tyty
#help-36
tired knot
granite tapir
final saddleBOT
final saddleBOT
Available help channel!
heavy grove
37, how are these equal?
final saddleBOT
37, how are these equal?
heavy grove
But I can’t
heavy grove
youre the one showing how theyre equal
I don’t get that they are equal
warm ether
what do your derivatives give
heavy grove
I get 1/(x+1)^2 and 1/x+1
solemn igloo
I get 1/(x+1)^2 and 1/x+1
am i tripping or is that second one not right
try chain and exponent rules
rocky tusk
indeed
heavy grove
We all good
Thanks
Wait in the second part how does it not contradict if
If they are equal the only variation in the functions can be a constant C
And I don’t see how a constant is the different between them
pliant shore
And I don’t see how a constant is the different between them
$-\frac{1}{x + 1} + \frac{x + 1}{x + 1} = \frac{x}{x + 1}$
soft zealotBOT
south
pliant shore
Just add 1
heavy grove
But is that a constant
final saddleBOT
pliant shore
No worries
final saddleBOT
Available help channel!
tranquil pine
final saddleBOT
tranquil pine
I want to know how i could solve this
rocky tusk
inland kettle
tranquil pine
i couldnt even start
rocky tusk
well do you know the kinematic equations
tranquil pine
well do you know the kinematic equations
yeah i do
rocky tusk
so what would the equation for the position of the money bag be
tranquil pine
uh idk i can't make out the values of acceleration and stuff if you know what i mean
rocky tusk
well it’s a projectile
rocky tusk
so it will have no horizontal acceleration but the vertical acceleration will be gravity
unreal topaz
It is physics not maths
rocky tusk
It is physics not maths
no way!
tranquil pine
Yes projectile motion
😖 i am a 10th grader i haven't learnt this
unreal topaz
Yup it is 11th projectile
rocky tusk
😖 i am a 10th grader i haven't learnt this
well you should know some projectile motion
unreal topaz
If you are from India
tranquil pine
can you solve it pls
rocky tusk
!noans
final saddleBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
final saddleBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
tranquil pine
No but we can help u
bro ikt i am a helper too
tranquil pine
then you should know
alright mr "help" me
rocky tusk
💀
unreal topaz
Use range formula
tranquil pine
so what is the first step
rocky tusk
i asked you a question
unreal topaz
Look it up in ur book
tranquil pine
Use range formula
ok
unreal topaz
And then use
unreal topaz
Then divide displacement by vel to get time
tranquil pine
you decided to ask for the answer
yeah cos i didnt know how to find it by using just velocity
rocky tusk
x=xo+vot+1/2at^2
tranquil pine
x=xo+vot+1/2at^2
it just makes it harder
rocky tusk
it just makes it harder
lol how
tranquil pine
i told you
tranquil pine
i dont have time and acceleration
tranquil pine
you have acceleration
where?
rocky tusk
gravity🤝🏻
tranquil pine
x=xo+vot+1/2at^2
like here
rocky tusk
naught
you don’t need xo
in this problem
you could just do deltax
which is the same as x-xo
either will be zero
depending on how you define your coordinate system
tranquil pine
depending on how you define your coordinate system
alright nvm i am closing this channel
rocky tusk
bruh
tranquil pine
its totally out of my league
tranquil pine
I need some sleep man
tranquil pine
can you give me a step by step procedure how i can do this
i will learn the concept and solve it
rocky tusk
you’re not even following what i’m telling you to do
so
you need to find the vertical position function
of the money bag
voy=vosintheta
a=-g
tranquil pine
you need to find the vertical position function
ok by using the kinematics
tranquil pine
voy=vosintheta
tranquil pine
you mean vy = sinx?
rocky tusk
this would just change the sign for
rocky tusk
you mean vy = sinx?
no
rocky tusk
the initial velocity in the vertical direction is the initial velocity times the sine of theta
tranquil pine
the initial velocity in the vertical direction is the initial velocity times the...
oh ok get it
rocky tusk
👍🏻
tranquil pine
and then we find the time and give the answer right?
rocky tusk
well you need to know if superman gets there first
tranquil pine
i think tht is easy
rocky tusk
yea so how would you do it
tranquil pine
.close
final saddleBOT
clever hamlet
the initial velocity in the vertical direction is the initial velocity times the...
Hold up I’m just re-reading this and quite new to kinematics myself but shouldn’t this be final instead of initial for the first time you mention it
rocky tusk
Hold up I’m just re-reading this and quite new to kinematics myself but shouldn’...
wdym
for the position function of the money bag?
it’s y=voyt+1/2 gt^2
clever hamlet
Yes we’ll you typed initial velocity twice
rocky tusk
yes
because
we’re taking the vertical position function
so we need the vertical component
of initial velocity
it has components in both the x and y direction
the x component is irrelevant to the vertical position
clever hamlet
Yes I understand that
rocky tusk
ok so what’s the problem
clever hamlet
In your explanation
You say initial velocity = initial velocity times the sien of theta
rocky tusk
no
i said initial velocity in the vertical direction
read
aka
vertical component
clever hamlet
Oh I see
Yeah ur right I completely misinterpreted what your wrote
Ty
I understand at and it now
.close
clever hamlet
Oh ok well then bye
drifting cosmos
final saddleBOT
Available help channel!
tranquil pine
final saddleBOT
For the Wronskian $W[y_1,\,y_2](t)$ how exactly does $\ds W'[y_1,\, y_2](t) = \...
soft zealotBOT
tranquil pine
i might be conceptualising this wrongly
because like
what i would expect instead is
,, Wy_1,, y_2' = \mat[v]{ y_1 & y_2 \ y_1'' &y_2''} \0r\ne W'y_1,, y_2
soft zealotBOT
worldly vale
Differentiate y1y2' - y1'y2?
tranquil pine
right, so you get [\8{y_1'y_2' + y_1y_2''} - \8{y_1'' y_2 + y_1' y_2'} = y_1y_2'' - y_1'' y_2] right lmao. i didn't actually expect you'd need to actually differentiate the thing to retreieve the above. I thought it was like some weird substitution idk
soft zealotBOT
final saddleBOT
worldly vale
Yeah well like not rly any other way around it lol
final saddleBOT
Available help channel!
blazing breach
is it possible to tile a square with noncongruent right isosceles triangles?
vital surge
oh i meant a finite construction is also possible*
blazing breach
ahh thats cool
vital surge
is very interesting indeed 🤔
vital surge
is it possible to tile a square with noncongruent right isosceles triangles?
did u come up with this problem from ur own curiosity?
blazing breach
yea
vital surge
oh that's fun
final saddleBOT
@blazing breach Has your question been resolved?
neon slate
yea
https://youtu.be/4HHUGnHcDQw?si=D_wStOJ78xOVJEg0&t=382
if you're curious about tiling stuff, i highly recommend to check out this story (starting at 6:20 in this video) about some fun and interesting tiling discoveries from last year : )
heavy laurel
Can someone help me with these problems?
final saddleBOT
Can someone help me with these problems?
@heavy laurel Has your question been resolved?
velvet saffron
in this this system of equations:
final saddleBOT
in this this system of equations:
velvet saffron
$$ \left{\begin{matrix}
I. 2x+3y = a\
II. \ bx+12y = 100
\end{matrix}\right.$$
soft zealotBOT
eitiel
velvet saffron
find a and b given this set of equations have an infinite solutions
how do I start? infinite soulutions means I and II are equal to each other right? cause they are the same equation
wet warren
Yeah
You might think of it as the second equation is a multiple of the first equation
Like here you can divide 12/3 to find the factor of multiplication between the two equations
Which is 4
Then by that you would be able to get a & b
@velvet saffron understandable?
final saddleBOT
@velvet saffron Has your question been resolved?
velvet saffron
.close
final saddleBOT
final saddleBOT
Available help channel!
tranquil pine
Just started learning about limits and continuity, found this to be slightly confusing:
final saddleBOT
Just started learning about limits and continuity, found this to be slightly con...
tranquil pine
for lim f(x) as x -> 3...
in the video it's said that the function is continuous.
but the function itself is not continuous correct?
only the part for where x approaches 3 the function is continuous.
please correct me where I'm wrong.
Because I did a quick search to understand what a continuous function is and what I got was a function that doesn't show breaks or disconnects/leaps.
which to me clearly isn't that.
static plinth
if we look at the function near x=3, is there any holes or discontinuities?
tranquil pine
Nope.
static plinth
that would imply that at x=3 the function is continuous
but that doesn’t necessarily mean that it is continuous for all other numbers
tranquil pine
Perfect that's what I thought as I said but had to confirm, sorry to waste your time. Thank you so much 🙏
You've helped me before as well, really appreciate your patience btw lol.
.close
final saddleBOT
final saddleBOT
Available help channel!
tranquil pine
im just a bit confused regarding the definition of homogeneity for ODEs. As far as I know there are three "definitions" (ill consider first order here)
1- if for y' + p(t)y = g(t), we have g(t) = 0
2- if for y' = f(t,y) we can have f(t,y) = f(y/t) = f(u)
3- if for y' = f(t,y) we have f(kt, ky) = k^n f(t,y)
final saddleBOT
im just a bit confused regarding the definition of homogeneity for ODEs. As far ...
final saddleBOT
@tranquil pine Has your question been resolved?
cyan kayak
If 1 and 2 are precisely the same then f(t, y) = f(y/t) implies that p(t)y - g(t) = f(y/t) which would demand that p(t) = 1/t and g(t) = 0. But clearly we have more complicated homogeneous ODEs than just this one. So 1 and 2 are incompatible in general except in the one specific case.
Similarly 3 and 2 are incompatible.
I would imagine that these are describing 3 different senses of homogeneous, rather than 3 facets of one larger sense.
However, I couldn't swear to it. I do know that this was never brought up in my particular ODE class.
tranquil pine
However, I couldn't swear to it. I do know that this was never brought up in my ...
Weird. I can never get a good grip of what homogenous is supposed to mean in this case
with the different ways of mentioning it like here
cyan kayak
Obviously they mentioned homogeneous itself many times, but I took the different usages to be just the homogeneous case of whatever particular solution case we were working on
It is interesting to think that they might be deeply related concepts, but I do not think they are
tranquil pine
alright so i guess the question becomes what exactly do you consider the "homogenous case" of some solution
i mean surely there is some sort of relevance to the word "homogenous" maybe
cyan kayak
Unfortunately, that's not something I'm equipped to answer, I took the engineering ODE class. 😦
I just learned homogeneous as the "nice and easy to solve" case lol
tranquil pine
hmmm
seems like the term itself is totally arbitrary in that case then. Well, I will let this stay open for further input from others I suppose
final saddleBOT
@tranquil pine Has your question been resolved?
dim brook
I do not know after I take three derivatives of YP, and the outcome is not same as the equation in red circle.
final saddleBOT
I do not know after I take three derivatives of YP, and the outcome is not same ...
@dim brook Has your question been resolved?
shell panther
How do u solve q1 and 2
final saddleBOT
How do u solve q1 and 2
silver roost
Do you know the period of sinx
steep tendon
yea 2pi/(1/2)
shell panther
So it’s D
steep tendon
yes
shell panther
I don’t rly understand q2
steep tendon
do u know which ones are definitly correct/definitly incorrect?
steep tendon
so CDE only has 1 correct or none, AB is the same
now A and B you can determine with the amplitude
and CDE u can determine by finding when sin(2pit/12-pi/2) is largest
shell panther
now A and B you can determine with the amplitude
For that do u have to also use the phase shift?
Or does phase shift only change the graph function
steep tendon
yea u need the phase shift because the time
it will move the graph pi/2 to the right
wait not pi/2
it will move it x amount right where 2pit/12 = pi/2
final saddleBOT
Available help channel!
alpine wind
am I the only one whose brain can't seem to comprehend this problem?
alpine wind
"is it likely that the guaranteed condition is verified", I mean I'm fucking looking at test data that doesn't meet the condition
what am I supposed to do here even?
static plinth
have you done hypothesis testing or is this just supposed to be a 95 percent confidence interval
alpine wind
this is part of the confidence interval section so I assume we use confidence interval
I already know how to conduct a hypothesis test and build a confidence interval
but what am I supposed to be testing against here anyway
static plinth
i see
well it is asking for us to test whether or not the “guaranteed condition” is verified
alpine wind
it's not we can see it
static plinth
or rather the alternative hypothesis would be that mu is less than 5
alpine wind
how does mu being less than 5 prove anything
static plinth
it's not we can see it
well we don’t know that unless we do hypothesis testing
it does look like it doesn’t
but we can’t know for sure
alpine wind
if the "average" is less than 5, that doesn't gaurantee that some values are not higher than 5
alpine wind
hence the test will be usless
static plinth
to show that most of them is less than 5
since we are doing it with 95 percent confidence
it will be even more accurate
where 95 percent of the samples would fall under the condition
alpine wind
but for the sake of what the question is already asking "is it likely that the guaranteed condition is verified?" isn't hte question already answered
static plinth
supposing that the hypothesis test proves our alternative hypothesis
static plinth
well that is more intuition
for stats we usually need statistical evidence to back it up
static plinth
we can’t really just say, oh one value is greater so it must not
a sample can have its outliers
alpine wind
if there exists one value which does not meet the condition, then the condition is not verified
if there exists outliers then by definition the condition is not met
the condition is "it is gauranteed to be less than 5"
static plinth
well the thing is, we are doing this with 95 percent confidence
not 100 percent
so there will be some samples that might not do something like that
but ig the question is a little extreme by saying that it is guaranteed
alpine wind
I don't think we're on the same page here
static plinth
regardless, we have to do hypothesis testing or a confidence interval whether you like it or not
alpine wind
the very context of the problem doesn't need a hypothesis test
you don't disprove mathematical theorems with hypothesis testing
for "for all ...." theorems, you can disprove them with a single counter example
same with here
static plinth
note how the question also asks if it is likely that the condition is verified, and not if the condition is verified
so just because there is one outlier that doesn’t satisfy the condition
doesn’t mean that it is unlikely that is satisfied
static plinth
for "for all ...." theorems, you can disprove them with a single counter example
what you’re going at here, you should probably talk about with your teacher
they will most likely have a better way to counteract that than i do
lucid tiger
whats up
alpine wind
sorry but I'm still not convinced
static plinth
what you said up there is true that, yes the condition is not verified because there is one counterexample
but it isn’t asking if it is, rather if it is likely that it is true
alpine wind
when we look at a sample we assume all values are sampled from the population
non of them are "false"
whether they represent the bigger population is what we're testing
but in an existence proof, just one single value from a sample is enough
as in this case
static plinth
again, that is verifying whether or not the condition IS true, not whether or not it is LIKELY to be true
alpine wind
I might be stupid but I don't see how there is a distinction between the two in this context
static plinth
let’s say this, from the sample that we got there, there is one number above 5 which disproves the condition about the entire population
but this is just one sample out of the many samples we could’ve taken
and maybe a majority of these samples don’t have a number above 5
then that shows that we got a sample that has a low probability of occurring that disproves this condition
meaning that it is more likely that the condition is true than it isn’t
based on the sample we’ve taken
like if we took multiple samples, there might be a higher chance that i get a sample that doesn’t have a number above 5
which shows how it is more likely to prove the condition than it isn’t
doing it this way proves whether or not the condition is likely to be true
but doesn’t necessarily mean that the condition is true
final saddleBOT
@alpine wind Has your question been resolved?
tranquil pine
final saddleBOT
tranquil pine
i am lost
the divisors is the prime factorization of n^2
$n = p_1^{k_1}p_2^{k_2}p_3^{k_3}....p_n^{k_n}$
soft zealotBOT
Derivative
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
final saddleBOT
tranquil pine
how do i use telescoping series for this
this is what i got, tell me if i got it good
$\lim_{n\to\infty} 1 + \dfrac{1}{2} - \dfrac{1}{nn!} - \dfrac{1}{n!(n+1)} = \dfrac{3}{2}$
soft zealotBOT
Derivative
tranquil pine
<@&286206848099549185>
urgent need to give back assigment
homework assigment
ah i used helpers tag for previous question i asked but then i asked another question and used again
i found the answer to my first question but to that question i did but wanted to make sure it is right
ye i know but scroll up i asked another question
ok so i broke the rules my bad
yes thanks for the explanation i wont do it again
final saddleBOT
@tranquil pine Has your question been resolved?
gentle swan
From personal experience is linear algebra or topology more fun(and or useful)? I don’t know which I want to take next year, I’m finishing up multi rn
final saddleBOT
From personal experience is linear algebra or topology more fun(and or useful)? ...
zenith pollen
linear algebra is like 50 times more useful and topology may/may not be more fun depending on how analysis heavy it is
royal gust
Linear algebra is very useful
I'm wondering how you're getting to decide between Lin Alg and Topology though
final saddleBOT
@gentle swan Has your question been resolved?
meager sky
Suppose we roll 4 6 sided die. What is the expected largest integer to appear on any of the four die?
final saddleBOT
Suppose we roll 4 6 sided die. What is the expected largest integer to appear on...
meager sky
I can imagine enumerating and finding an answer, but that’s too tedious obviously. I wanted to used linearity of expectation, but I’m not sure how to apply it
It may be neither approach
I can’t think of any other way so maybe I am just supposed to count?
So to find E(2) we might say
WLOG let one die roll 2. then the other 3 have 2 options. We then need to multiple it by 4 for each one we fix, Which I feel like tells us
E(2) = 24/1296
wait that overcounts
subtle juniper
Tbh I can’t think of any other way (there might be one) so I might just count all possibilities
We can count the probability of 1 with (1/6)^4
And the probability of 2 with (2/6)^4-(1/6)^4
pine crescent
hi. I'm new here. Why are there so many different help channels?
meager sky
hi. I'm new here. Why are there so many different help channels?
you can get your own help channel by going into one without a name next to the number and typing
meager sky
And the probability of 2 with (2/6)^4-(1/6)^4
I’m not confident I understand why
meager sky
np
subtle juniper
I’m not confident I understand why
For the highest number to be 2, each number must be 2 or less
Which is (2/6)^4
But this over counts the possibility we got all 1s or less
So we subtract (1/6)^4
meager sky
Which is (2/6)^4
oh you’re right
Also am I just supposed to put the one with the highest expectation? Seems obvious but I just want to make sure
subtle juniper
Also am I just supposed to put the one with the highest expectation? Seems obvio...
I’m not sure what you mean by that but you just add all the possibilities
meager sky
the problem asks what is the expected largest integer that appears on any of the four dice
meager sky
Can I be certain that evaluates to an integer?
subtle juniper
No
But expected value doesn’t have to be an integer
If you wanted the integer that would be most likely to occur
It would be 6
meager sky
My main worry is I’m not sure if my problem is a normal EV problem. It might be but it’s wording says “compute the expected value of the largest integer that appears on any of the four dice”
subtle juniper
Expected value is just an average so it should just be normal
The expected value of a dice roll is 3.5 and that’s not an integer
So it shouldn’t be a problem
final saddleBOT
final saddleBOT
Available help channel!
livid schooner
final saddleBOT
final saddleBOT
@livid schooner Has your question been resolved?
pliant shore
someone help pls
You're using the form of the Lagrange error bound that has M
$|R_n (x)| < \frac{M}{(n + 1)!} |x - x_0|^{n + 1}$
soft zealotBOT
south
pliant shore
So here M = 128/3
livid schooner
wait how did you get M
pliant shore
Now, if we want to find the error of the second degree term, what must n be?
livid schooner
It's in the question
pls continue
pliant shore
Now, if we want to find the error of the second degree term, what must n be?
Yeah so this
Second degree = x^2
livid schooner
Second degree = x^2
so the x part is 1/4 I assume?
pliant shore
so the x part is 1/4 I assume?
Not quite
pliant shore
Remember -1/4 < x < 1/4 cause that's your radius of convergence
livid schooner
ok
so what will x1-x0 be?
cuz n=2 since it is f prime prime but Idk what x1-x0 be
pliant shore
so what will x1-x0 be?
It depends on the x you have within that interval
pliant shore
so what will x1-x0 be?
So what other variable must be 1/4 then
livid schooner
So what other variable must be 1/4 then
wiat so since x is between 1/4 and -1/4, so 0?
pliant shore
Right, so what's the maximum value that |x - x0| can be
pliant shore
then what is x1 then?
There's no x1
livid schooner
oh ok I get it
pliant shore
Yep and if you can figure that one out, you just need to figure out what n is, given you have the Taylor series to x^2
I'm not sure if you've learned this, but the maximum error of any Taylor series is just the next... (fill in the blank)
livid schooner
I'm not sure if you've learned this, but the maximum error of any Taylor series ...
the next term in the order thing
like u expand the entire thing out
and the next one is error
livid schooner
yes
pliant shore
and the next one is error
Mhm, the Taylor series is constructed in a way that it's the best polynomial approximation for a polynomial of degree n
So it's accurate to x^n
And so the next precision it may not be accurate to is x^(n + 1)
livid schooner
And so the next precision it may not be accurate to is x^(n + 1)
oh so that's why it's the error then
pliant shore
And so the next precision it may not be accurate to is x^(n + 1)
But many functions such as sin x = x - x^3/3! + x^5/5! or cos x = 1 - x^2/2! + x^4/4! have some coefficients equal to 0, so that's an upper bound for the max error, as in if you have sin x stopping at x^3 then the next term is x^5
Sometimes the max error may never be that big at all
livid schooner
But many functions such as sin x = x - x^3/3! + x^5/5! or cos x = 1 - x^2/2! + x...
I literally remember the sin one is 1-x^3/3! that it is all odd numbers
and cos is all even numbers
livid schooner
Sometimes the max error may never be that big at all
ok
pliant shore
I literally remember the sin one is 1-x^3/3! that it is all odd numbers
Yeah that's actually where the names of even and odd functions come from
Even and odd powers of the Taylor series
livid schooner
Yeah that's actually where the names of even and odd functions come from
I did not know that but damn your knowledge is impressive
pliant shore
Yeah it is haha
livid schooner
.close
final saddleBOT
final saddleBOT
Available help channel!
final saddleBOT
lyric quiver
The factorial is throwing me off
steep tendon
see if every next number in the sequence gets smaller by a percent? idk
final saddleBOT
@lyric quiver Has your question been resolved?
silver maple
The factorial is throwing me off
Do you know the definition of factorial
What techniques have you tried
lyric quiver
I tried graphing / looking at the plots. Table graph, it looks like it goes to infinity, not to a specific number
I thought it diverges, but the answer key is almost stating that it converges? Not sure if I am reading that wrong or not though
Usually a factorial is more powerful than an exponent too
So to me, it's almost as if it's saying infinity / bigger infinity = goes to 0 ?
silver maple
I asked for the definition
You might be able to get the answer through inspection, however I would use the ratio test
lyric quiver
Ah, we have not learned about the ratio test yet
But this looks like... I could use the telescoping sum?
silver maple
I am afraid I can't help you
lyric quiver
That's ok, thank you for trying @silver maple
solemn igloo
seems like a pretty perfect fit for ratio test
weird problem to assign without that
oh im stupid
nth term
lyric quiver
Ah ok hmmm.. I'm trying to plug in the answers and see if I get any hits that way 💀
solemn igloo
Ah ok hmmm.. I'm trying to plug in the answers and see if I get any hits that wa...
i mean
just consider the limit of the individual terms as n->\infty
final saddleBOT
@lyric quiver Has your question been resolved?
lyric quiver
.close
final saddleBOT
final saddleBOT
Available help channel!
viscid frigate
can someone tell me how to solve fractions equations
final saddleBOT
can someone tell me how to solve fractions equations
viscid frigate
<@&286206848099549185>
sand hare
can someone tell me how to solve fractions equations
Example?
flat hearth
can someone tell me how to solve fractions equations
There are some tips and tricks in fraction equations
For addition
viscid frigate
viscid frigate
oh ok
flat hearth
5/7 = x/35
viscid frigate
what is this /
sand hare
It means fraction
flat hearth
It can represent a fraction bar
viscid frigate
oh ok
flat hearth
5/7 = x/35
We cross-multiply to get 7x = 175
Then we can cancel out the 7 in the left side of the equation
by dividing
So it becomes 7x/7 = 175/7
x = 175/7
Therefore x = 25
viscid frigate
can make in a pic so i can understand more
flat hearth
Wait for a bit
viscid frigate
ok
sand hare
As you can see here I’ve gotten rid of the fraction by multiplying evry term. Then just simply expand an solve, no fraction. (This is obviously more complicated because you can’t cross multiply)
So I always just get rid of the fractions then I solve
viscid frigate
Kinda messy, but it is what it is
So what do you do to simplify what is the first step and the final step do you always divide ?
viscid frigate
As you can see here I’ve gotten rid of the fraction by multiplying evry term. Th...
hmm
flat hearth
So what do you do to simplify what is the first step and the final step do you a...
Yep, just cross-multiply, cancel out, divide, and you're done
sand hare
Sorry if I got it more complicated 😂
viscid frigate
Yep, just cross-multiply, cancel out, divide, and you're done
rlly ?
viscid frigate
Sorry if I got it more complicated 😂
no u didn't but i just want an easy method since tom is a test yn
sand hare
If your not gonna come across the ones I did don’t worry bout it
viscid frigate
so i'm going to solve a fraction and you tell me if i'm correct
the fraction is x/5 = 4/7
5x4=20
and then i divide 20 with 7
am i correct ?
or did i miss some steps ?
sand hare
Yup ur correct
viscid frigate
so what is the answer ?
viscid frigate
oh
I saw the teacher looking for the lcm with fractions do i do the same thing to those type of fractions ?
and something about terms not sure
sand hare
Ok
So teach was talking about adding and subtracting fractions which is far different
For that you need a common denominator
I’ll show you
viscid frigate
ok
sand hare
Sorry did you want that with variables or without
sand hare
For multiplying and dividing fractions simply make multiply the numerators and multiply the denominators.
Sorry for division you do literally the same thing as multiplication but first you flip over one of the fractions then multiply them
sand hare
sand hare
im not talking about those fractions
Which ones? Like they equal something and you have to solve for x?
sand hare
Oh
Your teacher just multiples everything by 15 because you can’t get rid of all the fraction in one go that’s all
If you need more help just ask I can’t help with much but I can help with this
viscid frigate
idk how to solve those type of fractions
viscid frigate
<@&286206848099549185>
random elm
Uhm
random elm
<@&286206848099549185>
What is the problem
viscid frigate
could u help with how to solve those type of fractions
viscid frigate
steps ?
random elm
could u help with how to solve those type of fractions
Uhm
viscid frigate
ok
random elm
One moment please
viscid frigate
take your time
brittle mesa
Just multiply 6/7 by x and 4/x by 7 which is = 6x-28/7x=0
random elm
brittle mesa
bring 4/x to the other side first
random elm
Goodbye
viscid frigate
Just multiply 6/7 by x and 4/x by 7 which is = 6x-28/7x=0
how about divison ?
brittle mesa
Step 1: bring 4/x to the LHS which is: 6/7 - 4/x=0
Step 2: u wanna combine them so u multiply 4/x by 7 and 6/7 by x which is: 6x-28/7x=0
Then u gotta get rid of the 7x
U multiply 7x on both sides
And since the RHS is 0, then 7x*0 =0
So 6x-28 = 0
Then bring 28 to the RHS and divide it by 6
viscid frigate
what's the answer?
brittle mesa
x = 14/3
brittle mesa
Huh
viscid frigate
brittle mesa
no is 27/8
Did u find this answer or was it in the book?
Cuz I’m pretty sure it’s 14/3
viscid frigate
Did u find this answer or was it in the book?
my bad it's 45/2
brittle mesa
Ohh u meant this question?
viscid frigate
Cuz I’m pretty sure it’s 14/3
for which one
viscid frigate
Ohh u meant this question?
yea
viscid frigate
bro i'm failing my test 💀
brittle mesa
💀💀💀
viscid frigate
i'm cooked
brittle mesa
my bad it's 45/2
Do yk how to do this one?
viscid frigate
Do yk how to do this one?
that was the teache answer
viscid frigate
When’s ur test?
today
brittle mesa
that was the teache answer
Oh do u. Need help?
u can do it another way
I find it easier
viscid frigate
Oh do u. Need help?
why my here then lmao
viscid frigate
my test is on fraction and equations , 1 step equation 2 step equation .linear equations
bro..
brittle mesa
Damnn
viscid frigate
ya'll what do i doo
brittle mesa
U can study during ur other classs
viscid frigate
U can study during ur other classs
i can but it's gonna be useless since i don't know how to simplify equations or fractions equation
viscid frigate
@brittle mesa what grade ur in
brittle mesa
Wait a sec
brittle mesa
Huh
viscid frigate
my i......1.1.1.1.1.1.1.q is prob 5
brittle mesa
Chillout💀
viscid frigate
oh ur answering this question
brittle mesa
3k/5 - 6 = k/3
brittle mesa
oh ur answering this question
What else😭😭😭
viscid frigate
no
viscid frigate
hahaha
viscid frigate
hmm i'l try my best pls wish me gud luck on the test
viscid frigate
@brittle mesa have you failed any courses ?
brittle mesa
Nope
viscid frigate
brooo ur smart
brittle mesa
💀💀💀
viscid frigate
so luck i'm pretty i could understand if u follow my words
so what is the first step like the first step to solve those kind of fraction
brittle mesa
Ok so the first thing I did
viscid frigate
broo u aren't a helper sorry i took so much of ur time
brittle mesa
It’s ok lmfaooo
viscid frigate
u don't have school ?
brittle mesa
Holidays
viscid frigate
ur in the us ?
brittle mesa
I’m French
viscid frigate
oh bonjour
brittle mesa
…
viscid frigate
lmao
viscid frigate
Ok so the first thing I did
.
brittle mesa
Bring all the fractions together
So to do that
U need to put 3k/5 and k/3 to the same side
Which is what I did in the 2 first steps
viscid frigate
use the bot pls
viscid frigate
oh ok
brittle mesa
Which one is it?
viscid frigate
idk
brittle mesa
Idk what else to do
Call a helper or sum💀
Way more qualified
My teaching skills mid
viscid frigate
bro it's not u
i just lose braincells from learning math
@brittle mesa thank you
brittle mesa
Hahahaha
It’s better if u ask ur teacher to explain in detail what u didn’t get
Face to face is more practical
viscid frigate
too late
viscid frigate
my friends are stupid
you know what idc what i get on the test but i rlly need to improve
cause my average is 33.38 %
alr later
final saddleBOT
final saddleBOT
Available help channel!
heavy grove
If a company makes x hundred A tires and y hundred B tires.
0=<x=<4
y = 40-10x / 5-x
The profit on grade A tires is twice that of the profit of B tires Find the number of each tires to be made to maximize profit
final saddleBOT
If a company makes x hundred A tires and y hundred B tires.
0=<x=<4
y = 40-10...
@heavy grove Has your question been resolved?
molten raptor
Hello!
molten raptor
If I have the following
I'm well aware that I can do
ln( (1-x) / (x+3) ) = ln 1
e^ln(1-x/x+3) = e^ln(1)
(1-x) / (x+3) = 1
1-x = x+3
2x = -2
x = -1
however, say I didn't want to do the step where I put the ln terms together
what would that look like
would it be e^ln(1-x) - e^ln(x+3) = e^ln(1)
or would it be
e^ln(1-x) - ln(x+3) = e^ln(1)
lucid marsh
e^(entire rhs) = 1
molten raptor
lhs i guess you mean
lucid marsh
lhs i guess you mean
Yes
final saddleBOT
final saddleBOT
Available help channel!
tranquil pine
Can anyone once again explain where and how multisets are used?
final saddleBOT
Can anyone once again explain where and how multisets are used?
upbeat zephyr
can you help me with question 4?
tranquil pine
Can anyone once again explain where and how multisets are used?
And can be used in regular notions of set
upbeat zephyr
tranquil pine
Can anyone once again explain where and how multisets are used?
Some folk answered but ig I was busy and till I came
Channel vanished
tranquil pine
can you help me with question 4?
Lol I am not eligible to answer ur question
You can ping helpers after 10 min ig
tranquil pine
can you help me with question 4?
Channel occupied
upbeat zephyr
Lol I am not eligible to answer ur question
im having exam tomorrow and im having hard time understanding them
can someone help me?
tranquil pine
You should ask this in another channel
upbeat zephyr
which channel?
tranquil pine
Can anyone once again explain where and how multisets are used?
<@&286206848099549185>
@tranquil pine , sorry, but I don't know so much about multisets
Good luck!
tranquil pine
<@456226577798135808> , sorry, but I don't know so much about multisets
No issues bruv
Even I don't 🫂
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
Can anyone once again explain where and how multisets are used?
<@&286206848099549185>
final saddleBOT
@tranquil pine Has your question been resolved?
bleak fractal
yo
bleak fractal
.close
mint orbit
final saddleBOT
mint orbit
So I'm working on part 2, I understand it's supposed to be trivial, but I don't really understand.
soft zealotBOT
jan Niku
mint orbit
I'm not understanding the next steps from here though, in the proofs that I'm reading
We do want to introduce a pointwise limit, right?
final saddleBOT
@mint orbit Has your question been resolved?
final saddleBOT
@mint orbit Has your question been resolved?
final saddleBOT
Anyone?
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).
rain stirrup
i dont know how to work this discord server
void fjord
!occupied
final saddleBOT
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).
void fjord
Go to the channel and read.
mint orbit
while youre here please help @neon slate 
neon slate
while youre here please help <@218476117101772801> <:happy:908558103992225822>
i would be happy to but this is way out of my depth 😄
i dont know anything about analysis
final saddleBOT
@mint orbit Has your question been resolved?
final saddleBOT
@mint orbit Has your question been resolved?
versed crater
Where does this f_m come from do you know
mint orbit
Where does this f_m come from do you know
cauchyness
versed crater
Oh it’s just some other function in the sequence
I’m not sure what $|f_k-f_m|\leq ||f_k-f_m||_\infty$ means
soft zealotBOT
Frosst
versed crater
It’s a function on the left and a real number on the right
How can I have inequalities between those 2 things
mint orbit
How can I have inequalities between those 2 things
The infinity norm is a supremum
like if you have $||f|| = a$
soft zealotBOT
jan Niku
mint orbit
then almost everywhere, $a\geq f$
soft zealotBOT
jan Niku
mint orbit
or, $a$ is a supremum of $f$ except on some set of measure 0
versed crater
Oh as a constant
soft zealotBOT
jan Niku
mint orbit
sure
versed crater
Ok
versed crater
@mint orbit what are you struggling to get in this question
mint orbit
<@331558346333224964> what are you struggling to get in this question
im not certain how to start
versed crater
What about this
I think you’re just supposed to stack the Cauchy on the uniform convergence
Cauchy tells you you can squeeze that norm as tight as you wish
Then that tight bound is the same as picking any epsilon to show uniform convergence
mint orbit
What about this
thiis proof doesnt seem like a proof
i do not understand the one that i linked at all i just thought it might help bait someone to help me to be honest
i know the definition of cauchy
i just dont follow the rest of this proof
mint orbit
I think you’re just supposed to stack the Cauchy on the uniform convergence
the proof i showed in that image seems to just jump from being cauchy to being convergent which is the primary meat of the proof and the part i dont understand
glad dragon
ok
hearty scroll
Heyyy
chilly cloud
where are you stuck? (if you are still stuck)
mint orbit
where are you stuck? (if you are still stuck)
I guess I don't really know how to start, beyond "take some cauchy sequence"
I get the framework is like
#1 you need to find some candidate function that this cauchy sequence converges to
chilly cloud
you'r following this?
mint orbit
#2 you need to show it does converge to that
mint orbit
you'r following this?
i posted this to try to improve response rates
like "look the problem is easy"
i dont understand that proof at all
chilly cloud
Convergence in sup norm is uniform convergence iirc
sorry its been a while since i took this
mint orbit
I was working with another person in my dept
he suggested that i like
so take cauchy to mean that we can find some k such that $||f_k - f_j|| < \epsilon$ given $k < j$
soft zealotBOT
jan Niku
soft zealotBOT
jan Niku
mint orbit
Convergence in sup norm is uniform convergence iirc
my analysis is not strong enough to understand the 4 or 5 jumps the author makes in that proof
chilly cloud
Which jump specifically?
mint orbit
the proof just ends
it seems like it barely starts
I guess I need more details than this
like
i dont understand whats going on with the union
and then he just asserts that it converges uniformly but doesnt show it?
and then the proof just stops
the rest of this document is about p < infty
mint orbit
**jan Niku**
id like to try to track this out because i at least barely understand it
chilly cloud
Ok lemme write out the details (or attept to rn)
chilly cloud
at least this is step #1
by the way
mint orbit
does that step make sense
The limsup has to move closer to the fixed f_k
so you can use it as a candidate since its at least less than epsilon
but I'm not sure how to resolve this outside of some fixed k
Like the dream is that you just say
okay take $N_j$ to be the set where $|f_k - f_j| \geq \epsilon$ for some fixed $k,j$
soft zealotBOT
jan Niku
mint orbit
then call $N = \bigcup _J N_j$ has $|N|=0$ and on $N^c$ you have that $|f_k - f_j| < \epsilon$
soft zealotBOT
jan Niku
mint orbit
now it makes sense to propose the candidate $|f_k - \limsup _j f_j| < \epsilon$ because $\limsup _j f_j \leq f_j$ i think
soft zealotBOT
jan Niku
mint orbit
and well the limsup will be within the epsilon ball
mint orbit
**jan Niku**
but its not clear to me how to resolve the epsilon here, which is fixed because of the fixed k
once we want to involve other k, presumably, to get convergence
chilly cloud
and well the limsup will be within the epsilon ball
I think i got it
iirc it depended on completedness of reals
but im just doublechcking if im a crank now LOL
yea my prof literally said
'key ingredient is completedness of R' ill send pic
mint orbit
I think i got it
its not enough
limsup isnt guaranteed to converge to f_k
it will only converge along j,k
the limsup might actually eternally be some non-negative distance away from f_k, we can't actually bound it without un-fixing k
chilly cloud
its not enough
oh i didnt do it this way oops ill check again tho
chilly cloud
since atm epsilon is actually fixed
Ok so the only problem part here is
you want to pass to the reals at the end of the proof
All this Z_n,k nonsense is doing is carving out the bad set wher bad things happn
So you have: