we had to accept it
#help-13
fair geyser
cedar kilnBOT
✅
fair geyser
see my vague answer
slate lintel
it's a pretty easily graspable explanation of the (I think) Copenhagen interpretation of QM
coral jewel
saw somewhere that schrodinger cat is also used to show parallel universes might exist
always thought it was just a thought experiment to explain superposition, but apparently theres more to this than it meets the eyes
proven oar
always thought it was just a thought experiment to explain superposition, but ap...
thats what i thought as wel!! but i dont understand how it is more than just a though experiment
fair geyser
The CHSH game is a thought experiment involving two parties separated at a great distance (far enough to preclude classical communication at the speed of light), each of whom has access to one half of an entangled two-qubit pair.
two people each receive a random bit. To win, they have to answer with the same bit as each other, both 0 or both 1, unless they both receive 1, then they have to answer with different bits. The obvious optimal strategy is to answer 1, then 75% of the time they win, because they didn't both get 1.
tardy hull
thats what i thought as wel!! but i dont understand how it is more than just a t...
There's no mathematical content to Schrodinger's cat, I don't see how it could be any more than a thought experiment
fair geyser
but if they use their quantum things on their half-quantum entangled thing and correlate their answer with that, they win more
so this is magic
i don;t know if they ever did this, or it's a thought experiment
maybe someone did something equivalent
tardy hull
maybe someone did something equivalent
What you described sounds vaguely like the Bell tests that are interpreted as disproving the local hidden variables thing you mentioned earlier
fair geyser
yeah, they all sound like the same experiment
so i generalized it, things aren't anything
coral jewel
I know that I know nothing
proven oar
geez
I am still thinking
Cuz i connected that idea to the split experiment. how an electron is everywhere all at once untill you measure it
fair geyser
schrodinger cat is not applicable to real life, it's easy to see why
proven oar
no actually that might not be the split experiment. maybe another one im bad with names
fair geyser
the whole point is that it can't matter, or it would be measurement
if it makes a difference that it's actually OR and not AND, then your box is not properly sealed
proven oar
if it makes a difference that it's actually OR and not AND, then your box is not...
see this is what im not wrapping my head around properly
but maybe im a bit too uneducated to understand
cedar kilnBOT
@proven oar Has your question been resolved?
dense locust
cedar kilnBOT
hazy terrace
Do you mean (3/8)^n
dense locust
Do you mean (3/8)^n
Lemme check soemthing
No yeah
that makese sense
no wonder
lol
problem solved
ty
Sorry about that
.clost
cedar kilnBOT
Available help channel!
worthy hawk
Prev help channek got closed due to time limit someone pls help i found all vectors here but whenever tried an equation the k term canceled out
nimble mountain
you can find
AB, with OA, OB
AC, with AB
MA, with OA
MC, with MA, AC
find intersection of MC and OB
equate, OM+aMC=kON
worthy hawk
Ans for part b is a trapezium right?
Ans for part b
And for this the consitions must be a=kc and a+kc=2a
cedar kilnBOT
@worthy hawk Has your question been resolved?
worthy hawk
<@&286206848099549185>
cedar kilnBOT
@worthy hawk Has your question been resolved?
south tulip
The nullity of a 3x5 matrix is in what range?
cedar kilnBOT
The nullity of a 3x5 matrix is in what range?
south tulip
Zero to 2
2 to 5
Or zero to 3?
void sand
note that the rank of a matrix can be interpreted as the number of linearly independent rows
and then use rank-nullity
south tulip
note that the rank of a matrix can be interpreted as the number of linearly inde...
Rows right?
Not columns?
south tulip
They’re the same
What?
The column space is more than the row space here though?
So uh let's just get this straight
What's the max value of nullity?
void sand
What?
The column space is more than the row space here though?
So uh let's jus...
their ranks are still equal though
mental trail
their ranks are still equal though
for 3x5 matrices?
A 3x5 matrix is a linear map from R^5 to R^3
void sand
for 3x5 matrices?
oh wait it’s a 3x5
austere plume
Mb
mental trail
A 3x5 matrix is a linear map from R^5 to R^3
with this information
The image sits in R^3
south tulip
A 3x5 matrix is a linear map from R^5 to R^3
Exactly
mental trail
The image sits in R^3
If the image sits in R^3, what can be said about its dimension?
south tulip
So uh guys
What's the max value of nullity finally for a 3x5 matrix?
mental trail
we're getting to that
mental trail
If the image sits in R^3, what can be said about its dimension?
this is a first question
south tulip
If the image sits in R^3, what can be said about its dimension?
3?
south tulip
the dimension of the image is always 3?
<=3
south tulip
What's the max rank possible though
mental trail
What's the max rank possible though
what do you think
south tulip
what do you think
3?
south tulip
we can show that later if you want too
well, I am just thinking this in terms of the matrix 3x5
The number of zero rows in the matrix gives me its nullity right?
In row reduced echelon form I mean
south tulip
So then the nullity can atmax be 3?
mental trail
nonono it's not rows
south tulip
huh?
mental trail
the number of non-zero rows will give you the rank
but the number of zero rows is not the nullity
south tulip
but the number of zero rows is not the nullity
what???
mental trail
what???
you're not working with square matrices
consider the null map from R^5 to R^3
south tulip
Wait wait
This means...
the max rank can be 3... but the dimension is 5...
So the nullity must be between 2 to 5?
mental trail
Wait wait
This means...
the max rank can be 3... but the dimension is 5...
So th...
yes that's it
mental trail
consider the null map from R^5 to R^3
here's the "extreme" example
how many zero rows are there in the null map
south tulip
yes that's it
But this mandates that every 3x5 matrix
There will definitely exist a non trivial solution in the null space....
mental trail
But this mandates that every 3x5 matrix
There will definitely exist a non trivia...
yep
south tulip
damn
My concepts were so wrong
mental trail
if T:E->F is a linear map with dim(E) > dim(F), then null(T) > 0
in fact,
null(T) >= dim(E)-dim(F)
specifically because rank(T) <= dim(F)
and rank-nullity theorem
null(T) = dim(E) - rank(T) >= dim(E) - dim(F)
void sand
column rank = row rank
sorry for barging in again, but I could have sworn this was true for all mxn matrices… am I wrong?
mental trail
sorry for barging in again, but I could have sworn this was true for all mxn mat...
only square matrices, sorry
void sand
only square matrices, sorry
that’s not what the internet is telling me though
mental trail
well then you might want a counterexample
wait you're talking about rank
not nullity
void sand
yeah
mental trail
it's alright then
it's true in that case
but nullity(rows) is not nullity(columns)
void sand
I thought we could do a sort of “worst/best case scenario” check using the max/min values for the rank of this 3x5 matrix
And use rank nullity to deduce what the corresponding nullities must be
but perhaps that doesn’t work
mental trail
“worst/best case scenario” is very vague
better to just say "oh the image lies in R^3 so the dimension is between 0 and 3"
void sand
“worst/best case scenario” is very vague
what I mean is maximum/minimum number of lin ind cols
void sand
better to just say "oh the image lies in R^3 so the dimension is between 0 and 3...
This makes more sense though
and is probably easier to think about lmao
mental trail
but again
if you were tasked to find the bounds of the rank of a 5x3 matrix
then it would be VERY interesting to use the transpose
because then the transpose is 3x5
so the image sits in R^3, etc...
and so the rank of a 5*3 matrix doesn't exceed 3 either
void sand
interesting, that’s something for me to think about I guess
cedar kilnBOT
@south tulip Has your question been resolved?
south tulip
null(T) >= dim(E)-dim(F)
Fine
Ur right
I got you
Just tell me this that... where should I practice these kinda problems from... which'll yk.. thoroughly check my concepts and put me on the right track
Will I get this in Howard Anton?
south tulip
and so the rank of a 5*3 matrix doesn't exceed 3 either
Wait wait
Why is that?
cedar kilnBOT
@south tulip Has your question been resolved?
cedar kilnBOT
How do I make my bases even?
bleak thorn
We’re not using radicals yet
bleak thorn
Yes
sonic robin
understood?
sonic robin
bleak thorn
Ahhh
sonic robin
I’d need to fiddle with the math
take your time
bleak thorn
What now
Oh wait a minute
I ignore the last line I wrote and just distribute
No wait I go with the last line
But not the radical of x
I keep it as a fraction
Figured it out
bleak thorn
Yeah
sonic robin
nice
bleak thorn
Just exposant laws
sonic robin
yeah
bleak thorn
And I forgot to understand that the numbers and variables were separated because the first epxosants were outside of parenthesis
And not only on the variable
sonic robin
i see
bleak thorn
Thanks
sonic robin
have a good day
cedar kilnBOT
cedar kilnBOT
Available help channel!
teal seal
I help need to find the slope of this Tangent Line Parabola
cedar kilnBOT
I help need to find the slope of this Tangent Line Parabola
dire geode
I help need to find the slope of this Tangent Line Parabola
!original
cedar kilnBOT
I help need to find the slope of this Tangent Line Parabola
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.
teal seal
That is the original
dire geode
screenshot or picture is best
dire geode
find the sign of the slope of f at a few points and plot them
3-5 points should be enough
teal seal
So plot a few points?
dire geode
estimates should be enough
teal seal
Hm, okay
dire geode
the important part is the sign of f'
dire geode
f' is the derivative of f yes
dire geode
from the graph of f, can you find the sign of f' at a few points?
teal seal
Well I found (0,0), ~(-1,-3), ~(1,3) (-2,0) and (2,0)
I need to close this for now, thanks for the help
.close
crimson sedge
hi so my teacher was deriving bernoulli's theorem and we had considered work done by pressure and he wrote work done by pressure= PV_i - PV_f
crimson sedge
im just confused why he wrote that
im not sure if this is not enough context
i can provide more context by sending in his work if someone like but i just dont want to add extra stuff here which might be reduntant in this context
cedar kilnBOT
@crimson sedge Has your question been resolved?
dusty hazel
I think you're talking about equation of continuity?
And yes, work done is usually calculated by PdV (integral)
That's by definition.
cedar kilnBOT
@crimson sedge Has your question been resolved?
dim sonnet
Can someone plz show me the solution to this
cedar kilnBOT
Can someone plz show me the solution to this
crimson sedge
use polynomial division
crimson sedge
Can someone plz show me the solution to this
also yea the answer should be D
,w div (2 + 2x^3 - 4x^2)/(x^2+1)
wraith daggerBOT
crimson sedge
not what I wanted but okay
dim sonnet
also yea the answer should be D
is there any way it could become A?
dim sonnet
thank you
cedar kilnBOT
@dim sonnet Has your question been resolved?
crimson sedge
At a given moment, from the top of a mountain, a person observes an airplane that is 420 meters away with an elevation angle of 28 degrees. At the same time and in the same vertical plane, this person observes a boat that is 720 meters away with an angle of depression of 22 degrees.
a. What is the distance between the plane and the boat at that moment?
b. At what angle is the plane viewed from the boat?
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
kindred merlin
Do you know the . correct answer?
hasty pelican
the second answer is wrong?
why do you think it is wrong?
If your diagram is correct then it is the right answer
crimson sedge
Do you know the . correct answer?
This appears in the book that I am using
they put another answer
crimson sedge
If your diagram is correct then it is the right answer
oh okay, thanks
kindred merlin
I think you're meant to add the angle of depression. It says the angle of the plane viewed from the boat
Since the angle you calculated starts from the angle of depression, the correct answer should be (22+35.6)° = 57.6°
crimson sedge
I think you're meant to add the angle of depression. It says the angle of the pl...
Ohh this makes sense
thanks
.close
pseudo grove
cedar kilnBOT
spice pilot
i think is 3
pseudo grove
why
spice pilot
cuz rate of change
dy on [1,3] cant be 6 its
u start at 0 and you move to 6 in [1,3]
on the other hand between 3 and 5 you start at 6 and move to 18
that means u had to have a dy of 6 at one point
start y is 3 yea
3 + dy = 6 + dx
so dy average is 12 dx average is 2
thats in y x terms
pseudo grove
oh
pseudo grove
the AROC on interval [3,5] is 6
spice pilot
dont know what aroc is
pseudo grove
average rate of change
pseudo grove
and it is 6.5 at [7,9]
pseudo grove
i think its only two times its equal to 6
spice pilot
u gotta remember that y = (some for of x)
if you need to find rate of change
you do
y + dy = (some form of x) +dx
for example
y = x^2
y + dy = (x+dx)^2
y + dy = x^2 +2dx +dx^2
and then you put y in
you get
dy = 2dx +dx^2
but dx^2 is negligable becayse its of second order magnitute of smalles
so
dy/dx = 2x
pseudo grove
I think its 2 because it reaches 6 on interval [3,5] but then goes down to 5.5 on interval [5,7] then goes back to 6.5 on interval [7,9) so it had to pass 6 atleast once more
so i think its 2 times?
spice pilot
na na bro
u just add a bit to x and see how much added to y
in first case x = 1 , y = 0 we added 2 to x we got +6 for y
so dx = 2 dy = 6
dy/dx = 3
average rate
but this is not the best generall apllication for dy/dx
pseudo grove
so where are the 3 spots that you said dy/dx = 6?
pseudo grove
oh i found them
on interval (3,5), (5,9) and (3,9)
average rate of change is 6 in all 3 of them
spice pilot
oh yea ma bad
5,7 is 5,5
5.5
still same answer tho
cuz smaller interval where it is for sure is [3,5]
pseudo grove
okay so 3 fewest possibilities of f'(c) = 6
spice pilot
also question says possible
pseudo grove
will put that
pseudo grove
well it says fewest
spice pilot
it can be like this
f(x) = 0 if x = 1 , -100000 if x = 2 , 6 if x = 3 , -12492714891274 if x = 4 , 18 if x =
5
it only has to be possible
I mean they are kinda cunts as well because they dont speicfy if the function is continious
spice pilot
oh then it is true 100% in that case
answer is 3
because you are testing for interval [c,9]
cedar kilnBOT
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Available help channel!
turbid spoke
"In a meeting, five friends (Alex, Pedro, Carol, David, and Emily) are seated around a round table. The following is known:
Alex is not next to Pedro.
Carol is next to David.
Emily is to the left of Pedro.
David is not next to Alex.
Can you determine the order in which Alex, Pedro, Carol, David, and Emily are seated around the table?"
ashen shard
draw a figure
turbid spoke
wdym?
turbid spoke
but is a list?
turbid spoke
but i can get more two solution?
sour horizon
if that's the case it just means the answer is 'no'
cedar kilnBOT
turbid spoke
draw a picture of the scenario
.
weak otter
I am alright?
No, Emily needs to be to the left of Pedro
turbid spoke
No, Emily needs to be to the left of Pedro
Emily Pedro , Alex , Carol y David ?
cedar kilnBOT
Available help channel!
turbid spoke
I can use graph?
night swift
I think there are multiple answers but I got
Alex Emily Pedro David Carol
pliant atlas
"In a meeting, five friends (Alex, Pedro, Carol, David, and Emily) are seated ar...
isn't this
a ucat question
its pretty simple actually
If we go
If we go clockwise
it'd be
Emily, Alex, Carol, David, Pedro
Considering, we have them seated around the table in a star shape
Thats what i got, atleast
cedar kilnBOT
@turbid spoke Has your question been resolved?
crimson sedge
guys
crimson sedge
pls help
its asking to find the derivative
we just learned about chain rule in class but i dont know where to start
any help would be greaty appreciated
coral jewel
$(ab)'=a'b + ab'$
wraith daggerBOT
FungusDesu
coral jewel
product rule
crimson sedge
yes but then
coral jewel
then apply chain rule
crimson sedge
what to do about the
but is e^-x
e^-x
for derivative
or do you need to simplify
crimson sedge
i forgot how to do that
coral jewel
then multiply by derivative of -x
crimson sedge
wait ill try to write it out
then show work
@coral jewel
im not sure where to go here
coral jewel
- e^-x(x)
crimson sedge
ok
so then
is it
3e^3x?
and then that replace for e^3x
and that is the derivative
\
coral jewel
correct
coral jewel
its the same, but they merely grouped e^-x as common factor
coral jewel
see the original equation again
coral jewel
$e^{x^3} \neq (e^x)^3$
wraith daggerBOT
FungusDesu
crimson sedge
oh ye true because
x^3 doesnt = 3x right
so then how to take derivative of e^x^3
is it just e^x^3?
cedar kilnBOT
@crimson sedge Has your question been resolved?
severe elm
how do i figure out the angle
cedar kilnBOT
how do i figure out the angle
violet flume
hmm its not super convenient
but lets call the original circumference of the circle C
then before , we open up the cup, we have arc length there of C/4, yea?
but once you open up the cup, you have a circle ....
how many arc lengths make up the circumference of that circle?
severe elm
does that circle have a circumference_2 of C_1 / 4?
violet flume
not quite
its hard because they didnt really label anything super useful
maybe i can draw
,rotate 90
wraith daggerBOT
violet flume
@severe elm what do you think about it now
that red bit around the top is a circumference of a circle
it has some circumference ... we can write it in terms of original C
severe elm
so the cone radius is the circumference of the original circle, div by 4
severe elm
you pick up 2 of them, yea?
wdym 2
violet flume
i mean one arc of length C/4 is going to connect one edge to the other
severe elm
ohh because 2r=d?
severe elm
so its divided by 2 instead
violet flume
itd make more sense if you physically constructed this thing
maybe you can trust me that we pick up 2 arc lengths
so C/4 * 2
severe elm
ok that makes more sense
violet flume
okay now you are almost there
severe elm
because its folded is that why?
violet flume
because its folded is that why?
well, when you open it up like that
hmm its hard to explain
theres a few layers on top of each other
severe elm
yea i c what u mean
severe elm
theres a few layers on top of each other
yes its that one arc length, but theres 2 layers bc folded, so
its c/4 * 2
violet flume
you can kind of see it here
go to 1:10
he opens the cup ... and you pick up two of that distance from edge to edge
one on each side
violet flume
yes its that one arc length, but theres 2 layers bc folded, so
anyways
okay say you have a circle
it has circumference C/2
if you rotate this circle so that it just looks like a line
like, picture you have a ring, and you turn it so youre looking at it from the side
how long is the line?
severe elm
like, picture you have a ring, and you turn it so youre looking at it from the s...
half of the circumference of the ring
right
severe elm
yea
violet flume
were just looking at it from the side
violet flume
well, you loose some of the distance right
severe elm
ofc
severe elm
but how much, idk
severe elm
if i have a circle with d=6, then if i turn it to the side i will see 6in of the circle
violet flume
clearly 2 of those sides of the triangle you want the measure of are easy, yea?
but the third one is weird
but, the third side is diameter of a circle with circumference C/2
violet flume
if i have a circle with d=6, then if i turn it to the side i will see 6in of the...
maybe more illustratively
if you have a circle with circumference pi
and you turn it so youre looking at it from the side
youll see a line thats 1 unit long
severe elm
if i have a circle with d=6, then if i turn it to the side i will see 6in of the...
so just like this, but i said d=6 and not 1
violet flume
so just like this, but i said d=6 and not 1
well, if the diameter is 6, yea if you turn it to the side youll see a 6 inch line
i more wanted to relate the circumference to line you see when you turn it
violet flume
so, now you hopefully have all the pieces
violet flume
you have 2 of those, yea
violet flume
man i wonder if i can make a video
severe elm
mayb later
severe elm
yes
severe elm
yea
severe elm
thats your triangle right there
i got that
violet flume
you know two the sides: theyre the radius of the original circle
severe elm
but i need another side, or a not gith angle
violet flume
we can get the third side
severe elm
you know two the sides: theyre the radius of the original circle
i know the radius
that only accounts for 1 side
severe elm
yes
violet flume
each one is a radius of the original circlee
severe elm
ohhhhhhhhhhhhhh
severe elm
split it down the middle like the top left
severe elm
and do pyth & trig ratios to find the angle
severe elm
you will be missing a side
ill have the hypotenuse and the short leg
severe elm
but it doesnt seem to be a real triangle
violet flume
but you need to do some geometry
severe elm
wait nvm one sec
severe elm
https://cdn.discordapp.com/attachments/903430334681608232/1207911482419970098/33...
circle is c/2
violet flume
the circumference of the bottom circle is C/2
severe elm
c=6pi, so circle c is 3pi
severe elm
the circumference of the bottom circle is C/2
c/2 is 3pi
cedar kilnBOT
violet flume
cedar kilnBOT
Available help channel!
tight girder
hello again
cedar kilnBOT
hello again
tight girder
I need help
So i have a couple steps down
first I graphed it
and I saw the triangular region
So based off of the graph I see the triangular region is from 0 to where they intersecrt
and so what I did was I took the integral of arcsiny and subtracted it from arccos y from 0 to pi over 2
now I need to find the intersecting point
what do i do now?
how owuld I go abt it
actually i need help
<@&286206848099549185>
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
thorny urchin
What’s the next step? I think we have to make one of the equations into the form A*B but not sure how to do that?
cedar kilnBOT
What’s the next step? I think we have to make one of the equations into the form...
@thorny urchin Has your question been resolved?
thorny urchin
<@&286206848099549185>
Nvm got k as 0,12
But question says value not 2 values
So do we reject k=0
tame zodiac
read question again
crimson sedge
a ring of radius R and mass M is kept at rest on the surface of a liquid of surface tension T. What is the force required to lift the ring up?
crimson sedge
it should be Mg-4RTpi, right?
i am mostly confused by the direction of force due to surface tension
but my teacher did Mg + 4RTpi?
so i am kind of confused
sonic robin
but my teacher did Mg + 4RTpi?
its going to act downwards
crimson sedge
why tho?
sonic robin
this is after
crimson sedge
generally the rule is to see the curvature since we cant do that here we dont know what the liquid is. should we not use the fact that "the ring on was on rest"
sonic robin
generally the rule is to see the curvature since we cant do that here we dont kn...
initially it was
but now ur lifting it right
crimson sedge
yes
sonic robin
dont you notice when you lift something kept on the surface of a liquid
the curvature kinda changes
like this
surface tension is acting downwards
to resist
trying to resist
crimson sedge
resist why?
sonic robin
resist why?
first of all let me correct my self
surface tension
acts
tangentially
to the surface of the liquid
and also
cohesive forces are acting on the liquid
basically ur lifting the ring against the cohesive forces
thats why Mg + surface tension
crimson sedge
so basically the direction of force due to ST changes when i try to lift t=the object?
crimson sedge
net will be downwards
okay but what is the critrea for direction of force due to surface tension? is it always downwards when you try to pick something? will the surface of the liquid will always get concave shaped when i try to lift something?
no that doesnt sound right
sonic robin
to the surface of the liquid
^
crimson sedge
tangentially but pointing in which direction?
sonic robin
downwards in this case
basically the direction of surface tension is perpendicular to any line drawn on the liquid surface
sonic robin
im sorry im really confused on this
what I think is, the surface tension points in the direction opposite to the motion
therefore in the downward directin
crimson sedge
so if i wanted to push the ring into the liquid, then its direction would reverse from this case?
cedar kilnBOT
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rigid raft
i am not the best at algebra how did they get this
cedar kilnBOT
i am not the best at algebra how did they get this
short cedar
i am not the best at algebra how did they get this
you can pull out a common factor of 1/x from both terms
well there are multiple ways but i would have pulled out the factor 1/x, and then turned the remaining expression into a single fraction, and then simplified from there
it would look something like this:
$\frac{1}{x}(-\frac{1}{x+1} + 1)$
wraith daggerBOT
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cedar kilnBOT
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rigid raft
.close
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runic storm
We are using the 'complete the square method'.
I know how to do it without fractions but i find using fractions with ti really difficult. Im in year 11. Please help if possible
clear umbra
We are using the 'complete the square method'.
I know how to do it without fract...
which one do you need help with
clear umbra
so you say you're having problem with fractions
runic storm
yeah
clear umbra
what problems do you have with them
runic storm
when i divide the term, it becomes a fraction, for example, like -5 becomes -5/2.
so i dont know what todo or where to go from that
basically i just would like step by step instructions how to solve it
clear umbra
when i divide the term, it becomes a fraction, for example, like -5 becomes -5/2...
you have to add it on both sides yes?
runic storm
i think, yeah
clear umbra
then whats the problem
it just boils down to 2 + (-5/2)^2
adding fractions together
runic storm
i ust dont know to solve it, apparently the answer on cambridge gets to 5±√17/2
so i dont know how it gets to that
clear umbra
ok so for this first one
you have to add (b/2)^2 on both sides
which is (-5/2)^2 yes?
runic storm
yes
clear umbra
actually first
move the constant term to the other side first
the one without any x
runic storm
alright, do we know why or not rly
clear umbra
its to make the calculation easier
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royal loom
cedar kilnBOT
royal loom
pi:V->V/U
My professor says that this is surjective which I am trying to wrap my head around
V/U is the set {v+U:v in V}
so if we had an element from it that is just one translate of U?
so an arbitrary element, would be of the form, v+u, v in V, u in U?
crimson delta
the elements of V/U are sets
crystal raptor
Good example to keep in mind is all translates of some line through the origin in R²
crimson delta
yes. and you only need to hit the set. which is easier to think about imo
royal loom
so pi(given v) is equal to that set?
crimson delta
yes
crimson delta
when is p(v)=p(w)?
royal loom
I want to say when v=w
crimson delta
ok first, what is the zero element in the space V/U
royal loom
is it {0+U:0 in V}
royal loom
I thought elements of V/U were sets
crimson delta
but not sets of sets
royal loom
oh and U is a set
crimson delta
so if you want to add nothing, that would work for w=0
so U is the zero element of V/U
crimson delta
if w+U=U, does that mean w=0?
crimson delta
yes
crimson delta
thats quotient stuff for you
royal loom
and then it's definitely not injective right because take two u1, u2 in U and v(u1)=U=v(u2)
crimson delta
yes
royal loom
is there ever any scenario where it is injective
maybe if 0 is the subspace
I forget if that's possible
royal loom
ah
crimson delta
and the map is injective iff the kernel is {0}
crimson delta
how did you introduce polynomial rings mod a polynomial?
royal loom
idk if the definition excludes it
crimson delta
and \{0\} is a subspace right
yes
royal loom
how did you introduce polynomial rings mod a polynomial?
This is linear algebra
my other calss
crimson delta
yes I know
crimson delta
still
royal loom
We introduced them
first we said what F[x] is
the ring of polynomials with coefficients in F
F a field
and then we defined division alg for polynomials and those kind of things
and said F[x]/p(x) is the set of poylnomails in F[x] mod p(x)
crimson delta
yes what does "mod p(x)" mean
royal loom
the remainder when divided by p(x)
crimson delta
hmm ok
royal loom
A few times I've talked about people with this and they ask me if I've done ideals
so if that's what you're wondering
no
I don't know what an ideal is
crimson delta
I might have asked you this aswell and just forgot
the point is the following: you notice that both F[x]/(p(x)) and V/U have the same kind of notation, right?
royal loom
We do ideals next week I think
royal loom
the point is the following: you notice that both F[x]/(p(x)) and V/U have the sa...
yes just division symbol
/
royal loom
crimson delta
just one in the context of vector spaces, and one in the context of rings
royal loom
vector spaces have more structure than rings right
crimson delta
ehh
they both have addition and multiplication
in some sense
they have different structures. I dont wanna call one of them as having more structure
royal loom
fair idk really what my point was anyways
royal loom
both of them are the same construction
I didn't really get this
like sure they both look like division
but one actually feels like division
F[x]/p(x)
and this one doesn't
this is like weird addition
crimson delta
note that f and g are equivalent mod p, iff f-g is a multiple of p
in other words, f-g is in some set
and in V/U, v+U=w+U iff v-w in U
so again, difference of them is in some set
thats the connection
royal loom
I see
crimson delta
in terms of ideals, f-g are in the ideal generated by p(x)
crimson delta
but we can talk about that more next week
cedar kilnBOT
royal loom
@crimson delta
just clicked play on my lecture for another 15 seconds
after my professor says
this is surjective and hopefully thats obvious
and the kernel is this which should also be obvious
so I paused and im like
its not obvious
and go read my book
and then finally get back to the lecture
hit play
goes for like 30 seconds then she starts explaining
why its surjective
and the kernel
crimson delta
classic
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trim prairie
cedar kilnBOT
trim prairie
.
dusty hazel
!status
cedar kilnBOT
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
Then show work
dusty hazel
It's correct.
cedar kilnBOT
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polar mango
Calculate modulus, argument and goniometric form of the complex number (-1 + i) / root(2)
I went wrong somewhere, pls help me out
fallen moat
Calculate modulus, argument and goniometric form of the complex number (-1 + i) ...
maybe it's language barrier,
what is bgtan()?
is it arctan() or tan^(-1)()
polar mango
It's Arctan()
fallen moat
then you can't break the arctan(b/a) down like that 😦
polar mango
What do you mean?
polar mango
Okok, I'll try. Brb
fallen moat
you can also try to draw it out for reference 🙂
polar mango
Okay, but then I get cos(-1) + sin(-1)*i ???
polar mango
Yes
polar mango
How did you get 3pi/4 ????
fallen moat
so, we pick suitable n so that it's exactly where the point lies
which in this case -pi/4+pi=3pi/4
crimson sedge
Hi i cant figure out how to start with this question
surface of ABCD = 7.5, if you cant read the angle numbers do tell!
cedar kilnBOT
Hi i cant figure out how to start with this question
surface of ABCD = 7.5, if ...
@crimson sedge Has your question been resolved?
crimson sedge
Hi i cant figure out how to start with this question
surface of ABCD = 7.5, if ...
.
Yes sorry if it was unclear
Oh im sorry! the question is whats the length of AC
Wait ill send a new picture, hopefully making the question more clear
Sorry
crimson sedge
Im not sure how that would work
crimson sedge
Wait ill send a new picture, hopefully making the question more clear
Almost done
fallen moat
ok, so
let AC be x
then area of triangle ABC is x²/4
now, AB=x/√2, then area of triangle ABD is x²/(2√6)
then solve for x?
fallen moat
Almost done
I'll wait
crimson sedge
fallen moat
oh,B and C flipped
crimson sedge
Sorry it was unclear!
fallen moat
that's the original question, right?
crimson sedge
Yess
fallen moat
another triangle:
AC=x, AD=x/√3
crimson sedge
Why the devided by root 3?
fallen moat
And then?
oh, i thought you already figured the whole thing
and then
ABCD=7.5=ABC+ADC
we can find the area of those triangles using the values we have found
crimson sedge
Yea i see that abd+adc= 7.5. and then im stuck
fallen moat
did you write them down in terms of x?
crimson sedge
7.5 = .5•X•b + .5•x•d?
fallen moat
if you find typing painful, you can write it down and take a pic
crimson sedge
Wait then why is the x squared
fallen moat
fallen moat
Wait then why is the x squared
get it?
crimson sedge
so
7.5 = .5 x² + x²/2√3
O wow and now judt solve for x i see
Okay imma mess around with this some more thx so much!! 🙏
.close
cedar kilnBOT
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left bison
hellp
unique valley
start with doing the derivative right
left bison
start with doing the derivative right
oh its wrong, alr alr
unique valley
oh its wrong, alr alr
youve done the derivative?
cedar kilnBOT
@left bison Has your question been resolved?