rank completely decides the equivalence class of a matrix up to base change
#help-38
amber python
worldly wing
rank completely decides the equivalence class of a matrix up to base change
well the rank and the dimensions right
amber python
well thats kinda implicit because you're not comparing matrices with different dimensions
worldly wing
right
so what you're saying is that if A and B are matrices of the same size and rank then you can multiply B by some invertible matrices to get A
amber python
yes
worldly wing
ok that makes sense
we're just changing the basis of the input and output
thank you very much
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versed jasper
trim lichen
f(-1) is -4 it looks like??
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torpid hawk
I'm struggling with this: Trigonometry
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I'm struggling with this: Trigonometry
trim lichen
therefore cos330 = cos60
no
if you wanna do it that way you would get that cos(330°) = sin(60°) but this is quite a confusing way of doing it
jolly saffron
it's positive
torpid hawk
if you wanna do it that way you would get that cos(330°) = sin(60°) but this is ...
that's what my teacher said also
trim lichen
better to notice 330° = 360° - 30° and thus cos(330°)=cos(30°)
torpid hawk
wait
jolly saffron
there's an easy shortcut to do these in your head
but it's better if it's done in radians
torpid hawk
Okay, but why is my way incorrect?
torpid hawk
oh
jolly saffron
cos(270 + x degrees) = sin(x degrees)
trim lichen
cos(270 + x degrees) = sin(x degrees)
don't memorize that tho
torpid hawk
my teacher told me take any angle and if alpha * (pie/2) and alpha is odd or even they either change to sin or change to negative
safe loom
I'm struggling with this: Trigonometry
finding cos is essentially finding the x-value of the point
torpid hawk
ohhhhhhhhhh
jolly saffron
yeah that's a helpful way to look at it
torpid hawk
wait but wouldn't that be cos 330 = cos 30
safe loom
simply think of it like "what's x-value, y-value" and u will do it
in fact, with this method u can also prove lots of identities
trim lichen
wait but wouldn't that be cos 330 = cos 30
yes and i said that earlier
<@&268886789983436800> troll
knotty oriole
Don't troll here
trim lichen
b&? or just deleted
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frank bough
M
frank bough
Ppl help
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remote wave
frank bough
24
urban copper
1 multiplied by 2, 24 times
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wraith hinge
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wraith hinge
@fervent thorn
fleet bear
!help
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safe loom
seems like u can use Chinese Remainder Theorem here
wraith hinge
seems like u can use Chinese Remainder Theorem here
it feels like the info given is less ?
safe loom
no?
wraith hinge
we can use that theorem to get relation between coefficients
whats next?
@safe loom
safe loom
it probably is just P(x) = A(x)(x - 1)^3 + B(x)(x + 1)^3 where A(x) and B(x) are quadratics at most
wraith hinge
it probably is just P(x) = A(x)(x - 1)^3 + B(x)(x + 1)^3 where A(x) and B(x) are...
how can u say that ?
safe loom
yeah no idk what im doing :/
sorry, cant help
i'll provide my approach if i can
its just that i never used CRT for polynomials before
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mystic iris
I already looked at this one earlier and all the answer choices turned out wrong when i tried
stable crescent
@wraith hinge what did u try?
wraith hinge
<@456226577798135808> what did u try?
i just considered a 5 degree polynomial with coeff. as a,b,c,d,e
then used remainder theorem
to get a relation
nothing else, it feels like i dont have much info to figure out about the roots
fleet bear
It's still pretty exclusive to me tbh but this helps a bit
$$ P(x) + P(x) = g(x)(x-1)^3 + 1 + g(x)(x+1)^3 - 1 $$
$$ 2 P(x) = g(x) ((x-1)^3 + (x+1)^3) $$
$$ 2 P(x) = g(x) (...) $$
Find ... and you'll see
stable crescent
why did you suppose they have the same quotient? @fleet bear g(x)
stable crescent
just let $P(x) = A(x)(x-1)^3 -1 = B(x)(x+1)^3 +1$ find some condition on A and B @wraith hinge
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Goëtia
wraith hinge
hmm
stable crescent
also look at the polynomial $Q(x) = P(x) + P(-x)$ look at it from a perspective of congruency modulo $(x-1)^3, (x+1)^3$
solid kilnBOT
Goëtia
stable crescent
you'll end up with this expression of P(x) = ax^5 + bx^3 + cx
stable crescent
@wraith hinge got it?
fleet bear
It's still pretty exclusive to me tbh but this helps a bit
$$ P(x) + P(x) = g(x...
Wasn't sure if this would help before it worked fine:
Since P(x) / (x-1)^3 has a remainder of -1, then P(1) = -1, P'(1) = 0, P''(1) = 0
same for P(-1): P(-1) = 1, P'(-1) = 0, P''(-1) = 0
(You can prove that with differentiation)
Anyway, let P(x) = g(x) (x - 1)^3 - 1, g(x) = ax^2 + bx + c then
P(-1) = 0, P'(-1) = 0, P''(-1) = 0 should each give one linear equation in a, b, c. That's 3 equations That can then be solved via elimination or whatever
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wraith hinge
Ohhh
ripe valley
Wasn't sure if this would help before it worked fine:
Since P(x) / (x-1)^3 has ...
Still don't understand, how did we get P'(1)=0?
Oh wait
Ic
wraith hinge
Wasn't sure if this would help before it worked fine:
Since P(x) / (x-1)^3 has ...
only thing which i dont get is, why g(x) is quadratic ?
i assume that you considered P(x) to be a 5deg, but the question states that it has degree at most 5, P(x) can be anything even rational.
@stable crescent
wraith hinge
also look at the polynomial $Q(x) = P(x) + P(-x)$ look at it from a perspective ...
sorry but i dont have any idea about congruency modulo
ripe valley
only thing which i dont get is, why g(x) is quadratic ?
i assume that you consid...
No, afaik u can only define degree for polynomials
ripe valley
only thing which i dont get is, why g(x) is quadratic ?
i assume that you consid...
Covers the at most case as well
Because if it was indeed degree 4, the value of a would have been simply 0
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stable crescent
sorry but i dont have any idea about congruency modulo
Thats fine
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queen dagger
what am I overlooking? The formula in this matrix for the fibonacci sequence. Let's take 5 as our n, isn't it 6,5,5,4 according to the formula?
wooden plover
I don't understand what you're asking
what's supposed to be 6 5 5 4 ?
@queen dagger
queen dagger
Do you see the matrix with the formula for A^n?
wooden plover
ok
queen dagger
I don't understand it, I feel like I'm making a stupid mistake but still
pallid lake
A^5 = (F_6, F_5
F_5 F_4)
wooden plover
ah right
queen dagger
Right
wooden plover
i thought you meant literally 6 5 5 4, without the Fs
queen dagger
but that's different then what's written above?
queen dagger
i thought you meant literally 6 5 5 4, without the Fs
I see, I just didn't know how to write the matrix notation
wooden plover
nah I'm fine with the matrix in a line lol, I got that
pallid lake
Maar wat lukt nou niet dan
queen dagger
A^5 = (F_6, F_5
F_5 F_4)
ok great to know that I can still do 5+1 and 5-1, but why does that differ from the actual matrices above? I don't see how the formula is relevant to all the matrices above
queen dagger
Maar wat lukt nou niet dan
als je A^5 zelf berekent, kom je toch iets anders uit dan wat er bovenaan staat? Waarom staat die formule er? 🥲 is n mss iets anders dan ik denk of?
wooden plover
it's not differing if you're starting the fibonacci with F_0 = 0, F_1 = 1
pallid lake
Oh nee dat is idd een foutje denk ik
queen dagger
it's not differing if you're starting the fibonacci with F_0 = 0, F_1 = 1
yeah but it says for all n greater or equal to 2. They mean smaller than 2?
wooden plover
smaller than 2 wouldn't be a very interesting statement wouldn't it?
bigger than 2 yes
queen dagger
Oh nee dat is idd een foutje denk ik
HOERA, weetje hoelang ik mijn kop hier al over breek
wooden plover
als je A^5 zelf berekent, kom je toch iets anders uit dan wat er bovenaan staat?...
well what happens when you compute A^5 ?
queen dagger
well what happens when you compute A^5 ?
it's wrong if you take any n, 5 was just ad random
queen dagger
Moet je het ook bewijzen met inductie of nie
tis deel van een cursus waar ze uiteindelijk dit willen bewijzen
wooden plover
it's wrong if you take any n, 5 was just ad random
I still can't pinpoint why you think it's wrong
you say you might have made a stupid mistake, it's hard to tell if you don't show your computations
pallid lake
Okay wait
wooden plover
is it just a shifting issue ?
queen dagger
if you calculate A^n with the formula matrix you get something different to the 5 matrices up top. Am I interpreting something incorrectly or is there just straight up a mistake in the book? I need help coming to that conclusion
wooden plover
it's not differing if you're starting the fibonacci with F_0 = 0, F_1 = 1
that's why I've said that at the start, I just think you're using a different convention than them for the fibonacci sequence
queen dagger
@pallid lake versta jij mij? Ik snap gewoon de afbeelding niet. Ik denk niet dat het aan mijn interpretatie van de fibonacci rij ligt, ik snap gewoon niet waarom ze 5 voorbeelden geven en dan zeggen 'jupla, het werkt volgens deze formule' en de formule werkt niet met de voorbeelden.
"Zo ontdek je dat de machten van A als volgt opgebouwd worden met de getallen van Fibonacci:"
pallid lake
Heb je ooit inductie gehad?
Als het geldt voor de eerste geval n = 2, en het werkt voor n = k+1, dan werkt het voor alle getallen.
queen dagger
ah is dat wat ze hier stellen?
Tzou veel verklaren
ik zag het echt als een formule
pallid lake
Ja, je weet dat als A^2 = [F3,F2,F2,F1]
wooden plover
if you think it doesn't work with the examples you can't even start the induction you know
pallid lake
en A^k+1 = [Fk+1, Fk, Fk, Fk-1], dan geldt het voor alle k.
en dus klopt de formule die eronder staat
queen dagger
if you think it doesn't work with the examples you can't even start the inductio...
I think what I meant got lost in the translation, but thank you
wooden plover
maybe
queen dagger
en dus klopt de formule die eronder staat
jeej, merci held(in)
queen dagger
kvind wel wat ongelukkig geschreven
queen dagger
Ik weet nu al dat jij uit brabant komt
no no
queen dagger
zuidelijker xp
pallid lake
kvind wel wat ongelukkig geschreven
eens
pallid lake
succes drmee nog
spice wagon
what am I doing wrong
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what am I doing wrong
left oriole
what are you trying to do? can you show the original question?
spice wagon
left oriole
why are you assuming x = pi/4?
spice wagon
that's where cosx=sinx
left oriole
oh i missed that part ok, that's fine
spice wagon
i think the answer is supposed to be 45 degrees, but idk how to get that with the dot product
are my vectors wrong?
left oriole
no your work seems fine, why do you say it should be 45 degrees?
spice wagon
that's the answer google gave me
left oriole
does your web page or whatever have a "show answer" option for this question?
spice wagon
not for that question
left oriole
this MSE answer agrees with you: https://math.stackexchange.com/a/4116141
left oriole
yw
spice wagon
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azure pulsar
i dont understand how tf to approach this
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i dont understand how tf to approach this
trim lichen
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azure pulsar
think he left already
trim lichen
did he?
trim lichen
anyway whatever
trim lichen
do you know in general how to make the matrix of a linear transformation
azure pulsar
dont know how to latex ngl so
trim lichen
even so
trim lichen
it's the IMAGE of each input basis vector, written in coordinates wrt the output basis
azure pulsar
yea
trim lichen
point is you will need to project each one of your two basis vectors onto v
no real way around that i don't think
trim lichen
hm that would help certainly
im not sure i feel like redoing the number crunching rn tho
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azure pulsar
but like what do i even put for x? and wont that give me sum annoying result?
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azure pulsar
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sacred jackal
uhh well its P = [ [b1]a [b2]a ... [bn]a ]
as another helper has suggested, the n-th column of your desired transformation matrix is the image of the n-th basic vector (in the basis for the domain of the specified linear transformation) under the specified linear transformation with respect to the basis for the codomain of the specified linear transformation
i suggest using β = {(4,1,0)ᵀ, (-2, 0, -1)ᵀ}
using β to mean __ba__sis
It's possible to use Unicode to type many subscripts and superscripts, say the transformation matrix
P = [[b₁]ᵦ [b₂]ᵦ ⋯ [b ₙ]ᵦ]
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midnight pebble
Help
ionic pendant
,, \qty{250}{\s} = \qty{2.50 e2}{\s} = \qty{0.250 e3}{\s}
solid kilnBOT
cloud
midnight pebble
is hecto?
ionic pendant
as seen in the table, $\qty{1}{\hecto\s} = \qty{e2}{\s}$
solid kilnBOT
cloud
ionic pendant
therefore $\qty{2.50e2}{\s} = \qty{2.50}{\hecto\s}$
solid kilnBOT
cloud
midnight pebble
why is 2.5?
ionic pendant
because $250 = \num{2.50e2}$
solid kilnBOT
cloud
midnight pebble
Does this server have a table of physical quantities?
ionic pendant
no, it seems like you already have one
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thin vine
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thin vine
could someone please help me with this problem
im not really sure what to do
the first thing i thought that i could have done was like the synthetic divison
but im pretty sure the numbers would have grown big
edgy willow
the trick is probably that x^7, x^3, and x are odd functions
thin vine
oh ok
ancient crag
if f(-5) = 5 dosent F just flip the sign?
thin vine
i dont think so
becaues you have to take the -7 into account
then again i think we can use that
thin vine
no thats all good thanks for helping
left oriole
if f(-5) = 5 dosent F just flip the sign?
it flips the sign of the first three terms, which is enough to make this solvable
limpid dawn
becaues you have to take the -7 into account
bring it to the other side
solid kilnBOT
limpid dawn
f(-5) = 5 as given
thin vine
ok yeah
limpid dawn
so you get 12 = ...
thin vine
wait how did you get 12
limpid dawn
5+7
thin vine
where did the 5 come from?
limpid dawn
f(-5) = 5 as given
.
limpid dawn
now you can basically multiply by (-1) the equation
and then subtract 7
then you got on the right f(5) and on the left the value for it
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night mirage
Have I correctly moved the takeoff-point? Or am I not following the rule correctly?
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@night mirage Has your question been resolved?
night mirage
Or will it be like this?
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shy acorn
how is the answer c? when i did the questin i got D
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how is the answer c? when i did the questin i got D
empty orchid
how is the answer c? when i did the questin i got D
!show
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how is the answer c? when i did the questin i got D
Show your work, and if possible, explain where you are stuck.
shy acorn
the four subdivisions are 0,pi/4,pi/2,3pi/4,pi
and then you plug in the formula for trapezoidal approximation: pi/4 * (0+2(sqrt(2)/2+1+sqrt(2)/2)+0)
and i just evaluated it and got pi/2 * (sqrt(2)+1)
void gorge
who needs help
shy acorn
i do
past cargo
and then you plug in the formula for trapezoidal approximation: pi/4 * (0+2(sqrt...
uhhhh
where did you get that from
past cargo
f(x_0) + 2f(x_1) + 2f(x_2) + 2f(x_3) + f(x_4)
f(x_0) = f(x_4) = 0
what did you have for f(x_1) and f(x_3)?
shy acorn
ohhh wait i think i missed the coefficient in the front
void gorge
who needo helpo
shy acorn
i think it should be this pi/8 * (0+2(sqrt(2)/2+1+sqrt(2)/2)+0)
past cargo
i think it should be this pi/8 * (0+2(sqrt(2)/2+1+sqrt(2)/2)+0)
uhh looks good yeah
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past cargo
,w pi/8 (sqrt(2) + 2 + sqrt(2))
solid kilnBOT
past cargo
yeah okay factor out the 2 and you get exactly C
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lethal vigil
vague citrus
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lethal vigil
why this channel still open
frozen hedge
Managed to do this question somehow by manual counting, can anyone guide me to do it with combinations?
trim lichen
count all triangles first w/o regard to whether they share any sides with the octagon (which is 8C3)
then count the ones that share 2 sides and the ones that share exactly 1 side, and subtract those away
frozen hedge
then count the ones that share 2 sides and the ones that share exactly 1 side, a...
Thats how i did it yes
Im trying to figure out how to do with the formula they got
Where that formula came from
trim lichen
oh so they pulled it out of their ass huh
trim lichen
i have no idea how they got it to be completely honest with you
true kestrel
yeah i think i got it too
frozen hedge
Maybe uh
They first take 1 point using nc1
For the next point, we cant take the two points next to it, and after that we cant take the two points next to the other points we selected after it
So n-4C2 and accounting for double counting maybe they divide by half
Altho i just pulled that out of my ass
frozen hedge
Where did n-4 come from
Is it including the previous point
@true kestrel
Because if we can point 7 as the second point, then itll be n-5 because the adjacent points are not
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trim musk
8c3 - 8c1* 2* 4/2 -8
total - one side common -two sides common
one side common is a bit tricky:
8c1 for choosing any one vertice multiplied by 2 because you have to include one of the adjacent vertices for it to share one side with the octagon, and *4 because then you have 4 (n-4) vertices available to choose from, you finally need to divide by 2 because the trignales will be coutned twice, label the vertices a1, a2 a3... if i consider the triangle a1 a2 a6 it is counted when taking the first vertice as a1 as well as the first vertice as a2
slate hinge
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magic eagle
can u show the diagram
floral dew
magic eagle
@slate hinge
slate hinge
It's a vertical projection so I didn't draw any
magic eagle
ye lmao if that was the case part b wud be fked up
slate hinge
Damn
That makes no.sense though
It flew vert and then they just yeeted the bomb out
magic eagle
ye lmfao
slate hinge
Goodness
Thanks for the help
I would have to try the whole damn thing again I guess
It still made no sense
magic eagle
eh
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vapid mulch
"this is asking 14/x = 7"
"not 14/7 =x"
"so its not true"
is this comment correct, somebody who is math undergrad told me this
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"this is asking 14/x = 7"
"not 14/7 =x"
"so its not true"
is this comment corre...
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keen shuttle
"this is asking 14/x = 7"
"not 14/7 =x"
"so its not true"
is this comment corre...
it is asking 14/x=7
because a pack of yoyo-s has x yoyos
and we know we sold 7 packs of yoyos, with 14 total yoyos
so 14/x=7
vapid mulch
it is asking 14/x=7
because a pack of yoyo-s has x yoyos
and we know we sold 7 p...
so khan academy was wrong ?
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so khan academy was wrong ?
keen shuttle
so khan academy was wrong ?
14/7=x is correct but the other equation represents the question more accurately(or 7*x=14)
vapid mulch
14/7=x is correct but the other equation represents the question more accurately...
yeah that is division,
but he SPECIFICALLY said that 14/7=x is incorrect
keen shuttle
yeah that is division,
but he SPECIFICALLY said that 14/7=x is incorrect
I think they probably meant that 14/7 does not represent the problem at hand the best not sure
vapid mulch
imo he is wrong, but im asking for second opinion
vapid mulch
I think they probably meant that 14/7 does not represent the problem at hand the...
14 divided by 7 equal groups [packs of yo-yos] = 2 yo-yos per group(pack)
seems pretty good to me
keen shuttle
yes but even if it's true it doesn't mean it's correct here because it asks for the equations that helps to find it
vapid mulch
well 14/7 = x is an equation and it helps
keen shuttle
well 14/7 = x is an equation and it helps
I suppose so
vapid mulch
maybe <@&286206848099549185> can help ?
keen shuttle
You shouldn't ping for this probably, it's pretty much just pendatics whether it counts or not and ultimately helps
which is not the goal of the server
vapid mulch
You shouldn't ping for this probably, it's pretty much just pendatics whether it...
how is it pendatics ? the difference is between the answer being correct or not correct
keen shuttle
how is it pendatics ? the difference is between the answer being correct or not ...
Whether 14/7=x is correct or not is ultimately determined by how the person views the question being asked, for instance the person you mentioned before said it wasn't correct because they have a different definition of it and you are saying yes because you have a differing definition of it
just accept that khan academy views it as correct(and take this into account for it's questions) and move on to your other questions for it
vapid mulch
Whether 14/7=x is correct or not is ultimately determined by how the person view...
that is just not true, theres no "different definition of division" the question if this answer is correct
you can think of it in different ways, but I want to know if this answer is correct
keen shuttle
that is just not true, theres no "different definition of division" the question...
The question if it it would help us find out how many yo-yos are in each pack
you think it helps us because it's true
the other person thinks it doesn't because it isn't what it is asking and therefore does not help you find the solution
it isn't about the definition of division but exactly what helps which, is pedantics
vapid mulch
I dont agree with that at all
and I think we moved away from the question being asked
keen shuttle
and I think we moved away from the question being asked
Yeah but like, this isn't productive at all and is gonna get nowhere because people will inevitably disagree on whether it counts or not so just move on to another question please
vapid mulch
Yeah but like, this isn't productive at all and is gonna get nowhere because peo...
if you dont want to answer the question you can leave, but suggesting that I should not ask a question because people will disagree with the answer is the only thing not being productive here
keen shuttle
if you dont want to answer the question you can leave, but suggesting that I sho...
I'm saying that because I feel as if you aren't really using this for things related for mathmatics and so it isn't great but 
I'll leave it you can do what you want
vapid mulch
I'm saying that because I feel as if you aren't really using this for things rel...
I disagree, thanks for leaving
I will repeat the question since there are a lot of msgs unrelated to it
"this is asking 14/x = 7"
"not 14/7 =x"
"so its not true"
is this comment correct, somebody who is math undergrad told me this
but I think that it is wrong
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slate aspen
What is the problem? Both answers are indeed right, do you understand why the two others are wrong or?
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@vapid mulch Has your question been resolved?
vapid mulch
What is the problem? Both answers are indeed right, do you understand why the tw...
no I was just told that the 14/7 = x
is not correct
so im 99% sure that they messed something up
its not the "right way of thinking of division"
slate aspen
well, no, it just depends how you think of it
you might say 'I have 7 packs with X amount per pack and in total I have 14, so I have to do 7 times x to equal 14' or you think 'If I have 14 in total and I have 7 equal packs, I have 14/7 per pack'
vapid mulch
yeah, amount of stuff in a group vs amount of groups with equal amount of stuff
slate aspen
its both equivalent
vapid mulch
he must have gotten confused, thank you for clearing that up !
slate aspen
cheers!
vapid mulch
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paper saddle
hello!
paper saddle
I want to learn the basics of negative exponents
and it would be appreciated if someone could help me go over the basics and everything I need to know
I learned the whole lesson on the negative exponents, but I just can't get myself to solve large questions
zinc ginkgo
paper saddle
could you maybe go through the basics
slender shard
Do you have any idea of what is confusing you about negative exponents?
Does the concept of flipping it over in a fraction confuse you?
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paper saddle
<@&286206848099549185>
can someone just vc w me
I think it would be easier
u know what i got this
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thin vine
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thin vine
can someone please explain to me why the answer is d instead of c
i did 10/25 x 7/24
and got 7/60
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exotic tundra
i did 10/25 x 7/24
what about when you draw the blue one first
thin vine
what about when you draw the blue one first
should be the same
exotic tundra
should be the same
yea, so the probability will be 2 times your answer
odd tapir
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odd tapir
how do i solve this by rationalizing?
its easy to factor and cancel out
but the quetion asks to solve by rationalizing
restive vortex
could you rationalize 1/sqrt(3)
you could rationalize it by multiplying the root by it self @odd tapir
odd tapir
and then?
restive vortex
you could factor the x
odd tapir
you could factor the x
but the question asks to solve through rationalizing or using congugate
restive vortex
wait
i dont think there is a way to rationalize it more
or using conjugate
i think you need to factor the x in this part
if not the question couldnt be solved
btw you write it wrong
it should be
(x^2+x)(sqrt(x^2+2)
or you could use l'hopital rule
which will use the derivation of it
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limber aurora
I’m stuck on the slope because I counted the boxes however it’s still saying it’s wrong can I please have some clarification on what I’m doing wrong
granite tree
Count again LM. Also, slopes can be negative
limber aurora
Ohh okay. How do I know when a slope is a negative?
tawdry ferry
When the line goes down and to the right
limber aurora
So ON would also be a negative slope bc it’s going down and to the right?
tawdry ferry
If it’s positive it goes up as you move right
tawdry ferry
So ON would also be a negative slope bc it’s going down and to the right?
Right
I’d recommend you learn how to actually calculate slope to be more precise how positive or negative
tawdry ferry
Thank you!
Np
shy bison
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vagrant prism
Beräkna means calculate
summan av alla vinklar i en triangel är 180°
du har två vinklar, 35° och 90°
vagrant prism
exakt
vagrant prism
är vinkeln som ligger längst ner till höger 90°?
trim lichen
call the horizontal segment on the bottom CD (C on the left)
angle CDB = 90° as marked on the diagram
vagrant prism
jaha bra då
shy bison
so AB=125
but how do i calcualte
oHHHHH Wait
if x = 55
does that mean that the other side of x=35
vagrant prism
hint: side AB = side BD, which means angle BDA is the same as angle BAD
CDB is 90, CDA is 35, so BDA = ?
trim lichen
ABD är likbent triangel
shy bison
i svenska
vagrant prism
angle=vinkel
vagrant prism
precis
vagrant prism
använd pytagoras sats
vagrant prism
jo
vagrant prism
så 36x64=sidan under uphöhd med 2
du skulle inte multiplicera dem
vagrant prism
exakt
shy bison
najs
vagrant prism
tack so mkt
om du har inga frågor kvar kan du skriva ".close"
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vagrant prism
lol
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drowsy trench
b) A circle is inscribed in the right-angled triangle KLM (see the diagram). ∠LKO + ∠KOM = 155°. Calculate the measures of the acute angles of the triangle.
red mountain
can you show the diagram?
drowsy trench
red mountain
were you the same person with the 3x,7x,8x circle triangle thing?
drowsy trench
yea
red mountain
this is smth similar
drowsy trench
i know but i just dont know where to start
exotic pine
dont you jusg do LKO=MKO
exotic pine
think about triangle MKO
red mountain
KOM+MOL+LOK=360
red mountain
KOM is given
LKO is given
ah wait
its not explicitly given
just write one of the angles as x
red mountain
LMO = KMO = x, MKO=180-KOM-x
red mountain
other as y?
no
red mountain
LMO = KMO = x, MKO=180-KOM-x
LKO+MKO+KLM+LMK=180
basically
write one angle as x
and then find the other angles in terms of x
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gusty valley
This deduction is valid, right? Thanks in advance <3. (1), (2), (3) and (4) are my premises.
gusty valley
$$(1) ;;; \forall p (P(p \mid Ap) \leq P(p) \rightarrow P(p) < 0.45) $$
$$(2) ;;;P(s \mid A s) \leq P(s)$$
$$(3) ;;; s \rightarrow A\neg s$$
$$(4) ;;; A\neg s \rightarrow \neg As$$
$$(5) ;;; s \rightarrow \neg As ;;; ;;; \text{From (3) and (4)}$$
$$(6) ;;; As \rightarrow \neg s ;;; ;;; \text{From (5)}$$
$$(7) ;;; P(\neg s \mid As) = 1 ;;; ;;; \text{From (6)}$$
$$(8) ;;; P(s \mid As) = 0 ;;; ;;; \text{From (7)}$$
$$(9) ;;; P(s \mid As) \leq P(s) ;;; ;;; \text{From (8)}$$
$$(10) ;;; P(s) < 0.45 ;;; ;;; \text{From (9) and (1)}$$
$$(11);;; P(\neg s) < 0.45 ;;; ;;; \text{From (1) and (2)}$$
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gusty valley
I made a mistake, please ignore the above message.
The below deduction is valid, right? Thanks in advance <3. (1), (2), (3) and (4) are my premises. s is a concrete proposition (such as "I like cookies."), which is why I put no quantifier before (2). 'A' is a propositional operator that takes in a proposition and returns a proposition (such as "It's appears to me that p").
<@&286206848099549185> anyone here good with logic who is willing to help me?
patent birch
how does statement 11 make sense? I don't follow
gusty valley
how does statement 11 make sense? I don't follow
it just says that the probability that s is below 0.45. Since probabilities are always between 1 and 0, (11) does not violate the axioms of probability theory. Or am I misunderstanding your question?
patent birch
i mean how did you conclude statement 11
gusty valley
how does statement 11 make sense? I don't follow
Or are you asking from what (11) follows? It follows from (1) and (2) by modus ponens and universal instantiation
patent birch
i followed every step and then the statement in 11 was kinda just dropped outta nowhere
yea that
gusty valley
sorry, the proof is not very well-ordered
(11) is supposed to follow from (1) and (2) and really has nothing to do with (10)
patent birch
i dont agree that universal instantiation is applied correctly there
i dont see how to get 11 from 1 and 2
gusty valley
i dont see how to get 11 from 1 and 2
do you agree with the following inference?
$$(1) ;;; \forall p (P(p \mid Ap) \leq P(p) \rightarrow P(p) < 0.45) $$
$$\text{Therefore,} ;;; P(\neg s \mid A \neg s) \leq P(\neg s) \rightarrow P(\neg s) < 0.45$$
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! Oxford Phil-student
gusty valley
ohhh did i read it wrong the first time
no worries
gusty valley
i see it now gimme a min
sure, thanks, curious about what you think!
gusty valley
i see it now gimme a min
does it all make sense now to you?
patent birch
yeah, i see the contradiction
cant find an issue with the proof
it feels like the premises naturally should give rise to a contradiction like this but i cant seem to yet pinpoint exactly where or why
i think the problem is in premise 1
gusty valley
i think the problem is in premise 1
ye
patent birch
ok i have an intuition now
but havent worked out the details yet and gotta go to work soon
but i think premises 1 and 4 are sufficient to prove a contradiction
i think the contradiction is showing that P(x) and P(-x) are both <0.5
by showing that
whatever you do in the P(x) formula
can equivalently be done in the P(x | Ax) formula
or the P(Ax) formula
i think there might be a simple geometric/bayes explanation for this
gusty valley
can equivalently be done in the P(x | Ax) formula
thanks <3
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pastel crescent
In a box there are 12 textbooks in which 7 are algebra textbooks and 5 are geometry textbooks.
Find the probability of:
a. 2 geometry textbooks if the 2 textbooks are taken out of the box simultaneously.
b. getting at least one algebra textbook
pastel crescent
I'm a little confused on a
Are we supposed to take 5/12 * 4/11
I feel like it isnt right.
pastel crescent
I believe part (a) ?
Yep
wraith hinge
Are we supposed to take 5/12 * 4/11
That does look correct to me.
snow glen
sorry, i reconsidered the emoji due the rules 😅
wraith hinge
sorry, i reconsidered the emoji due the rules 😅
it's alright man
snow glen
That does look correct to me.
shoudnt it be lower?
pastel crescent
That does look correct to me.
Is there a difference to like taking 2 out simultaneously and taking one at a time 2 times
wraith hinge
Is there a difference to like taking 2 out simultaneously and taking one at a ti...
nope! exactly the same thing!
it has been phrased this way to confuse you
In fact the second question is actually tougher 👀
I thought you were going to ask that
If you do need help with the second, do lmk
pastel crescent
If you do need help with the second, do lmk
Yeah I needed help with that also
wraith hinge
Have you studied binomial distributions before?
P(atleast one algebra textbook) = P(exactly 1) + P(exactly 2) + ...
pastel crescent
Have you studied binomial distributions before?
Nope
snow glen
Is there a difference to like taking 2 out simultaneously and taking one at a ti...
but the total possibilities are 66 and the valid ones are 10
or am i applying wrong?
wrong message responded 😅
snow glen
That does look correct to me.
it was meant to be for this one
all the cases are all the combinations of books
covert thistle
In a box there are 12 textbooks in which 7 are algebra textbooks and 5 are geome...
i don't think part b is very well phrased as a question
snow glen
if i am right and the answer to a is 10 / 66 the b asks wahts the chance of getting 1 book of algebra and another of any kind by picking up simultaneously it should be 56 / 66
but Edmund got me doubting of myself
covert thistle
if i am right and the answer to a is 10 / 66 the b asks wahts the chance of gett...
your answer to part a is exactly the same as chocolate/edmund's
snow glen
your answer to part a is exactly the same as chocolate/edmund's
you are right pff i forgot to minimize the fraction, what a silly
covert thistle
anyways i don't think there's really a need to list out the entire table.
a faster way would be to use combinatrics directly like 5C2 / 12C2
same answer i think
snow glen
i wanted to check by graph cuz i havent used the formulas for this for long
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wraith hinge
i don't think part b is very well phrased as a question
yeah I'd agree with that
"getting at least one algebra textbook"
but in how many trials?
they never specify
if they pick out EVERY SINGLE textbook, they are bound to find atleast one algebra textbook
therefore the probability should be 1
however say they were taking 3 textbooks or 4 textbooks, the probability of finding atelast one algebra textbook would make sense
kindred current
x = 1 + 3 + 5 + ... + 225
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x = 1 + 3 + 5 + ... + 225
kindred current
how do we find x
dapper swift
how do we find x
try investigating the pattern
1 + 3 = 2^2
1 + 3 + 5 = 3^2
1 + 3 + 5 + 7 = 4^2
kindred current
what are you trying to say
thorn copper
novel kiln
First term 1, last term 225, Difference 2
kindred current
1 + 3 = 2^2
1 + 3 + 5 = 3^2
1 + 3 + 5 + 7 = 4^2
1 + 3 + 5 + 7 + 9 = 25 = 5^ 2 and so on
kindred current
1 + 3 + 5 + 7 + 9 = 25 = 5^ 2 and so on
that means we can re-write the terms based on the pattern
or not?
i am to confused
trim lichen
shoudnt it be?
your notation has a very high risk of confusing op
dapper swift
Isn't this also a simple AP
it is and you could also do it that way
dapper swift
that means we can re-write the terms based on the pattern
yes
snow glen
your notation has a very high risk of confusing op
the first + the last = the second + the second last i meant
tardy hemlock
x = 1 + 3 + 5 + ... + 225
As an alternative, in this case, your idea from before does make the problem easier. \begin{align*} 1 + 3 + 5 + \dots + 225 &= 1 + 2 + 3 + \dots + 225 - (2 + 4 + 6 + \dots + 224) \&= 1 + 2 + 3 + \dots + 225 - 2(1 + 2 + 3 + \dots + 112) \end{align*}
dapper swift
now try thinking, last term 3 is 2 squared
last term 5 is 3 squared
last term 7 is 4 squared
can you figure out the algebraic rule that connects the two?
trim lichen
the first + the last = the second + the second last i meant
you would have done better to just put that in words
snow glen
you would have done better to just put that in words
very much
kindred current
As an alternative, in this case, your idea from before does make the problem eas...
I did that and i got stuck a bit
Oh i got it now.
dapper swift
yes that's why it's the square of (225 + 1)/2 = square of 113
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Kepe
dapper swift
ah that's another method
kindred current
**Kepe**
i DID all of that but got stuck at 2+4+6+...+224
now i remember how it goes
tardy hemlock
Yeah, factor out 2
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cerulean quail
how does 1.8c work
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how does 1.8c work
cerulean quail
mhm
red mountain
e is eulers constant?
cerulean quail
ohh
nova spire
e is eulers constant?
but we need a vector
nova spire
this isn't a unit vector (for L^2 norm)
cerulean quail
this is the answer if it helps
nova spire
ok maybe e = (1,1,1)
trim lichen
from where do we know what e is though?
nova spire
because its norm is sqrt(3)
cerulean quail
ohh
nova spire
ohh
still doesn't excuse that the exercise makes no mention of what e is
did it get mentioned in previous exercises?
red mountain
lmao
cerulean quail
but still how do i do thi
W in R^3 except for the part where the norm is smaller or equal to sqrt (1/3)
but we know the norm is sqrt 3 which is bigger than sqrt 1/3 right
so for the case x = 0 its basically just in the domain R^3
ah and then for epsilon = 2/ sqrt 3, its at the boundary point of W
if epsilon becomes any larger, the norm will be smaller or equal to sqrt 1/3
and that is not in W
so we can take any epsilon smaller or equal to 2 / sqrt 3
am i saying correct things?
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azure dagger
help
urban copper
if x + 3 is a factor that should mean -3 is a root of the quartic
azure dagger
yes
azure dagger
if x + 3 is a factor that should mean -3 is a root of the quartic
same with 1/2
urban copper
similarly 1/2 should be another root, do you mind plugging x = 1/2 and x = -3 into the quartic and equal it to zero, maybe we can figure out a and b
azure dagger
okay
urban copper
,w 2x^4 + ax^3 + bx^2 + ax + 3 where x = -3
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azure dagger
,w 2x^4 + ax^3 + bx^2 + ax + 3 where x = 1/2
solid kilnBOT
azure dagger
that's useful
urban copper
- -30a + 9b + 165 = 0
- 5a + 2b + 25 = 0
azure dagger
oh okay yeah that works
once i get a and b
how do i get the other 2 roots
oh actually
long division
nice
urban copper
long divide and maybe rational root theorem if a,b are real coefficients
just, if this is a quartic divide by (x+3)(2x-1) and you get a quadratic
then use quadratic formula
azure dagger
yeah
urban copper
you don't need rational root theorem
urban copper
1) -30a + 9b + 165 = 0
2) 5a + 2b + 25 = 0
multiply 2) by 6 and sum them
urban copper
im going to get this open in case i need help with any other problems
ok, good luck 👍
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plain tusk
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latent crest
I need help making this in desmos
proper heron
I need help making this in desmos
Ask god for help 🙏
Back to the main problem
Take 0;0 and 4;5
latent crest
please I need help man
proper heron
Bro wdym
plain tusk
Take 0;0 and 4;5
ok
proper heron
I need help making this in desmos
Do you want to draw every single detail?
proper heron
Yea
proper heron
Y on top tho
plain tusk
oh
proper heron
5/4
plain tusk
so 5 over 4
proper heron
Yh
proper heron
Its better to choose points that you know are for sure on the line
Its not good to eyeball it
latent crest
Do you want to draw every single detail?
kinda
plain tusk
the formula is change in y over change in x right?
proper heron
the formula is change in y over change in x right?
Yh
plain tusk
does the gradient just represent the steepness of the line?
proper heron
Yea
plain tusk
proper heron
Steepness of the line?
Maybe the ratio between cup of water to cup of rice
So like for every 5 cups of water you need 4 cups of rice
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astral stump
Consider the following problem at the frontier of modern mathematics:
Let (X) be a smooth, proper Calabi–Yau variety over (\mathbb{C}), and let
[
\mathcal{D}(X) = D^b(\operatorname{Coh}(X))
]
denote its bounded derived category of coherent sheaves, which is known to carry a natural structure of a stable ((\infty,1))-category. Recent developments in homological mirror symmetry suggest a deep relationship between the autoequivalence group (\operatorname{Aut}(\mathcal{D}(X))) of this derived category and the symplectic mapping class group of a mirror dual symplectic manifold (Y).
Problem:
Formulate and prove (or provide substantial evidence toward) a precise correspondence between (\operatorname{Aut}(\mathcal{D}(X))) and a suitably defined version of the mapping class group of (Y). In particular, address the following questions:
-
Is there a natural, functorial construction that assigns to each autoequivalence of (\mathcal{D}(X)) an element in the symplectomorphism group (\operatorname{Symp}(Y)) of the mirror (Y), such that this assignment respects the composition laws in both groups?
-
Under what conditions (on (X), (Y), or the categories involved) can one prove that this correspondence is an isomorphism (or a fully faithful embedding)? How does this relate to the derived invariance of geometric structures on (X)?
-
What implications would such an equivalence have for our understanding of mirror symmetry, particularly in terms of predicting geometric invariants from categorical data?
Outline your approach to these questions, discuss any partial results or obstructions encountered, and describe the potential impact of resolving this problem on the broader program of homological mirror symmetry and higher category theory.
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hampter
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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.
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hampter
feral dragon
idk what they want me to input
trim joltBOT
idk what they want me to input
feral dragon
oh idk i think I was trying different things like adding or subtracting 180 from 165.19
tulip violet
Oh wait I might be wrong. I just reread that answer statement and I'm not sure what it wants, sorry
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amber egret
how exactly do i do question c? ive been stuck on it for around an hour now
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how exactly do i do question c? ive been stuck on it for around an hour now
@amber egret Has your question been resolved?
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King Leo [Ping For Help]
lone basin
Where $(h, k)$ is the vertex
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King Leo [Ping For Help]
amber egret
$y = a(x - h) + k$
oh we usually use p and q instead of h and k
lone basin
oh we usually use p and q instead of h and k
$$y = a(x - p) + q$$
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King Leo [Ping For Help]
lone basin
Anyways @amber egret can you identify the vertex
amber egret
y = 1/200(x-75)^2-q
q is unknown
u find q using
y = 1/200(x-100)^2-50
from another equation
lone basin
y = 1/200(x-75)^2-q
Wait how did you get p = 75
amber egret
from here to here
the length between each cable is 25ft
and the origin point is yhe 0,0
i mean i got 28.125
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coarse meadow
mike is 2 years older than his brother and 4 years younger than his sister their ages multiply to 3024 find mikes age
strong granite
mike is 2 years older than his brother and 4 years younger than his sister their...
you can say let mikes age equal x
so his brother is x-2 and sister x+4
those multiply to 3024
coarse meadow
you can say let mikes age equal x
yeah but the only problem is that we havent learnt cubic yet
and x(x-2)(x+4)=3024
@strong granite ?
strong granite
you could try to guess it? i’m not sure without using cubic
i cannot think of a way off the top of my head
coarse meadow
you could try to guess it? i’m not sure without using cubic
can u help me with this one then? consider the sequence 2(4-6) 3(6-6) 4(8-7) 5(10-8) find nth term in the form a(b-c) simplify fully