im really stuck on part i
#help-26
silent vine
topaz sinewBOT
im really stuck on part i
silent vine
(rn im trying to prove if A, B in R(S), then A \ B in R(S)
Let $S$ be a semiring of sets, and let
[
L = \bigsqcup_{j=1}^{r} B_j,
\qquad
M = \bigsqcup_{n=1}^{m} C_n,
]
where each $B_j, C_n \in S$.
Then
[
L \setminus M
= \left( \bigsqcup_{j=1}^{r} B_j \right)
\setminus
\left( \bigsqcup_{n=1}^{m} C_n \right)
= \bigcap_{n=1}^{m}
\left(
\bigsqcup_{j=1}^{r} (B_j \setminus C_n)
\right).
]
Since $S$ is a semiring, for each $j,n$ there exist finitely many disjoint sets
$D_{j,n,1}, \dots, D_{j,n,K_{j,n}} \in S$
such that
[
B_j \setminus C_n
= \bigsqcup_{k=1}^{K_{j,n}} D_{j,n,k}.
]
Hence
[
L \setminus M
= \bigcap_{n=1}^{m}
\left(
\bigcup_{j=1}^{r}
\bigsqcup_{k=1}^{K_{j,n}} D_{j,n,k}
\right).
]
thorny flameBOT
ashyboi
grim pike
Note that we have $E_{j,n} : = \bigsqcup_{k=1}^{K_{j,n}} D_{j,n,k} \in R(S)$ for each $j,n$. Try showing that these sets $E_{j,n}$ are disjoint.
thorny flameBOT
ucheo
topaz sinewBOT
Available help channel!
wraith sparrow
Hiii although it's not math, but it's just basic physics that i hope anyone can help me :(((((((
for this question, the trouble i faced are
- why Vx is same with 25V when their terminal is opposite
- I know that the current should be the same in series circuit but why the dependent current source is +15A at last :((((((( ( the arrow is opposite against the independent current source right ? )
- May i know what is the final flow of the whole circuit, and how do yall know it ?
Hope anyone can help me with dis :((, thank you
topaz sinewBOT
Hiii although it's not math, but it's just basic physics that i hope anyone can ...
loud oasis
vx = -25 V due to the opposite voltage directions
wraith sparrow
if it's -25V, then
avx = -15A ?
a(-25) = -15
a = 0.6
is it like this ?
<@&286206848099549185>
awwwww :((((
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
topaz sinewBOT
drifting swift
ok yeah so that's two matrices
pearl bridge
the question is supposed to be system of linear equation by inverse method
and after we got all the minors
he decided to change their signs
why did he do that
eternal sierra
he didnt change ALL the signs
drifting swift
mmm can you post the full context/video
drifting swift
ok right so
we're constructing adj(A), which i think this guy is denoting with C
the idea is A adj(A) = det(A)I
det(A) = sum_j a_ij C_ij = a_ij (-1)^(i+j) M_ij
am i making sense here
pearl bridge
the detrinemtn of a?
drifting swift
ouch spelling
pearl bridge
he already got it as 10
drifting swift
yes but the point is not what number det(A) is but how it is gotten
it has that sign alternation pattern yeah?
like you add each entry times its corresponding minor but you put the signs as + - in a chessboard pattern based on where it is in the original matrix
it's kind of tricky to explain bc there's a lot of moving parts in here
pearl bridge
yes but the point is not what number det(A) is but how it is gotten
this doesnt make sense. i know how detriment a was gotten nd it was explained in the video
this is something after that
drifting swift
detriment ≠ determinant
anyway ok i need to go bc im kinda tired
(not from this but from earlier shit, not your fault)
pearl bridge
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
sturdy flint
topaz sinewBOT
sturdy flint
,rotate
thorny flameBOT
sturdy flint
I am stuck on a point in my solution:
x = A cos(wt + phi)
At t = 0, for 1st particle
A/√2 = A cos (phi)
(Phi) = 45°
x = 2A cos(wt+ phi)
-A/√2 = 2A cos (phi) at t = 0
But this give phi as -1/2√2 whose value can't be written in 0 to 90 degree trigonometry table
For question 7
How to solve this question
gusty dust
extreme position of the second particle is -2A
gusty dust
I am stuck on a point in my solution:
x = A cos(wt + phi)
At t = 0, for 1st p...
-A/√2 = 2A cos (phi) at t = 0 this doesn't really make sense
sturdy flint
extreme position of the second particle is -2A
why the extreme position you decided to be -2A, 2A is the amplitude not position of it?
sturdy flint
extreme position of the second particle is -2A
Or can you tell me due to which misunderstanding I can't understand this
gusty dust
Its motion is around the origin with amplitude 2A right?
So the extreme position is when x=2A
sturdy flint
Its motion is around the origin with amplitude 2A right?
Yes on the st line on extereme position on other end of mean position of 1st particle
sturdy flint
So the extreme position is when x=2A
Okay got it
gusty dust
Yes on the st line on extereme position on other end of mean position of 1st par...
that doesn't matter really, 2A it's the second extreme position doesn't relate to the first
And since you set the other side positive for the first particle
sturdy flint
that doesn't matter really, 2A it's the second extreme position doesn't relate t...
Okay
sturdy flint
And since you set the other side positive for the first particle
For second it will be negative?
gusty dust
This side extreme position is -2A
gusty dust
For second it will be negative?
yeah
sturdy flint
So for 2nd particle -2A = 2A cos(phi)
Phi = π
180°
Then phase difference is 180-45 = 135
Right?
gusty dust
yea
I mean you could imagine it really
it's on the other side so can't be 90 degree or 45
180 also doesn't make sense cuz they have to have the same phi
sturdy flint
How do you imagine it like on graph or circle or what
gusty dust
How do you imagine it like on graph or circle or what
Using circle
sturdy flint
But in books graphs are mentioned mostly
gusty dust
Graph is such a confusing way for me
Even in a graph problem I still convert it to circle
But it depends on you really
gusty dust
The first particle is on first quadrant and the second one is on second
So it has to be in <180 and >90
But to know the exact is a whole technique
sturdy flint
I want to learn that technique
gusty dust
But it's easy to use when you get the hang of
gusty dust
In classes?
Yeah
sturdy flint
Then ill know it most prolly because I am studying this chapter before it starts in class
gusty dust
Then ill know it most prolly because I am studying this chapter before it start...
Yeah likely, when they relate circular motion to harmonic motion
sturdy flint
Yeah likely, when they relate circular motion to harmonic motion
I read that yesterday
Shm can be described as prjection of circulsr motion
gusty dust
Shm can be described as prjection of circulsr motion
well we reverse that step
sturdy flint
Oh ok then I know it I just need to practice on shm in cirucular motion
gusty dust
Oh ok then I know it I just need to practice on shm in cirucular motion
okayy
sturdy flint
I have one more problem
The maximum displacement of a particle executing SHM is 1cm and the maximum accleration is (1.57) ² cm/sec². Then the time period is ____
sturdy flint
drifting swift
ok
im really tempted to say that this 1.57 is really pi/2 in disguise
anyway you should know that max accel = omega^2 * max displacement right
sturdy flint
Yup yup
drifting swift
$x = A \cos(\omega t + \varphi)$ gives $\ddot{x} = - A\omega^2 \cos(\omega t + \varphi)$
thorny flameBOT
Ann
drifting swift
so you know $A$ and $A\omega^2$. you can figure out $\omega$ from here.
sturdy flint
Yes
thorny flameBOT
Ann
sturdy flint
I get wt + phi = π
A = 1cm
a max = w²
So d²x/dt² = w² = -Aw² cos (wt +phi)
=> cos(wt + pi) = -1
Wt +phi = π
From here w is not coming out
@drifting swift
Help ^
drifting swift
you are wrong to even think about the full motion equation here
or time
max x = A
max x'' = Aω^2
this only!
drifting swift
sure
drifting swift
okay I assume it at t = 0
you give exactly zero shits about t
this is not about movement at any particular pt in time but about overall parameters of the shm as a whole
sturdy flint
Is w = 1.57
topaz sinewBOT
@sturdy flint Has your question been resolved?
wooden kayak
how did he get pi/3 and pi + pi/3
topaz sinewBOT
how did he get pi/3 and pi + pi/3
topaz ledge
Do you know how to graph tanx
wooden kayak
Not really
topaz ledge
Not really
So we need to start with that
Tanx = sinx / cosx
At x=0 sinx = 0 this tanx= 0
As we increase x, tanx also increases and at π/2 cosx=0 hence tanx tends to infinity
From this we can create a rough graph of tanx
Which is strictly increasing with range [0, infinity) in this interval
topaz ledge
That is because of the sign of cosine being negative
In that interval
Thus when approaching from the right cosine increases from -1 to 0-
wooden kayak
That is because of the sign of cosine being negative
example?
topaz ledge
Have you done the unit circle definition of trig functions
wooden kayak
yes
topaz ledge
Then in the interval pi/2 and pi
The x coordinate is -ve
So that is why the graph of tanx is negative
topaz sinewBOT
@wooden kayak Has your question been resolved?
topaz sinewBOT
@wooden kayak Has your question been resolved?
static talon
Hi! One question:
$\frac{dy}{dx}=f(x, y)$
How can we prove that if we have the above equation where f is a function of x and y that y(x) is itself a function [and not generally a relation that may or may not be a function necessarily]?
thorny flameBOT
SeaSamak
marble gate
doesn't dy/dx only make sense if y is a function
static talon
I don't think so
Because you can still have dy/dx for an implicit relation of y, no?
static talon
**SeaSamak**
I am sure that I am missing the intuition here
static talon
**SeaSamak**
My book stated y must be a function
static talon
**SeaSamak**
if the equation is true*
Apparently f(x, y) is called a "scalar-valued function," I found online . . .
static talon
**SeaSamak**
Maybe some of the properties of scalar-valued functions forces y to be a function too?
marble gate
I'm spitballing here, but if dy/dx = f(x, y) where f is a function, then dy/dx exists over the entire domain of both x and y, and is well-defined
so you cannot have x R y1 and x R y2 (else your dy/dx would break)
static talon
so you cannot have x R y1 and x R y2 (else your dy/dx would break)
What does the R mean?
marble gate
some relation
static talon
oh, I see
marble gate
probably abuse of notation - maybe the correct would be x y a and x y b
x is related (by y) to multiple values
static talon
I got you, like it should pass the vertical line test
drifting swift
Hi! One question:
$\frac{dy}{dx}=f(x, y)$
How can we prove that if we have th...
you dont, rather a solution of the DE is by definition a function which satisfies a bunch of properties incl. making the eq true when plugged in
but practically speaking you MAY come across a situation in which the solution of your DE works out as an implicit function
then you conceptualize it as being split into a bunch of solutions along each "branch point" ie roughly when the tangent to the curve would be vertical
for example dy/dx = -x/y
this gives you x^2 + y^2 = C if you integrate it
that's a circle and not itself a function but it can be split into two arcs which are
static talon
for example dy/dx = -x/y
Yes I was thinking of this
drifting swift
y = sqrt(C-x^2) and y = -sqrt(C-x^2)
static talon
So then the form dy/dx = f(x, y) can technically lead to a solution y where it is an implicit relation of y where it isn't a function?
drifting swift
if you want something to UM-ACKSHUALLY with, then yeah ig
static talon
for example dy/dx = -x/y
What I can't determine is whether z=-x/y is a function
Like I would have to see than in 3 dimentional space
drifting swift
why do you think -x/y is not (or might not be) a function of x and y?
static talon
let's say we have x1 and y1, we should get only one value for z1 . . . So it makes sense for it to be a function if we have z=-x/y
What if the relation f(x, y) wasn't a function, though?
Would that change anything in the differential equation?
But basically my main question has been cleared, thanks all! But it's weird that my book explicitly states that y(x) has to be a function
if it were to be a solution to the differential equation
As we concluded the circle relation to be a counterexample to that
drifting swift
What if the relation f(x, y) wasn't a function, though?
then you're gonna have only the more general-general form F(x, y, dy/dx) = 0
little abyss
I think instead of cosec it should be cos
Because i couldn’t figure out any way to prove it
topaz sinewBOT
I think instead of cosec it should be cos
Because i couldn’t figure out any way ...
little abyss
I accidently send the flipped version
Here are the identites also if anyone needs them but again the main issue is that i think its a misprint , i just need to confirm it
true hamlet
Hard to help you without giving straight away the answer, but you can simplify the interior of the square root by multiplying and dividing by the same quantity
sharp wyvern
what have you tried
little abyss
I have tried the rhs first
Actually there was a question just like this
In that one instead cosec i had cos in the roots
smoky sparrow
this is impossible to prove
little abyss
So i think its a misprint as it seems impossible
smoky sparrow
the question statement is faulty
little abyss
this is impossible to prove
Thanks just what i wanted to hear
smoky sparrow
,w range of (1 + csc x)/(1 - csc x)
thorny flameBOT
smoky sparrow
anyways the range of the inside of the sqrt is [-infinity, 0]
topaz sinewBOT
topaz sinewBOT
Available help channel!
fringe terrace
I need help with question number 1 the solutions my teacher posted are different from mine I’m wondering what I did wrong or maybe if the solutions are just wrong
topaz sinewBOT
I need help with question number 1 the solutions my teacher posted are different...
fringe terrace
My teachers solution:
quasi depot
parenthesis
fringe terrace
Huh?
quasi depot
Your numerator is -3(x+b) where you teacher's is -3x+b
fringe terrace
Oh
I don’t really get her answer though bc the way I did it is the way we did it in class
I also don’t know where that four came from in her answer
quasi depot
To me it looks like she read it like x=1 and y=2
So instead of (2,1) she solved like it was (1,2)
fringe terrace
Oh true
I’ll ask her about it Monday, our test is Tuesday so I was lowkey stressing 😭
topaz sinewBOT
topaz sinewBOT
Available help channel!
weary zephyr
topaz sinewBOT
weary zephyr
Sooo, I need help with this exercise about Induction
I know how to do the Induction Basis, but the Induction Hypothesis... well, a bit difficulty for me, like, to grasp, how I should write it
This is my try of solving it
drifting swift
can you prove 2n+2 ≤ 2^n?
that's kinda going to be the crux of it
if you can prove that 2n+2 ≤ 2^n always, then your proof works
weary zephyr
can you prove 2n+2 ≤ 2^n?
I have a feeling that, I need work with "+1" and not with "+2"
drifting swift
i think there may be an alternative that's easier, actually.
instead of proving $n^2 \leq 2^n + 1$ why not try $n^2 - 1 \leq 2^n$? it's the same thing after all.
thorny flameBOT
Ann
weary zephyr
But I do know is that, if I add something on the left side (that is, "2n+1") then I have to add it to the other side of the unequation as well
rigid kelp
No one in help35?
weary zephyr
**Ann**
Huhhhh, interesting, but even then, I don't know How to prove it/formulate it. And the example solution the tutors gave us isn't helping me understand the topic either:
golden blade
Willst du es auf Deutsch erklären
weary zephyr
Willst du es auf Deutsch erklären
Ah ja, das wäre besser.
Also, wie ich sagte, ich hab bei "n power 2 + 2n + 1" blockiert und ich komme nicht weiter. Soll ich "2n + 1" auf der rechte Seite der Ungleichung als "(2 power n + 1) + 2n + 1" darstellen?
Und wenn schon, wie stelle ich die Ungleichung weiter?
golden blade
2n+1 < 2^n gilt erst ab n>=3 deswegen finde ich das schon komisch
weary zephyr
2n+1 < 2^n gilt erst ab n>=3 deswegen finde ich das schon komisch
meinst du, im obigen bild?
golden blade
Huhhhh, interesting, but even then, I don't know How to prove it/formulate it. A...
Hier
weary zephyr
2n+1 < 2^n gilt erst ab n>=3 deswegen finde ich das schon komisch
Ohhhhhh
Jaaa, deshlald verwirrt mich auch diese Lösung
Und ich bereite mich jetzt vor für ein mid-term und ich brauche eine zweite Meinung
odd pagoda
13<64 gilt bekannterweise nicht
golden blade
Bruh hab mich verkuckz
weary zephyr
sooooo, hat jemand von euch ein tip, wie ich den Beweis dastellen konnte?
golden blade
Du könntests zeigen dass 2^x-2x+2>0 und monoton wachsend ist ab einem x
odd pagoda
nenene. wenn schon dann halt noch ne zweite induktion
golden blade
oder machs induktiv wie du magst
weary zephyr
Ich muss aber das folgende Beweisen:
weary zephyr
This is my try of solving it
Ich meine, ich weiß wie, aber ich bin mir nicht sicher, ob diese Schreibweise richtig is
odd pagoda
der beweis ist fine. das einzige was halt fehlt ist 2n+2 <= 2^n. was du mit ner zweiten induktion machen könntest
golden blade
Ich muss aber das folgende Beweisen:
Ja um das fertig zu beweisen brauchst du quasid noch so nen zwischenbeweis
odd pagoda
warte mal du brauchst doch nur 2n <= 2^n
weary zephyr
Ja um das fertig zu beweisen brauchst du quasid noch so nen zwischenbeweis
ich bin mir nicht sicher, wie ich das auschreiben soll..
golden blade
warte mal du brauchst doch nur 2n <= 2^n
Wieso
odd pagoda
(n+1)^2 = n^2+2n+1 <= 2^n+2n+1 <= 2^n+2^n+1 = 2^(n+1)+1
odd pagoda
whoops
weary zephyr
ich bin mir nicht sicher, wie ich das auschreiben soll..
uhmmm
odd pagoda
wir zeigen zuerst dass 2n+2 <= 2^n
beweis: ....
jetzt zeigen wir die eigentliche aussage:
...
zum beispiel
weary zephyr
okay, aber... wie beweise ich 2n+2 <= 2^n, ich meine, ich weiß nicht wie
odd pagoda
induktion
weary zephyr
ist "2n + 2 <= 2n + 2n <= 2^n" genügend?
weary zephyr
2n =< 2^n zu zeigen dann ist noch einfacher
oder ich konnte zeigen dass n power 2 <= 2 power n
golden blade
Ich bin verwirrt was du anstellst
weary zephyr
Ich bin verwirrt was du anstellst
den 2 power n + 2n + 1 sollte ein quasi ein "Zwischenschritt" sein, zwischen den linken und rechten Seite
golden blade
oder ich konnte zeigen dass n power 2 <= 2 power n
Meinst du als neuen Beweis?
weary zephyr
Meinst du als neuen Beweis?
Ehr als ein Beweis der die von der linke zur rechte Seite führt
golden blade
den 2 power n + 2n + 1 sollte ein quasi ein "Zwischenschritt" sein, zwischen den...
Den brauchst du doch gar nicht aber
golden blade
This is my try of solving it
Das hier war alles top
weary zephyr
2n =< 2^n zu zeigen dann ist noch einfacher
aber ich habe noch den "+2" dahinter, wie kann denn auch noch beweisen?
golden blade
Entweder du zeigst für alle n>=3 dass 2n+2 =< 2^n oder für alle n>=4 dass 4n =< 2^n
Dann gilt der Induktionsschritt bis auf endlich viele n
So die anderen cases kann man ausrechnen
Ich denke Letzteres ist noch einfacher zu zeigen mit Induktion oder bisschen Analysis
golden blade
This is my try of solving it
Mach bei dem Schritt 2 =< 2^n eine Anmerkung mit * und dann vermerk auf den Zwischenbeweis für 4n =< 2^n
weary zephyr
Mach bei dem Schritt 2 =< 2^n eine Anmerkung mit * und dann vermerk auf den Zwis...
okayyyy, ich werde mir dies Anschauen, danke
.close
junior osprey
can someone whi knows about coding on maple help me?
topaz sinewBOT
can someone whi knows about coding on maple help me?
junior osprey
halo
hardy wing
!da2a
topaz sinewBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
hardy wing
You can try the CS server but Maple is a math nerd software, so odds are some people here know it
worthy storm
it's generally fine to ask such questions here, but no guarantee that someone will know the answer
you can also try #computing-software
topaz sinewBOT
@junior osprey Has your question been resolved?
plush ingot
how do i do this 😭
topaz sinewBOT
how do i do this 😭
thick jay
i have an idea but im not a 100% sure it's possible, still wanna hear it out?
plush ingot
i have an idea but im not a 100% sure it's possible, still wanna hear it out?
yes please
thick jay
oh mbmb, i thought this was meant to be solved with integration, it looks simpler than what i thought it was
just find the centre of mass then if its projection on the plane XY lies within the base, it's "stable"
plush ingot
oh mbmb, i thought this was meant to be solved with integration, it looks simple...
how
do i find centre of mass
thick jay
You know the total mass of the building, yes?
M= 6m where m is the mass on each vertex.
Then it tells you that the top floor is made by shifting the x, y, z coords
by x0, y0, 20
'so you know the vector equations that must be defined for each vertex's position vector
no?
yea thats the way
topaz sinewBOT
@plush ingot Has your question been resolved?
heavy timber
the 140 and 125 are forces
topaz sinewBOT
the 140 and 125 are forces
heavy timber
the question is asking to add the two torques of the two forces around point A
I keep getting 90
torque of 125 around A is easy its just -500
now for the torque of the 140, i drew that perpendicular line
using pytha's twice, i got the lengths of the triangle of which the perpendicular line is in
then used euclids to find its length, multiplied that by 140, got 590
so... 90
answer choices are 50 60 70 80
oh wait... ok i cant use euclids there
let me retry with cosine rule
ok i got 5sin(60) for the perpendicular length
is that wrong? still yields an answer thats not in the answer choices
heavy timber
the 140 and 125 are forces
<@&286206848099549185>
spice seal
can you send the original question as well
heavy timber
can you send the original question as well
loud oasis
to me it seems like the most straightforward way would be to split the 140 force into x- and y- components
heavy timber
to me it seems like the most straightforward way would be to split the 140 force...
i can try that
but is there smth wrong with my approach
ok
still yields 606, which when added to -500
yeah, not in the answers
btw i also got 606 with my approach
loud oasis
ok i got 5sin(60) for the perpendicular length
i got a different answer for the perpendicular length
heavy timber
i got a different answer for the perpendicular length
show me
or you can look at my drawing and see if theres any incorrect information
loud oasis
well can you show how you got 5 sin(60)?
loud oasis
how did you get a 60 degree angle?
heavy timber
cosine rule on the triangle of lengths 5, 4sqrt(10) and 15
triangle abc
and i got bc using pyth's on the 12 and the 9
and i got ba using pyth'\s on the 12 and the 4
so i got all the lengths
applied cosine, boom, 60
loud oasis
applying cosine rule does not give me 60 degrees
heavy timber
applying cosine rule does not give me 60 degrees
what did you get for the lengths of abc
or... which length did i get wrong
loud oasis
well assuming we're finding the angle C, then side c should be the side opposite that, 4*sqrt(10)
loud oasis
yes
heavy timber
ok i have an 18 in my calculations
😭
idk where that came from
53.13
is that the angle
loud oasis
something like that
i will also note that it would probably be easier to get that angle via right triangle trig
heavy timber
i will also note that it would probably be easier to get that angle via right tr...
OH.
i didnt see the big right triangle
omg the redundancy
ok 60
oh my godddddddd i cant be making these mistakesssss
ok ty cloud
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
fringe mountain
Prove that having 100 whole numbers, one can choose 15 of them so that the difference of any two is divisible by 7. the answer is For the difference to be a multiple of 7, the integers must have equal modulo 7 residues. To avoid having 15 with the same residue, 14 numbers with different modulo 7 residues can be picked ($14 * 7 = 98$). Thus, two numbers are left over and have to share a modulo 7 residue with the other numbers under the pigeonhole principle. hi, can i just clarify that modulo 7 residues are essentially the remainder when divided by 7. im not sure why the answer states that we want to avoid having 15 with the same residue, wouldn't having 15 with the same residue imply that the difference of any two is divisible by 7?
topaz sinewBOT
Prove that having 100 whole numbers, one can choose 15 of them so that the diffe...
thorny flameBOT
lalala
odd pagoda
its a proof by contradiction (more or less)
we are trying to our best to avoid getting those 15 differences
but we cant
fringe mountain
thanks that cleared up a lot
long pollen
I need to derivate this, any help...?
topaz sinewBOT
I need to derivate this, any help...?
long pollen
I have more derivates but I'm hella stuck here. 😭
lucid junco
⛓️
long pollen
⛓️
I tried to do it by this one but for some reason, the solution of my friend says (-2b/x^3) at the second step, I don't know what he did or is he even right.
I also can't completely understand the chain rule. 😭
lucid junco
How would you differentiate (3x+1)^100
long pollen
How would you differentiate (3x+1)^100
100(3x+1)^99?
lucid junco
Almost
long pollen
o
long pollen
Ah, that thing: 100(3x+1)^99 . d/dx (3x+1)?
quasi depot
yes
spare smelt
dy/dx = dy/du du/dx. The du's cancel, it's like a fraction
long pollen
So, for my case is:
3(a+b/x^2)^2 . d/dx (a+b/x^2)
Holy, I've never got like 3 users helping me at the same time, I appreciate it!
lucid junco
So, for my case is:
3(a+b/x^2)^2 . d/dx (a+b/x^2)
Yes
long pollen
Yes
3(a+b/x^2)^2 . (0 + d/dx b/x^2) = 3(a+b/x^2)^2 . ( + bx^-1)
Right?
Can someone remind me the command for the bot so I can easily type the exercise and my procedures? 😭
lucid junco
,w differentiate 1/x^2
thorny flameBOT
lucid junco
3(a+b/x^2)^2 . (0 + d/dx b/x^2) = 3(a+b/x^2)^2 . ( + bx^-1)
How did you get bx^-1?
copper sedge
In general $\frac{\mathrm d}{\mathrm dx}[f(x)^n] = nf'(x)f(x)^{n-1}$
long pollen
How did you get bx^-1?
Uh... I don't know, I got an exercise done by the professor and it's pretty similar, he did this: ...d/dx (a-b/x) = (0 - d/dx b/x) = (-d/dx (bx^-1) = (bx^-1-1)
thorny flameBOT
long pollen
Wha
flint cloak
[\rb{bx^{-2}}]
thorny flameBOT
Cooly
flint cloak
Hi water beam
long pollen
Do you know power rule?
I don't think so.
lucid junco
I don't think so.
What’s the derivative of x^3
long pollen
What’s the derivative of x^3
3x^2?
long pollen
10x^9
lucid junco
yes
long pollen
Is this the power rule?
lucid junco
Yes
long pollen
||BRUH||
lucid junco
What about x^-2
long pollen
What about x^-2
-2x^-3?
lucid junco
Like shown here
long pollen
Ah, I see...
long pollen
So it’s -2b / x^3
...d/dx (a+b/x^2) = (0 + d/dx (b/x^2)) = (-2b/x^3)
Sorry for the delay, I was trying to understand how this works, now I know that is the differentiation rule.
lucid junco
...d/dx (a+b/x^2) = (0 + d/dx (b/x^2)) = (-2b/x^3)
Yes
long pollen
3(a+b/x^2) . (-2b/x^3)
lucid junco
You are forgetting the ^2
lucid junco
You are done you leave it like that
If you want to make it nicer you can just move things around a bit and write it as
(-6b/x^3)(a + b/x^2)^2
long pollen
I wouldn't like to make it look like that I'm a professional, I can't even understand how derivates work. 😭
I'm doing a work of 9 derivates, I've done most of them but I'm missing 3, well, I was missing 2 with this one done. I'm missing the ones that have the circle, 36 & 38. Some classmates say that they are really hard, can you help me with these ones too? Please. 🙏
long pollen
There are both chain rules as well
In the 36 I got this: 1/2√1-cx/1+cx
And... I don't know what else to do. 😭
Nvm, I got them with my friend's help, thank you everyone!
.close
idle fulcrum
Hi
idle fulcrum
Can somebody help me with my geometryt
it is really hard
for me
<@&286206848099549185>
help me please
dusk bronze
This is a congruency case
Statements 1, 4 and 5 imply that SV and TV are congruent
Specifically this is the angle-side-angle case
idle fulcrum
oh ok I know i have to add a line and put cpctc
What do I put for hte statment though?
like traingle... is congruent to traingle...
dusk bronze
Yeah
idle fulcrum
The thing is I dont know what order because this ixl is so specific and i've been only getting that part wrong for soo long I have been working on this for 3 hours
dusk bronze
Understood
Maybe triangle SVW is congruent to triangle TVU first
then segment SV is congruent to segment TV
idle fulcrum
like this?
dusk bronze
Yeah that's basically it
dusk bronze
Nice 😄
idle fulcrum
Im sorry I dont wanna waste your time but can you help mne with the rest of the Ixl?
Im at 75 percent
if you dont want to I understand
dusk bronze
Yeah idk if it's allowed
I'm not familiar with IXL since I'm Brazilian, so idk if it falls into the homework/exam rule
Are you doing a self-assessment or is this homework
idle fulcrum
Oh ok it is for practice for an upcoming exam my teacher didn't assign but I asked her for any reccomendation and she said this
idle fulcrum
I just dont get between the statement of SSS SAS AAS and ASA, I understand HL and CPCTC
my teacher didn't explain properly in my opinion
dusk bronze
Oh ok
idle fulcrum
Yeah idk if it's allowed
I'm not familiar with IXL since I'm Brazilian, so idk i...
yo r a smart Brazilian for sure 😭
you*
dusk bronze
thank you ig 😅
idle fulcrum
if you dont mind me asking what grade r u?
dusk bronze
10
idle fulcrum
oh ok two grades ahead of me
dusk bronze
Basically if some correspondent parts of two triangles are congruent, you can conclude that the triangles are congruent
idle fulcrum
Yea Understand that part
like here this is my next question
Im pretty sure I got to put Segment GF ius congruent to segment EF but Im not sure
Im stupid
Its already shown
dusk bronze
Seems about it
idle fulcrum
...I hate Ixl
dusk bronze
darn
dusk bronze
by US I meant United states
yeah i got it
idle fulcrum
ok
dusk bronze
SAS here
idle fulcrum
ok and is it traingle WTX is congruent to triangle VUX?
dusk bronze
Mhm
As a tip you can check what congruencies are in previous statements
If three side congruencies, SSS
If two side congruencies and one angle congruency, SAS
If one side congruency and two angle congruencies, either AAS or ASA
dusk bronze
Seems about right
idle fulcrum
As a tip you can check what congruencies are in previous statements
If three sid...
Oh ok Thank you
dusk bronze
Can't say for sure about order though
idle fulcrum
ok 🤞
dusk bronze
As a tip you can check what congruencies are in previous statements
If three sid...
To decide between AAS or ASA, just check if the side is between the two angles
If yes, ASA
If not, AAS
idle fulcrum
Yay it is right!
dusk bronze
Nice!
idle fulcrum
To decide between AAS or ASA, just check if the side is between the two angles
I...
But sometimes The Side is not between it and it is still ASA?
or I could be wrong idk
dusk bronze
Understood
idle fulcrum
alr.. Next problem is this
Im thinking it is Traingle XVY is congruent to Traingle VXW
idle fulcrum
SSS?
dusk bronze
Yeah
dusk bronze
Seems about it
idle fulcrum
It was right
dusk bronze
Yay
dusk bronze
Not really
idle fulcrum
Well you are still smart 😭
dusk bronze
High school math in Brazil is actually less advanced than in the USA
We used to have calc in High School but we don't anymore
dusk bronze
I believe the current subject is related to Algebra ig
idle fulcrum
oh ok
dusk bronze
We're in arithmetic and geometric progressions
dusk bronze
Statements 1, 2 and 7
But idk if you need to include that VX is congruent to UY
in this case it would be SSS again
idle fulcrum
Traingle TUY is congruent to traingle WXV?
dusk bronze
Yea
idle fulcrum
okie
dusk bronze
I do a scientific initiation program for mathematical olympiads in a nearby university so I get more cover on general math topics
idle fulcrum
I do a scientific initiation program for mathematical olympiads in a nearby univ...
That is cool!
dusk bronze
Really is
idle fulcrum
is it hard?
dusk bronze
Depends on the person
dusk bronze
And idk how but I can somehow type these symbols
alt codes or smthn?
dusk bronze
Would this work? △VXW≅△UYT
probably
dusk bronze
Don't tend to much
But when I do I don't have a specific one anymore
I used to play Roblox quite a bit
idle fulcrum
Oh ok
dusk bronze
Would this work? △VXW≅△UYT
Did it work?
idle fulcrum
No it was TUY is congruent to WXV ):
dusk bronze
goodness
idle fulcrum
yea... 😭
dusk bronze
But do you feel like you're getting the hang of it
idle fulcrum
Yea
dusk bronze
As a tip you can check what congruencies are in previous statements
If three sid...
Because it feels like just using this repeatedly
idle fulcrum
Is this SAS?
dusk bronze
Yup
idle fulcrum
Ok
dusk bronze
All good?
idle fulcrum
yea
dusk bronze
😭
How many total questions?
Do you think you can handle the rest using the tip?
I might have to go
topaz sinewBOT
@idle fulcrum Has your question been resolved?
rare moon
I was working on this problem yesterday. I've gotten through part a but this material has been difficult for me to pick up. I don't know how to approach part b
topaz sinewBOT
I was working on this problem yesterday. I've gotten through part a but this mat...
rare moon
I understand that a normal subgroup N is such that gNg^-1 = N, or maybe rather gng^-1 is a member of N
I haven't had enough practice with any of this to have any intuition on what that notion is useful for, or why it might be preserved by a homomorphism
I'm assuming this is not true for homomorphisms in general, so it's not immediately obvious to me if there's something special about this one or what it might be
if we say we have some normal subgroup N bar of G bar, we might say the map in part a sends it to N, a subgroup of G containing K, being the set of all the preimages of every element from N bar.
I suppose that we might prefer to say g bar * n bar * g bar^-1 is a member of N bar, and if that's true then I suppose the image of that product by this map should belong to N. the image being the preimage of it by phi. this is getting a little confusing, maybe
I understand that gng^-1 != n, in general; that would be centrality
but anyway, I would suppose the homomorphism property applies to this inverse map too, which might be useful
so we might say phi^-1(g bar) phi^-1(n bar) phi^-1(g bar^-1) belongs to N. I'm still assuming that all the normal homomorphism things work here, so phi^-1 of g bar and g bar^-1 should still be inverses. I don't know how imporant any of this is, but I want to have done my due dilligence of exploration
I don't know. this seems kind of obvious in the sense that I don't know what I can say about it. phi^-1(n bar) belongs to N, yeah? and I just said before g bar and g bar^-1 should still be inverses after the map, so is there any more to be said? I feel like I've gotta be missing something
topaz sinewBOT
@rare moon Has your question been resolved?
topaz sinewBOT
@rare moon Has your question been resolved?
topaz sinewBOT
@rare moon Has your question been resolved?
pseudo sonnet
but anyway, I would suppose the homomorphism property applies to this inverse ma...
I know this is closed now, but I want to say that the inverse doesn’t necessarily exist, since we don’t know phi is injective
topaz sinewBOT
I know this is closed now, but I want to say that the inverse doesn’t necessaril...
pseudo sonnet
I was working on this problem yesterday. I've gotten through part a but this mat...
anyhow, you can get part b) done by expanding the definitions a little
rare moon
aw this is getting all the attention now that I've closed it :p
I've been chatting with a friend about it, he's helped me flesh it out
pseudo sonnet
I haven’t really read your messages but it should be quick with the definitions
pseudo sonnet
sounds like you got it already :o
pseudo sonnet
I haven’t really read your messages but it should be quick with the definitions
you want to show that B = phi^-1(B bar) is normal
that means you need to show that gBg^-1 = B for any g in G
but by definition, an element b is in B if phi(B) lives in B bar
so to show that gBg^-1 is a subset of B, you need to show that phi(gbg^-1) is in B bar for all b in B
but phi is a homomorphism and B bar is normal :p
so you’ll get it quickly from those
pseudo sonnet
I haven't had enough practice with any of this to have any intuition on what tha...
one last thing: you'll probably see this soon, but the normal subgroups of G are precisely the kernels of homomorphisms out of G
also, the group structure for a quotient group is only well-defined when you're quotienting by a normal subgroup :p
hopefully this provides a little more motivation for why we defined these things
digital veldt
one last thing: you'll probably see this soon, but the normal subgroups of G are...
hey i have a question
pseudo sonnet
I guess I'll close this now though, since you're done here 
digital veldt
I guess I'll close this now though, since you're done here <:giggle:137595258255...
no wait
pseudo sonnet
what's the question?
rare moon
(I actually could still use help on part c if anyones willing but I'm gonna stick around for this question)
digital veldt
what's the question?
iam taking this course now (logic, groups,subgroups, relations , operations etc)
do u have tips to easily be able to manipulate rules to help with exam tricks in this course?
pseudo sonnet
I'm not the one to ask for help with tricks or writing exams haha
digital veldt
I'm not the one to ask for help with tricks or writing exams haha
oh not writing exams , i want to be able to have a mindset where i can easily figure the trick in the question
yk
pseudo sonnet
this isn't the place to ask, I'm afraid
#study-discussion is the channel to head to 
digital veldt
this isn't the place to ask, I'm afraid
alrighty i just saw this channel is related to what iam taking rn so ye
pseudo sonnet
(I actually could still use help on part c if anyones willing but I'm gonna stic...
hmm, you might want to open another channel for that 
I don't quite know how to approach it off the top of my head, and I don't want to keep this channel open when it doesn't have your name on it 
I'm going to close this now, but please feel free to open another channel if you want to still ask 
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
hexed apex
when graphinh a rational function, how do i know where each asymptote goes
hexed apex
like you see how where they are is flipped between the 2 graphs, first left asmptote is at the bottom and the 2nd left asymptote is on the top
ANYONE please
@haughty drum
<@&286206848099549185>
anybody
i actually need to know this now
i have a test in like 3 hours
fallen vector
Ok i check
hexed apex
and graphing them
hexed apex
Ok i check
yeah so
u see how the graphs are flipped kinda
how do iknow when to do each one
torpid shard
like you see how where they are is flipped between the 2 graphs, first left asmp...
Try evaluating at the left and right side of the asymptotes
If its higher than your horizontal asymtote, then it goes up
If its lower, then down
Since I doubt you know how to evaluate limits in this case
hexed apex
Since I doubt you know how to evaluate limits in this case
yeah we didnt learn this
its basically just looking at the equation i should be able to tell some how
torpid shard
its basically just looking at the equation i should be able to tell some how
Yes, generally youll have easy enough equations so you can know just by looking and testing a few numbers
Either on paper or in your head
hexed apex
Yes, generally youll have easy enough equations so you can know just by looking ...
what do i test
chat gpt was talking about how the a value has to be like greater than 0 or what not
torpid shard
!nogpt
topaz sinewBOT
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).
torpid shard
Imagine you know the asymptote is at x = 2
torpid shard
Getting the roots of the lower function
Supposing it doesnt neatly divide the top function
hexed apex
zeroes of the denominator = VA
and f(x)=0 = HA
yeah
ik how to find those
can i use those to tell how my asymptotes gonna look? like if the left side is gonna be above or under
like ykwim
torpid shard
Yes
hexed apex
how
torpid shard
Again, example, if you know the asymptote is at x = 2
Try calculating the whole formula at x = 1 and x =3
aka, one at the left and one at the right
torpid shard
and f(x)=0 = HA
This is wrong too, anyways
hexed apex
sorry i meant
that was y intercept i got it mixed up
HA is if the top degree is higher than the bottom degree = oblique
if its the same then divide the coeffiencients
and if the bottom degree is higher, y=0
hexed apex
Try calculating the whole formula at x = 1 and x =3
wdym
thats confusing
wait i dont understand
thorny flameBOT
∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴
torpid shard
This function has asymptotic behaviour at x = -2
And it has Horizontal Asymptote at y = 1 (you dont really need to know this)
If you evaluate at x = -3 and x = -1 (one at the left, one at the right)
you get
$f(-3) = \frac{-3}{-3+2}=\frac{-3}{-1}=3, \f(-1) = \frac{-1}{-1+2}=\frac{-1}{1}=-1$
thorny flameBOT
∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴
torpid shard
So x=-3 is above the horizontal (it goes up)
x = -1 is below the horizontal (goes down)
And this is how x/x+2 looks like
hexed apex
and why do we spicifically sub in -1 and -3? @torpid shard
torpid shard
just because its one on the left and one on the right
the VA is at x = -2
-2 - 1 = -3
-2 + 1 = -1
hexed apex
oh so u sub -1 and -3 cus its before and after
yeah
wai
so were subbing it into the va but then comparing it to the HA?
torpid shard
so were subbing it into the va but then comparing it to the HA?
We are choosing the values of x based on the VA
and then checking if the result is above or below the HA
topaz sinewBOT
@hexed apex Has your question been resolved?
elder sentinel
can someone explain this to me i dont get how question 1 = T
topaz sinewBOT
can someone explain this to me i dont get how question 1 = T
lethal anchor
look at the y axis on the left
raven field
can someone explain this to me i dont get how question 1 = T
If you move forward or backward you are still either way displaced yes ?
lethal anchor
and also look at the line segments
which (red) line segment covers 65 kms?
for example, P covers 40 kms so it cannot be that
elder sentinel
but also S is 65 is it not?
elder sentinel
oh
raven field
How about trying to represent it on one axis, it would simplify the idea
elder sentinel
How about trying to represent it on one axis, it would simplify the idea
what do u mean
lethal anchor
yeah the time axis is not really relevant here
elder sentinel
wait so how is it T then?
lethal anchor
wait so how is it T then?
whats the highest point in T and what is the lowest point
elder sentinel
oh
lethal anchor
what is the length of the green line
elder sentinel
65km
lethal anchor
there u go
lethal anchor
ii i already kinda answered for you earlier lol
elder sentinel
where
lethal anchor
i mean think about it
which line segment doesnt cover new distance
it doesnt change locations
mild saddle
does OP still need help? if yes, where is OP at atm?
elder sentinel
does OP still need help? if yes, where is OP at atm?
i still need help
mild saddle
then please consider the second question too
(aka, where are you atm? which question?)
elder sentinel
im on question 2
mild saddle
what do you understand about the question, and what do you understand about the graph?
elder sentinel
i understand that Monica stopped for 1 hour but i dont get where and how
mild saddle
then what do you understand about the graph?
elder sentinel
what do u mean?
mild saddle
exactly what I said - what do you understand by looking at the graph? what does it tell you?
elder sentinel
that its 20km per hour
mild saddle
the graph doesn't directly tell you the speed of Monica
(nor does it matter)
look at the axes of the graph (the horizontal and vertical lines on the sides of the graph)
mild saddle
alright, then maybe we need to walk through what the graph actually means
the bottom part (called the x-axis) is usually the value that we can manipulate, or the independent value.
in this case, time is the independent value because it's down there
the left part (called the y-axis) is usually the value that changes according to the independent value.
in this case, it's Monica's distance from her house
so what this graph is really showing is the relationship between time, and how far Monica is from her house
or in other words, how far Monica is from her house at any given time
do you agree or understand?
elder sentinel
i understand
mild saddle
cool. so let's test your understanding
refer to the graph. how far is Monica is from her house at 10am?
elder sentinel
20km?
arctic minnow
Yeah
mild saddle
oops, sorry, but yes
now, let's tackle the line itself
if the line is sloping upwards, what does that tell you about Monica's movement?
what if it's going down?
mild saddle
not exactly
remember that the higher the line goes, the higher the distance between Monica and her house
so if the line is going upwards, it must then make sense that Monica is moving away from her house. agreed?
elder sentinel
yeah
elder sentinel
going closer to home?
mild saddle
fantastic!
so if an upwards line means that Monica is moving away from home, and a downwards line means that Monica is moving towards home, then what does a perfectly flat line mean?
mild saddle
in other words, she stopped moving. agreed?
elder sentinel
yeah
mild saddle
now look at question (ii)
can you now translate that statement into what you would expect to see on the graph?
to help you a little bit, one small block is 30 minutes
elder sentinel
so it would just move 2 blocks over since its 1 hour?
mild saddle
2 blocks is correct. but do you expect to see an upwards, downwards, or flat line?
elder sentinel
a flat line
mild saddle
good!
so all this question is asking is, where on the graph is a flat line spanning 2 blocks horizontally?
elder sentinel
so its S?
mild saddle
nope
look at the question again. they want you to find where Monica is moving away from her house
elder sentinel
ohhh
mild saddle
(in fact, look at the distance: she's going from 40km to 65km away from her house)
line Q is where she's stopped for half an hour, so that's a no-go for sure
mild saddle
R is correct! not so much because it's 15km from Q to R (the distance is 25km), but because R starts at 40km, and ends at 65km; exactly what the question wants.
mild saddle
what did we say a downward line represents?
elder sentinel
oh
makes sense
do u hve time to go over these short answer questions connected to the same question?
elder sentinel
for iv would it be 4pm?
elder sentinel
Oh so its when she starts going back home?
mild saddle
yes. the question implies this by asking for the time she turned around
elder sentinel
how do u know that she turns around to go back home?
mild saddle
because the graph starts going down
elder sentinel
so it would be 1:30pm
mild saddle
that's why you need to know how to interpret the graph
by this, I mean perfectly understand what the graph is conveying and what special points mean
elder sentinel
by this, I mean perfectly understand what the graph is conveying and what specia...
i see
so for V how do we know the total distance
?
mild saddle
well, this is quite simple
how far does Monica travel away from home?
(hint: what is the furthest distance she ever travels from home?)
elder sentinel
65km ?
mild saddle
excellent
so now, if she travels that far away from home, to return home, how far more does she have to travel?
elder sentinel
65km again?
mild saddle
absolutely
note that it doesn't matter how long Monica took to cycle those 130km
it doesn't even matter she stopped to take a break at Q
all that matters is that she covered 65km on the way out and 65km more on the way back
because we're asked for the total distance
mild saddle
yes
elder sentinel
for question vii how can u tell which is faster
mild saddle
have you learnt about the concept of gradient/slope?
elder sentinel
No
mild saddle
then the way we do it will not use the word directly, but it is the same spirit as calculating the gradients of those two lines
what grade is this, btw, if I may ask?
elder sentinel
year 8
mild saddle
I see
alright, so let's tackle P first
before that though, do you know what the units of speed are?
elder sentinel
uh km/hour
mild saddle
excellent
so this number describes how many kilometers an object covers in an hour
so it makes sense for us to use it here
now, let's take line P
in the journey described by line P, how far did Monica travel, and how long did Monica take to travel that distance?
elder sentinel
40km/3 hr?
mild saddle
you overcounted the number of hours
mild saddle
is that 2 blocks or 3?
oh ok 2
correct
now can you tell which journey was faster?
elder sentinel
line R as it did more km per hour?