In some problems some othe form would be easier to work with
#help-49
twilit field
tidal turret
wdym? but which one is most useful? because memorizing all of them idk if thats practical
is there a way to derive them or what? you have to memorize it?
also I am seeing that only cartesian and point normal form are the only ones containing the normal vector of the plane, correct?
tidal turret
In some problems some othe form would be easier to work with
does having access to only cartesian equation limit the number of exercises you can do? or you can also figure it out but will take longer?
there is like a gazillion equations for the plane, also for the lines, in 3D, is impossible to memorize them all, there must be a trick to this, or a reasonable explanation
.close
sacred gate
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gaunt nimbus
,w d/dx [(2x^2 - 4x + 3) ^3]
gaunt nimbus
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cursive swan
Find the value of root(1 + root(2 + root(3 + root(4 + root(5 + .............)))))
midnight plankBOT
Find the value of root(1 + root(2 + root(3 + root(4 + root(5 + .............))))...
exotic stratus
!status
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2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
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5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
$\sqrt{1+ \sqrt{2 +\sqrt{ \dots + \sqrt{100}}}}$?
cursive swan
= x_100
grand pondBOT
What a wonderful world !
cursive swan
We need to find \lim_x\to\infty x_{n}, where $x_{100} = \sqrt{1+ \sqrt{2 +\sqrt{ \dots + \sqrt{100}}}}$
thin tree
$\lim_{x\to\infty}$
grand pondBOT
dtm
exotic stratus
Pretty sure this is just a diverging sequence tbvh
grand pondBOT
Mathematician
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exotic stratus
so just $\infty$
cursive swan
No
grand pondBOT
@exotic stratus
cursive swan
pretty sure?
exotic stratus
**What a wonderful world !**
Oh you want it upto a specific value?
thin tree
$\lim_{x\to\infty} x_n , x_{100}=\sqrt{1+ \sqrt{2 +\sqrt{ \dots + \sqrt{100}}}}$
dreamy lichen
it doesnt seem to divege
im pretty sure it converges, but i dont think there is a nice closed form
grand pondBOT
dtm
cursive swan
I can prove its convergence.
twilit field
im pretty sure it converges, but i dont think there is a nice closed form
we can find it's value easily IMO
$x = \sqrt{1+x}$
grand pondBOT
What a wonderful world !
cursive swan
This limit is less than this one.
subtle blaze
I’m thinking this is less than $\sum_{n=1}^\infty n^{1/2^n}$
cursive swan
grand pondBOT
frosst
cursive swan
damn
subtle blaze
Which sounds like it converges
exotic stratus
Oh sorry ran the script with the variables reversed (whoops!)
dreamy lichen
$x = \sqrt{1+x}$
this is the golden ratio one
dreamy lichen
subtle blaze
Yeah that’s what I thought
cursive swan
Sad life
subtle blaze
You could be the first to find a closed form for it
fallow scarab
Nested radical constant
https://mathworld.wolfram.com/NestedRadicalConstant.html
Catchy name /s
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tidal turret
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fallen sparrow
Yo
tidal turret
,w {{1,3},{3,9}} * {{a,b},{c,d}}
grand pondBOT
tidal turret
,, \begin{pmatrix} a + 3c & b + 3d \3a + 9c & 3b + 9d \end{pmatrix} = \begin{pmatrix} 0 & 0 \ 0 & 0 \end{pmatrix}
grand pondBOT
938c2cc0dcc05f2b68c4287040cfcf71
midnight plankBOT
@tidal turret Has your question been resolved?
tidal turret
guys I need some help with 3)
I cannot figure it out
,w (1,3,3,9).(x_1,x_2,x_3,x_4) = 0
grand pondBOT
tidal turret
(x1,x2,x3,x4) = a(1,3,-1,0) + b(0,1,2,1)
- x1 = a
- x2 = 3a + b
- x3 = -a + 2b
- x4 = b
x1 = x1
x2 = 3x1 + x4
x3 = -x1 + 2x4
x4 = x4
(x1,x2,x3,x4) = (x1, 3x1 + x4, -x1 + 2x4, x4) = x1(1,3,-1,0) + x4(0,1,2,1)
,, \begin{cases} x_2 = 3x_1 + x_4 \x_3 = -x_1 + 2x_4 \end{cases}
grand pondBOT
938c2cc0dcc05f2b68c4287040cfcf71
tidal turret
,, \begin{cases} 3x_1 - x_2 + x_4 &= 0 \ -x_1 - x_3 + 2x_4 &= 0 \end{cases}
grand pondBOT
938c2cc0dcc05f2b68c4287040cfcf71
fiery scarab
,help
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storm remnant
how do I solve this with a calculator please?
midnight plankBOT
how do I solve this with a calculator please?
dawn nexus
with a calculator that can do integrals?
grand pondBOT
Nanigov
storm remnant
what do you mean like "what can I say about the value of it"?
dawn nexus
What would that value have to equal, given the fact that f is the derivative of H, according to the theorems/results of calculus you know?
dawn nexus
it's alright
I think you're on the right track, but to be clear, the change in value of what?
midnight plankBOT
@storm remnant Has your question been resolved?
storm remnant
I think you're on the right track, but to be clear, the change in value of what?
of the function from the point x = 2 to x = 5
please lmk if I'm wrong
dawn nexus
which function, f or H?
midnight plankBOT
dawn nexus
@storm remnant you might want to reopen
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wary trail
For a surface integral in spherical coordinates, do I need an area element like I do for the volume element l, which is r² sin theta?
midnight plankBOT
For a surface integral in spherical coordinates, do I need an area element like ...
wary trail
or is that just the cross of the two tangent vectors?
sharp coral
the area element is the cross product of the tangent vectors, yes
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grim sierra
take $\int_{-1}^{1} 1/x , dx$, which evaluates to $\infty - \infty$. however, the two parts of the integral (1/x from -1 to 0 and 1/x from 0 to 1) grow at the exact same rate. so why not just say zero?
grand pondBOT
MARETU
midnight plankBOT
take $\int_{-1}^{1} 1/x \, dx$, which evaluates to $\infty - \infty$. however, t...
grim sierra
this is also noting the fact that 1/x is odd and the net area from -A to A of that function will always equal 0
astral canyon
Good question, but you need an analysis background to rigorously understand why its not zero. As a sort of hand-wavey response, "grow at the same rate" is not really a quantifiable/valid way to evaluate integrals, and the odd function trick only applies if your function has a primitive on the closed interval, which 1/x does not (at zero). https://proofwiki.org/wiki/Definite_Integral_of_Odd_Function
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twilit field
In which of the following cases is $H$ a subgroup of $G$
\
\begin{enumerate}
\item $G =GL_{n}(\C)$ and $H= GL_{n} (\R)$
\item $G=R^{\cross} and H={-1,1}$
\item $G=Z^{+}$ and $H$ is the set of positive integers
\item $G= R^{\cross}$ and $H$ is the set of positive reals
\item $G=GL_{2}(\R)$ and $H$ is the set of matrices with $a_{11}=a,a_{12}=a_{21}=a{22}=0; a \neq 0$
\end{enumerate}
Note: $S^{+/\cross}$ refers to the group $S$ with. the operation being $+ / \cross$. $GL_{n}$ is the General Linear group of invertible $n \cross n$ matrices under the operation of multiplication
Answers:
\begin{enumerate}
\item True, every the identity matrix from $G$, $I$ , carries over. Moreover the product of two real-valued matrices is real, thus proving closure. Inverses are closed as every real matrix has a real-valued inverse $(\textbf{ Do I have to prove this ? )}$
\item. Is a group. HAs the identity $1$ of $G$ , has inverses (1 and -1). And is closed under $\cross$
\item False, not a group as it doesn't have inverses under $+$
\item In this case $\R$ doesn;t have $0$. Thus every element has an inverse , the identity $1$ is present, $\textbf{ I am however not sure of how to prove closure here}$
\item False, the determinant of any matrix in $H$ is $0$, thus making them all non-invertible
\end{enumerate}
midnight plankBOT
In which of the following cases is $H$ a subgroup of $G$
\\
\begin{enumerate}
\i...
grand pondBOT
What a wonderful world !
main current
No you likely won't have to prove that in 1
Obvious LA fact
4, you can just say that the product of two positive real is a positive real
main current
All 5 look good, yes
steep mirage
midnight plankBOT
steep mirage
For 4a I know the answer is 3^x because it goes through 1, 3
But b didn't show what the value is at 1, y
So how do you figure that out
coral glen
Which one?
You know that the equation for an exponential function is y=a(b)^x
We have (0,1) so plug that in
So a=1
It’s the same idea for 4b
We have the point (0,1)
So plug it in
a=1
Now use (-1,5)
So your answer for 4b should be (1/5)^x
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maiden badger
Needed help.
midnight plankBOT
Needed help.
golden comet
question?
golden comet
oof matrices, I am not the right person :>
someone else help him lol
maiden badger
oof matrices, I am not the right person :>
someone else help him lol
Its not that tough xd but a little confusing and headache
golden comet
never learned it before, don't want to learn new stuff at like midnight XD
maiden badger
never learned it before, don't want to learn new stuff at like midnight XD
Been waiting for more than 30 minutes, but no one becoming angel.
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maiden badger
.close
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fast nimbus
How do I do 22
midnight plankBOT
How do I do 22
fast nimbus
I tried binomially expanding it and managed to get to a contradiction, but it doesnt feel valid
tawdry laurel
i would mod 79
twilit field
wdym
fast nimbus
i would mod 79
this type of stuff not in my curriculum for school
fast nimbus
wdym
i like binomially expanded the lhs and let the irrelevant stuff = alpha, and did some shit and found that alpha = 1 which is a contradiction
twilit field
you could use calculus
twilit field
,w minima of (n+1)^41-79n^40
grand pondBOT
tawdry laurel
💀
fast nimbus
wait can you mod 2
yea idk about this mod stuff my curriculum doesnt have it
tawdry laurel
Both dont work i think
tawdry laurel
yea idk about this mod stuff my curriculum doesnt have it
Just say if n is even then contradiction if n is odd then contradiction
twilit field
prove that $2 \nmid ((n+1)^{41}-79n^{40})$ then
grand pondBOT
What a wonderful world !
fast nimbus
Just say if n is even then contradiction if n is odd then contradiction
Oh wait, if i rearrane the equation, move the 79 term to the other side, and let n=2k+1, then doesnt LHS be even and RHS become odd? which is a contradiction?
fast nimbus
**What a wonderful world !**
i lowkey dont know what this means 💀
rare maple
He is trying to say that LHS is odd
tawdry laurel
Wait you understand my method right
tawdry laurel
He is trying to say that LHS is odd
Regardless of the choice of n
fast nimbus
Regardless of the choice of n
how do you know???
fast nimbus
yea?
tawdry laurel
so odd^41 is odd right
fast nimbus
yar
fast nimbus
but what if n is odd?
fast nimbus
then its (even)^41? which is even no?????
tawdry laurel
then its (even)^41? which is even no?????
Yes lah
But then 79 times odd^40 is odd
And then even - odd is still odd
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real minnow
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real minnow
how to do this question thanks
the 1st part gives a condition that says there is a circle around abcd
thorn sorrel
so what does that tell you about abcd
lethal path
the 1st part gives a condition that says there is a circle around abcd
what must angle ABC be then?
pearl hull
ABCD 有外接圓，你能想到什麼？
pearl hull
跟角度有關的
real minnow
这个是对角互补吗
pearl hull
是
lethal path
I'm wondering if there's a less bashy way
than cosine rule to find side AC, then sine rule twicce on triangle ADC
real minnow
sin(45)/ac = sin(x) /sqrt(3)
find angle C
then use another sin law?
@lethal path
how about question 2?
lethal path
hmmm
pearl hull
第一題小題先找出角B的角度
用餘弦找出AC
用正弦定理找出DAC的角度
最後得到DCA的角度後就可以用餘弦找AD
lethal path
$\frac{AC}{\sin(ABC)} = \frac{2}{\sin(BAC)}$
$\frac{AC}{\sin(45)} = \frac{\sqrt{3}}{\sin(DAC)}$
$DAC + BAC = 60$
grand pondBOT
south
lethal path
I feel it's possible to do something with these equations
lethal path
I could actually do q2 with complex numbers if you'd let me
real minnow
AC = sqrt AD^2 + sqrt 3^2 - 2 ...
real minnow
I could actually do q2 with complex numbers if you'd let me
ok what is your idea
pearl hull
I could actually do q2 with complex numbers if you'd let me
Interesting
lethal path
or like coord geo
lethal path
complex numbers requires moving the origin so no
lethal path
https://www.desmos.com/calculator/zuzlhsmjwo
idk but hope this helps
real minnow
Hmm say angle BAC is alpha
sin(120-alpha)/AC = sin(alpha)/2
sin(45)/AC = sin(60-alpha)/sqrt3
Let’s see if this is useful
Dividing gives sin(120-alpha)/sin(45) = sin(alpha)/sin(60-alpha) * sqrt3/2
sin(120-alpha)sin(60-alpha) = sin(alpha)sin(45)sqrt3/2
Looks like it can be turned into a quadratic in tan(alpha)
lethal path
hopefully that works?
real minnow
sin(120-alpha) = sin(120)cos(alpha) - cos(120)sin(alpha)
sin(60-alpha) = sin(60)cos(alpha) - cos(60)sin(alpha)
Multiplying out gives
sin(120)sin(60)cos^2(alpha) + cos(120)cos(60)sin^2(alpha) - …sin(alpha)cos(alpha)
i dont think this works
you have …cos^2 + …sin cos + … sin^2 = …sin
but this doesnt turn into a quadratic
@lethal path @pearl hull
i got it
.close
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heavy ledge
Can anyone help me find the line between x-y+2z+4=0 and the xy plane?
midnight plankBOT
Can anyone help me find the line between x-y+2z+4=0 and the xy plane?
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
silk sail
You mean the intersection of x-y+2z+4=0 and xy plane?
heavy ledge
yes! :)
silk sail
Hint:the equation of xy plane is z=0, the intersection satisfies both equations
heavy ledge
z=0 right
silk sail
do you know an equation for the xy-plane?
Welp now he knows
steel crest
yeah, Cro is nicer than me in their hints it looks like lol
so now you have two equations
x-y+2z+4=0
z=0
when two curves intersect, or when two surfaces intersect, both equations are true at the same time
so what can you do to make both equations true simultaneously
rancid vigil
is he trying to find the line intersection of both planes ?
heavy ledge
x-y=-4
steel crest
x-y=-4
yeah, can you show your work if you need to? dont know how complete an answer your teacher needs
but that's right
🎉
heavy ledge
is (x-y =4) a line?
rancid vigil
is (x-y =4) a line?
Iirc , two planes always intersect on a line
heavy ledge
I need to make it a parameter thing
silk sail
is (x-y =4) a line?
Well, (x-y=-4) and (z=0) makes a line
If you're talking about how much restrictions you're putting on these are all the restrictions
steel crest
Iirc , two planes always intersect on a line
not quite
that's the usual case
but there are 2 degenerate cases
silk sail
Since z=0, do whatever you do on xy plane
heavy ledge
what are restrictions
silk sail
Think of x-y=-4 and z=0 as two restrictions placed on xyz space
steel crest
I need to make it a parameter thing
so what would it look like as a regular equation y=mx+b?
silk sail
These two are 2d flat surfaces, their intersection is a line you wanted
steel crest
I need to make it a parameter thing
it can be parameterized
rancid vigil
but there are 2 degenerate cases
Interesting, what would the intersection be ?
heavy ledge
so what would it look like as a regular equation y=mx+b?
. X= x_0 +at
L: Y=y_0 +bt
. z=z_0+c*t
L is the line
silk sail
. X= x_0 +a*t
L: Y=y_0 +b*t
. z=z_0+c*t
Yes now just choose your starting point and a b c
steel crest
here, since z=0 , the third one just becomes z(t) = 0
heavy ledge
Yes now just choose your starting point and a b c
how do I do either of those haha
steel crest
how do I do either of those haha
you want a general method or an easy method for this line in particular
this one is easy because one variable becomes 0
but its good to know the whole method
heavy ledge
general methos would be sick
rancid vigil
You just define a point that the line passes through and then find a director vector of the line
That's how I'll do it 🤷
steel crest
so, find an equation the represents a line in 2 variables
that will not be the whole line in general
so if I had for example
x-y =1
y+z = 2
then both of those are in terms of two variables only
note that the solution will not be unique
so, solve for one variable, let's say, x
so the first equation becomes y=x-1
choose a variable to be t, is usually easiest
x(t)=t
then y=t-1
y(t)=t-1
z=2-y becomes
z=2-(t-1)
z(t) = 1-t
or, if you want it in the notation you said
x(t)=0+1t
y(t)=-1+1t
z(t)=1-1t
(x,y,z)(t)=(0,-1,1)+t(1,1,-1)
make sense?
heavy ledge
how did you get X(t)=t
rancid vigil
Mine seems simpler
steel crest
remember the parameterization is not unique
the first variable you choose you can choose any injective function
the simplest choise is f(t)=t
steel crest
You just define a point that the line passes through and then find a director ve...
how do you find the direction vector of the line though
if not this way?
silk sail
how did you get X(t)=t
You should write down all the equations, run some random numbers through and see if it works
steel crest
anyway that wasnt for your problem specifically, that was for x-y=1//y+z=2
heavy ledge
You should write down all the equations, run some random numbers through and see...
like. randomly selecting x y and z values?
silk sail
And a b c yes, here's one for you (x, y, z)=(1, 7, 0) (a, b, c)=(5, 3, 0)
And then when will the numbers work?
steel crest
That's how I'll do it 🤷
yeah I looked this up, this is a good alternative, can be easier
for two variables only I think mine is easier but different strokes for different folks
heavy ledge
I'm really lost right about now haha
steel crest
I'm really lost right about now haha
so let'sjust finish up your problem and then you can learn the more general approach in a new question
you have the line
x-y=-4
z=0
z=0 only has one parameterization, z(t)=0t+0=0
x-y=-4
do you zee that z(t)=0t+0=0 is the only choice for z(t)?
midnight plankBOT
@heavy ledge Has your question been resolved?
rancid vigil
@heavy ledge if you don't understand both methods you should probably study parametric equations more
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oak fable
hi
oak fable
<@&286206848099549185>
two cars moved at the same time to a city which is 560km away, the first cars speed is 10km/hour more than the 2nd cars speed, the first car arrived 1 hour earlier in the city. FIND THE SPEED OF BOTH
pls thanks 😉
rancid vigil
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** After 15 minutes**, feel free to ping helpers
oak fable
okay
tawdry laurel
Yep
tawdry laurel
560/x = 560/x+10 = 1
But its plus
tight ravine
I got u
oak fable
💀
tight ravine
first cars speeds is X km/h right
oak fable
yea
tight ravine
second ones speed is X+10 km/h
oak fable
ye
tawdry laurel
sry was occupied
tawdry laurel
560/x = 560/x+10 = 1
When i meant plus
I meant the second equal sign should be changed to plus
tawdry laurel
Because youre essentially taking the time difference here
oak fable
560/x = 560/x+11
oak fable
oh
grand pondBOT
Carbonite
tawdry laurel
i had to take a bathroom break
is ok
oak fable
uhm so
tawdry laurel
Now can you solve the equation
oak fable
560/x = 550 + X
tawdry laurel
What
tawdry laurel
**Carbonite**
its here
tawdry laurel
Youre saying $\frac{560}{x} = 560+x$
oak fable
**Carbonite**
well in here
grand pondBOT
Carbonite
tawdry laurel
mhm
oak fable
oh shit nvm mb i made a mistake
tawdry laurel
it happens
oak fable
srry
tawdry laurel
isok
oak fable
whats isok
tawdry laurel
is ok
oak fable
**Carbonite**
so do u know how i could solve ts
oak fable
ye
tawdry laurel
okay
We can multiply both sides by x(x+10) to clear denominator
And simplify into an equation and solve
oak fable
u mean x(x+10)?
tawdry laurel
u mean x(x+10)?
yes sorry
oak fable
how do u multiply the 1 with x(x+10)
tawdry laurel
wait why x out of the bracket?
wdym
tawdry laurel
sorry im an 8th grader
Is ok
we multiply by x
And then x+10
so x(x+10)
So finally we get 560 (x+1) = 560 (x) + (x)(x+1)
and can you solve
tawdry laurel
yeah thanks so much
np
oak fable
.close
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kindred mango
how would i go about doing part b of this question?
midnight plankBOT
how would i go about doing part b of this question?
kindred mango
this is my answer for part a
carmine sigil
You skipped E and scribbled over D, but you have the correct idea for part a
kindred mango
sorry i cropped those out by accident, D is -2 and E is 2e^(4/3pi i)
carmine sigil
For the next part, you need to find the values of G-L first. You can do this by finding the midpoint of any two pairs, I recommend B and C
Then wB = H so w = B/H
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oak fable
help
oak fable
how do i find the Subelement of an element?
<@&286206848099549185>
Subelement
@gray widget
help
<@&286206848099549185>
lyric charm
.....
dreamy lichen
how do i find the Subelement of an element?
subelement?
dreamy lichen
also stop that ping spam
lyric charm
don't pingspam mate
oak fable
sorry
lyric charm
!xy
midnight plankBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
dreamy lichen
Someone might
charred canopy
dreamy lichen
or we might translate it
lyric charm
!occupied
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astral talon
!occupied
dreamy lichen
i dont think "subelement" is a term which is commonly used in math
oak fable
thats ezzz
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dreamy lichen
i dont think "subelement" is a term which is commonly used in math
its most likely a mistranslation
lyric charm
its in my language
what is your native language?
lyric charm
you need to share the entire problem with us though
give us both the original mongolian and your best translation into english
oak fable
hmm its like yk a big 2 circles and then if they share a same thing , those numbers go in the middle
oak fable
Let the set
𝐴
{
1
,
2
,
3
}
A={1,2,3}.
- How many subsets does set
𝐴
A have? - List all the subsets of set
𝐴
A.
@lyric charm
its subset mb
oak fable
A={1,2,3}.
.How many subsets does set
A have?
.List all the subsets of set
𝐴
oak fable
but also ok you meant subset and not "subelement"...
yea
thin tree
2^n?
lyric charm
strange how you decided not to send a photo, but OK
oak fable
Ann how would u do it?
thin tree
he wants you to help
oak fable
she"
lyric charm
i don't know how to help without spoiling it
oak fable
wdym spoil
oak fable
its fine do it 😉
lyric charm
not on this server
fallen sparrow
Well you can think about the choice of an element
lyric charm
anyway my advice for you to figure this out yourself would be to try writing down some subsets of {1,2,3}
without yet worrying about whether you got them all
@oak fable your pronouns say he/him btw, you should update that if it's inaccurate for you
thin tree
There is a formula for finding subsets, which you might get to know
Once you write all the subsets
oak fable
1,2,3
fallen sparrow
Think about the choice of an element
oak fable
figure it yourself
idk so i came here
thin tree
Yea write down the subsets
oak fable
(1,2,3)
thin tree
Or do you know what is a subset
oak fable
how?
thin tree
{ 1,2,3}
oak fable
why 1
oak fable
i thought u said like use formula 2'1 smth
thin tree
no
I will get to that later
You also need to write down all the subsets
So do that now
oak fable
whats a subset
oak fable
Let the set
𝐴
{
1
,
2
,
3
}
A={1,2,3}.
- How many subsets does set
𝐴
A have? - List all the subsets of set
𝐴
A.
thin tree
{} , {1} , {2} , {1,2}
oak fable
A={1,2,3}.
- How many subsets does set A have?
- List all the subsets of set 𝐴
thin tree
I know
oak fable
oh
oak fable
ohh i get it
thin tree
um
oak fable
and i forgot 1, 2 ,3
thin tree
You need to write in { }
oak fable
oh
thin tree
But yea there are more
thin tree
And {1,2} is the same as {2,1}
oak fable
oh
thin tree
Both have same elements
oak fable
{1}, {2}, {3}, {1,2} {1.3} {2.3} {1,2,3}
so like there
thin tree
{} is a subset of every set
thin tree
no
oak fable
why
thin tree
{1,1} is the same as {1}
oak fable
oh
thin tree
yes
oak fable
and thats how u find subset?
thin tree
yes
thin tree
I want you to try and figure it out
You got 8 subsets
You had 3 elements
Can you find a formula?
oak fable
times 2 by 3 times
thin tree
2*3=6
oak fable
how do i have 3 elements
oak fable
3
thin tree
then
thin tree
how do i have 3 elements
.
midnight plankBOT
If you are done with this channel, please mark your problem as solved by typing .close
oak fable
u should be a helper
thin tree
no
oak fable
why
thin tree
I don't want to get pinged
midnight plankBOT
thin tree
how do i find the Subelement of an element?
see the 3 pings
oak fable
ye..
thin tree
That's why
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Available help channel!
silent torrent
what exactly is line integral single integral is the area under the curve double is the volume under the curve , so line is the area under the curve i guess no what line integral for?
midnight plankBOT
what exactly is line integral single integral is the area under the curve double...
thorn crown
Could you reword that?
silent torrent
like i want to know what line integral for , line integral is a single integral right but line integral doesnt cal area under the curve
thorn crown
There's more than one type of line integral is the thing.
Two of them seem to come out of nowhere in their definitions but provide useful in deriving the work of a particle moving in a force field in terms of them
$\int_{\gamma} f(x, y) \dd{s}$ would give the area under the curve $f(x, y)$
grand pondBOT
stabulo
silent torrent
but line integral is single integral so it still calculate the area of this picture right?
thorn crown
Are you familiar with the subdivisions in the case of an ordinary Riemann integral?
silent torrent
yes
thorn crown
To obtain the area under thr curve as you would like in terms of a line integral
$\int_{\Gamma} f(x, y) \dd{s} = \sum_{k = 0}^{n} f(\phi(t_k), \psi(t_k)) \Delta{s_k}$
grand pondBOT
stabulo
thorn crown
Where t_k is any point in between the corresponding points of the subdivision.
Delta s_k is the length of the subinterval created
silent torrent
i get what u mean
thorn crown
so the line integral on the left will equal a ordinary Riemann integral
silent torrent
but line integral is single integral so it still calculate the area of this pict...
delta s is single small part in xy plane right and the f(t) is the height so we use reiman then we have the area right ?
thorn crown
delta s is single small part in xy plane right and the f(t) is the height so we ...
We can make it exact without resorting to the small increment arguments
thorn crown
delta s is single small part in xy plane right and the f(t) is the height so we ...
But essentially yes that's the idea
silent torrent
but line integral still find the area ?
thorn crown
**stabulo**
Yes the line integral will be the thing on the left but we evaluate it using ordinary Riemann integrals
silent torrent
why i have to learn same thing =))
thorn crown
My book doesn't have stuff on line integrals with respect to s so I just made it up
For the arc length part Delta(s_k)
$\int_{\Gamma} f(x, y) \dd{s} \
= \sum_{k = 0}^{n} f(\phi(t_k), \psi(t_k)) \Delta_{s_k} \
= \sum_{k = 0}^{n} f(\phi(t_k), \psi(t_k)) \sqrt{\phi'(\xi_k)^2 + \psi'(\eta_k)^2}[t_k-t_{k-1}]$
grand pondBOT
stabulo
silent torrent
ds just a small move and calculate by sqrt(dx^2 +dy^2) i know that is that whatu want to say
thorn crown
This can be shown to be equal to a Riemann integral even if all the points are not the same in the subintervals
Maybe I should avoid making it exact
silent torrent
**stabulo**
what u mean tk -tk-1
thorn crown
They are the start and end points of the subintervals of the curve
But essentially this is trying to say that you are defining the area under the function f(x, y) above a certain curve as the sum of the products of the length of all these subintervals times by the height of the function at some point in the interval
silent torrent
thank you for helping me
thorn crown
Glad to help, hopefully it wasn't confusing.
silent torrent
my teacher told me 4 years in uni not to solve a ton of exercises to get good grade but to understand the beautiful things about those subjects so i just want to have deep understand about everything =))
btw i live in VN and its 12am i really need to sleep
bye =))
thorn crown
Unfortunately not many resources do that. Good night
midnight plankBOT
@silent torrent Has your question been resolved?
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teal hemlock
not rly sure how to do this
midnight plankBOT
@teal hemlock Has your question been resolved?
steel crest
not rly sure how to do this
do you have the form of "wave solutions" you're supposed to use?
teal hemlock
do you have the form of "wave solutions" you're supposed to use?
no clue that's lal they given me
midnight plankBOT
no clue that's lal they given me
@teal hemlock Has your question been resolved?
austere maple
I have a quartic polynomial, and I need to identify and calculate the maximum and minimum points of the graph. The problem is that my teacher told me I can't do it by differentiating it. He told me I had to use the roots of the polynomial. I honestly didn't understand. Does anyone have any idea how to do it?
midnight plankBOT
I have a quartic polynomial, and I need to identify and calculate the maximum an...
gleaming latch
get your own channel
lyric charm
!occupied
midnight plankBOT
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austere maple
austere maple
I have a quartic polynomial, and I need to identify and calculate the maximum an...
<@&286206848099549185>
sorry
someone?
austere maple
I have a quartic polynomial, and I need to identify and calculate the maximum an...
<@&286206848099549185>
austere maple
are you allowed a computer?
I could just use the GeoGebra Extremum tool, but I feel like I'd still have to explain how to get it.
steel crest
well, if you're supposed to use roots
and it has no real roots...
then i dont know what your instructor means
austere maple
😞
steel crest
if youre allowed to use a computer then I would just say exactly how to do it with a computer
austere maple
then I will just use geogebra and then I will consult it
steel crest
"put this in this area on geogebra and whatever"
austere maple
okey
steel crest
this is all assuming youre not supposed to take the derivagtive
austere maple
this is all assuming youre not supposed to take the derivagtive
and I have another question, about something else
steel crest
👂
austere maple
👂
You see, I have two polynomial functions, one of degree 3 and one of degree 4, and I have this list of data. So my professor gave me the instruction: "Based on the above, draw a conclusion about the two functions (cubic function or quadratic function) that best fit the data presented." So I made the table by replacing the values of each function with its result.
What complicates things for me is that I supposedly have to do the remainder with absolute value, that is, make a table to compare how much the sum of everything gives me to see which function is closest, but I have no idea how to do it.
steel crest
the usual way to measure how good or bad your choice of model fits the data is the SSE, the sum of squared errors
also known as RSS residual sum of squares
so for example
I'll call predicted y "y-hat"
if for x = 0, y=25,y-hat=24.69
then you take the error ans square it : (25-24.69)^2
and do that for all the errors
however, actually, theres a problem
increasing the degree of the fit will ALWAYS lower the RSS even if it's a worse model
I'm not sure if you're supposed to account for that
steel crest
the square of the remainders
this is how to account for comparing models with a different numbers of variables
by number of variables I mean
for one you have a+bx+cx^2 + dx^3 so (a,b,c,d) you are finding 4 variables
except the note says "excluding the intercept"
so only (b,c,d)
steel crest
Is it adding the remainders of the square?
so, adding the square of the remainders
gives you the sum of squared errors SSE
austere maple
24.69
33.31
41.98
49.05
53.39
54.42
52.12
46.99
subtract that and raise it to 2?
steel crest
24.69
33.31
41.98
49.05
53.39
54.42
52.12
46.99
subtract that and raise it to 2...
subtract it from (25,32,44,48,53,55,52,47) entrywise
austere maple
subtract it from (25,32,44,48,53,55,52,47) entrywise
steel crest
anjyway i have to go, good luck
to summarize:
this is called the "sum of squared errors" or "residual sum of squares"
adding one more explanatory variable (like going from (b,c,d) to (b,c,d,e) in the model y = a+bx+cx^2+...+ex^4) will always reduce the RSS. If you want to adjust the number in such a way to compare two models with different number of explanatory variables, there's a more advanced formula called "adjusted r-squared", but it may be more than wha tyoure expected to know
gl
austere maple
midnight plankBOT
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night hawk
Are all functions infinitely differentiable, or are they only differential until some nth derivative is 0?
-# I do recognize that even the second part means some functions, like sin, can be differentiated infinitely.
midnight plankBOT
Are all functions infinitely differentiable, or are they only differential until...
vast swan
Both
First of all
0 is perfectly differentiable with derivative 0
Second
|x| is not differentiable even once
And infinitely differentiable functions
night hawk
|x| is not differentiable even once
Because it has a sharp corner at (0, 0)?
vast swan
We call smooth
vast swan
Because it has a sharp corner at `(0, 0)`?
Yes
night hawk
What's wrong with saying $\dv{x} |x| = \frac{|x|}{x}$?
grand pondBOT
@night hawk
vast swan
What would |x|/x be at x=0?
night hawk
What would |x|/x be at x=0?
It's undefined, just like the slope of |x|.
night hawk
So it isnt differentiable
One point of indifferentiability causes |x| to be completely impossible to differentiate?
vast swan
I mean you can
But you wouldnt call it differentiable
And even if so
There are still functions that are differentiable nowhere
night hawk
There are still functions that are differentiable nowhere
Can you give an example?
vast swan
Well
You can just take a function continous nowhere
Like a dirichlet function
But there are functions continous nowhere and differentiable nowhere
night hawk
You can just take a function continous nowhere
Does any such function exist?
vast swan
Like Weierstrass function
vast swan
Does any such function exist?
Dirichlet
f(x)=1 if x is rational f(x)=0 if x irrational
midnight plankBOT
@night hawk Has your question been resolved?
jovial crest
Hi! Does anybody know where I can find a good proof for the primitive root theorem?
midnight plankBOT
Hi! Does anybody know where I can find a good proof for the primitive root theor...
jovial crest
Or even just the p^k part
jovial crest
Hi! Does anybody know where I can find a good proof for the primitive root theor...
good = fairly understandable for someone fairly comfortable with nt
<@&286206848099549185>
midnight plankBOT
@jovial crest Has your question been resolved?
jovial crest
https://en.wikipedia.org/wiki/Primitive_root_modulo_n
What is O(log log n)
Like dors it have anything ti do w rhe indices table for U_n
fallow scarab
What is O(log log n)
log(log(n)) grows much slower than log(n) which grows much slower than any polynomial
jovial crest
https://en.wikipedia.org/wiki/Big_O_notation
Wair im sorry if O(log(log(n)) is a value how does it make sense that something belongs in it
fallow scarab
did you see this
jovial crest
Yes
midnight plankBOT
@jovial crest Has your question been resolved?
granite cipher
midnight plankBOT
granite cipher
I got 1+4t 1-18t 34+t instead
granite cipher
I got 1+4t 1-18t 34+t instead
Why did they get like plus instead of minus and then minus instead of plus?
Is it a mistake
final scroll
Okay Lets See...
The surface is given by F(x, y, z) = 2x² - 9y² + z - 27 = 0.
The point is P₀ = (1, 1, 34).
Find the Gradient Vector (Normal Vector):
The gradient ∇F will be normal to the surface.
∂F/∂x = 4x
∂F/∂y = -18y
∂F/∂z = 1
So, ∇F = (4x, -18y, 1).
Evaluate the Gradient at the Point P₀(1, 1, 34):
Substitute x=1, y=1, z=34 into ∇F:
∇F(1, 1, 34) = (4(1), -18(1), 1) = (4, -18, 1).
This is our normal vector n = (4, -18, 1).
Equation of the Tangent Plane:
The equation is n · ( (x, y, z) - P₀ ) = 0.
(4, -18, 1) · (x - 1, y - 1, z - 34) = 0
4(x - 1) - 18(y - 1) + 1(z - 34) = 0
4x - 4 - 18y + 18 + z - 34 = 0
4x - 18y + z - 4 + 18 - 34 = 0
4x - 18y + z - 20 = 0
So, z = -4x + 18y + 20.
This matches the answer in the image (z = 20 - 4x + 18y).
Equation of the Normal Line:
The normal line passes through P₀ = (1, 1, 34) and has direction vector n = (4, -18, 1).
The parametric equations are:
x = x₀ + at
y = y₀ + bt
z = z₀ + ct
So,
x = 1 + 4t
y = 1 + (-18)t = 1 - 18t
z = 34 + 1t = 34 + t
This matches what you got: x = 1 + 4t, y = 1 - 18t, z = 34 + t.
The answer in the image for the normal line is:
x = 1 - 4t
y = 1 + 18t
z = 34 - t
This means the answer key used the negative of our normal vector, (-4, 18, -1).
A line can be parameterized with a direction vector or its negative; both describe the same line. So (4, -18, 1) and (-4, 18, -1) are equally valid direction vectors for the normal line.
Your answer x = 1+4t, y = 1-18t, z = 34+t is correct.
The answer in the image x = 1-4t, y = 1+18t, z = 34-t is also correct as it just uses the opposite direction vector. Sometimes, to make the 'x' component negative for example, or for other conventions, one might flip the signs of the direction vector. Both parameterizations trace out the exact same line.
granite cipher
Oh so both are right
Why doesn’t it matter if you use opposite direction?
Just conventional?
I thought it would not give the same line but it does
flat spire
hes clearly using chat gpt
dusty portal
Okay Lets See...
The surface is given by F(x, y, z) = 2x² - 9y² + z - 27 = 0.
T...
!nogpt
midnight plankBOT
Okay Lets See...
The surface is given by F(x, y, z) = 2x² - 9y² + z - 27 = 0.
T...
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
dusty portal
dusty portal
I thought it would not give the same line but it does
They don't know the topic lmfao
final scroll
<:hmmcat:831508801646755850>
i didnt
dusty portal
Alas, neither do I
final scroll
i type in note pad
granite cipher
Soo do you lot know
flat spire
Alas, neither do I
@ moderator this person!!!
dusty portal
@ moderator this person!!!
No, not sufficient
I'll give them grace, I did not primarily sus gpt anyways
dusty portal
i type in note pad
Can you be less...paragraphy when you explain
Like make it understandable for OP
You there bro
I'm giving you grace
granite cipher
Can anyone confirm please
dusty portal
Sorry man, I just started learning multivar 😭
steel crest
Just conventional?
it's not even a convention
granite cipher
Soo
steel crest
unless it's an applied math problem dealing with a real world phenomenon or something
there's no way to determine what makes one direction forwards and one direction backwards
granite cipher
I don’t understand your point
steel crest
the only difference between the book's answer and yours is whether you use t or -t?
granite cipher
Yes
steel crest
then your answer is correct. you earlier asked
granite cipher
They used -t for some odd reason
granite cipher
then your answer is correct. you earlier asked
Okay
steel crest
Why doesn’t it matter if you use opposite direction?
^
granite cipher
Why did they use -t
steel crest
because there's no "correct" direction
granite cipher
Oh
steel crest
Why did they use -t
they would say you used -t
steel crest
and i'm saying even besides from sign trhe answer is not unique
you could get something like x=1+4t^3 , y=1-18t^3, z=34+t^3
(fixed a mistake in what I said, now it's correct)
hth
granite cipher
Oh
granite cipher
you could get something like x=1+4t^3 , y=1-18t^3, z=34+t^3
Ahh okay
And that would still be correct?
steel crest
yeah. it's just, a weird choice, but it's not a wrong choice
midnight plankBOT
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twilit field
Prove that every subgroup of a cyclic group is cyclic.
\
Consider an arbitrary subgroup of a cyclic group. The subgroup has the identity $1/x^0$, and for every element, its inverse is in the group too. We now prove that closure implies the group is cyclic.
\
$\textbf{I'm not sure of what to do from here, am I on the right track}$
midnight plankBOT
Prove that every subgroup of a cyclic group is cyclic.
\\
Consider an arbitrary ...
grand pondBOT
What a wonderful world !
lyric charm
you don't need to wrap a \textbf in dollars
twilit field
That is , does closure imply the (sub) group is cyclic
lyric charm
you're not on the right track bc you've not established any notation whatsoever
you're on track to drown
also 1/x^0 is sus
what is that slash doing there
twilit field
1 or x^0
lyric charm
"1 a.k.a. x^0" if you want
hard umbra
but what is x 
twilit field
Okay, so the notation, $x^a$ means $x$ multiplied by itself $a$ times, $x^{-a}$ is the inverse of $x$, multiplied by itself $a$ times. $x$ is the generator of the group
lyric charm
not the notation you needed to establish
grand pondBOT
What a wonderful world !
lyric charm
you're gonna have an impossibly difficult and unlubricated time distinguishing "the group" vs "the subgroup" if you refuse to give names to either one
twilit field
Let the group be G, the subgroup S
lyric charm
ok
also try to write simple shit
dont try to cram 1000 things into one big run-on sentence
given:
- there is a group G
- G is cyclic
-- G has a generator; call this generator x - S is a subgroup of G
goal: - show S is cyclic
twilit field
given:
- there is a group G
- G is cyclic
-- G has a generator; call this genera...
To show $S$ is cyclic, I have to show it has a generator
grand pondBOT
What a wonderful world !
twilit field
I suppose I say $x^{ka+r}= x^b$. From this I have to show $r$ is 0?
grand pondBOT
What a wonderful world !
midnight plankBOT
@twilit field Has your question been resolved?
twilit field
<@&286206848099549185>