#help-27
vivid topaz
for the triangle c b d how u choose who is negative
hollow pulsar
cause u have to really understand the point of the relation of chasles
any vector AC can be written as AM + MN
doesnt mattwr what the ppint M is
vivid topaz
b-d=C
hollow pulsar
yes
vivid topaz
the arrow need to be like this picture
hollow pulsar
exactlyy
hollow pulsar
well i cant know what u quickly understand with
plus triangles can be rotated
but its alright
C = b - d then replace d with the value u found for d
and do algebraic fractions
thats it
hollow pulsar
np
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lilac elbow
A problem about sequences. What is the next number in this sequence: 1/5,3/125,7/125,3/125,31/3125. What I have tried is to look for a common difference or common ratio to work out whether it is arithmetic or geometric however it seems to be neither. I was thinking it may be a polynomial sequence however that lead to nothing either. Any help would be much appreciated. Attached is also a photo of the problem.
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A problem about sequences. What is the next number in this sequence: 1/5,3/125,7...
topaz axle
lilac elbow
Why?
lilac elbow
Wow how did you see that??????
Thanks though, I have been so bugged about this for so long
.close
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sturdy mango
is desmos correct when it comes to checking if the point is non diff?
sturdy mango
or does it gives false positives
faint gorge
is desmos correct when it comes to checking if the point is non diff?
well yea desmos shouldn't have problems plotting functions
sturdy mango
i disagree it genreally doesnt give continuity correctly
faint gorge
and you can clearly tell that it has two different tangent slope from both sides if you get near the wedge
faint gorge
wdym
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floral badger
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opal valley
I need advice on one task, which I don't seem to find a solution to
primal isle
What is it
potent tusk
I love natural logg
opal valley
found the one
opal valley
I love natural logg
You do? 💀
opal valley
it's just 1
potent tusk
ohh okay
opal valley
sorry for the writing
potent tusk
so a and b are both either 0 or 1
opal valley
exactly
potent tusk
sorry i dont have much experience with this notation
opal valley
I meant
primal isle
What is ln
potent tusk
or between 0 and 1
opal valley
it's like
0 < a < 1
0 < b < 1
potent tusk
What is ln
the natural log
opal valley
yess
potent tusk
thats a g right?
primal isle
the natural log
Oh i havent been taught that yet
opal valley
If you have the second line in mind, it's a nine
potent tusk
ok so basically how to prove it
what are your workings so far
or are you unsure of how to proceed
opal valley
Using the known informations, we have to prove the third line
I feel as if I've been going in a circle for the past hour
potent tusk
what have you tried?
opal valley
One of the closest ways I've reached is something like
ln(ab) =< -6
other, much longer attempts, seem to be futile
wait I mixed it up
opal valley
It's
ln(1/a) * ln(1/b) = 9
in the second line
but I concluded that it'd also be equal to
[ ln ( a^-1 ) * ln ( b^-1) ] = 9
so that would equal to
lna * lnb = 9
as far as I'm concerned
But I'd also like to mention, that I went as far as to ask artificial inteligence about this
and for some reason it came up with
lna * lnb = -9
potent tusk
im back
opal valley
which honestly suprised me
potent tusk
i got garlic bread
opal valley
splendid
potent tusk
wait why would it be -9
opal valley
I have no dam clue
that's why I not only cannot read the solution it has written with these mashed symbols, but I also don't really respect it
potent tusk
fair
opal valley
Well, with all that being said, I'm back to square one yet again
potent tusk
what if you just try some random value for ln(a)
and you figure out what multiplies to get 9 from there
opal valley
now I came up with sth like this
but this doesn't help with the fact that ab can be lower than 1/e^6
so this still doesn't get me anywhere closer to proving this
I suppose that
lna * lnb = 9
is there to solve this, but I don't see any way I could break the left side down...
opal valley
neither am I...
and I'm loosing a great deal of time just because of this roadblock 😔
<@&286206848099549185> I call upon thee
afk for a bit, hope somebody'll find a way to deal... with this
opal valley
in case, this is the task itself:
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scenic adder
how do you infer starting at the y-intercept of 3, and then going up 1 and to the right 2 from there. from the equation?
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how do you infer `starting at the y-intercept of 3, and then going up 1 and to t...
opal valley
in case, this is the task itself:
Update: Attempt 27th successfull
winter torrent
how do you infer `starting at the y-intercept of 3, and then going up 1 and to t...
well, when the equation is in y-intercept form, as this one is, then it's sort of a pattern matching exercise
if y = mx + b, then b is the y-intercept and m is the slope
scenic adder
I see, going up 1 and 2 to the right is just doing the 1/2 slope,
didn't know y = mx + b either, good to keep in midn
close.
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wind elm
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wind elm
i’m having a hard time grasping the concept of integration by table
i know there’s more to substituting the u after defining what out u is but can someone explain how i actually solve this pls
i tried watching organic chemistry tutor and other videos as well but it’s still rlly confusing to me 💔
fresh elbow
are you talking about integration by table or integration by reverse chainrule/u-substitution? @wind elm
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wind elm
integration by table
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willow berry
Locus of points equidistant from a point
• Locus of points equidistant from a line
• Locus of points equidistant from a line segment
• Locus of points equidistant from two points
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Locus of points equidistant from a point
• Locus of points equidistant from a li...
willow berry
what do these mean??
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lean crest
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winged sail
im lost and dont know where to start
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im lost and dont know where to start
winged sail
like do i just plug in the bounds they give me and replace da for dx dy
acoustic leaf
yes
winged sail
oh bruh my friend made it seem like it was so much more complciated than that
limber tangle
🤣
winged sail
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spark hound
Which one is da secant? Da hypotenuse?
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Which one is da secant? Da hypotenuse?
supple knot
secant line is the dotted line
spark hound
secant line is the dotted line
Da hypotenuse yeah?
supple knot
ya
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spare isle
I have to show that this function is uneven. The explanation in the end says f(-x) = -f(x) therefor its uneven.
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I have to show that this function is uneven. The explanation in the end says f(-...
spare isle
The part i really didnt get in the explanstion is how they got to the second and third line
trail eagle
They show how they are adding 1 and subtracting 1
spare isle
They show how they are adding 1 and subtracting 1
But like how does whats on the left turn into whats on the right.
trail eagle
$\frac{e^x + 1 - 1}{e^x + 1} =\frac{e^x + 1}{e^x + 1} + \frac{- 1}{e^x + 1} = 1 - \frac{1}{e^x + 1}$
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Azyrashacorki
spare isle
**Azyrashacorki**
Oooh yeh that makes sense, thanks! But like how does this entail that f(-x) is the same as -f(x). Cause the answer says after this that the function is uneven because f(-x) is the same as -f(x)
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spare isle
<@&286206848099549185>
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spare isle
Could someone please explain how u get 2*-2 if u do f(2-p) + f(2+p) in the formula?
spare isle
$\frac{e^x + 1 - 1}{e^x + 1} =\frac{e^x + 1}{e^x + 1} + \frac{- 1}{e^x + 1} = 1 ...
How do u write equations like that?
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supple knot
Could someone please explain how u get 2*-2 if u do f(2-p) + f(2+p) in the formu...
that's a mistake. should be (2-p) + (2+p)
steel plume
I have to show that this function is uneven. The explanation in the end says f(-...
bruhhhhhhhhh
first of all there is no thing like uneven, its called odd
for odd fn, you just have to prove that f(x) = - f(-x)
steel plume
The part i really didnt get in the explanstion is how they got to the second and...
You can check this
steel plume
How do u write equations like that?
i think you should solve it yourself first instead of directly seeing the solution
steel plume
Could someone please explain how u get 2*-2 if u do f(2-p) + f(2+p) in the formu...
i think there is an error
they have written that they are taking a = -2
but in LHS they have written a as 2
so i think that would be -2
f(-2-p) + f(-2+p) and that'd work
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restive river
@spare isle its 7
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toxic night
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faint gorge
Was genau?
toxic night
Was genau?
my german is not that good so english would be better for me
faint gorge
Ok
toxic night
so?
toxic night
What have you been trying to understand for 2 hours?
i can’t proove it because it could also be equal to m
faint gorge
i can’t proove it because it could also be equal to m
What could be equal to m?
dry geyser
i can’t proove it because it could also be equal to m
If r=m then you could choose q‘ = q+1 and r‘ = 0
Or what do you mean
toxic night
If r=m then you could choose q‘ = q+1 and r‘ = 0
but like i can choose different ones but if there is 2 different ones that equal to the same thing one would make it incorrect
dry geyser
but like i can choose different ones but if there is 2 different ones that equal...
I don’t know what you mean. Could you give an example?
toxic night
I don’t know what you mean. Could you give an example?
so r+1 could be equal to m1 but also not has to be because q could change right?
or m
dry geyser
so r+1 could be equal to m1 but also not has to be because q could change right?
If for r+1 = m for your given m, then you don’t choose r_2=r_1 + 1. You choose r_2=0 and q_2=q_1 + 1
You can show that that means the equation holds
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toxic night
If for r+1 = m for your given m, then you don’t choose r_2=r_1 + 1. You choose r...
What i dont get is yes i can choose not to but i also can choose to do it that way right?
How would i show that with complete induction?
toxic night
<@&286206848099549185> i really need help please
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toxic night
someone please help
dry geyser
What i dont get is yes i can choose not to but i also can choose to do it that w...
It says „there exist numbers such that“. That’s shown if there’s one pair for which it works, even if it doesn’t work for another pair
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dry geyser
@toxic night I don’t think it’s clear to anyone what your question is. Maybe try rephrasing it or giving an example
toxic night
<@454280526145257472> I don’t think it’s clear to anyone what your question is. ...
I don’t know how to rephrase it, how do i solve this with mathemathical induction?
like the one with 3 steps
first one for the smallest n
seccond one for k
and third for k+1
dry geyser
I don’t know how to rephrase it, how do i solve this with mathemathical inductio...
Base case: n=0, m>0 is arbitrary. The case holds for q=r=0.
Induction hypothesis: say k=m*q+r for a given m and 0<=r<m
Induction step: if r+1<m, then k+1=m*q+(r+1)
If r+1=m then k+1=m*(q+1)+0
In both cases 0<=r<m
That’s the general idea
hot iron
What did I do wrong? I asked my professor, and they said this:
Help with Problem5:
Since the Series Index (n) and the Partial Sums Index (N) do NOT start at the same value (n=5 while N=1),
we must write out the Partial Sums and find a pattern in terms of N (not n).
Write out S_1, S_2, S_3, etc. simplify each and look for a pattern in the final expression in terms of N.
Let me know how it goes.
I still don't know what I did wrong
supple knot
What did I do wrong? I asked my professor, and they said this:
Help with Proble...
once again, show the formula
hot iron
once again, show the formula
so just the sum from 5 to infinity of the function?
supple knot
so just the sum from 5 to infinity of the function?
NO
it's something in your notes or book
go find it
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past prairie
What rule did they use to get rid of the h on 9h?
devout snowBOT
What rule did they use to get rid of the h on 9h?
past prairie
And can u explain why it works like that?
tall knoll
past prairie
@tall knoll so the numerator can be cancelled out based on the dividing variable on a complex fraction
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scenic flicker
For AP Calc am i suppost to know the deriviative of 11(pie)/6. I never learned the derivative of that and im just confused how it turned into 3(2squareroot3/3)^3
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For AP Calc am i suppost to know the deriviative of 11(pie)/6. I never learned t...
scenic flicker
Ping if responding
silent oriole
For AP Calc am i suppost to know the deriviative of 11(pie)/6. I never learned t...
you cant find the derivative of 11(pi)/6, that is just a constant, all they are doing is plugging in a value for x
scenic flicker
you cant find the derivative of 11(pi)/6, that is just a constant, all they are ...
so there just doing 11(pi)/6
silent oriole
yeah, if you plug 3sec^2(11pi/6) into a calculator, it should just come out as 4, just make sure you know how to do it without one
scenic flicker
yeah, if you plug 3sec^2(11pi/6) into a calculator, it should just come out as 4...
yea i have no idea how to do it without a calculator
silent oriole
do you know how to use a trig circle?
scenic flicker
isnt pi 180* here?
silent oriole
might be worth memorizing this if your teacher dosn't allow calculators in tests
silent oriole
scenic flicker
I remember the teacher saying 30* 60* and 90* is the only ones you hae to remember
for cos and sin
bc thats is what is going to be on the ap test
silent oriole
i mean fair enough, 45 is nice too though.
if you memorize those, you can use them to find the rest
scenic flicker
might be worth memorizing this if your teacher dosn't allow calculators in tests
i see there is 2 values for 11(pi)/6
would i use the x or y value one
i assume y?
silent oriole
nah, since its secant, that's 1/cos, and cos is the x value
watch the khanacademy video, he explains it pretty well, im supprised your teacher hasn't brought it up
scenic flicker
watch the khanacademy video, he explains it pretty well, im supprised your teach...
she has but i havent understood the unit circle or trig a lot
in geomotry i didnt do well
ima watch the vid now and hopefully it helps
silent oriole
thats fair, trig can be kinda tricky, but if you are planning on going into stem at all it can be worth spending some time getting trig down
scenic flicker
tbh after ap calc im going to prob throw it away
im just studying it so i can pass ap calc
silent oriole
you gonna need a lot more trig to pass ap calc to be honest
scenic flicker
oh great 😭
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scenic flicker
might be worth memorizing this if your teacher dosn't allow calculators in tests
Ive watched both khan academy vids but they dont show this at all
is it something i have to memorize with no tricks?
supple knot
just memorize the first quadrant and use identities to get the others
supple knot
trig identities. you should know most of these: https://www.mathsisfun.com/algebra/trigonometric-identities.html
and the ones in this section https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Reflections,_shifts,_and_periodicity
leaden coral
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leaden coral
what is this technique called?
for example, suppose you have to prove a statement for an operator with multiple elements
what you do instead is you prove it for two elements
and then for multiple elements we just do them in pairs
is this mathematical induciton?
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clear vine
My work is pretty messy, but I got
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My work is pretty messy, but I got
clear vine
my eigenvalue is = 0
the eigenvector is the 1/2 over 1
The thing I am the most unsure about is that last term
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clear vine
<@&286206848099549185>
soft nest
The eigenvalue is right, the eigenvector looks right. Where does the t come from?
clear vine
because its a defective matrix to find the second part of the equation we multiply C2 by the first eigenvector * e^(stuff) times t then add in the unknown vector
i think
its this equation
soooooo
clear vine
setting the Matrix * unknown vector = solved eigen vector
then solving for what that unknown vector is
soft nest
So you’re saying that is a separate eigenvector for the matrix?
clear vine
I'm.... just gonna go ahead and find someplace else to ask
soft nest
Wait
https://matrixcalc.org/vectors.html#eigenvectors({{4,-2},{8,-4}}) you should get the same eigenvector twice
clear vine
i dont mean this insultingly
but i know that
im solving for the unknown vector
the rho in the context of the equation i sent earlier
that equation is the format that the general solution should be in
soft nest
Okay yeah it’s been a long time since I’ve solved one of these problems
clear vine
It be like that, I can barely remember how to solve problems from classes i took only a year ago
soft nest
I took diff eq about 5 years ago, and it was tricky then lol
clear vine
anyway, unless you think pinging helpers will net me someone whos taken it more recently
im gonna go ahead and close this and hunt for someone else
soft nest
Yeah good luck, from what we did so far you’re on the right track
<@&286206848099549185>
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restive river
Determine for which X in the range -pi - 2pi the equation has true statements.
I'm stuck on the second solution, am I not supposed to subtract the first solution from pi to get the second one as it's a sinus function?
I get 0,93 for the second solution but it should be 4,08
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Determine for which X in the range -pi - 2pi the equation has true statements.
...
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restive river
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tribal linden
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tribal linden
I don't know how to do this
It's basic math sure but idk wethwr to answer from left to right or answer by doing different steps instead
Do I use pemdas??
Help??
Emergency cuase I need to go to bed in like 5 mins
I'm serious
Bro I don't wanna chatgpt this😭😭
next hearth
Do I use pemdas??
Yes I assume you should since the title says order of operations
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cedar sphinx
Ik I’m supposed to be mature in typing this but like I don’t even know what to do for this whole worksheet 😭 I swear I was crashing out today in class and the teacher was js yelling at the class 🧍♀️
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Ik I’m supposed to be mature in typing this but like I don’t even know what to d...
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cedar sphinx
chat how do I get help..
severe sparrow
chat how do I get help..
by being specific
severe sparrow
very vague still
severe sparrow
pick a problem perhaps
severe sparrow
how to begin on what?
severe sparrow
is there a problem you're stuck on? it looks like you're doing pretty well
cedar sphinx
is there a problem you're stuck on? it looks like you're doing pretty well
FR?
oh wait my bad
You mean it?
Are they all correct?
I mean for the ones I’ve answerd so far
severe sparrow
nah 4c is wrong
severe sparrow
and 5a angle 2
severe sparrow
nvm
cedar sphinx
..
cedar sphinx
No cause
To find X I have to label the bottom two Y to find like
I’m not sure how to explain it well
But
severe sparrow
yea
cedar sphinx
what
severe sparrow
i think you got confused is all
cedar sphinx
The Y’s are supposed to be there to solve for X tho?!
severe sparrow
wait can you explain what you tried to do?
cedar sphinx
okay let me show u
so basically
Since the triangle is an isosceles or whatever
The bottom has to be the same
And since the top part of the triangle is 33
That must mean that the bottom two have to be a variable
And since I’m solving for X I can’t use X cause then it’s gonna be funky
And to find X which is on the outside of the triangle if you look closely
The top part (33) then add the answer I got from 33+2x=180
severe sparrow
i don't see where you get that from
severe sparrow
can you explain?
cedar sphinx
okay let me like
draw this out
OH WAIT I SEE WHERE I WENT WRONG
STOP NO BUT LOOK
idk if this helps
but
severe sparrow
good job
cedar sphinx
I DID IT RIGHT?
severe sparrow
looks right
cedar sphinx
YAYYY
severe sparrow
imma go to bed, ask someone else if u need more help ig
severe sparrow
it's like 12:30, forgive me xd
cedar sphinx
I have to wait ten hours again chat..
cedar sphinx
Ik I’m supposed to be mature in typing this but like I don’t even know what to d...
hey chat I still need help solving the triangles at the top and the entire worksheet!! (I need help on how to begin ^~^)
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quick dome
Could you please send me the question again
cedar sphinx
I js need help with 6,7,8 and the back side
cedar sphinx
Could you please send me the question again
- If the legs of an isoceles triangle are 6x-6 cm and x+9 cm long and the base is 2x+10. Find the length of the base
- Explain why a triangle cannot have two obtuse angles in it
cedar sphinx
Okay
quick dome
Perfect!
So if x+9 is one side 6x-6 is the other side
Shouldn't they just be equal
?
cedar sphinx
I need an image to show this 😭
bc I don’t understand the legs
like Are the legs the two sides that are congruent or ?
cedar sphinx
Thank you
cedar sphinx
.
Uhajsshsjsishsiddhdidd
OH WAIT
AHHH
so like
don’t tell me
js tel me if I’m right or wrong
so it would be like
erm
6x-6=x+9 ?!!!
quick dome
Yup
cedar sphinx
Yup
Fr?
OKAY
I GOT IT
x=3
So to find the length of the triangle
I have to get all sides of the triangle
Erm
I got it
can we do 7 now
misty crest
can we do 7 now
what is the sum of the angles in a triangle?
dope name btw
wild bio though
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inner grove
Hiya, I'm watching this video: (https://www.youtube.com/watch?v=QA5ZTgnoHcs), and the guy is setting up his eigenvectors at 1:40 or so, from this matrix. He says that a is 0 (which I can see), but he sets b as 1 'for simplicity'. I know we can't have a zero length eigenvector, but I tried to set b as 2 and I got a completely different value for C2 (3/2) than his value (b=1, C2=3). I asked GPT why this is and it says something about 'automatic scaling of eigenvectors' for IVP's, but I'm not really understanding, as I got a different solution, which doesn't seem right to me.
devout snowBOT
Hiya, I'm watching this video: (https://www.youtube.com/watch?v=QA5ZTgnoHcs), an...
inner grove
Do I need to scale my C2 based on eigenvector length or something?
(If I'm using a 'non-convenient' second eigenvector - probably worth noting that this is a case of I don't understand why (0,1) is more convenient than (0,n))
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restive river
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restive river
need help with 11c
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restive river
<@&286206848099549185>
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cedar sphinx
what is the sum of the angles in a triangle?
OHHHHH
bro I am the slowest person on earth 😭
my bad cuh and thanks 🤑🙏
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stark anvil
static swallow
send in english plsss
boreal sand
gimmie a moment to translate wait
radiant hare
You have to find the angle v
boreal sand
b) Determine the acute angle v between the line l and the second axis.
static swallow
ok
static swallow
a sec
boreal sand
sure!!
static swallow
you can use trigonometry
boreal sand
yikes....
static swallow
3y = 8+12
static swallow
you MUST fix your algebra skills
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wet robin
how can simply this
devout snowBOT
how can simply this
wet robin
5(x+1)/(x-1)(x+4)
barren prawn
$\frac{5(x+1)}{(x-1)(x+4)}$
woven radishBOT
OHHELLNAH
barren prawn
you mean this?
wet robin
yes
wet robin
i see
rare merlin
nope
barren prawn
you need to write additional ( ) in the denominator 5(x+1)/((x-1)(x+4)) if you write it with text like you did
wet robin
you need to write additional ( ) in the denominator 5(x+1)/((x-1)(x+4)) if you w...
ty
sorry for this question it was kinda dumb but ty
go to an open help channel
barren prawn
sure
elder seal
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elder seal
Since when can you do this with logs. Bringing the 1 over to make -1💀
sharp trellis
hmm seams fine to me
upper schooner
You can do that with any equation, rearranging it to make the log the subject, of course logs are allowed to be negative
elder seal
They brought over the 1 to make -1
I didn't know you could do that
The log is ln(x+1)
So how can you just bring the -1 over
+1
upper schooner
Why do you think that wouldn't be allowed? What would you think stops you from subtracting 1 from both sides?
upper schooner
strange if it were in the log then
upper schooner
Yea if it was actually in the log to begin with, you can't do that, and neither can you drop the 
elder seal
Yeah, I was finding the y intercept and was like why isn't it working
X intercept I mean
They broke maths yet again😭
Surely I'm not wrong
They can't just leave that 1 there
upper schooner
Yea they've either quoted the original wrong, or used the wrong equation subsequently 
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rich wagon
hi, i need help with this proof, where have i made a mistake?
devout snowBOT
hi, i need help with this proof, where have i made a mistake?
quick dome
Hello
safe knoll
quick dome
@rich wagon I would recommend you recheck the step where you assumed u = lnx ^n
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boreal anchor
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boreal anchor
I'm not sure if I just big brained this and skipped a whole lot of trouble or just completely wrong
latent scaffold
fr
sharp raft
i dont see anything wrong xD
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cinder bobcat
f(t) represents an external force, but the position of the spring might be different. so I think you'd have to solve the ODE
but that's probably correct?
keen oxide
Hey ! I’ve been struggling with this one for a while now can yall please help me with it ?
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Hey ! I’ve been struggling with this one for a while now can yall please help me...
wicked turtle
did you try a substitution?
keen oxide
I tried but since I don’t really get the technique I kind of got lost in the process
quick dome
Okay i will give a hint
See if you can follow through.
Assume e^-x^2 as some u
See where you get from there
@keen oxide
quick dome
Umm
wicked turtle
take the derivative and see
quick dome
Not sure what you mean by that
When you took the derivative
What did you get?
@keen oxide
keen oxide
Like this ?
polar flower
Ok so is it 1/2 e^-x^2 ?
it shld be -ve 1/2
quick dome
Like this ?
keen oxide
Oh right I forgot the minus my bad , but thank you very much !
keen oxide
Added it 
keen oxide
Thanks !
quick dome
.close the chat if you have nothing else to ask @keen oxide
Got anything else to ask?
keen oxide
.close
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karmic hatch
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karmic hatch
The question is to find p(A)
Can someone tell me does the way is to find
2A^2 -3A -1
or
matrix
p1 p2
p-1 p1
faint gorge
Can someone tell me does the way is to find
2A^2 -3A -1
or
matrix
p1 p2
p-1 p1
the first 1
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primal tusk
eyo
primal tusk
combine
i think i have it done
but
im second guessing myself
common denominator makes it -3(5x+3)-(3x+1)/(3x+1)(5x+3)
right?
and from there
-15x-9 - 3x+1 = -18x-10
rotund umbra
common denominator makes it -3(5x+3)-(3x+1)/(3x+1)(5x+3)
this is correct 🙂
rotund umbra
yes
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strong igloo
"The Least Squares method requires that the regression curve is linear in the unknown parameters (e.g. m and b, or a, b, and c). In fact, there is an exact formula for finding these values"
I'm confusing, how is a quadratic equation linear?
devout snowBOT
"The Least Squares method requires that the regression curve is linear in the un...
strong igloo
when using the sum of least squares, if we try to find an equation of the form ax^2 + bx + c, that's not linear, that's quadratic
small nest
Linear in the parameters
That means, a, b and c need to follow a linear form
What it's not allowed is something like $\frac{x^a + b \cdot x} {c}$
woven radishBOT
Max Hetfield
small nest
Got it?
strong igloo
That means, a, b and c need to follow a linear form
im a little confused what this means. Why would a, b, c, or m be able to be anything other than a scalar multiplicative?
pale bolt
Max gave an example of how they aren't, like $x^a$, the a is not a scalar multiple
strong igloo
like for f(x) = e^(gx)
g is a scalar value
woven radishBOT
strong igloo
i still dont really get that.. a is a constant coefficient, a doesn't change
pale bolt
linear in the parameters means that the parameters don't appear in exponents, and can't be multiplied by another parameter
strong igloo
what do you mean by "can't be multiplied by another parameter"? 😅
pale bolt
https://datascience.stackexchange.com/questions/12274 has a pretty good explanation I think
strong igloo
my prof didn't really teach this very well
pale bolt
first checked answer explains linearity over something
strong igloo
what does "parameter" mean in this context? Like if you have an equation f(x) = 5x^2 + 2x - 3
5, 2, and -3 are fixed... I thought x was the parameter to the function f?
float f(float x){
return 5*(x^2) + 2*x -3;
}
No, precisely 5, 2, and -3 are the parameters
strong igloo
so a parameter is different to a variable?? But then that means a parameter is a variable too?
small nest
so a parameter is different to a variable?? But then that means a parameter is a...
First question: Yes. Second: No, although I may understand a bit your confusion
I would say that a, b, c are only a "variable" when you're fitting the model.
strong igloo
my brain kinda thinks of this programmatically, I know it's a bit of an issue 😅
small nest
my brain kinda thinks of this programmatically, I know it's a bit of an issue 😅
It's not bad to think like that in this context
Think for example
linear_regression(a, b, c, x)
When you're fitting the model, a, b, c are free
But once you find their values
it becomes
linear_regression(5, 2, -3, x)
strong igloo
oh I think I get it...
small nest
And x is the thing that will always be varying
strong igloo
does linear in hte context of parameters refer to the change of those parameters? Like they can only vary linearly?
OH, WAIT
what if it was.. (a^2)*(x^2)?
would a still be "linear"
strong igloo
my head hurts.. I guess my issue is that linear when referring to coefficients isn't the same "linear" as when talking about the form of an equation
small nest
my head hurts.. I guess my issue is that linear when referring to coefficients i...
It's exactly that
Don't worry, it was the same for me when I learned it
strong igloo
so... they aren't the same?
woven radishBOT
Max Hetfield
small nest
Linear coefficient and non-linear variables
$a \cdot \ln{x} + b \cdot (x \cdot y) + c$
woven radishBOT
Max Hetfield
woven radishBOT
Max Hetfield
small nest
Non-linear coefficient and non-linear variables
Well, you can imagine that one...
The first 2 cases can be dealt with using linear regression
The last 2, you need non-linear methods
strong igloo
agh, my head hurts
woven radishBOT
Max Hetfield
small nest
Although you can easily transform that to a linear form
And after that you can use linear regression on it
small nest
agh, my head hurts
Nah, don't worry. Just remember by definition:
Linearity of parameters: a, b, c's grade needs to be 1 or 0
strong igloo
im so lost... im sorry.. My teacher just dumped this on us and didn't explain a single thing
small nest
Linearity of variables: x's grade needs to be 1 or 0
strong igloo
Linearity of parameters: a, b, c's grade needs to be 1 or 0
if the degree of a b or c were 0 then it'd just be 1, no?
small nest
if the degree of a b or c were 0 then it'd just be 1, no?
Yup, thus fitting the linear form as a constant (intercept)
strong igloo
a^0 = 1
oh
oh
wait but.... I still don't get how a can be linear in x^a. x^a is not linear (it's a polynomial), a is just some number... it's a^1 = a
small nest
wait but.... I still don't get how *a* can be linear in `x^a`. x^a is not linear...
No, a is not linear in such case, because it is behaving as a power
small nest
Nah, it's easy
Actually the way you solve those parameters makes a lot of sense, computationally speaking
And precisely non-linear regression is way harder, because you usually cannot use closed-form solutions
As in there are no analytical/exact/easy solution for that, so you got to use numerical methods
While you can solve linear forms via linear algebra
And that linear algebra can be sped up via decompositions and algorithms
strong igloo
say I have x and f, where f(x) = ax
x -> ax
it's scaled by some value a at a constant rate, therefore linear, I think I get this.
Now say I have x and g, where g(x) = x^b
x -> x^b
it's... exponentiated? It's scaled by some ever-increasing value? How would I describe b
small nest
say I have x and f, where f(x) = ax
x -> ax
it's scaled by some value a at a con...
x is a polynomial of grade b.
strong igloo
x is a polynomial of grade b.
right, but what is b? Is b linear? Is b exponential?
small nest
right, but what is `b`? Is b linear? Is b exponential?
b is exponential in this context
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@strong igloo Has your question been resolved?
strong igloo
b is exponential in this context
so the location of the parameter determines whether or not something is linera or non-linear?
small nest
so the location of the parameter determines whether or not something is linera o...
Yes, not a very formal way to put i, but yeah. Also if it's enclosed or participating in a function
small nest
This can help you too https://datascience.stackexchange.com/questions/12274/what-does-linear-in-parameters-mean
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somber isle
Hello can someone help me isolate the Y
devout snowBOT
Hello can someone help me isolate the Y
somber isle
Write Y with x only
wild drift
what's that 1st symbol under the root btw
wild drift
ok
somber isle
Never mind I found it
wild drift
so
sqrt(1 + y^2) - y = x
sqrt(1 + y^2) = x + y
1 + y^2 = (x + y)^2
1 + y^2 = x^2 + 2xy + y^2
1 = x^2 + 2xy
1/x = x + 2y
1/x - x = 2y
y = (1/x - x)/2
smth like this
wild drift
ayy np
somber isle
.close
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rapid bear
,kù
hexed berry
So
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hexed berry
Alright, different question then.
Gotta find the angle ABC.
But I end up with 1/√2
Maybe I did something wrong? Perhaps?
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hexed berry
<@&286206848099549185>
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@hexed berry Has your question been resolved?
tender cobalt
you seem to keep forgetting that dot-product is to multiply the components then sum them
- recheck c, use component-wise definition of dot-product
- recheck d, you need to copy down the parentheses too, its ((6; -8) + (6, -9)) • (-25; 0) which is (12; -17) • (-25; 0)
- recheck e, the dot product v • w is incorrect, then multiply this number with ||u||
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outer badger
Hello, I am working on real analysis and am trying to solve the following problem.
devout snowBOT
Hello, I am working on real analysis and am trying to solve the following proble...
outer badger
It's a summation of an infinite series, and I'm not sure how to approach it. I don't have much experience with solving infinite series at this level, and most of the resources I found online discussed things which were much simpler than this.
There is no definition for alpha
When q = 0, it converges to 0
This makes me think that the infinite sum of all different q would be 0, but I need to prove that
If alpha = 0, it converges to 0
timber pebble
This makes me think that the infinite sum of all different q would be 0, but I n...
try bounding it
what do we know about sin
can we bound this term by term using another series that may converge?
very helpful is $|\sin \varphi | \leq 1$ is true $\forall \varphi$
woven radishBOT
jan Niku
outer badger
I can show you the original question
timber pebble
are you tasked to find a value?
outer badger
outer badger
are you tasked to find a value?
Yes
But the only information provided is the |q| < 1
timber pebble
hmm i didnt think this was closed form
outer badger
What do you mean?
timber pebble
searching suggesting using exponential form of sine
woven radishBOT
Requested by janniku
timber pebble
What do you mean?
so if you rewrite
distribute
group under an exponent
all terms without n are constant
all pieces with n should form a geometric series
seem reasonable?
timber pebble
twilit comet
that's using euler's identity
timber pebble
indeed
twilit comet
very cool stuff involving complex numbers, you should check it out later
outer badger
Ok then
I'll check it out later then
I'll do my best to solve the problem using this and see where I get too
sand dove
you can alternatively use sin(x) = Imaginary(e^(ix))
though it only works if q is real
so euler formula for sin is good
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rocky laurel
So I can't solve this problem can someone help?
devout snowBOT
So I can't solve this problem can someone help?
rocky laurel
x and y
frosty portal
and b is any constant
frosty portal
well let b = 1 or b =0
you can do that
cuz b is "any" constant
so the equation must hold true
for every value of such b
hence u can take any arbitray value of b
and solve for x and y
that is completly valid
rocky laurel
this is what I did
rocky laurel
Idk
frosty portal
oh i think i have seen ur mistake
rocky laurel
Where?
frosty portal
rocky laurel
asked chat gpt this is what he said
rocky laurel
I added the /6
to remove the 6 from both sides
nvm I will move to the next one
.close
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worn ivy
Can someone help me work out the Norton Equivalent current. I've managed to work out the Equivalent Resistance but can't seem to work out the current?
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Can someone help me work out the Norton Equivalent current. I've managed to work...
acoustic leaf
Can someone help me work out the Norton Equivalent current. I've managed to work...
find the amount of current that passes between terminals a and b if you place a short circuit between them
