I think if you stick it through for the long division you will get the result you are looking for
#help-0
vapid shuttle
not too terribly bad because the top and bottom are only binomials aswell
just be careful with sign errors and stuff
strong prism
How would you prove that there's no vector in the set {v1, ..., vk} in R^n (each vector is different) that does not have only 1 linear combinations?
There's also a vector w that have infinite linear combinations of v1, ..., vk.
I was thinking on proving by contradiction, and try to show that a vector 'u' have only one combination and get to a contradiction.
strong prism
I'm not sure how to approach it tho, is there a nicer way to prove it?
lone heartBOT
@strong prism Has your question been resolved?
wind cloak
$\sum_{n = 1}^{\infty} \frac{n^2 + 6n + 10}{(2n + 1)!}$
lone heartBOT
$\sum_{n = 1}^{\infty} \frac{n^2 + 6n + 10}{(2n + 1)!}$
ocean sealBOT
NEONPerseus
lone heartBOT
@wind cloak Has your question been resolved?
wind cloak
Eh I think I figured something out
lone heartBOT
bright heart
.close
lone heartBOT
Available help channel!
ember sigil
Can someone show me the procedure? Is with substitution method right?
raven haven
Can someone show me the procedure?
we're not gonna do the work for you
Is with substitution method right?
you answered your own question.
gray isle
you can go straight for power rule
ember sigil
> Can someone show me the procedure?
we're not gonna do the work for you
> Is wi...
Damn, it isn't even hw, just wanted to check my procedure
solar crown
I'm so confused about this.
lone heartBOT
I'm so confused about this.
solar crown
If i have more questions can i still send them here? 😭 Very confused year one
solar crown
I think A&D are right
echo socket
Nope, D is wrong
echo socket
You can simply recall that generally
[
\emptyset \cap A = \emptyset
]
solar crown
idk how this is in the homework
ocean sealBOT
A Lonely Bean
echo socket
This is better
echo socket
Sure
echo socket
A∩B is the set containing all elements from A and B, right?
echo socket
So those elements have to satisfy the conditions |x - 1| <= 2 and |x| >= 1 simultaneously
Yeah A∩B = {-1}U[1, 3]
echo socket
Formally or informally speaking?
echo socket
Infinity is not a number thus you can not compare it to other numbers
echo socket
Finding B∩C is equivalent to solving the system of equations |x| >= 1 and |x + 2| < 3
If |x| >= 1, then x >= 1 or x <= -1
solar crown
im alright with that so far i think
echo socket
im alright with that so far i think
Do you want me to continue or?
echo socket
Okay, so we have x <= -1 and |x + 2| < 3
We can rewrite |x + 2| < 3 as -5 < x < 1
And simply find the intersection of the intervals (-inf, -1] and (-5, 1)
That is (-5, -1]
So the second answer is 4
echo socket
Alright
solar crown
are the next ones 1&2?
echo socket
Yes
cosmic niche
I=∫[0,∞] 1 / (1 + x^{(1+sqrt(5))/2})^{(1+sqrt(5))/2} dx= solve
mint wadi
tex:
whole shell
I=∫[0,∞] 1 / (1 + x^{(1+sqrt(5))/2})^{(1+sqrt(5))/2} dx= solve
no one can read that lmao
mint wadi
$I = \int_{0}^{\infty} \frac{1}{1+x^{\frac{1+\sqrt{5}}{2}^{\frac{1+\sqrt{5}}{2}}}} dx$
is that what u meant @cosmic niche?
ocean sealBOT
The Impostor
echo socket
I think he meant
[
I = \int_0^\infty(\frac1{1+x^\frac{1+\sqrt5}{2}})^\frac{1+\sqrt5}{2} dx
]
cosmic niche
ocean sealBOT
A Lonely Bean
echo socket
Yup
cosmic niche
yes
echo socket
Cuz I have seen that integral in a thunbmail once
wind cloak
I think I've seen a video by BriTheMathGuy
yeah
He used some properties of phi I think
wind cloak
$\phi = \frac{1}{\phi} + 1$
ocean sealBOT
NEONPerseus
lone heartBOT
@cosmic niche Has your question been resolved?
cosmic niche
no
lone heartBOT
@cosmic niche Has your question been resolved?
idle pivot
Hi, I would like someone to show how to do one iteration of Gauss Seidel's method using the golden ratio algorithm. The task can be done for any "n" and for any quadratic function
alpine sable
if you have an algorithm, just follow through the steps one by one
lone heartBOT
@idle pivot Has your question been resolved?
desert rose
Hello, I don't know where I should post my problem. It's more a physic problem (second quantization) but I am stuck on a math issue ! (It is about topological insulator)
Should I post it here anyway?
desert rose
Okay perfect !
Well unfortunately, on the physics server I did not know pings were not allowed. And today I pinged someone who helped me yesterday and in the ping message I told him that I was sorry about the ping because I know how annoying they can be, but in case he did not see my message I wanted to make sure he did.
Unfortunately the moderator was not happy about my first ping and banned me for a day ^^'
anyway, I will post my issue here if it's okay 😄
So, I am trying to reproduce simulations from an article in which they use the following tight binding model :
And, from this Hamiltonian written in k-space I need to find the diffrents parameters of the system (such as the hopping parameter, the on site term etc)
In order to do that, I need to perform a Fourier Transform of the Hamiltonian.
But, from this expression I have no idea how to start it...
Usually, when the hamiltonian is expressed with the annihilation and creation operators I get how to perform the Fourier Transform, but here I don't see it..
So, first I've expressed the vector v in term of $z_{\downarrow}, z_{\uparrow}$ and its conjugate but I don't know if it's relevant
ocean sealBOT
Valentiiin
alpine sable
sounds research level, maybe ask in #odes-and-pdes or one of the advanced channels too
desert rose
It is indeed
Okay I will look there ! Thank you very much for your kindness 😄
alpine sable
gl trying to get it solved!
lone heartBOT
@desert rose Has your question been resolved?
south matrix
Hey, so how can I visualize partial derivatives in 4D, for a function like f(x, y, z)? My book shows the following diagram for a function that looks like (see image attached) for a function f(x, y), and mentions a partial derivative "is the slope of the tangent line to trace curves through the graph."
In 4D however, we don't have trace curves, we have trace surfaces (iirc). How would the concept of a slope work in this case? Or is it even possible to visually understand this?
lone heartBOT
Hey, so how can I visualize partial derivatives in 4D, for a function like f(x, ...
@south matrix Has your question been resolved?
south matrix
<@&286206848099549185>
lone heartBOT
@south matrix Has your question been resolved?
lilac thicket
Hi everyone , I have a question on SVD , question follows:
lone heartBOT
Hi everyone , I have a question on SVD , question follows:
lilac thicket
given this, which is false
It was explained that the following would be true
$| det(A) | = \Pi_{i=1}^{n}\sigma_{i}$
ocean sealBOT
barış
lilac thicket
- can someone explain to me exactly why that is
- Wouldnt it also be true that:
$det(A) = \prod_{i=1}^{n} \sigma_{i}^2$
vale wigeon
$| det(A) | = \Pi_{i=1}^{n}\sigma_{i}$
\prod not \Pi
and where are you getting it from that det(A) should be the product of sigma_i^2??
lilac thicket
\prod not \Pi
thank you , is there a semantic difference ?
lilac thicket
and where are you getting it from that det(A) should be the product of sigma_i^2...
arent the singularvalues the squareroots of the eigenvalues of a matrix
and the det(A) is the product of the eigenvalues
ocean sealBOT
vale wigeon
if A is rectangular it does not have a det
lilac thicket
thats new to me
But do you understand why I wrote the 2. thing ?
and more importantly do you agree ?
Sorry I forgot that A is given as a square matrix in this case
ocean sealBOT
barış
vale wigeon
no, i don't think the sigmas are square roots of the eigenvalues
they are the eigenvalues themselves, surely
lilac thicket
but the text says that doesnt it ?
oh wait I cant read
my bad
the singular values for A are the square roots of the eigenvalues for AA^T and A^T A, thats correct right ?
vale wigeon
sounds like it...?
lilac thicket
I am sorry for asking stupid questions
I am just not that skilled in linear algebra yet
and a bit slow
lilac thicket
1. can someone explain to me exactly why that is
2. Wouldnt it also be true that...
Thank you for answering my second question. If someone can help me understand the first one I'd really appreciate it a lot
lone heartBOT
@lilac thicket Has your question been resolved?
lilac thicket
<@&286206848099549185>
lone heartBOT
@lilac thicket Has your question been resolved?
lone heartBOT
@lilac thicket Has your question been resolved?
lone heartBOT
@lilac thicket Has your question been resolved?
lone heartBOT
@lilac thicket Has your question been resolved?
short trail
lone heartBOT
short trail
yup
short trail
okay
prisma elbow
step by step
calculate the triangles' area
prisma elbow
and then take that away from the area of the rectangle
prisma elbow
Don't interrupt
ur not supposed to be giving answers to begin with
short trail
60?
prisma elbow
this isn't "answer hw for them"
sly snow
?
prisma elbow
explain to them HOW to do it by guiding them and letting them think about the problem
sly snow
this isn't "answer hw for them"
Why interfere like the pesky US of A
short trail
if triangle is 60
sly snow
Yea
prisma elbow
if triangle is 60
which triangle ru calculating?
short trail
which triangle ru calculating?
the big
sly snow
200 -42.5
sly snow
--> 157.5 cm2
prisma elbow
you're here to explain the logic and guide them, not burst in spitting out answers
prisma elbow
we all have been clueless abt smth
short trail
--> 157.5 cm2
thats wrong
sly snow
be considerate
If you interfer continuusly i might nuke your house
prisma elbow
and ur not even giving a correct answer
short trail
so confusing
prisma elbow
If you interfer continuusly i might nuke your house
<@&268886789983436800>
i don't have time for this
alpine sable
<@&268886789983436800>
sly snow
I'm answering right
sudden igloo
wrong
prisma elbow
I'm answering right
40+12.5≠42.5
sly snow
Dude. what moderators.
prisma elbow
the answer is 147.5 cm^2
but u literally sped thru it when raj clearly has 0 idea what ur doing
night geyser
@sly snow this server is not for you to verify your ego by showing off how much math you know
this server is for other people to get mathematics help
rudely pasting answers without trying to help people goes against the purpose of the server
take a chill pill and come back tomorrow
sudden igloo
yes thats right
prisma elbow
@short trail if ur still willing i can go thru it
prisma elbow
or someone else here
prisma elbow
can do it if they want to
alpine sable
triangle AED?
median oar
In these kinds of problems, it can often be easier to find the whole shape then subtract the unshaded areas, do you see how this concept applies here?
prisma elbow
if one triangle is 60
the large triangle is 10*8/2
short trail
isnt that since 5x5 is 20. the triangle is half
prisma elbow
that's not 60
alpine sable
for Triangle AED, identify which side is the base and which is the height
short trail
the large triangle is 10*8/2
oh ok
alpine sable
for Triangle AED, identify which side is the base and which is the height
can you see which is which?
prisma elbow
oh ok
(base * height)/2
the other triangle would be (5*5)/2 since both the base and height are 5
prisma elbow
20-8
ah wait
i have a question
ru calculating the big SHADED triangle
or the big UNSHADED triangle
short trail
big shaded
prisma elbow
big shaded
if ur doing that then yes it's 60
sudden igloo
maybe writing like triangle AED will help more
prisma elbow
giving the answer to be...
short trail
147.5
prisma elbow
yep
prisma elbow
there are 2 obvious ways of doing it
short trail
have a nice day
prisma elbow
one way is your way
the other is to taking the area of the entire rectangle
so 10*20
and subtract the unshaded triangles
8*10/2=40
5*5/2=25/2
prisma elbow
200-40-25/2
prisma elbow
unshaded triangle
?
it's just the same formula
all triangles share the same area formula
regardless if they are right triangles or not
lone heartBOT
lone heartBOT
Available help channel!
lavish pier
lone heartBOT
lavish pier
having some trouble on question 2 ( i dont know what the lines on top of the sides neither do i know what 6 is
lone heartBOT
@lavish pier Has your question been resolved?
lavish pier
<@&286206848099549185>
alpine sable
yea?
alpine sable
parallelogram, huh
lavish pier
im confused what 2 and 6 are
i dont know what cpctc is
nor do i know why they did ab dc ad bc
does it mean the sides are parallel ive never seen a notation like it
lavish pier
so are they saying ab is congurent to dc>
no we just need to prove that the diagonals bisect eachother
theyve done that already
alpine sable
oohh
lavish pier
im just confused on the working out
like the reasoning for 2 and 6
what do they mean
ok i know what cpctc means know
alpine sable
wait give me a sec
lavish pier
coul;d u help me with two though?
what is that notations on 2
exotic belfry
definition of a parallogramm
lavish pier
whats the part before that though
theres line on top and its listing sides
im guessing that means parallel
but i just ant to be sure ive never seen anythiong like it in maths
alpine sable
yea i have a lot of ideas
alpine sable
like the reasoning for 2 and 6
if one pair of opposite sides are both congruent and parallel
lavish pier
im talking about question two rn @alpine sable
alpine sable
im talking about question two rn <@456226577798135808>
wha-
exotic belfry
lines on the top means the side beetween two points
X || Y means X and Y are parallel.
exotic belfry
yes
lavish pier
how do i prove a paralleogram with a right angle is a rectangle
exotic belfry
in a paralleogram:
- the opposite angles are the same
- adjacent angles sum up to 180
so if on angle is 90 -> all angles are 90.
lavish pier
ah okay
so i dont need to draw a diagram or anything like that with proving it
@exotic belfry
exotic belfry
that depends. if someone accepts the arguments 1. and 2. then you do not need. if someone (eg. teacher) asks you to explain 1 and/or 2 then you maybe need to draw a diagram.
lavish pier
how would i explain it with a diagram and sides with proper reasoning
my teacher is a bit draconic
exotic belfry
its a little bit difficult for me to argue against questions someone maybe would ask if I do not know this person or the type of questions.
lavish pier
thats fine
exotic belfry
the opposite angles are the same: like 3 in your example.
cunning locust
whats next math wizards
lone heartBOT
whats next math wizards
cunning locust
,rotate
ocean sealBOT
vale wigeon
the next step is to scrap all this and simplify the function itself prior to differentiating it.
at least that is what i would have done
cunning locust
i wanted to do this
but after asking before
i was told you cant manipulate fractions unless it only has product
on num and denom
vale wigeon
i was told you cant manipulate fractions unless it only has product
who told you this and what were their exact words
cunning locust
think her name was ann
with horns
i dont remember
someone did though
for example
this you cant simplify
vale wigeon
think her name was ann
so, what was it that i said
if you're going to make claims about what i said, you had better make sure you can prove you are not twisting my words
vale wigeon
cunning locust
like i did
yesterday
anyway someone else told me
that you couldnt subtract poly's
but maybe there was miscommunication
i dont hold things against people
i just want to improve my math
vale wigeon
i take it very seriously when someone claims sth i said but which i didn't.
cunning locust
so can this be simplified?
vale wigeon
well, x^4 + 4x^2 + 4 can be written as (x^2 + 2), sure.
cunning locust
yes
but when its expanded out
top left
why cant you subtract
num from denom
if you can do (new example) (4x^2)/(2x^2) = 2
if the exponents are different you can still subtract
but what i was told is if you add another variable like "a" -> (a+b^2)/(a+b^2) you can not do anything about it
vale wigeon
there is a lot of miscommunication going on here
in particular i do not understand what kind of manipulation you are talking about at all
cunning locust
its ok
cunning locust
so how would you have simplified this? (in the beginning)
vale wigeon
$\frac{x}{x^{-1}+4} = \frac{x^2}{1+4x}$, for a start.
ocean sealBOT
Ann
cunning locust
ok how did you get that
besides changing x^(-1) to x
(1+4x) denom how'd you get that
ruby current
they multiplied the numerator and denominator by x
jagged cobalt
multiply the fraction by x/x
ruby current
(which is fine to do because we can assume that x is nonzero due to the existence of x^(-1))
ruby current
to get rid of the fraction x^(-1)
ruby current
it's due to the fact that multiplication by 1 doesn't change the quantity
you can multiply by x/x because x/x is 1
cunning locust
got it.
is there a particular reason we are getting rid of -1 in the denom though
vale wigeon
it is essentially a nested fraction you're dealing with.
ruby current
you now can do long division if you want
cunning locust
you now can do long division if you want
no thanks 
if it was x^-1, would that need to be changed to 1/x then?
cunning locust
so like an inception of fractions
vale wigeon
you could say that
vale wigeon
would probably leave it at that
can apply the quotient rule now to take the derivative
cunning locust
theres no way to get rid of the 1?
no magic tricks
cause id love to just subtract x^2/(4x) then find derivative 😄
vale wigeon
no there is no way to "get rid of the 1".
ruby current
if you really want a trick, after long division you'll get something with degree 1 in the numerator, which you can get rid of using the +c -c trick, after which you're left with taking the derivative of 1/(1+4x) which is an easy chain rule
but just use quotient rule
vale wigeon
you could do that sure
ruby current
probably more steps
cunning locust
vale wigeon
sigh
cunning locust
.close
lone heartBOT
ruby current
you have to take two derivatives of polynomials to do quotient rule from here
not too bad
cunning locust
thanks guys
lone heartBOT
Available help channel!
wide onyx
lone heartBOT
wide onyx
how do i describe this
in terms of
acceleration
and velocity
like describe a
and b
and c
alpine sable
Whats A B and C
wide onyx
the lines
alpine sable
The length ?
wide onyx
ya
shadow needle
alpine sable
What is velocity
wide onyx
velocity is on the side
alpine sable
@shadow needle u have to create ur own channel
wide onyx
left one
alpine sable
I mean to ask
wide onyx
v = d/t
wide onyx
ya
wide onyx
i needd to desribe the line
like start from reference point then move south for 5 seconds at a xonstant velcoity
at an acceleration
of
wtv
yea
alpine sable
Acceleration is the slope of velocity time graph
wide onyx
4m/s^2
wide onyx
5s
alpine sable
$$v^2 = u^2 + 2as$$
ocean sealBOT
Umbra
alpine sable
Oh
wide onyx
it just wants me to describe it in terms of acceleration and velocity
alpine sable
Ah I see
wide onyx
yea
wide onyx
0
alpine sable
Correct
wide onyx
bec its a straigjt line
alpine sable
Yes
wide onyx
how do i desribe it
wide onyx
constant movement for 15 seconds?
alpine sable
V = U
wide onyx
no acceleration
wide onyx
ya
alpine sable
Acceleration means change in velocity
wide onyx
yea
alpine sable
Since there is no change in velocity throughout B its 0
wide onyx
ya
alpine sable
What will be a at C
wide onyx
6m/s^2
wide onyx
oh whops
wide onyx
ya
wide onyx
ya
alpine sable
Need anything else
wide onyx
nope tysm
alpine sable
👍
wide onyx
.close
finite fiber
hey im just wondering how i would start this question
lone heartBOT
hey im just wondering how i would start this question
finite fiber
-i know it has something to do with the normal vector (under that category in the questions)
but im just used to being given the two vectors i have to put in the matrix but now i have 3 and it's being wacky for me
thick grail
couldn't you find vector ab and ac
then find their magnitudes
then find the dot product between them
then use the formula Area = 0.5 * a * b * sinc
finite fiber
how would you start that
finite fiber
okie dokie i'll go try that
sorry for fried brain had physics and chem exam so i seem little bit stupid
thick grail
nw
vernal saddle
Why is 1/3 % 3016
= 2011?
lone heartBOT
Why is **1/3 % 3016**
= 2011?
limpid turret
One third modulo three thousand sixteen?
mortal trellis
There are probably some typos here or you are rounding stuff that you shouldn't
A third of 3016 is 1005.3333...
If you subtract that from 3016 you get 2010.666....
vernal saddle
I really don't get why it is 2011.
It clearly says the solution is 2011.
This is part of the RSA algorithm.
d = e**(-1) mod N
d=(1/e)modϕ
lone heartBOT
@vernal saddle Has your question been resolved?
lament forge
"1/3" is a number that, when you multiply it by 3, you get 1
modulo 3016, if you multiply 2011 by 3, you get 1
pale kestrel
1/3 is pretty poor notation, its usually written 3^-1
thick depot
lone heartBOT
thick depot
I know I need to find out which trigonometric ratio to use but don't know how to start
lunar palm
try drawing a diagram of the information you have
rapid island
lone heartBOT
rapid island
don't know how to solve
rapid island
yes
rapid island
2
thick depot
and what do these 2 edges have to have in common for it to be a rectangle
rapid island
90 degree angle
thick depot
which means...
rapid island
180 after addition
thick depot
the top line of a rectangle is at what angle
rapid island
180
thick depot
which means that it is what type of line
rapid island
straight
thick depot
so a straight line means what for the top edges
what do they must have in common for the line to be straight
thick depot
gradient and angle have nothing to do with it
rapid island
no idea
thick depot
If I had a straight line, with points (1,2) (6,2), what is common about these points?
rapid island
no idea
thick depot
think about the co-ordinates
rapid island
same gradient
thick depot
gradient has nothing to with it
rapid island
I cant think of anything
rapid island
both are positive
thick depot
What else
rapid island
same y axis
thick depot
and a rectangle needs what?
rapid island
same height
thick depot
same y axis on 2 sets of lines
rapid island
meaning
thick depot
a rectangle has 2 horizontal straight lines on top and bottom
thick depot
so that gives you a clue on where one of the points may be
rapid island
yes
thick depot
so this could be an example of such
red maple
red maple
<@&286206848099549185>
lone heartBOT
@red maple Has your question been resolved?
rocky grove
What do you find troubling in the question?
rocky grove
Hmm
red maple
my work is rly messy and i lowkey did this a week ago so i cant remember what my og thought process was 😭
rocky grove
$R = \frac{1}{10^{12}} e^{-\frac{t}{8223}}$
ocean sealBOT
VulcanOne
red maple
yeah
ocean sealBOT
VulcanOne
red maple
yeah
rocky grove
You did well by plugging in
$\frac{1}{8^{14}} = \frac{1}{10^{12}} e^{-\frac{t}{8223}}$
ocean sealBOT
VulcanOne
ocean sealBOT
VulcanOne
red maple
am i supposed to change it to log here
red maple
ohh
red maple
so it would be
ocean sealBOT
VulcanOne
rocky grove
So like
red maple
1 sec
rocky grove
$\ln\left( \frac{10^{12}}{8^{14}} \right) = -\frac{t}{8223}$
ocean sealBOT
VulcanOne
red maple
so this is -t?
rocky grove
Yep
rocky grove
red maple
.close
mellow reef
The annual basketball tournament starts with a field of
sixty-four teams. After six rounds of play, the squad that
remains unbeaten is declared the national champion. How
many different configurations of winners and losers are
possible, starting with the first round? Assume that the initial
pairing of the sixty-four invited teams into thirty-two first-
round matches has already been done.
lone heartBOT
The annual basketball tournament starts with a field of
sixty-four teams. After ...
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
prime badge
it's not clear but i think it's just the same as the results of all 63 matches
there are 63 matches by the way
prime badge
one team remains, each match eliminates a team
prime badge
yes
mellow reef
it doesnt make sense to me
prime badge
that's my answer
mellow reef
can u expalin more
prime badge
so hard to explain 
basically after the first round you get 2^32 results, and that determines winners and losers of the first round
and then 2^16 results determine winners and losers of the second round
and that's what they mean by configuration, this sequence of 6 "megaresults"
sturdy yacht
car makes it from point a to point b in 23hrs half of the distance he covers going 80km/h one third he covers with 60km/h and the rest with 40km/h. how much km is there between point a and b
pseudo ice
Call e.g. the total distance d [and ideally set it to be in km]
Can you find how long each section of the journey takes, in hours and in terms of d?
exotic belfry
lets start with the first part. if the whole distance is d, which distance is the car going with 80km/h?
sturdy yacht
d/2
exotic belfry
how long will the car need for this - expressed in terms of d?
sturdy yacht
if d = 23hrs then 11.5hrs ?
exotic belfry
ok, lets make it a little bit simpler. if you make 80 km per hour, how long will you need for e.g. 160 km?
sturdy yacht
2hours
exotic belfry
and for 240 km?
sturdy yacht
4hours
exotic belfry
no, 3 hours.
exotic belfry
and for e.g. 200 km?
sturdy yacht
200/80
exotic belfry
perfect. and for d/2?
sturdy yacht
d/160?
sturdy yacht
aight
exotic belfry
whicht distance with 60 km/h?
sturdy yacht
d/60 ?
exotic belfry
first the distance.
sturdy yacht
60km?
exotic belfry
on third -> d/3
exotic belfry
yes.
sturdy yacht
aight we getting somewhere
exotic belfry
and how long is the rest, if we had a half and a third? whats remaining?
sturdy yacht
one sixth (1/6
exotic belfry
yes, and which time with 40 km/h?
sturdy yacht
d/240 ?
exotic belfry
exactly. no we have the time for each part, and we know the whole time is 23 hours.
exotic belfry
not splitting, sum up. d/160 for the first part + d/180 for the second part + d/240 for the third part = 23 hours. Solve for d.
exotic belfry
youre welcome.
dim matrix
lone heartBOT
dim matrix
How 3alpha gamma derived here?
vale wigeon
what is it with this routine confusion between the letters r and gamma?
also this work is full of typos
for real
anyway, $\frac{\alpha + \beta + \alpha + \alpha - \beta}{(\alpha - \beta)(\alpha)(\alpha + \beta)} = \frac{3\alpha}{(\alpha - \beta)(\alpha)(\alpha + \beta)} = 3 \alpha r$
ocean sealBOT
Ann
dim matrix
anyway, $\frac{\alpha + \beta + \alpha + \alpha - \beta}{(\alpha - \beta)(\alpha...
and how the last term is derived? 1/alpha^3 -p/alpha^2 . . .
exotic belfry
Put x = 1/a
vale wigeon
As 1/α is a root of x^3 - px^2 + qx - r = 0,
dim matrix
> As 1/α is a root of x^3 - px^2 + qx - r = 0,
Can we substitute among other two roots instead of 1/alpha
exotic belfry
@vale wigeon, why does the first line work? let roots be ...?
vale wigeon
sure you can. you will suffer.
vale wigeon
<@183668144404037632>, why does the first line work? let roots be ...?
the roots are known to be in harmonic progression
which means their reciprocals are in arithmetic progression (and nothing else)
exotic belfry
oh, thanks. didnt know H.P.
lone heartBOT
@dim matrix Has your question been resolved?
dim matrix
$\frac{\alpha + \beta + \alpha + \alpha - \beta}{(\alpha - \beta)(\alpha)(\alpha + \beta)}$
@vale wigeon How this term derived? When I am dividing equation 3 with equation 1, I'm getting eq. 2
ocean sealBOT
Sirius
vale wigeon
... ??
vale wigeon
$\frac{1}{(\alpha - \beta) \alpha}+ \frac{1}{\alpha (\alpha + \beta)} + \frac{1}{(\alpha - \beta)(\alpha + \beta)}$
ocean sealBOT
Ann
vale wigeon
add the fractions here
dim matrix
add the fractions here
okay
dim matrix
@vale wigeon I stuck here
dim matrix
(alpha-beta)(alpha)(alhpa+beta)?
vale wigeon
(alpha-beta)(alpha)(alhpa+beta)?
yes
plain hill
lone heartBOT
plain hill
how i can solve it?
sudden igloo
whats the purpose
plain hill
semplify
sudden igloo
then try opening brackets first
plain hill
i should try to semplify what is inside the brackets?
sudden igloo
u know whats $(a+b)^2$
ocean sealBOT
BLAZE
sharp girder
Open both brackets add them and see what happens
sudden igloo
you can see (a sin alpha + 2 sin alpha)^2
also this u expand (a sin alpha - 2 sin alpha)^2
plain hill
(a sin alpha)^2 - 2(a sin alpha)(2 cos alpha) + (2 cos alpha)^2
sharp girder
Same for other, use a pen or something
sudden igloo
u will realise -2ab + 2ab cancel out each other
sharp girder
And sin5π/2 is 1 for your last step
sudden igloo
and after expansion when you common out a^2 it will become (sin^2 alpha + cos^2 alpha) which is equal to 1
same do it with 4
a^2 + 4 - 4 + a^2 = 2a^2
lone heartBOT
@plain hill Has your question been resolved?
pale needle
How can the proof in intermediate value theorem be used to prove that there's such a number that satisfies the conditions in the question?
pale kestrel
3p...
whats p
i don't understand the question myself, but if it makes sense to you I'd advise drawing a diagram
OH thats not part of the Q
3p as in 3 points =...=
pale kestrel
i don't understand the question myself, but if it makes sense to you I'd advise ...
What I said then
lone heartBOT
@pale needle Has your question been resolved?
pale needle
3p as in 3 points =...=
Yes
lone heartBOT
@pale needle Has your question been resolved?
north hemlock
recall the IVT:
If a function $f:[a, b]\to \mathbb{R}$ is continuous, there there exists some $c$ such that $f(a) < c < f(b)$ or $f(b) < c < f(a)$ and there exsists some $k$ such that $f(k) = c$. Now you can you this idea and notice that if the two endpoints are the same, then you have a few options for how the function behaves in between. It is either constant, concave up, concave down, or some combinations of those 3
ocean sealBOT
Juke | ping me if no response
lone heartBOT
north hemlock
sorry, I meant to say "for all c, with f(a) < c ..."
plain flame
ray?
grand wave
tropic oasis
lone heartBOT
tropic oasis
cna someone help me see what happened to get the last answer?
i understand everything up until the last two steps
i know how he got the idenity
but how do i get the integral of that
rustic coral
$\frac{1}{2}-\frac{1}{2} \cos 2x$?
ocean sealBOT
Civil Service Pigeon
tropic oasis
why does the 1/2 replace the 1 ?
rustic coral
I just split the fraction tbh
tropic oasis
i'm so confused 😭
this whole section has my brain in jumbles
he pulled out the constant of 1/2
rustic coral
$\frac{a-b}{c}=\frac{a}{c}-\frac{b}{c}$, that's all I did from $\frac{1-\cos 2x}{2}$
ocean sealBOT
Civil Service Pigeon
rustic coral
You could also do distributive on $\frac{1}{2}(1-\cos 2x)$ and just not combine it into one fraction
ocean sealBOT
Civil Service Pigeon
tropic oasis
okay i think i see a bit more now
one last question
if we do it his way where we pull out the constant
@rustic coral
how did he get the -1/2(sin(2u))?
i know integral of cos(x) is -sin(x)
but where's the -1/2 from in his problem?
rustic coral
but where's the -1/2 from in his problem?
$\frac{d}{du} \sin(2u)=2\cos(2u)$ by chain rule, so divide out by $2$
ocean sealBOT
Civil Service Pigeon
tropic oasis
$\frac{d}{du} \sin(2u)=2\cos(2u)$ by chain rule, so divide out by $2$
ohh okay
so we do the opposite of what the deriviative would be
cos(2u) * 2
and doing the opposite we divide the 2 to remove it
ohh okay
ty!
rustic coral
^_^
tropic oasis
.close
torpid horizon
The matrix at the top was used to multiply the result below. To obtain the orinal matrix, would I need to multiply the 2nd matrix by the inverse of the 1st one?
https://media.discordapp.net/attachments/878646111525568593/1078042439874531378/image.png
torpid horizon
if so... is this correct? I cannot manage to get the result in the form of a matrix
@crisp iron :D
drifting fable
What do you mean exactly, is the matrix at the top the result of multiplying num5_b with another matrix or constant etc.?
torpid horizon
num5_b is the result, num5_a is the multiplicator
I'm trying to go back to num5_b before it was multiplied with num5_a
drifting fable
aha ok, well conventionally you would have to do this by hand as the rules that apply to variables do not apply the same to matrices e.g. num5_a^-1 would be the inverse rather than 1 over the matrix. Try considering and empty matrix and what numbers would fill in the columns such that when multiplying this by num5_a the result would be num5_b
Also consider the dimensions of the matrices, this is quite important
torpid horizon
isn't that
num5_b_before = num5_a * num5_b
num5_a^-1 * num5_b_before = num5_a^-1 * num5_a *num5_b
num5_a^-1 * num5_b_before = i * num5_b
num5_a^-1 * num5_b_before = num5_b
?
like doesn't this work?
drifting fable
I think I might have misunderstood the problem, are you trying to find the matrix num_b_before which when multiplied by num5_a gives num5_b
torpid horizon
nvm, the issue was that the matrixes were not multiplied in the correct order
result:
works like a charm!
.close
whole shell
do you know how to find the gradient of a line
not sure what you want me to do with that info
pick any 2 points
that the line goes through
oh right i get what this is asking for
basically
yh pick any 2 points
and draw a right angled triangle
yh
that should be the answer
dont you know how to find the gradient of a line
the lines or the slope
wait what did you answer for the slope
also ive never seen anyone in my entire life draw the rise and run as up then right, instead of right then up
what did you get for the slope, did you type 1 in?
wait, if you got the last 2 right, why did you need help with this one