and we didnt do it in class
#help-19
keen scroll
whole gyro
send
keen scroll
whole gyro
write
p intersection q has x elements
meaning the rest of p has 10-x elements
rest of q has 13-x elements
now eveything except p or q has 5 elements
and the universal set has 20 elements
meaning p or q has a total of 20 - 5 = 15 elements
so 10 -x + x + 13 - x = 15
so x = 8
@keen scroll got it?
whole gyro
but did you understand
keen scroll
now eveything except p or q has 5 elements
where u get dis
whole gyro
n ( P U Q)' = 5
whole gyro
bye
odd edgeBOT
odd edgeBOT
Available help channel!
shut zephyr
vernal yacht
.close
odd edgeBOT
vernal yacht
You accidentally claim a channel
odd edgeBOT
Available help channel!
mystic saffron
Just to double check, is this answer correct? My answer sheet says x=7 but I got 3.5. But, if I plug in 3.5 to the 4x-7 I get 7
mystic saffron
Idk I’m just a lil paranoid
sturdy cape
Just to double check, is this answer correct? My answer sheet says x=7 but I got...
You sure the bigger triangle has side-length 6?
mystic saffron
My drawings can be confusing sometimes, sorry. here’s the original
Should I have added those up and done something different?
sturdy cape
You sure the bigger triangle has side-length _6_?
I'm referring to your conversion
The small triangle, that's fine
Are you sure that's what you get for the big one?
mystic saffron
9 😔
sturdy cape
yeeee
mystic saffron
lol
sturdy cape
[fwiw, your working out was otherwise correct, so you shouldn't have much difficulty getting to x = 7]
[do dw, it was just misinterpreting the diagram, was all]
mystic saffron
Thank you for correcting me lol I have the tendency to miss lil things like that
.close
odd edgeBOT
odd edgeBOT
Available help channel!
coarse condor
hey using the trigonometric identity
$ y = \tan^{-1} \left( \frac{1}{x} \right) $
coarse condor
$$ y = \tan^{-1} \left( \frac{1}{x} \right) $$
clever fjordBOT
PHYSIC🅰HOLIC
sturdy cape
Don't put spaces before/after the dollars
coarse condor
$y = \tan^{-1} \left( \frac{1}{x} \right)$
clever fjordBOT
PHYSIC🅰HOLIC
coarse condor
wait a min let me reframe the question
short terrace
Yeah I was wondering what exactly you're asking
coarse condor
$$y = \tan^{-1} \left( \frac{1}{x} \right) = \cot^{-1} \left(x)$$
we see that the $tan^{-1} \left(\frac{1}{x}\right)$ is not differentiable at x=0 but the $cot^{-1}(x)$ is
so while changing tan inverse 1/x to cot inverse x how could we say its differentiable
clever fjordBOT
PHYSIC🅰HOLIC
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
grand narwhal
I'm new and icl, ts is weird I mean, a dc server to do Mathematics?
CRAZY.
coarse condor
**PHYSIC🅰HOLIC**
Compile Error! Click the <:errors:504266556054962196> reaction...
anyone? plss help me
rapid echo
**PHYSIC🅰HOLIC**
Compile Error! Click the <:errors:504266556054962196> reaction...
that isn't right for x < 0
coarse condor
but they differe by a constant onlyy
for x < 0
tan inverse 1/x = cot inverse x - pi
but as the pi is constant it turn zero while differentiating
so for all x the differentiation of tan inverse 1/x = differentiation of cot inverse x
i need to know what happened at x = 0 or very close to zero
<@&286206848099549185>
zealous reef
hell how to write this language
you need to use \right to copmlete the bracket
zealous reef
so for all x the differentiation of tan inverse 1/x = differentiation of cot in...
the definition of a derivative requires the function to be continuous
tulip bolt
Guys I'm very basic at math whats this tan thing
coarse condor
$\int_{-1}^{1} \frac\left({d tan^{-1}\left(\frac{1}{x}\right)}\right){dx},dx$
then how to solve this
strange aspen
Guys I'm very basic at math whats this tan thing
look up "trigonometry"
coarse condor
@zealous reef
zealous reef
$\int_{-1}^{1} \frac\left({d tan^{-1}\left(\frac{1}{x}\right)}\right){dx},dx$
th...
the derivative is defined at all points but 0
clever fjordBOT
PHYSIC🅰HOLIC
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
zealous reef
so split it into the integral from -1 to 0 + the integral of 0 to 1
coarse condor
so split it into the integral from -1 to 0 + the integral of 0 to 1
yeah that's the correct point but what my textbook has done is
coarse condor
so split it into the integral from -1 to 0 + the integral of 0 to 1
anyways i go with it
thnks for the help
guyzz
.close
split badger
- Let p > 2 be an odd number and let n be a positive
integer. Prove that p divides 1^p^n + 2^p^n ............ + (p-1)^p^n
How to approach this question?
obtuse nest
odd edgeBOT
@split badger Has your question been resolved?
deft viper
Can someone help with this
odd edgeBOT
Can someone help with this
lean yew
what do you understand about this, and what have you tried?
amber schooner
Can someone help with this
nice bio bro
deft viper
It’s my summer work so I don’t know much about this
unkempt lichen
have you learnt about linear equations?
lean yew
so far, what have you learnt about them?
umbral jolt
Ochem tutor 🔥
turbid comet
2. Let p > 2 be an odd number and let n be a positive
integer. Prove that p divi...
You can try to pair the first and last terms
odd edgeBOT
@deft viper Has your question been resolved?
frail lintel
which formula of integration is used here
odd edgeBOT
which formula of integration is used here
faint knot
which formula of integration is used here
if you squint at the integral on the left, its just $\int_0^v\frac{dv}{A+Bv}$
clever fjordBOT
mtt
faint knot
so $\int_0^v\frac{dv}{A+Bv}=\frac1B\left[\ln(A+Bv)\right]_0^v$
clever fjordBOT
mtt
frail lintel
OHH
faint knot
the constants hide that its a simple integral
faint knot
np
frail lintel
.close
odd edgeBOT
odd edgeBOT
Available help channel!
supple jasper
Need help with this corollary I have tried previously but it's wrong
supple jasper
supple jasper
Need help with this corollary I have tried previously but it's wrong
Also it's a part of this theorem
bronze citrus
stable sequoia
that's the statement itself
i think you should
use the sine law on this one
:3
hearty nest
Also it's a part of this theorem
u can prove it by applying this theroem twice
let PQR be a triangle
stable sequoia
that works too... i guess...
hearty nest
Also it's a part of this theorem
apply this on any two angles
stable sequoia
$\angle{A}=\angle{B}=\angle{C}$ so $\frac{a}{\sin{\angle{A}}}=\frac{b}{\sin{\angle{B}}}=\frac{c}{\sin{\angle{C}}}$ then just use the equality and $a=b=c$ ?
clever fjordBOT
parabolicinsanity
stable sequoia
unless sine law isn't
taught or something
then the isoceles triangle proof will do
hearty nest
taught or something
most prob not
stable sequoia
🥀 then yeah use the isoceles triangle proof
supple jasper
Bruh
supple jasper
unless sine law isn't
Sine law isn't taught
hearty nest
its like saying a=b coz a=b
supple jasper
Man I am getting more confused
hearty nest
should i send solution
supple jasper
Ok
odd edgeBOT
@supple jasper Has your question been resolved?
visual cape
odd edgeBOT
visual cape
using this i got sqrt2*sin(3x-3pi/4)
answer is sqrt2 * sin(3x-5pi/4)
the answers have these like this
but isnt b = -1 and a =1?
summer wave
maybe because it's 3x - alpha and not 3x + alpha
visual cape
yeah i noticed that but i dont think it would have an effect on anything?
summer wave
expanding the right side gives $r\sin(3x-\alpha) = r\sin(-\alpha)\cos(3x) + r\cos(-\alpha)\sin(3x)$
clever fjordBOT
bloubbloub
summer wave
so this flips the sign of sin alpha
visual cape
sin -alpha = sin beta
summer wave
yeah
visual cape
so its the same
oh its not
-a = 3pi/4
so a = 3pi/4
and then 3x+3pi/4 is just the same as 3x-5pi/4
oh so the answers just use cos-x = cosx and sin-x = -sinx
that makes more sense thank you
.close
vernal yacht
~~@summer wave ~~ @hollow sky post your question here
crystal charm
~~<@700680837603000350> ~~ <@1109663860736147478> post your question here
I think that's the wrong ping
hollow sky
how do i find the centroid of a triangle
vernal yacht
mb
summer wave
what
crystal charm
how do i find the centroid of a triangle
if we're talking about the coordinate of it, it would be this.
hollow sky
ok thank you
vernal yacht
ok thank you
Any further questions?
hollow sky
no thank you
odd edgeBOT
vernal yacht
Let’s bring it to hlounge
odd edgeBOT
Available help channel!
bitter folio
odd edgeBOT
bitter folio
I need help with understandint why the first line of the complex number solution holds.
i.e. why is $d = 2 \cdot \frac{f + a + b - ab\overline{f}}{2} - b$
clever fjordBOT
量
bitter folio
i get that the foot from F to AB is $\frac{f + a + b - ab\overline{f}}{2}$
clever fjordBOT
量
bitter folio
But why the -b at the end? Help is appreciated
odd edgeBOT
@bitter folio Has your question been resolved?
bitter folio
<@&286206848099549185>
odd tartan
hi
vernal yacht
hi
bitter folio
帮帮我 pls
odd tartan
我几何是强项但是还是这么烂
specifically traditional chinese..
bitter folio
thanks for helping or trying to help btw
odd tartan
i want to know, do the lowercase letters indicate sides? if so, what sides?
bitter folio
i want to know, do the lowercase letters indicate sides? if so, what sides?
they are the points in the diagram
in complex numbers
so for example 点 A <=> 复数 a
odd tartan
e sorry im not the best at geometry, but ill take a look
bitter folio
e sorry im not the best at geometry, but ill take a look
没问题
odd tartan
guess ill ask gemini ai, heres what i got:
imma take a look at it to see if it makes any sense
odd edgeBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
odd tartan
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they ...
alright, then i guess ill just do it the normal way
(flip around and find out)
bitter folio
question bump
odd tartan
first things first, what does it mean to multiply 2 complex numbers?
(a+bi)(c+di)
ac+adi+bci-bd
(ac-bd)+(ad+bc)i
might be useful for understanding what all the point multiplications mean. this basically means that:
(a, b) x (c, d) = (ac-bd, ad+bc)
were getting somewhere..
lets try multiplying some points and see what happens!
(1, 0) x (0, 1) = (0, 1)
alright... interesting result
(1, 1) x (2, 3) = (-1, 5)
again.. interestin result. any pattern we can make sense of this? well, lets see how it looks if we make it a line!
the slope of the from (1, 1) to (-1, 5) is -2. the slope of the line from (1, 1) to (2, 3) is 2/1 = 2. interesting! it seems like we... made a perpendicular line!
lets try to generalize this:
(a, b) to (ac-bd, ad+bc) has a slope of (ad+bc-b)/(ac-bd-a)
(a, b) to (c, d) has a slope of (d-b)/(c-a)
(ad+bc-b)(c-a) = -(d-b)(ac-bd-a)?
bitter folio
hmm how does this help me
you are making complex numbers in terms of coordinate system geometry and introducing gradient
meanwhile the purpose of complex geometry is to get rid of that
really appreciate the effort tho
odd tartan
well, its a good way to see how we can translate complex geometry into coordinate geometry. to make it seem more clear
bitter folio
But i dont want to deal with coordinates, thats why i want to complex bash
if its easier i would have used coord geom but its not
odd tartan
are you in pre-uni or undergrad? just wondering
bitter folio
that's why complex is more viable in most options
bitter folio
are you in pre-uni or undergrad? just wondering
中学
bitter folio
初
odd tartan
im from hong kong (btw)
bitter folio
im from hong kong (btw)
ah cool
odd tartan
i heard that chinese maths education is much more rigorous than hong kong's
bitter folio
i heard that chinese maths education is much more rigorous than hong kong's
i am not Chinese, i am singaporean
and i do olympiads
odd tartan
fun
i was always considered the person that was the best at maths. but its usually because i learned advanced mathematics (e.g. group theory, differential equations, etc..), not because i was good at the mathematics we were currently learning, albeit i was still good at that. still, im rusty with geometry and its my least favourite branch of math
id rather just do differential equations, theyre much more fun
bitter folio
i was always considered the person that was the best at maths. but its usually b...
ah
i am olympiad sweat
odd tartan
im stumped, so uhh yeah. imma see the solution when someone solves this so i know what happened
odd tartan
i am olympiad sweat
same here too, except the math olympiads here, you have to train for. its very hard to go into it directly, even if youre good at math. so even if youre really good or even gifted at math, you might still only get 3rd or 2nd prize (note: 3rd prize doesnt mean 3rd place)
basically its for people that joined multiple olympiad classes and just do 50 practice problems every day
bitter folio
same here too, except the math olympiads here, you have to train for. its very h...
三等奖 is pain
bitter folio
basically its for people that joined multiple olympiad classes and just do 50 pr...
yup thats me
singapore math olympiads arent that easy either look at our imo performance
i have very tough competition
odd tartan
yup thats me
its not a healthy lifestyle and really doesnt make you that much better at math. just makes you more competitive and feel 'better' at the subject, when what youre actually training for is just the problems that come out every single time, in some variation or another.
bitter folio
its not a healthy lifestyle and really doesnt make you that much better at math....
thats fine for me
because i do physics olympiad as well
odd tartan
thats fine for me
really doesnt make you that much better at math
when what youre actually training for is just the problems that come out every single time, in some variation or another.
bitter folio
and i do so many things i have to time for rest
but i dont mind
i really dont mind
it feels so good topping my school in my level
odd tartan
yeah i do that too, except i dont train for olympiads religiously
i mean, its fine if you want
bitter folio
lmao
odd tartan
but i just dont recommend it
its not going to make you better at math, not by a lot, itll just make you better at the competition
bitter folio
i suppose..?
bitter folio
you have to define math competency here
odd tartan
you have to define math competency here
thats fair. i just never felt like olympiad classes were making you better at math. ive joined a couple of them, and yeah they do the same thing over and over again
you do previous test questions
that are the same thing but slightly different
over and over again, until your brain is crammed with some random formulas that you will (probably) never use in engineering, physics, or anything really
at least, thats just my perspective in hong kong
bitter folio
you do previous test questions
my classes are different
my goated teacher makes his own
and he has such a good personality that we love him
odd tartan
idk what singapore is like
bitter folio
messages didnt load mb
odd tartan
and he has such a good personality that we love him
good for you. really good for you. us hong kongers can only dream of that
odd tartan
most of our teachers are just teachers that were paid to just be there, teach some random things, with 0 spirit, then leave
bitter folio
most of our teachers are just teachers that were paid to just be there, teach so...
that must suck
odd tartan
my goated teacher makes his own
eeeeee then make a PDE for heat change of a rod
also dang there are so many emojis
bitter folio
<:this:489575168314966026> <:this:489575168314966026> <:this:489575168314966026>...
pls dont clutter my channel
odd tartan
e ok
odd tartan
eeeeee then make a PDE for heat change of a rod
a
also why is no one (trying to) help(ing) you?
like its just me
bitter folio
also why is no one (trying to) help(~~ing~~) you?
its normal
bitter folio
bro pls dont clutter my channel
bitter folio
Bump
frank inlet
i think thats correct
bitter folio
i think thats correct
My question is
bitter folio
But why the -b at the end? Help is appreciated
.
frank inlet
Its the formula
bitter folio
Which
frank inlet
D in exactly on the a and b intersection
bitter folio
D in exactly on the a and b intersection
? Please explain
How can two complex numbers intersect
frank inlet
d - a = f - ab/f
bitter folio
d - a = f - ab/f
How did you get that?
bitter folio
its an equation to solve two line
?
bitter folio
well the question it to prove not solve
smh i think you dont know the question
its fine
no worries its not easy anyway
frank inlet
frank inlet
smh i think you dont know the question
which question btw. u asked about - b
bitter folio
which question btw. u asked about - b
the one in the image i posted
see the complex bash
i dont get the first line of setup
frank inlet
oh the first image
bitter folio
indeed
frank inlet
kind of different from what ive learnt but if i say transform ad=ae into algebraic identity would u be confused?
ngl im confused too
bitter folio
kind of different from what ive learnt but if i say transform ad=ae into algebra...
this is complex number geometry so uh okay i dont know what you are saying
<@&286206848099549185>
frank inlet
this is complex number geometry so uh okay i dont know what you are saying
oh please u said bash urself
we can simplify the equation
frank inlet
scroll up, sigma
odd tartan
im studying undergrad maths and even i dont know this 
simple inlet
Ok
odd tartan
but geometry has never been my subject
bitter folio
we can simplify the equation
why is this true
odd tartan
i just always found algebra and calculus more fun
bitter folio
Where is question
check pins
frank inlet
why is this true
algebraic.
crystal charm
https://tenor.com/view/vue-gif-18509468
let's not shitpost in the help channels, you can move it to #chill
bitter folio
https://tenor.com/view/vue-gif-18509468
Dont clutter my channel
bruh
i have to say so many times to yall
odd tartan
let's not shitpost in the help channels, you can move it to <#342850939306246145...
ok.... i dont have access to it
crystal charm
ok.... i dont have access to it
you have the studying role on, probably that's why
type in ,iamnot studying in #bots if you wanna remove it 
odd tartan
,iam notdying
clever fjordBOT
odd tartan
,iamnot dying
clever fjordBOT
Removed the studying! role from you.
odd tartan
there we go
crystal charm
alright I guess here as well
clever fjordBOT
Gave you the studying! selfrole.
frank inlet
bro can you be serious
do i look like im joking
odd tartan
love how they see 'dying' as 'studying' lol
bitter folio
please
bitter folio
do i look like im joking
i do not understand you at all
frank inlet
geometra and algebra connected so you cant run
bitter folio
geometra and algebra connected so you cant run
and you dismiss my questions
of course bruh thats why i am bashing
odd tartan
geometra and algebra connected so you cant run
finally, someone who understands it
frank inlet
i want to show you the equation but ive been warned b4
odd tartan
are we all confused?
bitter folio
whatever im opening a new one later
frank inlet
we can simplify the equation
the big equation in the middle, u can simply it. is that clear enough?
bitter folio
the big equation in the middle, u can simply it. is that clear enough?
yes
i am not asking that question
frank inlet
so what?
bitter folio
But why the -b at the end? Help is appreciated
.
bitter folio
<:reallyMad:1399553225408905216> so what?
Bro check what i asked
bitter folio
i spoke english tho or u dont understand
ok i am done with this
why is the foot of the perpendicular having a -b term
do you understand that
frank inlet
@fair token
frank inlet
why is the foot of the perpendicular having a -b term
ur question is why is it '-b' or?
d must be expressed as a linear combination of ab, when u simply it, it'll subtract to b
it's not arbitrary
ur question is not exactly clear. u couldnt just say that i missed smth cuh
crystal charm
<:reallyMad:1399553225408905216>
<@&268886789983436800>, at this point you're just trolling rather then helping
bitter folio
ur question is not exactly clear. u couldnt just say that i missed smth cuh
ok bro
frank inlet
<@&268886789983436800>, at this point you're just trolling rather then helping
great another warning.
bitter folio
bump for more serious people
frank inlet
well i tried. really getting into your appreciation
bitter folio
.close
odd edgeBOT
digital shore
why is the name different
odd tartan
what
bitter folio
why is the name different
i changed
odd tartan
Have a great day <@905131558028050503>
ah ok
bitter folio
digital shore
oh ok
odd edgeBOT
Available help channel!
upbeat stump
odd edgeBOT
upbeat stump
Guys how to draw a cot graph? A sec graph and a 1/sin graph(I forgot the name)
unkempt lichen
(the last one is cosecant/cosec)
upbeat stump
Thanks👍
But like, idk wtf happens when I 1 over those graphs
Like how do ik the way the graph shifts
.close
odd edgeBOT
odd edgeBOT
Available help channel!
wet ferry
does anyone know how to date a sample using the quantity of Carbon 14 as well as it's activity ?
wet ferry
cause the only methods i've seen is by calculating the ratio C14/C12
mystic saffron
like in irl
odd edgeBOT
@wet ferry Has your question been resolved?
odd shell
odd edgeBOT
odd shell
This question seems quite tough
errant gust
what have you tried? drawing a diagram would probably help
modest nacelle
What kind of notation is 1·2 m? Decimal point, or multiplication?
glass vault
first you should find the horizontal distance to the baloon so you have something to compare the 60 and 30 degree cases
odd shell
what have you tried? drawing a diagram would probably help
Roger
Let me try drawing a diagram
This is the diagram given
I am assuming to start with Triangle PST and write PS/ST= tan60
odd shell
What kind of notation is 1·2 m? Decimal point, or multiplication?
1.2 m refers to distance
magic hedge
This question seems quite tough
What have you done as of now
Try and sketch a diagram on paper
odd shell
Ok
magic hedge
I am assuming to start with Triangle PST and write PS/ST= tan60
That's right
You can kinda neglect the girl's height here as it doesn't affect horizontal distance
odd shell
odd shell
You can kinda neglect the girl's height here as it doesn't affect horizontal dis...
Got it
Done till here
odd shell
Ah ok
magic hedge
Do the same thing
odd shell
Yup
magic hedge
Alright cool
odd shell
.close
odd edgeBOT
magic hedge
It's been closed already
modest nacelle
1.2 m refers to distance
The book writes 1·2 m, though, not 1.2 m. Usually middle dot indicates multiplication.
odd shell
The book writes 1·2 m, though, not 1.2 m. Usually middle dot indicates multiplic...
Printing mistake most probably
But yes , you are right
odd edgeBOT
Available help channel!
celest osprey
odd edgeBOT
vernal yacht
question 7?
north sparrow
pick a point in it like (100,50) and see which of the conditions break?
celest osprey
Yes
Q.7
@weary pelican if you say that W is not a number, then it is not a real number
If 27 is the only nice solution
It is the only real solution to the problem
Un nice solutions won't be considered as real solutions
celest osprey
pick a point in it like (100,50) and see which of the conditions break?
How?
Where does this 100 and 50 come from
Why do we need to see if the conditions break by the way
north sparrow
pick a point in it like (100,50) and see which of the conditions break?
wait (100,20) would work better, i eyeballed a value from your drawing but the x - 2y >= 0 is drawn a bit inaccurately
north sparrow
Why do we need to see if the conditions break by the way
it’s a test to see which side of the line contain points satisfying the constraint
if it is not satisfied, the other side (the one not containing the test point) is the good one
celest osprey
Constraint?
north sparrow
x-2y>=0 is one of the 3 constraint on x and y for example
celest osprey
Oh the conditions
So after making the graph we also have to test which region satisfies
.close
odd edgeBOT
odd edgeBOT
Available help channel!
gusty jolt
I need help finding the equation for the red line in the image. I have no idea where to start from
amber veldt
I need help finding the equation for the red line in the image. I have no idea w...
so if you know two points do you know how to find the equation of a straight line between them?
gusty jolt
tangency point?
amber veldt
nope
for example
let's say a line goes through (0,0) and (-2,4)
can you find the equation of that line?
amber veldt
so you just need to find the two points here
gusty jolt
mhm
amber veldt
it looks like the red line and blue curve cross the x-axis at the same point
what are the roots of y=ln x?
where does y=lnx=0?
gusty jolt
so x=1
gusty jolt
1,0
amber veldt
(1,0) you mean, yes
halfway there
for the other point, they tell you whjat the x-coordinate is
(e^a, ?) we just need the y-coordinate
any ideas
gusty jolt
nope
amber veldt
well if y=ln x is the general curve of the blue line
than y evaluated at x=some particular x is the y-coordinate of that point
for example, at x = 2, you have the point (2, ln 2)
gusty jolt
so at e^a would be (e^a, ln e^a)?
amber veldt
yes! but it simplifies
remember e^x and ln x are inverses of each other, meaning
e^(ln x) = x for all x >0
ln(e^x) = x for all x
amber veldt
needs more parentheses
gusty jolt
y=a/(e^a-1)*(x-1)
amber veldt
,w plot y=ln x, x=e^2, y=a/(e^2-1)(x-1)
clever fjordBOT
gusty jolt
yeah exactly
clever fjordBOT
amber veldt
noooo
whatever
its because i left in a
,w plot y=ln x, x=e^2, y=2/(e^2-1)(x-1), x = e^2
clever fjordBOT
amber veldt
there we go
gusty jolt
thanks for your help
amber veldt
gusty jolt
.close
odd edgeBOT
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vast crater
Apparently one of these is wrong but i cannot figure out which one
unkempt lichen
2 and 3 look wrong
vast crater
wait why would that be
for #2 isnt it simmilar to the first one
where like x=0 and then y=0 and 0=0
for #3 simmilar thing
unkempt lichen
wait nvm my dumbass legit misread #2
#3 i can almost guarantee it's not a unique solution
look at row 3
unkempt lichen
yes. if there is an all-zero row, there is at least one free variable
lavish slate
How does one get started on this?
odd edgeBOT
How does one get started on this?
rough birch
whenever a problem has tangent circles, it's always a good idea to draw radii from centers of circles to tangent points
you often can form straight lines or right angles
draw those first, see what you can infer about the resulting shapes
lavish slate
draw those first, see what you can infer about the resulting shapes
Alr
It's late, so I will try tomorrow, but thanks
.close
odd edgeBOT
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random thunder
they seperate NRMA and country road but dont they earn interest together in the last 10 days leading up to the bill being paid?
like for eg i brope my answers down into two parts
3rd - 26th august: & 27-6th september
you get the same answer nvm
i realised there was an unrelated error in my calcs
.close
odd edgeBOT
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serene patio
Cross Product
I watched 3blue1brown cross product in the light of transformation
At 8:23, he says that x(v₂* w₃ - v₃ * w₂) is the same as ihat(v₂* w₃ - v₃ * w₂) however ihat is a unit vector and is equal to 1 while x could be any number.
serene patio
can someone explain why is x and i hat can be said as same
wooden python
(previous channel on the same question: #help-3 message)
but i will repeat that "x and i are the same thing" is a misconception
they are 'related' in the sense that i, the vector, is parallel to the x-axis
!noclopen btw
odd edgeBOT
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
@serene patio Has your question been resolved?
odd edgeBOT
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toxic meteor
Guys does this have a limit
odd edgeBOT
Guys does this have a limit
toxic meteor
tall ivy
At 0?
toxic meteor
Yes
tall ivy
It should, yes
toxic meteor
How
tall ivy
Do you know the l'hopital rule
tall ivy
Ahhh yes, yeah it shouldn't, mb
toxic meteor
So it doesn’t have a limit
marble laurel
$\frac{\cos(x)}{\sin(x)} = \cot(x)$
tall ivy
I was counting on an extra x, but it's just gonna be 1/x
clever fjordBOT
VulcanOne
tall ivy
So it doesn’t have a limit
Yeah it does not
odd edgeBOT
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ashen hatch
Let m and n be positive integers where m≥n
1/m+1/n=2/33
Find the maximum value of m-n
ashen hatch
pretty damn sure the answer is ||m=561, n=17. thus, it's 544||
mystic nova
,calc 1/561 + 1/17
clever fjordBOT
Result:
0.060606060606061
,calc 2/33
clever fjordBOT
Result:
0.060606060606061
I rearranged the terms as (2m-33)(2n-33)=1089
it is probably possible to rearrange in the form of 1m
mystic nova
,w factor 1089
ashen hatch
(nvm it's not. it wouldn't be an integer value)
clever fjordBOT
mystic nova
,calc 363*3
clever fjordBOT
Result:
1089
Result:
198
m=198, n=18
clever fjordBOT
Result:
1089
Do you know how to find these cases?
ashen hatch
2m-33=121
m=72
ashen hatch
Do you know how to find these cases?
yeah, just throw in the factor and calculate
cedar path
Hi teacher, I have a question about proofs.
When we want to prove certain statements, we sometimes use proof by contradiction. This involves assuming a false statement, which then leads to a contradictory conclusion. From this, we can infer that the negation of our initial assumption must be true—and this negation is often the statement we set out to prove.My question arose while working on proving that the recursive sequence defined by $(x_n = \frac{2}{3}\left(x_{n-1} + \frac{1}{x_{n-1}}\right))$ converges to (\sqrt{2}), using Newton’s method (or more generally, when proving the convergence of this sequence to the square root of 2).I’ve looked at solutions where the approach is to assume the sequence converges to some limit A. After some steps, this leads to solving the equation (A^2 = 2). Here’s my confusion: shouldn’t we first prove that the sequence converges before assuming it has a limit A? why can we use the assumption as a tool, doesn't this lead to circular reasoning?
clever fjordBOT
Starland
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
summer wave
yeah you should prove it has a limit
wanton bison
This approach is more like a way of "guessing" some upper or lower bound which then hopefully you can use to prove the sequence is bounded
This is often done in combination with the monotone convergence theorem
cedar path
This approach is more like a way of "guessing" some upper or lower bound which t...
how does this "guessing" work, when we don't know we've guessed correct or wrong?
wanton bison
that's what is called a guess
odd edgeBOT
cedar path
.reopen
odd edgeBOT
✅
summer wave
I was wondering what you meant
summer wave
if the following implication make sense?
by this
wanton bison
i was wondering too and then forgot this channel
btw closing/reopening shouldn't be done, so your channel appears above others
summer wave
no, I was typing after he closed, that's why
wanton bison
Though, I don't know what to say further; again, by taking the limit (even illegally) you are trying to find a possible upper/lower bound (depending on how your sequence behaves monotonically) that you can then use to prove your sequence is bounded somehow. That bound can fail to work of course, and also by "taking the limit" you are not trying to use that as a proof that the sequence converges, but rather you are doing scratch work.
this channel is occupied
you can get one in the available list
summer wave
Also, sometimes you can prove a sequence diverges by assuming it has a limit
odd edgeBOT
@cedar path Has your question been resolved?
summer wave
newton's method isn't always monotone though
faint knot
Hi teacher, I have a question about proofs.
When we want to prove certain state...
you can assume it in either direction, because you still have to prove that it converges regardless of the order you choose
odd edgeBOT
odd edgeBOT
Available help channel!
trim kiln
Hello! I'm working on math homework at the moment, and I need to figure out how to factor this trinomial. I couldn't do it using the X method my teacher taught me, so I'm kinda lost
trim kiln
summer wave
did you find any roots?
trim kiln
You mean √ the trinomial?
Also, I have a question- can you factor a trinomial by using the quadratic formula or am I misremembering
elfin zodiac
You can complete the square and after the difference of squares and you got your factored form.
late dust
Also, I have a question- can you factor a trinomial by using the quadratic formu...
You can
Mind telling us what the "X method" is?
summer wave
after looking it up on the internet, it's a rather mysterious method...
I think it works on "nice" polynomials only
trim kiln
So basically, I was taught that a trick you can do is to multiply the first and last # in the trinomial, then split the center number into two factors that multiply to make one and add to make the other
Mb if it's worded weird
trim kiln
I think it works on "nice" polynomials only
Yeahhh it only works on certain kinds
cursive pendant
just do the quadratic😭
late dust
Right, that method works but good luck finding the correct numbers in this case
summer wave
I would advise you to just doing the quadratic as well
elfin zodiac
You should start by factoring out 5, so your polynomial is easier
late dust
Tbh if you're going to use the quadratic formula, factoring 5 doesn't matter
(I mean kinda, depends if you understand it correctly)
trim kiln
he said no formula right?
Who? Me?
elfin zodiac
wasn't you talking about a mysterious x method? 😄
trim kiln
Ohhhh yeah that lmao
elfin zodiac
whatever, you can do this in tons of ways
learn them all
so you can choose the best on each case
late dust
Any other question?
trim kiln
Hold on, give me a moment
Okay, so I got
-40 ± 6√10
10
(Which I feel like I could probably simplify to -40 ± 6√10/10)
trim kiln
This might be hard to write
Isn't it:
-b ± √b² - 4ac
2a
Ok you can use sqrt(...) for the square root, b^2 for the square, and just parenthesize the numerator and denominator so you don't have to write it in multiple lines
So like that:
(-b +- sqrt(b^2 - 4ac)) / (2a)
(+- to be interpreted as "plus or minus" of course, not +(-(...)) )
Anyway, we have a = 5, b = 40, c = -10, right?
trim kiln
Yeah
late dust
(-40 +- sqrt(40^2 - 4*5*(-10))) / (2*5)
40^2 - 4*5*(-10) = 40^2 + 5*40 = (8+1)*5*40
Do you agree with that?
trim kiln
40^2 - 4\*5\*(-10) = 40^2 + 5\*40 = (8+1)\*5*40
It makes sense up until the (8+1) part
Where does that come from?
late dust
Just factoring
Ok hold on I'll try making it clearer
$$40^2 - 4 \cdot 5 \cdot (-10) = 40^2 + 5 \cdot 40$$
$$= 8 \cdot 5 \cdot 40 + 5 \cdot 40 = (8+1) \cdot 5 \cdot 40$$
$$= 3^2 \cdot 5^2 \cdot 2^2 \cdot 2 = 30^2 \cdot 2$$
trim kiln
Ohhh okay
clever fjordBOT
Nel
late dust
Yeah?
So (-40 +- sqrt(30^2 * 2) ) / (2*5)
= -4 +- 3sqrt(2)
(your 6sqrt(10) was off)
trim kiln
Alright
That kind of makes sense
late dust
It's just boring calculations, practice and you get better
late dust
If it's related to the question, sure
trim kiln
https://cdn.discordapp.com/attachments/1110223603355623454/1410382058886271196/1...
When do you ever use the secret second one /genq
Is it for checking your answer or smth else
noble ether
No
It comes by rationalisation of the original formula
It's just there
It's pretty neat
Tho
late dust
In some situations when you're doing numerical stuff you can get poor accuracy with one formula and better with the other
Probably used by some software, but idk enough about that
Not very useful to learn either way
trim kiln
Ok
Thank you!
late dust
So anyway, the factorization is 5(x - root1)(x - root2)
noble ether
Well
The first formula has a clear preference
Because if c = 0
Then the second one only yields one root
Yet
The other can be easily figured out
late dust
Tbh if c=0 you don't need a quadratic formula
late dust
Sure
noble ether
Yet if we consider the penultimate case, if a = 0, the original formula becomes undefined
As it isn't a quadratic
At that point
Neither does the second
So first better
trim kiln
.close
odd edgeBOT
late dust
Neither does the second
The second does give you the answer if a=0, just the other half is undefined
odd edgeBOT
Available help channel!
mighty granite
odd edgeBOT
mighty granite
im at after the quadratic formula my problem is with X2=-(5/3)
vivid wyvern
Can u show ur work?
vivid wyvern
How did u get the values of x here?
mighty granite
i just put it into the quadratic formula and got those two
vivid wyvern
i just put it into the quadratic formula and got those two
I'll be check that but did u try middle term splitting
mighty granite
i did not, ill try
sweet dagger
I thought there was a spider there 😵💫
vivid wyvern
Seems correct
mighty granite
I thought there was a spider there 😵💫
it was '*'
vivid wyvern
it was '*'
Asterisk
mighty granite
Seems correct
sorry im just having a problem cause its a fraction in a fraction
and those are scary
vivid wyvern
sorry im just having a problem cause its a fraction in a fraction
In a fraction?
mighty granite
yea, coz i have to put in the original formula to show that one side is equal to the other
like to show my work and stuff, thats what after i got those x1 and x2 i started putting them in the formula. coz i need to also write that why they would work
vivid wyvern
like to show my work and stuff, thats what after i got those x1 and x2 i started...
Did u do it?
mighty granite
yea at the bottom u can see i tried X2, failed, put an asterisk to mark that i was having a problem and moved on
vivid wyvern
yea at the bottom u can see i tried X2, failed, put an asterisk to mark that i w...
Lemme check
,rccw
clever fjordBOT
mighty granite
yes i added together the -7 to it
and thats the fraction i got
26/5
OHHH
my bad
ill try again
vivid wyvern
Yea i did it and got the same answer on both sides,so it works
vivid wyvern
Np,good work
mighty granite
.close
odd edgeBOT
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tiny talon
hi is there a way to deform a trefoil (where it has a rope and we only consider the surface) into a torus
tiny talon
im not sure if it is homeomorphic to torus but i dont see what else it could be
im looking for a more visual explanation than a formal proof, thanks
if this is not the right place to ask, can someone redirect me
west light
im not sure if it is homeomorphic to torus but i dont see what else it could be
It could be not homeomorphic to a torus.
pastel orbit
hi is there a way to deform a trefoil (where it has a rope and we only consider ...
remember that any knot is the image of an embedding of S^1 into R^3, including the trefoil
tiny talon
im currently not at the level to know much topology and manifolds
pastel orbit
that means the trefoil is homeomorphic to S^1, which isn't homeo to the torus
pastel orbit
im currently not at the level to know much topology and manifolds
ah, hm
pastel orbit
I mean, one way to think about this is that a trefoil is 1-dimensional - if you stand on it, it looks locally like a line
tiny talon
i did try a lot of methods to try to turn it into one
pastel orbit
whereas the torus is 2-dimensional
it looks flat locally when you stand on its surface
so they can't possibly be the same object, no matter how we perform our deformation
tiny talon
sorry by trefoil i didnt mean the actual knot. i was describing how the shape looked, which consisted of a trefoil done by a rope, and isolating the surface of the rope
west light
Ah then yes that's homeomorhic to a torus.
tiny talon
im not sure how to deform it to make it a torus
tiny talon
i see. i think i was given a temporary definition
in which you could deform one to another and call it homeomorphic
sorry if that messed stuff up
west light
Yes, it does apply in one direction
If you can deform one to another continuously without self-intersection etc, then they're homeomorphic.
But not all homeomorphic objects can be deformed to each other in this way.
tiny talon
oh i see. i guess ill get to that later
this does solve my question though thanks
.close
odd edgeBOT
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Available help channel!
blazing valve
odd edgeBOT
blazing valve
Im not understanding what this problem is asking for 😭
lone elbow
, rotate
clever fjordBOT
meager juniper
@blazing valve looks like a related rates problem
Notice that the point (x,y) is always on a particular circle. And notice that this point on the circle is a particular distance from some point. How can you relate, for instance, the distance from the top of the building to some point (x,y)?
Because this is a related rate problem, you'll be chaining together several different variables using a few different equations.
blazing valve
😭 uhh the a2 + y2
Is
C2
But im not understanding how the rope is changing rate
Like its pulled towards rhe building ?
odd edgeBOT
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Available help channel!
flat furnace
hi i need help doing basic algebra, i think its distributive property but i cant seem to find a yt vid for an equation like this, idk i just dont know how to look for it on yt, please help me understand
lavish jackal
which question?
flat furnace
um .. i guess just the concept in general
sorey im just struggling with this right now
lavish jackal
im guessing u stuck at 2nd question?
flat furnace
yeahhhh
lavish jackal
well try distributing 4.2(15+5x) first
flat furnace
yup
lavish jackal
no
indigo dirge
21x - 21 ?
ur missing a negative sign, do you see where and why?
flat furnace
OHH -21x
flat furnace
-21x - 21 ??
lavish jackal
yes
flat furnace
so then what do i do
lavish jackal
move the x's on left side and the numbers to the right side
just to make it easier to solve
for x
flat furnace
wait what do you mean