<@&286206848099549185>
#help-19
magic notch
warm sentinel
magic notch
<@&286206848099549185>
desert jolt
Form a DE by using fbds
magic notch
whats fbds
desert jolt
Free body diagram
DE means differential equations
Have you learnt how to solve ODEs?
desert jolt
Yeah which translates to ode after writing the equations
a = (kv^2)/m + g
a = dv/dt
@magic notch you've done the intellectual shit nicely
I believe now its just some writing mistake or silly mistakes somewhere
desert jolt
but it feels wrong since you dont get a solvable v0 equation
Yeah which is why I said there's some solving error
magic notch
ok i will try
magic notch
but u have a v on top so how is that an issue
magic notch
no
odd edgeBOT
@magic notch Has your question been resolved?
magic notch
:(
desert jolt
I think you did some sign errors
While going downwards and upwards
Cuz im getting an answer
odd edgeBOT
@magic notch Has your question been resolved?
wooden oar
Hi! Could someone check my solution for task 1.9 and 1.10?
For 1.9 i answered A = {1, 2, 3}, B = {4} and C = {3, 4, 5, 6}.
For 1.10 i chose A = {1} and B = {2, 3}.
Also, if the translation is a bit unclear, tell mee.
wooden oar
Thanks in advance.
tribal thorn
Hi! Could someone check my solution for task 1.9 and 1.10?
For 1.9 i answered A...
looks good to me
wooden oar
looks good to me
yayy, thanks for checking
wooden oar
Alsoo, i am not sure how to prove task (1.11). By definition, a set A is a subset of a set B if all elements in A are also elements in B. Lets say we have a set X, and now someone says that X is a subset of X, how do i prove it? I would say, because they are equal, they would contain the same elements, therefore X would be a subset of X (itself), right? But i dont think its enough to say that for a proof..
cold depot
I think what you said with the definition is enough. Just say let x be arbitrary element of X. Then x is in X. Since x is arbitrary, any element of X is in X. Therefore, X is subset of X
I know it feels redundant/weird, but these simpler proofs are usually this way
wooden oar
I think what you said with the definition is enough. Just say let x be arbitrary...
um, but what do you mean by arbitrary element?
cold depot
um, but what do you mean by arbitrary element?
I say arbitrary element as in x represents one element that is in the set X, but we don't know which one. This way, if you can prove for this element, you can prove for any other. Example A={1,2,3}, then x could be 1, 2 or 3.
It's a way to generalize to all elements of the set, which you often must do to ensure there are no "holes"/counterexamples in your proof
wooden oar
I say arbitrary element as in x represents one element that is in the set X, but...
understood, so when you say an arbitrary element in X, it simply means any element in X?
wooden oar
It's a way to generalize to all elements of the set, which you often must do to ...
aah, okai
cold depot
understood, so when you say an arbitrary element in X, it simply means any eleme...
Yes yes
wooden oar
Yes yes
got it, but can i prove "the empty set is a subset of X" similarly? cause a counterexample wouldnt make sense - "the empty set is not a subset of X, cause not all elements in the empty set are in X" however, an empty set has no elements, its empty, and so therefore we can say that it is a subset of X?
i cant think of any other way to prove that "the empty set is a subset of X" is true..
warped glacier
got it, but can i prove "the empty set is a subset of X" similarly? cause a coun...
isn't that an axiom
the empty set is a subset of anyset
https://math.stackexchange.com/questions/631042/direct-proof-of-empty-set-being-subset-of-every-set
I guess you can look at these answers
wooden oar
https://math.stackexchange.com/questions/631042/direct-proof-of-empty-set-being-...
uuh, thanks
warped glacier
np
cold depot
For the empty set, there are no elements that are outside of X, therefore it is a subset of X
It's what they mean with vacously (there are no counterexamples)
wooden oar
For the empty set, there are no elements that are outside of X, therefore it is ...
aah, now it all makes sense
thanks!
wooden oar
It's what they mean with vacously (there are no counterexamples)
yess
patent parcel
Hello
patent parcel
~(matrix A is invertible)
Is it correct in question 2
steel quarry
this question kind of sucks
patent parcel
Anything else from u
patent parcel
<:thonkzoom:533366356536721418> this question kind of sucks
Fr
steel quarry
Nothing, you're correct
patent parcel
Ok
patent parcel
Nothing, you're correct
Ok for question 10 (x belongs to A) and ( x belongs to B)
Right?
Ni
No wait
steel quarry
notice how $\cup$ and $\vee$ look similar
clever fjordBOT
jewels!
patent parcel
I didn't get
wanton bison
It's not necessarily and
x can only be for example in A and it would still be in the union of A and B
patent parcel
Oh right
wanton bison
So it can be in A or in B or both
wanton bison
**jewels!**
Also notice, the former is used for sets, and the latter for statements.
wanton bison
\cup refers to union
\vee to logical OR
patent parcel
Ok i got iy
It*
Ok last one question 12
are they two statements
With "And"
What second statement should be to form symbolic way
"happy family are all alike but each unhappy family is unhappy in its own way"
S_1: Happy family are all alike
S_2: unhappy family are all alike
S_1 and not S_2
patent parcel
S_1 and not S_2
Is it correct
odd edgeBOT
odd edgeBOT
Available help channel!
obtuse saddle
how can I prepare for precalc ? I got precalc coming in 48 days and was wondering if I can do anything to prepare for the class I'm pretty rusty tbh
obtuse saddle
precalc _class_?
class
wooden python
right
algebra, algebra, algebra
and arithmetic i'd say
make sure you're able to manipulate algebraic expressions without hitting snags
factorization's a big thing
applying things like (a ± b)^2 = a^2 ± 2ab + b^2 or difference of squares as well
obtuse saddle
so would khan academy be a good option ? like algebra 1 and 2 ?
wooden python
yes
perhaps even look through their precalc stuff to see a sampler of what might be coming
plain ruin
how can I prepare for precalc ? I got precalc coming in 48 days and was wonderin...
Well just study it fully beforehand. This topic is not that complicated
obtuse saddle
so is there anything I can skip to save time or would I have to go through all units in both like for example this is the algebra 1 section
wooden python
don't skip anything
sand horizon
Functions in algebra?
obtuse saddle
don't skip anything
I don't think ill be able to get through it all in time
mystic saffron
Maths is a field where your knowledge builds onto itself, dont skip anything so you have a well rounded foundational knowledge for future application
mystic saffron
I don't think ill be able to get through it all in time
Don't stress too much about trying to finish everything beforehand, go at pace you find challenging but not overbearing
plain ruin
I don't think ill be able to get through it all in time
48 days is a lot braza
mystic saffron
You will surely cover all those concepts once you start regardless
wooden python
I don't think ill be able to get through it all in time
5 days a section seems pretty manageable i think
but if you're pressed on time i would at least get your feet wet in every section
obtuse saddle
48 days is a lot braza
thanks braza but I haven't done math in a while thats why I'm kinda worried
mystic saffron
What maths have you done before
obtuse saddle
5 days a section seems pretty manageable i _think_
yeah but this is only algebra 1
not 2
obtuse saddle
What maths have you done before
college algebra was my last class more than 5 months ago
it was basically algebra 2 and a bit of precalc
obtuse saddle
oh it's 17 units my bad
yeah thats what I am saying so Im not sure I have enough time
wooden python
<@&268886789983436800> advertising
errant galleon
<@&268886789983436800> advertising
bruuhh
wooden python
advertising is still against server policy and this includes personal discords.
in any case you're intruding in an occupied help channel too
mystic saffron
yeah thats what I am saying so Im not sure I have enough time
Looking at that khan academy course, my piece of advice is don't stress over it too much, most of those concepts, atleast from your maths knowledge, should be relatively easy to pick up – I doubt it will take 48 days to revise algebra 1, but that will depend on how quickly you pick up maths and your dedication to learning
wooden python
^
obtuse saddle
Looking at that khan academy course, my piece of advice is don't stress over it ...
max I got is like 2 hours a day
then I burnout
wooden python
that and also there's gonna be a review thing at the beginning of your class
so like even if you dont get everything in thats not something to worry about
obtuse saddle
alr so I'm gonna just go through as much as i can for algebra 1 and 2 I've already done 2 units in algebra 1 so I'm gonna continue there
wooden python
yeah fair
oblique cargo
Can someone help me with this question?
odd edgeBOT
Can someone help me with this question?
solar peak
according to ur ans its independant of t?
oblique cargo
according to ur ans its independant of t?
didn't realize the question was cut off
this is what I did
solar peak
oh sorry have no clue what leibniz rule is..wait for someone else to help
oblique cargo
alright
odd edgeBOT
@oblique cargo Has your question been resolved?
quasi sparrow
this is what I did
What happens when you enter your answer
oblique cargo
that's the preview of what I wrote in the box
I think I messed up something when I did the u sub
quasi sparrow
Well your input isn't fully shown
oblique cargo
the preview box above is the output
quasi sparrow
,tex .FTC2
clever fjordBOT
riemann
quasi sparrow
Did you use this
oblique cargo
this is what I did
i think I did
quasi sparrow
this is what I did
Your first line still has an integral
quasi sparrow
**riemann**
This is not enough then
Show the leibniz rule you learned then
Should just be an additional term
weak fossil
odd edgeBOT
tepid pelican
I'd just count the total number of ways and then subtract those which make some row empty
there aren't that many of them
odd edgeBOT
@weak fossil Has your question been resolved?
odd edgeBOT
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
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.
fervent pewter
Forget the constraint of "no row remains empty" for now..how will u place the 5 letters amongst the 8 boxes?
mystic saffron
Forget the constraint of "no row remains empty" for now..how will u place the 5 ...
True tho
weak fossil
Forget the constraint of "no row remains empty" for now..how will u place the 5 ...
horizontally / vertically
fervent pewter
Forget the constraint of "no row remains empty" for now..how will u place the 5 ...
start with this..and then remove the cases which violates the condition of "no row remains empty"..you will have ur answer
inner moth
correct me if i'm wrong, i'm not really good at combinatorics
Chose 3 out of 5 letters to fill in the 3 rows in different orders using 5P3, then count the number of left boxes after filling one box in each row (which is 5) and chose 2 of them for the rest 3 letters, so it's 5C3, now 5P3*5C3
weak fossil
start with this..and then remove the cases which violates the condition of "no r...
how do i write cases individually now
fervent pewter
I will help u with that thought process
answer my intial question first
tell me the no. of ways u will place the 5 letters amongst the 8 boxes
weak fossil
correct me if i'm wrong, i'm not really good at combinatorics
Chose 3 out of 5 l...
so its 600?
weak fossil
tell me the no. of ways u will place the 5 letters amongst the 8 boxes
8C5?
fervent pewter
no it will be more..the letters are unique and u can permute them
inner moth
oh right, that's wrong sorry, let me try again
weak fossil
so 8P5?
fervent pewter
yes correct!
weak fossil
but we're only talking about placing right and not about arranging are we..?
fervent pewter
arrangement is important as well
inner moth
but we're only talking about placing right and not about arranging are we..?
different arrangements also count as different ways
weak fossil
arrangement is important as well
okay
fervent pewter
now try to think the cases in which any row will be empty
weak fossil
different arrangements also count as different ways
yeah but i thought we were only concerned about placing
fervent pewter
it will be less and easier to identify
weak fossil
it will be less and easier to identify
okay jam
inner moth
now try to think the cases in which any row will be empty
but then we have to check for different cases right? one row empty, two rows empty
fervent pewter
but then we have to check for different cases right? one row empty, two rows emp...
yep but its not difficult
weak fossil
4 ways?
fervent pewter
tell me those 4
weak fossil
wait row is horizontal right?
fervent pewter
yes
late sinew
Wrong channel lol sry
weak fossil
wait i get 3
fervent pewter
ok explain those 3
weak fossil
- first and second row filled, 3rd row empty
2)second and third row filled, 1st row empty
3)third and first row filled, 2nd row empty
weak fossil
wdym
weak fossil
5! * 3?
fervent pewter
for each of those cases count no. of ways of placing 5 letters in the 2 filled rows
inner moth
so he's asking the number of ways you can arrange the letters in the filled rows
weak fossil
yeah like if a row has to be left empty then in the provided 2 row we can interchange the given 5 alphabets in 5! ways isn't it?
fervent pewter
no not in all cases..what about the case of 3rd row being empty? You sure it will be 5!?
fervent pewter
no
think again
u have 6 boxes and 5 letters..tell me the no. of ways to place those 5 letters in those 6 boxes
weak fossil
6p5 or 6!
fervent pewter
good!
weak fossil
Ohhh got it
fervent pewter
the remaining 2 cases will be 5! each
weak fossil
right
fervent pewter
now subtract these values from the original 8P5..u will have ur answer
weak fossil
so 8P5-5! * 5! * 6!?
weak fossil
right, are we supposed to add?
fervent pewter
yes
the cases needs to be removed from the original 8p5
those cases and other cases in which none of the rows add up to give 8P5..
I guess we are done..u can close before leaving
weak fossil
damn
i got the answer
5760
Thanks a lot
i have a couple of more doubts but anyway i'll start them in new channels
really grateful to you cause i actually understood the problem inc the concept
.close
odd edgeBOT
odd edgeBOT
Available help channel!
shrewd trellis
,rccw
clever fjordBOT
shrewd trellis
what did i do wrong?
tacit wasp
An x has disappeared
late sinew
forgot the x
shrewd trellis
which line
late sinew
figure it out
sick plaza
try keeping the 2/3 outside of the fraction
shrewd trellis
numerator
sick plaza
yes
shrewd trellis
try keeping the 2/3 outside of the fraction
why?
sick plaza
i think the 2 in the 2/3 was obscuring the x
as you fill in x = 2
so you might've mistaken that 2 as the x =
2
odd edgeBOT
odd edgeBOT
Available help channel!
steady edge
How does the step from the top to the below goes?
odd edgeBOT
How does the step from the top to the below goes?
steady edge
I dont get it
sharp oak
If you multiply out (x+7)(x-1), you get x² + 6x - 7. So, they're the same
We say that (x+7)(x-1) is the "factored form" of x² + 6x - 7, we call the practice of finding this "factoring"
steady edge
But what happens to the 2x²... is it the null facotr theorem, so u say tahts 0?
sharp oak
If AB = 0, we can choose to look at each of the factors individually. That is, we can look at A = 0, and we can look at B = 0
still depot
im assuming they deal with that later
sharp oak
Yes, they will probably look at the 2x² ... later
steady edge
Why do they do the step with the(x+7)... ?
still depot
Basically, both [(x^2) + 6x - 7] = 0, and [2(x^2) - 5x - 3) = 0 are solutions to the equation
So
To find the solutions for x^2 + 6x - 7 = 0
they factor it out
Getting (x + 7) • (x - 1) = 0. This means the solutions for that one are -7 and +1. But that's just the first part
Is factoring the part your trying to understand better?
steady edge
Oh i got it now
still depot
Then they have to do the 2x^2... = 0 part
by also factoring
did that make sense lol
steady edge
After the (x + 7) • (x - 1) = 0 they did rhe null factor theorem again with x+7=0,
-7=x right?
odd edgeBOT
steady edge
.reopen
odd edgeBOT
✅
steady edge
@still depot i got an question, is there any trick / rule to make the equation from x²+6x-7 to (x+7)(x-1)
still depot
uhm
graceful hatch
first into last method ?
steady edge
I mean did rhey just make this in their head
graceful hatch
first into last method ?
Y'all know about this?
steady edge
No lemme check
graceful viper
still depot
goated oct
graceful hatch
No lemme check
It might not be known so internationally ig
graceful hatch
goated oct
Is matcha that bad?
still depot
There's the diamond method
restive kayak
<@535971995980922890> i got an question, is there any trick / rule to make the e...
with simple blade
still depot
https://youtu.be/qeByhTF8WEw?si=mQkNQJmtZphgxya8
Which really is just what he's doing here but it helps understand it more
restive kayak
or else the general formula
graceful viper
everyone is going to name a method they learnt in middle school. just watch the video
graceful hatch
Sorry. Are there some rules to shut up when others are discussing?
still depot
lol
restive kayak
x-x
still depot
Is matcha that bad?
yes
steady edge
Ok ty i would close now, or u wanna chat?
late sinew
Close it
steady edge
.close
late sinew
Chatting can be done in discussy
odd edgeBOT
graceful hatch
@steady edge yk, while they were teaching us these typa equations we had two methods to solve it. Either the first into last method or the quadratic equations method. So, idk whether yk this but, let's see ok:
As in your eqn look at the numbers in the ends. We got 7 and x². Multiply the two. You get 7x². Now, look at the middle number. It's 6. Now, look at the sign after the second number, it's a minus. Now, you gotta think of two numbers whose product is 7 and when you subtract them, you get 6. So, you it's 7 and 1. You gotta put it like it's replaceable yk like:
= x²+6x-7
=x²+(7-1)x-7
=x²+7x-x-7
=x(x+7)-1(x+7)
=(x+7)(x-1)
It only works when the exponents match tho. Like in this question you got x². You just gotta get it. I can further explain in dm. Sorry i am annoying. I just wanted to help.
odd edgeBOT
Available help channel!
shrewd trellis
which rule should be used? I believe the quiotient rule should be used
tribal thorn
which rule should be used? I believe the quiotient rule should be used
if you're talking about differentiating yes
tacit wasp
Yes
shrewd trellis
and 1 is not a function
green elm
f(x) = 1, there, it's a function
tacit wasp
Wdym?
shrewd trellis
is that a function?
shrewd trellis
my friend said
"thats just 3x^-2
its not a function over a function"
"is 3 a function or a constant"
tacit wasp
Sometimes there are more than one rule that can be applied
shrewd trellis
yep, i know that
tacit wasp
But some are of course quicker
solemn zenith
Sometimes there are more than one rule that can be applied
absolutely😍
shrewd trellis
But some are of course quicker
yep so when should i use the quotient rule over the power rule
tacit wasp
The power rule is only when you have... a power
tacit wasp
which rule should be used? I believe the quiotient rule should be used
But not here
tacit wasp
Because that's not a power, it's not x^something
solemn zenith
yep so when should i use the quotient rule over the power rule
so use quotient when u cant simplfy the num- fx and the den- fx
shrewd trellis
which rule should be used? I believe the quiotient rule should be used
i could make it intoo x(x^2+a)^-1
tacit wasp
Sure
tacit wasp
And you can use product rule
solemn zenith
u.v Would Appear
shrewd trellis
but the quiotient rule, there is also u and v
steep mantle
i like product+chain cause i cant memorize quotient rhle
tacit wasp
but the quiotient rule, there is also u and v
Yes, so?
shrewd trellis
u.v Would Appear
so then what do u mean?
solemn zenith
so then what do u mean?
a function would be multipied by another function and therefore the power rule cannot be applied directly
shrewd trellis
I understand how to use the product role but are u saying the quotient rule is easier
in this case?
tacit wasp
in this case?
In my opinion, yes
solemn zenith
u can solve it however u like
tacit wasp
But there's no that big difference
solemn zenith
But there's no that big difference
fr😭
tacit wasp
Best is: try both ways and find the most comfortable for you
shrewd trellis
So here you can (and should) use power rule
u cant use the power rule direectly, u need to manipulate it first into 3x^-2
solemn zenith
u cant use the power rule direectly, u need to manipulate it first into 3x^-2
i mean only if u do know how to turn it into that
shrewd trellis
ya i do
solemn zenith
ya i do
u can use it then
but wait a sec
i think the question cant be manipulated
😔🙏
solemn zenith
in any cases
in this case
i think quotient is the way to go
but if u cant remember the formula
then u can use product rule
i actually prefer quotient
and it is not that hard to remember
odd edgeBOT
@shrewd trellis Has your question been resolved?
carmine idol
It's basically which you are more comfortable with
odd edgeBOT
carmine idol
All ways to differentiate get the same answer
odd edgeBOT
Available help channel!
outer sun
hi please help
outer sun
.close
shrewd trellis
odd edgeBOT
shrewd trellis
is this correct?
shrewd trellis
u sure?
modest hare
lemme read it
modest hare
i assume yk how to factor
modest hare
haha im playing ik you do
shrewd trellis
haha im playing ik you do
😔
modest hare
ok u factor out the gcf correct
shrewd trellis
yep
modest hare
got it
modest hare
did u solve it yet
shrewd trellis
i solved it but its incorect
shrewd trellis
shrewd trellis
yh
modest hare
since they are multyping each of the factors must be equal to zero
so u can set each of them to 0
shrewd trellis
ohh ok i knowww the ans
modest hare
goood
shrewd trellis
(2x-1) is a dooble root right
modest hare
yup yup
modest hare
so looks like u grouped
shrewd trellis
yp
modest hare
that x
shrewd trellis
oh
shrewd trellis
can i show u my other problems i had before?
modest hare
sure
shrewd trellis
q, 9b
modest hare
which one did u have problems
solemn zenith
he is saying b
shrewd trellis
can u show ur work
one sec, ill redo the q
shrewd trellis
ofc
solemn zenith
ok
modest hare
alr thx im bck
celest osprey
(a) F'x = 2pi
solemn zenith
he is still solving ig
wooden python
(a) F'x = 2pi
actually incorrect
celest osprey
Na^n-1 when a^n
wooden python
and bad notation on top of that
modest hare
F means integral
solemn zenith
(a) F'x = 2pi
more likely 0
safe kiln
Na^n-1 when a^n
pi is a constant
brittle plinth
(a) F'x = 2pi
freshman's dream (calc variant)
wooden python
Na^n-1 when a^n
no, pi^2 is a constant.
also you should not drop the brackets in function notation
you should never ever EVER write fx for f(x)
celest osprey
OK thanks
solemn zenith
you should never **ever** **EVER** write `fx` for `f(x)`
real
merry finch
Hey never say never, sometimes it’s convenient to write fx
shrewd trellis
im gonna do a
modest hare
alr
shrewd trellis
yea i did the rest
modest hare
a should be easy to shw
wooden python
Hey never say never, sometimes it’s convenient to write fx
in the context of calculus it's not
like i get linear algebra where such parenthesis-dropping is appropriate sure
shrewd trellis
wooden python
pi^2 - pi^2 is not 1
modest hare
1/h would be undefined cuz the left and right but yeah ann is correct
shrewd trellis
cuz the left and right?
modest hare
from both sides 1/h would be DNE
shrewd trellis
pi^2 - pi^2 is not 1
the numerator would be 0
wooden python
yes
shrewd trellis
i mean
wooden python
pure 0, at that
shrewd trellis
1*
wooden python
no!!!
modest hare
x-x=0
wooden python
pi^2 - pi^2 is 0.
wooden python
when you subtract a number from itself you get 0.
shrewd trellis
if there was notihing
wooden python
this is basic arithmetic even
celest osprey
do u know first principle?
Lim x ->0 x -h/h
celest osprey
Lim x ->0 x -h/h
That's undefined 😮
wooden python
That's undefined 😮
you completely fumbled it my dude im so sorry
nimble hull
it only becomes 1 when you divide (because x/x = 1 for the most part)
if you subtract, it becomes 0 (because x-x=0)
modest hare
for those it would become 1 but dont forget the domain and range
wooden python
you need to distinguish dividing sth by itself (which gives 1) vs subtracting sth from itself (which gives 0)
shrewd trellis
if you subtract, it becomes 0 (because x-x=0)
okay makes sense
modest hare
x cant be -3 or -7
wooden python
until you do that, the word "cancel" is on the top shelf for you
solemn zenith
apple-apple=nothing(0)
dawn scarab
apple-apple=nothing(0)
Apple arithmetic 🔥
shrewd trellis
One last question, im sure this one will be tricky
celest osprey
Tricky or treaty?
celest osprey
These are implicit functions
modest hare
u would set it to -2?
modest hare
the derivative
odd edgeBOT
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
copper quarry
how many helpers do you have cuh
shrewd trellis
I just coudnt solve the last question
toxic rose
because honestly if ur done with a,b,c i think u can do d
shrewd trellis
I have solved for the first 3 but i may have lost the answers
celest osprey
First differentiate 3x³ then 3x² then x then 1 separately
toxic rose
I just coudnt solve the last question
well what do you know about the tangent to any curve
shrewd trellis
this was questions from a while ago
toxic rose
First differentiate 3x³ then 3x² then x then 1 separately
CAN U PLEASE WAIT?
toxic rose
These are implicit functions
and also, NOT HELPFUL.
celest osprey
K
shrewd trellis
yep
urban jackal
I just coudnt solve the last question
first differentiate the given the equation and equate it to -2 and show that for no value of x it shows -2
toxic rose
okay yeah i give up do wtever tf u want
solemn zenith
first differentiate the given the equation and equate it to -2 and show that for...
gradient of the line = -2
modest hare
i was helping uu a while ago can i continue
urban jackal
gradient of the line = -2
the last line right?
modest hare
ok uu we check the slope of the linear right
urban jackal
u didnt understand?
urban jackal
ok uu we check the slope of the linear right
yeah
shrewd trellis
ok uu we check the slope of the linear right
wdym
modest hare
we find if any point is tangent to it
urban jackal
@shrewd trellis did u get what i said
modest hare
rewriting y=1-2x as y=-2x+1 seems easier
urban jackal
what diff does it make
shrewd trellis
we find if any point is tangent to it
wdym by that
modest hare
so we set the derivatives equal
clever fjordBOT
modest hare
he knows how to differentiate
solemn zenith
i am not sure how u got x
modest hare
so we check if any point of f'(x) has a slope of -2
solemn zenith
u forgetting smth?
celest osprey
Sorry, 3x² 🙏
urban jackal
for lines to be parallel there slopes have to be equal and the last lines slope is -2 so u have to differenetiate the first line and equate it to -2 then u will come to understand there is no solution of x which satisfies the equation
modest hare
i aint reading allat (joke)
solemn zenith
how did dx/dx = x?
shrewd trellis
i aint reading allat (joke)
do u wanna just dm me too many people speaking at the same time
solemn zenith
So it's 9x² + 9x + x
nuh
solemn zenith
So it's 9x² + 9x + x
"-"? (3x*2=9??) dx/dx =x?????
urban jackal
9x²-6x+1=-2
which comes down to
3x²-2x+1=0
urban jackal
I suck at maths it seems
ouchhh
then its discriminant is lessthan 0
so it is imaginary
solemn zenith
so it is imaginary
have u read the question
urban jackal
yeah
show that it doesnt have a root
i mean no point
so which obviously means no value of x
solemn zenith
which comes down to
3x²-2x+1=0
i donot think it comes down to this
urban jackal
9x²-6x+1=-2
bring the -2 to lhs and take 3 common
solemn zenith
yess
urban jackal
so question is solved ig?
urban jackal
he was asking about the last subquestion
shrewd trellis
@urban jackal gimme a sec
urban jackal
kk
odd edgeBOT
@shrewd trellis Has your question been resolved?
modest hare
hes almost there
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
Can someone help me understand what this identity is? How does this make any sense at all?
wooden python
do you need help deciphering the notation or do you need it explained why this thing is true
rich wasp
Can someone help me understand what this identity is? How does this make any sen...
sum alpha^4 means alpha^4 + beta^4 + gamma^4
here
it's a concise way to use sigma notation
sum alpha beta means alpha*beta + beta*gamma + gamma*alpha
if you want a proof of the identity, recall (a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)
now use the above stated sigma notation to get the desired form
stable sequoia
symmetric sum notation 🤔
brittle plinth
!occupied
odd edgeBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
shrewd trellis
oops
odd edgeBOT
@mystic saffron Has your question been resolved?
vagrant orbit
can someone help me with this
odd edgeBOT
can someone help me with this
dense star
isn't there a physics server
vagrant orbit
none
brittle plinth
odd edgeBOT
@vagrant orbit Has your question been resolved?
desert jolt
!status
odd edgeBOT
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
@vagrant orbit Has your question been resolved?
vagrant orbit
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
1
odd edgeBOT
@vagrant orbit Has your question been resolved?
odd edgeBOT
@vagrant orbit Has your question been resolved?
modern palm
can someone help me solve this polynomial division?
outer jolt
can someone help me solve this polynomial division?
!occupied
odd edgeBOT
can someone help me solve this polynomial division?
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
coarse ocean
can someone explain why 0
odd edgeBOT
can someone explain why 0
oak crown
Calculate it
narrow crypt
determinant like that kinds find a volume, no?
dapper canyon
determinant like that kinds find a volume, no?
det is like the signed volume of its columns
which is the same as signed volume of rows
more precisely, the volume of the parallelipiped formed by the column/row vectors
with sign accounting for orientation
solar peak
can someone explain why 0
Do C1-->C1+C2
So now C1 is the same value and C3 is the same value..if any 2 columns are same it means det=0
coarse ocean
Do C1-->C1+C2
So now C1 is the same value and C3 is the same value..if any 2 col...
yes i got it thanks
.close
odd edgeBOT
odd edgeBOT
Available help channel!
manic grail
can someone explain this formula
odd edgeBOT
can someone explain this formula
manic grail
or show how we get it
i am famuliar of how to get it when the differential isnt a vector but idk here
the only difference is that the r'(t) isnt a norm
odd edgeBOT
@manic grail Has your question been resolved?
manic grail
wdym by "how we get it", it's a definition
how is it a definition
its not definition its parametrization
desert jolt
how is it a definition
What
desert jolt
its not definition its parametrization
???
wanton bison
or show how we get it
Multiply by dt/dt 
manic grail
and then what
manic grail
Multiply by dt/dt <:sotrue:826971355542192148>
yes ik about the one where dr isnt a vector
narrow crypt
or show how we get it
Since we are doing a line integral along ${C}$ parameterised by ${\vec{r}}$, we can see that ${\vec{F}}$ along the line is ${\vec{F(\vec{r}}}$.
Also, by chain rule,
[ d\vec{r} = \frac{d\vec{r}}{dt} dt]
So, combining these two
[ \int_{t=a}^{t=b} \vec{F}(\vec{r}) \cdot \vec{r'}(t) dt]
manic grail
but not sure about it now
clever fjordBOT
k
manic grail
then why is it a norm when its not a vector
narrow crypt
or u can divide the line integral into small panels as usual
manic grail
when dr isnt a vector
green elm
then why is it a norm when its not a vector
who says it's a norm?
wanton bison
There are two versions, one for vector fields and one for scalar fields
green elm
that's calculating something different
quasi sparrow
can someone explain this formula
Because there's no dS here
manic grail
that's calculating something different
yes indeed
in that case its norm
but why dont we do the same here
where we got dr and r is a vector
its still a small vector dr in the curve we are integrating
green elm
that's the analogue to "area under a function", whereas the one with the dot product is capturing the notion of "net work done by a force on a particle that travels along the path r(t)"
manic sleet
that dS and the norm came from when f(x) was scalar
manic grail
i meant when we have f(x,y) dS over a curve
manic sleet
here it is a vector function
green elm
and?
manic sleet
we use Pythagorean theorem
right, that is when f(x) returns a scalar value
green elm
that's not what you are computing here, it has nothing to do with that
manic sleet
here f:R3->R3
green elm
because the goal is to calculate what i said above
manic grail
here f:R3->R3
its f: R^2 -> R
manic sleet
its f: R^2 -> R
that's a scalar function, that's when we use int f(x,y)dS
manic grail
because the goal is to calculate what i said above
oh
manic sleet
in the img you asked about
manic grail
here in the vector field
manic sleet
the function is f:R3->R3
manic grail
f is outputing 3 value
i see
and why wouldnt the pythagorean theorem work here
to make it dx^2 vector etc
and put dt inside
green elm
you could do that but it would just be computing the "scalar" integral of the three components of f
which is not the same thing
manic grail
how though
manic sleet
this integrals means computing the "work" done by the vector field over the curve C
manic grail
if i used purely correct mathematical equalities the last part should be the same as first
where is the mistake
which part isnt correct
manic grail
this integrals means computing the "work" done by the vector field over the curv...
yes but whats not valid in what i said
where am i making a mistake
green elm
for one thing, if you compute the integral of f times dS and f is a vector, then the result is a vector, not a scalar
whereas the integral of f . dr is a scalar
manic grail
no no wait
thats not what i said
i said if we have the integral of vector function F dot dr
why dont we sub in sqrt dx^2 +dy^2 + dz^2
as in vectors dx dy dz
green elm
dr is a vector
manic grail
yes
green elm
dx^2 +dy^2 + dz^2 is a scalar
manic grail
we use dx and dy and dz vectors
green elm
how would you "substitute" that?
manic grail
dx with x being a vector
manic sleet
dx, dy, and dz are not inehrently vectors
wanton bison
I would really advice to take a look at here:
https://mathinsight.org/line_integral_vector_field_introduction
manic sleet
they're scalars representing how "fast" the function is moving is one direction, dr=<dx,dy,dz>
which is why dr is a vector and dx, dy, and dz are not
manic grail
dx, dy, and dz are not inehrently vectors
cant we analyze vector dr as sums of vectors dx dy dz
manic grail
or that wouldnt help into calculating the integral
manic sleet
you mean dr=<dx,0,0>+<0,dy,0>+<0,0,dz>?
manic sleet
well wouldn't that just be <dx,dy,dz> 
manic grail
you mean dr=<dx,0,0>+<0,dy,0>+<0,0,dz>?
no like dr vector = dx + dy + dz vectors
manic grail
well wouldn't that just be <dx,dy,dz> <:pandathink:524885344995508235>
oh yea it doesnt really help in solving it
yea i see there is no point in doing it
green elm
even if you do that, the length of dr isn't gonna be involved
you are still computing a dot product
manic grail
yes and now i have (dx + dy + dz) vectors
its more complicated like this yea nvm
ok so we just multiply by dt/dt
and use one dt as derivative of vector r
odd edgeBOT
manic grail
.reopen
odd edgeBOT
✅
manic grail
but how do we show that dr = dr/dt dt
isnt dt a symbolization rather than a number/variable
tidal matrix
to replace dS with root dx^2 + dy^2
wanted to also point out: if we used this same strategy on a vector field F, then we would have (some scalar) * vector (field), which would only stretch the vectors. we want the area of the rectangles instead, hence F(r) · r'(t)
manic grail
wanted to also point out: if we used this same strategy on a vector field F, the...
yea what i was trying to do just makes it more complicated and doesnt change much
tidal matrix
i mean, it would change something, just not in a helpful way
heavy brook
impressive
manic grail
Can someone explain how dr = dr/dt dt
green elm
Can someone explain how dr = dr/dt dt
chain rule
manic grail
since dt is a symbolization how would this be proven
heavy brook
i wish i was smart enough to do this shit
tidal matrix
i wish i was smart enough to do this shit
it just comes with time. for now, get really comfortable with the basics :)
manic grail
i wish i was smart enough to do this shit
its really not about smartness most of the time dont discourage yourself
narrow crypt
Let ${\vec{r} = g(t)\hat{i} + k(t)\hat{j} + h(t)\hat{k}}$.
[ d\vec{r} = \frac{d}{dt}\left( g(t)\hat{i} + k(t)\hat{j} + h(t)\hat{k} \right) \cdot dt]
By differential, i think?
clever fjordBOT
k
manic grail
its really not about smartness most of the time dont discourage yourself
all it takes is time to spent and choosing to spend it its liturately knowledge the only reason you cant understand
oak crown
Let ${\vec{r} = g(t)\hat{i} + k(t)\hat{j} + h(t)\hat{k}}$.
\[ d\vec{r} = \frac{d...
\dv exists btw
manic grail
i was taught not to treat dt as a multiple or do math with it
narrow crypt
dt represents an infisimal cahnge
manic grail
yes we cant just move it around always
oak crown
i was taught not to treat dt as a multiple or do math with it
Sometimes, breaking convention is just for the best
narrow crypt
\dv exists btw
oh damn
oak crown
You know how u-subsitution works?
manic grail
yes
oak crown
Ok
narrow crypt
yes we cant just move it around always
ye, normally (except ur in engineer)
manic grail
You know how u-subsitution works?
oh nice example
oak crown
Let's take $\int_a^bf(x^2)2xdx$, for example
clever fjordBOT
;(
oak crown
oh nice example
Ah, you got it already 
oak crown
Yes
manic grail
like dx/dt = 3 means always dx = 3dt
narrow crypt
ye
manic grail
ok
narrow crypt
differential
oak crown
This is basically the entire concept of differentials
narrow crypt
[ \dd f = f'(x) \dd x]
clever fjordBOT
k
oak crown
d(variable) is approaching zero
manic grail
yes i recently started using that notation
oak crown
It is not necessarily zero
narrow crypt
its from single val calc
tidal matrix
another "proof:" Pick a variable that isn't involved, like $x$. Then by the Leibiniz Chain Rule, $$\dv{\vec{r}}{x} = \dv{\vec{r}}{t} \cdot \dv{t}{x}.$$ Integrate both sides $\dd x$ to get $$\int \dv{\vec{r}}{x} \dd x = \int \dv{\vec{r}}{t} \cdot \dv{t}{x} = \dv{\vec{r}}{t} \int \dv{t}{x} \dd x,$$ treating $\dv{\vec{r}}{t}$ as a constant relative to $x.$ Then apply FTC on both sides to get $$\dd \vec{r} = \dv{\vec{r}}{t} \cdot \dd t. \quad \blacksquare$$
tidal matrix
latex hates me specifically i guess
manic sleet
I think its not recognizing the vv command
oak crown
YAY
tidal matrix
WOO
oak crown
the comma looks ugly, pls fix
manic grail
uhm
tidal matrix
anyways i hope that helps with the rigourous part
oak crown
We had a bit of a TeX session there
clever fjordBOT
haseeb
manic grail
chain rule has proof?
narrow crypt
chain rule has proof?
yes
oak crown
Yeah
narrow crypt
using approximation of a function
manic grail
yea that basically what im asking
manic grail
wdym type
oak crown
There's one from first princples
tidal matrix
my calc 1 prof wrote one using the epsilon delta definition it was like 5 pages long
manic grail
a correct proof
manic grail
There's one from first princples
first principle is what
narrow crypt
my calc 1 prof wrote one using the epsilon delta definition it was like 5 pages ...
epsilon-dwelta defn to prove a derivative? 😭
oak crown
using approximation of a function
And this
manic grail
sorry idk the english names
narrow crypt
i left that shit since limit
clever fjordBOT
PajamaMamaLlama
oak crown
first principle is what
$\lim_{h\to 0}\frac{f(x+h)-f(x)}h$
clever fjordBOT
;(
oak crown
God how the FUCK do you have that just at the ready
manic sleet
this is one I wrong from a while ago, ignore hte epsilon stuff idk wtf I was doing there 😭
tidal matrix
aww how come his compiles perfectly
manic sleet
God how the FUCK do you have that just at the ready
from a latex document I wrote a while back :)
wanted to prove everything from calc
from the ground up
manic grail
**PajamaMamaLlama**
how do we know that k(x) is differentiable
narrow crypt
blud's doing real analysis
manic sleet
my proof of the exponential rule is crazy lmao
south plume
**PajamaMamaLlama**
pretty sure there is a proof that doesn't depend on k(x+h)-k(x) \neq 0
manic grail
yes but to split the limits
narrow crypt
f(x) approximation 🥀
manic grail
we need to know k(x) is differentiable
lyric dust
**PajamaMamaLlama**
bro whipped this shit out from his pcoket T+T
manic grail
to know the limit exists
tidal matrix
how do we know that k(x) is differentiable
we assume it is for the chain rule, as well as the fact that g is differentiable at k(x)
oak crown
we need to know k(x) is differentiable
Technically speaking it is still a limit
manic grail
ok
tidal matrix
i left that shit since limit
wait till you take real analysis that shit comes sprinting back
manic grail
~~Technically speaking it is still a limit~~
yes but we cant split it
alr uhm 1 more thing
lyric dust
u can
narrow crypt
dr/ds = T
manic sleet
remember how ds=||r'(t)||dt
narrow crypt
from the tnb frame fuckass unit
oak crown
I pray you know what ds is
manic grail
remember how `ds=||r'(t)||dt`
yes with pythagorean theorem
manic grail
I pray you know what ds is
its a small part of the curve
narrow crypt
unit tangent => unit change vector per arc length
manic grail
i need to translate this 1 sec
manic sleet
yes with pythagorean theorem
plug that into the formula he has:
[\int_C F\cdot dr=\int_C F\cdot Tds=\int_C F\cdot \frac{r'(t)}{\cancel{||r'(t)||}}\cancel{||r'(t)||}dt=\int_C F\cdot r'(t)dt]
manic grail
what is unit tangent
manic sleet
damn I failed LaTeX 
manic grail
translation doesnt make sense
narrow crypt
unit tangent vector
clever fjordBOT
PajamaMamaLlama
narrow crypt
manic sleet
when we have a tangent vector it can be any length (and still have the same direction)
manic grail
i prob know but idk it in english 💔
manic sleet
we like it to have a length of 1