Available help channel!
#help-28
full forumBOT
Available help channel!
fierce stirrup
Hello, I'm solving exercise 4.15 from "quantum computation and information" by Nielsen/Chuang, but I'm kinda confused about the minus sign on the second equation before the cross product term, this minus sign does not appear on other places like here https://math.stackexchange.com/questions/382760/composition-of-two-axis-angle-rotations . Which is correct?
fierce stirrup
This is my work to solve the exercise, also no minus sign in the answer, but maybe some sign got messed up (X, Y, Z are the Pauli matrices)
full forumBOT
@fierce stirrup Has your question been resolved?
full forumBOT
@fierce stirrup Has your question been resolved?
gritty rose
Hello, I'm solving exercise 4.15 from "quantum computation and information" by N...
Maybe ask in #diff-geo-diff-top
full forumBOT
@fierce stirrup Has your question been resolved?
zinc steeple
full forumBOT
zinc steeple
i have one of these wrong
i am pretty sure it must be one of the g
but not sure which one and why
i think it must be 5
oh nvm it should be line for 5
.close
tawny pond
is gradient the derivative at a specific point or is derivative the gradient at a specific point
flint kraken
unless you are using the word gradient in another way than i am used to the convention is that the gradient is the derrivative in all "directions" at a specific point
so they are interchangeable definitions in R^2 but not in higher dimensions
tawny pond
im so confused but that helps thanks
flint kraken
what confuses you?
pure basin
the derivative is a function which helps you to find the gradient at any point
tawny pond
in straight lines the gradient is equal at all points but isnt the derivative same at all points
pure basin
in a straight line, the gradient is equal yes
tawny pond
the derivative is a function which helps you to find the gradient at any point
thats the simplest explanation ive heard, thanks
pure basin
therefore, the derivative is the same at all points
pure basin
thats the simplest explanation ive heard, thanks
np
tawny pond
therefore, the derivative is the same at all points
but in a currveed line the gradient is not same at all points so is derivative also different at all points
pure basin
but in a currveed line the gradient is not same at all points so is derivative a...
yes basically
flint kraken
in straight lines the gradient is equal at all points
gradient of what exactly? Gradient is a concept that is (in my experience) mostly used to describe multidimensional fields, I am unsure why you are making a distinction between gradient and derrivative for this. But if everything is clear now thats good
pure basin
> in straight lines the gradient is equal at all points
gradient of what exactly...
he means gradient as in change in y over change in x
for any curve/line
tawny pond
wait what else does gradient mean
flint kraken
he means gradient as in change in y over change in x
oooh ok my bad, i didnt learn maths in english.
pure basin
wait what else does gradient mean
dw about it just miscommunication
flint kraken
wait what else does gradient mean
yeah i misjudged your level of maths
be happy that you dont have to worry about that^^
scenic yarrow
full forumBOT
vague solstice
Quick question:
Am i allowed to do this am i using the rules correctly ?
pure basin
yes as long as they are the same base
vague solstice
well if its ln isntthe base e ?
full forumBOT
full forumBOT
Available help channel!
unreal spoke
im too dumb for this
full forumBOT
im too dumb for this
unreal spoke
its homework
gritty rose
$x = 0.034\overline{78}$. what's $1000x = ?$
glossy valveBOT
riemann
sweet void
do you understand what the line represents
unreal spoke
ohhhh
slate hemlock
it just repeats forever
slate hemlock
Tried to write it in a way that was understandable but it got really confusing, I suggest to watch this video to understand how to do it, it's pretty short and explain this particular case: https://youtu.be/o2lx_8lU_SI.
Basically you have $\frac{3478-34}{99}=\frac{3444}{99}$
glossy valveBOT
Andrea276
unreal spoke
so 3444/99 is the answer?
glossy valveBOT
slate hemlock
no wait
that's not what the question was asking for
it was asking to express 0.03478787878.... as a fraction, not 34.7878787...
unreal spoke
yea..
slate hemlock
well divide the fraction by a 1000 then
unreal spoke
3.444/99?
slate hemlock
you can't use decimals in fractions
unreal spoke
right
slate hemlock
$\frac{\frac{3444}{99}}{1000}=\frac{3444}{99\times1000}=\frac{3444}{99000}$
glossy valveBOT
Andrea276
slate hemlock
,w 3444/99000
glossy valveBOT
slate hemlock
that's the answer you're looking for
unreal spoke
alright thank you so much
slate hemlock
yw
slate hemlock
what does the exact result mean
wdym?
unreal spoke
in this
slate hemlock
oh it's just simplified, yes
torn jolt
doesnt {s_n} = E since all finite sequences in R converge to their last term and for each [x is a member of {s_n}], we can construct a finite subsequence of {s_n} (lets call it A) with x being the sup of A and hence x being what A converges to.
also implies that limsup and lim are equivalent functions
nova basin
First, you can't have a sequence be equal to a set, because one ordered and one is not.
Second, they may not even have the same cardinality: for sn = sin n, E = [-1, 1]
Thirdly, we never talk about limits of finite sequences
torn jolt
.close
full forumBOT
nova basin
Btw it's called the set of limit points of the sequence
full forumBOT
Available help channel!
viscid moon
My friends and I are trying to figure out what the equation would be for the column on the right, as all the columns are related by some pattern.
We were coming up with equations for the first, middle, and right but are stuck on the last column on the right.
Does anyone know what type of mathematics this is called so that I may do further research?
viscid moon
rare dock
+55, +60, +65, +70?
this isn't really a type of mathematics
I guess you could call it inductive reasoning
full forumBOT
full forumBOT
Available help channel!
high gale
full forumBOT
high gale
Ik this is basic but getting confused any help
torn jolt
Circle itself will answer you now
deft zodiac
take the area of a quarter of a circle minus the area of an isosoles triangle of lengths 2.5
torn jolt
A = πr²
area of tow circles is
A = (3.14)(2.5)² = 19.6 cm²
so the two shaded is a half circle area A/2 = 19.6/2 = 9.8 cm²
if they was two quarters
but i think they are creating quarter circle like what circle said so A/4 = 4.9 cm²
spark shell
you cant just assume that the circle is being divided into a quarter
im thinking about it
torn jolt
True
deft zodiac
i mean u can show its a quarter and it isnt too hard but it requires a bit of work and normally u dont really show that
torn jolt
im thinking about it
if we move the top one and remove the bottom one. to create a complete circle against the white circle. we will see that shaded circle is half of the complete colored circle. or at least some of half complete circle
deft zodiac
unless the question is specifically about that
high gale
Thank for the help but they not quarters
torn jolt
high gale
Oh thank you
torn jolt
nope
high gale
But I told my teacher that I was struggling and she said they are not quarters
deft zodiac
ok the easiest way is
these red points are the centre, the purple bits are all the radius of the circles, so they are all length 2.5cm
so we get a square and we can thus see that it is 90 degrees aka quarter of a circle
@high gale
high gale
But there is still that green left over
torn jolt
Can i know if you are trying to know the area of white circle or the shaded parts ?
Because
deft zodiac
But there is still that green left over
to find that u can just take a square minus the area of a quarter of a circle
high gale
Can i know if you are trying to know the area of white circle or the shaded part...
Shaded
torn jolt
to find that u can just take a square minus the area of a quarter of a circle
"take a square" you mean area of the square ?
(2.5)² - 4.9 = 1.35 cm² ?
high gale
My one smart friend said the answer is 12 cm2 but won't tell me the answer
*the method
deft zodiac
area 1 and area 2 is a quarter of a circle,
area 4 is half a circle,
so area 3 is the answer, 2.5*5=12.5
alternatively u can calculate area 1 + area 2 + area 3 - area 4
deft zodiac
yes
btw that quarter of a circle thing is if u wanna calculate the parts individually, which u normally do u dont do it here i guess as theres the shortcut
full forumBOT
@high gale Has your question been resolved?
magic canyon
full forumBOT
magic canyon
spice orchid
What is the range, in general?
magic canyon
-2 to 3?
spice orchid
Well yeah you got it
magic canyon
maybe i typed it wrong in interval notation
i did typed it but it was wrong
i put (-2.3] or (-2,3)
<@&286206848099549185>
full forumBOT
@magic canyon Has your question been resolved?
earnest harness
A B and C are going to split on 12.000 SEK, A gets 2x more than B and C gets 50% more than A, how much does C get?
hot bone
did you try anything so far ?
earnest harness
honestly ive tried to make equations but i didnt get far
earnest harness
X + 2X + 2X ^0.5 = 12.000?
hot bone
x in this case is the amount of money B gets ?
earnest harness
yes
hot bone
can you explain why 2x^0.5 ?
deft zodiac
the last one, 50% more means * 1.5, not ^ .5
hardy elm
earnest harness
oh very true
deft zodiac
u shld go to another chat that isnt used..
hot bone
@hardy elm #❓how-to-get-help
hardy elm
ok ok
earnest harness
X + 2X + 2X ^1.5 = 12.000?
or is the equation wrong
hot bone
It doesn't need to be a power of 1.5
deft zodiac
sry, ^ mean to the power of, use *
earnest harness
since its 50% more than 1, yes
that leaves us with 5x*1.5 = 12000
12.000 / 5*1.5 = 1073?
X = 1073?
hot bone
that leaves us with 5x*1.5 = 12000
Not quite.. you've ignored order of operations here
you need to multiply by 1.5 before you perform addition
hot bone
5x * 1.5 = 7.5x
how did you get to 5x*1.5 ?
earnest harness
x + 2x + 2x*1.5
hot bone
okay thats the original expression
hot bone
What do you get if you simplify it following the rules of operations ?
hot bone
u prolly do the multiplication first right
yea\
earnest harness
6x = 12000?
hot bone
6x = 12000?
Looks right to me
hot bone
yep
hot bone
awesome
earnest harness
.close
vast forum
I tried to solve this and got stuck at x^2 - 2x - 1 =< 0.
full forumBOT
I tried to solve this and got stuck at x^2 - 2x - 1 =< 0.
vast forum
can u proceed further?
How did you get (x-1)^2 <= 2
(x-1)^2 <= 2
Then maybe like x^2 - 2x + 1^2 <= 2
floral bobcat
(x-1)^2 <= 2
Then maybe like x^2 - 2x + 1^2 <= 2
x^2-2x+1<=1+1
vast forum
Where did 2 come from
If bring everything to left side then we get x^2 - 2x - 1 =< 0.
Then we can do smth like (x^2 - 2x + 4) -3 =< 0.
That's bascially (x-2)^2 - 3 <= 0
Ok how do I solve it
I've never used quadratic formula before. That sounds complicated
vast forum
x^2-2x+1<=1+1
Ah
full forumBOT
@vast forum Has your question been resolved?
uneven bronze
My daughter is in 8th grade and is doing these simplify problems. I’m just trying to check one thing so I know how they’re wanting her to do them. So like for numbers 1, 3, and 4, is she supposed to just multiply the actual numbers together since they are multiplication problems? She was saying that in class they were just adding them together but my wife and I were thinking that she was remembering wrong because for number 3 she wrote 11 but we were thinking it’d be 24. As for number 1, she had another problem where they just added exponents for numbers that were the same. For example she had a problem that was 2x2x5x5x5 and the answer was 2^2 5^3 and that was written in pen by her teacher. So I assumed number 1 on this sheet would just simply be 3^9
full forumBOT
My daughter is in 8th grade and is doing these simplify problems. I’m just tryin...
@uneven bronze Has your question been resolved?
torn jolt
You are right. She is supposed to multiply.
uneven bronze
But what about when the numbers are the same like on number 1?
Would she just add an extra exponent to it since it’s the same number. So make it 3^9 rather than 9^8
torn jolt
3^9 - you are right too
uneven bronze
Alright. Awesome. Thank you.
torn jolt
Help pls
torn jolt
full forumBOT
@torn jolt Has your question been resolved?
torn jolt
<@&286206848099549185> ?
full forumBOT
@torn jolt Has your question been resolved?
calm nacelle
yo
lemme see
okay it's kinda hard to read your work, but what did you get as the rectangular form for w?
okay I see it now
why did you take arctan(2pi/5)?
that's not right
torn jolt
Oh maybe that's why
calm nacelle
arg z = 2pi / 5 here
not b/a
remember that tangent is opposite over adjacent
so tan(2pi/5) gives you y/x
torn jolt
so tan(2pi/5) gives you y/x
Oh I do this instead right?
And continue with what I was doing before
Just fixing the mistakes I made
calm nacelle
if I'm reading what you wrote correctly then yea
torn jolt
Awesome ty, I'll come back if I get it wrong
Also why doesn't arg z start from the origin?
@calm nacelle
calm nacelle
it just starts from wherever the start of the arrow is
where you begin the arrow is somewhat arbitrary
it's just the length and angle that matter
torn jolt
Ahh alr alr
torn jolt
@calm nacelle thanks it worked
calm nacelle
np!!
torn jolt
.close
dry steppe
decisions to stop at any of the tourist attractions in an independent event
dry steppe
how do i answer this
dry steppe
gotcha
torn jolt
oh p(the total) is just 1
stiff musk
the last sentence was cut off but i assume it's something like "assume decisions to stop at each site are independent of the others"?
dry steppe
decisions to stop at any of the tourist attractions in an independent event
yea i wrote it here
dry steppe
means p(the total) - p(15 stops) - p(16 stops)
okay so im going to first find at most 14 using this
what number is represented by the 16 and 15 stops
it is 1 - p(16) - p(15)
dry steppe
i know but how do i find that answer
stiff musk
this is where the independence comes in
P(stop at all 16 stops) = P(stop at one stop)^16
due to independence
dry steppe
so P(stop at 16 stops) = 0.87 ^ 16?
full forumBOT
@dry steppe Has your question been resolved?
stiff musk
so P(stop at 16 stops) = 0.87 ^ 16?
yep
dry steppe
ok i will do that now
15 stops is 0.87 ^ 15 which equals 0.123819
16 stops is 0.87^16 which equals 0.107723
total equals 1
so 1 - 0.123819 - 0.107723 = 0.768458
therefore p(at most 14) = 0.768458 ?
is that correct
fleet cedar
15 stops is 0.87 ^ 15 which equals 0.123819
you also need to factor in which spot they dont stop at
there are 16 spots that could be chosen as the one to skip
and theres a 1-0.87 chance you skip it
full forumBOT
@dry steppe Has your question been resolved?
full forumBOT
@dry steppe Has your question been resolved?
deft zodiac
16 stops is 0.87^16 which equals 0.107723
this is correct for p(16)
deft zodiac
15 stops is 0.87 ^ 15 which equals 0.123819
this on the other hand should be 0.87^15 * .13 * 16 = 0.25754440779
15 times where u stop at an attraction and 1 times that u dont, and also there is 16 ways to arrange the attraction u visit/dont visit
dry steppe
this on the other hand should be 0.87^15 * .13 * 16 = 0.25754440779
ok so 1 - 0.25754440779 - 0.107723?
deft zodiac
yep
dry steppe
okay i got 0.63473259221
deft zodiac
yep
dry steppe
that is correct?
deft zodiac
i think so yes
dry steppe
perfect thankyou
deft zodiac
.close
full forumBOT
@dry steppe Has your question been resolved?
dry steppe
.close
modern sentinel
what's the meaning of exhaustive set, does it mean domain of the function
amber sapphire
in sets
rare dock
it just means all
amber sapphire
exhaustive means the union of all results in the super set
ya basically all soltuions
modern sentinel
so it means range?
rare dock
exhaustive means the union of all results in the super set
what???
amber sapphire
i don't really think you can use those terms here
amber sapphire
what???
ya haven't you heard about it in the probability theory?
it is basically what you meant dw
modern sentinel
what's the meaning of exhaustive set, does it mean domain of the function
so what do i need to do in here
rare dock
what does that have to do with this
it's asking for all real numbers $x$ that make $\log_{|x|}(x^2+x+1)\geq 0$ a true sentence
glossy valveBOT
layla💜
modern sentinel
oh
rare dock
for example, $\log_{10}(111)\geq 0$, so 10 is one of values of $x$ that satisfy that
glossy valveBOT
layla💜
modern sentinel
okay ill try solving
@rare dock did u do it? im getting d as the answer
but i dont have the ans key to verify
anyways ty
.close
full forumBOT
rare dock
I haven't done it but I can take a look if you want
modern sentinel
okay thnks
full forumBOT
Available help channel!
manic nacelle
Q d
modern sentinel
write tan square as sin square/ cos square
thick crown
tan x = sin x / cos x
sin² x + cos² x = 1
The rest is just algebra.
hasty pagoda
.reopen
mellow kettle
full forumBOT
mellow kettle
How to justify that these functions are infinitely continuous
Like that the first derivate is continuous
The second too
Until the n-th one
Sorry if unclear , i can try to explain more
opaque helm
How to justify that these functions are infinitely continuous
You mean infinitely differentiable ?
Oh it's in french
mellow kettle
Can you speak French ?
opaque helm
Du coup pour f tu peux déjà dire que f est C^1 par le théorème fondamental de l'analyse. Ensuite sa dérivée est le quotient de fonctions C^inf dont le dénominateur ne s'annule pas sur R_+^*
Euh d'ailleurs c'est $[1,+\infty)$ l'intervalle que tu regardes, ou $(0,+\infty)$ ?
glossy valveBOT
Twenty
mellow kettle
On peut en discuter en privé ? Jsp si on peut parler fr ici 
opaque helm
Je pense que si, je l'ai déjà fait 😇 et on peut switch back in english si besoin
mellow kettle
Okay
Donc avant cette question y’en a une autre vraiment bateau mais j’ai peur de mal justifier
Faut justifier que les deux fonctions que j’ai envoyé sont définies sur R+*
La fonction g c’est évident
Et f est définie sur R non ?
opaque helm
Ok, alors la fonction f n'est pas définie en 0
$t \mapsto \frac{1}{t}$ n'est pas intégrable en 0
glossy valveBOT
Twenty
mellow kettle
D’acc elle est pas intégrable en 0 mais def pourquoi ?
opaque helm
(ni en +inf d'ailleurs)
mellow kettle
On peut intégrer de 0 à 1 en mettant un moins
opaque helm
Alors oui mais non ^^ oui on peut faire ça quand la fonction qui est à l'intérieur (l'intégrande) est intégrable, mais pas ici
mellow kettle
Oh ok
opaque helm
Ici exp(t) s'approche de 1 en t->0
Donc ton intégrande ressemble à 1/t lorsque tu t'approches de 0 (c'est un développement limité ou un équivalent si tu veux justifier ça proprement)
ça va jusque là ?
mellow kettle
On est d’accord sur la fait que l’intégrande est pas intégrable à cause du t au dénominateur ?
En 0
opaque helm
Ouaip
mellow kettle
Ok
mellow kettle
La fonction (l’integrande) est intégrable
Donc l’intégrale existe
Pour tout x > 0
opaque helm
La fonction (l’integrande) est intégrable
Ouais. Une justification rapide ?
mellow kettle
e^t/t est continue sur le segment [ 1;x] où x appartient à R*?
opaque helm
e^t/t est continue sur le segment [ 1;x] où x appartient à R*?
(petit détail, lié à ce que tu as déjà évoqué : ça peut être [x,1] ou [1,x] suivant si x est avant ou après 1. Mais pas très grave)
mellow kettle
On peut justifier par « definie sur R+*par différence de telles fonctions »?
opaque helm
Ouais
mellow kettle
Ok, je dois après calculer les dérivées premières et secondes de ces fonctions
Pour f j’ai envie de dire qu’on retombe sur e^t /t quand on dérive mais je sais que c’est faux x(
opaque helm
C'est pas faux ^^
mellow kettle
Ça me paraissait bizarre parce qu’on dérive en fonction de x
Et on va se retrouver avec du t à la fin , le x ayant disparu
opaque helm
Ah, ok j'ai mal lu
Mais "enlever l'intégrale" c'est l'idée
C'est juste que en effet ça va être du x à la fin
C'est encore un coup du théorème fondamental de l'analyse
Comme c'est marqué, t c'est une variable muette. Elle "existe" pas en dehors de l'intégrale
mellow kettle
Donc à la fin on aura du x à la place du t
opaque helm
Ouais
mellow kettle
Merci beaucoup ! Je pourrais t’envoyer un mp si je rencontre d’autres soucis par la suite ?
Ton aide a refait ma journée
opaque helm
De rien ^^
opaque helm
Merci beaucoup ! Je pourrais t’envoyer un mp si je rencontre d’autres soucis par...
Je préfère ici car il y a le LaTeX !
(si tu as fini tu peux .close le salon)
full forumBOT
@mellow kettle Has your question been resolved?
mellow kettle
.close
tawny pond
how do I prove that if a pair of opposite sides of a convex quadrilateral are equal and parallel, then it is a parallelogram
faint dock
Write down the formal definitions of all the things you are working with and go from there
tawny pond
i know that the oppposite sides and angles in a parrellogram are ueqal
full forumBOT
@tawny pond Has your question been resolved?
grizzled halo
yes, your proof is simply saying that because 2 sides are parallel and equal, the other 2 sides to complete the quadrilateral will also be parallel and equal
What the helpers said find your defintions, define them, then prove the the next 2 sides must also be parallel and equal, then by the definition of parallegram we have the answer.
full forumBOT
@tawny pond Has your question been resolved?
tawny pond
What the helpers said find your defintions, define them, then prove the the next...
yeah but I'm not sure how to prove the other 2 sides will be parallel and equal
tawny pond
.close
full forumBOT
full forumBOT
Available help channel!
prisma tusk
full forumBOT
nocturne creek
Im learning the ratio test
I have no idea what the ratio test is but do we just need to find this limit?
prisma tusk
yeah basically
nocturne creek
Is the answer 1
prisma tusk
yeah i thought its (n+1)*n!
prisma tusk
so (8+n)! must be (8+n)*n!
nocturne creek
No no
prisma tusk
ah
nocturne creek
(n+1)!= 1.2.3....n.(n+1)
(n+2)!=1.2.3...n.(n+1)(n+2)
Do you see what (n+8)! will be now
nocturne creek
So now you can do it
prisma tusk
wait but whats the simplified version
oh wait i get it
give me a second
oh i seee
(8+n)/(n+1)
= 1
limit as n approaches inifnity
thank you very much!
.close
mellow kettle
full forumBOT
mellow kettle
I have to prove the circled formula by induction
gritty rose
looks like integration by parts
mellow kettle
For the integral yeah
gritty rose
did you try?
gritty rose
Yeah I got t^2n+2 in the new integral
show your work
i don't see how you get t^(2n) instead of t^n unless you just integrated by parts too many times, in which case the two sums won't be correct either
mellow kettle
I’m gonna send what I did
full forumBOT
@mellow kettle Has your question been resolved?
mellow kettle
.close
full forumBOT
full forumBOT
Available help channel!
torn jolt
I used (83)(80)+(20)(x)=80 for the equation and got 68%. Is this correct or incorrect?
topaz valley
it is correct
torn jolt
.close
weak tusk
Can you guys help me with question 3a f.g
full forumBOT
Can you guys help me with question 3a f.g
slate hemlock
g-f is going to be a subset of g with the elements that are in g but not in f
slate hemlock
Is this correct for a
So it's not correct
weak tusk
Like this?
slate hemlock
Nope, don't think about (-4,4) as 2 elements but as just 1
slate hemlock
For example, you shouldn't split (-4,2) in two parts, but leave it as it is. If (-4,2), which is in g, is not in f, then it's going to be part of the set g-f you're looking for
weak tusk
Is there a way you can show me I’m kinda a visual learner
slate hemlock
Try to watch this:
https://youtube.com/watch?v=2B4EBvVvf9w
full forumBOT
@weak tusk Has your question been resolved?
full forumBOT
@weak tusk Has your question been resolved?
cursive badger
full forumBOT
torn jolt
after you find the values of $\alpha$ and $\beta$, just expand $(x-\frac{\alpha}{\beta})(x-\frac{\beta}{\alpha})$ and you'll get the equation you want
glossy valveBOT
R00tKiT
torn jolt
$\alpha$ and $\beta$ should not be equal to 0 though
glossy valveBOT
R00tKiT
strong steeple
Hey all, I've been trying to adapt this sub-linear time approach for calculating the divisor summatory function for squares to work for $$d(2n^2)$$ instead. Any suggestions on how I could go about doing that?
glossy valveBOT
Grandmaster Shadow Morgue
strong steeple
I can see that $$d(2n^2) = d(2)d(n^2)$$ for odd numbers but still somewhat stumped on how I could tweak everything to give me a sub-linear method for calculating $$D(N) = \sum_{n=1}^{N} d(2n^{2})$$ overall
glossy valveBOT
Grandmaster Shadow Morgue
full forumBOT
@strong steeple Has your question been resolved?
strong steeple
<@&286206848099549185>
nimble fable
strong steeple
https://tenor.com/view/who-asked-me-trying-to-find-who-asked-spongebob-spunch-bo...
Anything I could do to make it easier, I get there's quite a fair amount of background there in what I'm trying to get help for
nimble fable
This might be a bit too advanced for #❓how-to-get-help
nova basin
Let $(U, V) \in \mathbb{M}_{p, 1}(\mathbb{R})^2 \setminus {(0, 0)}$, show there exists $A \in \mathbb{M}_p(\mathbb{R})$ such that
$\begin{vmatrix}
A & U \
^t V & 0
\end{vmatrix} \neq 0$
glossy valveBOT
themateo713
nova basin
I thought of taking inspiration from the proof that $GL_n(\mathbb{R})$ is dense in $\mathbb{M}_p(\mathbb{R})$ to show that writing the determinant as a polynomial of p² indeterminates shows it can't always be 0, but I don't know how to actually show the polynomial can't be constant equal to 0
glossy valveBOT
themateo713
nova basin
It ought to be, but I don't know how to prove it
nova basin
**themateo713**
at least in a clean way, and I don't really want to do dirty stuff
gritty rose
what's $\mbb{M}{p,1}$ and $\mbb{M}{p}$ here?
glossy valveBOT
riemann (eric tao for honorable)
nova basin
px1 matrices and pxp matrices
U, V are vectors, A a square matrix
so the determinant is that of a p+1 square matrix
written in block notation
gritty rose
Nonzero vectors right?
nova basin
they can't be both zero
gritty rose
oh one of them can be
nova basin
yes
gritty rose
but if U is zero, then the last column zero?
nova basin
actually
might be a mistake
because that's clearly how it's written
but the following questions basically make me believe they start off by having that one of U or V be zero
gritty rose
i interpret this as U and V are neither zero this was wrong
nova basin
it's the set of all pairs (U, V) except for the pair {(0, 0)} though
otherwise you'd write (M_(p, 1)(R) \ {0})²
nova basin
but the following questions basically make me believe they start off by having t...
because 5) would be to show that for a given matrix, it's always either U = 0 or always V = 0
nova basin
otherwise you'd write (M_(p, 1)(R) \ {0})²
so I guess we can assume it's this
instead
gritty rose
no wait you're right
yea it implies $(U, V) \neq (0, 0)$ but one of them could be. just a mistake i think by the author
glossy valveBOT
riemann (eric tao for honorable)
nova basin
but if one of them is 0 the det is 0 then ? I don't see how this couldn't hold ?
gritty rose
otherwise you'd write (M_(p, 1)(R) \ {0})²
exactly. the mistake is it should have been this
nova basin
so that's that but I'm still not sure how you'd prove it though
nova basin
looks weird, because only 1 out of p+1 sub-matrices keeps the 0 in the bottom right
gritty rose
OH right. jesus
nova basin
looks weird, because only 1 out of p+1 sub-matrices keeps the 0 in the bottom ri...
also p has been constant for the whole assignment. Not that it rules out induction but it feels somewhat out of place
any other ideas ?
gritty rose
could get p+1 equations by contradiction. try assuming T is invertible. then
$Tx = 0$ if and only if $x$ is 0
glossy valveBOT
riemann (eric tao for honorable)
nova basin
its \\
nova basin
could get p+1 equations by contradiction. try assuming T is invertible. then
the goal is to prove it's invertible though
gritty rose
$T = \begin{bmatrix}
A & U \
^t V & 0
\end{bmatrix}$
glossy valveBOT
riemann (eric tao for honorable)
gritty rose
oh i mean assume $T$ is not invertible
glossy valveBOT
riemann (eric tao for honorable)
gritty rose
Then there is a nonzero $x$ that satisfies $Tx=0$
glossy valveBOT
riemann (eric tao for honorable)
nova basin
that forces V.x = 0
so if you choose lines of A such that (A_i U_i)x != 0 for every x orthogonal to V and U that works
can we have that ?
gritty rose
that forces V.x = 0
this is almost right. v is only length p while x is length p+1
nova basin
so if you choose lines of A such that (A_i U_i)x != 0 for every x orthogonal to...
letting V also be (V 0) we get: if x is in Ker T then
Vx = 0 so x is orthogonal to V
x is orthogonal to every line of (A U)
gritty rose
oh nice that makes the math easier
gritty rose
the only we know is x is nonzero, but some of its components can be zero. did you use that somewhere?
nova basin
can we guarantee that though ?
there are several x vectors though
gritty rose
suppose T is not invertible. then its rank is at most p, so suppose it's p. then the kernel has dimension 1. x and all its scalar multiples are this line
nova basin
" so suppose it's p" isn't WLOG though
the point is to say there exists such a matrix A, so I'm not sure this is the right way. The idea looks sound but somewhat off track
maybe more like x needs to be orthogonal to (V 0), which is a vector space of dimension p, and you choose the p lines of A such that they each eliminate a different dimension ? That looks like a good idea
basically choosing the line as being colinear to one of the basis vectors of the orthogonal space, with the right constant so that U works with it. The only problem is if the value of U is 0 though
full forumBOT
@nova basin Has your question been resolved?
full forumBOT
Available help channel!
tulip lodge
Do you have to do distributive property if there's an expression in absolute value? ex. 4Ix+3I
torn jolt
Wdym
tulip lodge
ivory cairn
yes, the 4 would distribute to the y and the 3
tulip lodge
got it thanks
deft zodiac
i mean u can but i would say u have to.. it would depend on context
tulip lodge
alright I'll give you the whole equation
I have to solve the function
so if y=1
-4|1+3|
I still have to do distributive property I assume
deft zodiac
i dont think u can solve for just a function?
ivory oriole
Good afternoon, I'm currently stuck on a U-substitution problem that I can't seem to figure out. I'm most likely unfamiliar with the technique I'm suppose to used, and that is the only problem I have.
ivory oriole
other sources say I should do the U-substitution on the left
but I'm afraid I don't quit understand how to get there
ivory oriole
I have no clue
ivory oriole
I the integral calculator I used does that for some reason
oh
That makes more sense
stiff musk
and you should have a (-du) on the rhs
from there it should be fairly easy, just split it into the sum of two integrals
ivory oriole
.close
full forumBOT
full forumBOT
Available help channel!
humble thunder
I can't figure out how to get the angle in radians
full forumBOT
I can't figure out how to get the angle in radians
eager violet
What have you tried
humble thunder
theta=tan^-1(-1/4)
eager violet
And what do you get?
humble thunder
-0.2449 radians
eager violet
Remember that the angle has to be between 0 and 2pi
Also remember that you can add 2pi to any angle and get the same thing
eager violet
You added 2pi to your answer, right?
humble thunder
yes
eager violet
2pi represents a full rotation. Rotating an angle 360 degrees doesn't change the angle
humble thunder
So I added 2pi because I got negative radians?
eager violet
Yes, and the question specifically asked for an angle between 0 and 2pi
humble thunder
How about arctangent having to be in quadrants 1 and 4?
is that why he adds pi
to do a half rotation and get into quadrant 1
eager violet
Well, there's two distinct angles that give the same tangent
Arctan only gives angles in the first and fourth quadrant
So you'll need to see if the angle your given is in the second or third quadrant
If it is, the other angle will be + π
Because tan(x + π) = tanx
full forumBOT
Hey can Somone help me
light sonnet
Hey can Somone help me
kind grail
Oh mb then
I’m stuck on we’re to begin
Here is the problem
So far I have (6 squared -4)- (6x-6
)
I’m in Alg 2 btw
astral sinew
6 squared?
kind grail
Yea
Because on the other side it’s 6x
So doesn’t that mean 6x is on both
Or is it jus 1x
hot herald
what's "it"
kind grail
X
hot herald
well x is 1x if that's what you mean...
kind grail
Yea
eager violet
f(x) is x² - 4
kind grail
I missed the first 2 days because I had Covid so I’m behind sry
eager violet
It's not 6² - 4, nor is it x - 4
humble thunder
Just subtract the two things
hot herald
no
eager violet
When did an expression become an equation
hot herald
no
humble thunder
combine like terms
eager violet
This is incorrect
humble thunder
wdm
hot herald
missing ()
kind grail
So 1x squared is 1
hot herald
no
humble thunder
you still have to combine and rearrange
eager violet
Parenthesis are important
kind grail
1x -6x = 5x
hot herald
no
kind grail
I’m confused
eager violet
x² is very much not the same thing as x
hot herald
stop going ahead when we say no, implying what you did/ currently have is wrong
hot herald
note that the whole of g(x) is being subtracted
so you shouldn't be only applying the - to whichever term appears first
after the initial step you should have
$$(f-g)(x) = f(x)-g(x) = x^2 - 4 - \red{(} 6x - 6 \red{)}$$
kind grail
?
kind grail
Ok I’m confused on that part so
glossy valveBOT
ℝamonov
humble thunder
You just distribute the negative to the stuff in the paranthesis 🙂
hot herald
x^2 is x^2, do NOT change that to x, 1, 🍎, 🍌 or whatever you feel like that isn't x^2
kind grail
That’s what u guys said
hot herald
no?
hot herald
that is NOT what we said
kind grail
Ok I’m majorly confused then
hot herald
where did we say
(x^2squared -4) (X)
kind grail
It’s confusing do you guys have a YouTube vid I can learn from here i wasn’t in class for this
kind grail
where did we say
`(x^2squared -4) (X)`
So what do I do from there
light sonnet
So what do I do from there
Nothing because that's wrong
hot herald
rub it out?
kind grail
How do I do this then
hot herald
humble thunder
dude
kind grail
.close
full forumBOT
humble thunder
Distribute the negative
kind grail
.reopen
full forumBOT
✅
humble thunder
plz
kind grail
Bro I don’t get what you mean by that
This is my first time learning this unit I wasn’t here for the class
light sonnet
This is my first time learning this unit I wasn’t here for the class
Maybe it would help if you learned it?
light sonnet
now you have
Why exactly are you doing the problem for them? You shouldn't be doing that
humble thunder
Did you really get it?
full forumBOT
@kind grail Has your question been resolved?
rocky kelp
full forumBOT
rocky kelp
I'm not really sure what I'm doing wrong here. What I have is close but not quite right
is my implicit differentiation wrong, or am I not applying algebra correctly?
rocky kelp
wait... what?
I didn't integrate anything, where did the C come from?
(y - ln|y| = x^2 + 1) is the implicit solution I'm trying to prove for dy/dx = 2xy/y-1
I'm trying to do implicit differentiation of it to verify the ODE
gritty rose
(y - ln|y| = x^2 + 1) is the implicit solution I'm trying to prove for dy/dx = 2...
You just need to multiply the top and bottom by y in the right hand side
Finish the bottom multiplication
zenith kernel
You better ask your question clearly, you didn’t say what the question is, giving y-In|y|=x^2+1, to prove dy/dx=2xy/(y-1) or solve differential equation dy/dx=2xy/(y-1)
I assumed the latter
rocky kelp
but, if I multiply the right hand by Y don't I have to multiply the left hand by Y?
I'm trying to isolate dy/dx on the left side
multiplying the right by Y would make the right hand side 2xy/1-y but then it would make the left hand side y dy/dx too no?
actually, I think that would be wrong for the right hand too, wouldn't it make it 2xy^2/y-1?
gritty rose
You just need to multiply the top and bottom by y in the right hand side
Read this more carefully
rocky kelp
ohhhhh wow that was not obvious at all
multiplying everything by y in step 2 leads to a solution though, if that's what you mean't
thanks for the help 👍
gritty rose
Sure there are multiple ways to do it. Glad it works
full forumBOT
@rocky kelp Has your question been resolved?
odd summit
full forumBOT
odd summit
How exactly do you solve this question? Thanks 🙂
nocturne creek
How exactly do you solve this question? Thanks 🙂
Use the formula
round gust
How did you get from basic trig to this
odd summit
I'm doing some calculus review
round gust
Ok
odd summit
.close
full forumBOT
glass rune
full forumBOT
Available help channel!
next flume
Make LHS a common denominator then cross multiply
full forumBOT
Make LHS a common denominator then cross multiply
dry mirage
how many millions are there in 86,953,061
full forumBOT
how many millions are there in 86,953,061
onyx glen
can you write the number 86,953,601 in words? the answer might become clear.
also please don't just .close without saying a word if your question was resolved. at least thank the person or people who responded or something.
dry mirage
oh
dry mirage
can you write the number 86,953,601 in words? the answer might become clear.
can u do it for me
dry mirage
oh
full forumBOT
dry mirage
.reopen
full forumBOT
✅
dry mirage
can you write the number 86,953,601 in words? the answer might become clear.
eighty-six million nine hundred fifty-three thousand sixty-one
simple ridge
Hi
simple ridge
Is this correct or no
<@&286206848099549185>
Also pls don't tell me that I should wait 15 mins before I use @ helpers bc I had too channels closed from waiting and this is the third
I made one from abt 4-5hrs and it closed so I made another at 1hr ago prob and it closed now I made this
Why isn't anybody answering my question
calm osprey
Why isn't anybody answering my question
So this discord consist of only volunteers. This means that that there might not be anyone eligible to help online depending on complexity of the question. They might not have time or any other reason. There is no one on the discord that is obliged to answer questions for better or worse.
You can only hope someone is available.
simple ridge
Ik but many people already have their questions answered in this time that I am trying to find someone to answer my question
It's ok if no body wants to answer my question but just inform me to know what to do instead of just waiting
Nvm I'll just close the channel
And sorry if my way wasnt so good forgive me
.close
torn jolt
full forumBOT
onyx glen
yes, very.
deft zodiac
yea u treated the first + as a *
torn jolt
oh i see mb
onyx glen
if you wanted to isolate h you could have subtracted 6x^2 then divided by 6x
torn jolt
deft zodiac
seems right
supple briar
why is it 0.9j shouldnt it be 9j ?
full forumBOT
why is it 0.9j shouldnt it be 9j ?
deft zodiac
use a calculator
supple briar
use a calculator
i did it says 9 not 0.9
rugged harbor
I get 0.9 too, did you forget the **0.**5?
supple briar
hmm ill try gain
deft zodiac
send a pic of what u entered in the calc along with the result
supple briar
nevbvermind
rugged harbor
I get 0.9 too, did you forget the **0.**5?
It's that or you wrote 0.3² as 0.9, which is wrong, it's 0.09
cursive badger
full forumBOT
cursive badger
how would i show that for this question
i know how to normally do this type of question
but idk what to do with the 2
onyx glen
let θ = arcsin(3/5), then you know that sin(θ) = 3/5 and θ ∈ (0, π/2) [and in fact θ ∈ (0, π/4) since 3/5 < sqrt(2)/2]. find sin(2θ).
cursive badger
full forumBOT
torn jolt
try drawing the unit circle and constructing a triangle with height x
or u can sub x=sintheta maybe
in (a)
full forumBOT
@cursive badger Has your question been resolved?
torn jolt
ok
cursive badger
ok
noble pelican
[Italian Linear Algebra]
I really need somebody to guide me here, our professor's explanation is so disjointed and minimal that its useless. I tried other sources but what he asks of us its to advanced.
I'll translate it shortly. Please I need help.
nova basin
V is the set of all polynomials with what that's at least 3 ?
I if understand correctly (cause I don't speak italian)
noble pelican
Question A) Prove that only one Linear Operator F: exist so that:
Ker(F) has linear system ->
F(0,...
Write the matrix of F in regards of the Standard Basis R^5, taken as a starting basis in R^5 and at {1, t, t^2, t^3} taken as a basis of arrival to T
spice orchid
at most degree 3 i imagine