Vet du det?
#help-27
versed wyvern
cold bough
jag är inte den bästa på dessa
iron sun
Vet du det?
Min hjärna orkar tyvärr inte tänka 😭
versed wyvern
Fattar, klockan är ju nästan 11
Jag får alltid hjärnsläpp på lektionerna
Jaha. Eftersom det finns chans för både 5 och 6 är det 4/47+4/47=8/47
Då fattar jag...
iron sun
Om du får en god natts sömn kommer du förmodligen lösa problemet, sömn löser nästan allt!
Ah
versed wyvern
Om du får en god natts sömn kommer du förmodligen lösa problemet, sömn löser näs...
När jag kodade spel brukade jag alltid tänka på problem jättelänge, men sedan under maten kom jag på de.
Matte 1c är dock jobbigt, eftersom vi går igenom en ny grej varje lektion
Fysik är nog svårast dock
iron sun
Jo det är mycket man måste lära sig utan en kanske djupare förståelse
Ifall du väljer att plugga vidare till matematik vid universitetet
versed wyvern
Men alltså på fysiken gick vi igenom kinetisk energi, sedan friktion nästa lektion
iron sun
Så kanske det kan komma som en chock hur annorlunda man lär sig
versed wyvern
Då är det väl bara föreläsningar?
iron sun
Det är oftast uppdelat på liknade sätt, föreläsning, sen räkneövning
Men skillnaden är i materialet
versed wyvern
Det är oftast uppdelat på liknade sätt, föreläsning, sen räkneövning
Vi fick typ 30 minuters pluggtid efter kinetisk energi
Sedan gick vi igenom friktion
iron sun
Oj
iron sun
Personligen föredrar jag hur man lär sig i universitet, men många jag känner som tyckte om matten vid gymnasiet blev lite chockade när dem fick reda på skillnaden
versed wyvern
Personligen föredrar jag hur man lär sig i universitet, men många jag känner som...
Ja.. Men det finns matte spec och matte 5 här också
Då lär man sig komplexa tal
iron sun
Så ifall du redan nu tycker att du inte får en så djup förståelse så kommer du att föredra universitet
versed wyvern
Det är väl en ganska bra övergång?
iron sun
Typ..
Många av dem gick det också, och det var fortfarande inte representativt
Vid gymnasiet är det mindre fokus på varför saker funkar, men snarare någon typ av metod eller formel (detta är väldigt grovt sagt)
iron sun
Under vilka förutsättningar? Att härleda något med symboler ger egentligen väldigt lite och är inte så djupt
Det är skillnaden vid universitet
versed wyvern
Under vilka förutsättningar? Att härleda något med symboler ger egentligen väldi...
Symboler?
iron sun
Dvs. en algebraisk härledning ger inte en djup förståelse av något, det bara faller ut från en beräkning
Och sen är detta under vissa förutsättningar som man gömmer
Detta är mera sagt bara en grov jämförelse
Från vad du kan förvänta dig vid universitetet
Inget illa menat, men bara en reflektionen; då många studenter får denna chock
versed wyvern
Dvs. en algebraisk härledning ger inte en djup förståelse av något, det bara fal...
Men hur förklarar de på universitetet?
iron sun
Det är istället mindre fokus på en metod eller formel, oftast får du istället lära dig saker på en mycket mer djupare nivå
versed wyvern
Det är istället mindre fokus på en metod eller formel, oftast får du istället lä...
Men alltså hur exakt?
Ska jag tipsa min lärare om något?
iron sun
Men alltså hur exakt?
Det är helt enkelt högre krav på att tänka själv och inte förlita dig på metoder.
versed wyvern
Det är helt enkelt högre krav på att tänka själv och inte förlita dig på metoder...
Just det, man lär sig mer genom att testa själv
iron sun
Ska jag tipsa min lärare om något?
Inte riktigt? Det är mer av en konsekvens av att inte alla vill fördjupa sig på den nivån
Ett bra tips om man vill få ett smakprov av universitet är att gå någon typ av basårs kurs på ett universitet
versed wyvern
Men läraren brukar ge exempeluppgifter som vi diskuterar med klasskamraten bredvid, sedan går han igenom hur man löser
versed wyvern
Ett bra tips om man vill få ett smakprov av universitet är att gå någon typ av b...
Basår? Det kan jag väl göra när jag har tagit studenten?
iron sun
Men läraren brukar ge exempeluppgifter som vi diskuterar med klasskamraten bredv...
Jo som sagt jag försökte bara ge en grov uppskattning av vad jag har lagt märkte till i de första gymnasium; detta måste inte sjävklart alltid stämma
versed wyvern
Jo som sagt jag försökte bara ge en grov uppskattning av vad jag har lagt märkte...
Jaha, okej.
Men vad menar du med basår?
iron sun
Basår? Det kan jag väl göra när jag har tagit studenten?
Jo ville precis nämna problemet att det är just efter du är klar med gymnasiet du kan söka till dessa.
Men kan vara bekvämare oftast om man gör på detta sätt, även om ämnena i sig är behörigheter för kurser från gymnasiet, så är dem på djupare nivå och i en miljö som faktiskt speglar livet i universitet
Jag tror dock du kommer klara dig utmärkt utan dessa
Mer av ett tips för elever i allmänt
Ialla fall
versed wyvern
Jag tror dock du kommer klara dig utmärkt utan dessa
Jaa men jag fick bara C på fysikprovet
Var ganska krångligt
iron sun
Oj :(
Jag fick F på matte1B i tre år vid gymnasiet
Men sen sista året klicka allting plötsligt
versed wyvern
Jag fick F på matte1B i tre år vid gymnasiet
I tre år? Du pluggade matte 1b i tre år?
iron sun
Japp!
versed wyvern
Men sen sista året klicka allting plötsligt
Gick du 4 år?
iron sun
Hatade matematik
versed wyvern
Gymnasieingenjör?
iron sun
Gick du 4 år?
Lyckades få C sista terminen innan studenten
versed wyvern
Lyckades få C sista terminen innan studenten
Bra
iron sun
Gymnasieingenjör?
Estet!
iron sun
Men nu går jag Matematik programmet i universitet, även om jag trodde jag hatade matematik
iron sun
I min linje behöver man inte göra matte i 3an
Mhm
versed wyvern
I alla fall, klockan är jätte mycket och måste gå upp innan 7 imorn
Tack så mycket igen för det intressanta snacket
iron sun
Men nu går jag Matematik programmet i universitet, även om jag trodde jag hatade...
Har även fått VG (A betyg) i alla kurser än så länge, så betygen du har just nu spelar absolut ingen roll för din förmåga som jag märker du har väldigt gott av :)
versed wyvern
Har även fått VG (A betyg) i alla kurser än så länge, så betygen du har just nu ...
Vad bra, jag fick A på matteprovet även fast jag råkade skippa en 3 poängare 😅 (jag såg inte frågan)
Jag var orolig att jag inte skulle få det
iron sun
Vad bra, jag fick A på matteprovet även fast jag råkade skippa en 3 poängare 😅 ...
Bra jobbat!
versed wyvern
Tack! Och god natt igen, på riktigt den här gången 😂
iron sun
Jag var orolig att jag inte skulle få det
Så fort man inte förväntar något betyg har jag märkt att det är just då jag gör bra av mig, dem kan vara frestande när man lyckats få dem innan
iron sun
Tack! Och god natt igen, på riktigt den här gången 😂
God natt nu på riktigt!
versed wyvern
.close
devout snowBOT
devout snowBOT
Available help channel!
violet umbra
Hey guys!
If i have a linear system of ODE's in the form of x'=Ax+b. A (n by n matrix) and b (n-dim vector) are both complex. How do i find a particular solution?
violet umbra
We had something really similar were A and b were both with real Numbers. Can i just do the same?
We had this in another exercise even tho i dont know how the Integral would be defined on complex functions, we definitely never had such things so i dont think this is a solution too
devout snowBOT
@violet umbra Has your question been resolved?
violet umbra
<@&286206848099549185>
runic prawn
Hey guys!
If i have a linear system of ODE's in the form of x'=Ax+b. A (n by n ...
x = e^At + bt
violet umbra
Mhhhm, have to think about this
runic prawn
what part
runic prawn
x = e^At + bt
nvm this may be wrong
devout snowBOT
@violet umbra Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
ebon mist
Could someone help me with descriptive geometry?
devout snowBOT
Could someone help me with descriptive geometry?
ebon mist
what will the cube look like?
on the top left is the right side
on the top right is the front
and on the bottom right is the top
<@&286206848099549185>
devout snowBOT
@ebon mist Has your question been resolved?
devout snowBOT
@ebon mist Has your question been resolved?
devout snowBOT
@ebon mist Has your question been resolved?
scenic surge
Why am I getting a different answer here? Im using the correct formula
(Image 1 + 2): Formula I used
(Image 3 + 4): The answer my prof got
scenic surge
this is like the original question for this
shouldnt I be getting the same answer as prof
devout snowBOT
@scenic surge Has your question been resolved?
devout snowBOT
@scenic surge Has your question been resolved?
scenic surge
<@&286206848099549185>
devout snowBOT
@scenic surge Has your question been resolved?
dapper fable
if an integer sequence ,for example a_n,is in between some ranges for all n, does this mean a_n,repeats?
devout snowBOT
if an integer sequence ,for example a_n,is in between some ranges for all n, doe...
uncut crow
what does repeats mean?
topaz axle
it's not obvious if it has or doesn't have to be periodic
uncut crow
there are only so many integers in the range. if you have more elements than that (which you do in an infinite sequence), there must be a repeat
dapper fable
it's not obvious if it has or doesn't have to be periodic
oh
dapper fable
there are only so many integers in the range. if you have more elements than tha...
i see
i was doing an imo problem and didnt know where to go next, thanks guys
topaz axle
yeah ok even with just 2 possible integers, it doesn't have to be
devout snowBOT
devout snowBOT
Available help channel!
grave ermine
just a lil bit of help on this one
devout snowBOT
just a lil bit of help on this one
grave ermine
was sick for class and couldnt attend
and they gave homework
i do not understand that one guy on youtube with a black background
so if possible, with solution please
fierce lagoon
nah bruv
thats fck up
i think i will solve a few cases then u solve the rest
hows that
u gonna learn it the hard way
like how i was raised
like an asian
grave ermine
yes
grave ermine
i was sick for class today
fierce lagoon
alr bet
grave ermine
did not attend school at all
fierce lagoon
"The intersecting secants theorem states that when two secants intersect at an exterior point, the product of the one whole secant segment and its external segment is equal to the product of the other whole secant segment and its external segment. This is also known as the secant theorem or the secant power theorem."
just wikipedia it tho
grave ermine
i see
grave ermine
dunno anything about the lesson
fierce lagoon
bet
grave ermine
ill check
fierce lagoon
do you have the notes from ur friend or sth?
i think you should take a look at it tho
be4 i solve ur problem
grave ermine
waa
i dont have a single shit
mb i responded late
i was lookin at the theorem ands tuff
fierce lagoon
i was lookin at the theorem ands tuff
alr bet
devout snowBOT
@grave ermine Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
stuck locust
How to solve standard deviation?
devout snowBOT
How to solve standard deviation?
stuck locust
..
How this work bruh
How to solve standard deviation
What the sigma
Ohh now i get it
I need a clear explanation about how to solve variance and Standard deviation
And also the meanings of the symbols
fossil locust
How to solve standard deviation?
for variance:
- add all the numbers up then divide by the total number of numbers, to get the mean
- for each number, subtract the mean
- square all the numbers you have after doing step 2
- add all the numbers you have in step 3
- divide by the number of numbers
for standard deviation:
6) all of the above, but square root your answer in step 5
also, this gives you the population variance and population s.d
for sample variance and s.d you need to divide by (n - 1) instead of n in step 5
stuck locust
for variance:
1) add all the numbers up then divide by the total number of numbe...
Step 3 is where i get confused
I dont know about how to square the numbers
fossil locust
Step 3 is where i get confused
say if I want to do step 3 on the numbers 3, 4, and 11 for example
their mean is
,calc (3 + 4 + 11)/3
woven radishBOT
Result:
6
so you do (3 - 6)^2 + (4 - 6)^2 + (11 - 6)^2
I've jumped ahead and added all the squares, so we have done step 4 actually
devout snowBOT
@stuck locust Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
young aurora
how do i find these points for the second part
devout snowBOT
how do i find these points for the second part
young aurora
.close
devout snowBOT
devout snowBOT
Available help channel!
fierce lagoon
devout snowBOT
fierce lagoon
i need help with this problem
fossil locust
try taking ln
fierce lagoon
try taking ln
Already and this is where i stuck
fossil locust
try using the Maclaurin series $\tan u \approx u + u^3/3$
then sub in $u = \pi x /2$
wait
no sorry you need the series around x = 1 arrghh
fossil locust
at least you know that $\ln(2 - x) \approx 1 - x$
cause $\ln(1 + u) \approx u$ and now sub in $u = 1 - x$
fossil locust
it's the tan part that is annoying
fossil locust
,w tan(pi x/2) taylor series at x = 1
woven radishBOT
fierce lagoon
But not workin tho
fossil locust
yeah the vertical asymptote screws it up
fossil locust
ah I think I might know
rewrite $\tan(\pi x/2) = \cot(\pi - \pi x/2) = \cot(\pi/2 \cdot (1 - x))$
woven radishBOT
southlander!
fossil locust
then you're just looking for $\lim_{u \to 0} \cot(\pi/2 \cdot u) \cdot u$
woven radishBOT
southlander!
fossil locust
now applying the limit of (tan u)/u as u goes to 0
this equals 1/(pi/2) = 2/pi
so the original limit must equal e^(2/pi)
I've checked on Desms
fierce lagoon
Yea
fierce lagoon
The answer should be e^pi/2
Ikr
fierce lagoon
**southlander!**
Wait but why $\cot(\pi-\pi x/2) = \cot(\pi/2 \cdot (1 - x))$
woven radishBOT
danto
devout snowBOT
devout snowBOT
Available help channel!
fierce lagoon
,w 1/x^2-2x-3 taylor series at x = 4
devout snowBOT
,w 1/x^2-2x-3 taylor series at x = 4
fierce lagoon
,w 1/(x^2-2x-3) taylor series at x = 4
woven radishBOT
lavish nimbus
Do you got the original question? Or is your question asking for Taylor series for the function when n=4?
restive river
Hmm interesting
fierce lagoon
Hmm interesting
nah bro just to make sure im correct tho
still have to do these shit manually tmr
.close
devout snowBOT
devout snowBOT
Available help channel!
sand quarry
Could someone explain to me why the DFT of a signal x[n] is real if the magnitude of the DFT is even and its argument is odd?
devout snowBOT
Could someone explain to me why the DFT of a signal x[n] is real if the magnitud...
sand quarry
I dont think I conceptually get this
For context: I don't quite understand the real and even reasonings
devout snowBOT
@sand quarry Has your question been resolved?
hollow shoal
by evaluating the integral using part two of the fundamental theorem of calculus and then differentiating
g'(x) =
devout snowBOT
by evaluating the integral using part two of the fundamental theorem of calculus...
hollow shoal
I turned it into 5t - cost | 1 -> x
but when I tried to F(a) - F(b) I get some weirdness and I think I did something wrong
because I get cos(1)
river knot
are you purposefully not using ftc p1
river knot
oh so you solve the integral with both methods
river knot
I turned it into 5t - cost | 1 -> x
why is it 1 to x
hollow shoal
Oh
Why did I write 1, wtf
I think that was from the previous problem, okay let me fix that
river knot
yep
hollow shoal
$[5x - cos(x)] - [5(0) - cos(0)]$
woven radishBOT
Xbye
hollow shoal
Idk what the vocabulary is for this but I got that, but cos(0) is -1 let me see where this goes
$g(x) = 5x-cos(x)+1$
woven radishBOT
Xbye
hollow shoal
So then I have to find the derivative of that?
river knot
yep
hollow shoal
Okay, so cos = -sin
which makes me get back to the same as the FTC1 then
I got it, thank you. I'll probably be back in another channel with harder ones 🤣
river knot
np lol
hollow shoal
.close
devout snowBOT
devout snowBOT
Available help channel!
marsh obsidian
devout snowBOT
restive river
"Divisible by 5" = the last digit must be a 0 or 5
Of the 720 possibilities, how many end in a 5?
floral barn
"Divisible by 5" = the last digit must be a 0 or 5
Of the 720 possibilities, ho...
yea hes right, you could just count the ones that are devisible by 5 since theres not a lot. You could also use combinations but thats a bit more advanced
restive river
You wouldn't have to list them out and literally count
Just try to compute the number of strings like - - - - 5 and subtract from 720
marsh obsidian
"Divisible by 5" = the last digit must be a 0 or 5
Of the 720 possibilities, ho...
ohh
verbal vector
You wouldn't have to list them out and literally count
Just try to compute the ...
complementary counting yeah
restive river
Yes
marsh obsidian
okkkk
sorry wifi problems
what about thisss
i dealt with questions that say
it has to be even and greater than so so number
but not with this
verbal vector
this is a constructive counting question i believe
last number always has to be a 2 or 4
then case work on 1 digit, 2 digit, and 3 digit cases
only thing to be careful of is that 5 isn’t the first number on the 3 digit case
verbal vector
oh right even
yes even
devout snowBOT
devout snowBOT
Available help channel!
floral lodge
"If three normal dice are thrown, what is the probability, P(C), that the the last C will be equal to the sum of the two first dices"?
floral lodge
I started by noting that for the first two dices, there are 6^2 = 36 combinations. Out of these 36, by drawing a multiplication table and only counting where the sum is equal to or less than 6, I get 15 such entries
The possibilities that I get those sums is therefore 15/36
The last dice can't be 1, as there is no way to get that sum
so there are 5/6 possibilities for the first dice
my answer is therefore P(C) = 5*15/6^3
but the correct answer is 15/6^3
verbal vector
yeah i believe it should be multiplying by 1/6 not 5/6 because after you throw the first 2 dice, only one of the 6 faces will complete the problem
(one of the six faces on the last dice)
floral lodge
wait wait
is it because the sum... can only be expressed by one of the faces?
But the first face is invalid, i.e when it is 1
wouldn't that leave us with 5 valid ones?
ohh nonono
uncut crow
,w expand (x+x^2+x^3+x^4+x^5+x^6)^2
verbal vector
wouldn't that leave us with 5 valid ones?
if that logic you would multiply by 1/5, but you can still roll a 1 so you need to factor that into the probability
woven radishBOT
floral lodge
if that logic you would multiply by 1/5, but you can still roll a 1 so you need ...
Yeah
I mixed up the valid cases vs the total possible cases
verbal vector
yeah all good
faint zinc
so for each selection from the table of 36 values, there's only 1 throw of the third die that will match.
so the chance of this occurring is 1/6
which is why it is 15/6^3 not 5*15/6^3
(for instance, if you throw a 1, 1, 2 that fits, but any of 1, 1, 3, or 1, 1, 4, etc will not.)
uncut crow
chance of rolling a sum <= 6 is 15/36, then your chance of rolling whatever the sum was is 1/6
floral lodge
yes
spring oasis
\textbf{Exercise 4.} It is known that for a certain ( \alpha \in (\pi, \frac{3\pi}{2}) ), ( \sin(\alpha) = -\frac{1}{5} ). \textbf{Without using a calculator}, calculate ( f(\alpha) ) for the function
[
f(x) = \tan(x) + \tan(2x).
]
\textbf{Note:} It is not required to find ( \alpha ).
devout snowBOT
\textbf{Exercise 4.} It is known that for a certain \( \alpha \in (\pi, \frac{3\...
woven radishBOT
Renato Chavez
devout snowBOT
@spring oasis Has your question been resolved?
spring oasis
<@&286206848099549185>
lusty sapphire
<@&286206848099549185>
Write everything in terms of $\sin\alpha$ and $\cos\alpha$
woven radishBOT
SWR
devout snowBOT
@spring oasis Has your question been resolved?
spring oasis
.solved
stone thorn
?
eager nova
stone thorn
.close
signal mountain
the cyrrilc does not matter. i am so confused what the point of having a defenition of a subset
devout snowBOT
the cyrrilc does not matter. i am so confused what the point of having a defenit...
signal mountain
the defention of a subset by defeniotn must make it equal.
whats the point of having a convulted defeniton if it just means equal?
wheat pawn
,rotate
woven radishBOT
wheat pawn
pay more attention to the definition
A is a subset of B: Every element in A is also in B.
A is a Proper subset of B: Also, A is not B.
signal mountain
right, subset means that every element of A cant be found in B but by def proper subset says that if there is another element in B that is not in A then it is a proper subset
the only way for something to be just a subset is to have them equal then no?
im confused on what you mean by A is not B
wheat pawn
the set A is not the same set (aka does not contain the exact same elements) as set B
for example. Let B={1, 2, 3}
A={1, 2, 3} would be a subset.
A'={1} would be a subset, and a proper subset
signal mountain
right, so A and B are equal
so whats the point of calling it a subset
if it just means equal
wheat pawn
for proofs, basically
to prove that two sets are equal, very often you prove that A is a subset of B, AND B is a subset of A, thus A=B
signal mountain
thats is so stupid and convulted for a introduction to sets imo
wheat pawn
not really
definitions simply need to be precise
because if they arent, Bad Things happen
signal mountain
but then why not define it as equal in the first place
wheat pawn
i already did. A={1}
signal mountain
wait wait wait
so a set can be considered a subset and proper subset?
it breaks the def of a subset tho
wheat pawn
it breaks the def of a subset tho
no it doesnt
let's use my example
is every element in A also in B? yes, because 1, which is the only element of A, is in B. Thus, A is a subset of B
signal mountain
but B contains 2 and 3 which are not in A tho, def says if B contains elements that are not in A, then A is called a proper subset of B
like can a set basically be considered both in that case?
like as long as it fits the criteria it gets the title subset and proper subset?
wheat pawn
yes
sometimes the distinction is important
when it isnt, you go by the more relaxed "subset"
devout snowBOT
devout snowBOT
Available help channel!
rigid fern
hi can someone help with proofs i cant do this 😔
devout snowBOT
hi can someone help with proofs i cant do this 😔
still zephyr
hi can someone help with proofs i cant do this 😔
What can you say about AED and BEC being congruent
devout snowBOT
devout snowBOT
Available help channel!
pure sapphire
help
upper schooner
If you have a question, you can ask it, and if anyone can help, we will 
I'll close the other one for you 
pure sapphire
I'll close the other one for you <:catlove:920698762932920370>
thanks
upper schooner
How comes you want to DM me? I may not be able to help with your question, after all 
upper schooner
Awwww, that's fine, you can ask anything here (and we're all [or at least mostly!] understanding and friendly here) 
pure sapphire
tysm
upper schooner
Did you like have a worksheet or anything? 
pure sapphire
no sadly
upper schooner
Awwww 
that's fairs
pure sapphire
im in winter break 😦
upper schooner
I'm not super great with helping in general unless I have something to like reference personally 
upper schooner
im in winter break 😦
Ah that's fair, was there anything from before you went on break you were working on?
upper schooner
i can search
Yep, if you can find something (and then ping me if you get anything!) 
devout snowBOT
@pure sapphire Has your question been resolved?
devout snowBOT
hint please
devout snowBOT
autumn fjord
helo
devout snowBOT
Available help channel!
hexed berry
this doesn't have a maximum
but, how can I tell wheter it has a maximum minimun or not
vital hinge
You can find a maximum or minimum by taking the derivative of the function and solving for the values where x=0
As a max or min will look like a mountain or a U, where the peak or valley has slope 0
hexed berry
You can find a maximum or minimum by taking the derivative of the function and s...
yeah but like
hexed berry
But like what
not, what do you see.
How can we make this x=0?
WE CANT
so, what do we do in cases like this.
river knot
so, what do we do in cases like this.
the max/min can be at critical points
and critical points are where the first derivative is 0 or undefined
vital hinge
Sorry I forgot that part^
hexed berry
and critical points are where the first derivative is 0 **or undefined**
Okay, now
What do we do next
one would use second derivative
river knot
use the first or second derivative test to see if it’s actually a maximum or minimum
river knot
use the first or second derivative test to see if it’s actually a maximum or min...
and/or*
hexed berry
we cannot replace x with 1
So, what happens in that case?
Secons derivative is not possible, so far.
river knot
to begin with x=1 isnt in the domain of m
and therefore the function has no critical points
and no possible extrema
critical points are in the interior of the functions domain
hexed berry
to begin with x=1 isnt in the domain of m
What?
But aren't critical points points where derivative doesn't exist?
Such derivative doesn't exist hehehe.
river knot
to be exact
A critical point of a function f is the point in the interior domain of f at which the graph of f has a horizontal tangent (first derivative = 0) or where f is not differentiable (first derivative undefined)
hexed berry
A critical point of a function f is the point in the interior domain of f at whi...
so
if the funcion is not defined in the first place
no critical point, right?
river knot
yes
devout snowBOT
@hexed berry Has your question been resolved?
devout snowBOT
devout snowBOT
@void knot Has your question been resolved?
devout snowBOT
Available help channel!
lone skiff
devout snowBOT
frozen aurora
,rccw
woven radishBOT
lone skiff
im confused about this whole section
im trying to answer 3a
but
im confused
the only one that looks parralel is plane JKL
strange nimbus
OK, what does parallel mean?
lone skiff
its means they are going the same direction or is simalair i understand what it means but not how to explain it
same direction for a line
but im unsure for a plan
strange nimbus
For lines in the same plane, the lines don't intersect.
For planes, the planes don't intersect.
lone skiff
yup
strange nimbus
The idea is that they stay the same distance apart and so they can't cross each other.
lone skiff
so wouldnt plane JKL be the answer
strange nimbus
Yes.
strange nimbus
Yes.
strange nimbus
Right.
strange nimbus
OK, skew means there's no plane that has both of them, they're not parallel, and they don't intersect.
strange nimbus
OK, is there a plane that has both of them?
lone skiff
yes
strange nimbus
OK, so that can't be it.
lone skiff
then HG can be the answer
strange nimbus
Is there a plane that has both of them?
lone skiff
yup
strange nimbus
What plane?
strange nimbus
OK, are they parallel?
lone skiff
no
strange nimbus
Do they intersect?
lone skiff
no
strange nimbus
OK, so that's correct.
strange nimbus
OK, do you have something that defines the properties?
lone skiff
what do you mean
strange nimbus
Like that just lists the properties on the right.
Do you have anything that tells you what each property means?
lone skiff
no i dont have any notes
but is the first one reflexive property?
because i think i remember doing this
strange nimbus
No.
lone skiff
oh
strange nimbus
Reflexive is like AB = BA, but that's not what you have there.
That defines them.
lone skiff
ah
wait
im confused again Symmetric Property of Equality: If m∠A=m∠B
, then m∠B=m∠A
strange nimbus
strange nimbus
Yes, it is.
lone skiff
and i beleive then next one is either transative property or substitution
its transativ
?
transative property for the 2nd one
and last one is reflexive
strange nimbus
Note that the last one has the ms disappearing.
strange nimbus
Reflexive means you have a = a, same thing on both sides (it's like a reflection).
lone skiff
ok
strange nimbus
What book is this from?
strange nimbus
lone skiff
the third one is it definition of midpoint
strange nimbus
What is a midpoint?
lone skiff
a point that is in the middle of a line
strange nimbus
It's a point that's halfway between two other points.
lone skiff
yes
strange nimbus
But we don't know if S is halfway between them.
lone skiff
oh ok
strange nimbus
It could be somewhere else between them.
lone skiff
ok
strange nimbus
Yes, that's right.
lone skiff
is the next one substition property?
strange nimbus
lone skiff
oh so its wrong
strange nimbus
Maybe, maybe not.
lone skiff
i see now
strange nimbus
But substitution is like if b = c, then a + b = a + c.
But you kind of have the reverse.
If a + b = a + c, then b = c.
lone skiff
but would it still not be substition?
strange nimbus
So, the substitution property won't be it.
strange nimbus
No, when you say "if then", it's a one directional thing.
The 'if' being true makes the 'then' true.
But you're going the other way.
You're saying that the 'then' is true, so the 'if' must be true.
lone skiff
ok
strange nimbus
You start with JK + KL = MN + KL.
lone skiff
yes
strange nimbus
How can you change that to JK = MN?
lone skiff
meaning JK+2KL
strange nimbus
Sorry?
strange nimbus
What do you add?
strange nimbus
Sorry, how did you get that from JK + KL = MN + KL?
lone skiff
well oh wait
i mixed it up
i read it wrong
i saw this seciton by itself
JK + KL = MN
strange nimbus
Oh, OK.
lone skiff
it can be substition or relfexive
strange nimbus
What is equal to itself?
lone skiff
it cant*
strange nimbus
No.
lone skiff
what
strange nimbus
It's not doing anything.
It's an equation.
You need to manipulate the equation to get the second equation.
lone skiff
well they are equal to eachother
strange nimbus
No, you can't.
lone skiff
what
strange nimbus
You're starting with JK + KL = MN + KL.
That's all you know.
You don't know anything else.
You don't know that JK = MN.
lone skiff
oh ok
strange nimbus
You're trying to prove JK = MN, not start out knowing it.
strange nimbus
No, definition of congruence is where two things that have the same measure are congruent.
lone skiff
ok
strange nimbus
Like if two angles have the same number of degrees, they're congruent.
lone skiff
ok
strange nimbus
Or if two segments are the same length, they're congruent.
lone skiff
ok
strange nimbus
How would you go from JK + KL = MN + KL to JK = MN using algebra?
lone skiff
subtraction get rid of both KL
strange nimbus
Right, so which rule is that?
lone skiff
property of subtraction
strange nimbus
Right.
strange nimbus
What are you substituting?
strange nimbus
OK, that's a good guess, but there's a better rule.
strange nimbus
No, there are no congruence symbols.
strange nimbus
OK, so the reflexive property means a = a (same thing on both sides). The symmetric property means that a = b leads to b = a (you switch the sides). The transitive property means that a = b and b = c leads to a = c.
lone skiff
so it is transitive?
lone skiff
but we already used it?
strange nimbus
Which problem did we use it in?
strange nimbus
That's like the fourth problem.
lone skiff
is it addition property?
strange nimbus
Oh, never mind.
lone skiff
what do you mean
strange nimbus
It's not like the fourth problem.
lone skiff
oh
lone skiff
so its substition
strange nimbus
Right.
lone skiff
that was my second guess
strange nimbus
Transitive also works, but you have to use the symmetric property to flip one of the equations.
So, it would be more than one rule.
lone skiff
ah okay
strange nimbus
VW + WY = ZY and VW + WY = XZ
VW + WY = ZY and XZ = VW + WY
XZ = VW + WY and VW + WY = ZY
XZ = ZY
urban fulcrum
Hey,
could anyone help me draw x²-|x| 's chart?
strange nimbus
To use transitive, yes.
strange nimbus
Hey,
could anyone help me draw x²-|x| 's chart?
See #❓how-to-get-help for how to get help.
lone skiff
ok
strange nimbus
But substitution is much easier.
strange nimbus
OK, which rule is that?
strange nimbus
No.
strange nimbus
Right.
lone skiff
can we use addition property here
strange nimbus
Yes.
lone skiff
so it would be addition property
strange nimbus
Right.
strange nimbus
Right, it's reflexive.
lone skiff
can it not be congruence?
strange nimbus
Reflexive is like reflecting, where it's the same thing on both sides.
Definition of congruence takes numbers like angles in degrees or lengths.
Then it says that if the numbers are equal, the things are congruent.
lone skiff
well it says measure meaning the number is the same
strange nimbus
Right, but we're not converting an equation to a congruence.
That's the kind of thing it's used for.
lone skiff
ah ok
strange nimbus
Equal numbers means you have a congruence.
lone skiff
ok
strange nimbus
But this is reflexive, so we can just use that.
lone skiff
next one has to be multiplcation right?
strange nimbus
Right.
The "x property of equality" ones are algebra rules.
Like do the same thing to both sides kind of thing.
lone skiff
ah
ok
this next one has to be
congruence because its the only one that justifies the statment
strange nimbus
You're welcome.
devout snowBOT
strange nimbus
Have a good one.
devout snowBOT
Available help channel!
violet rampart
$(n): ; 0 + 1 + 2 + \dots + n = \frac{n(n+1)}{2}.&$
devout snowBOT
$(n): \; 0 + 1 + 2 + \dots + n = \frac{n(n+1)}{2}.&$
woven radishBOT
Benjamin Libet
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
woven radishBOT
Benjamin Libet
violet rampart
How do we get on $n = \frac{n(n+1)}{2}.$
woven radishBOT
Benjamin Libet
devout snowBOT
Available help channel!
queen tapir
How many different ways are there to write A in the form A=L+U where L is a lower triangular matrix and U isan upper triangular matrix?
devout snowBOT
How many different ways are there to write A in the form A=L+U where L is a lowe...
queen tapir
this is a homework question and i wanna solve it but i dont have a single idea how
now ik that there r infinite ways to write it but idk how did we even get to that and idk how to get to the example thing
cuz i also have to give example of L and U
so can someone just guide me through this ?
devout snowBOT
@queen tapir Has your question been resolved?
sturdy mango
How many different ways are there to write A in the form A=L+U where L is a lowe...
you need to have knowledge of fundamental principle of multiplication
it is pretty simple after that u make cases according to your conditions
restive river
Q. Prove that x^2 congruent to 1 (mod p) implies that x is congruent to +-1 (mod p).
devout snowBOT
Q. Prove that x^2 congruent to 1 (mod p) implies that x is congruent to +-1 (mod...
restive river
x ≡ y(mod p)
so,
x² ≡ y²(mod p)
so, y² =1
=> y = +1 or -1
=> x ≡ -1 or +1 (mod p)
Why is this not correct?
sonic smelt
Why is y^2 necessarily 1? Which set are you taking y from
restive river
x^2 ≡ 1 (mod p) (given)
x^2 ≡ y^2 (mod p)
y^2 = 1
Can you give an example to show why this may be wrong?
sonic smelt
3^2 = 1 mod 2
3^2 = 3^2 mod 2
3^2 =/= 1
devout snowBOT
restive river
.reopen
devout snowBOT
✅
restive river
.close
devout snowBOT
devout snowBOT
Available help channel!
nova abyss
For what do you use sin, cos, tan?
devout snowBOT
For what do you use sin, cos, tan?
nova abyss
Like to find what?
restive river
It's used for many purposes.
zenith jacinth
a lot of things actually :
in geometry it links the angle to the sides of a triangle
in physics, to study waves and other things
devout snowBOT
@nova abyss Has your question been resolved?
nova abyss
a lot of things actually :
in geometry it links the angle to the sides of a tri...
But like what does it show?
restive river
What do you mean what does it 'show'?
topaz axle
it shows your coordinates as you move around a circle
when you're at the bottom, your y corrdinate is −1 and it changes slowly
your x coordinate is changing fast
like the middle of the circle is 0 and the radius is 1
sin is y and cos is x, the graph is a wave
devout snowBOT
@nova abyss Has your question been resolved?
nova abyss
it's not hard
I don’t understand
topaz axle
if this circle has radius 1 you can roughly guess the coordinates of the point i marked
devout snowBOT
@nova abyss Has your question been resolved?
nova abyss
if this circle has radius 1 you can roughly guess the coordinates of the point i...
How?
.close
devout snowBOT
devout snowBOT
Available help channel!
inner mango
Any convex optimization experts?
inner mango
<@&286206848099549185>
devout snowBOT
@inner mango Has your question been resolved?
hearty carbon
I have to calculate the sum of this series and i have no idea how. Anyone can help?
devout snowBOT
I have to calculate the sum of this series and i have no idea how. Anyone can he...
supple horizon
?
hearty carbon
i asked chatgpt and it showed me smth totally nowhere that
supple horizon
fuck chat gpt
hearty carbon
@polar chasm telescopical series?
hearty carbon
my teacher said smth about that but i don't understand shit
supple horizon
ye
hearty carbon
i completely forgot i could do that
hearty carbon
what do i do afterwards tho
hearty carbon
how do i like, calculate the rest?
hearty carbon
where are you going w this
supple horizon
do you know it or not
hearty carbon
nope
i'm dead honest, the math i did in highschool was very basic
now i'm a clueless year 1 student
hearty carbon
welp
hearty carbon
god damn wtf
how about this one
did i solve it right?
my teacher solved one similar to this
supple horizon
cant understand the q
hearty carbon
the q?
hearty carbon
oh
it was just to calculate the sum of the series
just like i asked on the exercise before
that's why i am so confused about the way you solved it
cause it's nowhere near how i did this one
supple horizon
both the questions are related as they're just inf series summations
but the second one is geometric progression
while the first is not
yeah the second one looks right
hearty carbon
but the second one is geometric progression
isn't it a telescopic progression?
supple horizon
telescopic is different
in telescopic terms actually cancel out
here theres no canceling
supple horizon
this is a polynomial
supple horizon
you'll learn slowly
supple horizon
where can i actually learn how to solve those
youtube
there are so many good channels
restive river
f is continuous / for all x€ R f(x)=f(2x) I should show that f is constant
lone ravine
f is continuous / for all x€ R f(x)=f(2x) I should show that f is constant
Hint: Show that for any x we have f(x) = f(0)
olive snow
Écoute notre ami error
lone ravine
Oui oui
lone ravine
J'ai déjà vu beaucoup des personnes aujourd hui qui parlent francais. Malheureusement, je ne peux pas lire tous les question