square
But I don't think your explanations of why each line follows from the last are sufficient.
mellow yew
the only part i completely do not understand is why you did this
that is a self-terminating operation, why did you do it?
dreamy lance
The perfect square trinomial formula has a 2 on the x term. If I mult and divide by 2 like that it is in perfect square trinomial form.
By perfect square trinomial formula I mean that x^2+2Bx+B^2 = (x+B)^2 (here B is unrelated to our earlier problem)
dreamy lance
Okay, it's fine if they cancel each other out?
mellow yew
also wdym it is in perfect square if the perfect square was unassociated with the value itself
dreamy lance
The point is we want to write the quadratic in a particular form.
mellow yew
as you can see they simply added the perfect square to the right being (b/2)^2
why do similar operations on the left if you already have the perfect square and why to the number youre trying to get it for?
dreamy lance
By perfect square trinomial formula I mean that x^2+2Bx+B^2 = (x+B)^2 (here B is...
"Perfect square trinomial" is just a common term for this formula
The "perfect square" in that terminology is not referring to the squares in my derivation.
We can drop that wording
Lets say we don't use that term
dreamy lance
By perfect square trinomial formula I mean that x^2+2Bx+B^2 = (x+B)^2 (here B is...
I know this is always true
I want the x^2+bx part of the given equation to resemble that formula
But that formula has a 2Bx and our given does not have a factor of two on the bx coefficient.
This is no problem, because b=2(b/2).
So if I want I can just rewrite the x^2 + bx part as x^2 + 2(b/2)x
The value doesn't change. The two expressions are equal.
You see what I mean right?
dreamy lance
By perfect square trinomial formula I mean that x^2+2Bx+B^2 = (x+B)^2 (here B is...
We CAN do that and it gives us something a little closer to this formula.
mellow yew
why do you want that formula
dreamy lance
Completing the square like you said lol
A more intuitive way to see it
Is we want to gather all the x terms into a single squared thing
mellow yew
why do you want anything, cant you just divide by 2 and exponentiate in any scenario so long as it has real solutions
dreamy lance
https://cdn.discordapp.com/attachments/905286165316403271/1330345829243944960/20...
Look closely at line 4
Now all the x terms are gathered up inside that square
There are no other x's in the equation
So once we get to that point, solving for x is easy
Subtract out the c, square root both sides, subtract out the b/2
dreamy lance
why do you want anything, cant you just divide by 2 and exponentiate in any scen...
When you have something like x^2+bx+c = 0 and you want to solve for x, there's no way to obviously isolate the x immediately
You can't just divide thru by x
Nor with x's
Nor can you solve for x^2and square root both sides
None of the these isolate the x
mellow yew
im curious if ill ever be able to not perceive the explanations people give as just terrible due to reverse tunnel vision sigh
dreamy lance
Wow what a shitty thing to say
Have you considered that you aren't doing your end of the work by saying shitty things like that
mellow yew
are you just saying that you cant get it into (x + 6/2) without converting B to 2(b/2) because it wouldnt multiply to itself without that?
dreamy lance
You have an obligation to try and understand people if people are willing to try and offer you help for free when you seek out help
mellow yew
Wow what a shitty thing to say
it isnt
dreamy lance
I disagree
mellow yew
this is part of what im saying
dreamy lance
I've seen you say things like this multiple times.
mellow yew
you think that thats rude but you actually agree with me whole heartedly
mellow yew
that isnt your choice to make shrug
dreamy lance
I'm choosing to help you
mellow yew
its just the wind
dreamy lance
Meet me half way by choosing to make an effort to understand
mellow yew
I've seen you say things like this multiple times.
i already told you why I think that and you cant interpret how I mean that
you only were offended because you took your interpretation of what I said
and were offended by your own interpretation
mellow yew
sorry i guess if the resonating memetic form of what I said offended you from your perspective
dreamy lance
Multiple people have complained about you
If many people are complaining to me about you is the issue me and everybody else or you?
dreamy lance
My point here is you have to make an effort to understand people
dreamy lance
If you understood you would be able to give me succinct single sentence justifications for each line in the above pic
mellow yew
but you still dont choose the things you think you do nor do you represent yourself in the way you think you do
if you look into phenomenology youd know what I mean
dreamy lance
You should not try and act smart while misunderstanding elementary algebra
mellow yew
? youre the one acting smart
dreamy lance
Nobody cares about how smart you want to feel
mellow yew
when youre really smart you know how much you dont know
you are smart so you think you know what you dont and you interpret things through a somewhat faulty lense
dreamy lance
I have a degree in math and cs. I am in a math PhD program. I am literally teaching a precalc class right now.
I feel like I understand thus enough to tell you that you don't
mellow yew
you arent choosing to do what you are you doing right now you are just resonating from a faulty lense your brain told you was true which your emotions then manipulated you into thinking was an attack
dreamy lance
And the way you respond to people is unnecessarily prolonging you learning this.
mellow yew
I am completely outside of myself and the world is completely within me
mellow yew
I feel like I understand thus enough to tell you that you don't
well sorry but did you think that maybe the reason i act like that is because nobody can interpret what I mean when I say those things?
do you think that maybe you actually proved my point?
you didnt just prove it, you embodied it, though you yourself did not
dreamy lance
well sorry but did you think that maybe the reason i act like that is because no...
Have you considered the things you say are dumb and people just ignore them rather than engaging idiotic statements?
Get off your self congratulating high horse lmao
We're doing math.
unique jackal
if nobody can interpret what you mean, I feel that that's a communication problem on your end, rather than an understanding problem on everyone else's
dreamy lance
Focus on the math
mellow yew
Have you considered the things you say are dumb and people just ignore them rath...
Alright, you are currently experiencing an emotional reaction, I will not further this as this is immature on your end, sorry.
I hope later you will come to clarity.
dreamy lance
Alright, you are currently experiencing an emotional reaction, I will not furthe...
I feel like if you cannot explain why each line of the above image is justified in a single sentence (per line), YOU need to go review why you can.
dreamy lance
Every single line is justified by simple algebra you should know by now.
Things like b=2(b/2)
mellow yew
if you dont get it, I dont fault myself because I cannot explain what I fundamentally dont know
ebon pagoda
im curious if ill ever be able to not perceive the explanations people give as j...
sorry to butt in -- what do you even mean by "reverse tunnel vision", do you expect helpers to get what you mean by it, or empathize, or somehow not get offended by you calling their explanations "shitty"
genuine question lol
mellow yew
but you can, shrug
dreamy lance
At some point the problem fails to be EVERYBODY ELSE giving you shitty solutions
mellow yew
None of it is rocket science
you do realise by insulting my intelligence you are proving my point even more that your intelligence puts you on a semi-high horse meaning you fundamentally cannot perceive how others perceive your explanations and thus your explanations would be false to others perspective due to lack of experiental understanding
ight, bye
mellow yew
sorry to butt in -- what do you even mean by "reverse tunnel vision", do you exp...
sup bro
dreamy lance
you do realise by insulting my intelligence you are proving my point even more t...
Who's insulting your intelligence?
I'm telling you you're overthinking the justifications to each line
unique jackal
if nobody can interpret what you mean, I feel that that's a communication proble...
I'll reiterate this once more, if you feel that there's a communication breakdown
mellow yew
I'll reiterate this once more, if you feel that there's a communication breakdow...
there is, yes
dreamy lance
You realize smart people can overcomplicate things?
You're not above overcomplicating simple things homie
mellow yew
sorry to butt in -- what do you even mean by "reverse tunnel vision", do you exp...
i didnt?
they did actually
they had no idea what i was talking about and tried talking about an abstract concept they had no idea what I meant by
shrug
dreamy lance
Yeah clearly you could never misunderstand anything.
You could never talk out your ass either.
mellow yew
doot that wasnt even the topic
dreamy lance
Everybody else is the problem!
mellow yew
you dont understand the topic fundamentally thats why ive been ignoring you
because you arent in control rn
dreamy lance
I don't understand the topic?
mellow yew
no you dont?
dreamy lance
Dog I passed intro precalc lmao
mellow yew
i didnt even tell you what the topic was
this isnt even about math
its a phenomenological concept you tried intruding on about how people perceive explanations
and you immediately called it shitty
:/
ebon pagoda
i didnt?
ok I misquoted you, meant to say you called their explanations "just terrible" in that message. same thing really
dreamy lance
Then why are you here? Go join the philosophy server. We're here to do math. Not listen to you crank ramble about philosophy you've misunderstood.
keen flower
This is going off the rails
mellow yew
ok I misquoted you, meant to say you called their explanations "just terrible" i...
"same thing" no it is not xd and I specified it was my perception and get this (out of the desire to change that perception) tu qoque fallacy doesnt work here either
mellow yew
This is going off the rails
for real
i tried pulliing out multiple times but shrug
ima just make sure this time
keen flower
Did you learn to expand?
mellow yew
cuz they are being manipulated rn by their emotions
wait
wait
axe
axe can we like
go somewhere private
to discuss this
mellow yew
Did you learn to expand?
i think i solved everything
well almost
like a few details are off here and there but we ball
keen flower
Cool
mellow yew
can we like idk go to dms or like a private thread idk somewhere
cuz they are gonna ruin it
dreamy lance
I'd definitely fail somebody explaining completing the square like you tried above.
ebon pagoda
my impression is that the average helper here understands the subject well enough, but don't care enough to get lost in useless sophistry about how people perceive things or such lol
dreamy lance
Your explanation was not a correct one.
keen flower
can we like idk go to dms or like a private thread idk somewhere
I guess just this once 
calm coralBOT
crystal forge
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Available help channel!
gusty lance
calm coralBOT
gusty lance
Once i find 4nCr2 what can i do
if i dont want to find all the ways it can be written
like
1,2 2,3, 2,4
1,3 1,4
3,4
and then find which cases 2 is the greates which is obv 1/6
and so on
how do I find it like using the fact that a + b + 1/2 =1
calm coralBOT
@gusty lance Has your question been resolved?
gusty lance
.close
calm coralBOT
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muted ibex
what does this convention in maths mean? v index m raised to j?
muted ibex
It could mean a lot of different things
tell me the different things
in calculus
what does it represnet
@bold bear
muted ibex
nope
bold bear
And s_i is probably a permutation of the vectors
It's not a standard notation used all across math
muted ibex
in algorithms?
bold bear
Yeah no sorry
stoic oyster
like read your paper more carefully idk
bold bear
If it's in an algorithm then it probably said further up in the code what it meant
But I can't really help you
stoic oyster
we can't always divine the meaning of every symbol thought by every author in existence
especially when it's something super generic looking like this
they gotta have defined it before as depression said
potent igloo
what does this convention in maths mean? v index m raised to j?
!xy
calm coralBOT
what does this convention in maths mean? v index m raised to j?
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.
eternal shard
καλά σου λένε
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potent igloo
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hidden pine
is a manifold in $R^n$ always $\sigma$-compact?
calm coralBOT
is a manifold in $R^n$ always $\sigma$-compact?
potent lotusBOT
Sheymes
hidden pine
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static dirge
or no?
swift laurel
what limit?
static dirge
what limit?
y = x(3) + 4 , then
c -> 4
for example
or is it not doable bc of the graphhhh?
swift laurel
i don't understand what you mean
static dirge
i don't understand what you mean
sorry sorrryy 😭 can i evaluate limit from this graph?
like finding
lim = x(3) + 4
x -> 4
like thiss
static dirge
i don't understand what you mean
and also if from this graph can i get the limit of positive and negative side of a certain constant?
calm coralBOT
@static dirge Has your question been resolved?
devout meteor
i'm stuck with how to integrate absolute value of 7-x. i think i need to do u sub but im also not sure
ancient grotto
i'm stuck with how to integrate absolute value of 7-x. i think i need to do u su...
okay.
do you know how absolute values are defined?
devout meteor
do u mean that its only positive?
ancient grotto
do u mean that its only positive?
i’m talking about the piecewise definition.
devout meteor
um im sure i did at one point but can u remind me
ancient grotto
um im sure i did at one point but can u remind me
$|x|=\begin{cases} x&x\ge 0 \ -x&x<0\end{cases}$
potent lotusBOT
;(
ancient grotto
so, what do you think we should define |7-x| as?
Also note that |7-x|=|-(x-7)|=|x-7|
devout meteor
well wouldn't it depend on x?
because if x is larger than 7 then it is less than 0
ancient grotto
because if x is larger than 7 then it is less than 0
yep
well, have you ever graphed an absolute value function?
drifting seal
$|7-x|=\begin{cases} 7-x& (7-x)\ge 0 \ -(7-x)&(7-x)<0\end{cases}$
potent lotusBOT
knief
ancient grotto
$|7-x|=\begin{cases} 7-x& (7-x)\ge 0 \\ -(7-x)&(7-x)<0\end{cases}$
well, i was going to lead them to this, but yeah, that works
drifting seal
"x" was just taken to be the input
if it was hotdog then you would do hotdog instead
ancient grotto
its a v
yes, but what about |x-a|, where a is a constant? where would the “turning point” be, specifically?
devout meteor
if it was hotdog then you would do hotdog instead
what is hotdog?
drifting seal
what is hotdog?
🌭
ancient grotto
yes, but what about |x-a|, where a is a constant? where would the “turning point...
.
devout meteor
wouldnt it be 7 because that would make 0
drifting seal
wouldnt it be 7 because that would make 0
yes
devout meteor
okay so does that have significance with the bounds of the integral? or why is this important in order to integrate?
drifting seal
okay so does that have significance with the bounds of the integral? or why is t...
because the function you’re integrating "changes" beyond that point so you should split the integral at that point
drifting seal
brilliant yes
but remember to write dx btw
and the 1/6 factor is on both
integrals
devout meteor
but remember to write dx btw
its a bad habit i need to get better at this!
drifting seal
indeed
drifting seal
you can
but you have to do that if you don’t want it on both
or else you might make the mistake of only having it on the first after calculation
devout meteor
better?
drifting seal
yes but why the second integral being subtracted now?
devout meteor
oh when i eraed the plus sign to write in dx i must have rewritten a - instead of +
i fixed it in my notes now
okay now do i just integrate what is in the absolute value signs?
drifting seal
use the definition
devout meteor
less than 0
drifting seal
why is that?
devout meteor
because it is the left half of the function
devout meteor
like this (it it were centered at the origin)
drifting seal
you’re thinking of it like |x| and how the "left" branch is for x < 0
drifting seal
you’re thinking of it like |x| and how the "left" branch is for x < 0
ok but now consider what would happen if i asked you the same thing but |-x|
i’m asking where is the input, -x > 0 and where is it < 0
that’s a different question isn’t it
devout meteor
oh
drifting seal
here you can think of 7-x being the negation of x-7
which is why you shouldn’t just go based on what |x| is like
7-x is certainly < 0 for x < 7
and the interval 4 to 7 satisfies that doesn’t it
take any x value in that interval, say 5
7-5 = 2 > 0
since it’s greater than zero we look back to our definition
7-x >= 0 hence for that interval |7-x| = 7-x
devout meteor
okay ya this makes sense!
so do i need to put a negative sign before the absolute value on the interval 7 to 10?
drifting seal
yes exactly
as per our definition
in the interval 7 to 10 we have 7-x <= 0 which means we must negate it
|7-x| = x-7 for x > 7
notice why we do this
since the inside (7-x) is less than zero we negate it to make it positive which should make sense with the way you originally defined absolute value (just making it positive)
so if we have a negative input in the absolute value we have to negate it to make it positive
but when it’s already positive we just leave it as is
drifting seal
yes
did you set them up?
by getting rid of the absolute value and changing to the appropriate functions for each interval?
devout meteor
like this?
drifting seal
yes
devout meteor
okay i should be able to finish the algebra thank u!
drifting seal
you’re welcome
shy mantle
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tender cradle
I'm kinda stuck i dont know if what im doing is right
calm coralBOT
I'm kinda stuck i dont know if what im doing is right
tender cradle
sorry for the handwriting im writing on a really old tablet
tender cradle
ok so lcd for that would be x + h?
or (x)(x+h)
and for the left side
do i factor out an h?
and cancel it out
because thats what i was going to do
@leaden thunder ?
flat gorge
or (x)(x+h)
This would be the denom for 1/(x + h) - 1/x
tender cradle
i see
flat gorge
Proceed further and you should be getting -h/[x(x + h)] for the difference
Along with the rest of the terms, you would be able to cancel out the h from the denominator of the whole expression
tender cradle
Proceed further and you should be getting -h/[x(x + h)] for the difference
i dont factor the h out yet
ok ok
i am now stuck again i have no clue
leaden thunder
Use (a+b)/c = a/c + b/c on the first term
And the last term you can just plug in h=0
tender cradle
the question said h must not equal 0
leaden thunder
Yea but sometimes when you're evaluating limits, you can just plug in h=0
,tex .calculate limit
tender cradle
i see
potent lotusBOT
riemann
tender cradle
is this the final equation?
leaden thunder
Closer but no
tender cradle
hmm
leaden thunder
What's the limit of h as h goes to zero
tender cradle
0
flat gorge
They didn't ask for limit though. It's fine to conclude with the difference quotient
tender cradle
so is my first answer the right one?
flat gorge
$\Delta f = 2x + h - \frac{1}{x(x+h)}$
potent lotusBOT
Arya
flat gorge
Is what you should get
flat gorge
is this the final equation?
This yes
leaden thunder
is this the final equation?
Yea my bad I forgot the original question
civic delta
hi is this correct? Assuming that a blank (0 g/mL) ethanol concentration produces no color change and that a 0.0001 g/mL ethanol concentration produces an absorbance of 0.2, how can we model this relationship using a mathematical function? If this function exists, would we expect it to be continuous within the relevant range of ethanol concentrations in breath?
calm coralBOT
hi is this correct? Assuming that a blank (0 g/mL) ethanol concentration produce...
@civic delta Has your question been resolved?
civic delta
💔
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@civic delta Has your question been resolved?
flint mist
Im stuck.
I need to prove that hat(beta_0) and hat(beta_1) in 7.12 (first image) in Example 7.3.1b are the same as in (6.5) and(6.6)
flat gorge
Im stuck.
I need to prove that hat(beta_0) and hat(beta_1) in 7.12 (first imag...
start replacing then. replace: sum x_i = n x(bar), sum y_i = ny(bar), sum x_i^2 = (nx(bar))² - 2sum (x_i)(y_i)
flint mist
alright brb
flint mist
start replacing then. replace: `sum x_i = n x(bar)`, `sum y_i = ny(bar)`, `sum x...
theres something confusing me
is this (i * x_i^2)?
flat gorge
no
flint mist
or is it \sum_i
flat gorge
that's sum of x_i^2 over all i
flint mist
why did they add the _i here but didnt for the other sums
isnt it over all i for the others too
flat gorge
Im stuck.
I need to prove that hat(beta_0) and hat(beta_1) in 7.12 (first imag...
the denom is rightfully n sum x_i^2 - (nx(bar))² = n[sum x_i^2 - 2x(bar) sum x_i + sum [x(bar)]² = n[sum (x_i - x(bar))²]
flint mist
the denom is rightfully ```n sum x_i^2 - (nx(bar))² = n[sum x_i^2 - 2x(bar) sum...
Im kinda confused
where did you get - 2x(bar) sum x_i from
flat gorge
sum x_i = nx(bar)
- 2x(bar) sum x_i = -2nx(bar)^2
if you're confused at any step, write it down.
flint mist
isnt it
n sum x_i^2 - (nx(bar))^2 = n sum x_i^2 - n^2 x(bar)^2 = n (sum x_i^2 - n x(bar)^2) = n(sum (x_i - x(bar))^2) ?
flat gorge
start replacing then. replace: `sum x_i = n x(bar)`, `sum y_i = ny(bar)`, `sum x...
this'll solve most things
no
flint mist
what did I do wrong
flat gorge
that doesn't give you what you want ._.
you want to change the 7.12 into desired form
flint mist
but i got to the same conclusion as you...
flat gorge
no
flint mist
the denom is rightfully ```n sum x_i^2 - (nx(bar))² = n[sum x_i^2 - 2x(bar) sum...
i was talking about this
fixed the typo mb
i was just confused how u did it
i fixed it
i was tripping
so now we have 1/(n(sum(x_i - xbar)^2) outside
what should the next step be should i start replacing the term inside the big brackets
flat gorge
n (sum x_i^2 - n x(bar)^2) = n(sum (x_i - x(bar))^2)
How?
flint mist
and u got
n[sum (x_i - x(bar))²]
flat gorge
how'd you go from second last step to last step
flat gorge
alr then, if I knew you knew that, this conversation would've been easy for both of us
flint mist
my bad
flat gorge
and yes, you're right. that is indeed the case
so you know how to change the denom
work on the num, and tell me how far you get
flint mist
work on the num, and tell me how far you get
this part?
flat gorge
yes
flint mist
so should i start replacing terms here aswell
flat gorge
yes
flint mist
alr brb
flint mist
yes
one more q
is this a combination? im kinda confused
or is this one long equation fit in 2 lines
flat gorge
one long expression that wasn't fitting in 1 line
flint mist
one long expression that wasn't fitting in 1 line
this is what I have so far idk what to do from here:
sum x_i^2 (n y(bar)) - (n x(bar))(sum x_i y_i) - n^2 x(bar) y(bar) + n sum x_i y_i
= n (y(bar) sum x_i^2 - x(bar) sum x_i y_i - n(x(bar) y(bar)) + sum x_i y_i)
sum x_i y_i - n(x(bar) y(bar)) = sum (x_i - x(bar))(y_i - y(bar)) (do i sub this?)
idk what to do with
"y(bar) sum x_i^2 - x(bar) sum x_i y_i"
flat gorge
put (x_i + y_i) in place of x_i in this eqn. and see what you get. (x_i + y_i){bar} would replace (x_i){bar}
idts it should be this messy tbh, the result would be easier to prove in an opposite fashion
show that (6.5) , (6.6) is 7.12
and reverse the steps
flint mist
put (x_i + y_i) in place of x_i in this eqn. and see what you get. (x_i + y_i){b...
sum((xi + yi) - (x_i + y_i)(bar))^2 = sum(xi + yi)^2 - n(xi+yi)(bar)^2 ?
kinda confused where would I use this
flint mist
show that (6.5) , (6.6) is 7.12
alright
flint mist
show that (6.5) , (6.6) is 7.12
wait isnt that what we are doing rn
flint mist
my bad
alright let me restart
with the reverse way
wait
im even more confused now wow
what exactly am i suppose to compare this to?
what exactly is Beta_1(hat) here?
😵💫
calm coralBOT
@flint mist Has your question been resolved?
flint mist
<@&286206848099549185>
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@flint mist Has your question been resolved?
flint mist
😢
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@flint mist Has your question been resolved?
eternal shard
In an exercise I was asked to verify:
If a,b are elements in a commutative ring that are null divisors then the product ab is always a null divisor.
I thought this was true, because for some x,y in R ax = 0 = by so you can choose xy and do (ab)(xy) = axby = 0, but it said it was wrong because in case of 0 you also get 0 but 0 is not a null divisor, I don't understand where I am wrong tho?
jade quartz
you need to show that $xy\neq 0$
potent lotusBOT
Arnavutköy
jade quartz
the point in a non-zero divisor is that you are multiplying by a non-zero number to get 0
eternal shard
but a,b,x,y must not be 0
that is in the assumption
if a,b are null divisors then there exist x,y and they are not 0
jade quartz
yes, but $x\neq 0, y\neq 0\not\implies xy\neq 0$
potent lotusBOT
Arnavutköy
jade quartz
it is possible that x and y are both not zero but xy=0
eternal shard
so we must additionally assume x,y are not null null divisors for the statement to be true then?
glass heart
but they are. ax=0
jade quartz
so we must additionally assume x,y are not null null divisors for the statement ...
this statement isn't even necessarily true
for example, if we are working in the integers mod 4,
eternal shard
but i dont understand, intuitively it does
eternal shard
for example, if we are working in the integers mod 4,
i dont understand this example
2 is a null divisor
jade quartz
wait sorry that doesn't work
eternal shard
the only one
jade quartz
wait the statement may be correct actually
your proof is wrong still though
you need to show that $xy\neq 0$ still
potent lotusBOT
Arnavutköy
jade quartz
and that is non-trivial
eternal shard
i feel also impossible without restricting x,y in some sense
anyway i think i get it
need to be more meticulous
jade quartz
i feel also impossible without restricting x,y in some sense
yes you need to have restrictions on x,y which you can come up with
this is interesting, im going to try it
eternal shard
well one obv is x,y in R s.t. xy != 0 
jade quartz
well one obv is x,y in R s.t. xy != 0 <:KEK:586240877358350341>
well yeah the question is how do you construct such x,y
eternal shard
hmm yea
potent lotusBOT
Arnavutköy
eternal shard
oh yea but then you are kinda changing the statement
i mean of course the product of a null divisor with a not null divisor is 0
jade quartz
well i mean this statement implies the original statement?
jade quartz
i mean of course the product of a null divisor with a not null divisor is 0
the product of a null divisor with any number is a 0 by my logic?
eternal shard
yes sorry
i meant null divisor
wait i get it
hä
If a and b are null divisors and to show ab is one too, just pick either x or either y so that (ab)x = ax * b = 0
i am so lost
I will ask my professor
exotic cosmos
ancient thistle
whats your definition of null divisor?
eternal shard
ax = 0 where a,x != 0
ancient thistle
okay so you require specifically that both elements are non-zero?
eternal shard
yes
ancient thistle
okay sure
well uh
take a and x in the definition of null divisor
ax = 0, so ax is not a null divisor because its 0 itself
which feels kinda strange but aight
eternal shard
yes
I did this now
Suppose a,b in R are null divisors. Then there are x,y in R s.t. ax=0=by.
Then wlog choose x then (ab)x = (ax)b = 0b = 0
ancient thistle
no no like
ancient thistle
take a and x in the definition of null divisor
here
ax = 0
a and x are null divisors
ax is not
ancient thistle
well yes
eternal shard
ancient thistle
which is like kinda dumb because it feels forced by the weird choice of definition but aight
eternal shard
but then where is the proof going wrong
ancient thistle
well
choose a = a and b = x in your proof
and see where it goes wrong
ab = 0
eternal shard
this is so horrendous
this is like
you wanna trap your students
or i am not careful 
ancient thistle
idk this all feels very silly
ancient thistle
👍
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terse shore
is the answer for i) 84%? the answers right 68%
calm coralBOT
is the answer for i) 84%? the answers right 68%
calm coralBOT
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trail escarp
Hello, everyone! I'm working on graph theory (using Ore's book with practical examples), and I'm stuck on a term.
We're discussing the concept of a 'chain' in a graph. Ore defines a chain as a path that can include duplicate vertices, but the edges must be unique (this is my understanding).
However, when I search for 'chain in graph' on Google, I find definitions stating that a chain is a path where all vertices must be unique.
amber bolt
wikipedia doens;t know it at all
so it's not like one is obviously wrong, choose whichever you like
exotic cosmos
@flat gorge what do you mean with this?
calm coralBOT
<@706934233012371577> what do you mean with this?
exotic cosmos
yeah a_1 is the first term
but the issue is what is meant by the "sum of the first n terms", no?
i guess you mean a_359 is the last term you can add up to
and thus n has to be 359
flat gorge
but the issue is what is meant by the "sum of the first n terms", no?
no. first term is 1 and so your "first n terms" starts with n = 1 up till n
exotic cosmos
no. first term is 1 and so your "first n terms" starts with n = 1 up till n
i guess
😭
i just moved on from the question
but yeah okay valid
exotic cosmos
idk these questions don't specify much
so some of the questions are ambiguous
so maybe why
😭
exotic cosmos
why'd you start with a_0 ?
i think i could've answered 359
intuitively feels right
anyway what's done is done 😭
thanks tho
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simple musk
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938c2cc0dcc05f2b68c4287040cfcf71
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@simple musk Has your question been resolved?
simple musk
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clear delta
q quiere decir Nu?
simple musk
ker
potent lotusBOT
938c2cc0dcc05f2b68c4287040cfcf71
simple musk
x1 = -x4
(-x4,x2,x3,x4) = x4(-1,0,0,1)+x2(0,1,0,0)+x3(0,0,1,0)
S =<(-1,0,0,1),(0,1,0,0),(0,0,1,0)>
Is it me or they want me to define a projection
no
because in a projection the image and the kernel are in direct sum
f(v1) = w1
f(v2) = w2
f(v3) = w3
f(v4) = w4
f(v1) = (-1,0,0,1)
f(v2) = (0,1,0,0)
f(v3) = (0,0,1,0)
f(v4) = 0
f(-1,0,0,1) = w1
f(0,1,0,0) = w2
f(0,0,1,0) = 0
f(v4) = w4
f(1,0,1,-1) = (-1,0,0,1)
f(0,1,0,0) = (0,1,0,0)
f(0,0,1,0) = 0
f(0,0,0,1) = (0,0,1,0)
I did it
let's check
,w det {{1,0,1,-1},{0,1,0,0},{0,0,1,0},{0,0,0,1}}
potent lotusBOT
simple musk
determinant non zero
we have a basis of R4
{(1,0,1,-1),(0,1,0,0),(0,0,1,0),(0,0,0,1)}
is a basis dim 4
Ker(f) = <(0,0,1,0)>
Im(f) = <(-1,0,0,1),(0,1,0,0),(0,0,1,0)>
S =<(-1,0,0,1),(0,1,0,0),(0,0,1,0)>
(1,0,1,-1) not in Im(f)
the problem is that Im(f) can't be equal to S
because then (1,0,1,-1) is in Im, because is in S
what we can do is
just repeat one vector in S
and then the image is two dimensional
f(1,0,1,-1) = (-1,0,0,1)
f(0,1,0,0) = (0,1,0,0)
f(0,0,1,0) = 0
f(0,0,0,1) = (0,1,0,0)
Im(f) = <(-1,0,0,1),(0,1,0,0)>