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Use .reopen if this was a mistake.
#help-10
static pebble
obtuse pebbleBOT
static pebble
Not sure what to do
static pebble
,rotate
warm shaleBOT
light raft
let d be the total distance travelled. then, we have that 24 = a(1) + b(d-1). then we just solve for d
do you understand how i got this equation?
light raft
cool
static pebble
Tyy
light raft
nwnw
static pebble
.close
tropic lantern
help
steel parcel
it seems like you rotate the shape clockwise then perform a reflection across the y axis
earnest cairn
can someone help me with 11b
earnest cairn
.close
sweet lake
obtuse pebbleBOT
light raft
have you done sums of arithmetic sequences?
sweet lake
Yes
light raft
letting a_n = -4n -3, there are 2 formulae that we can use, (i) n/2(a_1 + a_n), and (ii)n/2(2a_1 + (n-1)d), where in this case n = 31
have you seen these formulae before?
sweet lake
Yes the first one
light raft
okay cool, so lets use that
we have that n = 31 (summing 31 terms), now we need to find a_1 and a_31
how should we do that
light raft
correct
sweet lake
Then we use a of 1 to find a of 31
light raft
we can just directly sub in 31 into the a_n equation
sweet lake
372?
light raft
what were your steps?
sweet lake
Used the equation
light raft
nah we have found a_1 and a_31
now we use the formula
the sum from n=1 to n=31 is 31/2(a_1+a_31), which is...
sweet lake
tyyy
light raft
nw
obtuse pebbleBOT
@sweet lake Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
meager silo
Before i go any further, have i set this up correctly?
obtuse pebbleBOT
Before i go any further, have i set this up correctly?
@meager silo Has your question been resolved?
meager silo
<@&286206848099549185>
meager silo
<@&286206848099549185>
mighty jacinth
short ore
The answer i want is the smallest number HIJ
obtuse pebbleBOT
@short ore Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
chilly gate
obtuse pebbleBOT
chilly gate
can someone help
dark stirrup
Guys help please ****
!help
obtuse pebbleBOT
Guys help please ****
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
dark stirrup
!status
obtuse pebbleBOT
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
pine sail
sin(x)/x is wrong, yes.
You're going to have to open another channel, this one's closing soon.
shrewd drift
Ok
obtuse pebbleBOT
Available help channel!
atomic compass
How does D(ln5) become 0
obtuse pebbleBOT
How does D(ln5) become 0
atomic compass
So you dont need to know what the answer is?
What if its some infinite decimal number
pine sail
it is some infinite decimal number.
But even as it is, it's a constant.
Like those infinite decimal places won't ever change.
atomic compass
So just e becomes 0 too
pine sail
yeah.
timid silo
How do I determine the convergence/divergence of the following sum
obtuse pebbleBOT
How do I determine the convergence/divergence of the following sum
timid silo
I know that the sequence converges to 1
Can I directly affirm that the series is divergent?
,w sum from 1 to infinity (k(k+2))/(k+3)^2
warm shaleBOT
timid silo
.close
half lodge
obtuse pebbleBOT
half lodge
why is my answer here incorrect?
i took the antiderivative of each term and plugged in 5
obtuse pebbleBOT
@half lodge Has your question been resolved?
half lodge
.close
fallow cove
So 0 isn't a purely imaginary number right?
obtuse pebbleBOT
So 0 isn't a purely imaginary number right?
fallow cove
just checking
kind hawk
depends a bit on your definition of "purely imaginary"
I would generally count it because most stuff that is true for purely imaginary numbers should also be true for zero
except for the usual problems with zero like division
dense imp
So 0 isn't a purely imaginary number right?
it's also part of the sets of real numbers, as well as set of integers, so it is also a real number, and an integer
last anvil
someone answer these for me i can't wait till the grade comes out 
obtuse pebbleBOT
someone answer these for me i can't wait till the grade comes out <a:wiggle360:8...
last anvil
wymmmm
stone spoke
Bruh y more than 1 question it’s too much for my brain to process 
plain stag
We don't answer questions, we help you answer them yourself
last anvil
i already did i just need to get em checked
stone spoke
last anvil
Bruh y more than 1 question it’s too much for my brain to process <:sully:651816...
its pre calc bruh cmon
plsssssssssssssssssss
plain stag
Post your answers and we'll verify, then
last anvil
alr alr
just tell me if its correct or not
the grade won't come out until Thursday and i cant wait that long
obtuse pebbleBOT
@last anvil Has your question been resolved?
pine sail
Look right to me.
obtuse pebbleBOT
@last anvil Has your question been resolved?
lilac matrix
obtuse pebbleBOT
lilac matrix
Im supposed to calculate the angle cfd.
Aefg and adbc are squares
Im not sure what to do I'd appreciate your help.
I speak German and English
This is what I've thought of so far
winter jacinth
i have been trying it for like 15min isnt there any other information?
obtuse pebbleBOT
@lilac matrix Has your question been resolved?
lilac matrix
It's 2c
It says
We have 2 squares abcd and aefg
D is on the extension of side fg
And b is on the extension of ef
Right now we're at the topic of
circumferential angle theorem (I google translated that I'm not sure if it's the right term)
If that helps
sinful plover
interesting ques.
past sand
Let P be the intersection between AD and EF, can you say something about the triangles AEP and DFP?
lilac matrix
The angle dpf and the angle EPA are the same?
winter jacinth
they are simmilar triangles but what do you get from that?
lilac matrix
Anything else?
I'm thinking
EPD and apf are also the same of course but I'm not sure about what else
past sand
What about the lines AE and FD?
lilac matrix
They are parallel!
lilac matrix
Well actually you already know AEP is a right angle and you should see PFD is to...
Yes I wrote that on the picture
past sand
What does that mean for the triangles?
lilac matrix
I don't know the English word but the 2 other angles are the same size
past sand
Yes, so all angles are equal, that's called similar triangles
What about side lengths?
sinful plover
wow I figured it out finally.. damn this is a really good question
@lilac matrix try to focus on the quadrilateral BFDC
that's your hint
past sand
No
lilac matrix
do you know cyclic quadrilateral?
I don't know what that means can you describe it in words?
lilac matrix
I think we did do something like that
But how do I know that all those points even are on the circle?
Or are they always gonna be on a circle?
sinful plover
ok
sinful plover
so the opposite of 2nd point also holds true
lilac matrix
so the opposite of 2nd point also holds true
What do you mean by that
past sand
We have two very different ways of solving this
@lilac matrix which one do you want to go for?
sinful plover
which means when opposite angles of a quadrilateral sum up to 180 degree then the quadrilateral becomes cyclic or in other words all 4 points lie on a circle
lilac matrix
Which ever one is easier to understand
past sand
Arguably his is easier if you memorize this cyclic quadrilateral thing
lilac matrix
Am I allowed to take a break and ask for help later again?
sinful plover
channel gets closed due to inactivity I think
sinful plover
you can do that..but I rarely open discord
lilac matrix
Ok thank you for all the help I'll try on my own and come back later if I don't understand
sinful plover
@past sand you can explain her the solution if you are present at that time
past sand
Sure
obtuse pebbleBOT
@lilac matrix Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
opaque galleon
Can someone explain to me how this was turned into the second line?
obtuse pebbleBOT
Can someone explain to me how this was turned into the second line?
pseudo swift
idk crap about this subject but it seems like
the 3R(0) corresponds to X(1)^2 + X(2)^2 + X(3)^2 (as they mentioned in a, E(X(t)^2) = 3 = R(0) for any t)
2R_X(-1) corresponds to 2X(1)X(2) (delta in time of -1)
2R_X(-2) corresponds to 2X(1)X(3) (delta in time of -2)
2R_X(-1) again corresponds to 2X(2)X(3) (delta in time of -1)
but don't ask me what it means, I just tried to pattern match the start with the end
@opaque galleon
opaque galleon
idk crap about this subject but it seems like
the 3R(0) corresponds to X(1)^2 + ...
wait I think it didn't say for any t
pseudo swift
they said at time t
the only thing it can mean is that the formula works for any time
opaque galleon
ohh okok
obtuse pebbleBOT
@opaque galleon Has your question been resolved?
opaque galleon
but don't ask me what it means, I just tried to pattern match the start with the...
yeah you right
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
brazen gorge
a semigroup with an identity is a monoid right
obtuse pebbleBOT
a semigroup with an identity is a monoid right
obtuse pebbleBOT
Available help channel!
violet rapids
T
violet rapids
Problem 69
idk what it’s looking for or idk what “determine the numbers so that their product is the greatest” means
is it looking for the x intercepts ?
high lily
ultimately you want the vertex
the average of the x-intercept/roots tell you the location
violet rapids
ok
I did it right then ok
I thibk
was it when it said “their product is the greatest” = looking for vertex ?
high lily
after getting a quadratic after expressing the product in terms of a single variable, pretty much
high lily
yeh
violet rapids
y = -f (x)
we flip over the x axis
nvm got it
y=1/2f(x)
it getting wider ?
or smaler
nvm
got it
hidden sparrow
Help
cosmic tulip
nerd
cosmic tulip
joke
hidden sparrow
Ok
cosmic tulip
i am gonaa live sirver
hidden sparrow
If I was a nerd I wouldn’t be asking for help lol
Anyway I do need help
<@&286206848099549185>
obtuse pebbleBOT
@hidden sparrow Has your question been resolved?
hidden sparrow
<@&286206848099549185>
lol I’m not getting help anytime soon it seems
<@&286206848099549185>
timid silo
what is your problem with this exercise?
hidden sparrow
what is your problem with this exercise?
I don’t know how to solve it
And my approach is incorrect
So I’m lost
No help….
<@&286206848099549185>
lilac torrent
Are you familiar with what the modulus/argument are for a complex number and what an Argand diagram is?
obtuse pebbleBOT
@hidden sparrow Has your question been resolved?
feral acorn
obtuse pebbleBOT
feral acorn
can someone please explain how 1 - 1/e approx equals to -1/e
obtuse pebbleBOT
@feral acorn Has your question been resolved?
obtuse pebbleBOT
hot horizon
if you miltiply by 0 you can just get rid of that whole term
0n = 0
am i missing something?
azure badger
so it would just be:
1/2n^2 + 1/2n + 1/8 i believe
oops
didnt see the original question
hot horizon
it does, 1/8 just means remainder was 1 when you divided by 8
hot horizon
although idk how to feel about the 1/2 in the answer, i think since they are both odd it can be written to add the two 0.5s
azure badger
0n + 8 = 8
4n^2/8 = 1/2n^2
4n/8 = 1/2n
1/8 = 1/8
basically just dividing by 8
and multiplying by 8 to see the remainder of 1
hot horizon
½n² + ½n + ⅛
8 / (4n^2 + 4n + 1)
4n + 0 + 0
4n + 0
1
and since we have half an odd number plus half another there must be some way to put them together so that we aren't halving anything
azure badger
yep
hot horizon
so we have
½(4n² + 4n + 1) + ½(2n + 1) + ⅛
which is
2n² + 2n + ½ + n + ½ + ⅛
combine like terms
2n² + 3n + 1 + ⅛
still ⅛ which is a remainder 1 after division by 8
hot horizon
R1*
^
(1 * 8) + 1 is 9
because remember n is our odd number so n = (2n + 1) (yeah should probably change variable names lol)
actually we could san n = 2p + 1
so then we have p^2 / 8 = 2p² + 3p + 1 + ⅛ when p is odd
hang on
no i think im wrong actually
actually now im just confused
:|
ok, lets say n is our odd number. n = (2p + 1).
then we square n and get 4p² + 4p + 1
we divide by 8 and get ½p² + ½p + ⅛
ok, so we have ½p² + ½p + ⅛
½p² + ½p must necessarily be a whole number because if you half two whole numbers and add them together the 0.5 parts will add back together into a whole 1. this means that the answer is (some whole number) + ⅛ which proves that if you divide an odd number squared by 8 you get a remainder of 1.
im just not sure how to put it in figures
yw :)
hmm?
we still haven't figured out the first one
it depends if an explanation via text is accepted as opposed to figures
but it probably is
so i guess you could say we have
its basically remainders again, your proving that a^2 mod 10 cant be 3
because if a number ends in 3 then when you divide it by 10 the remainder will be 3
for example 13 / 10 = 1 remainder 3
azure badger
yeah same idea
void parcel
obtuse pebbleBOT
hot horizon
all paths which go down by a row at each step are shortest paths, so it would start with 3 options, then in all cases have 3 options again. so its 3^<how many rows are there - 1>
hot horizon
what isnt
drifting wraith
there are 3 options, but also there are 5 options and all kinds of options
hot horizon
oh man i didnt see that lol
yeah its more complicated than that
i dont understand what numbers your putting in, but this isnt my help channel and i should be doing school, so bye for now
obtuse pebbleBOT
@void parcel Has your question been resolved?
untold flower
In need of help.
brazen gorge
Regarding sectors
close this channel
untold flower
.close
obtuse pebbleBOT
untold flower
/end
obtuse pebbleBOT
Available help channel!
spice chasm
is it true that $v(t)=v(0)+\int_0^t a(s)ds$
obtuse pebbleBOT
is it true that $v(t)=v(0)+\int_0^t a(s)ds$
warm shaleBOT
Jash
spice chasm
matches with suvats lmao
but wfa says its false
spice chasm
,w does f(5)=f(0)+integrate from 0 to 5 of f'(x)
warm shaleBOT
Requested by jashxdlol
obtuse pebbleBOT
@spice chasm Has your question been resolved?
tough parcel
forgot how to do these
obtuse pebbleBOT
forgot how to do these
latent walrus
you multiply the frequencies by the midpoints, and sum them
then divide by the total frequency
i believe anyway, its been a long time
tough parcel
how do i find the midpoint 🥹
latent walrus
midpoint of 20 to 25 is 22.5 for example
tough parcel
oh
latent walrus
you can just find the average of the boundary numbers
dim quest
Hi can someone prove this formula to help me understand it better for my exam?
obtuse pebbleBOT
Hi can someone prove this formula to help me understand it better for my exam?
@dim quest Has your question been resolved?
obtuse pebbleBOT
@dim quest Has your question been resolved?
hexed agate
Hi can someone prove this formula to help me understand it better for my exam?
Better go to physics at #old-network
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
brittle plover
obtuse pebbleBOT
brittle plover
is there a method for finding the eular path or is a lot of it just trial and error
I know you have to start and end with an odd node
which in this case is Z and Y
obtuse pebbleBOT
@brittle plover Has your question been resolved?
brittle plover
.close
rough mango
help
rough mango
stone spoke
Have you made any progress so far? Or is there anything from the original problem you don’t understand?
stone spoke
Maybe you could start by understanding what it means to be in Thom class (&Thom Space) and the normal bundle before you start the problem
rough mango
Okay
obtuse pebbleBOT
@rough mango Has your question been resolved?
minor harness
trying to expand this log expression, not sure where I'm going wrong:
obtuse pebbleBOT
trying to expand this log expression, not sure where I'm going wrong:
minor harness
.close
inland thistle
can someone explain how the ^15 turned into those?
obtuse pebbleBOT
can someone explain how the ^15 turned into those?
inland thistle
maths 1 but yea it includes it
empty cypress
you can either convert it to the e^(i theta) form, or you can use this equation
sec lemme type it
fathom flicker
You should rewrite it into polar form like bunny suggested
or use the binomial theorem if you hate yourself
empty cypress
$(a+bi)^n = \sqrt{a^2+b^2}^n(\cos(n\theta) + i \sin(n\theta))$
warm shaleBOT
empty cypress
did i get this first try?
empty cypress
and of course $\tan(\theta) = \frac ba$
warm shaleBOT
empty cypress
nth power of the square root?
should be square root (then to the n)
lemme check that i wrote this out correctly though, see if it matches the work above
yeah i think this works out
@fathom flicker have you checked?
but like either way the "easier" way is surely just use polar form unless you want to memorize this
empty cypress
inland thistle
.close
obtuse pebbleBOT
fathom flicker
<@779131727338930196> have you checked?
I’m not familiar with that form off the top of my head
Seems plausible though
empty cypress
oh i meant to ping the question asker, my bad
im pretty sure it directly derives from the polar form method anyways
obtuse pebbleBOT
Available help channel!
worldly plover
is that graph a rational graph?
obtuse pebbleBOT
is that graph a rational graph?
obtuse pebbleBOT
@worldly plover Has your question been resolved?
zenith raft
what is a rational graph?
worldly plover
I mean I just wanted to take one of those lines into account
obtuse pebbleBOT
@worldly plover Has your question been resolved?
obtuse pebbleBOT
@worldly plover Has your question been resolved?
obtuse pebbleBOT
@worldly plover Has your question been resolved?
uneven sedge
can anyone help me with a few questions on my pre-test? i have an exam coming up tomorrow and i really need to understand all this cuz im not confident at all
obtuse pebbleBOT
can anyone help me with a few questions on my pre-test? i have an exam coming up...
uneven sedge
obtuse pebbleBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
I don't know where to begin.
winter jacinth
try to bring it to a simpler form
then you substitute (2x + pi/3) with u
and it turns into
sin(u) = 1
winter jacinth
ok so since sine is a periodic function (meaning it repeats) there could be multiple solutions for example the solution is x = 90 deg but x = 360 + 90 could also be a solution
but after you get it into the form that i said, then u can be 90 deg, 350 deg, 610 deg etc, then you solve like 2 or 3 equations like 2x + pi/3 = pi/2 and check if x is in the [0, 3pi] range
uneven sedge
i am trying to understand
gimme a sec
im still kinda confused
how do i find how many solutions
there are
winter jacinth
you try it until x gets out of the range thats given to you
if you still dont understand we can go on a call
winter jacinth
so should i call you?
uneven sedge
yeah
winter jacinth
okay
obtuse pebbleBOT
@uneven sedge Has your question been resolved?
sinful iron
Did I do this right?
obtuse pebbleBOT
Did I do this right?
winter jacinth
wait isnt the decks corner where the two lines intersect?
sinful iron
Ah?
winter jacinth
y = x-2 intersects y at -2 and x at 2
you made it intersect x at 1
also the other one y = -2x +1 is wrongly drawn
obtuse pebbleBOT
@sinful iron Has your question been resolved?
sinful iron
also the other one y = -2x +1 is wrongly drawn
Ohhh
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
violet rapids
obtuse pebbleBOT
violet rapids
Why did he get two different answers using synthetic division versus polynomial divisions
Omg name
Nvm
.close
graceful marten
Hia
graceful marten
Short question
How do you know just because PX = 1/3 of PR, that the rest are 1/3 each
.
Also if you wanted to calculate XY would it just be -1/3a +1/3b
Becuase 'apparently' its split into 3
obtuse pebbleBOT
@graceful marten Has your question been resolved?
obtuse pebbleBOT
@graceful marten Has your question been resolved?
graceful marten
.close
weary nacelle
How do i solve this
obtuse pebbleBOT
How do i solve this
weary nacelle
What steps do i do first
heavy seal
Y=mx+c
heavy seal
Also product of slopes of this one and perpendicular line is -1
weary nacelle
Will it be 3y = 2x + 6?
weary nacelle
Also product of slopes of this one and perpendicular line is -1
Oh
How do i know if it’s -1
heavy seal
Will it be 3y = 2x + 6?
Divide both sides by3
boreal cliff
Do i need to change it to y =mx + b
yes
heavy seal
For perpendicular line...y=m2 x + c
weary nacelle
Oh
heavy seal
Slope of perpendicular line
heavy seal
2/3 times m2 is -1
2/3 (m2)=-1
heavy seal
Ye
heavy seal
Ye
weary nacelle
Ok
heavy seal
-3/2
heavy seal
So for like two..y=(-3/2)x+c
heavy seal
Ye
weary nacelle
Will 3/2 be positive then
heavy seal
Flip sign?
weary nacelle
like it’s 2/3
heavy seal
Why flip sign
heavy seal
No need
heavy seal
-3/2
weary nacelle
ye
heavy seal
So for like two..y=(-3/2)x+c
.
heavy seal
Now (6,-1) lies on both lines
heavy seal
We substitute
heavy seal
just use slope point form
They don't know it...im helping derive intuition
boreal cliff
do you know slope point form of a line
weary nacelle
Yes
heavy seal
Of course u can derive standard results
boreal cliff
slope@point form is y = mx + b?
no thats just slope intercept
heavy seal
-1y = -3/2(6) + b
It's almost over
boreal cliff
They don't know it...im helping derive intuition
ah right
weary nacelle
i replace y and x
boreal cliff
you could think of it as rise over run for this line is ofc -3/2
weary nacelle
What’s the easiest way to do
weary nacelle
you could think of it as rise over run for this line is ofc -3/2
Oh
boreal cliff
assume a point x,y
weary nacelle
I’m confused what are we talking about
heavy seal
-1y = -3/2(6) + b
Why is there extra "y"...u already substituted value
weary nacelle
Why is there extra "y"...u already substituted value
Then what is it supposed to be
weary nacelle
What
boreal cliff
thats the line
weary nacelle
x-6/y-(-1)=-3/2
Oh
heavy seal
I’m confused what are we talking about
DW it's over almost
weary nacelle
DW it's over almost
Ok
-1 = -3/2(6) + b
?
is this rifht
then
Or what is the right equarion
boreal cliff
what
boreal cliff
Or what is the right equarion
i just told you
heavy seal
-1 = -3/2(6) + b
Find b
heavy seal
Then what is it supposed to be
-1=-3/2x +c
weary nacelle
Oh
heavy seal
so y=-3/2x+8
weary nacelle
Which equarion is easier
heavy seal
Over
weary nacelle
Percy or this one
heavy seal
Percy
weary nacelle
Oh
boreal cliff
slope point form is a derived result
weary nacelle
Whag is derived
weary nacelle
Oh
Let me redo but
Let me try to do the steps
So first i change the equation to
weary nacelle
Let me try and i will see if i get 8
heavy seal
That's better
heavy seal
tribal tide
obtuse pebbleBOT
heavy seal
Lighting...
tribal tide
U need a better picture?
heavy seal
Yea or send the question
obtuse pebbleBOT
@tribal tide Has your question been resolved?
tribal tide
<@&286206848099549185>
obtuse pebbleBOT
@tribal tide Has your question been resolved?
tribal tide
<@&286206848099549185>
is it possible to get some help or?
been waiting for over an hour
hot sonnet
Hello. Notice that it's 1/2 -1 = -1/2, so the exponent in x and y is -1/2
obtuse pebbleBOT
@tribal tide Has your question been resolved?
tribal tide
Hello. Notice that it's 1/2 -1 = -1/2, so the exponent in x and y is -1/2
oh Okay but What will i do further down to solve the question?
hot sonnet
oh Okay but What will i do further down to solve the question?
you can isolate lambda in one eq and substitute in the other one
also use 3000-x-5y = 0
for example, x = 3000-5y
tribal tide
How do i isolate the lambda?
hot sonnet
you have
50/sqrtx - lambda = 0
and
50/sqrty - 5lambda = 0
you can isolate lambda in one of these 2 eqs
and replace in the other one
tribal tide
oh okay and then use the 3000-x-5y after
hot sonnet
yes
obtuse pebbleBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
north quarry
sorry, plus u wont get better if i give u the answer
high python
high python
help me please
dark stirrup
Stay in your original channel please
dark stirrup
You closed it after i sent my message. Also, you should generally stay in the channel you first opened instead making a new one just because no one came to help you quickly enough.
high python
idgaf
dark stirrup
People are less likely to help you if you abuse the system or act hostile
high python
.close
vague isle
I'm trying to understand this part of linearizing.
I'm not sure what is happening here
obtuse pebbleBOT
I'm trying to understand this part of linearizing.
I'm not sure what is happeni...
vague isle
why they make that substitution y = p+u ?
what's that u ?
its from this page
https://ocw.mit.edu/courses/18-03sc-differential-equations-fall-2011/resources/mit18_03scf11_s11_1text/
balmy mortar
I think you need to give more context yh
yh ok
dont think i can help out myself
ok so i understabnd something just reading the screenshot
vague isle
it's a recap of diff equations studied so far in the course basically, in the form of a conversation
balmy mortar
The idea is to center at your equilibrium
so, redo the axes and make the equilibrium the origin
thats the effect y = p + u has
p is your new origin
u will be the relative change from that origin
Don't know if that made any sense
vague isle
mmmm kinda but still forming the image in my head
p would be the value at equilibrium basically
cause i don't care what happens in the transient
right?
warm shaleBOT
balmy mortar
If you were to compute this, a sensible thing would be to 'center' the limit at 0
that is making the substitution u = x - 1
I think the same idea is being used here
vague isle
mm ok
balmy mortar
that is making the substitution u = x - 1
x = 1 + u
is another way to write this
and thats just like the y = p + u here
vague isle
i'm not used to think this way but i understand
i mean never had to recenter to compute the limit
but ok
not sure why it would make more sense
i think i understand the parallel now.
vague isle
If you were to compute this, a sensible thing would be to 'center' the limit at ...
why would be better to center it?
balmy mortar
Whenever you focus on a random point
isnt it better to make it the new origin
In this particular case, try and you will see it makes things a bit easier
This is a bit of intuition that makes sense to me though, having encountered the same idea in many places.
Topology, algebra, analysis etc etc
vague isle
im trying yes
balmy mortar
If you only care about the change relative to a point
then that point is essentially your origin
If you only write down the change
then it is.
vague isle
why u = x-1 ? that 1 is from the limit or from the numerator?
i'm not sure i understand the processing of ideas here
you see that function and you see ... something, the makes you think , i can shift this to origin!
what do you see?
cause even if i have just u in the numerator the denominator becomes messier.. how am i shifting this?
this is super interesting i didn't find it explained so far...
vague isle
If you only care about the change relative to a point
could you tell me what should i look for to study this or make practice over this? so i don't keep spamming the server
remote skiff
I think you're overly worrying about the change of variables and missing the point that is interesting to begin with.
You have some function y(1-y/p) = y- y^2/p and as y tends to p. This tends to 0 as y tends to p, but that doesn't really give you any insight into what's going on near p.
If your limit was near 0 instead, you could use an approximation by dropping the highest power of the polynomial, so any change of variables that accomplishes that would achieve the same goal
From y(1-y/p) you could just use u = 1-y/p so that y = 1-u/p. All I did was choose a linear function of y that was easy to substitute into the equation, then you have (1-u/p)u and as y tends to p u tends 0 so that you can drop leading terms.
The whole point was the strategy of changing the equation to study a polynomial near 0 so you can drop a leading term to simplify. The substitution itself wasn't particularly magical
vague isle
thanks for taking the time!
i don't understand what you mean by
"that doesn't really give you any insight into what's going on near p."
what sort of insight you mean?
remote skiff
It's not obvious what the behavior of the differential equation looks like near p
vague isle
so in the end i would get this
and you say "as y tends to p u tends 0 so that you can drop leading terms."
why y tends to p?
ok i think i see, its for the substitution you made
u = (1-y/p)
i think i see what's happening here now, can you confirm @remote skiff ?
i'll look up for linearization i think that's just a topic that has not been explained yet
obtuse pebbleBOT
@vague isle Has your question been resolved?
mystic bough
D is middle point of AC, and i need to find DEBC area
obtuse pebbleBOT
D is middle point of AC, and i need to find DEBC area
lilac pebble
is 12 the length of AD or AC
mystic bough
Ac
obtuse pebbleBOT
@mystic bough Has your question been resolved?
obtuse pebbleBOT
@mystic bough Has your question been resolved?
fervent cradle
D is middle point of AC, and i need to find DEBC area
find the area of ADE and subtract it from the area of ABC
obtuse pebbleBOT
@mystic bough Has your question been resolved?
final matrix
obtuse pebbleBOT
final matrix
is my proof correct? the instructions were:
grizzled basin
looks good but you carry (k+1)/(k+2) the entire way through
you dont have that equality from the start, so only write it at the bottom when you show it
otherwise it seems like you're assuming its true, which is what you're supposed to show
fossil crag
I don’t understand the line where there's (1/k+1) on the left, where are the parentheses ?
final matrix
Ah, ok, sweet thank you! I feel great right now because I haven't been able to understand induction for the last couple of days
fossil crag
And how do you go from that line to the next ?
final matrix
I don’t understand the line where there's (1/k+1) on the left, where are the par...
I was just showing that I was factoring out (1/k+1), I don't think it was necessary but it was part of my workflow to keep it straight in my mind
fossil crag
And how do you go from that line to the next ?
I repeat this question jic
final matrix
I repeat this question jic
(k/1) + (1/1) = (k+1)/1
(k+1)/1 * (1/k+2) = (k+1)/(k+2)
fossil crag
(k/1) + (1/1) = (k+1)/1
(k+1)/1 * (1/k+2) = (k+1)/(k+2)
Did you forget order of operations?
fossil crag
(k/1) + (1/1) = (k+1)/1
(k+1)/1 * (1/k+2) = (k+1)/(k+2)
And this would also imply the 1/(k+1) you factored out disappeared
fossil crag
The way to do it : put everything on the same denominator
final matrix
my factored term is my +1, not the (1/k+2), correct?
fossil crag
Ill write it with parentheses so we all agree
$\frac{1}{k+1}\Big(k + \frac{1}{k+2}\Big)$
warm shaleBOT
rafilou2003
fossil crag
This is your 2nd to last line rewritten with parentheses
Now try to put everything on the same denominator
final matrix
$\frac{k}{1} + \frac{1}{k+2} = \frac{k^2+3}{k+2}$
fossil crag
You didn't do it properly
final matrix
Am I dumb am I failing algebra rn
final matrix
yeah
fossil crag
$k = \frac{k(k+2)}{k+2}$
final matrix
k(k+2) = k^2 + 2k
warm shaleBOT
rafilou2003
fossil crag
And then you add it to the other fraction
final matrix
damn I am forgetting all kinds of things
fossil crag
$\frac{k}{1} + \frac{1}{k+2} = \frac{k^2+3}{k+2}$
Ok so can you edit this to get a correct statement?
final matrix
$\frac{k(k+2)}{k+2} \cdot \frac{1}{k+1} = \frac{k(k+2)}{(k+2)(k+1)}$
warm shaleBOT
ronin
final matrix
$\frac{k(k+2)}{k+2} \cdot \frac{1}{k+1} = \frac{k(k+1)+1}{(k+2)(k+1)}$
warm shaleBOT
ronin
fossil crag
Why did it become a multiplication instead of addition?
final matrix
I dont know 😭
fossil crag
Complete this statement: $\frac{k(k+2)}{k+2} + \frac{1}{k+2} = ...$
warm shaleBOT
rafilou2003
final matrix
k(k+2)+1/(k+2)
fossil crag
Yes, can you expand the numerator?
fossil crag
Yes, does this seem familiar?
final matrix
No to be honest
fossil crag
look at your quadratic identities
Try to factor the numerator is what I'm hinting at
final matrix
(k+1)(k+1)
fossil crag
Yes
final matrix
then (1/k+1)[(k+1)(k+1)/(k+2)] becomes k+1/k+2
fossil crag
Yes
final matrix
Wow my algebra is rusty, thank you so much
ngl I was like "why so much rigor when can I start handwaving" 😭
.close
hallow owl
Does anyone know anything about the college classes: Topics math and Contemporary math
obtuse pebbleBOT
Does anyone know anything about the college classes: Topics math and Contemporar...
hexed agate
What is your question bro
unreal musk
Possibly, though you'll probably have much better luck if you have specific questions related to stuff within those classes... 
hexed agate
Possibly, though you'll probably have much better luck if you have specific ques...
I have a video on my watchlist from computerphile something about origin of bytes
unreal musk
@warm canopy 
unreal musk
I have a video on my watchlist from computerphile something about origin of byte...
I don't think I have anything useful that I could say myself 
obtuse pebbleBOT
@hallow owl Has your question been resolved?
timid silo
i have no clue how to do this
obtuse pebbleBOT
i have no clue how to do this
inner stratus
thales ?
regal parcel
we can use the fact that T and W are midpoints of the legs
meaning, the increment in length from SR to TW is the same increment as from TW to UV, afaik
here we can see that on the right, the addition green length is twice the additional blue length
same works for the left side
obtuse pebbleBOT
@timid silo Has your question been resolved?
hallow owl
What is your question bro
Mb😭I got the option of either taking College algebra/pre calc or topics math/contemporary math
obtuse pebbleBOT
Mb😭I got the option of either taking College algebra/pre calc or topics math/co...
hallow owl
I want to know which is simpler
hallow owl
Possibly, though you'll probably have much better luck if you have specific ques...
If it’s easier than the above
I have no clue what the classes consist of
obtuse pebbleBOT
@hallow owl Has your question been resolved?
hallow owl
<@&286206848099549185>
unreal musk
If it’s easier than the above
Might be a better question for the discussion #math-discussion #discussion channels, these channels are more for like specific homework flavoured questions tbh
hallow owl
Might be a better question for the discussion <#359052581022203914> <#2688823173...
ok ty
obtuse pebbleBOT
@hallow owl Has your question been resolved?
quick estuary
Sorry for the pic in spanish. I've been trying with a group of friends to solve this, however we just get constantly stuck. There's no intersection between S and v or H and v, and we need to somehow get a 3 vector subspace to transform into a 2 vector subspace, while having that second subspace transform into a single vector.
obtuse pebbleBOT
Sorry for the pic in spanish. I've been trying with a group of friends to solve ...
@quick estuary Has your question been resolved?
quick estuary
<@&286206848099549185>
quick estuary
What really bothers me is that you cannot do something like SintH to Sintv
quick estuary
<@&286206848099549185>
quick estuary
<@&286206848099549185>
obtuse pebbleBOT
@quick estuary Has your question been resolved?
quick estuary
<@&286206848099549185>
quick estuary
.close
rugged plume
help
forest sinew
how awful that they make you write this using text
it doesnt really seem like youve used enough parens
not that this will make it more legible
obtuse pebbleBOT
@rugged plume Has your question been resolved?
obtuse pebbleBOT