Available help channel!
#help-33
marsh citrusBOT
Available help channel!
still temple
marsh citrusBOT
still temple
idk whats next
marsh citrusBOT
@still temple Has your question been resolved?
still temple
but dont know how do get there from there
marsh citrusBOT
still temple
.reopen
marsh citrusBOT
✅
still temple
thanks for your help 💀
craggy quartz
what does rounding to the nearest half cm mean?
marsh citrusBOT
what does rounding to the nearest half cm mean?
marsh citrusBOT
@craggy quartz Has your question been resolved?
balmy pivot
marsh citrusBOT
still temple
what hav u tried
still temple
you should use tاales rules
dawn spear
find out the value of AC and AB in one variable and find value of that variable with the help of hypotenus
marsh citrusBOT
@balmy pivot Has your question been resolved?
granite locust
marsh citrusBOT
cobalt sentinel
Show ur work
dawn spear
bro how do u know that their sum is 0
granite locust
Ah that's a good question
dawn spear
u fked it up at the first step
granite locust
💀
Wait ye ye
Lemme retry brb
Should I just whole square it
And apply (a+b)²
?
Lemme try nvm
dawn spear
Should I just whole square it
yes
celest wyvern
why tho?
dawn spear
show me ur working
timid idol
,rotate
elfin berryBOT
timid idol
why did you square the whole thing?
timid idol
no but I dont think you can square the whole thing at first
$\sqrt{25+10\sqrt{6}}+\sqrt{25-10\sqrt{6}}$
elfin berryBOT
ItzAine
granite locust
Ye
timid idol
yea but its not = to anything yet
granite locust
Ye true
dawn spear
u can do the root of its square tho
timid idol
you would have to square both sides
dawn spear
a = root of a^2
granite locust
OH
YE
so if I root over my ans now
I should get it?
Ryt?
√60
Ye
2√15
Gottem
timid idol
yea you could 
granite locust
Oh jesus
granite locust
All I can think of is 17¹²-1973^6
celest wyvern
-1973^6
sleek lake
that's 9 not 6
granite locust
Fr
nova totem
This isn't too bad
celest wyvern
are u familiar with long multiplication
granite locust
What is 7^3
63
celest wyvern
without calc like 1976*5678 without calculator
granite locust
without calc like 1976*5678 without calculator
Yeye
nova totem
3 is the units digit for 7^3, correct?what's the units digit for 3^4
granite locust
3 is the units digit for 7^3, correct?what's the units digit for 3^4
Ooo
I get it
I power shit their unit digits
Then subtract them
nova totem
I think that works. It should work
celest wyvern
well u can see it thru long division
the last digit is affected inly by teh product of teh last digits
granite locust
I can see it Rayquaza
celest wyvern
do it once to see
granite locust
granite locust
Lol
tulip night
I think it’s 0
granite locust
the last digit is affected inly by teh product of teh last digits
Ye ye true
nova totem
It's legit 2
tulip night
I’m only doing multiplication of last digit
nova totem
Bruh it's legit 2 he even got it right
tulip night
But I’m 2 lazy to get calculator
nova totem
You just use numerical analysis
You only care what's gonna go on with the units digit
granite locust
But I’m 2 lazy to get calculator
(The questions aren't meant to be solved with calculators bruh)
celest wyvern
But I’m 2 lazy to get calculator
ur too lagy to be right
he needs one for the product of single digits so yeah..
granite locust
💀
nova totem
(7^3)^4 is gonna have a units digit of 1. 1973^9 is gonna have a units digit of 3. 1-3 = -2 but it's asking for the digit, so it's 2
If you really wanna like
,w calc (17^3)^4 - 1973^9
celest wyvern
wow a hiphop playlist thanks
elfin berryBOT
fiery musk
This is calculus 1.
This is the stewart 9th edition 6.2 section
I just want to know how the integral changed from -4 s 4 to 0 s 4
marsh citrusBOT
This is calculus 1.
This is the stewart 9th edition 6.2 section
I just want to k...
rose fox
This is calculus 1.
This is the stewart 9th edition 6.2 section
I just want to k...
you are from viet nam.
fiery musk
i live in cali, but I'm viet though!
rose fox
Are you vietnamese? Are you American? Where is your homecountry?
fiery musk
my parents immigated to the u.s and I was born here in so cal
my ancestry hometown is hanoi
rose fox
my parents immigated to the u.s and I was born here in so cal
my ancestry hometo...
oh
are you freshmen in an university?
fiery musk
i'm in community college right now 😵💫
freshman 💀 trying to transfer to like UCLA
anyways whats up with your integument in me being viet 😂
rose fox
i'm in community college right now 😵💫
freshman 💀 trying to transfer to like...
I thought you were in university.
rose fox
i'm in community college right now 😵💫
freshman 💀 trying to transfer to like...
Oh. When you transfer a university next sophomore?
fiery musk
probably fall 2024 as a junior
transfering as a sophomore isn't a "good" idea
bro 💀
rose fox
transfering as a sophomore isn't a "good" idea
why?
fiery musk
cuz that's the same like as EA for high schoolers
fiery musk
wait but who are you are though
bro is just coming up here and asking me questions 😂
fiery musk
What is it?
like a junior trying to get into uni
instead of a senior
rose fox
like a junior trying to get into uni
instead of a senior
What major do you study?
rose fox
wait but who are you are though
bro is just coming up here and asking me questio...
Who am I? Lol. Someone answer my question in this server. 🙂
fiery musk
What major do you study?
comp sci till i die 😩
i'm self studying calc 2 rn so I can study physics later
marsh citrusBOT
@fiery musk Has your question been resolved?
worn nimbus
what the hell is that letter
marsh citrusBOT
what the hell is that letter
hasty ruin
hmm? seems to just be a choice of notation for me
elfin berryBOT
Gijs
worn nimbus
$\mathscr{I}^1$
elfin berryBOT
Gijs
marsh citrusBOT
elfin berryBOT
IV
hasty ruin
oh it's actually I lol
marsh citrusBOT
Available help channel!
silent musk
marsh citrusBOT
nova totem
Assign letter points to each corner and intersection
silent musk
😦
i only need to find the yellow angle
from this step i can move
i only need the yellow one
nova totem
Why would you need it
You can easily figure it out using triangle and vertical angle properties
silent musk
i find it easier for me when i dont know the properties
silent musk
There's an isosceles triangle
idk if one of those is isoscele
if there is, its not in the description of the example
nova totem
You don't need to be given
There is a triangle in the diagram that has distinct properties that make it isosceles
If you're gonna heavily rely on everything given to you idk how you're gonna do in the class lol
silent musk
If you're gonna heavily rely on everything given to you idk how you're gonna do ...
lol idk if its phylosophy or math
nova totem
Circle the isosceles triangle. Google isosceles triangle properties if you can't find it
But you should memorize them
silent musk
i know what is isosceles triangle but none of those looks isosceles
nova totem
Well the diagram gives you one. What's true about the base angles of an isosceles triangle?
nova totem
The base angles are congruent
There's one triangle with two congruent angles
That description is literally given to you
It would be dumb if the shaded angles weren't congruent
Actually wait
They just shaded them for visuals sake didn't they
Oh bruh
That's so dumb
None of them are isosceles, your teacher just gave a shit diagram
silent musk
okey so
nova totem
Is that angle (in the triangle, next to the 30) 40°?
Because then you can use the angle-sum property for all triangles, straight and vertical angle properties
marsh citrusBOT
@silent musk Has your question been resolved?
nova totem
So if you have a triangle, two of the angles are 30 and 40, what's the other angle
marsh citrusBOT
@silent musk Has your question been resolved?
nova totem
Well you see the arc
You don't need that yellow angle
Where they intersect is not the center
That's where the 80 is from
That's why I said you don't need the yellow angle
marsh citrusBOT
@silent musk Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
still temple
im trying to find the determinant of this matrix via levi civita symbol. But I get 98, although I may do something wrong or missed something. ¿What Im missing?
marsh citrusBOT
im trying to find the determinant of this matrix via levi civita symbol. But I g...
lilac bane
Is the matrix the one in the bottom?
still temple
Yes, i just summed all the products. I may missed something
lilac bane
Hmm
still temple
Its supposed to be 56
lilac bane
Why don't you try the nested determinant method?
still temple
I have to use this
lilac bane
Hmm
I think you missed some signs
Not sure though. Levi Civita Symbol is pretty new to me
marsh citrusBOT
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Available help channel!
dense gulch
marsh citrusBOT
dense gulch
I been trying to do this problem but I'm not sure if the anser is A or c because if the probability space total is w1 and w2 then its A but if there are more outcomes possibilitys then its c
marsh citrusBOT
@dense gulch Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
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burnt abyss
y=x^2 - 4x
marsh citrusBOT
y=x^2 - 4x
burnt abyss
How do i find the origin of the parabola
late geode
wdym by origin of the parabola
burnt abyss
Like the lowest point
late geode
vertex?
burnt abyss
Yeah
late geode
complete the square and/or apply properties of the vertex
haven't you asked this a few weeks ago already?
still temple
find the roots (i'll call them r1 and r2)
burnt abyss
Yeah those are the intersections with the x axis
still temple
find the roots (i'll call them r1 and r2)
and then try to plug (r1+r2)/2 for x
because the vertex is always at the center of the two roots
(idk how to explain)
but you get the idea
burnt abyss
Ok
And for then i just plug that x into the function to get the y coordinate of the vertex?
still temple
yeah
hidden plaza
just differentiate tbh
still temple
i don't think they got to calculus yet
hidden plaza
hm they were just differentiating something a minute ago
still temple
oh
burnt abyss
hm they were just differentiating something a minute ago
Can you continue?
Im asking for the 3rd time
late geode
apply properties of the first derivative to get the location of the stationary point (which in this case will be the turning point / vertex of your parabola)
burnt abyss
What properties
burnt abyss
Points where dy/dx is 0
late geode
yes that will be
the location of the stationary point (which in this case will be the turning point / vertex of your parabola)
plug that into the original
y = x^2 - 4x
to get the y-coordinate
crimson frost
Hi! I've been trying to prove that
a · sin(x) + b · cos(x) = sqrt(a² + b²) · sin(x + arctan(b/a))
As it turns out, it's wrong, because the actual identity has a sgn function:
a · sin(x) + b · cos(x) = sgn(a) · sqrt(a² + b²) · sin(x + arctan(b/a))
But I didn't knew it.
The first one is true when a < 0 only
I have two proofs, and I have a question for each of them
First one:
This seems to be the proof that actually works, because the identity I tried to prove (without the sgn) is only true when a > 0 and that's what I get, but why am I meant to say that it's not true for a < 0? Is it enough to say that that final equation gives 1 = -1?
Second:
This instead is a wrong proof, because it's proven that it works for every a and b ∈ ℝ, but that equation is true only when a < 0.
Where did I go wrong?
marsh citrusBOT
Hi! I've been trying to prove that
a · sin(x) + b · cos(x) = sqrt(a² + b²) · si...
crimson frost
First one:
elfin berryBOT
Nonna
crimson frost
Second:
elfin berryBOT
Nonna
spark otter
Is arctan(tan(theta)) always equal to theta ?
crimson frost
only when -π/2 < theta < π/2
spark otter
Exactly
crimson frost
Oh wait I see whats going on
so it's true only when -π/2 < theta < π/2, a is the x coord of the point P, so it's only true when a > 0 (a must be in either the first or fourth quadrant)
crimson frost
Which one?
spark otter
The one using absolute value
I don't understand which
spark otter
Like a×sin + b×cos = |a|(sin + b/a×cos)
crimson frost
yes it's true only when a > 0, because if you split the cases a < 0 and a > 0, for a < 0 you get 1 = -1
But I can't give any other reasoning
marsh citrusBOT
@crimson frost Has your question been resolved?
spark otter
Just use a×sin + b×cos = sqrt(a²+b²)[a/sqrt(a²+b²)×sin + b/sqrt(a²+b²)×cos]
Since the two factors a/sqrt(a²+b²) and b/sqrt(a²+b²), squared and added together give 1
You can find theta such that cos(theta) equals the first one and sin(theta) equals the other
spark otter
<@246787399991033858> ?
And then a×sin(x) + b×cos(x) = sqrt(a²+b²)sin(x+theta)
crimson frost
I don't understand exactly what you mean, but I think I'll stop here for now and re-read it later, I'm kinda tired
Thank you so much @spark otter 
spark otter
Np
crimson frost
.close
thin hinge
any way i can do this without dividing it fully
marsh citrusBOT
any way i can do this without dividing it fully
elfin berryBOT
marsh citrusBOT
@thin hinge Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
meager wave
Hi, I have a question, Is this true?
marsh citrusBOT
Hi, I have a question, Is this true?
meager wave
Why is the answer positive
Why can't it be negative?
marsh peak
Is it $\sqrt{x^2} = |x|$?
elfin berryBOT
A Lonely Bean
meager wave
What should I do with the bot reactions
marsh peak
Nothing
marsh peak
**A Lonely Bean**
Is this what's on the screenshot you sent though?
meager wave
yes
marsh peak
It's positive because sqrt is defined to be always positive
marsh peak
Yeah, if you no longer have any questions
marsh citrusBOT
marsh citrusBOT
Available help channel!
wet forge
marsh citrusBOT
wet forge
How can you add a point X to a vector H?
marsh peak
You'll often see points and vectors being treated as the same thing
Just add up the corresponding components
wet forge
okay 
solid echo
How can you add a point X to a vector H?
They tell you the vector sum directly
wet forge
.close
ancient maple
Hi Can I get help with this please.
marsh citrusBOT
Hi Can I get help with this please.
marsh citrusBOT
@ancient maple Has your question been resolved?
ancient maple
<@&286206848099549185>
marsh citrusBOT
@ancient maple Has your question been resolved?
marsh citrusBOT
@ancient maple Has your question been resolved?
marsh citrusBOT
@ancient maple Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
native halo
marsh citrusBOT
still temple
Nobody can read this.
native halo
IM GONNA SPOIL WAKANDA FOREVER IN THE NEXT 5 MINS
alr lemme type it then
1st image is describing about distance time graphs
calculating rate of change of the line segements
each point of (y) is 0 - 700 adding it up by 100 each tim
marsh citrusBOT
@native halo Has your question been resolved?
gentle cradle
is y axis the speed ?
@native halo
use the following formula
for example BC would be (400-200)/(12-4)
marsh citrusBOT
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Available help channel!
eternal flicker
marsh citrusBOT
eternal flicker
can someone help me answer true false or sometimes true
marsh citrusBOT
@eternal flicker Has your question been resolved?
eternal flicker
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
abstract wyvern
Hi all! I want to map non-linear data, but I'm not sure how to go about it. Basically, the input will be the motor position(0 - 255), and I want to send the according angle (0-90deg) as the output. We have a set data already from testing, I just need to figure out the best way to convert the position to angle. We are using Arduino and have been told maybe using multimap would work, but we are also looking for other possible solutions. Any form of assistance is appreciated!
marsh citrusBOT
Hi all! I want to map non-linear data, but I'm not sure how to go about it. Basi...
devout mauve
what exactly do you mean with non-linear here. do you have some example values that should be satisfied? like f(0), f(127), f(255) or something?
what exactly does motor position mean? do you have a sketch of the situation?
abstract wyvern
Motor position is basically the distance the actuator would extend or retract to. The relationship between the position and angle measured by a goniometer is non-linear in a way that f(0) = 0, f(100) = 30, f(200) = 80, f(255) = 90
abstract wyvern
I'm sorry but what do you mean by sketch? what do you wanna see?
Arccos like the trigonometric function?
abstract wyvern
We actually don't have a sketch for this yet. We're still figuring out the best approach to this. Right now, as the motor is extending we increment our distance variable every millisecond and we decrease when retracting.
abstract wyvern
Motor length - input
We want to get angle
H and l is fixed
devout mauve
rugged igloo
I need to solve this function (find the roots I think it's in English, aka the parts where it's 0) but idk where to start, I did all I know how to do aka change it to "="
marsh citrusBOT
I need to solve this function (find the roots I think it's in English, aka the p...
rugged igloo
<@&286206848099549185>
sage valley
I need to solve this function (find the roots I think it's in English, aka the p...
You can factorise it
rugged igloo
You can factorise it
What's the common factor?
sage valley
(x^4 - 35x^2 -36) can be factorised into (x^2 - 36)*(x^2 + 1)
rugged igloo
(x^4 - 35x^2 -36) can be factorised into (x^2 - 36)*(x^2 + 1)
huh how am I supposed to realise that just like that
sage valley
You can take x^2 as some ‘t’
Then the given biquadratic will be a quadratic function in ‘t’.
Then you can factorise that quadratic of ‘t’ and then keep t=x^2
rugged igloo
huh this some next level stuff
i'm not even close to this far
ig ill close this
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
still temple
how do i use double containment to
marsh citrusBOT
how do i use double containment to
main idol
show your attempt
still temple
uh if i break down the left side first, i think its like x is a subset of a and x is a subset of B, but I dont know how to make that into P(a intersect b)
main idol
x in A and x in B implies x in (A intersect B)
still temple
like by definition?
main idol
what's the definition of x in (A intersect B) ?
still temple
intersect is like x belongs to A and x belongs to b
i did this but i dont know if its valid\
main idol
that's only a single containment.
double containment argument for showing sets $X, Y$ are equal means proving two things
elfin berryBOT
riemann
main idol
$1. X \subset Y$
elfin berryBOT
riemann
main idol
$2. Y \subset X$
elfin berryBOT
riemann
still temple
i dont know how to prove the other direction
main idol
it's almost the exact same calculation but in reverse
x in A intersect B implies x are in what sets?
still temple
they are subsets?
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
tropic zenith
how can i solve a
marsh citrusBOT
how can i solve a
proper zodiac
Do the integration
tropic zenith
ok i will try
a=-2/3
The velocity of a body falling downwards in a certain liquid for tt seconds is given by v(t) = 3tv(t)=3t [m/s]. (In a vacuum, the speed is about 9.8t9.8t [m/s], but the liquid slows down the body somewhat.)
Calculate how far the body falls in the sixth second, i.e. from t = 5t=5 to t = 6t=6. Answer in meters, but omit the unit from the answer.
marsh citrusBOT
@tropic zenith Has your question been resolved?
tropic zenith
.close
tropic swift
I got this question which asks "how can we get system B from system A"
tropic swift
this is the answer although I don't understand the steps, could someone help me out?
boreal osprey
um. you subtract the two equations from system A?
glass silo
yeah but isn't 1y-7y = -6y?
Should be 1y - (-7y)
hollow helm
test
hollow helm
I would like help with the steps for this problem.
Solve the following equation for β, where −π≤β<π
$5tan^2β+5tanβ=0$
elfin berryBOT
cyanometer
tropic swift
damn that looks complex haha
hollow helm
Its Just a unit circle problem but its messing with my head right now.
tropic swift
is it university level?
hollow helm
yes
still temple
factor out tan b?
echo bough
hollow helm
.close
marsh citrusBOT
Available help channel!
knotty talon
explaining
marsh citrusBOT
explaining
knotty talon
Can someone explain what this statement means in a builder notation?
So I have the relation S = {(x,y) membership of A x B : 2 | (x-y)} what is the 2 | (x-y)
crystal lintel
unfortunate notation
still temple
How can I memorise the multiplication table, i cant find a song that is not stupid.
marsh citrusBOT
How can I memorise the multiplication table, i cant find a song that is not stup...
main idol
How can I memorise the multiplication table, i cant find a song that is not stup...
how old are you
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
thorn pebble
Can someone help me with this calc problem
marsh citrusBOT
Can someone help me with this calc problem
rotund violet
okay so whats the formula of A in terms of h and w
thorn pebble
A=wh+.2w^2
thorn pebble
P=2h+1.8w
rotund violet
P=2h+1.8w
no its not that
so we have 2h+w for the bottom 3 segments
but than for the triangle on the top
use pythagorean theorem to calculate each of those sloped side lengths
so what are those sloped side lengths
thorn pebble
rotund violet
Can someone help me with this calc problem
okay so here is how we calculate those side lengths
so each of those upper side lengths is sqrt((w/2)^2+T^2) right?
because they have a horizontal length of w/2 and a height of T
so our formula becomes 2h+w+2*sqrt((w/2)^2+T^2)
thorn pebble
so its 2h+2.28w
rotund violet
so its 2h+2.28w
yeah but i wouldn't round
thorn pebble
ok
rotund violet
so is this multivariable calc or single variable
thorn pebble
single variable
rotund violet
okay
rotund violet
so its 2h+2.28w
and we know replace w in this equation with our substitution
rotund violet
would that be h=(A-.2(P-2h)^2)/2
um no
rotund violet
and we know replace w in this equation with our substitution
our LHS remains P
and our right hand is 2h+(1+2*sqrt(.41))w
and so now we make it 2(A/w-2w)+(1+2sqrt(.41))w
thorn pebble
then what do we do
rotund violet
and so now we make it 2(A/w-2w)+(1+2sqrt(.41))w
okay this is correct
we should replace it with h, not w, as that is what our substitution calculates this
rotund violet
and so now we make it 2(A/w-2w)+(1+2sqrt(.41))w
we now find the derivative of this monstrosity
rotund violet
and so now we make it 2(A/w-2w)+(1+2sqrt(.41))w
further simplified, this is equal to 2A/w + (2sqrt(.41)-3)w
thorn pebble
the derivative should be (-3.44(w^2+.58a))/w^2
rotund violet
the derivative should be (-3.44(w^2+.58a))/w^2
okay
so now the maximization happens when the derivative is 0
so when is that thing equal to 0
(other than the case where w=0)
rotund violet
the derivative should be (-3.44(w^2+.58a))/w^2
check your a coefficient again
thorn pebble
ok
serene heart
set theory: how is this incorrect?
marsh citrusBOT
set theory: how is this incorrect?
proud ice
mystic minnow
and a missing element
marsh citrusBOT
@serene heart Has your question been resolved?
hazy lion
i need help 
marsh citrusBOT
i need help <:bearlain:762653539092529182>
hazy lion
if i can be honest neither direction seems straightforward
elfin berryBOT
jan Niku
hazy lion
from which you can write the ith column of the LHS as
elfin berryBOT
jan Niku
hazy lion
but beyond this im really not sure
marsh citrusBOT
@hazy lion Has your question been resolved?
hazy lion
so ive found that I could also write
well its an eigenvalue problem, i think
$AP_i = \lambda _i P_i$
elfin berryBOT
jan Niku
main idol
i need help <:bearlain:762653539092529182>
This is just spectral theorem
main idol
oh <:bearlain:762653539092529182>
Sorry I didn't mean to say "just"
It's a hard proof that most grad students can't even do
hazy lion
well i guess im confused
that theorem connects normal and unitarily diagonalizable
at least our statement of it does
let me see
,w spectral theorem
elfin berryBOT
main idol
I've taken that class. UCSC actually have a respectable math series for physics professors
9 pages though 
hazy lion
I guess im just trying to parse how this is the spectral theorem
that may involve 9 pages though
main idol
i need help <:bearlain:762653539092529182>
One direction should be easy. P is just the matrix where the columns are eigenvectors
main idol
I guess im just trying to parse how this is the spectral theorem
Ignore that. I was mistaking your matrix for Hermitian matrices
hazy lion
**jan Niku**
this
but maybe im going about it in the wrong way
i mean if you assume the entire part of the reverse direction
it seems to just give diagonalizability right
assume there exists a diagonalization of A
show A is diagonalizable
main idol
it seems to just give diagonalizability right
Yes
hazy lion
or am i nuts? i was mis understanding this on another problem
and i mean, the same in the other direction
silent jolt
man whoever works at WA is super into themselves
richard feynman had a funny quip about this to stephen wolfram who works at WA but i cant find it
i just wanted to join in on the WA hate but i dont even know the question being asked otherwise
hazy lion
i just wanted to join in on the WA hate but i dont even know the question being ...
ah youre good
and sorry i said 
benji
and not riemann
which is how i really felt
no offense benji
tepid hound
Can anyone explain me what N means?
marsh citrusBOT
Can anyone explain me what N means?
tepid hound
I am actually confused with the whole definition
hazy lion
Can anyone explain me what N means?
its basically like this
someone gives you an epsilon
its really really small
if the sequence converges, then you have some way of telling me how far into the sequence you have to go such that all terms further on than that are less than epsilon away
(from the limit)
@tepid hound https://www.youtube.com/watch?v=RFsQHVFLxVQ
i found this video pretty helpful when i took analysis
goes through the definition in a couple ways, what the negation is, a picture, a sketch of how a proof goes, including the scratch, then an example, in 8 minutes
😌
tepid hound
Ok thanks
marsh citrusBOT
@tepid hound Has your question been resolved?
placid oak
Which of the following functions are differentiable at (0,0)?
marsh citrusBOT
Which of the following functions are differentiable at (0,0)?
placid oak
I can reject option 3 as it is clearly discontinuous at (0,0).
How do I check for others?
proper zodiac
I think 3 is continuous at (0,0)
placid oak
proper zodiac
Why do you think its not?
placid oak
Can you explain how?
proper zodiac
Well why did you claim its not continuous at (0,0)
placid oak
Ok nvm, I overthought certain things
elfin berryBOT
proper zodiac
3 is almost definitely still not differentiable at 0,0 but you can't use discontinuity to prove it
placid oak
,w plot x^(1/3)
The function is (xy)^(1/3)
sage heath
3 is almost definitely still not differentiable at 0,0 but you can't use discont...
why do u say so 
placid oak
Ok
sage heath
i don’t really wanna spoil it by plotting
placid oak
Yes
hard sluice
Can anyone help me of how to do zeros of functions
sage heath
sweet raptor
What do I do here? I find the intergral and substitute?
marsh citrusBOT
What do I do here? I find the intergral and substitute?
proper zodiac
<@&268886789983436800>
sweet raptor
I already did
delicate prairie
ty
proper zodiac
Pewsky you need to make the substitution in order to evaluate the integral
u-substitution is an integral method, look it up if you're not sure
unreal wharf
why did we take k×alpha < epsilon? can't alpha be greater than epsilon?
twin girder
why did we take k×alpha < epsilon? can't alpha be greater than epsilon?
wdym? we can pick our alpha
unreal wharf
wdym? we can pick our alpha
why did we take it smaller than epsilon?
twin girder
if K<1 its not smaller than epsilon
but if you think logically we always pick alpha small. Since we say it works for any x with distance less than alpha away from x_0
so if alpha=1 works then obv alpha=0.5 or alpha = 0.0003219312939193919 or whatever also works
unreal wharf
hmmm i see, thanks for the help 😄. ig i have to study more cause im having a difficult time wrapping my head around them
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hollow sparrow
Hello! I have this quotient ring: $\mathbb{Z}_3[x]/\langle x^2 + x + 2 \rangle$, and I'm asked whether or not $\mathbb{Z}_3[x]/\langle x^2 + x + 2 \rangle$ is isomorphic to $\mathbb{Z}_9$.
marsh citrusBOT
Hello! I have this quotient ring: $\mathbb{Z}_3[x]/\langle x^2 + x + 2 \rangle$,...
elfin berryBOT
MellowDramaLlama
hollow sparrow
I want to say yes since we have equal cardinalities
but I"m not 100% sure
like if we let I = <x^2 + x + 2>, then we could map f(I) = 0, f(I + 1) = 1, f(I + 2) = 2, f(I + x) = 3, ... f(I + 2x + 2) = 9. Is there a way to verify this without tables or trial and error
?
or would it be from the 1st isomorphic theorem?
crap I gotta head to class. I'll ask this later on if I don't get a lightbulb moment for an answer
.close
winged light
I’m pretty sure this converges and the value is 3, but I would like to double check with someone else and see if they get the same
marsh citrusBOT
I’m pretty sure this converges and the value is 3, but I would like to double ch...
night mica
very hard
marsh citrusBOT
@winged light Has your question been resolved?
proper zodiac
It's not very hard, do a usub and then undo the power rule
marsh citrusBOT
@winged light Has your question been resolved?
winged light
It's not very hard, do a usub and then undo the power rule
Did you get 3?
marsh citrusBOT
@winged light Has your question been resolved?
winged light
<@&286206848099549185>
elfin berryBOT
winged light
,w int from -1/2 to 4 of 1/sqrt(2t+1)
Does this mean our integral converges?
devout mauve
if it has a value then it converges
safe spoke
marsh citrusBOT
safe spoke
The approach I tried is to assume a permutation function Permute(n) that generates the set of all permutations of Σ of length n
Essentially I'm trying to create a polynomial verifier for HALF(L) since that would prove that HALF(L) is NP
The challenge is that the permutation function can only be O(|Σ|^n), which is exponential, so my verifier is no longer polynomial
<@&286206848099549185>
marsh citrusBOT
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marsh citrusBOT
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smoky epoch
ill be with u in a sec hol up
is that the equation itself?
well lets see
a binomial has 2 terms
like 5x-1
Lets use pemdas,
give me a sec to write it out
so
lets just take out the 70
so 70-70=0
and that leaves us with -34x+4x^2
which we can do as 34x-4x^2
which is simplified
😄
because
let me show u smth
look
34x-3x
is the same as -34x+3x
watch
if x was 1 right
exactly
sure
lets see
well
we would want a normal denominator for all of them
so
but thats not the same for all of them
we want them to have all the same deniminator
is that - 1/x-1?
theres a little dash
do u wanna like solve for x?
kk
hol up
peak mauve
You can bring the -1/x-1 to the left hand side of the equation
And take the -3/x to the right side
smoky epoch
wait hold on
peak mauve
Ok
smoky epoch
lets multiply all terms by
(x-1)(x)
that way they'll share a common denominator
8 years old?
peak mauve
No
smoky epoch
ohhhh
smoky epoch
i remmber doing that
ok
lemme simplify it for u
so
we have 1/x-1 right
if we mult by (x-1)(x)
we get
1x−3(x−1)=−1/x−1(x−1)(x)
which if we simplify
would equal
to get a common denominator
we mult by both denominators that are different
to get one they would both have
like so
look
yes
yes
now if we simplify on the other isde
we get
hold on
if we add it to the other side we get
hm
yes
watch this
4/5+1/3=x/5
now we multiply by 15
so 12 +5=3x
like that
you get it?
sure
let me be more clear this time
so
peak mauve
what
smoky epoch
ok, now the only way we can make it a common denominator
is by multiplying the 2 different denominators
which are?
exactly
so those two multiplied are (x-1)(x)
peak mauve
Ohhhh okk yea
peak mauve
I didn't know you were doing that
smoky epoch
well hold on
(x-1)(x)
= x^2-x
by simplifying
so in reality, we're multiplying everything by x^2-x
but for the sake of simplifying it
we'll leave it at (x-1)(x)
so now look
smoky epoch
1(x-1)(x)
this equals (x-1)(x)/x-1
so we can cross out the x-1
now we just have x right?
ok now for the 2nd part
3(x-1)(x)
3x-3(x)/x
we can cross out the x
yes?
3(x-1)
so now we have x-3x-3
yes
ok
now for the last one
-1(x-1)(x)/x-1
we can cross out the x-1
so -1(x)
exactly
so now we have what
x-3x-3=-x
yes!
so simplify,
2x-3x-3
-x-3=0
x=???
yes
my mistake
still temple
Helo
smoky epoch
so now x=3
still temple
Can someone help me
smoky epoch
dude wait ur turn
smoky epoch
@still temple
do you get it now
hol up
yes
hmm
we must of made an error some where in our equation
lets see where
ohhh
i found it i think
its -3/x
so -3(x-1)
-3x+3
x-3x+3= -x
perfecto!
now plug it back in a check if its correcto
yes, perfect
peak mauve
now plug it back in a check if its correcto
Yea
smoky epoch
np
marsh citrusBOT
marsh citrusBOT
Available help channel!
somber galleon
Which of the given sequences converge? If necessary, determine the limit value. Justify your answers.
marsh citrusBOT
Which of the given sequences converge? If necessary, determine the limit value. ...
somber galleon
marsh citrusBOT
@somber galleon Has your question been resolved?
somber galleon
<@&286206848099549185>
void granite
do you need help
somber galleon
yep
void granite
for what
somber galleon
look up
Which of the given sequences converge? If necessary, determine the limit value. Justify your answers.
void granite
i forgr
somber galleon
he is trolling so helpers you can help me
proper zodiac
Try bound it above
marsh citrusBOT
@somber galleon Has your question been resolved?
marsh citrusBOT
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somber galleon
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