ohh
#help-36
crisp spade
see if you can make this out
normal shuttle
They have a rate
normal shuttle
I got it
normal shuttle
if you can't I can't help you
A littlr unnecessary but thank you
dense badge
imo you can also do it with trig if you prefer that
dense badge
normal shuttle
Im intrigued
dense badge
then pythagoras or more trig for AB the base of ABCD
final saddleBOT
final saddleBOT
Available help channel!
outer grove
Hello does anyone know how to get the distance between two angles, so distance of angle A to angle B? (maybe the correct word is difference)
final saddleBOT
Hello does anyone know how to get the distance between two angles, so distance o...
pliant shore
Hello does anyone know how to get the distance between two angles, so distance o...
what information do you have already?
steel talon
!original
final saddleBOT
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.
outer grove
what information do you have already?
im not sure what information your interested in, im coding this thing
it isnt a school thing
so
pliant shore
im not sure what information your interested in, im coding this thing
cause it's just the distance between two points, which you can use the distance formula for
outer grove
i have a angle which is a car's perpendicular angle then another angle which is the direction of its velocity
pliant shore
i have a angle which is a car's perpendicular angle then another angle which is ...
do you have a picture of this?
I think you mean vectors when you say 'angles' but I need to confirm
outer grove
cause it's just the distance between two points, which you can use the distance ...
sorry this might be due to my poor explanation but positions shouldnt be a factor, it should only use angles
outer grove
do you have a picture of this?
okay
outer grove
I think you mean vectors when you say 'angles' but I need to confirm
possibly, im sorry for my wording
ill show picture
i dont think a picture will help but ill show a picture
fiery pine
I think you mean vectors when you say 'angles' but I need to confirm
it could be like angle pi/2 is the straight up direction
and pi is “west”
outer grove
do you have a picture of this?
like i said, im not sure what information you are seeking because im making a car game, there is no other information except the rest of my irrelevent code and 2d picture of a car
fiery pine
yknow
pliant shore
like i said, im not sure what information you are seeking because im making a ca...
okay, why do you want to find the distance between those two vectors?
what are you trying to achieve
outer grove
okay, why do you want to find the distance between those two vectors?
so im making a car game, i need the distance between two angles, angle A is the car's direction of movement/velocity then the car's perpendicular angle. If i get the difference or distance between these two directions/angles then i can dampen the car's velocity to make it stop drifting.
im not very good at explaining the car's physics because this is my own super simplified idea of it
you know how when a car drifts, it slows down really quickly
pliant shore
one sec
outer grove
ight sorry for loading my poor explanations on you
You know when cars do this, you notice their velocity or speed slows down really really quickly
pliant shore
You know when cars do this, you notice their velocity or speed slows down really...
yes, I know what drifting is
outer grove
their wheels angle/direction doesnt line up with their velocity
pliant shore
like i said, im not sure what information you are seeking because im making a ca...
wait so which arrow is the direction of the car's wheels here?
outer grove
im trying to make my car slow down when the direction of the car and its velocity are very distant
outer grove
wait so which arrow is the direction of the car's wheels here?
in the first picture i sent?
pliant shore
in the first picture i sent?
yes
outer grove
yeah so i simplified it and have just made the wheels simulated, so the front wheels will always just point in the direction of the car, (for now)
so the "wheels" are really just the car's direction
pliant shore
so the "wheels" are really just the car's direction
ohhh, and the red arrow in that picture is the car's velocity?
outer grove
ohhh, and the red arrow in that picture is the car's velocity?
oh sorry about that, i had that painted on the car so i knew which direction the car is facing
heres the velocity variables
pliant shore
oh sorry about that, i had that painted on the car so i knew which direction the...
this is my best guess but I think you're looking for vector addition
have you ever heard of the parallelogram rule?
outer grove
this is my best guess but I think you're looking for vector addition
what is that
outer grove
have you ever heard of the parallelogram rule?
no
pliant shore
pliant shore
no
you add the two vectors together by making a parallelogram
the two vectors that are relevant to drifting are the velocity and the frictional force
you add those together
and then you can show the car will move in the direction of the orange arrow
outer grove
yeah, i already solved that part, can i show one video to show an idea and if we dont get it from there, ill try another time with a better explanation or with some better knoledge
pliant shore
I find it hard to believe you solved that part without knowing how to add (and subtract) vectors
outer grove
to show i already have the two vector thing down but to also show something else. i get the car to accelerate then i stop accelerating and the car slows down then i do it again BUT this time, i accelerate the car and let go of the accelerator (w key) and turn the vehicle 90 degrees, and it slows down at around the same pace. Real cars would slow down much faster when facing perpendicular to its velocity (drifting)
sorry ill convert it
pliant shore
to show i already have the two vector thing down but to also show something else...
well if you want realistic drift
you have to model the car as being on a circular track (this is an idealisation of course)
then there will be some friction pushing the car to the inside of the circle
yeah I think you understand that concept from what you wrote
pliant shore
yeah cause you're not adding the velocity vector and the friction vector in your code, right
so your car will always be moving in a straight line
even if it is rotating while it's moving in a straight line
outer grove
yeah cause you're not adding the velocity vector and the friction vector in your...
sorry heres a better video to show the vector thingy
pliant shore
oh that's interesting
yeah I'm out of my depth here then
honestly just share your code and someone else can take a look at it
well if it's Scratch then you have to take screenshots ofc
outer grove
honestly just share your code and someone else can take a look at it
well if it'...
okay thats good idea
.close
final saddleBOT
pliant shore
honestly just share your code and someone else can take a look at it
well if it'...
cause I have no idea how the car behaves
final saddleBOT
Available help channel!
woeful void
Is this how I would prove that if m|x and n|x and gcd(n, m)=1 then nm|x
Since m|x, there exists an integer p st x=mp, similarly, there exists integer q st x=nq
And since gcd(n, m)=1, using Bezout’s identity there are integers a and b such that an+bm=1
1x = x therefore x=mp(an+bm)
x=mp and therefore x/p=m, nq/p=m
Substitute, x=mp(an+bnq/p), take the n out and put p in, x=mn(ap+bq), therefore mn|x
final saddleBOT
Is this how I would prove that if m|x and n|x and gcd(n, m)=1 then nm|x
Since m|...
lofty seal
If 𝑚∣𝑥, what does that tell you about x?
Can you express 𝑥 in terms of m and some integer?
final saddleBOT
@woeful void Has your question been resolved?
timid jasper
Why can't i divide z with either x or y before adding the two values in
x+y/z
rancid zenith
Not sure what you mean
Assuming you have the correct bracketing, you can divide y by z and then add x. Thats what that notation means.
If you meant (x+y)/z, you can divide x and y individually by z then add as well
final saddleBOT
@timid jasper Has your question been resolved?
timid jasper
If you meant (x+y)/z, you can divide x and y individually by z then add as well
Ok but can i divide z with x as well?
dusty quarry
if you actually meant (x+y)/z, it's the same as x/z + y/z
rancid zenith
Ok but can i divide z with x as well?
What?
timid jasper
if you actually meant (x+y)/z, it's the same as x/z + y/z
Well the equation was 6+x/2
And i divided 2 with 6 but apparently it's not right
dusty quarry
Well the equation was 6+x/2
And i divided 2 with 6 but apparently it's not righ...
could you show the original question?
rancid zenith
The brackets tell you what to evaluate first
(6+x)/2 is saying: first add up 6 and x then divide the result by 2
6+x/2 is saying: add up 6 and the result of dividing x by 2
rancid zenith
or this
The bracketed version corresponds to this
The unbracketed version is the other one
dusty quarry
!done
final saddleBOT
If you are done with this channel, please mark your problem as solved by typing .close
timid jasper
6+x/2 is saying: add up 6 and the result of dividing x by 2
I transpose 2 to the other side and it ends up as 6+x/2 like this eqn.
Should there be a parenthesis or not? I'm confused about that
Also could u give any examples of how an eqn could end up as 6+x/2 ?
I can't really imagine any equations where there isn't a parenthesis
@dusty quarry
dusty quarry
wait wait wait
i don't see an equation
there's no equal sign
this is an expression
unless you have the full question?
timid jasper
what are you asked to do?
Solve for y
I was solving for multiple variables including x so it kinda confused me
severe canyon
Well, if x = 2, what's the value of 6 + x?
dusty quarry
if you're asked to solve for y i think you got the right answer already? what are your steps and your final equation in terms of y?
timid jasper
Well, if x = 2, what's the value of 6 + x?
2
timid jasper
if you're asked to solve for y i think you got the right answer already? what ar...
No I'm just confused as to whether there should be a bracket or not
dusty quarry
huh??
dusty quarry
No I'm just confused as to whether there should be a bracket or not
depends on how you write it
timid jasper
Yeah
dusty quarry
i mean when writing on paper
i hope you are not writing like you do here?
and using proper fraction notation?
timid jasper
Ofc
timid jasper
but more importantly how is this 2
Because that's the value of x
I solved for it
Do u need to see how i solved it
dusty quarry
but he asked for 6+x given x = 2
anyway
so have you gotten the final equation in y?
timid jasper
so have you gotten the final equation in y?
Well yeah it's 4
Pls ping btw
But i don't know if i should add a bracket or not
final saddleBOT
@timid jasper Has your question been resolved?
timid jasper
Someone helpi mi
final saddleBOT
@timid jasper Has your question been resolved?
timid jasper
.close
obtuse knoll
so i have the following question:
f: [0,1]->R is a continous function, such that f(0)=0, f is differentiable on 0 from the right and f(x)>0 for every x in (0,1]. we need to prove that the improper integral from 0 to 1 of 1/f(x) diverges.
my idea: we use the fact that it's differentiable on 0 from the right, which means that the limit of f(x)/x as x approaches 0 from the right exists. we then say that f'+(0)=L and say that it has to be positive using f(x)>0, and then we pick an epislon such that L+epsilon=1, and then put that epsilon in the in the limit defintion and get a delta such that for every x in (0,delta) we get that 1/x < 1/f(x).
we know that the improper integral from 0 to delta of 1/x diverges, so anything bigger than it will also diverges
we then separate the improper integral of 1/f(x) to two integrals and say that since one diverges then the original integral also diverges
final saddleBOT
so i have the following question:
f: [0,1]->R is a continous function, such that...
obtuse knoll
i'm not 100% sure about my solution and I haven't really tried to formally prove it
tired walrus
well your idea is basically that your function kinda behaves like Lx near 0 right
obtuse knoll
my idea is basically finding a window between 0 and a number between 0 and 1 where 1/x < 1/f(x) and then from that we can conclude that the improper integral diverges
although theres an issue where if L>1 then we cant pick a positive epsilon such that L+epsilon=1
obtuse knoll
well your idea is basically that your function kinda behaves like Lx near 0 righ...
if we pick a small enough epsilon then yeah it should behave like Lx
tired walrus
so i think the play here is to bound f(x) from below by Lx/2
ie say that f(x)/x is greater than L/2 in an epsilon nbhd of 0
obtuse knoll
what exactly is from below? i dont study in english
grave fossil
just wanted to check if this is a legal a way to solve this problem if i didnt want to use tan⊖
final saddleBOT
just wanted to check if this is a legal a way to solve this problem if i didnt w...
grave fossil
:)
tired walrus
if you're tan-phobic then yes
final saddleBOT
grave fossil
.reopen
final saddleBOT
✅
grave fossil
why is tan applicable here
zenith cedar
?
tired walrus
i mean tan(theta) = Q_y/Q_x it's fairly simple
tired walrus
there is a right triangle involved yes
grave fossil
niceeee
tired walrus
same reason why you were able to do cos(theta) = Q_x/|Q|...
final saddleBOT
grave fossil
.reopen
final saddleBOT
✅
grave fossil
nvm nvm co pilot ftw
i'll keep it open for a while around 5-10mins if no question arise i'll close it
thank you!
✅ or ❌?
warm python
theta is the angle b/w r and x?
grave fossil
Yea
warm python
check sin again
warm python
ya
grave fossil
So sin=y/r
warm python
sin and cos are interchanged
grave fossil
Thanks
should be correct, but i want to know is there any other way i can solve this problem?
prisma forge
yes
grave fossil
What would be it
prisma forge
to your hearts desires
just gotta believe in the me that believe in you
all poetic and shit
final saddleBOT
final saddleBOT
Available help channel!
grave fossil
Answer is wrong, i just don’t where i went wrong? Do i have to always swap for row 1?
final saddleBOT
Answer is wrong, i just don’t where i went wrong? Do i have to always swap for r...
grave fossil
dusty quarry
wait were you the one i helped the other day with this also
grave fossil
different question but yes :(
edgy mauve
Cramer's rule
eager shore
Cr*mer's rule
grave fossil
nah
dusty quarry
don't think he learnt it yet
edgy mauve
Mentioned matrix tho
grave fossil
EROs
dusty quarry
if you're confident you don't necessarily have to, but this is a structured way to do this, yeah
i recommend following this
grave fossil
ooo
dusty quarry
minimizes chances of randomly making careless mistakes
eager shore
,w solve 2x - y + 3z = 9, x + y + z = 6, x - y + z = 2
soft zealotBOT
eager shore
yeah honestly just follow thw algorithm
grave fossil
i have the answer i have done correctly previously somehow
"somehow"
but this was a different approach
dusty quarry
try this again, but this time, start by swapping either r2 or r3 up to r1
oh so you have done this before
grave fossil
yep took me two pages of EROs to solve this
dusty quarry
ah i see what happened here
grave fossil
wanted to solve it one page but eh
dusty quarry
r1 - r2 into r1 right
column 1 is 2-1 = 1, correct
column 2 is -1 - 1 = -2, not 0
grave fossil
thank you!
out of topic, but did you guys get interviewed for helpers role in the server?
grave fossil
ayo
dusty quarry
but be prepared for ping after ping
dusty eagle
you can just grab em
Yes
grave fossil
ayo wha
dusty quarry
yea
cuz when people wait too long, they're gonna ping helpers
not uncommon for me to come back from school to 5-6 pings
dusty eagle
not uncommon for me to come back from school to 5-6 pings
Only????
dusty quarry
Only????
depends of course
just an example
but most problems either get ignored and OP forgot about them
or they get solved too quickly for the helper ping to come up
but some people also forgot about this rule and ping helpers straight away
!15m
final saddleBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
dusty quarry
so yeah if you want to be notified of others needing help grab the role
yes you can! i mean i suck at math but i still grabbed it
grave fossil
no way, you're way better than me
dusty quarry
nah
grave fossil
eh
dusty quarry
anyway, any other questions?
we can talk about other stuff elsewhere, like in #chill
final saddleBOT
If you are done with this channel, please mark your problem as solved by typing .close
inner mountain
where did the 5 come from in the third line?
final saddleBOT
where did the 5 come from in the third line?
atomic moon
division by fraction <=> multiplying by the reciprocical
sage meteor
where did the 5 come from in the third line?
erm its literally written there though, 0,2 = 1/5
final saddleBOT
final saddleBOT
Available help channel!
lime crest
Prove that there exists a polynomial $P(x,y)$ with real coefficients such that $P(x,y) \geq 0$ for all real numbers $x,y$, which cannot be written as the sum of squares of polynomials with real coefficients
final saddleBOT
Prove that there exists a polynomial $P(x,y)$ with real coefficients such that $...
soft zealotBOT
Copter
terse crypt
!occupied
final saddleBOT
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).
lime crest
wait am i stupid
yes i am nvm 😭
$P(x)=x^4y^2+x^2y^4 + 1/27 -x^2y^2 \geq 0$ by AM-GM
soft zealotBOT
Copter
final saddleBOT
final saddleBOT
Available help channel!
inner mountain
confused on the third line first term
final saddleBOT
confused on the third line first term
terse crypt
,w integrate ln(x^2 - 1) + (2x)/(x-1)
soft zealotBOT
terse crypt
eh
stuck juniper
confused on the third line first term
What is the confusion
terse crypt
prolly how they go from 2nd to third line
i got how the thing is [ \ln(x+1) + \ln(x-1) + \frac{2x}{x-1}]
soft zealotBOT
k
stuck juniper
Did they even try it first 😨
Or are they just blindly copying whatever is being written
inner mountain
trying to figure it out
idk i got up to the second line and then checked the answers cos idk whats going on
terse crypt
@stuck juniper does the thing even simplify as (x+1)log(x^2 - 1)
inner mountain
in the first place i dont think i was taught how to integrate ln?
magic coyote
fix this
stuck juniper
in the first place i dont think i was taught how to integrate ln?
Bruhh
Are u ljke
Memorising the process
terse crypt
go learn chemistry
stuck juniper
This is occupied
stuck juniper
go learn chemistry
Bro is learning integration like inorganic 💀😭
@inner mountain do u know ur basics 🙏
Cause i saw u ask questions like why the 3 come and now ur doing this
terse crypt
stuck juniper
That’s plenty
inner mountain
like they taught this stuff?
terse crypt
u have time to cove the basic
terse crypt
like they taught this stuff?
yes
stuck juniper
like they taught this stuff?
This is supposed to be trivial
Ur like supposed to learn
Why it came
Instead pf memorising
Its almost like u learn integrals by understanding and not memorising 😔
terse crypt
Bro is learning integration like inorganic 💀😭
a valid hypothesis
stuck juniper
Even i learned definite integrals in one week
terse crypt
But i practiced 600 questions that week
wtf
thats prolly more than ive ever done tbh
in my entire math career
stuck juniper
Least work i have done for jee:-
terse crypt
oh dear
inner mountain
what was the original question
terse crypt
do u know ftc
inner mountain
no
stuck juniper
💀
terse crypt
if F is an antiderivative of f
[ \int_a^b f(x) \dd x = F(b) - F(a)]
soft zealotBOT
k
stuck juniper
Area
terse crypt
but the thing is always negative
terse crypt
Integrals give area
they should 😭 🙏
inner mountain
i do know that
terse crypt
ok
stuck juniper
🗣️🗣️ur not cooked
soft zealotBOT
k
terse crypt
am i right
inner mountain
yea???
inner mountain
OH MY GOD
terse crypt
whats [ \int_{-5}^{-2} \ln(x^2 - 1) + \frac{2x}{x-1} \dd x]
soft zealotBOT
k
terse crypt
tunnel vision happens to all of us
inner mountain
that i was already given the integration for that bit so the whole time i was thinking what rule i should use to integrate it
but like
the original function was already given to me beforehand
inner mountain
its got like 3 other topics in it
stuck juniper
If i was the teacher i woulda done the funny
inner mountain
but part of it would be on integration
stuck juniper
but part of it would be on integration
More like ‘copy whats given’ 🗣️🗣️
final saddleBOT
final saddleBOT
Available help channel!
slim wave
What's 4^5 times 8.9 divided by ⅛
final saddleBOT
What's 4^5 times 8.9 divided by ⅛
terse crypt
Calculator 😭
dapper hull
I don't know how to do the squared on a cal
what calc you using ?
slim wave
The Samsung app one
soft zealotBOT
Result:
72908.8
dapper hull
the x y thing next to the 1
terse crypt
dapper hull
write 4 then press it then do 5
slim wave
Oh ok thanks
dapper hull
thx 
dapper hull
Oh ok thanks
!done
final saddleBOT
Oh ok thanks
If you are done with this channel, please mark your problem as solved by typing .close
@slim wave Has your question been resolved?
heavy lance
how do i put these in my calculator? ive tried like 20 different ways and i cant do it right
final saddleBOT
how do i put these in my calculator? ive tried like 20 different ways and i cant...
dapper hull
all i need is the calculator format for a TI calculator non graphing
guess you just need to abuse brackets
heavy lance
has to be TI30X, which makes this 10x harder, cuz i cant use the other calculator
the other TI calculator (which is NOT allowed for the class) does it 100% correctly
the correct calculator doesnt work at all
dapper hull
guess you just need to abuse brackets
then still abuse the brackets
heavy lance
i tried that
my guess is you have to manually do one part at a time inside then outside type shennigans
dapper hull
do it one part at a time then (write the result on an outside paper so you don't forget the values)
dapper hull
think you could break it down for me
i'd start with the 0.055/4 find the value and add 1 (first)
write it out whatever you wrote exponentiate it to whatever the question asks (second) ofc write the value
then multiply by the starting value (the P)
i'll try to work it out on the side given these limitations and see what i'll get
heavy lance
try using the TI30X if you have it
as i said my other calculator did it successfully, unfortunately that calculator is banned for tests so itd be useless
dapper hull
try using the TI30X if you have it
i don't have so i did it as the way i said and answer is so close i got 39422.1
heavy lance
i see...
i wonder if anyone here has the required calculator
ngl i think its a calculator issue, not a math issue
dapper hull
the easier way work out the inner then go out a little by little
dapper hull
ngl i think its a calculator issue, not a math issue
yea i think so too
heavy lance
<@&286206848099549185> yo anyone here got a TI-30X calculator that can help me
this problem is restricted to that calculator
terse crypt
the fact that i recognise the app 
dapper hull
the fact that i recognise the app <:devilish:882819553686609981>
like who doesn't lol
ripe jewel
i don't
dapper hull
(photomath btw)
heavy lance
well then, google says you have to do the inside out using this calculator and im struggling to find out what the order is, as pearson doesnt tell you
dapper hull
well then, google says you have to do the inside out using this calculator and i...
a(b+c)^d
do b+c first
then ^d
then *a
heavy lance
What is each
Like what is a b c and d
For the example problem I sent
If I know it once I should be able to know it more then once
dapper hull
b is just the 1
c is r/n
d is nt
a is P
nocturne cedar
The polygon below represents the floor plan of a hall designed by an architect. Angles AJH and BCD each measure 135°, and all other angles formed by two consecutive sides are right angles. With the exception of segment AB, all other sides of the polygon measure 10 meters.
Given that √2 = 1.41, the area of this hall, in square meters, is
final saddleBOT
The polygon below represents the floor plan of a hall designed by an architect. ...
jagged flare
draw FJ, FC, CJ and calculate each part independently
nocturne cedar
edgy mauve
Area of Fcj?
At first with (1/2)×bh
Later onwards with heron's formula
To determine the side?
nocturne cedar
Bruh chat gpt cooked me
jagged flare
!nogpt
final saddleBOT
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).
nocturne cedar
At first with (1/2)×bh
Later onwards with heron's formula
Ya
I asked him what cos45 was he said sqrt2/2
jagged flare
At first with (1/2)×bh
Later onwards with heron's formula
you dont need herons lmao use sine rule
nocturne cedar
I asked him what cos45 was he said sqrt2/2
🥀
jagged flare
or better yet literally b×h/2
edgy mauve
Wait isnt cfj 90°
Cant we js find the hypotenuse which is x and proceed to find the area of rectangle
nocturne cedar
I did that
edgy mauve
No like 100 is bh
Area is supposed to be half of that
nocturne cedar
Area = 7*14=98 98/2=49
edgy mauve
7?
edgy mauve
R u finding the area of
wait lemme mark
nocturne cedar
R u finding the area of
wait lemme mark
Yes triangule
edgy mauve
edgy mauve
Half of the given triangle?
nocturne cedar
No
edgy mauve
Okay tell me how did u get the area which is 100
nocturne cedar
Don’t we just have to do cos45 =1/sqrt2
edgy mauve
Don’t we just have to do cos45 =1/sqrt2
That much is ryt
(I/2)bh is the area of triangle
nocturne cedar
Oh cause there’s a formula to find height
edgy mauve
So (1/2) 10×10
Gives u 50 ,that's supposee to be the area
edgy mauve
Oh cause there’s a formula to find height
?
nocturne cedar
edgy mauve
Similar triangles?
warm dagger
can anyone do my sparx maths for me?
edgy mauve
!occupied
final saddleBOT
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nocturne cedar
Similar triangles?
Uh
It’s just to find smth if it’s missing
In my case I knew hipotenusw = 14
And both b and c
So
10*10=14*h
edgy mauve
Makes sense
nocturne cedar
I see
I think x is wrong
Or
Well smths wrong
Lemme try to do it again showing my works
Better
nocturne cedar
How
nocturne cedar
Oh
edgy mauve
It's supposed to be ryt
We just to approximate values
Instead of exact
If we took exact ot would be 5sqrt2 which is approximately 7
edgy mauve
Yea
nocturne cedar
Now it should be easy
edgy mauve
No input this in hx=100
edgy mauve
And triangle
Yes that too
U could hv found the area of triangle without h and x anyway
nocturne cedar
Triangle area is 50
nocturne cedar
U could hv found the area of triangle without h and x anyway
How
edgy mauve
(1/2)bh
Since it's a right angle the perpendicular and base r h and b
So basically (1/2)bh
And there was a way to find x easily
Through pythagoras
nocturne cedar
Mhm
nocturne cedar
(1/2)bh
Since it's a right angle the perpendicular and base r h and b
Isn’t that what we did
edgy mauve
What area did u use for yhe triangle
nocturne cedar
Like formula?
edgy mauve
Isn’t that what we did
So ur area was 50?for the triangle
nocturne cedar
(b*h)/2
nocturne cedar
141
nocturne cedar
Ye it’s remember what I said just now
I put 1,414
Instead of 1,41 like the question said
final saddleBOT
@nocturne cedar Has your question been resolved?
woeful void
is this proof fine if i wanna prove that if a and b are odd integers then a^2-b^2 is a multiple of 8
since a and b are odd, they can expressed as a=2k+1 and b=2r+1 where k and r are integers
a^2-b^2=(a+b)(a-b)
a+b = 2(k+r+1)=2(k-r+2r+1), a-b = 2(k-r)
When k-r is even, a-b is a multiple of 4 and k-r+2r+1 is odd, thus a+b is a multiple of 2
When k-r is odd, a-b is a multiple of 2 and k-r+2r+1 is even and thus a+b is a multiple of 4
wlog assume that a+b is a multiple of 4, then 4|a+b and 2|a-b. Then 8|(a+b)(a-b)
final saddleBOT
is this proof fine if i wanna prove that if a and b are odd integers then a^2-b^...
rare girder
wlog? how do you know generality isn't lost?
is there a way to rewrite so that you don't even need to say wlog?
woeful void
well either way their product is a multiple of 8
dapper hull
you could from the step (a+b)(a-b)
rewrite it as 4(k+r+1)(k-r) and then try and show that
(k+r+1)(k-r) is even then it could rewritten in form 8(something) and it'll show it's divisible by 8
woeful void
sure, it just feels a little off by the wording
yeah idk how to fix it
woeful void
you could from the step (a+b)(a-b)
rewrite it as 4(k+r+1)(k-r) and then try and...
oh okay, what if i write (k+r+1)(k-r) as (k-r+2r+1)(k-r)? if k-r is even then so is (k-r+2r+1)(k-r), if k-r is odd then (k-r+2r+1) is even so (k-r+2r+1)(k-r) is too
a and b are both odd, this means a and b can be written as a=2k+1 and b=2r+1 where k and r are integers
a^2-b^2=(a+b)(a-b)
a+b = 2(k+r+1)=2(k-r+2r+1), a-b = 2(k-r)
Hence (a+b)(a-b) is a multiple of 4, 4(k-r)(k-r+2r+1)
If k-r is even then so is (k-r+2r+1)(k-r), if k-r is odd then (k-r+2r+1) is even so (k-r+2r+1)(k-r) is too, hence a factor of 2 can be taken out and thus 8|(a+b)(a-b)
dapper hull
a and b are both odd, this means a and b can be written as a=2k+1 and b=2r+1 whe...
this feels nicer ngl
woeful void
ty
also is this proof fine as well
prove that if m|x and n|x and gcd(n, m)=1 then nm|x
Since m|x, there exists an integer p st x=mp, similarly, there exists integer q st x=nq
And since gcd(n, m)=1, using Bezout’s identity there are integers a and b such that an+bm=1
1x = x therefore x=mp(an+bm)
x=mp and therefore x/p=m, nq/p=m
Substitute, x=mp(an+bnq/p), take the n out and put p in, x=mn(ap+bq), therefore mn|x
final saddleBOT
@woeful void Has your question been resolved?
final saddleBOT
Available help channel!
foggy wren
final saddleBOT
foggy wren
I'm confused how you use the last boundary condition to solve for the last constant
$u_n(x,y) = \sum_{n=1}^{\infty} 2C_n Sinh(\frac{n\pi x}{b})Sin(\frac{n\pi y}{b})$
soft zealotBOT
Katrro
foggy wren
How do I solve for Cn with this and the last condition?
final saddleBOT
@foggy wren Has your question been resolved?
cobalt perch
How do I solve for Cn with this and the last condition?
-# you can ping helpers if you want :3
foggy wren
<@&286206848099549185>
finite hinge
You can apply boundary condition to use Fourier sine series
final saddleBOT
final saddleBOT
Available help channel!
covert girder
Hey! I have never touched this part of maths but I kept seeing infinite sums and I was also awestruck on how people do them, I think I picked a relatively easy example. Can anyone tell me what's the catch here?
final saddleBOT
Hey! I have never touched this part of maths but I kept seeing infinite sums and...
covert girder
If this was a geometric series it would have been pretty nice, but it isn't, everything I know gets put under the rug
stuck juniper
Vn method
covert girder
Okay, what's vn?
covert girder
Now what?
covert girder
((n+2)-n)/2the denominator
Well that is a mouthful. I tried to find why but I got stuck
lime crest
Hey! I have never touched this part of maths but I kept seeing infinite sums and...
represent 1/n(n+1)(n+2) as a sum of fractions
hint: ||let A/n + B/(n+1) + C/(n+2) = 1/n(n+1)(n+2) then compare coefficients to find A,B,C||
covert girder
Yay! I am doing it right then
It reminded me of those nasty integrals
Alright, one moment
Like this?
lime crest
It reminded me of those nasty integrals
same tech yeah
lime crest
yep
tired walrus
why'd you write m instead of n eveerywhere 
covert girder
It is n
lime crest
absolute handwriting
tired walrus
doesn't read as such to me :P
celest tendon
hi friends
covert girder
Force of habit
covert girder
hi friends
Hi
covert girder
Which numbers though?
celest tendon
covert girder
They are just number assigned for a help channel
No requirement, you can select an available channel from the category just above it
The reason is because of high traffic obviously, one channel means chaos
lime crest
So now I just plug that in
you can try to write it out, and then notice that some of the adjacent terms cancel out
covert girder
you can try to write it out, and then notice that some of the adjacent terms can...
And like, write it for each single fraction
Let me try then
lime crest
you can try to write it out, and then notice that some of the adjacent terms can...
most of the terms cancel after that and you should get your sol
covert girder
Like this?
I forgot to cancel out 1/8 at 1/4x5x6 but I think this is the pattern
Ah wait
I completely butchered it
It was 1/2n and I still wrote the first terms with 3 or 4
My bad, I'll come back soon
lime crest
Like this?
id recommend you write the terms as (1/2)(1/n) - 1/(n+1) + (1/2)(n+2) instead
and then just match the terms with the same denominator (ignoring 1/2)
final saddleBOT
@covert girder Has your question been resolved?
covert girder
I guess this is it?
lime crest
Determine whether there exists non-constant polynomials with real coefficients $P(x), Q(x)$ such that $$\ P(x)^{10}+ P(x)^9 = Q(x)^{21}+Q(x)^{20}$$
final saddleBOT
Determine whether there exists non-constant polynomials with real coefficients $...
soft zealotBOT
Copter
lime crest
note that this is exponentiation btw
can someone check? im kinda not sure on my "P and Q have shared roots" part
further question, whats the condition of P^n + P^(n-1) = Q^m + Q^(m-1) existing?
tranquil pine
I"VE PLAYED THESE GAMES BEFOREE
tranquil pine
**Copter**
yo that's so easy
lime crest
yo that's so easy
true it wasnt that hard compared to my other qns
im just unsure if my implications thingy is correct
tranquil pine
true it wasnt that hard compared to my other qns
sorry but
how do u solve it?
non constant meaning like
having multiple answers so non linear right
torn summit
Determine whether there exists non-constant polynomials with real coefficients $...
what kind of school work is this
tranquil pine
what kind of school work is this
does the bot basically give u the answers?
lime crest
having multiple answers so non linear right
deg(P,Q) > 0
torn summit
does the bot basically give u the answers?
which bot
tranquil pine
deg(P,Q) > 0
what concept of math is this
torn summit
wolfram does not know polynomials
lime crest
what kind of school work is this
my friend gave me these
tranquil pine
ik this aint basic polynomials
lime crest
what concept of math is this
algebra
lime crest
well is this correct?
lime crest
further question, whats the condition of P^n + P^(n-1) = Q^m + Q^(m-1) existing...
also ^^
torn summit
polynomials base our concept of far too many things.
tranquil pine
also ^^
can you tell us what concepts we need to know prior?
like give us some context?
lime crest
can you tell us what concepts we need to know prior?
i mean you have to just solve the problem
theres probably a lot of ways to do this one
i just chose degree argument and differentiation
tranquil pine
i just chose degree argument and differentiation
isn't that a form of calculus
lime crest
yeah
lime crest
<@&286206848099549185>
final saddleBOT
@lime crest Has your question been resolved?
lime crest
.close
undone tiger
I wanted to ask a previous question again
25sin^2x+16cosec^2x minima will be
tired walrus
this morning we went over the same question but with different numbers
terse crypt
😭
undone tiger
You will find it amazing
terse crypt
isnt this the exact same now
undone tiger
Because i have cooked something
terse crypt
👀
undone tiger
Okay so let's find the minimum by derivative
undone tiger
I edited
terse crypt
Minimum is 55?
no
stuck juniper
U changed again
stuck juniper
40 i think
undone tiger
25t+16/t
25-16/t^2
And again we got t^2=16/25
4/5 which is in our interval
(0,1]
So we will keep it as it is
tired walrus
oh the numbers are flipped my bad
stuck juniper
Yes
terse crypt
yes
undone tiger
25×4/5+16×5/4
20+20=40
terse crypt
u put the wrong number in the question didnt u
undone tiger
So morning question was having t>1
stuck juniper
😔
terse crypt
oh so this is a new case 
final saddleBOT
final saddleBOT
Available help channel!
woeful void
by this, does it mean u can't have both A ⇔ B which would mean A is both sufficient and necessary for B and B → C which means that C is necessary for B because then A is obviously no longer sufficient since both A and C are necessary for B
final saddleBOT
by this, does it mean u can't have both A ⇔ B which would mean A is both suffici...
stone wagon
by this, does it mean u can't have both A ⇔ B which would mean A is both suffici...
define A,B, and especially C
your text right now is very hard to parse
"by this, does it mean u can't have both
- A ⇔ B, which would mean A is both sufficient and necessary for B, and
- B → C, which means that C is necessary for B
because then A is obviously no longer sufficient
since both A and C are necessary for B"
woeful void
define A,B, and especially C
just general events? I mean is it possible to have both A ⇔ B and B → C true at the same time
stone wagon
just general events? I mean is it possible to have both A ⇔ B and B → C true at ...
if A ⇔ B and B → C then A → C
A is sufficient for both B and C
stone wagon
no problem :)
final saddleBOT
@woeful void Has your question been resolved?
tranquil pine
,,\int\sqrt{3-2x-2x^2}, dx
final saddleBOT
,,\int\sqrt{3-2x-2x^2}\, dx
soft zealotBOT
!
tranquil pine
Can some1 explain this step by step from the start to the final answer?
polar salmon
Can some1 explain this step by step from the start to the final answer?
try making a square inside the square root
like a-b²
or a+b²
but its gonna be a-b²
then you can use trig sub
tranquil pine
Um i dont understand
ripe jewel
do you know how to complete the square of a quadratic expression
! might not now that
polar salmon
x²+x+1= (x+1/2)² +3/4
tranquil pine
! might not now that
What
polar salmon
x²+x+1= (x+1/2)² +3/4
here@tranquil pine
ripe jewel
x²+x+1= (x+1/2)² +3/4
do you know how to do stuff like this
tranquil pine
Oh
uneven python
Anyone wanna help?
tranquil pine
My ans is $\sqrt{2},(\frac{2x+1}{4}),\sqrt{\frac{3}{2}-x-x^2}+\frac{7}{4\sqrt{2}},\sqrt{\frac{3}{2}-x-x^2}+C$
soft zealotBOT
!
tranquil pine
Is this right?
tranquil pine
do you know how to complete the square of a quadratic expression
And u
ripe jewel
the expression I would expect to have inverse trig in it so i doubt it's right
tribal jackal
Yeah its not
tranquil pine
How does $\int \frac{e^u}{u}, du$ gets canceled when $u=\log x$
tranquil pine
Yeah its not
Oh so its not right huh?
soft zealotBOT
!
ripe jewel
but notice you didnt follow anyoine's advice here so
not surprising
that it's wrong
tribal jackal
How did you do it then?
tranquil pine
!occupied
tribal jackal
This is an occupied help channel
final saddleBOT
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).
tranquil pine
I solved using $\int\sqrt{a^2-x^2}, dx$
soft zealotBOT
!
tranquil pine
I wanna edit my final ans
ripe jewel
So idk how to do it
but Adam asked you to complete the square first. it will make the next part of explaaining easier
ripe jewel
you never showed us
tranquil pine
My ans is $\sqrt{2},(\frac{2x+1}{4}),\sqrt{\frac{3}{2}-x-x^2}+\frac{7}{4\sqrt{2}},\sin^{-1}({\frac{2x+1}{\sqrt{7}})+C$
soft zealotBOT
!
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
tranquil pine
you never showed us
Oh
tribal jackal
**!**
Compile Error! Click the <:errors:504266556054962196> reaction for more in...
I think this is correct
tranquil pine
,,(x+\frac{1}{2})^2 + (\frac{\sqrt{7}}{2})^2
soft zealotBOT
!
ripe jewel
ah okay, well, if you used a table that showed the answer in terms of arcsin, then it does the trig substitution for you
but perhaps you want to see it once in a simple example?
tranquil pine
I solved using $\int\sqrt{a^2-x^2}, dx$ applied this yk
soft zealotBOT
!
ripe jewel
yes it hides the trig sub under the rug
i think it's good for a student to knoiw how to do it though
tranquil pine
Oh
ripe jewel
want to try with a simple example?
tranquil pine
Why not
soft zealotBOT
gfauxpas
tranquil pine
Also dont skip this, How does $\int \frac{e^u}{u}, du$ gets canceled when $u=\log x$
soft zealotBOT
!
ripe jewel
that integral doesnt have a closed form
tranquil pine
,,(x+1)^2 + (\sqrt{5})^2
soft zealotBOT
!
ripe jewel
great
now let's make this (something)^2 + 1
by factoring out the right constant
you'll see why
tranquil pine
Oh
ripe jewel
$$\frac 1 5 \int_0^t \frac{\mathrm dx}{\left({\frac{x+1}{\sqrt 5}}\right)^2 + 1}$$
soft zealotBOT
gfauxpas
tranquil pine
Idk
tranquil pine
Now that square = tan x or cot x?
soft zealotBOT
gfauxpas
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
soft zealotBOT
gfauxpas
ripe jewel
and that's how you do trig substitution when integrating
here i would take the first one and divide both sides by cos^2
tranquil pine
No i dont know anything abt hyperbolic functions
ripe jewel
so dont worry about it
all that matters for this is that they satisfy that identity
c^2-s^2=1
so that's why theyre used
but you can use trig for ours
divide both sides by cos^2
tranquil pine
Oh
ripe jewel
$$\tan^2\theta +1 = \sec^2\theta$$
soft zealotBOT
gfauxpas
tribal jackal
For this, can't you use inverse tangent?
ripe jewel
yes sure you can
I was just showing ! what one can do in general because he said he's never seen trig sub done
tribal jackal
Oh right
tranquil pine
Oh
ripe jewel
$$(x+1)/\sqrt 5 = \tan \theta$$
soft zealotBOT
gfauxpas
ripe jewel
$$x = 0, \theta = \arctan(1/5)$$
$$x=t, \theta = \arctan((t+1)/\sqrt5)$$