I give you guys 3 mins
#help-36
drowsy epoch
Your question seems incomplete
jade fable
Clear reason and correct answer
desert mantle
you do know we arent your guinea pigs, right?
tired walrus
@jade fable this is disrespectful.
strange coral
That means for integer solutions
desert mantle
if you want help, be less of an ass
jade fable
<@708594064060055583> this is disrespectful.
My bad
jade fable
May I know what are the potential factor of a
jade fable
It is 5 mod 10
Why, would you mind explaining it sir
tired walrus
we can at least translate and figure out what they want from you
strange coral
For integer solution a = 10x+5, x belongs to z, and c = 11x +4, x belongs to z
jade fable
post the complete question please
But that’s not relevant to my confusion
tired walrus
But that’s not relevant to my confusion
post it even if it isn't relevant
the more context we know, the better.
jade fable
the more context we know, the better.
I cannot. I’m a lazy ass, it is deemed a torture to take a shot at the book
I can only move my fingers
tired walrus
lazy asses don't get help here.
jade fable
Not the entire wrist
strange coral
I answered for Diophantine solutions only
jade fable
For integer solution a = 10x+5, x belongs to z, and c = 11x +4, x belongs to z
What is x
jade fable
Oh
jade fable
For integer solution a = 10x+5, x belongs to z, and c = 11x +4, x belongs to z
Why would you came to that conclusion
strange coral
Standard number theory
jade fable
Standard number theory
I do not know them. That’s why I’m struggling to understand it. Could you elaborate sir
I’m cryingggggggggg
I need to move on to the next question
final saddleBOT
tired walrus
I have too many work to do
too much work to do
tired walrus
who are you calling zesty
final saddleBOT
Available help channel!
harsh solar
final saddleBOT
bleak granite
night raft
This is what I did so far
your first answer is wrong though for part(a)
x > 1/2 is correct
harsh solar
your first answer is wrong though for part(a)
which part?
night raft
which part?
the x > -3 is incorrect
harsh solar
the x > -3 is incorrect
why?
harsh solar
substitute for example x = -2 and you'll see why
why -2?
night raft
why -2?
you got x > -3 right? and x = -2 is just an example of being in this interval since -2 is greater then -3
harsh solar
you got x > -3 right? and x = -2 is just an example of being in this interval si...
yeah
harsh solar
-5
harsh solar
no
night raft
now can you see why it's wrong to say x > -3
our quadratic we were solving was 2x^2 + 5x - 1 > 0
harsh solar
now can you see why it's wrong to say x > -3
but isnt it x+3>0 becomes x>-3?
night raft
our quadratic we were solving was 2x^2 + 5x - 1 > 0
notice here, that if we went x >-3, the y axis falls below 0?
night raft
but isnt it x+3>0 becomes x>-3?
it should be x < -3
harsh solar
it should be x < -3
how so
night raft
notice here, that if we went x >-3, the y axis falls below 0?
look at here
night raft
how so
generally what you do is solve the quadratic first as if it was an = sign to avoid confusion. Then graph it to identify which interval it is
harsh solar
generally what you do is solve the quadratic first as if it was an = sign to avo...
I dont understand what you mean by graphing it
night raft
I dont understand what you mean by graphing it
as in sketching the quadratic like you did in the diagram
harsh solar
but even then wouldnt the inequality sign stay the same just like x> 1/2?
final saddleBOT
@harsh solar Has your question been resolved?
night raft
but even then wouldnt the inequality sign stay the same just like x> 1/2?
the x > 1/2 part is correct
but the x >-3 isn't
https://www.youtube.com/watch?v=xdiBjypYFRQ. watch this video, so you can understand a bit more on what I mean
harsh solar
the x > 1/2 part is correct
but arent they both the same way of solving?
night raft
but arent they both the same way of solving?
wdym?
harsh solar
since flipping of the inequality sign is not needed for x>1/2, shouldnt it be the same for x>-3
night raft
since flipping of the inequality sign is not needed for x>1/2, shouldnt it be th...
no
you have to flip it as x < -3
tired walrus
you have to flip it as x < -3
...which imo is a horrendous way of explaining it
like, elaborate arcane rules for what to flip when???
eurgh
night raft
like, elaborate arcane rules for what to flip when???
I was trying to explain to them before that your inequality depends on your sketch but I guess you might do a better job than me
night raft
notice here, that if we went x >-3, the y axis falls below 0?
from here
tired walrus
i feel a bit uncomfortable launching into an explanation without OP present and ready to engage
night raft
ah okay 
harsh solar
you have to flip it as x < -3
I really dont get why we have to flip for the second inequality and not the first
final saddleBOT
@harsh solar Has your question been resolved?
edgy mauve
I really dont get why we have to flip for the second inequality and not the firs...
When u multiply noth sides of an inequality by a negative number,ur sign flips
severe canyon
notice here, that if we went x >-3, the y axis falls below 0?
@harsh solar can you tell only by looking at this (correct) figure where the parabola is above the x-axis? Either mark it on the figure or write it down
final saddleBOT
@harsh solar Has your question been resolved?
jagged flare
how did they get the upper bound
final saddleBOT
how did they get the upper bound
desert mantle
so m has one representation as 1+1+1+...+1+a_n where a_n in {1,...,n}
so that means m <= 1+1+1+...+1+n
and m also has one representation as 1+2+3+...+(n-1)+a_n
so 1+2+3+...+(n-1)+1 <= m
thats how I'm reading it
jagged flare
why would it be <=
desert mantle
which one
jagged flare
both
jagged flare
ohh
so the first one is like m=n+1+a_n<=m+1+n=2n+1 and the bottom is m=(n-1)n/2+a_n>=(n-1)n/2+1?
desert mantle
yes
gentle zephyr
final saddleBOT
gentle zephyr
guys I have tried a couple things but didnt managed to get anywhere with this
for example |x| = √(x^2) and proving sqrt is monotonically increasing in the domain [0, R)
i am not sure what to do really with this
ripe jewel
MT:
tired walrus
i guess he also needs to spend another 17 pages proving that y^2 ≥ 0
ripe jewel
lol
proper dagger
i'm waiting for the monologue
gentle zephyr
can that not be taken as obvious?
I think its fine to assume sqrt is increasing, I can prove it in my own time
desert mantle
well then what else is stopping you from that approach
|x| = sqrt(x^2) <= sqrt(x^2+y^2) = norm(F)
thats literally it
gentle zephyr
then it follows x^2 <= x^2 + y^2
desert mantle
wrong direction
because x^2 <= x^2+y^2 it follows that sqrt(x^2) <= sqrt(x^2+y^2)
thats the direction you are using
gentle zephyr
then what?
desert mantle
thats it
tired walrus
QED
gentle zephyr
i guess he also needs to spend another 17 pages proving that y^2 ≥ 0
i dont get it 😭
gentle zephyr
thats the direction you are using
why not the other direction?
tired walrus
writing (goal) => ... is bad in a proof
gentle zephyr
what?
tired walrus
hm maybe i phrased that badly too, sorry.
gentle zephyr
our goal was to show that |x| <= |F| for F a vector in R2
tired walrus
saying "from sqrt(x^2) ≤ sqrt(x^2+y^2) follows x^2 ≤ x^2+y^2" is a bit... how do i put it
putting the cart before the horse
desert mantle
you want sqrt(x^2) <= sqrt(x^2+y^2)
you know x^2 <= x^2+y^2
tired walrus
when doing a proof there should be a clear distinction between assertions (what is known) and goals (what needs to be shown)
something something language problems, i don't speak spanish.
desert mantle
so you use (x^2 <= x^2+y^2) => (sqrt(x^2) <= sqrt(x^2+y^2)) instead of <=
tired walrus
yknow dena that might have been better in LaTeX
gentle zephyr
you know x^2 <= x^2+y^2
can we take it as granted or should we prove
gentle zephyr
I mean, F is a vector in R2, so i think we can take it as granted
desert mantle
and we seriously hope that you dont have to prove that squares of real numbers arent negative
desert mantle
yknow dena that might have been better in LaTeX
yeah but oh well
gentle zephyr
for the case in R3
|x| <= sqrt(x^2 + y^2 + z^2)
sqrt(x^2) <= sqrt(x^2 + y^2 + z^2)
and since x^2 <= x^2 + y^2 + z^2 and sqrt is monotonically increasing
we conclude |x| <= ||F||
?
is this proof correct or no?
what would u fix?
desert mantle
yes thats correct
gentle zephyr
what about the graphical approach
turbid burrow
im assuming you meant to write x^2 instead of z^2
turbid burrow
what about the graphical approach
what is the shape of the norm of a vector
gentle zephyr
what is the shape of the norm of a vector
idk
gentle zephyr
what is the shape of the norm of a vector
its the magnitude of the arrow
turbid burrow
yes indeed
gentle zephyr
gentle zephyr
this is in R2
turbid burrow
all vectors (in the plane) of the same length would point to the circumference of the circle
turbid burrow
this is in R2
right
if you let the vector start at the origin, then where it points to is equal to its coordinates
gentle zephyr
all vectors (in the plane) of the same length would point to the circumference o...
they have same magnitude, same length of a vector
turbid burrow
they have same magnitude, same length of a vector
correct
gentle zephyr
if you let the vector start at the origin, then where it points to is equal to i...
so? whats your point
turbid burrow
so? whats your point
so it means the coordinate values of a vector cannot be bigger than its norm
bc it falls on the circle
gentle zephyr
yes it would exceed the circle
if that would take place
the problem here is that
why is the radius of the circunference equal to the norm of F
turbid burrow
yes it would exceed the circle
give me an example then
turbid burrow
why is the radius of the circunference equal to the norm of F
bc the definition of the norm of F in the problem you gave is equal to the radius of a circle
gentle zephyr
give me an example then
example of what
gentle zephyr
bc the definition of the norm of F in the problem you gave is equal to the radiu...
i just realized yeah
turbid burrow
example of what
that any of the vector's coordinates value would be bigger than the vector norm
gentle zephyr
that any of the vector's coordinates value would be bigger than the vector norm
its impossible
turbid burrow
hence this is the graphical explanation
the norm of F in the problem has this geometric property
gentle zephyr
hence this is the graphical explanation
I appreciate it
turbid burrow
not only in this problem, in everywhere
exactly
gentle zephyr
bc the definition of the norm of F in the problem you gave is equal to the radiu...
what?
we have |x| <= sqrt(x^2 + y^2) = ||F||
@turbid burrow
where did the circle came from?
x^2 <= x^2 + y^2
cada componente de F es menor o igual a la norma de F
el radio de la circunferencia es la norma de F
|x| <= ||F|| porque sino se sale del circulo
pero no es que haya una circunferencia de por si
sino es que todos los vectores de norma F forman una circunferencia
asi mismo los vectores con norma menor a F tambien forman otra circunferencia, la que va a tener un radio mayor o igual que la norma de x
si, la norma de x fuera mayor estricto que el radio de esta circunferencia entonces se saldria del circulo con radio de norma de F
en ningún momento me dieron la circunferencia, esto lo tengo que inferir yo
|x| <= sqrt(x^2 + y^2) = ||F|| lo único que dice es que |x| <= ||F||
lo cual es cierto porque todos los vectores con norma ||F|| forman una circunferencia de radio ||F||
en todo momento se cumple que |x| <= ||F|| porque sino se sale del circulo
el círculo tiene como radio la norma de F, es el vector que va desde el (0,0) hasta (x,y)
en R3 me imagino forma una esfera
.solved
final saddleBOT
final saddleBOT
Available help channel!
rustic narwhal
An intuitive understanding of limsup and liminf is: when sequence do not converge and oscillate, limsup and liminf give the "tail" of a sequence a boundary.
final saddleBOT
An intuitive understanding of limsup and liminf is: when sequence do not converg...
rustic narwhal
Is that right?
unique aspen
desert mantle
well more or less but you can still be bigger than limsup and smaller than liminf infinitely often
final saddleBOT
@rustic narwhal Has your question been resolved?
dark viper
i know this is a maths dc but please i need help with a physics question i have a test in a few hours
final saddleBOT
i know this is a maths dc but please i need help with a physics question i have ...
dark viper
no one is online on the physics servers please help
with this derivation my physics teacher shared
like what have they done in it ?
how is work energy theoram being applied here i dont get it
thin cloud
!xy ig?
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.
thin cloud
What's k in the middle of two block?
iron dagger
spring constant
thin cloud
Oh okay
dark viper
they introduced F at the end with no explanation
which F ?
ripe jewel
at the last line
iron dagger
it probably is just the same f
ripe jewel
but anyway i cant figure out how they got rid of the square root
dark viper
there's only F1 and F2 ?
ripe jewel
it's f2 and f1 most of the problem
capitalization matters with variables but i guess not to them
square root missing is more problematic
iron dagger
but anyway i cant figure out how they got rid of the square root
they factored out of x1 and x2 a big part of the expression you see in RHS of last line
iron dagger
then canceled with one of the (x1+x2) on the RHS 2nd to last line
dark viper
can someone please tell how they applied work energy theoram here
ripe jewel
can someone please tell how they applied work energy theoram here
because at maximum seperation, as it says, there's 0 velocity, hence all energy is potential
and at rest it was also 0 velocity
dark viper
so the system started from rest and finally it is at rest so change in K.E for both block =0 then ?
dark viper
okk same thing 🙂
dark viper
and also can work energy theoram be applied for 2 blocks simultaneously ?
ripe jewel
anything defined by an integral has the superposition property
hard stratus
For clarity when something is instantaneously not moving but is being accelerated I often see this referred to as being "instantaneously at rest"
ripe jewel
meaning you can add seperate things and consider them together, roughly speaking
ripe jewel
For clarity when something is instantaneously not moving but is being accelerate...
good phrase to know!
unfamiliar with it
and
dark viper
For clarity when something is instantaneously not moving but is being accelerate...
okk
ripe jewel
$$W = \int \mathbf F \cdot , \mathrm d \mathbf s$$
soft zealotBOT
gfauxpas
ripe jewel
anything defined by an integral has the superposition property
this is a bit imprecise but
i mean the same type of integral throughout but on different objects
like work, or velocity
dark viper
if we apply work energy theoram seperately will then also we get the same result ?
ripe jewel
if we apply work energy theoram seperately will then also we get the same result...
in theory we should, but it may not be solvable
because of incomplete information at each part
but , fundamentally, in principle, yes
dark viper
no one is online on the physics servers please help
also won't why is only a single term used for work done by spring wont it be [k(0-x1^2) +k(0- x2^2 ) ]/2 ?
ohh wait never mind spring force is k(x1 +x2) here so whole will on the whole term
dark viper
but , fundamentally, in principle, yes
okk i will try that case too then
ripe jewel
okk i will try that case too then
sure but as I said, it may not be doable with the information you have, so be willing to give up :)
did you take linear algebra yet?
dark viper
did you take linear algebra yet?
no 🙂
ripe jewel
ah, okay
dark viper
isnt this possible without it ?
ripe jewel
well, that gives you a different perspective on when and why superposition works
sure
it would just have led me to explain it in a different way
not necessary
dark viper
ohkk thank you soo much for your help lemme try do this on my own once and then ill close the channel
dark viper
no one is online on the physics servers please help
uhh why isnt minus sign applied here for the m1 block ?
wont work done by the forces F1 + m1ac be -(F1 +m1ac)x1 ?
w.r.t the C.O.M as force is in negative ?
sorry to bother you again, @ripe jewel
ripe jewel
hi
final saddleBOT
ripe jewel
oh okay! i didnt even figure out your question@!
:)
because i just caqme to see i was tagged, glad youre good
final saddleBOT
Available help channel!
tranquil pine
final saddleBOT
tranquil pine
need help solving this
tired walrus
!status
final saddleBOT
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
pretty sure there is a theorem saying that PQ:QR:RS = AB:BC:CD in a setting like this.
given that the four vertical lines are all parallel to each other
tranquil pine
still, i couldn't find out their lengths
tired walrus
PS is known, and AD is not hard to calculate
final saddleBOT
final saddleBOT
Available help channel!
supple nest
#4
vital crag
,rotate
soft zealotBOT
vital crag
There's more to say than just "exist in R"
supple nest
Does my 2nd axiom follow as well, or am I going about this fundamentally wrong
vital crag
You have to actually do the calculations in terms of the polynomials
sly herald
Yes
final saddleBOT
final saddleBOT
Available help channel!
glacial scroll
@final saddle
final saddleBOT
<@805217272087838750>
deep condor
,rccw
soft zealotBOT
soft zealotBOT
glacial scroll
5x+20=4x+1
-4x -4x
x+20=1
-20 -20
x=-19
I just wanna see if that's right so far
iron dagger
you don't equate AB to AC
glacial scroll
you don't equate AB to AC
Oh ok
night raft
for starters if you plug it into the equation, you get lines with being negative length
glacial scroll
for starters if you plug it into the equation, you get lines with being negative...
Yeah, just realized
glacial scroll
I think I misread it
Ok, I think I fixed it
2(4x+1)=5x+20
8x+2=5x+20
-5x -5x
3x+2=20
-2 -2
3x=18
÷3 ÷3
x=6
tranquil pine
final saddleBOT
shell condor
Area yeah?
tranquil pine
ye
tranquil pine
Area yeah?
how can we find
shell condor
I'm thinking just that
tranquil pine
ye
shell condor
Sorry but I'm taking too much time, I'll be here thinking and I'll inform you if I leave but still see if anybody else answers faster
tranquil pine
Sorry but I'm taking too much time, I'll be here thinking and I'll inform you if...
ok
dw this too hard anyway
shell condor
True, I've tried drawing a perpendicular on AD to E and do some stuff with similarity but I'm getting nowhere
tranquil pine
ye
shell condor
how about the diagonal BD, any similarity ideas between EDF and EBF?
tranquil pine
no
shell condor
Alright
tranquil pine
where is F?
tranquil pine
oh
shell condor
So, any ideas of similarity?
tranquil pine
no
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.
tranquil pine
:o
lean bloom
...
sullen gale
uh
lean bloom
how did you found 34?
sullen gale
that's not how it works
shell condor
Yeah I've had it with this question, sorry but I'm leaving
tranquil pine
lol ig
tranquil pine
how did you found 34?
its wrong nvm
scarlet sequoia
Am I wrong? (Genuinely asking sorry if I did something wrong)
if the question has been picked up and then deserted by a helper in between pings, it's only normal to ping another time
latent dragon
if the question has been picked up and then deserted by a helper in between ping...
Okie sorry!
lean bloom
its wrong nvm
maybe why was it wrong?
scarlet sequoia
if there are two consecutive messages on the chat that are pings, it's when the "ping once" applies
latent dragon
if there are two consecutive messages on the chat that are pings, it's when the ...
Ah okay. I apologize again!
shell condor
Spent like 30 mins on this to no avail (with some progress with nothing to back it)
tranquil pine
maybe why was it wrong?
jst wrong statements
lean bloom
do you have an idea on where to start
tranquil pine
no
shell condor
My advice, extend BE to CD, because angle(DEG) (G is point of intersection at CD) is 45 degrees, as DEB was 135
tranquil pine
mhmm
shell condor
Aside from that I just did some minor stuff, nothing concrete
tranquil pine
ye
shell condor
Yeah and also, if you get either of the two angles (equiangles inside DEA and BEA) as 45 degrees, then it's just wrong
tranquil pine
mhm
shell condor
Yeah that's all I can help you with, good luck!
tranquil pine
do you have an idea on where to start
can you help
lean bloom
The first thing I see is that you have two triangles
tranquil pine
ye
lean bloom
DAE and EAB
which are symmetric (i am not sure that this is a saying in english)
and have the same length for the "sides"
tranquil pine
which are symmetric (i am not sure that this is a saying in english)
ye
shell condor
Hey sorry to interrupt but try drawing the diagonal AC and working on the triangles and others inside ABC
tranquil pine
ok
tranquil pine
ye
shell condor
Yeah it's pretty complicated with barely anything to work with
tranquil pine
how
lean bloom
we know that $s^2 = h^2 + \left(\frac{b}{2}\right)^2$
soft zealotBOT
Amiso_
tranquil pine
ye
lean bloom
where h is the height and b the base and s what we are looking for
the only thing that we miss is h, however if we use pythagore, we can replace h by an relation with s and b
tranquil pine
ye
lean bloom
which gives us two equations and two variablles
tranquil pine
ye
tranquil pine
which gives us two equations and two variablles
can u walk me through it?
lean bloom
for the biggest triangle
tranquil pine
yea
lean bloom
you have that the height $s^2 = h^2 + 18$
soft zealotBOT
Amiso_
lean bloom
$18 = (\frac{6\sqrt{2}}{2})^2$
soft zealotBOT
Amiso_
tranquil pine
mhmm
lean bloom
you have that $h = \sqrt{s^2 - 18}$
soft zealotBOT
Amiso_
tranquil pine
yea
tranquil pine
?
lean bloom
**Amiso\_**
I look up this on internet
tranquil pine
ye
lean bloom
but this is just pythagore
tranquil pine
oh
lean bloom
and the $h$ for the equation is not the same in both triangle
soft zealotBOT
Amiso_
tranquil pine
oh
lean bloom
I feel like it misses a relation but I can't find what
tranquil pine
oh
tranquil pine
ye
lean bloom
because $s$ is the same everywhere we have that
$h_1^2 + \left(\frac{b_1}{2}\right)^2 = h_2^2 + \left(\frac{b_2}{2}\right)^2$
soft zealotBOT
Amiso_
tranquil pine
ye
lean bloom
$h_1 = \sqrt{h_2^2 + (\frac{b_2}{2})^2 - (\frac{b_1}{2})^2}$
which then can
soft zealotBOT
Amiso_
lean bloom
you have then $s^2 = h_2^2 + constant$ and
$s^2 = h_2^2 + otherconstn$
soft zealotBOT
Amiso_
tranquil pine
mhmm
lean bloom
then you can solve it
tranquil pine
ok
lean bloom
it is kind of rough
tranquil pine
i'll thell u when im done, then u can verify
lean bloom
yes
tranquil pine
wait
tranquil pine
then you can solve it
what do i solve for again im so confused
lean bloom
for $s$
soft zealotBOT
Amiso_
soft zealotBOT
✪bugged micro-ronin✪
lean bloom
yes
lean bloom
and the constant if find as said before
tranquil pine
and the constant if find as said before
i got it i think
lean bloom
does it work?
tranquil pine
i think..
tranquil pine
does it work?
can u check?
lean bloom
I'll try
tranquil pine
kk
tranquil pine
ye im cooked
lean bloom
hmmm
opal plinth
I haven't read your discussion but it's a very easy solve if you extend BE and form a right triangle with BD as hypotenuse
tranquil pine
I haven't read your discussion but it's a very easy solve if you extend BE and f...
how though
shell condor
I haven't read your discussion but it's a very easy solve if you extend BE and f...
I tried that
tranquil pine
how bout we try this
shell condor
there's no right angle, because that bloody BE extends to be slightly more that 90
opal plinth
tranquil pine
how bout we try this
i got 1/2 for this
tranquil pine
:o
shell condor
okay now that's just bonkers
tranquil pine
?
shell condor
IDK if that works, but if it does then there's no way I would have thought of that
opal plinth
There was a hint in the problem description, with the sqrt(2) value
tranquil pine
can we be done with the question in 10 mins?
opal plinth
Yea
shell condor
can we be done with the question in 10 mins?
I'll start with the second one
tranquil pine
ok
opal plinth
You see that circle? What's the exterior angle BAD?
opal plinth
exterior
tranquil pine
wait 270
tranquil pine
uh
opal plinth
They have the same arc BD
opal plinth
135º is correct
tranquil pine
okay
opal plinth
Half of 270
tranquil pine
oh yea
opal plinth
So when you extend with EF, what's the angle FED?
opal plinth
Right
tranquil pine
kk
opal plinth
Now if I want to make a square with diagonal ED, do you see how F is a vertex of that square?
tranquil pine
Now if I want to make a square with diagonal ED, do you see how F is a vertex of...
ye
shell condor
Yeah I found all that, 45 degree and 135 degree
opal plinth
So DFE is a right angle, do we agree?
tranquil pine
wut'
opal plinth
... F is a vertex of the square with diagonal ED
tranquil pine
ok
opal plinth
If that square thing confuses you we can just make it an isosceles triangle
tranquil pine
no need
opal plinth
Alright, so given DE = 6sqrt(2), what's DF and FE?
tranquil pine
ok
opal plinth
That was a question
opal plinth
Do you know that the diagonals of a square of side-length x have length sqrt(2)*x?
tranquil pine
they 6
opal plinth
Right so now you have a right triangle DFB, you know two side lengths, compute the hypotenuse
Then you have the diagonal of the big square, and from that, its side lengths, and its area
opal plinth
Yeah
opal plinth
AB would be 5sqrt(2), square that and it's 50, correct
tranquil pine
yay
shell condor
how bout we try this
Yeah about this
Check if ABM ~ DMN
Because I'm getting something
opal plinth
Check if ABM ~ DMN
That's obviously not the case, the small angle is different
shell condor
Wait no I think I messed up, carry on
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shell condor
That's obviously not the case, the small angle is different
Yeah I figured
Angle(AMB) is equal to the other equiangles
Again 30 minutes, again reached somewhere that feels concrete but I can't find anything to follow through with it
Yeah I've had enough, I apologize
If anybody else wants to take over then they can, I'm out
quasi plume
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cursive moth
sry didint see
quasi plume
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soft heart
in q no. 30... i think they are reaching a common distance at different timestamps..as 80cm one will reach early to the common shared distance but in q no. 31 , they are being rung at the same time..
is it possible in the que no. 30 that they meet at the same time as also being at the shortest distance..
i hope i wrote it clearly..please ask if you don't understand something
final saddleBOT
in q no. 30... i think they are reaching a common distance at different timestam...
proper dagger
hint: LCM. both questions
proper dagger
the question never said the people in q30 took steps at the same rate at each other
in fact, the timing of the steps don't matter in q30
<@&268886789983436800> possible tos
just in case
going back to your question
all that matters is that whether the three people can take some whole number of steps and arrive at the same spot
the three of them will take different numbers of steps
soft heart
all that matters is that whether the three people can take some whole number of ...
omay
okay
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tranquil pine
Eyo, the name's Henry, and I need help
more of a guide tho
fiery bluff
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gray steppe
hii could someone tell me what I did wrong here? (trying to find the derivative of y wrt x) Ik I could’ve made it easier for myself by using the laws of logarithms but I wanna know im particular how I messed up here :<
final saddleBOT
hii could someone tell me what I did wrong here? (trying to find the derivative ...
soft zealotBOT
tired walrus
assuming i didn't miss anything either, your dy/dx seems to be correct if potentially unsimplified @gray steppe what is making you say it is wrong?
gray steppe
half your x's don't look like x's 😭
my bad i js like to write them in one stroke 😞
gray steppe
oh
WELL I NEED TO SIMPLIFY IT FURTHER cuz its supposed to be (1/(x-3))-(1-(x+4))-(1/(x-1))
and idk how to go about that
tired walrus
WELL I NEED TO SIMPLIFY IT FURTHER cuz its supposed to be (1/(x-3))-(1-(x+4))-(1...
thats defo the wrong way to put brackets with fractions
gray steppe
thats defo the wrong way to put brackets with fractions
I CORRECTED IT.
tired walrus
but if you want to pull it apart into 3 fractions like that, ig you will need to use partial fractions.
gray steppe
jesus
gray steppe
but if you want to pull it apart into 3 fractions like that, ig you will need to...
oh D:
i havent studied that yet
tired walrus
aight then you have no choice but to rewind and apply log laws before diff
gray steppe
ill js learn partial fractions instead
ty for the help btw @tired walrus ^^
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gray steppe
WAIT NO
gray steppe
hii could someone tell me what I did wrong here? (trying to find the derivative ...
my denominator turns out to be a cubic here no?
severe canyon
No
tired walrus
i worked out the derivative of the stuff inside the ln
to check it against your g'(x)
gray steppe
what did u get
gray steppe
then why am i not getting the right answer ;(
gray steppe
So it's not wrong at all
the denominator differs
severe canyon
Which two denominators?
gray steppe
hii could someone tell me what I did wrong here? (trying to find the derivative ...
uhh this
gray steppe
and this
severe canyon
As you can see there's no logarithm here
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old quarry
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old quarry
i tried writing denominator as (x+1)^2+1
and then putting x+1 = tan^2 theta
but it wasnt working
barren hound
tired walrus
why not u = sqrt(x+1)
i believe this reduces us to something like $k \int \frac{\dd{u}}{1+u^4}$ doesn't it
soft zealotBOT
Ann
tired walrus
where k is some constant i cbf to figure out but which i also dont wanna get wrong
old quarry
i believe this reduces us to something like $k \int \frac{\dd{u}}{1+u^4}$ doesn'...
yes i got that with the other method also
except i got
2dt/(t^4+2)
eager shore
yeah youll get a 2 for completing the square
tired walrus
ugly ugly crap
eager shore
yeah expected
old quarry
help
eager shore
sub u = 2^(1/4)t first
old quarry
except i got
2dt/(t^4+2)
in this?
soft zealotBOT
maison
eager shore
I think this is what you'll have
now you multiply and divide by 2
and do + t^2 - t^2 in the top
old quarry
but why do we need to multiply and divide by 2
soft zealotBOT
maison
old quarry
t=sqrt (tan theta)?
eager shore
nah
old quarry
bro ur pfp is v weird
soft zealotBOT
maison
eager shore
bro ur pfp is v weird
thank you
old quarry
yeah
eager shore
divide the top and bottom of each fraction by t^2
eager shore
then complete the square in t - 1/t in the first one and t + 1/t in the second one
old quarry
yeah 👍 seems its standard from there
thank u
i dont think ill waste my time with the calculations
eager shore
okay
old quarry
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supple nest
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supple nest
4
My main question is did I do this right?
I wanna make sure I’m going about this the correct way
versed crater
I’m unhappy about part e
I believe you need an extra line to write the sum as caₙxⁿ + … + ca₀ + cbₙxⁿ + … + cb₀
supple nest
So just a formatting error there?
versed crater
Then you bracket it as (caₙxⁿ + … + ca₀) + (cbₙxⁿ + … + cb₀), then factor out the c so you get c(aₙxⁿ + … + a₀) + c(bₙxⁿ + … + b₀) = cp + cq
floral nova
If I submitted these when I was taking linear algebra, I would have gotten part marks at best for basically all of these.
supple nest
If I submitted these when I was taking linear algebra, I would have gotten part ...
Woah
This is my first homework assignment lol
versed crater
The other thing upon closer inspection is see how they wrote addition
floral nova
For example, b you did not start with the polynomial for p+q and algebraically rewrite it to give the polynomial for q+p. Look at how your textbook writes (p+q)(x) and compare it to what you wrote.
versed crater
They actually bracket the coefficients together then did the x^power outside
A lot of the proofs should come down to ℝ is a field
supple nest
They actually bracket the coefficients together then did the x^power outside
I mean even without the brackets and writing it in its entirety, it’s the same thing right
versed crater
Not by the definition given
supple nest
(a+b)x is the same as ax+bx though
versed crater
Maths is about following very very specific and arbitrarily determined rules
versed crater
(a+b)x is the same as ax+bx though
That’s not always true
supple nest
That’s not always true
If I prove distribution of multiplication over addition it is
versed crater
But thats what you’re trying to do already
versed crater
(a+b)x is the same as ax+bx though
You say that “this is the same” but it’s only “the same” because that’s how they defined addition of polynomials
You’re using the definition for the claim that they are the same
supple nest
Well if they’ve already defined the addition of polynomials that way, shouldn’t I follow that definition?
versed crater
Well you didn’t write it
For example in a
You want to show that (p + q) + r = p + (q + r)
Your first line says aₙxⁿ + bₙxⁿ + …
As far as we know, that is not a valid statement
We have no idea what it means to write + between 2 things that look like aₙxⁿ and bₙxⁿ
versed crater
You want to show that (p **+** q) **+** r = p **+** (q **+** r)
The second line of this by definition of + should say (aₙ + bₙ)xⁿ + … + (a₀ + b₀) + cₙxⁿ + … c₀
The pluses you see in the polynomial aₙxⁿ + … are NOT the same pluses as the + between polynomials
supple nest
so I should write the whole polynomial out first for (a+b) before writing out the polynomial for C
versed crater
Well that’s what it means to have p + q
supple nest
Ok
versed crater
It is exactly what is written in the definition and you are practicing to not imagine things that aren’t there
supple nest
As far as the proofs outside of the first two, am I chilling
versed crater
It’s hard to unlearn it but you should try to
supple nest
besides that E one
Because the ones I seem to trip up on are the ones where I write out the polynomials themselves
versed crater
You can be more clear on all of them
Even the 0 polynomial
The nth degree 0 polynomial is of the form 0xⁿ + … + 0
supple nest
Wait I’m in a different class, would you be ok if I DM you later showing pictures of my textbook? I want to show you the proofs they wrote for a previous vector space
versed crater
For d you should show that it indeed is the additive element
versed crater
Wait I’m in a different class, would you be ok if I DM you later showing picture...
Don’t dm me open a channel
And also every uni has a different bar to get marks
I’m only saying to be completely rigorous
supple nest
Don’t dm me open a channel
Could I tag you when that happens (since you already have a good idea of what’s going on)
supple nest
And also every uni has a different bar to get marks
I’m at a pretty high tier uni
versed crater
I might be asleep but sure
supple nest
Like a top 50
versed crater
Yeah I’ve seen top 20 unis with pretty shit bars too though
supple nest
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supple nest
#4
@versed crater if ur still awake im back
I was told A and B weren’t good enough by other people in server
final saddleBOT
@supple nest Has your question been resolved?
supple nest
Please bruh
supple nest
<@&286206848099549185>
fiery pine
they are not good enough
supple nest
Well yes how would I go about fixing them
fiery pine
you want to show (p + q) + r = p + (q + r). but what you wrote at the start isn't (p + q) + r
i mean it is but not immediately
supple nest
How
fiery pine
the more immediate equality you should start with is $$(p + q) + r = \left(\sum_{i=0}^n a_n x^n + \sum_{i=0}^n b_n x^n \right) + \sum_{i=0}^n c_n x^n$$
soft zealotBOT
swashbuckler
fiery pine
did you or the book already prove real polynomials form a vector space?
if so, associativity and commutativity are inherited from that one
supple nest
did you or the book already prove real polynomials form a vector space?
Wdym
the entire question is proving that Pn(R) is a vector space
fiery pine
yea i know. but what's F(R) the book mentions in the example?
supple nest
F(r) is all functions
I think they want you to do the same proofs that they did for F(R), which are all the axioms
fiery pine
all functions or all polynomial functions?
supple nest
F(R) is all functions iirc
fiery pine
well i guess it doesn't matter if you have to write the proof from scratch anyway
supple nest
Yeah
like they want us to use the proofs for F(R) as a guideline, rather than using the existence of F(R) as a vector space to prove Pn(R) is a vector space
It’s just tough because if we know R is a vector space we can just use that to prove all subsets of R are vector spaces lol
fiery pine
i was just trying to bring up that polynomials in general are commutative and associative with addition
and this is just a special case
where the polynomials are degree less than or equal to n
supple nest
Yeah they are, I think it’s tough for me to write proofs just knowing those as simple facts
It’s like “all oranges are orange, prove that the oranges in this bag of oranges are orange”
It’s hard to make more complicated than that
fiery pine
oops, i wrote some of the letters wrong here. but to start you off, $$\left(\sum_{i=0}^n a_i x^i + \sum_{i=0}^n b_i x^i \right) + \sum_{i=0}^n c_i x^i =\sum_{i=0}^n (a_i+b_i) x^i + \sum_{i=0}^n c_i x^i = \sum_{i=0}^n (a_i+b_i+c_i) x^i$$
soft zealotBOT
swashbuckler
fiery pine
yea
fiery pine
some of the other axioms you need to prove are not quite as immediate i guess
supple nest
I tried to say 10+15 is the same as 15+10, but my proof was saying 2+5+2+5+2+5+2+2=25
Like I broke up the polynomials into parts when I should’ve done them as a whole
fiery pine
yea
supple nest
Like I’m technically right but made the proof way too convoluted
to the point where I’m saying something else
fiery pine
nothing you wrote was wrong, just that to justify the things you wrote, you'd need to know things about polynomials that would make the proof trivial in the first place
supple nest
ok so I’m going off of things that I technically shouldn’t know yet in A and B
And E
fiery pine
if your proof of (p+q) + r = p + (q+r) just stated (p+q) + r = p + (q+r)
that also wouldn't be saying anything wrong
supple nest
Yeah but I need to like, prove that that’s true right?
fiery pine
yea
supple nest
Just by doing the polynomial addition again in a less convoluted way
fiery pine
i find it a little weird to do this instead of proving the more general fact that polynomials are associative and commutative, since you'd have to do that anyway to prove real polynomials form a vector space. and then this would just be a special case
supple nest
I know, the question kinda sucks
fiery pine
yea i don't think questions like this are very interesting but you should know how to do them at least
supple nest
Ok so just remember to add whole polynomials instead of by parts right?
fiery pine
proving two expressions are equal with basic algebra comes up a lot but it's frequently messed up
hm just remember that every time you write something like a = b = c = ..., you should be able to explain why a = b pretty simply. it could be from a definition, or an already known fact. same with why b = c, etc
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@supple nest Has your question been resolved?
pulsar axle
hello
rustic sinew
how could i solve this question via regression?
Are you supposed to use regression?
pulsar axle
Are you supposed to use regression?
welli mean
i could solve it just by using the gradient
of the radius
pulsar axle
i could solve it just by using the gradient
but i wanna know how to do it w regression just incase i get a problem which i cannot just do this with
rustic sinew
Regression is a pretty inappropriate tool here
pulsar axle
How so
rustic sinew
Regression to the mean suggests you have observations and are fitting a curve to that data. Do you mean like generically using optimization?
rustic sinew
Like this? Im not familiar with desmos
pulsar axle
yes the ~ thing
rustic sinew
no whatever this is 😅
But the ~ regression is referring to this type of analysis
pulsar axle
Ah ok
rustic sinew
Which is why thats a weird tool to use to solve a tangency problem
pulsar axle
i see
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@pulsar axle Has your question been resolved?
pulsar axle
<@&286206848099549185>
south crown
Hi
quasi plume
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quasi plume
I'm confused on how the values inside the parenthesis were chosen
where is the "pole" or whatever that we use to shoot the rays
like I can tell the 3+2sin(theta) is the "big" one
but like idk where the lines are being drawn from to determine that
from 0,0, from -1,0 ?
.close
steady wraith
how do you do the first one
final saddleBOT
how do you do the first one
steady wraith
so 0 = a + b
so a = -b
1 = ac + bd
(im going to call lambda "c" and mu "d" because it's easier)
steady wraith
1 = ac + bd
but you can also write this as 1 = ac - ad
but 1 also equals ac^2 - ad^2
so ac^2 - ad^2 = ac - ad
(root(a)c - root(a)d)(root(a)c + root(a)d) = ac-ad?
wow this really doesn't look messy at all with the root(a)s
rocky tusk
why would you do that
steady wraith
why would you do that
idk
rocky tusk
no reason to bring root(a) into this
steady wraith
i dont know how you get to lambda^2 + lambda(mu) + mu^2
rocky tusk
a(c - d)(c + d) = a(c - d)
steady wraith
no reason to bring root(a) into this
sorry i just saw a difference of two squares and ran with it
steady wraith
a(c - d)(c + d) = a(c - d)
oh yeah
i could have done it that way
bruh
why didnt i just do that
scarlet sequoia
a(c - d)(c + d) = a(c - d)
am I hallucinating or did some squares disappear
rocky tusk
🤔
rocky tusk
a(c^2 - d^2) = ac^2 - ad^2
steady wraith
a(c - d)(c + d) = a(c - d)
wait so (c+d) = 1?
rocky tusk
wait so (c+d) = 1?
that would be the case provided that a(c - d) ≠ 0
steady wraith
that would be the case provided that a(c - d) ≠ 0
it says a is positive
idk about c - d
rocky tusk
👍🏻
steady wraith
it's either c-d = 0 or c+d = 1
do you just square (c+d)
c^2 + 2cd + d^2 = 1
i need to change the cd part somehow
bleak granite
this seems like overcomplicating it, plug in n=3 you get ac^3-ad^3=a(c^3-d^3) (from b=-a)
use difference of cubes formula
c^2+cd+d^2 should pop out
steady wraith
this seems like overcomplicating it, plug in n=3 you get ac^3-ad^3=a(c^3-d^3) (f...
oh yeah
i should have done that
nvm
late bolt
The formatting was giving step
steady wraith
The formatting was giving step
yeah
late bolt
I can't remember if I've attempted this one tbh
Either way I'm done with that shit now
late bolt
I'm sitting STEP next year so uh
Good luck, its not for the weak 😭
steady wraith
Either way I'm done with that shit now
wait you sat STEP?
steady wraith
Good luck, its not for the weak 😭
yh
late bolt
wait you sat STEP?
Yeah unfortunately
steady wraith
I guess a start would be actually getting the offer tho
late bolt
I had a cambridge offer
steady wraith
i think I'm probably gonna get rejected pre-offer rather than from STEP
late bolt
And flopped