#help-49
gusty falcon
midnight plankBOT
gusty falcon
This may be a dumb question but this person who answered this question is wrong about the green part right?
Like he's assuming that the % score is positively correlated with the probability of being hired
is that why he wrote 0.64 or lower? But that makes no sense because it feels like the assumption is unfounded
dreamy lichen
they probably shouldve written less than 0.65 instead, ye
gusty falcon
they probably shouldve written less than 0.65 instead, ye
that's fair enough but still
where did they get the upper bound of 0.65?
dreamy lichen
Like he's assuming that the % score is positively correlated with the probabilit...
using this assumption
dreamy lichen
purely mathematically, you cant make that assumption
radiant roost
It's sloppy notation
dreamy lichen
but it's a reasonable assumption to make irl anyway
gusty falcon
yeah i mean even in real life, this assumption might be wrong cuz someone might have other factors besides grades
but also he's an "expert" so i wanted to clarify
dreamy lichen
yeah i mean even in real life, this assumption might be wrong cuz someone might ...
its not grades, its skill test thats part of the application
gusty falcon
oh yeah
okay here's my mathematical reasoning
without this assumption
Quantity A can be anything between 0 and 1,inclusive, because the two events are independent
The complement of "an applicant who scores 80 percent of greater on the test..." -> an applicant who scores 80 percent or lower on the test is 0.35 but this doesn't say anything about Quantity A, so i guess it's just word play?
dreamy lichen
its a pretty weird question honestly
i just read the paragraph below it and I dont like it
dreamy lichen
i just read the paragraph below it and I dont like it
here he literally says "hey, the probability will be different if he scores 10% and if he scores 70%"
gusty falcon
but am i being dumb or i'm missing where exactly the question is supposed to be hard
dreamy lichen
He also said "this question is hard"
only apparently
if i understand that correctly, i think he meant sth like
"This question appears to be hard, but it's really not"
gusty falcon
here he literally says "hey, the probability will be different if he scores 10% ...
Okay i think this is his way of saying quantity A can be anything between 0 and 0.65 i think
and he's showing that Quantity A can be on either side of 0.35
hence a comparison can't be made
gusty falcon
if i understand that correctly, i think he meant sth like
"This question appears...
oh
but i still don't get it
what's so hard about this question
wouldn't everyone get this right
cuz there's just no information
dreamy lichen
Okay i think this is his way of saying quantity A can be anything between 0 and ...
we shouldn't assume anything else about the applicant
gusty falcon
we shouldn't assume anything else about the applicant
is it okay if i say quantity A can be anything between 0 and 1
cuz we don't know about other outside factors?
and not bound it above by 0.65
digital leaf
quantity A is indeed any probability
dreamy lichen
is it okay if i say quantity A can be anything between 0 and 1
that depends
purely mathematically, yeah
gusty falcon
yeah cuz there are many factors that could've influenced a person's score, but that doesn't take away from his chances of landing a job?
idk i don't rsee a reason to bound it above by 0.65
Lol
Like okay kinda makes sense but surely there are exceptions too?
digital leaf
the question only mentions what happens to a >=80% scorer, and nothing about a <80% scorer, so yee
dreamy lichen
but if you take reality into account, 0.65 is a reasonable bound to make, and what if this bound actually made the question solvable?
gusty falcon
the question **only** mentions what happens to a >=80% scorer, and nothing about...
yeah exactly
radiant roost
They could hire 65% of those who score well and none who don't, or they could hire 65% of those who score well and all who score poorly. You can't know
gusty falcon
but if you take reality into account, 0.65 is a reasonable bound to make, and *w...
yeah but the bounds have to be the only case?
this is maybe a bit subjective?
digital leaf
we do not even know if the test is supposed to be graded positively - what if 0% was the maximum? ;)
gusty falcon
I saw in another site that this question was also listed hard with some entry level olympiad questions
That's why i thought
i'm missing something lol
dreamy lichen
They could hire 65% of those who score well and none who don't, or they could hi...
if we are supposed to solve the problem purely mathematically, then I agree. But if you were supposed to solve it from persepctive of e.g. an economist or someone like that, then you should take the other factors into account
digital leaf
strictly speaking, I'd also think that this is too little context to even fit into reality
gusty falcon
if we are supposed to solve the problem purely mathematically, then I agree. But...
no perspective
wait
maybe this is a logic test
but also this is a math portion
so i think anything goes right?
Okay i guess that's that
This question is pretty stupid
digital leaf
ye
gusty falcon
😭
dreamy lichen
the solution is more stupid though
digital leaf
the solution is stupidest
dreamy lichen
i just read the paragraph below it and I dont like it
especially this paragraph
gusty falcon
the solution is more stupid though
why?
digital leaf
the question is stupid, but ultimately acceptable
dreamy lichen
What's the probability that a natural number between 1 and 100 is even?
gusty falcon
i just read the paragraph below it and I dont like it
why? isn't this just his way of saying that quantity A is bounded below by 0 and above by 0.65
digital leaf
the solution writer believed that score change must mean pass probability change
gusty falcon
so you can't compare with quantity B
digital leaf
quantity A should not have been bounded to 0.65, at all
dreamy lichen
What's the probability that a natural number between 1 and 100 is even?
"Well, we cannot know, because if the number was not divisible by 4, the probability would be different"
dreamy lichen
What's the probability that a natural number between 1 and 100 is even?
"Well, w...
this is literally how the solution works
gusty falcon
why? isn't this just his way of saying that quantity A is bounded below by 0 and...
no but isn't he doing this
because ultimately the question is like
to compare with 0.35
digital leaf
the solution writer was doing it, yes
digital leaf
only that their answer was wrong
digital leaf
their final choice is right, but their reasoning is wrong
gusty falcon
but i think that's debatable?
dreamy lichen
he says that in case he scored 10%, the probability would be <0.35, and in case he scored 75% the probability would be >0.35
he is splitting it up into cases to argue that we cant know what the probability is
dreamy lichen
What's the probability that a natural number between 1 and 100 is even?
"Well, w...
thats the same thing I did here
dreamy lichen
if he argued that it could be >0.35 and <0.35 depending on how strict the company is, it would be completely fine
dreamy lichen
he says that **in case he scored 10%**, the probability would be <0.35, and **in...
but this is just stupid
gusty falcon
if he argued that it could be >0.35 and <0.35 depending on how strict the compan...
yeah i think he was providing examples with this
not sure why
dreamy lichen
the previous assumption was at least "common sense"
dreamy lichen
yeah i think he was providing examples with this
its not providing examples, its the core of his argument unfortunately
he argues that B could be < 0.35 if the applicant scored 10%
but you cant handle the cases seperately like that
digital leaf
the two cases should not have yielded something relative to 35%
each case is just from 0 to 1, amirite 😎
dreamy lichen
there is just one probability
gusty falcon
should've written "for example" maybe lol
dreamy lichen
should've written "for example" maybe lol
then the argument would be incomplete
gusty falcon
isn't it just like a proof by contradiction, to an extent
10% is attainable and it is striclty less than 35%
and also 75% is assumedly attainable too which is greater than 35%
dreamy lichen
the core of his argument is this:
it's possible that B < A, which happens when applicant scores 10%
it's also possible that B > A, which happens when applicant scores 75%
dreamy lichen
10% is attainable and it is striclty less than 35%
10% is the score on the test
gusty falcon
so two examples could work as a proof here? cuz this isn't an proof by example but rather just contradiction ro something like that
gusty falcon
the core of his argument is this:
it's possible that B < A, which happens when ...
why does "for example" not fix his solution?
dreamy lichen
why does "for example" not fix his solution?
The 10% is the score on a test, not probability
he doesnt compare 10% to 0.35 at all
digital leaf
the solution writer does not mean that at all
gusty falcon
radiant roost
Idk what the solution is trying to say
gusty falcon
the solution writer does **not** mean that at all
mmmm
i think maybe i should write a solution on that site
😭
digital leaf
let me write it lol
gusty falcon
this is all way too confusing
gusty falcon
"part of the solution involves explaining why the expert is wrong"
gusty falcon
oh so it's between 0 and 1
dreamy lichen
if he compared 10% on a test to 0.35, it would be wrong as well
gusty falcon
yeah okay, so?
gusty falcon
if he compared 10% on a test to 0.35, it would be wrong as well
oh
i think i get your point
righttt
i think he was doing too much
idk why
digital leaf
this is all way too confusing
Read the question.
The stem tells us that an applicant scoring 80% or greater on the test has a 65% chance of being hired.
It does not tell us what happens to applicants scoring less than 80% on the test.
Therefore, we cannot assign a probability to quantity A.As such, D is the answer.
dreamy lichen
I read this as
"The applicant could score 10%, in which case quantity A < 0.35", in other words, the probability that he gets accepted < 0.35
digital leaf
that's also how I read that
dreamy lichen
I read this as
"The applicant could score 10%, in which case quantity A < 0.35"...
and this is really stupid
digital leaf
it's not "0.10 is less than 0.35", but rather "0.10 on the test means a probability of passing less than 0.35"
and both views are incorrect.
dreamy lichen
What's the probability that a natural number between 1 and 100 is even?
"Well, we cannot know, because if the number was not divisible by 4, the probability would be 33%, but if it was divisible by 4, it would be 100%." Therefore D is the right answer
digital leaf
ye
dreamy lichen
yeah, that solution is just senseless
it doesnt make sense from the mathematical perspective, nor from the common sense perspective
gusty falcon
so you mean he just brought up the test score of the applicant
digital leaf
ye
gusty falcon
which has nothing to do with the comparison
dreamy lichen
which has nothing to do with the comparison
exactly
digital leaf
ye * 2
dreamy lichen
you were supposed to determine the probability of the applicant getting the job given just that his score was below 80%
gusty falcon
right i seee now
dreamy lichen
and you are supposed to calculate that probability as a whole
gusty falcon
okay i get how the question was hard
it was his solution all along
which was hard
dreamy lichen
that probability doesnt change if you are given a different applicant
gusty falcon
that probability doesnt change if you are given a different applicant
yes fair enough
gusty falcon
75% on the test is basically = 30% on the test
cuz they're both
less than 80%
for this question
so for quantity A it gives you the same answer
mmmm okay
digital leaf
that's how you were supposed to group them, ye
dreamy lichen
75% on the test is basically = 30% on the test
you should treat them equally basically
digital leaf
you can propose to edit the solution :3
digital leaf
oopid site lol
dreamy lichen
thanks
digital leaf
...not recent - it's nearly 6 months old
gusty falcon
A) recent
B) 7 months old
😭
recent could be 8 months so A > B but recent could also be yesterday so B > A
digital leaf
lol
gusty falcon
also it's recent bc uh i think all his solutions
digital leaf
in the context of answering questions, 3 months or older is already not ideal
I swear
gusty falcon
like most of it are an year old
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frail cosmos
hey anyone from econ background?
midnight plankBOT
hey anyone from econ background?
frail cosmos
yea
frail cosmos
maths+ stats
last slate
but ive never experienced it
frail cosmos
okay
last slate
umm, do you have like an actual question or formula
frail cosmos
kk
smoky forge
thanks
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surreal moon
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tidal turret
Cicadas have an unusual life cycle. The adults live for a few weeks to lay eggs underground before dying. The offspring spend several years underground as eggs and larvae before they emerge as adults to repeat the cycle. All the cicadas of the same species emerge as adults in the same year. Four different species of cicadas have life cycles of $2,$ $4,$ $13$ and $17$ years. If all four species were present in their adult form in the year $2000,$ what is the next year in which the adults of exactly three of the four species will be present?
midnight plankBOT
Cicadas have an unusual life cycle. The adults live for a few weeks to lay eggs ...
grand pondBOT
938c2cc0dcc05f2b68c4287040cfcf71
tidal turret
guys can someone explain what they mean with the exercise statement
"all the cicadas of the same species emerge as adults in the same year"
"four different species of cicadas have life cycles 2,4,13 and 17 years"
<@&268886789983436800>
why post that in my help channel?
hollow helm
"all the cicadas of the same species emerge as adults in the same year"
All of the eggs laid by a single species will hatch in the same year
hollow helm
"four different species of cicadas have life cycles 2,4,13 and 17 years"
The life cycle of a species is the time it takes from the eggs being laid until they hatch and lay new eggs.
tidal turret
"four different species of cicadas have life cycles 2,4,13 and 17 years"
if all were present in their adult form in the year 2000
in year 2000 they layed eggs even though they are from different species
such a coincidence
hollow helm
Yes, and the question wants to know what would be the next year this coincidence happens, given that it happened in 2000.
tidal turret
but depending on which three species the year changes
it wants to find the year in which different three random species layed eggs by coincidence
hollow helm
Yes. Let $a,b,c,d$ be the four species, and $\ell_x$ be the length of the life cycle of each species $x \in {a,b,c,d}$. So $\ell_a = 2$, $\ell_b = 4$, $\ell_c = 13$ and $\ell_d = 17$. Notice that a species $x$ will lay eggs in the year $2000+t$, where $t \in \mathbb{N}$, if and only if $\ell_x | t$.
grand pondBOT
ucheo
hollow helm
From that, you can find $t$ such that exactly three species lay eggs in $2000 + t$.
grand pondBOT
ucheo
tidal turret
why l_x div t
hollow helm
We have that species $a$, for example, lays eggs every 2 years. Since they laid eggs in 2000, we know that they will lay eggs in 2002, 2004, 2006, etc. That is, they lay eggs exacly after a multiple of $\ell_a$ has passed since 2000.
grand pondBOT
ucheo
hollow helm
Can you see that?
hollow helm
Yes. So species $x$ will lay eggs after $t$ years since 2000 if and only if $\ell_x | t$.
grand pondBOT
ucheo
tidal turret
so?
hollow helm
So you want to find the smallest $t$ such that $\ell_x | t$ for exactly three values of $x \in {a,b,c,d}$.
grand pondBOT
ucheo
tidal turret
also, the year in which three species lay eggs at the same time doesnt it changes if the three chosen species changes
hollow helm
Yes!
You just want to find the smallest year for which that happens for any 3 species.
tidal turret
You just want to find the smallest year for which that happens for any 3 species...
how
like I need to compare lcm (a,b,c) with lcm (b,c,d)
hollow helm
Yes, you want to find the smallest lcm of three of the four values (:
If it helps, notice that 2, 13 and 17 are prime
grand pondBOT
hollow helm
Think about the prime factorization of $t$
tidal turret
ohh
grand pondBOT
ucheo
hollow helm
This specific values of $t$ satisfies what we want!
grand pondBOT
ucheo
hollow helm
But is it the smallest one?
hollow helm
yes because 4 > 2
It is not
hollow helm
4 = 2 × 2 in prime factorization
Right!
So, the smallest $t$ that is divisible by 2, 4 and 13 is $4 \times 13 = 52$ :)
grand pondBOT
ucheo
hollow helm
Since that is the smallest multiple of three of the four values, that would be the smallest number of years in which exactly three species will lay eggs
hollow helm
Did you understand the thought process?
tidal turret
kinda yeah, but is hard to explain with words
lcm(2,4,13) is the least
common multiple
hollow helm
Yes
midnight plankBOT
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velvet nebula
Hi
surreal moon
@velvet nebula stop spamming help channels. If you have a math question, ask it. If you just want to chat, go to #discussion or #chill
worthy wing
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elder viper
hi
elder viper
Not exactly a question but advice
I have a C+ like 79.73 percent I want to boost my grade upto a b+ and i have one month only before the semester ends
any tips shall i do extensions
or anything to improve my quiz or tests scores
ping me
carmine sigil
Well, do you know how much percentage of the course grade you are done with?
elder viper
What do you mean by that.
carmine sigil
As in, you currently have a 79.73%
carmine sigil
If this represents 50% of the weight of your grade, then if you get a 100% on every single test from here on in, then you can achieve a B+ but not an A. (100% * 0.5 + 79.73% * 0.5 = 89.5ish%)
But if this represents 80% of your grade then it's not possible.
elder viper
I don't need a A because if I get b+ or higher for first semester then I can join geometry.
next year
carmine sigil
My recommendation is if you need to get your grade up, the number one thing you can do is ask your teacher or professor for extra credit and for direction
elder viper
My recommendation is if you need to get your grade up, the number one thing you ...
I will try that
carmine sigil
He or she will have a much stronger idea of your weaknesses and the material you need
elder viper
He or she will have a much stronger idea of your weaknesses and the material you...
Tysm for the tip.
I always wondered why I get bad scores in Math
but I get straight A's in everything else
I don't go to any outside extra learning or extra curs for now
rain wasp
math is not for everyone, it is totally okay
like omni said, try asking your teachers on resources and credits
some practice would help too, look for problem sets and practice them until you master the concepts you are struggling with
midnight plankBOT
@elder viper Has your question been resolved?
tight jasper
what formula do i use to solve this
midnight plankBOT
what formula do i use to solve this
hearty rune
up to you
could be something like y=A2^{t/20}
or y=Ae^{kt} and find k
just something exponential
tight jasper
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remote owl
I need help
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I need help
knotty frost
its -i
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tidal turret
Euler discovered that the polynomial $p(n) = n^2 - n + 41$ yields prime numbers for many small positive integer values of $n$. What is the smallest positive integer $n$ for which $p(n)$ and $p(n+1)$ share a common factor greater than $1$?
midnight plankBOT
Euler discovered that the polynomial $p(n) = n^2 - n + 41$ yields prime numbers ...
grand pondBOT
938c2cc0dcc05f2b68c4287040cfcf71
lavish venture
well do you know the first value of n such that p(n) is not prime
viral dagger
well if you plug in p(n+1)=n^2+2n+1-n-1+41=n^2+n+41
gcd(p(n),p(n+1))=gcd(n^2-n+41,n^2+n+41)
continue with euclids division algorithm
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fossil urchin
what happens to a k dimensional linear surface under a homorphism h mapping R^n to R^m
midnight plankBOT
what happens to a k dimensional linear surface under a homorphism h mapping R^n ...
west iron
a homomorphism of what kind?
spark gazelle
for this problem
midnight plankBOT
for this problem
lavish venture
is that a property of logs
spark gazelle
im not sure thats what my teacher told me
but im doing it with this method and for some reason im getting my questions wrong
lavish venture
$\ln(x^n) = n\ln x$
grand pondBOT
knief
lavish venture
you should also use $\ln \left(\frac{a}{b}\right) = \ln a - \ln b$
spark gazelle
im trying to do derivatives though
grand pondBOT
knief
lavish venture
im trying to do derivatives though
yes it makes it easier
instead of having to do quotient rule
for your chain rule
spark gazelle
oh
austere hare
yo can soemeone help me rq
lavish venture
quandale
austere hare
ye
lavish venture
!occupied
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austere hare
oops
spark gazelle
**knief**
ok let me try it with this
im still getting the wrong answer
What am I doing wrong
its supposed to be 48x^2
spark gazelle
i did the derivative of ln(x^5)
uhh derivative of ln is 1/x
so i put 1/x^5
did chain rule
and power rule x^5 to get 5x^4?
its wrong up there but i changed it when i was going down
to 5x^4
terse robin
the fathers age is six time his sons age. four years hence, the age of the father will be four times his sons age. find the present ages (in years) of the son and the father
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the fathers age is six time his sons age. four years hence, the age of the fathe...
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prime hornet
humble drift
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strong lava
last slate
i am sendin my question
last slate
<:opencry:586078614865444865>
?
dawn dagger
i am sendin my question
today is no help channel day
twilit jetty
Anjali I’m literally typing one right now can you please go to a different channel, it’s not easy to copy paste on mobile
Hello, just wondering if what I’m thinking of makes sense:
If you graph the derivative of x^2 sin(1/x)
strong lava
its envelope near 0 is a double-parabola yes
twilit jetty
However it is not
viral dagger
you were 10 seconds close from seeing the light
twilit jetty
What are it’s coefficients
strong lava
coefficients as what?
twilit jetty
I’ve computationally figured out that it fits
1 + 2x^2 - 2x^4 + 4x^6 - 10x^8 + 28x^10 at least so far
Now I don’t see a pattern here since the method I’m using to find them is very manual
strong lava
you're trying to Taylor approximate f'(x) near 0?
twilit jetty
I would recommend that you plot this, I can’t show you since I’m on mobile
I’ve got a solution for showing you I think
This graph is a year old so it is mostly unorganized
You can see the nested fraction which from there the coefficients come out, edit and see
The general look is for the peaks to appear constant (or for the parabolic peaks in the center to have a “y-intercept” of 0) before moving on to the next nest, also it’s assuming the coefficients are all integers (which shouldn’t be the case if this was more rigorous)
In retrospect this isn’t very solid, but that it appears and simplifies similar to a series is what’s keeping it to me
Now I am going to sleep zzzzzzzz
last slate
.lol
rancid flame
I wanna ask the math wizards or math enthusiast on how should one understand/study mathematics in general? And how should one cope with every defeat of confidence in each failed process of solving or a mind gobbling sessions of "what the heck does that thing means" or "how does that work"?
I'm starting to try and build a passion on learning mathematics, but it seems that in each lessons or process or solutions i gather, i have this troubling question of, "how should i understand this?" Or how should i approach into trying to understand this one? But in each process of trying to feel my way of understanding it, i always end up being all drained and is still not confident on the idea that i did understood what ive been studying for a couple of hours.
midnight plankBOT
I wanna ask the math wizards or math enthusiast on how should one understand/stu...
tawdry laurel
I wanna ask the math wizards or math enthusiast on how should one understand/stu...
Which level are you at
weary fjord
That’s a big yapp
tawdry laurel
(grade)
tawdry laurel
That’s a big yapp
...
tawdry laurel
Understandable
rancid flame
That’s a big yapp
Just a kid asking for a help, yap police
rancid flame
Treat math like a game
But im starting math at algebra 1
tawdry laurel
What
rancid flame
I wanna ask the math wizards or math enthusiast on how should one understand/stu...
As what you can read here
rancid flame
Im having trouble on conceptualizing what it means to "i understand this shit at its core"
astral bough
Yes, cause im trying to understand each concept at its core
Pick up Principia Mathematica then. That's as fundamental as math gets.
tawdry laurel
Just make sure you can do questions about the topic at a certain accuracy
And you understand the sols
Taking time to understand is normal
rancid flame
Then practise is key
Are you suuureee??? Isnt that just being like a follower to a certain techniques and such, and having know idea how and why they work
tawdry laurel
...
weary fjord
Im at grade 12 rn, like a senior high type shit going around my country
Oh! I think you accidentally put 1 in there.
rancid flame
Just make sure you can do questions about the topic at a certain accuracy
Wdym?
last slate
Oh! I think you accidentally put 1 in there.
or 2
rancid flame
Oh! I think you accidentally put 1 in there.
Hey
tawdry laurel
@weary fjord very polite.
rancid flame
Anyway as long as youre satisfied with the accuracy
So basically, just ask the right question and thats it?
Thats the way on understanding every concept in a way that you could get them by its how and why they work
(?)
tawdry laurel
I meant do more questions, as long as you understand the sols and get more than like say 80% correct then youre good
rancid flame
I meant do more questions, as long as you understand the sols and get more than ...
Wdym by sols...
rancid flame
I meant do more questions, as long as you understand the sols and get more than ...
Questions, like problems and stuff to answer?
tawdry laurel
Wdym by sols...
Solutions
tawdry laurel
Questions, like problems and stuff to answer?
Do you have worksheets or mock tests
rancid flame
Do you have worksheets or mock tests
As far as i know, i do. Whyd u ask?
tawdry laurel
Do them blud
last arch
Frfr
rancid flame
@tawdry laurel but then my worry would be that, i should just memorize techniques and solutions?
Until i perfected them?
tawdry laurel
<@1037315397143244860> but then my worry would be that, i should just memorize t...
No lah
devout cove
What do you mean by techniques
tawdry laurel
应用做题
rancid flame
What do you mean by techniques
Like the how to solve this one
last arch
Second guess taiwanese
tawdry laurel
Some methods have to remember tho
tawdry laurel
I'll guess you're Singaporean
My bio
tawdry laurel
But if you didnt look there then youre a good guesser
last arch
It's the lah fr
devout cove
Like the *how* to solve this one
You understand them as you practice, you are not gonna invent something that has already been invented
last arch
Average singlish moment😭
rancid flame
You understand them as you practice, you are not gonna invent something that has...
So just do the problems and then you'll get it?
The much you do them, the much you'll understand them(?)
tawdry laurel
So just do the problems and then you'll get it?
Yes siah
last arch
<@1037315397143244860> but then my worry would be that, i should just memorize t...
Memorizing techniques is fine but you should also know how they work
devout cove
You will not recall anything if you do it without understanding
You’ll forget it after a week or so
tawdry laurel
😂
devout cove
I suggest you to get a teacher
rancid flame
Memorizing techniques is fine but you should also know how they work
Now what do you mean by knowing how they work(?)
devout cove
They’ll accelerate the learning process
last arch
Now what do you mean by knowing how they work(?)
The reasoning behind why we use such techniques
Can you give an example of what you mean by technique
last arch
Because I'm not sure if we're thinking about the same thing frfr
rancid flame
Because I'm not sure if we're thinking about the same thing frfr
Say in system of equations, isnt substitution a form of technique to solve them?
Now what i want to know is why do they work
I cant seem to visualize them or something
tawdry laurel
Now what i want to know is why do they work
Nah we cant help with that
tawdry laurel
I cant seem to visualize them or something
Graph
rancid flame
Graph
Nah i meant, i cant understand why they work in a way that i could see it and be able to explain why they work
last arch
Nah i meant, i cant understand why they work in a way that i could see it and be...
So in substitution we find one variable in terms of another
And use that expression in the other equation
devout cove
Nah i meant, i cant understand why they work in a way that i could see it and be...
https://youtu.be/jLhMemW5pfI?si=Jypfq9kxXOLCmR0s this guy explains stuff in-depth, I recommend watching his videos
rancid flame
So in substitution we find one variable in terms of another
We find the variable in a way that we're finding its equation or how its graphed technically?
Oh man....
But at its core, i should just do more problems and learn along the way?
Or should i first understand the why and how they work and stuff(?)
devout cove
Practicing first then looking at the theory part makes stuff less foggy
Going in head first not knowing what the topic is about is kind of difficult
rancid flame
Practicing first then looking at the theory part makes stuff less foggy
Ohhhh.. okioki ill try this method next time i learn something new
So i first try to figure out how they are solved
Then move to why they work
devout cove
Sure , gotta revise them though
You’re gonna forget about this if you will not revise frequently
I assume you’re an entrant
rancid flame
I assume you’re an entrant
Ig soo
devout cove
If you’re trying to get into a university, I would just get a teacher if I were you
I wouldn’t worry about the theory part
In the entrance exams you’ll not be asked to explain a topic
rancid flame
In the entrance exams you’ll not be asked to explain a topic
But ion know, ig im more concerned with the idea of learning things than just simply passing
tender vector
midnight plankBOT
tender vector
yo no clue what to do here
twilit field
Try arcatn(x/5)=u
midnight plankBOT
full ridge
who tf even made this server lmao
tawdry laurel
who tf even made this server lmao
...
last arch
who tf even made this server lmao
Someone probably
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Available help channel!
last slate
Hi
grand pondBOT
last slate
$a_{21}x + b_{21}y= b_1$
grand pondBOT
last slate
The book said that these would represent 2 lines
And the solution of these equations would give us the intersection of these 2 lines
How to relate this to vectors 😅
rotund oar
And the solution of these equations would give us the intersection of these 2 li...
That's right yeah. Each equation is true along some line, so if you find where both equations are true at the same time, it has to be a point that is on both lines. There's only 1 (or 0) possible intersection points like that.
_ _
One way to relate it to vectors is by turning the equations into dot product equations, like this for your 1st:
If you do this for both, you can then notice that it's the same as this matrix equation:
Which is the more complete vector picture
(not fond of the double-use of b in your eqs btw lol)
last slate
That's right yeah. Each equation is true along some line, so if you find where _...
But having just one basis vector doesn't make any sense
rotund oar
Neither of those vectors are basis vectors
It's just an equation that is true at every point on the line
You have some constant vector [a11, b11], and you dot that with your position vector [x, y]. The result of that dot product is constant (= b1) along the line.
If I call the first vector A, and the second vector r, then the dot product is |A| |r| cos(θ). Clearly |A| is constant. Now |r| cos(θ) is the distance to the position |r| from the origin in the direction of A.
last slate
You have some constant vector [a11, b11], and you dot that with your position ve...
Isnt the constant vector the transformed basis vector?
I should be watching 3B1b videos again ig 😔
Hmm
rotund oar
If I call the first vector `A`, and the second vector `r`, then the dot product ...
The dot product equation means that |r| cos(θ) is constant, which describes a line
Constant offset from the origin along the direction of A
That's the geometrical picture if you really want it
last slate
Could you give me some time
rotund oar
(A can be any length, I've just drawn it up to the line for neatness)
Yea
At this point I'm not talking about any sort of change of basis or anything like that
It's just regular vector geometry stuff
Honestly it would be enough just to see that the dot product equation is exactly the same thing numerically as the original, if you multiply it out
last slate
Yeah that clears it up but
Alright
I was stuck at the thought of a matrix multiplication always having one basis vector and the other being an arbitrary position vector :p
last slate
(not fond of the double-use of b in your eqs btw lol)
Lol I will use a_12 from next time
Thanks
.close
midnight plankBOT
rotund oar
Np 👍
You can think about basis vectors once you're at the matrix equation
The matrix M changes the vector [1, 0] into [a11, a21], and the vector [0, 1] into [b11, b21], so you can think of it as this kind of change of basis
last slate
.reopen
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rotund oar
Solving the matrix equation is finding the answer to the question "How do I express [b1, b2] in that new basis?"
rotund oar
Perpendicular to it - the line of your equation is the upper dotted line there
last slate
Shitz
rotund oar
Since you require that the component of r in the direction of A is constant, which is true all along that dotted line
(The length of the blue line is constant)
last slate
The dot product gives me the component of x y along the vector a b
rotund oar
Yeah with an extra factor
last slate
Wait how can the length of the blue line be a constant ?
Doesn't it change with changing x y
rotund oar
If I add a second r to compare it to:
As long as r is on the line, that distance is constant
rotund oar
Yeah it depends on a11, b11, and b1
last slate
Which is just the slope and the intercept
Lol I'm overcomplicating it
Thanks a lot!
.closr
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tidal turret
Given that $a$ is an odd multiple of $1183$, find the greatest common divisor of $2a^2+29a+65$ and $a+13$.
midnight plankBOT
Given that $a$ is an odd multiple of $1183$, find the greatest common divisor of...
grand pondBOT
938c2cc0dcc05f2b68c4287040cfcf71
tidal turret
hmm
can I have some help tbh
do I need to know the prime factorization of 1183?
I never understand this gcd exercises tbh
wind oxide
**938c2cc0dcc05f2b68c4287040cfcf71**
Factorise your quadratic.
tidal turret
using synthetic division?
or can I do long division of polynomials?
let me bring pen and paper
wind oxide
using synthetic division?
Its a quadratic 💀
wind oxide
or can I do long division of polynomials?
Bro sure u can do that..do u not know middle term splitting?
tidal turret
middle term splitting?
grand pondBOT
grand pondBOT
tidal turret
hmm?
fathom tendon
well first thing i notice is both of them must be even
so maybe that might mean something idk
tidal turret
why even
fathom tendon
since a must be odd
a+13 is even
(odd) + (odd) = (even)
and 2a² + 29a + 65 is even
(even)(odd)² = (even)
(odd)(odd) = (odd)
(even) + (odd) + (odd) = (even)
tidal turret
so?
fathom tendon
they both have common factor 2
that might not be their gcf but they atleast have a common factor 2
tidal turret
okay
I never understand why he wanted me to factor the polynomial
$\polylongdiv{2x^2+29x+65}{x+13}$
grand pondBOT
938c2cc0dcc05f2b68c4287040cfcf71
tidal turret
2a^2 + 29a + 65 = (a+13)(2a+3) + 26
fathom tendon
ok so maybe you need to know the prime factorization of 1183
tidal turret
,calc 1183/7
grand pondBOT
Result:
169
1183 = 7 × 169
fathom tendon
169 is 13²
tidal turret
i have them already
13 is prime
fathom tendon
so its 7 x 13 x 13
fathom tendon
ok so lets say a = 1183N
where N is some odd number bec odd multiple and what not
try plugging a in for the first eq
but dont evaluate bec youll get a headache doing so
tidal turret
wdym
tidal turret
in where
midnight plankBOT
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tidal turret
An equilateral triangle $ABC$ shares a common side $BC$ with a square $BCDE,$ as pictured. What is the number of degrees in $\angle DAE$ (not pictured)?
midnight plankBOT
An equilateral triangle $ABC$ shares a common side $BC$ with a square $BCDE,$ as...
grand pondBOT
938c2cc0dcc05f2b68c4287040cfcf71
tidal turret
main owl
tidal turret
What about dae
tidal turret
Idk
tidal turret
Im not sure
last blade
Can you find DCA?
urban eagle
you sure?
tidal turret
Isoceles
tidal turret
15
tidal turret
Dae = 30
urban eagle
yes, how did you arrive at that?
tidal turret
Because 15+15+30=60
tidal turret
Thank you, it was hard tho
urban eagle
as you practice more they become easy and obvious
practice makes perfect
you can close now
tidal turret
.solved
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grand pondBOT
Quaster
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
midnight plankBOT
surreal moon
rip
deft ravine
Oops it closed sorry
deft ravine
**Quaster**
Compile Error! Click the <:errors:504266556054962196> reaction for m...
But yeah was wondering for that, and sorry my english might be a little bad
surreal moon
But yeah was wondering for that, and sorry my english might be a little bad
Yes, you could. It's just the same idea.
(but proving may be difficult)
deft ravine
Yes, you could. It's just the same idea.
Oh alright! Thanks!
thorn sorrel
!done
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tidal turret
midnight plankBOT
tidal turret
Let the line $\mathcal{L}: \lambda(-1, 1, 3) + (0, -1, 1)$ and the point $P = (-5, 7, 4)$. Determine, if possible, a line $\mathcal{L}'$ that simultaneously satisfies:
[
\mathcal{L}' \cap \mathcal{L} \neq \emptyset, \quad P \in \mathcal{L}', \quad \text{and} \quad \mathcal{L}' \perp \mathcal{L}.
]
grand pondBOT
938c2cc0dcc05f2b68c4287040cfcf71
tidal turret
if L' is orthogonal to L, their directions vectors are orthogonal aswell
,w (-5,7,4) × (-1,1,3)
grand pondBOT
tidal turret
,w (-5,7,4).(17,11,2)
grand pondBOT
tidal turret
let me bring pen and paper
we know this lines intersect right, so lets find the intersection, shall we
grim vector
Well if there perpendicular they neccessarly have a non-empty intersection
tidal turret
help
grim vector
if L' is orthogonal to L, their directions vectors are orthogonal aswell
Vectors are orthogonals, lines are perpendiculars
tidal turret
oh
grim vector
Its equivalent
tidal turret
like when I was
grim vector
No sense
P is a point
But
Think
Think of a vector that can start from the line and go to the point
tidal turret
doing (a,b,c).(-1,1,3) = 0
I got a = b+ 3c
now
(b+3c,b,c) = b(1,1,0) + c(3,0,1)
so its a 3d subspace <(1,1,0),(3,0,1)> the possibles direction vectors for L'
,w (1,1,0) x (3,0,1)
grand pondBOT
tidal turret
Think of a vector that can start from the line and go to the point
I am trying
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tidal turret
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@tidal turret Has your question been resolved?
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twilit field
Prove that $
midnight plankBOT
Prove that $
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twilit field
.reopen
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✅
twilit field
prove that $\frac{2n+1}{5n+4}$ converges to $\frac{2}{5}$
grand pondBOT
ƒ( wai ina teacup)= I don't know
twilit field
$\abs{\frac{10n+5-2(5n+4)}{5n+4}} < \varepsilon \implies \frac{3}{5n+4} < \varepsilon$
grand pondBOT
ƒ( wai ina teacup)= I don't know
twilit field
$n>\frac{1}{5} \left(\frac{3}{\varepsilon}-4 \right)$
grand pondBOT
ƒ( wai ina teacup)= I don't know
twilit field
so something like this suffices for n
right
Thanks!
One more limit
just a minute
Same question for $\frac{2n^2}{n^3+3}$
grand pondBOT
ƒ( wai ina teacup)= I don't know
fallow scarab
Why not 2n^3 in denominator
grand pondBOT
ƒ( wai ina teacup)= I don't know
twilit field
so $\frac{1}{n} < \varepsilon \implies n> \frac{1}{\varepsilon}$
grand pondBOT
ƒ( wai ina teacup)= I don't know
fallow scarab
**ƒ( wai ina teacup)= I don't know**
Oh wait did the original question not have a 2
fallow scarab
You just need to multiply your 1/eps by 2 or 1/2
twilit field
$\frac{sin(n^2)}{n^{\frac{1}{3}}}$
grand pondBOT
ƒ( wai ina teacup)= I don't know
twilit field
This is a bit more tricky as the numerator can be negative
sage helm
doesn't matter you're working with absolute values anyways
twilit field
$\abs{$\frac{sin(n^2)}{n^{\frac{1}{3}}}} < \frac{1}{\varepsilon}$
grand pondBOT
ƒ( wai ina teacup)= I don't know
Compile Error! Click the reaction for more information.
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twilit field
[
\abs{\frac{\sin(n^2)}{n^{\frac{1}{3}}}} < \varepsilon ]\
grand pondBOT
ƒ( wai ina teacup)= I don't know
sage helm
do you need help or do you got it
sage helm
yes
twilit field
hmm
sage helm
if you need a hint ||use the fact that |sin x| is bounded||
sage helm
yep
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twilit field
Give an example of a seqeunce with an infinite number of ones that doesn't converge to 1
midnight plankBOT
Give an example of a seqeunce with an infinite number of ones that doesn't conve...
twilit field
I was thinking of $a_n= (-1)^n$
grand pondBOT
ƒ( wai ina teacup)= I don't know
misty gorge
Give an example of a seqeunce with an infinite number of ones that doesn't conve...
12121212…
misty gorge
**ƒ( wai ina teacup)= I don't know**
this works
twilit field
Thanks!
misty gorge
if you have an infinite number of 1’s in your sequence, the sequence will either approach 1 or diverge.
by the way
twilit field
twilit field
**ƒ( wai ina teacup)= I don't know**
I suppose I have to prove the limit doesn't converge , don't I?
misty gorge
I suppose I have to prove the limit doesn't converge , don't I?
the limit is a number so it can’t converge or not converge
one can show that the sequence doesn’t converge from a specific choice of epsilon
twilit field
one can show that the sequence doesn’t converge from a specific choice of epsilo...
I suppose epsilon =1 works here
misty gorge
yeah
twilit field
$\abs{-1-1}$ isn't less than $1$
grand pondBOT
ƒ( wai ina teacup)= I don't know
misty gorge
yep
twilit field
Next question
A seqeunce with an infinite number of ones that converges to a number not equal to 1
This sisn't possible
fallow scarab
This sisn't possible
Are you saying this as a guess or do you have a proof
twilit field
I'm trying to think of a proof
misty gorge
if you have an infinite number of 1’s in your sequence, the sequence will either...
i am so good at foreshadowing
i just made this remark out of nowhere lol
twilit field
Let's suppose such a sequence did exist. Let this limit be $a$. It then implies for all $n \geq N, \abs{x_n-a} < \varepsilon$ for all $\varepsilon >0$
grand pondBOT
ƒ( wai ina teacup)= I don't know
clear void
**ƒ( wai ina teacup)= I don't know**
does this seq count as diverging?
twilit field
yea
clear void
alr
twilit field
Let's suppose such a sequence did exist. Let this limit be $a$. It then implies ...
Now what
clear void
if a is not 1 then..
twilit field
Let's suppose such a sequence did exist. Let this limit be $a$. It then implies for all $n \geq N, \abs{x_n-a} < \varepsilon$ for all $\varepsilon >0$. If $a \neq 1$. Then we have two cases. Suppose $a>1$, then setting $\varepsilon =x_n-1$, we arrive at a contradiction
grand pondBOT
ƒ( wai ina teacup)= I don't know
twilit field
similarly for $a<1$
grand pondBOT
ƒ( wai ina teacup)= I don't know
clear void
how do you know xn -1 is positive
clear void
then also do you need to take two separate cases?
clear void
|x_n-1|
also, what's the logic behind setting epislon to xn-1
doesn't seem right to me
you have yo show that for some epsilon ( you have yo tell which one)
there will always be a Xn for some n that |Xn-a| is not less than epsilon
twilit field
|x_n-a|/2
clear void
yeap
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twilit field
Does a sequence exist such that for every $n \in \N$ it is possible to find $n$ consecutives ones somewhere in the sequence
midnight plankBOT
Does a sequence exist such that for every $n \in \N$ it is possible to find $n$ ...
grand pondBOT
ƒ( wai ina teacup)= I don't know
twilit field
I don't think such a sequence exists
surreal moon
!occupied
midnight plankBOT
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).
surreal moon
no. you are not.
brazen moth
💀
surreal moon
<@&268886789983436800> trolls
brazen moth
Gone
twilit field
💀 , what was that
brazen moth
Reduced to atoms
surreal moon
**ƒ( wai ina teacup)= I don't know**
I'm not following what you are asking here
sage helm
Does a sequence exist such that for every $n \in \N$ it is possible to find $n$ ...
won't this just be (1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1 ...)
sage helm
won't this just be (1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1 ...)
I mean I guess this diverges so yeah
surreal moon
god dammit why is there a show called "the divergent series". Ruining my google searches
twilit field
won't this just be (1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1 ...)
But I'd have to show it diverges
sage helm
sure do that
twilit field
I mean intutively it can only converge to 0 or 1
sage helm
you can't get arbitrarily close to 1 since there's always a 0 somewhere
twilit field
But I have to show it cannot converge to any other value either
twilit field
I don't know cauchy sequences 😭
I mean the book doesn't explicitly ask for a proof
so idk
sage helm
then skip it
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barren onyx
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barren onyx
.close
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vast junco
john and pete have 3 pieces of paper each of the boys pick up one piece teares it up and puts the smmaller peices back john only ttears a piece of paper into 3 smaller peices while pete only tears a piece of paper into 5 smaller piece aftera few minutes can there be exactly 100 peices
my working was each time john tears its (2n + 1) + 2 when oete tears its (4p+1) + 2 so it is possible
midnight plankBOT
john and pete have 3 pieces of paper each of the boys pick up one piece teares i...
twilit field
I'm trying to understand the proof of : Every convergent sequence is bounded
formal blade
The idea is usually that the tail of the sequence is bounded. So you can take that bound and all the finitely many remaining terms then take the max.
subtle zinc
I don't get how n is in the interval (l-1,l+1)
u mean x_n
twilit field
yes
subtle zinc
|x_n - l| < 1
formal blade
Do reverse triangle to the above and you get the bound for the tail basically.
fervent ember
I don't get how n is in the interval (l-1,l+1)
because of that:
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