Channel closed
Closed by @proven oriole
Use .reopen if this was a mistake.
#help-27
devout snowBOT
drifting sierra
.reopen
devout snowBOT
✅ Original question: #help-27 message
drifting sierra
@proven oriole I forgot to tie it back to the first step I made you do
This
You found both solutions, 1 and 3, but you need to check whether they satisfy those preliminary conditions
In this case, they obviously do, both x=1 and x=3 satisfy x >= -1/8, but in the future you might encounter exercises where it gets slightly more complicated
Anyway, that's pretty much it
.close
devout snowBOT
<@859289922584969217>
pseudo basin
@chrome gyro do you have a math question to ask right now
chrome gyro
I do
how would I do this in the triangle method rather than the parrelolgram
@fast garden
fast garden
np
so you find out "how much" force you have in 2 perpendicular directions
that way you can result them in 2 different directions
as a result, you have 1 final triangle
and from there you can work out the total force and angle
chrome gyro
and from there you can work out the total force and angle
I’m soooo confused
Can you draw it
fast garden
yh give me a few min, i just finished cooking dinner
chrome gyro
yh give me a few min, i just finished cooking dinner
👍
fast garden
oh i see
this is basically just the same as the parallelogram but with just one side
chrome gyro
this is basically just the same as the parallelogram but with just one side
I don’t understand
How would I draw it in this case
Can you do it and show me
fast garden
just imagine moving one of the arrows you drea earlier to the tip of the other
chrome gyro
How would I do it becuase it goes left
fast garden
there is not much more to it
chrome gyro
But I can’t
fast garden
why?
chrome gyro
becuase one triangle is facing left whole other is down
could you show me what you mean please
fast garden
fast garden
yes
devout snowBOT
@chrome gyro Has your question been resolved?
stiff karma
Does this give us intersection with y axis?
devout snowBOT
Does this give us intersection with y axis?
faint gorge
it can give intersection with the two lines or none if they parallel
and not identical
you would have to try x=0 to really see if they intersect at the y-axis
civic umbra
What's the question? what language is it?
stiff karma
What's the question? what language is it?
“The solution to a system of equations is a point of intersection with the y-axis.”
dusky parrot
-x + 2 = -2x + 1
-x +2x = -2 + 1
x = -1
stiff karma
@dusky parrot
dusky parrot
<@1001754195986227280>
?
civic umbra
If it means the y coordinate of the solution of both of these equations, then 3
dusky parrot
y = 3
x = -1
Intersection Point is
(-1, 3)
the equation is not giving the y axis answer
but the x axis answer
and from the x axis we can get the y axis
stiff karma
system of equations is basically a function?
dusky parrot
wdym
stiff karma
What does it give us?
dusky parrot
-x + 2 = -2x + 1
-x +2x = -2 + 1
x = -1
.
civic umbra
There should be something wrong with the question. Maybe because of the translating in other another language??
dusky parrot
Can you send image of the whole question? @stiff karma
stiff karma
It’s basically not a question
I just want to understand what systems are
@dusky parrot
dusky parrot
ok so a system of equations is a collection of two (or more) equations that share the same variables the goal is to find a single set of values for those variables that makes every equation in the system true at the same time
stiff karma
ok so a system of equations is a collection of two (or more) equations that shar...
Give example
dusky parrot
ok
stiff karma
When I can create it into an systems
lunar sandal
hi guys
dusky parrot
ok
dusky parrot
so if we have
devout snowBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
stiff karma
y = x + 1
y = -x + 2
No…
lunar sandal
who do you guys watch on youtube that explains domains and ranges well pls
fossil locust
who do you guys watch on youtube that explains domains and ranges well pls
organic chemistry tutor
willow helm
who do you guys watch on youtube that explains domains and ranges well pls
This channel is already occupied
lunar sandal
idk if im overcomplicating it or my teacher didnt explain it well
ocean gale
!nosols
devout snowBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
lunar sandal
This channel is already occupied
wdym
stiff karma
!nosols
devout snowBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
lunar sandal
Nenni has already claimed it
i dont understand :ccc
willow helm
Open your own (#❓how-to-get-help) or #study-discussion for your specific question
fossil locust
i dont understand :ccc
if the channel doesn't have your name, it's not yours
stiff karma
i dont understand :ccc
Just leave?
dusky parrot
if we have a system like that:
y = -x + 2
y = -2x + 1
the x must be -1
because if we put it in the system equations we will get
1 + 2 = 3
and
2 + 1 = 3
dusky parrot
but the x cant be 1 because it will not fit in the system equations
stiff karma
if we have a system like that:
y = -x + 2
y = -2x + 1
the x must be -1
because ...
But like when do I use it
dusky parrot
But like when do I use it
you can use a system to get a y axis intersection
in a graph
stiff karma
you can use a system to get a y axis intersection
When?
Show me example when you use it
willow helm
But like when do I use it
Well, initially you will only be given problems where you have to explicitly solve systems
Otherwise you construct your own
stiff karma
And when you change it to system
willow helm
For all kinds of things
stiff karma
Otherwise you construct your own
Exactly so I wanna know how to make one
That’s the point
Don’t need to show me how to solve it cause I know
dusky parrot
ok
you need to first identify your unkowns
like x or anything else
or y
and define the relationships
and then assemble the system
civic umbra
For basics, what a system of equations represents: if you take two equations that have their own sets of solutions for each value of Y at X, and both equations are part of a system. Then the solution for the system of equations will be the intersection of both sets (solution of both equations).
stiff karma
.close
devout snowBOT
devout snowBOT
Available help channel!
minor junco
guys is dy²/dx² same as minimum and maximum?
devout snowBOT
guys is dy²/dx² same as minimum and maximum?
willow helm
guys is dy²/dx² same as minimum and maximum?
no
willow helm
guys is dy²/dx² same as minimum and maximum?
First of all, $\frac{d^2y}{dx^2}$ is the second derivative
woven radishBOT
USS-Enterprise
willow helm
d^2y, not dy^2
fossil locust
how do I get minimum and maxiumam in graphs?
first derivative = 0
fossil locust
so the 2nd why do I use it?
there's the second derivative test
the 2nd derivative tells you the concavity, so whether the function looks like a smiley face (+) or a frowny face (-)
minor junco
tysm
fossil locust
no worries!!
rustic jetty
Rewrite as an expression without a fraction $$\frac{\csc(x)}{1-\sin(x)}$$
woven radishBOT
dork9399
fossil locust
or i might js be blind
I think the idea is to multiply by 1 + sin(x) on top and bottom
fossil locust
that gives (csc+1)/cos^2
yes then I think they're just looking for (csc + 1) sec^2
devout snowBOT
keen wind
devout snowBOT
Available help channel!
lucid rock
doees anyone know how to apply lagrangian operators for solving a linear SVM using DUAL mode?
devout snowBOT
doees anyone know how to apply lagrangian operators for solving a linear SVM usi...
devout snowBOT
@lucid rock Has your question been resolved?
small inlet
<@&268886789983436800> is it concerning that this person's server tag is suspicious
lucid rock
<@&268886789983436800> is it concerning that this person's server tag is suspici...
isnt concerning that this chat is for asking for help and not tagging mods?
lucid rock
doees anyone know how to apply lagrangian operators for solving a linear SVM usi...
I understood a bit from this it is like you see relations between points or something
upper schooner
isnt concerning that this chat is for asking for help and not tagging mods?
Nonetheless, we do have to make sure that this server is appropriate, so may I ask you change the tag please 
lucid rock
Nonetheless, we do have to make sure that this server is appropriate, so may I a...
okay, that is fine, if you ask properly I will do it, but not on other other ways
upper schooner
okay, that is fine, if you ask properly I will do it, but not on other other way...
How do you mean "ask properly"? 
jagged heron
Can someone help me find the ARIMA of this ACP and PACF
devout snowBOT
Can someone help me find the ARIMA of this ACP and PACF
devout snowBOT
@jagged heron Has your question been resolved?
jagged heron
<@&286206848099549185>
devout snowBOT
@jagged heron Has your question been resolved?
jagged heron
nope
uncut crow
jagged heron
<a:sadcatpat:1153169273888444487>
i'll get the hang of this one day 
devout snowBOT
@jagged heron Has your question been resolved?
devout snowBOT
@jagged heron Has your question been resolved?
quiet jackal
Can someone explain for me why the underlined portion =0?
devout snowBOT
Can someone explain for me why the underlined portion =0?
quiet jackal
From what I can tell, the fourth term should be omega subscript y, is a typo
Never mind, was specified in the question that those commute to 0
.close
pseudo basin
have you done riemann sums before
severe prairie
devout snowBOT
fossil locust
do i deadass have to differentaite arsech(x+1/2)
yeah
this should be in your formula booklet though
fossil locust
do i deadass have to differentaite arsech(x+1/2)
actually, what's the previous part?
severe prairie
i found
this
sry
i think i got tha tpart
but i got another enquiry
for b
so like
im finding y(0) rn
and turned it into coshy(2)
and i moved it to e^x nd got 2+-sqrt3
but theyre both positive
so how dik which to pic
aa nm
nvm
the - gives a - ln
for a i got
coshy is (x+1/2)^-1
and sinhydy/dx is that
so like
how do i use that
is 1st derivative the coshy
devout snowBOT
@severe prairie Has your question been resolved?
severe prairie
<@&286206848099549185>
sm1 please help me
im deadass tweaking
how do i find y’(0)
steel sage
x+1/2=sech(y)
derivative both sides
1=sech’(y) y’(x)
steel sage
Yeah, you said you wanted y’(0), now you have it
devout snowBOT
@severe prairie Has your question been resolved?
severe prairie
Yeah, you said you wanted y’(0), now you have it
wha
severe prairie
how do i have it
steel sage
y’(x)=1/sech’(y(x))
devout snowBOT
@severe prairie Has your question been resolved?
lost laurel
This notation is kind of confusing me
devout snowBOT
This notation is kind of confusing me
lost laurel
$\mathcal{O}= \mathcal{O_{\Q(\sqrt{D})}}$?
woven radishBOT
wai
stone stump
so much for one more problem
fast garden
just your ring of integers of Q(\sqrt D) and they wanted to write it shorthand as \mathcal O
fierce matrix
devout snowBOT
fierce matrix
∀A,(x:1→A,f:A→A)
⇒ ∃! h:N→A s.t. h∘o=x ∧ h∘s=f∘h.
A=N′
⇒ h:N→N′, symmetric k:N′→N.
unicity
⇒ k∘h=id_N ∧ h∘k=id_N′ ⇒ iso
tribal void
In statistics and probability, why are proofs and definitions often multiple equalities at once? Should I read it as "these are all basically the same" or should I read it as a left to right break down of reducing the equation? Example is attached.
devout snowBOT
In statistics and probability, why are proofs and definitions often multiple equ...
vital edge
In this specific case, the idea is that it's symmetric
A ∩ B is the same as B ∩ A
So the order doesn't matter
rain summit
!done
devout snowBOT
If you are done with this channel, please mark your problem as solved by typing .close
tribal void
.close
devout glen
hey need some help on this problem!
devout snowBOT
hey need some help on this problem!
devout glen
for finding the derivative? i understand you make the exponent 1/2
but would it look like
$\frac{2h^(1/2)}{|g|}$
woven radishBOT
evan
sand quarry
No, it would not be
devout glen
oh gosh it looks bad
sand quarry
the square root applies for the entire term
devout glen
ohh okay
sand quarry
with what you wrote, you are only applying it to the h variable
sand quarry
,, T(h) = \3{\4{2h}{\abs g}} = \8{\4{2h}{\abs g}}^{1/2}
woven radishBOT
sand quarry
no
celest frigate
Separate the constants
devout glen
how so
sand quarry
use the property [
\3{ab} = \3a\2\3b
]
woven radishBOT
devout glen
sorry! how do i do that
sand quarry
in [
\8{\4{\0b2h}{\0b{\abs g}}}^{1/2}
]
you can notice that the highlighted terms are constants, yes?
woven radishBOT
devout glen
ok yeah
sand quarry
your goal is to separate the square root into two, using this identity, such that the constants are all in one square root and the variable, h, is in the other
woven radishBOT
evan
devout glen
oh yess i got it
sand quarry
$\frac{2^{1/2}}{|g|^{1/2}} * h^{1/2}$
yes!
nailed it
so
what is [
\dv x(a\3x)
]
where $a$ is a constant
slate peak
**evan**
^^ if you want, you can combine the square roots for the constant term (not necessary)
woven radishBOT
devout glen
wouldnt i use chain rule or something?
sand quarry
you would not
devout glen
idk! sorry
pseudo basin
wouldnt i use chain rule or something?
only if you're a real bourbakist
which is to say, no
devout glen
lmao!
pseudo basin
if you know how to differentiate 5x^3 then you also know this one
sand quarry
use the property of derivatives where [
\dv x (af(x)) =a\2\dv x(f(x))
]
woven radishBOT
devout glen
well 5x^3 is 15x^2
sand quarry
where, again, a is a constant
pseudo basin
well 5x^3 is 15x^2
not "is", "becomes"
devout glen
oh yeah
devout glen
ohhh
pseudo basin
constant multipliers stay intact always
devout glen
so i would do the f'(x)g(x) + f(x)g'(x) formula
pseudo basin
read what lex said, read what i said...
devout glen
would it turn into
$\frac{1^{\frac{-1}{2}}}{|\frac{1}{2}g|^{\frac{-1}{2}}} * \frac{1}{2}h^{\frac{-1}{2}}$
fiery cape
so i would do the f'(x)g(x) + f(x)g'(x) formula
It's the constants you're having a problem with. For example, What would be the derivative of $\sqrt(2x)$?
mystic scarab
$\frac{1^{\frac{-1}{2}}}{|\frac{1}{2}g|^{\frac{-1}{2}}} * \frac{1}{2}h^{\frac{-1...
For starter, what's the derivative of √x ?
devout glen
It's the constants you're having a problem with. For example, What would be the ...
$1x^{-\frac{1}{2}}$
woven radishBOT
evan
devout glen
For starter, what's the derivative of √x ?
umm 1/2x^-1/2
mystic scarab
By using this
faint zinc
$\dv{x}(\sqrt{x}) = \frac{1}{2 \sqrt{x}}$
woven radishBOT
OmnipotentEntity
faint zinc
for clarity
faint zinc
im soo sorry, im not processing it
the derivative?
devout glen
no like how would i use that for my problem?
im truly so lost in this class, so for some formulas imma need some extra assistance 😭
faint zinc
\begin{align*}
\qty(\frac{2h}{|g|})^{1/2} &= \qty(\frac{2}{|g|})^{1/2} \sqrt{h} \
&= a \sqrt{h}
\end{align*}
woven radishBOT
OmnipotentEntity
devout glen
how come h turned into a square root?
faint zinc
\begin{align*}
\qty(\frac{2h}{|g|})^{1/2} &= \qty(\frac{2}{|g|} h)^{1/2} \
&= \qty(\frac{2}{|g|})^{1/2} h^{1/2} \
&= \qty(\frac{2}{|g|})^{1/2} \sqrt{h} \
\end{align*}
woven radishBOT
OmnipotentEntity
faint zinc
@devout glen does the above make sense?
devout glen
ohh
ok
ohhh wait, i didnt know equations to the power of one half become square root
okay i now know that
thank you!
faint zinc
you're welcome!
devout glen
ok how do i go forward
fiery cape
Do you see why g is treated as a constant and so you don't have to use the product rule or anything with it?
sand pumice
ohhh wait, i didnt know equations to the power of one half become square root
might be useful: x^(1/n) is the nth root of x
faint zinc
ok how do i go forward
so you know everything you need to know to solve the first part.
devout glen
Do you see why g is treated as a constant and so you don't have to use the produ...
is it because its an absoolute value
faint zinc
can you walk me through it?
devout glen
the first part?
faint zinc
is it because its an absoolute value
no, because it is constant
devout glen
ohh mkay like 2?
faint zinc
part A. Find the derivative of T(h), T'(h).
faint zinc
ohh mkay like 2?
as in, g doesn't vary, it's just a number, it could be any number, but we fix it and say it doesn't change.
devout glen
ok
fiery cape
as in, g doesn't vary, it's just a number, it could be any number, but we fix it...
Specifically because T is a function of h, T(h). g will stay the same no matter what h you choose, so it's basically just a number as Omni says
devout glen
okay so from square root 2h over |g|, it becomes 2h over |g| to the power of 1/2, i take out constantsnand im left w/
$\frac{2^{1/2}}{|g|^{1/2}} * \sqrt{h}$
woven radishBOT
evan
devout glen
yeah?
fiery cape
looks good
mystic scarab
This is only the original function, isn't it?
You still need to find the derivative
devout glen
oh okay
do i use power rule for everything? or like quotient rule for the fraction and power rule for h?
devout glen
You can take it out
like cross it out completely?
then im just left with
$\frac{1}{2}h^{-\frac{1}{2}}$?
woven radishBOT
evan
fiery cape
**evan**
Yes, that is how you differentiate the h part, but the constant part is still multiplied to that. For example, think about differentiating 3x^2. You don't just get rid of the 3, it stays multiplied to the derivative of x^2, i.e. 3 * (2x) = 6x.
In other words, the derivative of a constant c multiplied by function of x f(x) is just c multiplied by the derivative of that function
$\dv x (af(x)) =a\2\dv x(f(x))$
woven radishBOT
Weaboo Jones
$\dv x (af(x)) =a\2\dv x(f(x))$
```Compilation error:```! Undefined control sequence.
l.49 $\dv x (af(x)) =a\2
\dv x(f(x))$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.
Preview: Tightpage -1310720 -1310720 1310720 1310720
[1{/usr/local/texlive/2023/texmf-var/fonts/map/pdftex/updmap/pdftex.map}{/usr/l```
devout glen
**Weaboo Jones**
```latex
$\dv x (af(x)) =a\2\dv x(f(x))$
```Compilation error:`...
like i dont understand im sorry! could you explain how my equation correlates to this?
fiery cape
Yeah the formatting is a little weird
devout glen
like how would i know to use this formula?
fiery cape
**evan**
Multiply that to the fraction here, the 2 over g part
I'll clear it up in a second
devout glen
$\frac{1^{-\frac{1}{2}}}{\frac{1}{2}|g|^{-\frac{1}{2}}}$
woven radishBOT
evan
devout glen
?
toxic rain
Can sm reply to the og question?
fiery cape
toxic rain
hey need some help on this problem!
.
devout glen
ok yeah
fiery cape
The left part (2/g) is a constant, and the right is a dependent on h
So the derivative looks like this
Because the derivative of a constant times a function of h is just the constant times the derivative of that function of h
devout glen
oh? okay so i just put a variable for the fraction?
fiery cape
Now you can replace c with what it was originally
I used c just to clarify that its a constant part
devout glen
**evan**
so how is that any different some this tho? instead but with h differentiated?
fiery cape
This is your final answer. And yes, its different because the h part is differentiated
devout glen
$\frac{2^{1/2}}{|g|^{1/2}} * \frac{1}{2}h^{-\frac{1}{2}} $
ohh okay
thank you
and i could just leave it like that?
fiery cape
You could make it a bit nicer just with some algebra
devout glen
how so
fiery cape
For example, switch the ^1/2 back to square roots
Put the 1/2 in front of the equation instead of just before the h
I dont think its necessary though, since you arent really using the equation for the rest of the problem
Aside from plugging numbers in for h
devout glen
ohh ok
devout glen
hey need some help on this problem!
omg that took more than an hour, ok for b, is it meters over seconds multiplied by height?
fiery cape
First of all, what are the units of T?
devout glen
seconds
fiery cape
And what happens to the units when you differentiate with respect to some other unit?
For example, if I take a displacement (in meters), and differentiate with respect to time (in seconds), what are the units then?
devout glen
im sorry i have no idea
lilac moat
im sorry i have no idea
think about the definition of derivative
$$\dfrac{\mathrm dy}{\mathrm dx} = \lim_{\Delta x \to 0}\frac{\Delta y}{\Delta x}$$
devout glen
instant slope
woven radishBOT
gfauxpas
lilac moat
seen this before?
devout glen
umm im pretty sure but i cant explain it to you
lilac moat
$$\frac{\Delta y}{\Delta x}$$ is slope
woven radishBOT
gfauxpas
lilac moat
rise/run
when you look at it instantaneously, it still has the same units
the units of slope
devout glen
okay im sorry, this has gone a lot longer than i expected and i still need to study for my other exam, ill have to come back for this questin
okay yeah slope
fiery cape
im sorry i have no idea
Basically, if if you take a function in one unit, and differentiate it by another, you "divide" them. I.e., meters differentiated by time becomes meters/seconds
devout glen
oh okay so its meters over seconds?
fiery cape
The reverse, because our original unit is time, and its being differentiated by h which is in meters
So seconds/meters
devout snowBOT
devout snowBOT
Available help channel!
fading sundial
I have $$\lim_{n \to \infty} (\frac{n^2}{\sqrt{n^3 + 4n}})$$ and I want someone to check my work
devout snowBOT
I have $$\lim_{n \to \infty} (\frac{n^2}{\sqrt{n^3 + 4n}})$$ and I want someone ...
woven radishBOT
leo
ionic harness
Looks good to me, I know some textbooks would have 1/0 as lim = infinity and some use 1/0 as lim = DNE
tender cobalt
I have $$\lim_{n \to \infty} (\frac{n^2}{\sqrt{n^3 + 4n}})$$ and I want someone ...
does your class do $\lim_{n\to\infty}n=\infty$ or $\lim_{n\to\infty}n$ DNE
woven radishBOT
mtt
crimson tundra
exact
fading sundial
**mtt**
they sometimes use both 🥲
thanks guys :) i think the more correct answer should be infinity though so ill use that instead
.close
devout snowBOT
devout snowBOT
Available help channel!
quartz nova
Can someone check my work
devout snowBOT
Can someone check my work
deep abyss
Ques?
quartz nova
solving for lambda and theta
in terms of x and y
i didnt plug in a and h for the sake of simplicity/neatness
devout snowBOT
@quartz nova Has your question been resolved?
mint cairn
Where is the original question?
quartz nova
I mean ill just try to recite it to the best of my ability. Its an inverse kinematics question if it helps. You have limbs l1, l2, l3 that are lengths 79, 25, 77, respectively. L1 is anchored to (0,0) and the end effector is at point (x,y). You know that l3 and l2 are at a fixed 90 degree angle. Find the angle between l1 and the "floor" (x axis) and the angle between l1 and l2 - 90 degrees
@mint cairn
mint cairn
well its my diagram
Oh, so it's worded.
mint cairn
Okay.
quartz nova
Ye it isnt
mint cairn
Sorry.
quartz nova
hmm?
mint cairn
I just saw the l3...
mint cairn
Let me visualise it myself then.
mint cairn
So.
l2 and l3 are perpendicular to each other...
At where?
The end effector of l1?
quartz nova
So they're all connect at the ends of the limbs
l1 connects to l2 which connects to l3
basically image a line segment that has 2 points on it
that divide it into 77 25 and 79
segments
each of those points allow the segments to rotate
but you know that 77 (l3) and 25 (l2) "joint" is fixed at 90 degrees
sorry for the poor wording
from memory so
mint cairn
So basically it should look like this right?
l1 touches (0,0)
l2 touches end of l1 with length 25.
And l3 joins perpendicularly at the end of l2 with length 79.
mint cairn
Oh typo.
It is 77.
My brain.
So what are we solving for again?
Angle between l1 and x axis.
quartz nova
2 things
angle between l1 and x axis
and angle between l1 and l2
subtract 90 degrees
mint cairn
subtract 90 degrees
Oddly specific...
quartz nova
uhh ye it is
its like the problem isnt exactly that
but like it boils down to that
mint cairn
angle between l1 and x axis
In terms of x and y you said?
quartz nova
Yes
mint cairn
Like this?
quartz nova
Umm yes assuming that that point is 77 away from the l2l3 joint
mint cairn
Umm yes assuming that that point is 77 away from the l2l3 joint
It is.
I hide the circles to make it less confusing.
Okay.
Let me try now.
quartz nova
ight
devout snowBOT
@quartz nova Has your question been resolved?
mint cairn
Alright...
I actually don't think you can express it in terms of x and y only...
Like the whole system is not even unique...
mint cairn
https://www.desmos.com/calculator/bl9ja0j3rd
I'll share this graph here.
Hope it helps.
quartz nova
Ok thx
devout snowBOT
devout snowBOT
Available help channel!
cerulean violet
Can someone help with this?
devout snowBOT
Can someone help with this?
cerulean violet
I just can't figure out how to solve from the very starting, I can only find out the general term
rough nova
With this kind of problem, you want the "coefficients" (n²+1) to be expressed in terms of (n-1) and (n+1) so that the adjacent terms cancel each other out
Can you do that?
devout snowBOT
Available help channel!
agile garnet
im tryna plot thomae function
devout snowBOT
im tryna plot thomae function
sand pumice
so now i wanna understand the graph
would KIND of look like this
devout snowBOT
devout snowBOT
Available help channel!
agile owl
Any hint for 59
devout snowBOT
Any hint for 59
agile owl
cold haven
,rccw
woven radishBOT
cold haven
!status
devout snowBOT
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
dense raft
l
devout snowBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
cold haven
Any hint for 59
Integration by parts with 𝑢 = log(𝑥² + 2) and 𝑑𝑣 = 1/(𝑥+2)² seems good here. 
agile owl
Integration by parts with 𝑢 = log(𝑥² + 2) and 𝑑𝑣 = 1/(𝑥+2)² seems good here...
I so hate integration by parts
Is it rlly the only option
😢
cold haven
IBP is not the only option, but any other effective method is really equivalent to IBP or more cumbersome…
@agile owl
cold haven
warped beacon
How do I find the probability of something not happening?
My question is if there are 5 white marbles and 20 non white marbles, what are the chances of pulling at least 1 white marble when picking 5 randomly.
I know that I need to find the probability of finding no white marbles and then reverse it, but I’ve forgotten how to do that.
So far all I’ve done was make a combination of (25, 5) to get a total of 53,130.
lilac crescent
How do I find the probability of something not happening
i mean if its not happening , then its probability is 0
||didnt read the rest of the question||
rare kernel
How do I find the probability of something not happening?
My question is if th...
atleast 1 = 1 - probability of picking 0
warped beacon
Yee
urban harbor
How do I find the probability of something not happening?
My question is if th...
youre right, you could think of the probability of finding no white marbles:
e.g. for first one it would be 15/20, then 14/19 etc. and multiply those 5 quantities together
that gets you probability of no white marbles, then you could do 1 - that
onyx torrent
How do I find the probability of something not happening?
My question is if th...
you would need to find the probablity of picking 5 non white balls that would be the probability of not picking a white ball
warped beacon
youre right, you could think of the probability of finding no white marbles:
e.g...
I thought there was a formula for this?
If not that’s fine, I’ve been overthinking it a lot
urban harbor
well its easier to see where the formula comes from when you do the multiplications together, yes you can write it in terms of some factorials
but those fractions make immediate intuitive sense right? see if you can write out the multiplications and consider how you'd write it in terms of factorials for the general case
warped beacon
Yee
rare kernel
I thought there was a formula for this?
yes there is
x=number of successes
n=number of attempts
and p = probability of success
warped beacon
but those fractions make immediate intuitive sense right? see if you can write o...
Oh so it’s 15/20, 14/19, 13/18, 12/17, 11/16 because every time I take one out, the total decreases along with the ones that I want to pull out
warped beacon
yes there is
Is there an easier way to look at this 
I don’t recognize it at all either…
rare kernel
ok take 1-p = q where q is probability of failure
then the expression that u see there is
general term of (p+q)^n
if u know binomial theorem
warped beacon
I don’t think I do
daring mesa
The formula... well, it seems overkill for the problem we're asking to solve.
warped beacon
Do you know of a simpler option 
daring mesa
We're trying to find the probability we pull at least one white marble, right? As you noted, it's probably easier to relate this with another probability, that being that we pull no white marbles.
warped beacon
Yee 
daring mesa
How would we calculate that second probability? How would that help us find the probability we're asking for?
warped beacon
Well it would be the probability of finding no white marbles -1
Or
1-no white marbles
And then we would have the probability of at least 1
I just don’t know how to find the probability of no white marbles
daring mesa
Is there a combinatorical way we could think about finding that probability? That is, can we count the number of 'favored outcomes' vs. the number of 'total outcomes'?
warped beacon
Well I know the total outcomes are 53,130
But I’m yet to find out the number of favored outcomes
daring mesa
How did we compute the number of total outcomes? Why so?
warped beacon
Combination of (25,5)
And I did it because I knew I’d have to compare total outcomes to desired outcomes
daring mesa
What does a favored outcome look like?
warped beacon
No white marbles
daring mesa
If we have no white marbles, then what else would be true for any given outcome?
warped beacon
All non white marbles.
I’m sorry but is this going anywhere?
daring mesa
Yes. How many ways can we pick all non-white marbles? (It'll be similar to the way we computed the ways we can pick any kind of marbles)
warped beacon
Ok I feel like you’re hinting at a combination but it’s not clicking in my head how that’ll work
There’s no way it’s just (20,5) right???
daring mesa
Why not? We have 20 black marbles, and we're picking 5 black marbles from them, right?
daring mesa
I suspect you have a good path from here 
strong cypress
I suspect you have a good path from here <:catthumbsup:614540188747563008>
Can I ask a question abt derivatives :p
ionic harness
!occupied
devout snowBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
strong cypress
Oh sorry
warped beacon
So if I’m doing this correctly, the probability of finding at least one white marble is 37626/53130
ionic harness
,calc 37626/33130
woven radishBOT
Result:
1.1357078176879
dull parrot
So if I’m doing this correctly, the probability of finding at least one white ma...
how did you get that?
also since it's greater then 1, the probability doesn't make sense
ionic harness
,calc 37626/53130
woven radishBOT
Result:
0.7081874647092
I have edited it
ionic harness
Yep that's what I got too
Probability of choosing at least 1 white marble when picking 5 randomly =
probability of choosing 1 white marble on the first + prob of choosing 1 white marble on the second (and non white on the first) + prob of choosing 1 white marble on the 3rd (and non white on the first and second) + ...
= 5/25 + (20/25)(5/24) + (20/25)(19/24)(5/23) + (20/25)(19/24)(18/23)(5/22) + (20/25)(19/24)(18/23)(17/22)(5/21)
= 0.7082
devout snowBOT
rare kernel
,calc 1-(4/5)^5
woven radishBOT
Result:
0.67232
huh
rare kernel
Is there an easier way to look at this <:JockSweat:892406076656484362>
hey sorry but u cant use this formula here anyway cause the probability changes after each draw
my bad
knotty salmon
@rare kernel If your question have been resolved please close this channel
rare kernel
<@728482160927047742> If your question have been resolved please close this chan...
this is not my question and the channel is already closed
knotty salmon
it says it's occupied
rare kernel
^
knotty salmon
well I think I'm stupid
devout snowBOT
Available help channel!
lilac briar
.help
devout snowBOT
Commands:
- clopen:
.close,.reopen - factoids:
.tag - help:
.help - version:
.version
Type .help <command name> for more info on a command.
lilac briar
.help math
devout snowBOT
No command called "math" found.
granite bough
hello
granite bough
i dont understand vectors
i am learning about vector spaces
and how you can express a vector in different basis
in a vector space i need a basis to reach all the points in the space
olive snow
in a vector space i need a basis to reach all the points in the space
Indeed
olive snow
and how you can express a vector in different basis
Depends what the basis are
granite bough
but then i can look at some other vector outside that basis, and i can see how i have to manipulate the vectors that make up the basis to reach that other vector
olive snow
Mostly computing
granite bough
is that what people mean by change of basis, im so very confused about this
im talking about the same vector but expressing it in different ways
olive snow
but then i can look at some other vector outside that basis, and i can see how i...
Not sure to understand correcrly, yes reaching a vector that is in the space is the purpose of having a basis and you just express any vector as a linear combination of the basis vectors
granite bough
one way is just the "standard basis" way of just saying, oh, that's (1,0)
and another one might be
"oh, i need 1 of this vector x and -1 of this vector y to reach that same point"
and that basis would be like [x,y]_(name of basis) or something
idk what the notation is
granite bough
also what is a kernel, someone explained it to me as it being the space where things have been turned to the 0 vector
or are the 0 vector?
so if someone gives me this equation x + y + z = 0, then is (1,1,0) a part of its kernel?
sry i meant
(1,-1,0)
olive snow
Given a linear application f, the set of vectors v such that f(v) = 0
Thats what ker(f) is
{v \in vector space, f(v) = 0}
granite bough
and f(v) means i feed the function f a vector v
like could my f be x + y + z = 0
or am i misunderstanding what f is
olive snow
so if someone gives me this equation x + y + z = 0, then is (1,1,0) a part of it...
You have to say f : R³ -> R such that f(x,y,z) = x+y+z and then yes
granite bough
ah okay, and then when i feed f(x,y,z) the vector v=(1,-1,0), then it is part of the kernel because f(v)=0?
granite bough
ah okay, and then when i feed f(x,y,z) the vector v=(1,-1,0), then it is part of...
sry if this isnt quite right, but can someone explain what is so special about being part of the kernel
why do i care about the guys who got turned to 0
olive snow
ah okay, and then when i feed f(x,y,z) the vector v=(1,-1,0), then it is part of...
Exactly
olive snow
why do i care about the guys who got turned to 0
Good question
granite bough
im very happy with how you have explained it so far i didnt understand for sure that this is what the kernel was
granite bough
but yeah i dont understand the significance of the kernel yet
damn i forgot what injective means
olive snow
but yeah i dont understand the significance of the kernel yet
Its the set of vector such that their image by f is 0
ionic harness
Since when did we learn math because it was significant 🏃♂️ I think once I reached university all the significance went out the window
granite bough
and f is a function/linear transformation/square matrix?
olive snow
Linear transformation
granite bough
so if a linear transformation turns something into the 0 vector it is part of the kernel, how is this useful for problem solving i dont quite understand
im terrible at problem solving so im probably missing something obvious
granite bough
so if a linear transformation turns something into the 0 vector it is part of th...
sorry if this is not rigorous enough also
olive snow
If ker(f) is reduced to {0} then f is injective
It turns out that if the starting set of f has a finite dimension then f is bijective
ionic harness
so if a linear transformation turns something into the 0 vector it is part of th...
Tells us a lot of things about the characteristics of f, like injectivity but also the dimensions of its column space and null space (and the basis for the nullspace if we know exactly what is in the kernel), etc.
granite bough
is injective that the input leads to one output, and bijective that the input leads to one output, and the output leads to one input?
wicked rover
injective = different inputs have different outputs
granite bough
ah im sorry i will revise
on what injective and bijective means later
and what it means
and relates to this
but
if im given just a vector, any vector some vector v
is it expressed in a basis
or not
like, do i have to define some vector space
before i can say i am expressing it in a basis
or rather do i have to define a basis
wicked rover
talking about a vector assumes you already have a vector space in mind
granite bough
talking about a vector assumes you already have a vector space in mind
right okay
that makes sense
someone told me otherwise so that confused me
and if not explicitly written, i assume the basis is the standard basis?
wicked rover
but you can talk about a vector space without knowing a basis
granite bough
but you can talk about a vector space without knowing a basis
or this maybe
maybe i just dont know the basis okay
there has to be a basis otherwise talking about my vector wouldnt make any sense
wicked rover
the set of functions from an interval to R is a vector space without an easily describable basis
granite bough
okay, but there could be/is definitely a basis for it
even if it isnt easily describable
wicked rover
every vector space has a basis if you accept axiom of choice
granite bough
okay i had to google that
but i can definitely accept that!
:)))
hmmm
do i dare ask what span is
like if im in R^3
and i have 3 vectors linearly independent of one another
and make a base that way
they are linear too
then, that's a basis
wicked rover
knowing what basis means requires you to know what span means
granite bough
oh no uhm
yeah i definitely dont know what span is but i feel like i know what a basis is
to some degree
what is a span
do i have a span of a vector or span of a vector space
or span of a basis
wicked rover
how do you define basis if you dont know what span means?
granite bough
i am not rigorous so i cant describe how i define it, i think of it as 3 linearly independent whatzadootzitzs, meaning if scaled or added to one another, they cant create one another, and if i have 3 or 4 of these whatzadootzits they can reach all the points in some space of certain dimensions
i feel like the basis is like a weird handle
and you can find a bunch of different basis
by just grabbing that handle
and twisting it
wicked rover
"reach all points" is close to the idea of span. have you heard of how to formalize that?
granite bough
even if the handle is four dimensional or in some abstract polynomial space
granite bough
"reach all points" is close to the idea of span. have you heard of how to formal...
maybe, i think i have seen someone write c_1v_1 + c_2v_2 + .... but i dont remember
c would be the ting that scales the vector
and the yeah you just add some arbitrary amount of them
and depending on what c you choose and as long as the vectors arent parallell to eachother
you can reach some point in your more or less abstract space
sorry yeah no i have no clue how to formalize it
and i dont even know if im thinking of it right but i hope so
i definitely dont know what a span is though like
like maybe i have a vector named "Bridge"
in the English basis
but in the Swedish basis maybe it is called "Brygga"
but idk what span is
wicked rover
lets say we know some vectors $v_1,\dots,v_n$. we define a linear combination of these vectors to be another vector of the form $c_1v_1+\dots+c_nv_n$ where $c_1,\dots,c_n$ are some scalars
granite bough
sorry does it say and are a linear combination of those vectors?
sorry i dont understand the text you wrote :(((
woven radishBOT
ロケット・ジャンプ
wicked rover
does that help
granite bough
okay yeah and a linear combination is just like alpha v_1 + beta v_2 and so on?
and yeah i think that helped
thank you!
wicked rover
now there are two slightly different usages of the word span. heres the first
the span of vectors $v_1,\dots,v_n$ is denoted $\Span(v_1,\dots,v_n)$. we define it as the set of ALL linear combinations of $v_1,\dots,v_n$
woven radishBOT
ロケット・ジャンプ
wicked rover
heres the second
granite bough
is this what it is meant with linear combination: $c_1v_1+\dots+c_nv_n$?
woven radishBOT
Neo
wicked rover
yes but we must take ALL linear combinations to get the span
granite bough
yeah yeah, and the one i asked about is just one linear combination
so there might be a different linear combination but it is like $c_(11)v_(11)+\dots+c_nv_n$
oops
woven radishBOT
Neo
granite bough
eww
yeah idk how to use that
im trying to jus tname them something else XD
but not just 2, because i get 2 will be the next one in that same linear combination
wicked rover
taking ALL linear combinations means varying all the scalars and collecting the combinations they produce
granite bough
like i can scale a vector by SOMETHING, add it to another one that is also scaled by SOMETHING, but i could also do that same process, but just scaled by SOMETHING different
and then it would be different linear combinations
then i take all those different linear combinations
okay so upon collecting them
is that when i reach all the points, or is it greater than that, and not only do i reach all the poitns in my space, i also reach all of the points in all of the ways i can reach them?
wicked rover
the span may or may not equal the whole vector space
granite bough
hmm okay that doesnt make sense to me i would have definitiely guessed it equalled all of it
wicked rover
that leads me to the second usage of the word span
we say that vectors $v_1,\dots,v_n$ span a space $V$ if $V=\Span(v_1,\dots,v_n)$
woven radishBOT
ロケット・ジャンプ
granite bough
damn i feel like im not following it
wicked rover
the first usage of span is as a noun, the second usage as a verb
granite bough
because i feel like if we have all the ways we can reach a point in a space
then there is nothing else to say, like it would just be every way to reach every point and it would be reaching every point
so i think im misunderstanding
wicked rover
not every set of vectors will span your vector space
easy example, let v=(1,0). does it span R^2?
granite bough
okay so say c_1 = 1 and c_2=1, all the other c = 0, then i dont span the entire space
i just span... what?
v_1 and v_2?
can i say that? idk
im sorry :<
wicked rover
i only gave u one vector v
granite bough
oh sorry let me look at ur example
wicked rover
so its span is the set of all cv, c is a scalar
granite bough
i was trying to come with an example of my own sry
let me read it
okay so c=1 for v, and all the other c equal 0?
in that case i think i would say it does not span R^2
or is it important that c may vary
if i let c vary it can reach a line
but not R^2
but now i feel like im talking about a basis again and not a span
but then again i dont know what a span is
cv=(c,0), then (c,0) can reach every point along a line if c is a member of the real numbers
like every point along the x axis if we are working in the standard basis
but does that mean it spans the x-axis?
im sorry ty for the help but i have to go my campus is closing in 10 minutes
wicked rover
i have to go too
granite bough
and merry christmas to you and also happy new year if i dont get to message you again before then
wicked rover
ur right that v spans the x axis but not R^2
wicked rover
so thats an easy example of not spanning our vector space
granite bough
yes that helps
i still have some confusion but that is actually very good for me
now i understand much more thank you
wicked rover
np glad it helped, have a good day
devout snowBOT
devout snowBOT
Available help channel!
visual stone
devout snowBOT
visual stone
how can i find the norm of this vector
acoustic leaf
can you give more context?
visual stone
can you give more context?
the orientation of the vector 400 N is 34 degree
and the orientaiton of that ? vector is 28
acoustic leaf
is there any relationship between them?
visual stone
whats a relationship
acoustic leaf
like anything connecting them
because it seems like you just have two random vectors next to each other right now
visual stone
well it said the vector with 400 N has an angle of 34
and it said that ? vector has an orientation of 28
so i thought 34 was the orientation of that vector so i put it on top of it
hardy trail
so i thought 34 was the orientation of that vector so i put it on top of it
Well yeah, that works out for the angles - but there's nothing here that allows us to figure out what the length of the ? vector.
So that's why we need some additional context.
visual stone
Well yeah, that works out for the angles - but there's nothing here that allows ...
hey again
hm
visual stone
if i can remember
it said that angle for 400 N was 34
with no other thing explaining it then it said one angle has a orientation of 28
and it told me to find the norm of that vector with an orientation of 28
visual stone
oh alright
hardy trail
If you're basing this off memory, I can only assume that you got this problem in class or during an exam. Might want to ask your teacher for some clarification on that problem.
visual stone
im trying to remember
visual stone
If you're basing this off memory, I can only assume that you got this problem in...
i forgot my document
hardy trail
oof
visual stone
that i was working on but that number i understood 0
hardy trail
Maybe you could ask a classmate if they have a copy?
Idk perhaps if you get the original context, that might help you solve the problem lol
visual stone
Maybe you could ask a classmate if they have a copy?
they dont know either
hardy trail
Rip
visual stone
it said Adam throws a ball at beatrice with (35,20) components
then it said Beatrice throws one to Charles with (8,-3) components
then Charles throws to Diana (-40,-20)
find the norm of the vector of Diana to Adam
hardy trail
Hmmm, well - what are your thoughts on this problem so far?
visual stone
well i know where the vectors are in which quadrant
like adam to beatrice is in the 1st quadrant beatrice to charles is in the 4th and charles to diana is in the 3rd
so adam to beatrice is AB
hardy trail
like adam to beatrice is in the 1st quadrant beatrice to charles is in the 4th a...
Okay, not too bad.
visual stone
i thought that AB + BC + CD = DA
but wheni drew it
it didnt lok like that
ill show you why
ill draw it again
hardy trail
Indeed, it does look a little strange.
What do you think AB + BC + CD is equal to then?
hardy trail
Hmm well, out of curiousity,
If you just drew the vectors AB + BC + CD, what would that look like?
visual stone
a paralelogram
hardy trail
Hmm, well, draw it for me :)
visual stone
Hmm, well, draw it for me :)
like properly?
hardy trail
Yep.
hardy trail
Like what you did here.
visual stone
the thing is i dont know how to draw this
hardy trail
Wait,