yes
#help-19
tacit haven
nocturne belfry
no need for examples you can write out the solutions explicitly
$\pm 3 \sqrt{\frac 89 n - 1 }$
clever fjordBOT
jan Niku
nocturne belfry
take $x_1, x_2$ are the roots of this
clever fjordBOT
jan Niku
nocturne belfry
your solutions should be all n such that $x_1 \leq \pm 3 \sqrt{ \frac 89 n -1} \leq x_2$
clever fjordBOT
jan Niku
nocturne belfry
well, all x such that n satisfies that i guess
tacit haven
ah ok
nocturne belfry
the n arent solutions
but really this is just solving $\frac{x^2+9}{8} = \floor x$ in disguise
make sense?
clever fjordBOT
jan Niku
nocturne belfry
tacit haven
.close
odd edgeBOT
odd edgeBOT
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cloud basin
I have a question.
odd edgeBOT
I have a question.
elder vault
I love you
cinder elk
I have a question.
cinder elk
I love you
I also have a question 
elder vault
I also have a question <:0ashcry:875913512365486092>
I love you too
cloud basin
What are the units of precalc and list them in chronological order.
cinder elk
That can vary from teacher/professor and institute
But generally they cover more complicated algebra techniques
Unit 4 wasn't covered in my pre-calc class
cloud basin
Is that normal precalc?
cinder elk
I think AP precalc
forest sky
you can see the units for khan academy's precalculus course here:
https://www.khanacademy.org/math/precalculus
the AP precalculus curriculum is listed here:
https://apstudents.collegeboard.org/courses/ap-precalculus
cloud basin
you can see the units for khan academy's precalculus course here:
https://www.kh...
does khan cover everything for precalc
forest sky
precalculus varies between schools, but most likely it does
cloud basin
precalculus varies between schools, but most likely it does
can someone tutor me
odd edgeBOT
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cloud basin
.close
unique gazelle
can anyone help me find the limit of this series please
robust pollen
What is u?
odd edgeBOT
@unique gazelle Has your question been resolved?
unique gazelle
What is u?
just like a ordinary variable mate
ah forgot to show more vital informations
here
suppose we have a serie of numbers (U(n)) that are defined by
with every n ∈ N*
find the lim of the serie
summer river
Hmm
Yes @unique gazelle
Can you try to derive a general formula for u_n
Write out what u_2 and u_3 is
And u_4
unique gazelle
for predicting the structure of the general formula right?
i do remember that this problem has a hint that we have to set up some unrevelant numbers
like this
summer river
for predicting the structure of the general formula right?
Yes
summer river
Keep going
unique gazelle
now we let V_n be (n+2)(n+1)n*u_n then
we have a serie that defined by
and V_n is a geometric progression have a merit q= 3
=> V_n=9.3^(n-1)=3^(n+1)
what your description
odd edgeBOT
@unique gazelle Has your question been resolved?
near owl
hi, im stuck on factorizing trinomials, i dont know if my method is correct,
in the first line i multiplied the first term with the third one
in the third line i splited the 5x, so i could factorize,
but i dont know what to do after i did factorized that, could anyone help me if someone sees an error or how to do my problem?
near owl
yeah im here
lucid hollow
ok
near owl
could u tell me what do i need to do or what did i had wrong?
lucid hollow
why is -3 now -6x^2
mystic saffron
you dont have to actually physicaly multiply them in the equation because that just changes the eqn
lucid hollow
i have a way that we don't have to multiply 2x^2 with 3
near owl
why is there a two? at the end?
clever fjordBOT
Nguyễn Tuấn Minh
soft wharf
guys
lucid hollow
??
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soft wharf
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devout sierra
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devout sierra
<@&286206848099549185>
fluid tundra
descartes' rule of signs
odd edgeBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
devout sierra
descartes' rule of signs
but how do i find the exact number of real roots
tepid pelican
descartes' rule of signs
Is that sufficient?
tepid pelican
We also need to know whether or not is there a perfect square factor
devout sierra
since its a 6th degree polynomial, we can see that it has 6 roots R or C
tepid pelican
since its a 6th degree polynomial, we can see that it has 6 roots R or C
what if it was e.g. (x-3)^6?
or (x-2)^3(x+i)(x+1)(x-i)
fossil hawk
At 1 it's negative and at infinity and -ve infinity it's +ve so atleast 2 real roots
tepid pelican
it would be easier to just check that it's negative at 0 lol
fossil hawk
And by Descartes rule of sign change atmost 2 real roots
fluid tundra
Is that sufficient?
in this case yes
fossil hawk
it would be easier to just check that it's negative at 0 lol
yea
fluid tundra
Not really
no the answer is yes
devout sierra
are you sure?
fossil hawk
And by Descartes rule of sign change atmost 2 real roots
So there should be 2 real roots and rest imaginary
fluid tundra
We also need to know whether or not is there a perfect square factor
this is not necessary descartes' rule of signs already accounts for multiplicity
devout sierra
because i asked and the teacher said to give the exact number of real roots
he said descartes rule of signs wont be enough
tepid pelican
this is not necessary descartes' rule of signs already accounts for multiplicity
even for non-real roots
devout sierra
so we have to see how many roots are real and not just come up with a lazy answer that isnt even a proper answer to the question.
according to him at least
fluid tundra
even for non-real roots
multiplicity of non-real roots has no bearing on the number of real roots
fluid tundra
according to him at least
this makes no sense
according to descartes' rule of signs, there is exactly 1 positive real root and exactly 1 negative real root
tepid pelican
according to him at least
their approach is right for real roots
the problem is that we still need to find the number of complex roots
fluid tundra
when the problem says "imaginary" does that mean of form 0 + bi
devout sierra
no i know but my teacher doesnt want us to use the table and write the appropriate possibilities
fluid tundra
the problem is that we still need to find the number of complex roots
but
exactly 2 real roots implies 4 non-real roots
devout sierra
yeah but he wants to know how we get that number without using descartes rule of signs and without graphing the polynomial
tepid pelican
exactly 2 real roots implies 4 non-real roots
what if there are perfect squares in the factorization
iron bear
without using descartes rule of signs specifically?
descartes rule of signs gives you the exact number of real roots here
zinc glacier
doesnt it only give parity
fluid tundra
doesnt it only give parity
for this specific polynomial it is exact
devout sierra
He said that we have to count the number of distinct real roots and locate them in intervals. By subdividing the intervals containing some roots, it can isolate the roots into arbitrarily small intervals, each containing exactly one root.
iron bear
no it's an upper bound and parity
zinc glacier
oh right ok
iron bear
descartes rule of signs handles all of that in one go though
devout sierra
yeah but he doesnt count that as an answer
iron bear
so it's just banned as a solution??
devout sierra
basically
iron bear
even though it gives the right answer
devout sierra
yeah
devout sierra
because he says “its just a lazy way of doing math. you need to show your work by using any method to find those roots in given intervals whether its a arbitrarily small interval. it should give you the amount of real roots which arent complex.”
iron bear
using a true theorem to prove your result is "a lazy way of doing math"?
you need to get a better teacher
devout sierra
well he doesnt count descartes rule of signs as a theorem
tepid pelican
using a true theorem to prove your result is "a lazy way of doing math"?
Yeah, everyone should probably start from axioms and re-derive whole math themselves. Just don't be lazy
iron bear
of course, why hadn't i thought of that
devout sierra
Yeah, everyone should probably start from axioms and re-derive whole math themse...
haha
guess we should all be damn math prodigies according to my teacher
iron bear
i'll come back to you in 2937392919191 years after i've proven that 1 + 1 = 2
devout sierra
man i hate him
fluid tundra
what if there are perfect squares in the factorization
(doesn't matter. the problem makes no distinction between non-unique roots)
tepid pelican
(doesn't matter. the problem makes no distinction between non-unique roots)
If we also count multiplicity, then ye, it should be doable quite easily
devout sierra
alright lets just move on to the other 3 questions. ill just ask him tomorrow what he wants for that problem
now its just solving polynomials haha
so yeah thats the easy part
tepid pelican
You could just accidentally copy over proof of descartes rule of signs and accidentally rediscover some theorem, of which you didnt know is banned
merry finch
that's what newton said
devout sierra
how do we do that?
iron bear
quartic depression
clever fjordBOT
ビジヨン
devout sierra
thus i get $y^4-15y^2-6y+28=0$
clever fjordBOT
ビジヨン
devout sierra
but i still need to remove the linear term
odd edgeBOT
@devout sierra Has your question been resolved?
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@devout sierra Has your question been resolved?
urban timber
i dont know how to do this quwstion
odd edgeBOT
i dont know how to do this quwstion
hardy panther
i dont know how to do this quwstion
which question, trucknut?
proper solstice
use 1/2 ab sin(C)?
urban timber
yeah but i dont understand the 3QR = 4PR thing
proper solstice
let PR be x
it means that 3 times the lenght of QR is the same as 4 times the lenght of PR
so 3*QR = 4x
QR = 4/3 x
odd edgeBOT
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Available help channel!
woeful rivet
guys can u help me
odd edgeBOT
guys can u help me
woeful rivet
where is the derivative used and applied in a real world context
copper quarry
hello bum chicken
woeful rivet
hello bum chicken
hi
mental lotus
Derivatives are used in many places, you use them in any and all kinds of simulations
Stock market predictions
Animations
copper quarry
u should do astrophysics and rockets 😎
woeful rivet
u should do astrophysics and rockets 😎
hows it used in rockets
wait ima do acceleration
wait but i dont even know how rockets work tf
copper quarry
Lol
copper quarry
only in y10
copper quarry
they are free marks
copper quarry
gg
woeful rivet
.close
odd edgeBOT
wide drift
fossil hawk
Try to make cases
When b is a multiple of a
When a and b are coprime etc
odd edgeBOT
@mystic saffron Has your question been resolved?
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Available help channel!
quartz bridge
odd edgeBOT
quartz bridge
Can someone help me with this
clever fjordBOT
tepid pelican
Q8?
quartz bridge
9
tepid pelican
Okay
let's start with the parallel line
parallel line should have the same slope, right?
quartz bridge
Yes
tepid pelican
so we are looking for a line of form 3x + 2y = k, that passes through point (3, 5)
this way the slope stays the same
and we are able to shift it up and down
tepid pelican
so we are looking for a line of form 3x + 2y = k, that passes through point (3, ...
Try making an equation that will find k
(do you understand it till now btw? Or is something unclear)
quartz bridge
Am confused ngl
tepid pelican
Okay
so we have the line 3x + 2y = 8
and we want to find a line that is parallel to this one and has the same slope
tepid pelican
so we have the line 3x + 2y = 8
so let's start in a different way, by finding slope of this line
can you rearrange it to the slope-intercept form?
So that we can easily read of the slope and y-intercept
tepid pelican
x is the coordinate in horizontal direction
y is the coordinate in vertical direction
tepid pelican
Like it goes right 3 up 2 right
3x + 2y = 8
Graph of this equation would be the set of all points (x, y), such that 3x + 2y = 8
so e.g. the point (0, 4) would sit on that line
because 3*0 + 2*4 = 8
tepid pelican
Like it goes right 3 up 2 right
Now if we go 3 units down and 2 units right, then we get another point on the line
(2, 1)
we can again verify that 3*2 + 2*1 = 8
this is how the whole graph looks like
we can also rearrange the equation like this
3x + 2y = 8
2y = 8 - 3x
y = -3/2 x + 4
this is the so called slope-intercept form
-3/2 is the slope of this line
4 is the y-intercept
and when we want to find a line that's parallel to this one, we want the slope to stay the same, and only the y-intercept to change
quartz bridge
I think I get it
tepid pelican
cool
so we can now set up an equation of line like this:
y = -3/2 x + c
where c is some number we dont know yet
and we want this line to pass through the point (3,5)
so we need to set up an equation and solve for c
the way we do it is that we plug in the coordinates (3,5) to the equation y = -3/2 x + c
so we get 5 = -(3/2)*3 + c
can you solve for c now?
quartz bridge
C is 3,5 right?
tepid pelican
C is 3,5 right?
not quite
quartz bridge
Is c the y intercept
tepid pelican
yep
tepid pelican
C is 3,5 right?
how did you get 3.5?
quartz bridge
I mean we need to find the line that goes through there right
tepid pelican
I mean we need to find the line that goes through there right
no, we want line that goes through point (3, 5)
not the line that has y-intercept 3.5
this is a line with y-intercept 3.5, and the point above it is (3, 5)
quartz bridge
Oh I meant that, didn’t mean to be confusing how do we find it
tepid pelican
you can see that the line doesnt pass throug hthat point
tepid pelican
Oh I meant that, didn’t mean to be confusing how do we find it
alright
y = -3/2 x + c
So we have this general equation
and we need to find c, such that it goes through the point (3,5)
to do that, we set up an equation by plugging in the coordinates (3,5) in the equation y = -3/2 x + c
so we get 5 = -3/2 * 3 + c
and using this equation, we solve for c
quartz bridge
Where did the 5 come from
tepid pelican
5 is the y-coordinate of the point (3, 5)
quartz bridge
Oh
tepid pelican
to do that, we set up an equation by plugging in the coordinates (3,5) in the eq...
we are basically plugging in y = 5 and x = 3 in the equation y = -3/2 x + c
because we want to make sure that it passes through point (x, y) = (3, 5)
quartz bridge
👍
quartz bridge
Ngl I got to go can you finish it cause my teacher won’t let me on my phone and I can just read it later
odd edgeBOT
@quartz bridge Has your question been resolved?
hearty kite
would someone be able to tell me what the degrees of freedom is for this questions? I feel like my answer is wrong
hearty kite
<@&286206848099549185>
fossil hawk
would someone be able to tell me what the degrees of freedom is for this questio...
Degrees of freedom 
The number of independent ways in which a molecule of gas can move
hearty kite
bruh i had a feeling somone would say this
shall we keep it in the context of statistics?
fossil hawk
Was jk sry
sudden lotus
shall we keep it in the context of statistics?
that could statistic and probability problem?
sudden lotus
wait I could probably help you from that problem
odd edgeBOT
wait I could probably help you from that problem
hearty kite
oh?
sudden lotus
just give me a minutes to let me try solve this problem
odd edgeBOT
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odd edgeBOT
sudden lotus
Reopen
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smoky estuary
I'm confused by a coding challenge I'm working on. Imagine an Equilateral triangle where you are given the orientation of one side (radians away from the positive x-axis), the side length, and the center x,y coordinates. How would you "find the rotation" around the z-axis? Isn't that just the orientation?
ivory dock
Depends
on where the center is
also depends on the initial orientation
try to sketch some cases for yourself
smoky estuary
Initial orientation wasn't give, so I assume 0 radians. say the center is (225.05, 265.596). Orientation of one of the sides is 1.87115 radians.
I guess my real question is how is orientation supposed to affect the values I'm asked to calculate? Assume we are looking at the 2D shapes through a camera in 3D space. We're asked to provide the area, perimeter, and centroids for each shape along with other geometric properties. Wouldn't orientation have zero affect on other geometric properties?
ivory dock
Note that you know the orientation of A side, not the baseline side
smoky estuary
correct
ivory dock
Suppose you're given this blue side, see how the placement of the center can change the orientation?
The image won't send 😦
smoky estuary
Yes
ivory dock
So the orientation of the given line does not singlehandedly define the orientation of the triangle since it's not necessarily the baseline
Or even if you view it as such, there's always at least 2
smoky estuary
So what I'm hearing you say is that more information is needed to calculate rotation around the z-axis?
smoky estuary
Got it
Well wait
The center coordinates are given
along with orientation of one side, wouldn't that define the orientation/rotation (not sure the difference now) of the entire triangle?
ivory dock
yup
you asked if the side is enough
it's not
but the side and the point are
or at least if I understood your question right
smoky estuary
which is why you get the point
ah, I misunderstood you here
But my question is, how would orientation (taking all other information we have into account) affect whatever information I can provide about this shape? In order words, what can I say about this shape and/or its position in space that is affected by orientation. Initially, I'm asked to provide area, perimeter, and centroid, which of course don't depend on orientation. Then, I'm later asked to describe the rotation of the shape around the z-axis. What does that mean? Isn't the orientation, again with all other information taken into account, the rotation about the z-axis? What more information is there for me to deduce?
ivory dock
Well I guess you have to deduce if the orientation is on one or the other side
based on the point
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limpid notch
i'm stuck in multiplying a trinomial and a binomial, the problem is the following:
(x^2 + xy + y^2) times (x - y)
I was simplifying by distributing and multiplying x^2 by x which got me x^3, and multiplying x^2 by -y which got me -xy^3, but when i get to xy times x i completely fall apart in that step
help would be much appreciated
tacit wasp
Well, first you multiply x² by each term on the other brackets
So x³ - x²y
Now do the same but with xy
You get x²y - xy²
And finally the same but with y², which leads you to xy² - y³
If you sum the three results you get x³ - y³
odd edgeBOT
@limpid notch Has your question been resolved?
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merry finch
So I’m sort of confused about systems of odes and I’m terrible at understanding them
merry finch
So there’s just weird A that pops up
And it’s the matrix with the coefficients of the system given
crystal zinc
At first glance A is an operator
merry finch
Of course it’s a matrix so it needs to be written wrt some basis
What is this basis?
crystal zinc
presumably you mean a set of linear ODES?
merry finch
Uh yes linear odes
crystal zinc
where f=(f_1, f_2)^t
merry finch
Yes
crystal zinc
matrices don't have a basis?
merry finch
Well matrices need to be written wrt some basis
crystal zinc
not particularly
merry finch
So I need a basis of C² and C¹ no?
crystal zinc
what is the function space C^2? twice differentiable functions?
sorry been a while for me
merry finch
I have 2 linear operators d/dt and A, and I want to say that they do the same thing to some special f’s
merry finch
what is the function space C^2? twice differentiable functions?
Yes
crystal zinc
ah, in that case, let's not get into what the bases of those vector spaces are
because that's not important
all your matrix is going here is encoding information about a system into a more easily digestible form
merry finch
Well I don’t agree from here that A is what you said it is
I would need to be given bases to write down the numbers in the matrix
But it seems to be given in the form by the question being a system
Thats sort of what I’m confused about
clever fjordBOT
crystal zinc
crystal zinc
indeed
merry finch
I still don’t really get why A is that matrix
crystal zinc
the crux is just the last two lines
merry finch
Third line is fine
crystal zinc
have you done linear algebra before?
merry finch
Fourth is okay as well
And now why do we have on the 5th line that S^-1 d/dt = d/dt S^-1
merry finch
have you done linear algebra before?
Yes
crystal zinc
you've done systems of linear equations?
merry finch
I’m just really stuck on the part where a matrix is only a representation of some linear transformation with respect to some basis on the domain and the codomain
crystal zinc
And now why do we have on the 5th line that S^-1 d/dt = d/dt S^-1
because multiplication by a scalar and differentiation are commutative
merry finch
A matrix can’t just pop up by itself
crystal zinc
write a general matrix ((a00, a01)...)
and multiply it by a general vector
(x1, x2)
and tell me what you get
should get another vector as a sanity check
merry finch
But matrix multiplication is weird and archaic
merry finch
I understand that you do get what is desired
crystal zinc
But matrix multiplication is weird and archaic
this is why you don't understand what's happening
merry finch
Is there not a basis-free version of this
And I don’t even see a basis anywhere
Matrices written without basis are meaningless
crystal zinc
you don't need to know the basis is my point
crystal zinc
Matrices written without basis are meaningless
no they are not, more abstractly they are linear maps
which don't really need a basis to work
merry finch
They’re only linear maps wrt some basis
The numbers in the matrix depend on the basis you pick
So when you say it’s (1,2),(2,1), what basis did you pick to say that
That’s what doesn’t make sense to me
crystal zinc
in that case, f1 and f2
merry finch
But somehow when you do (1,2),(2,1)f it does indeed recover the conditions given
crystal zinc
that's your basis
merry finch
Huh
crystal zinc
i really don't understand what you don't understand
because you understand where the numbers in the matrix come from
and then you understand how to make it solve your odes
(i think)
@merry finch you still here/need any help?
merry finch
I’m thinking
crystal zinc
on the matrix bit?
okay lets consider a one dimensional basis of one meter
i can use a linear transformation which is a stretch of 1000 to make the new basis a unit of a kilometre
but i could use the same transformation to map a gram to a kilogram
hell i could map a banana to a kilobanana but that's probably enough potassium to cause ten heart attacks
@merry finch I'm off bed, gn
odd edgeBOT
@merry finch Has your question been resolved?
odd edgeBOT
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Available help channel!
graceful parrot
odd edgeBOT
graceful parrot
What is 5.a. Even asking me to do?
Find average velocity of the pebble for t=4 you just put 4 in the y= equation right
But what does and lasting part mean
Ok so I’m wrong and dumb
Can someone explain please
brittle beacon
You'd want the average between two times, so they tell you that you "start" your time at t = 4, and they give you three choices of how long you'll be measuring for
So from t = 4 to each of t = 4.1, 4.05 and 4.01 respectively
graceful parrot
Oh ok so like y(4.1)-y(4)/4.1-4
@brittle beacon how would I find the instantaneous velocity in 5b?
brittle beacon
Well, as you do each of those averages, you should, theoretically, see that they approach a certain value, and what you think it'd end up as should be your estimate for the instanteneous velocity
graceful parrot
So like my guess what be
Whatever it approaches to at like 0.0001
0
To 0
I mean
brittle beacon
Yeah, the instantaneous velocity is basically what happens to your average velocity when the time period you take it over shrinks to zero
graceful parrot
Yeah, the instantaneous velocity is basically what happens to your average veloc...
Ok cool
graceful parrot
Yeah, the instantaneous velocity is basically what happens to your average veloc...
Same thing for 6? Like do 1.00001 into the equation
And see where it approaches
brittle beacon
Same thing for 6? Like do 1.00001 into the equation
Basically yea, as you do each of the 6a intervals, you see (at least in theory) that it gets closer and closer to something, and what it gets closer to is your instantaneous velocity
graceful parrot
Basically yea, as you do each of the 6a intervals, you see (at least in theory) ...
Why can’t I just insert 1?
brittle beacon
Into the average velocity, or?
brittle beacon
As in, doing ( y(1) - y(1) ) / (1 - 1), or do you mean something else?
graceful parrot
Like 10(1)-1.86(1)^2
brittle beacon
That only tells you your position, and not even a rate, is why
As @copper quarry is hinting at, there is a way you could skip a lot of work and just put in t = 1 "somewhere", but it isn't into the equation for y as it is
graceful parrot
Yes
brittle beacon
(assumedly you're probably at a point where they're motivating the definition of the derivative, so they're first making you do stuff "the long way")
compact steppe
is there a way to simplify this furhter : $$(\ln n)^{\ln (\ln n)} = e^{\ln((\ln n)^{\ln (\ln n)})}=(e^{\ln (\ln(n))})^{\ln(\ln(n))}$$
clever fjordBOT
atif
compact steppe
ideally i'd like to have n as the base, instead of e
odd edgeBOT
@compact steppe Has your question been resolved?
compact steppe
<@&286206848099549185>
for context, the original problem is this $\sum \frac{1}{(\ln n)^{\ln (\ln n)}}$
clever fjordBOT
atif
compact steppe
i.e. it should be solved by comparison test im p sure, i just need to transform the denominator so that i can bound it
which is what i tried above but i didnt get anything easily boundable
odd edgeBOT
@compact steppe Has your question been resolved?
sly egret
clever fjordBOT
NulledOutChicken
compact steppe
@sly egret thanks, but I don't see how to proceed from here
odd edgeBOT
@compact steppe Has your question been resolved?
somber vault
Condensation test- the sum converges iff-
Sum{2ⁿ/(ln(2ⁿ)^(ln(2ⁿ)))}=Sum{2ⁿ/(nln(2))^nln(2))}≤Sum{(2/ln(2)n)ⁿ}
somber vault
Condensation test- the sum converges iff-
Sum{2ⁿ/(ln(2ⁿ)^(ln(2ⁿ)))}=Sum{2ⁿ/(nln(...
That's a start
If you're only trying to show convergence and don't care about the actual value
compact steppe
@somber vault thanks, but a very similar problem $\sum \frac{1}{(\ln n)^{\ln n}}$ I've seen solved with comparison test, so I'm trying to do the same. although the slight difference might make it unsolvable w solely comparison as I intended
clever fjordBOT
atif
compact steppe
and I'd especially like to learn whatever logarithm manipulation is needed to make it happen/make the problem approachable
somber vault
<@781209059084075059> thanks, but a very similar problem $\sum \frac{1}{(\ln n)...
You can compare it to 1/n^ln(n) probably and from there use the condensation test (or not)
But yh give solutions <@&286206848099549185> with only comparison if existant
odd edgeBOT
@compact steppe Has your question been resolved?
odd edgeBOT
@compact steppe Has your question been resolved?
maiden badger
This shi is clearly no solution
odd edgeBOT
This shi is clearly no solution
maiden badger
what the hell so i write than?
forest sky
reduce it to RREF. the augment column is treated as a regular column in the matrix for this
forest sky
leading 1's
maiden badger
.close
odd edgeBOT
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full crane
odd edgeBOT
earnest nebula
get the gradient and get the intercept
and add them to the y=mx=c equation
gradient = y2-y1/x2-x1
intercept is the point where the line cuts the y axis
for example, in the first question intercept is 4
odd edgeBOT
@full crane Has your question been resolved?
rancid ingot
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rancid ingot
Wood cutter in the shape of the function cuts into a piece of wood
Defined between 0 and 1
Im having more issue with the understanding how this translates into an equation i guess, and how the function gets put to the power of 2, the equations below are the answers
If i just put the f(x) in an integral in calculator it doesnt know the answer
Nvm, i just wana know how f(x) can be put to the power of 2
How does that work
odd edgeBOT
@rancid ingot Has your question been resolved?
hollow quarry
Nvm, i just wana know how f(x) can be put to the power of 2
There are multiple things that notation can refer to but in this, it means (f(x))^2
south musk
can anyone help how to start this question
odd edgeBOT
can anyone help how to start this question
@south musk Has your question been resolved?
odd edgeBOT
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naive sigil
odd edgeBOT
@naive sigil Has your question been resolved?
carmine vault
Hey, we need some help for our linear algebra course, we are working 2022 exam to study and we are stuck on this problem.
in question a we calcuated the determinant easily and we got -3a + 18
In question b we used the fact if the determinant is 0 then there is pivot collumn therefore there is only one unique solution
in part 3 where there is no solution we are completly stuck. We have an idea in regards to free variables but we can't compute any solution.
MATLAB/Python is allowed for us if that helps.
Thanks.
tulip niche
Hey, we need some help for our linear algebra course, we are working 2022 exam t...
Hmm for part b, you’d want the determinant to be nonzero for a unique solution
carmine vault
Hmm for part b, you’d want the determinant to be nonzero for a unique solution
wait what? :D Could you please explain this in a bit more detail?
tulip niche
So, to have exactly one solution to a linear system (with a square matrix), you need the determinant to be nonzero
If the determinant is 0, then either you have no solutions, or you’ll have infinitely many solutions
carmine vault
Ah gotcha, probably mixed up my definitions
tulip niche
Yeahhhh sometimes that’s how it goes
carmine vault
Any ideas for c on a conceptual level? If i had a way to get started then I'll go and write some code, but no ideas on how to get started
crystal zinc
Well you check for when determinant is zero
That gives you your not unique exact solutions case
And then you check for whether there are any solutions
tulip niche
Yes, so if the determinant is 0 and there’s at least one solution, then there must be infinitely many solutions
odd edgeBOT
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elfin bear
y=a
prove: y'=0
odd edgeBOT
y=a
prove: y'=0
elfin bear
I only get y'=1
green sage
limit definition, no?
elfin bear
limit definition, no?
show ne
green sage
limit as h goes to 0 of (a-a)/h
elfin bear
limit as h goes to 0 of (a-a)/h
h is 0, h=x-x0
green sage
yea but x-x is always 0
elfin bear
yea but x-x is always 0
therefore cancels out and 1
green sage
that’s not how limits work
tacit haven
since y = a is a line you can directly find the slope of it
elfin bear
since y = a is a line you can directly find the slope of it
I want a rigirous proof
green sage
therefore cancels out and 1
you can use table method to verify, but that only works if they both go to zero at the same rate
since x-x is always 0
and h is not always 0
the limit must be 0
since 0/anything = 0
odd edgeBOT
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quaint panther
Hello
tepid pelican
okay, so we will need to consider prime factorization of 26!
quaint panther
Okey
tepid pelican
then if we separate all the 3's from there, we will be left with 3^x * A
and since we've seperated all 3's, the x will be maximal
tepid pelican
But how do i prime factorize 26!
We will get to it right now
quaint panther
Alright
tepid pelican
we actually don't need to do whole the factorization
quaint panther
Thanks btw
tepid pelican
we only need to count how many 3's are in there
quaint panther
👍 yup
tepid pelican
note that 26! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * ... * 26
quaint panther
Exactly
tepid pelican
obviously, numbers like 2, 4, 5, 7... which aren't multiples of 3 won't contribute any 3's to the overall count
quaint panther
Okey
mystic saffron
u just need the amount of 3's here, since question has nothing to do with A , but does with x
tepid pelican
on the other hand, numbers like 3, 6, 9, 12, 15... which are multiples of 3, will contribute 3's to the overall count
quaint panther
Okey
quaint panther
u just need the amount of 3's here, since question has nothing to do with A , bu...
Aight
mystic saffron
answer is 10?
tepid pelican
so it would be a good idea to count the number of multiple of 3, up to 26
quaint panther
answer is 10?
Yea
mystic saffron
should be 8 no??
quaint panther
so it would be a good idea to count the number of multiple of 3, up to 26
Hmm okey
tepid pelican
okay! you have even listed them
that'll be useful now
how many 3's does each of them contribute to the prime factorization?
quaint panther
Wait how
mystic saffron
got it 10
quaint panther
2
quaint panther
How 3+3
tepid pelican
Ahh we look at multiplication
indeed, because that's what factorization is
quaint panther
Okey
quaint panther
21 has 1
24 has 1
tepid pelican
Or is 18 2
18 is 2, we wanna find the maximum x and so we wanna use all the 3's
quaint panther
Then it should add up to 10
tepid pelican
Then it should add up to 10
indeed it does
quaint panther
18 is 2, we wanna find the maximum x and so we wanna use all the 3's
Okey
So know i know why its 10 thank you all for that but now i have another quick question
tepid pelican
So know i know why its 10 thank you all for that but now i have another quick qu...
okay, sure
quaint panther
The tesbook show hiw to do it
tepid pelican
it probably does stuff like 26/3 and 26/9, right?
tepid pelican
Yea
okay i'll explain it
26/3 counts the number of multiples of 3
so instead of listing them all, we can just count them
tepid pelican
26/3 counts the number of multiples of 3
and we need to round it down btw
so there are 8 multiples of 3
quaint panther
But we just divided it with 26 not with 26!
mystic saffron
@tepid pelican dont ,ind me asking, youre a professor? u seem like u know ur shit.
tepid pelican
<@951190447185874994> dont ,ind me asking, youre a professor? u seem like u know...
lol no, im 16
tepid pelican
But we just divided it with 26 not with 26!
26! = 1 * 2 * 3 * 4 * 5 * ... * 26
quaint panther
Okey
tepid pelican
and we want to count how many multiples of 3 are in that sequence 1, 2, 3, ... 26
quaint panther
Yes
mystic saffron
lol no, im 16
damn
tepid pelican
so we dont care about 26! anymore, we just want to count the number of multiples of 3 up to 26
and every third number is a multiple of 3
so we divide 26 by 3
quaint panther
Ahh okey yea
tepid pelican
so we divide 26 by 3
and we get 8
when we round it down
but there are also some multiples of 3, that contribute with more than one 3 to the factorization
namely, 9 and 18
those are multiples of 3^2 (9)
tepid pelican
correct
we already counted them once, because they are also multiples of 3
but we need to count them for the second time now
so we do 26/9
and we get 2
so we do 8 + 2
and we get 10
quaint panther
Hmm okey
İ think i kinda got it
But if its like this
Why is there an A in the question
tepid pelican
Why is there an A in the question
it's just to formulate the question correctly
and also to make you think about it a bit more
quaint panther
Okey thanks a lot!
tepid pelican
to be specific, you have to realize that A can't be a multiple of 3, otherwise x wouldnt be maximal
and then the key idea is counting 3's in factorization of 26!
quaint panther
Ahh yes thats true
mystic saffron
if A would be a multiple. then again powers would add up as per the exponential rules
and then maximum wouldnt be attained
quaint panther
True
Thanks both of you for helping
And sorry that i took your time
Have a nice day
mystic saffron
youre good homie
tepid pelican
Have a nice day
you too :)
odd edgeBOT
odd edgeBOT
Available help channel!
worldly sleet
How to solve x^4 -1
odd edgeBOT
How to solve x^4 -1
craggy jasper
How to solve x^4 -1
Use the identity a² - b² = (a + b)(a - b)
stoic torrent
Yes
worldly sleet
worldly sleet
Okok
craggy jasper
Do you know how to solve a cubic equation
stoic torrent
Here you found x-1
stoic torrent
Do you know how to solve a cubic equation
Bruh general solution is impractical
worldly sleet
stoic torrent
Here you found x-1
Yez
Yes
Can you factorize x²+1 further ?
ie finding more roots
worldly sleet
Even further
stoic torrent
Correct
The two remaining roots are not real numbers
If you only study real numbers
stoic torrent
You can not go any further, that is an irreducible polynom
Which are degree 2 polynoms with no roots
Or x + a
Here you have 2 degree 1 polynoms
1 irreducible
That gives you all the possible solutions
worldly sleet
Okey cool then i get 4 roots in total
stoic torrent
If you count the imaginary ones yes
mystic saffron
yes
stoic torrent
Counting imaginary roots and double roots as 2, a degree n polynom always has n roots
worldly sleet
its +-sqrt(-1)
I did that no?
worldly sleet
.close
odd edgeBOT
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Available help channel!
errant atlas
Hello, I had a quick question. I am trying to figure out how to convert 60kg of downward force in gravity to newtons. I haven't done anything relating to anything like this in maths before so I just need some general help
uneven osprey
Hello, I had a quick question. I am trying to figure out how to convert 60kg of ...
isn't it supposed to be physics?
either way
errant atlas
I understand that gravity is 9.8m/s so what would be the equation from there?
uneven osprey
Force = Mass times the Acceleration
errant atlas
oh my god
uneven osprey
Force = Mass times the Acceleration
ig this is fine for your work
uneven osprey
and what unit comes out the end?
unit of force in Newton
proper solstice
wait
proper solstice
the unit of force is N not kg
uneven osprey
And Newton= kg meters per second^2
proper solstice
so downward force can't be in kg
if you're asking the downward foce of an object of mass 60kg, on earth it's mass * g (acceleration due to gravity) = 60 kg* 9.8 m/s^2 = 588 N
Note:
1N = 1kg m/s^2
9.8 m/s^2 is an approximation only. Sometimes g = 10 m/s^2 is taken for ease.
weary compass
My question says "ten times the sum of half a number and 6"
weary compass
How would I make that into a equation
Like would I do 10 (1/2x +6) or 10 • 1/2x + 6
weary compass
expression not equation,
Idk homework says translate description into equation
Also why is it the first and not second
nimble blaze
sum of: [what follows here is expected to be a list of expressions]
the latter would be something like
sum of ten times half a number and six
mystic saffron
Also why is it the first and not second
you're multiplying 10 by whatever (x/2 + 6) is, whereas with the second you're multiplying 10 by x/2 and then adding 6 to that. If x were 4, for example, the first options would give 80 and the second would give you 26
mystic saffron
sum of: [what follows here is expected to be a list of expressions]
this
weary compass
Wait isn't sum just mean like plus
nimble blaze
in this case its a list of two expressions separated by "and"
its associated with +
sum is the result of addition
sum of: ...
is the result of adding those things together
mystic saffron
Wait isn't sum just mean like plus
yes, the sum of [half a number and (+) 6]
nimble blaze
e.g. sum of 5 and 7 is
5 + 7
weary compass
.close
odd edgeBOT
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Available help channel!
slim summit
odd edgeBOT
slim summit
Do I use pv=nRT for this
forest sky
yes
odd edgeBOT
@slim summit Has your question been resolved?
limber quarry
Hey so we are told to calculate the fourier transform of this graph but what i dont understand is that in the solution theyve said that due to the linearity property of fourier transforms, we can simply add together the fourier transforms of each segement. However, for the rectangle parts theyve used the general fourier transformation of rectangular signal but we dont actually have a signal at the top (ie. by the dotted lines) so how come we can use the fourier transformation of rectangular signals there?
odd edgeBOT
Hey so we are told to calculate the fourier transform of this graph but what i d...
@limber quarry Has your question been resolved?
sage helm
If M is a matrix, and i-hat is the basis vector [1, 0, 0], is the following result correct?
sharp girder
you could do the multiplication and check yourself
sage helm
The learning material that I'm learning from uses row vectors. I'm trying to verify if my column-vector answer is correct.
sharp girder
well it would be correct
but you can also check it by doing the multiplication yourself
row x collumn
sage helm
.close
odd edgeBOT
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young sedge
odd edgeBOT
young sedge
my P'(t) = 520 * ((210-2t^2)/(70+t^2)^2
silk quail
$P'(t)=570\left(\frac{3}{70+t^2}-\frac{6t^2}{(70+t^2)^2}\right)$
clever fjordBOT
fish
silk quail
yes
silk quail
yes, also you have to use chain rule for the t^2 at the bottom
young sedge
the (70+t^2)^2?
silk quail
well, the t^2 inside it
young sedge
brah im so lost theres a gazillion steps 😭
silk quail
3 is already there, so you get -6t^2, which simplifies fully to $P'(t)=570\left(\frac{270+3t^2-6t^2}{(70+t^2)^2}\right)$
clever fjordBOT
fish
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
young sedge
right so 270-3t^2
silk quail
yeah, but you can just multiply all the stuff in the parenthesis
young sedge
im going insane
silk quail
let me try going step by step
silk quail
yeah that's correct
odd edgeBOT
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Available help channel!
drowsy timber
Hey, I'm doing work for AP Calculus and I was wondering if this answer would be 1/2 or -1.
drowsy timber
I got told that if both sides approaching the limit on the first one go up, I should take into account the left side if it its split on the second f but I don't know if this applies here as there is a hole on the left side
orchid torrent
$\lim_{x \to -1} f(f(x))=f \left(\lim_{x \to -1} f(x) \right)$
clever fjordBOT
Civil Service Pigeon
orchid torrent
Now, consider ||the “direction” that f approaches 3 from as x approaches -1||
drowsy timber
yeah I understand up to that point, I just repeat the process but with x=3
orchid torrent
Uh sure ig
orchid torrent
Now, consider ||the “direction” that f approaches 3 from as x approaches -1||
… ?
This determines the direction you approach 3 from
drowsy timber
so from - or below
that means that although there is a hole on the left side, it does not matter, and the answer is -1?
orchid torrent
Yes
drowsy timber
thank you so much mate, I really appreciate what you are doing and I hope you have a great day
.close
odd edgeBOT
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visual iris
is this statement true or false?
odd edgeBOT
is this statement true or false?
low locust
what do you think
visual iris
it could be false right?
visual iris
coz if A = 1 B = {1,2,3} and C = {{1,2,3},4,5}
A in B
and B in C
but C has the set in the set
not specificly 1
does it work like that or am i doing too much
slate hinge
yes, well, the question doesn't define is A B C are elements, sets
just, random topological spaces
visual iris
oh right
slate hinge
but I think they want the answer to be yes
low locust
just, random topological spaces
are you just trying to throw in random words?
slate hinge
Set's are complicated
slate hinge
cool thanks 🙏
maybe think of it as "San Francisco is in California, California is in US, therefore San Francisco is in US"
low locust
your example shows that it is false
slate hinge
you presented an exemple where is false, it is enough to show that it's not always true.