(A x B subset of B x C) means if (a, b) in A x B then (a, b) also in B x C
#help-19
late dust
low locust
you gain intuition about whether its true by looking at examples
wide drift
you gain intuition about whether its true by looking at examples
I have been all day 😭
I dont get it what am I looking for
What should I notice or pay attention to
Idk how to practice with no starting point
I get that there is no 1 way to solve every question but idk the intuition to solve ANY question
All the advice is so value its literally just IYKYK
warped badger
Sometimes, for questions like these, you should try to start proving it
If the proof works out and everything is logically sound, then that's perfect(do pay attention to all the steps you make though)
And if some step fails/requires an assumption you do not have, that will most likely give you some idea on how to construct a counterexample
wide drift
Sometimes, for questions like these, you should try to start proving it
Ive been doing that and sometimes, but sometimes I just waste a bunch of time which can NOT happen in my exam. Anytime I put a question in the discord channel everyone always knows, someones like 'seems false' and they all react with thumbs up. Any time I ask about it they say 'its intutition' like its magic or some shit
And tell me to do examples as if I havent been all day 😭
warped badger
Well, those two are the only ways to grasp what's going on
This takes time and effort, no one will deny that
wide drift
Omg pls just explain the intuition. just for 1 question so I know what to practice
Like idk what to look for
When looking for intuition
When doing these questions
Like practice, ok
Practice what??
late dust
in the discord channel everyone always knows
You shouldn't compare yourself to the people helping you, most of the time there is a gap of experience so it's unfair to you
wide drift
How do I practice if idk what to look for
Pls just explain the intuition just for this 1 example
late dust
(A x B subset of B x C) means if (a, b) in A x B then (a, b) also in B x C
Do you understand this?
wide drift
Even if it doesnt work for any others
late dust
So my intuition here is that the whole thing means A subset B and also B subset C, which directly leads to A subset C
Then I check if that's actually true
wide drift
Ok, I get it
Thank you that actually makes sense to me
Can I send another example and you tell me your intuition
late dust
Sure
late dust
That's really just understanding what the cartesian product is
warped badger
The elements on AXB will be pairs of the form (a,b) where a is an element of A and b is an element of B, in particular, if A⊆C and B⊆D, this implies a∈C and b∈D
wide drift
Idk if weve covered that
warped badger
Do you see how it follows from here?
warped badger
Idk if weve covered that
The cartesian product is the X thingy
wide drift
The elements on AXB will be pairs of the form (a,b) where a is an element of A a...
So its potentially true?
warped badger
So its potentially true?
If there's a proof of it, it's true, not just potentially
wide drift
yeye but were just theorizing at the start right
warped badger
The elements on AXB will be pairs of the form (a,b) where a is an element of A a...
Do you see how your intended proposition follows from here though?
wide drift
Do you see how your intended proposition follows from here though?
Yes I see it maybe it was too easy of an example
ok 1 sec
This one is false right?
My intutition is guessing
late dust
Yeah, that's false
wide drift
Okkkkkkkkkk I think im getting it
late dust
Here I would visualize A and B as in a Venn diagram or something
wide drift
Here I would visualize A and B as in a Venn diagram or something
When would you use a diagram and when not
Like when would it be helpful
late dust
The only part of the universe that is not in A^c u B^c is the intersection of A and B, right?
wide drift
The only part of the universe that is not in A^c u B^c is the intersection of A ...
Yes thats what I was thinking
late dust
When would you use a diagram and when not
I usually use one (I don't actually draw it but if you need to, you can) whenever there's a complement
late dust
Yes thats what I was thinking
Right and the part of the universe that is not in (A u B)^c is simply A u B
So the opposite is actually true
wide drift
I usually use one (I don't actually draw it but if you need to, you can) wheneve...
Thank you these are exactly the kind of tips i need
Do you have any other random advice when doing set questions like this
late dust
Know some logic
tacit wasp
With complement showing up it might help recall de Morgan's laws
late dust
Like De Morgan's is very important to know
tacit wasp
Lol we thought the exact same thing in the same time 😬🙈
late dust
I would say there are usually two stages to my intuition for these kinds of set questions
First I think in terms of sets, maybe with a Venn diagram, but really just visualizing where the elements can be, what each term means exactly
Then I think in terms of logic, taking an element from each set and translating union into "or", intersection into "and", and so on
That helps with the next step which is writing down a proof
(since usually you want to think in terms of elements for a proof, not in terms of whole sets)
wide drift
So are you looking for possible counter examples? Or looking to solve?
When you look at them first in terms of set then in terms of logic
late dust
Well if I can't find the correct intuition to prove something, I'll try to construct a counter example, yeah
wide drift
Okkkkkk I see
late dust
But that's entirely different
Like you can try to prove something in terms of sets or in terms of elements, and you can also try to construct a counter example in terms of set or elements
late dust
This one is false right?
Let's say you realize you can't prove this one so you want a counterexample
If you take A as the empty set, the LHS becomes the universe, which is hard to be included into something else
In particular, if B is not empty, then the RHS simply becomes B^c which is not the universe
wide drift
Yeyeye I get it
tacit wasp
Another hint when working with sets is remembering how to prove two sets are equal.
In this case, usually the lemma/definition that is used is the following:
$$A = B \iff A \subseteq B \wedge B \subseteq A$$
clever fjordBOT
Alberto Z.
wide drift
If you take A as the empty set, the LHS becomes the universe, which is hard to b...
This is a good way at looking at things
late dust
Trying the empty set is useful because it's an extreme, and extremes tend to work as counterexamples
wide drift
Alright, thats a lot of info hahaha
I wanna go try some examples
Thank you soooo much everyone and especially @late dust ❤️ ❤️ ❤️
.close
odd edgeBOT
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Available help channel!
mighty scaffold
tryna graph this on desmos it's not working
brazen hare
tryna graph this on desmos it's not working
https://www.desmos.com/calculator/a...
remove the , in your 10,000
mighty scaffold
how do I write the following constraints in terms of the curve equation and the domain only?https://www.desmos.com/calculator/aqnrtjpuhw
crystal saffron
ye we dont rly talk Ive just seen u xd
brazen hare
how do I write the following constraints in terms of the curve equation and the ...
wdym?
mighty scaffold
Something like:
y = x+2 for 0 < x < 2
brazen hare
Something like:
y = x+2 for 0 < x < 2
anyways this server is not for help on desmos
go read the documentation
brazen hare
anyways this server is not for help on desmos
unless you have something to ask about the specific math of it
odd edgeBOT
@mighty scaffold Has your question been resolved?
odd edgeBOT
Available help channel!
unreal blade
odd edgeBOT
cold sage
why do you think that?
unreal blade
why do you think that?
7/3 ?
cold sage
yeah, why do you think that answer
unreal blade
cuz the average value formula we have to multiply the definite integral by 1 which is 1/2 in this case
and then (2x+3) ^ 2
from -3 to -1 u get 14/3
and times that by 1/2
gives us 7/3
cold sage
youre not wrong, si that works
unreal blade
Its either A or D
worn saddle
and times that by 1/2
well to find the avg for an interval you first integrate the function and divide it by the distance of the limits
unreal blade
but Im not sure
cold sage
seems fine
unreal blade
seems fine
so Im correct C?
cold sage
indeed
odd edgeBOT
@unreal blade Has your question been resolved?
odd edgeBOT
unreal blade
.reopen
odd edgeBOT
✅ Original question: #help-19 message
odd edgeBOT
@unreal blade Has your question been resolved?
odd edgeBOT
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Available help channel!
astral pendant
this is question and answer i dont understand how they eliminate 3/7
undone skiff
(3/7)- 4 gives negative value and m-4 cant be negative so 3/7 gets eliminated
astral pendant
why cant m-4 be negative
undone skiff
It would make the quadratics constant term negative which is impossible for a perfect square,,
astral pendant
i get what u mean but also dont
whats like the
definition of perfect square
why does the constant need to be positive
OH ITS BECAUSE FUCK
ITS BECAUSE THE NUMBER IN THE BRACKET MULTIPY WITH ITSELF
AND WHEN TWO NUMBERS MULTIPLY IT CANT BE NEGATIVE
like (a+b)^2 b^2 is always positive
WOAHHHHH
undone skiff
Ye lol
astral pendant
question and my working and now im stuck
odd edgeBOT
question and my working and now im stuck
woeful briar
a^2 -2ab +b^2 is something you should recognize
warped glacier
(a-b)^2 + 4c^2 > 0
correct, but you should explain what that means
it's not exactly obvious
warped glacier
wait is that the answer
needs some justification of why it's > 0 exactly
how do you know that it can't equal 0, for instance?
astral pendant
ye idk
thats what i was tryna figure out
when i started expanding
i thought everything but c would cancel out
clever fjordBOT
south
warped glacier
yep, and what about c^2
warped glacier
what is the condition for c, firstly?
astral pendant
therefore c^2 has to be greater than 0
warped glacier
therefore c^2 has to be greater than 0
yes!
astral pendant
therefore 4c^2 has to be greater than 0
and since (a-b)^2 is greater or equal to 0
that whole thing is greater than 0
therefore theres two distinct points
warped glacier
question and my working and now im stuck
yes so in your work, don't write >0
that's what you want to show
warped glacier
at the very last line, you can rewrite that as $(a - b)^2 + 4c^2$
clever fjordBOT
south
astral pendant
ic
warped glacier
then you need to write $(a - b)^2 \ge 0$ for all $a, b$; $c^2 > 0 \ (c \ne 0)$
only then can you write >0
at the very end
clever fjordBOT
south
warped glacier
no worries!
astral pendant
.close
odd edgeBOT
odd edgeBOT
Available help channel!
wise vale
28x^4 ÷ 56x
odd edgeBOT
28x^4 ÷ 56x
wise vale
Please help me solve
wooden python
do you know how to simplify fractions generally
vernal yacht
Are you looking for simplification? What have you tried so far?
odd edgeBOT
@wise vale Has your question been resolved?
whole imp
28x^4 ÷ 56x
$(28x^4)/56x = 28/56 * x^4/x = 1/2 *x^(4-1) = (x^3)/2$
clever fjordBOT
KB
whole imp
seperate the fraction into its components and simplify each part using your index laws
woeful briar
!nosols
odd edgeBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
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Available help channel!
proper ivy
I'm trying to figure out the missing number in this sequence. I’d appreciate it if someone could explain the logic or pattern behind it. Thanks!
odd edgeBOT
I'm trying to figure out the missing number in this sequence. I’d appreciate it ...
@proper ivy Has your question been resolved?
slate radish
Hi @proper ivy
I assume there are multiple ways to solve any sequence completion question
But what I see here is two interleaving independent sequences
On the odd indices we have 2,5,8,11, and on the even indices we have 8,6,_
Therefore, I would choose 4.
odd edgeBOT
Available help channel!
pallid apex
$\sum_{n=1}^{+\infty} \sin(\pi n +\frac{1}{n^2})$
odd edgeBOT
$\sum_{n=1}^{+\infty} \sin(\pi n +\frac{1}{n^2})$
clever fjordBOT
Richard Mullin
pallid apex
I Need to solve this in 120 seconds
dapper canyon
lol
pallid apex
Mmm
dapper canyon
can u simplify sin(pi + x)
tacit wasp
**Richard Mullin**
Qui si risolve, right? 😅😬
dapper canyon
sin(πn)•sin(1/n^2)+cos(nπ)•cos(1/n^2)
= sin(pi + x)?
pallid apex
I use sin(x+y)
pallid apex
1
dapper canyon
what's cos(pi)?
dapper canyon
yeah
pallid apex
what's cos(pi)?
(-1)^n
dapper canyon
$\sum_{n=1}^{\infty} (-1)^n \cos(\frac{1}{n^2})$
clever fjordBOT
69th-order logician
pallid apex
but I was wrong here
pallid apex
sin(πn)•sin(1/n^2)+cos(nπ)•cos(1/n^2)
.
dapper canyon
alr
pallid apex
$\sum_{n=1}^{\infty} (-1)^n \sin(\frac{1}{n^2})$
clever fjordBOT
Richard Mullin
pallid apex
However, more than 120 seconds have passed
😭
Anyway
$\sum_{n=1}^{\infty} | \sin(\frac{1}{n^2})|$
clever fjordBOT
Richard Mullin
pallid apex
$~1/n^2$
clever fjordBOT
Richard Mullin
dapper canyon
**Richard Mullin**
are you supposed to find the value of this sum?
odd edgeBOT
dapper canyon
🤔
meager juniper
why the 120 second time limit? @pallid apex
odd edgeBOT
Available help channel!
visual apex
Solve the systems of equations using the algebraic method.
winter berry
Solve the systems of equations using the algebraic method.
what have you tried?
last rune
visual apex
what have you tried?
I get it to 10x-2x^2=12 but dont know where to go after
winter berry
I get it to 10x-2x^2=12 but dont know where to go after
can you show your work?
I think you made some mistake in the process
nvm, it's correct
well, do you know how to solve a quadratic equation?
visual apex
well, do you know how to solve a quadratic equation?
Dont think ive been taught but I do have it on my formula sheet, dont know how to solve it though
winter berry
what do you have on your formula sheet?
visual apex
it says x^2+px+q=0
ax^2+bx+c=0
and then two other equations that I cant write on computer
here I found a picture
winter berry
okay, so on the right you have the formula for a generic quadratic equation
you can rewrite what you got in the form ax^2+bx+c=0
visual apex
the thing is I should probably not need to use quadratic equation since it hasnt been taught yet?
winter berry
there is no way to solve this if you don't solve that quadratic equation
visual apex
honestly this question might be missplaced
because im sure that I dont need to know quadratic equations yet
winter berry
either way you will need to know how to deal with quadratic equations to solve this
be it factoring or using the formula
winter berry
2x^2+10x-12=0
it should be -2x^2+10x-12=0
or 2x^2-10x+12=0 if you multiply both sides by (-1)
visual apex
I dont understand how you get to there
honestly I might close this, thanks for the help but this is just not needed for me to know right now
have too much other stuff to worry about so cant really try to learn this right now
winter berry
I dont understand how you get to there
well i don't understand how you got 2x^2+10x-12=0
alright, you can close the channel
visual apex
.close
worthy scaffold
how is it that the one on the right is correct and not the one on the left? shouldn't x is not an element of B intersection C be the one on the left; since x needs to exist in every other parts of those sets including the universal set if considered BUT the intersection between them in both cases?
clever fjordBOT
Bungo
green elm
so $$\begin{aligned}
x \not\in B \cap C &\iff x \in \overline{B \cap C} \
&\iff x \in \overline{B} \cup \overline{C} \
&\iff x\in \overline{B}\text{ or }x \in \overline{C} \
\end{aligned}$$
clever fjordBOT
Bungo
odd edgeBOT
@worthy scaffold Has your question been resolved?
worthy scaffold
wdym by this?
I apologize i forgot to include that x is an element B minus B intersection C
although now that i think about it there seems to be some logical contradictions in my expression
and if so excuse me because set theory is a very new topic to me
because if x is not an element of B the following expression describing how it is an element of be seems to be illogical
green elm
well $x$ can't be in both $\overline B$ and $B \setminus (B \cap C)$
clever fjordBOT
Bungo
green elm
because if it's in $B \setminus (B \cap C)$ then it's in $B$
clever fjordBOT
Bungo
worthy scaffold
well $x$ can't be in both $\overline B$ and $B \setminus (B \cap C)$
right but what i am confused about here is that i don't think that when we say x is not an element of B intersection C is equivalent to saying x is not an element of B or C because when you say "or" it means either one or the other, so considering the first case when x is not an element of B would include everything else but B. Which can't be because B is included in the first statement. Same thing happens when considering the other case.
i hope that made sense
green elm
i may be misunderstanding, but i think you may be getting confused by the use of "or" here
"x is not in B or x is not in C"
does not mean the same as the typical english usage "x is not in B or C", i.e. "x is neither in B nor in C"
the latter, written mathematically, would be "x is not in B and x is not in C"
whereas the statement "x is not in B or x is not in C" means "x is not in both sets" (but it could be in one of them)
bold lake
"x is not in B *or* x is not in C"
does not mean the same as the typical english...
When you say "or" it probably means that it's either in B or C
worthy scaffold
"x is not in B *or* x is not in C"
does not mean the same as the typical english...
Oh! yes right that would explain it then. It seems i misinterpreted the use of the word "or".
thank you
green elm
yw
pallid apex
I came across this interesting problem while visiting Disneyland.
Does anyone know how to solve it?
[
\iint_{0 \leq \text{thepooh} \leq \text{whinnie} \leq \text{WhinnieThePooh}}
(\text{whinnie})^{5},\text{thepooh};
d(\text{thepooh}),d(\text{whinnie})
]
clever fjordBOT
Richard Mullin
wooden python
<@&268886789983436800> troll question
narrow crypt
oh dear
pallid apex
<@&268886789983436800> troll question
Why
tacit wasp
And you also dare asking why???
tropic remnant
Please let's keep help channels to sincere questions only
we can make jokes in #chill
pallid apex
I can let a=whinnie
tropic remnant
I'm going to close this channel now; let's please not do this again.
tropic remnant
Thanks omni
odd edgeBOT
wooden python
he's been a repeat offender, I'll take care of it.
rip bozo
odd edgeBOT
Available help channel!
bold topaz
anyone got an idea on how to find DE?
odd edgeBOT
anyone got an idea on how to find DE?
quasi sparrow
is DE supposed to be parallel to BC
bold topaz
is DE supposed to be parallel to BC
no
it's just DE
not told its parallel or anything
brazen hare
is there any information on AE?
bold topaz
is there any information on AE?
there isnt, ill write whats given one sec
bold topaz
AB = 100
AC = 200
<B = 100 degrees
DE is divided into 2 equal parts (area same)
DB is 20
bold topaz
just show the original problem
not in english, i took out all the info i was given
quasi sparrow
AB = 100
AC = 200
<B = 100 degrees
DE is divided into 2 equal parts (area same)
...
yes well this was important
brazen hare
AB = 100
AC = 200
<B = 100 degrees
DE is divided into 2 equal parts (area same)
...
as in the area of triangle ADE = area of DECB?
bold topaz
yes well this was important
oh did i miss anything
bold topaz
as in the area of triangle ADE = area of DECB?
yes correct
ah the area part i forgot to mention, apologies
brazen hare
do you know the formula 1/2 ab sinC = area of a triangle? i think that may help here
bold topaz
do you know the formula 1/2 ab sinC = area of a triangle? i think that may help ...
yeah
not sure what im supposed to rreplace to get DE though
brazen hare
anyone got an idea on how to find DE?
Area of $\triangle ADE$ = Area of $\triangle ABC$ - Area of $\triangle ADE$
clever fjordBOT
brazen hare
you can compute the area of triangle ABC, and for the area of triangle ADE, that can be expressed in terms of AE
bold topaz
you can compute the area of triangle ABC, and for the area of triangle ADE, that...
sorry but english isnt my first language, could you show me what u mean?
is computing like
3 * 2 = 6
2 = 6 / 3
brazen hare
im gonna assume your $\alpha$ and $\beta$ are correct since the working looks correct
clever fjordBOT
bold topaz
im gonna assume your $\alpha$ and $\beta$ are correct since the working looks co...
yeah those should be correct already
brazen hare
is computing like
3 * 2 = 6
2 = 6 / 3
it means you can get the answer as a number
without any unknowns
bold topaz
what's your first language? someone here might be able to speak it
estonian, highly doubt it
bold topaz
use 1/2 ab sin C
how would i go about finding AE?
brazen hare
how would i go about finding AE?
you're trying to solve for AE
which you can then use to solve for DE
bold topaz
ahh right i think i get what u mean now
clever fjordBOT
brazen hare
to avoid rounding errors from precision loss
bold topaz
to avoid rounding errors from precision loss
teachers fine with me not using exact values, she said rounding is fine as long it's solved the correct way
brazen hare
teachers fine with me not using exact values, she said rounding is fine as long ...
oh that's interesting lol
over here you either use exact value or round to at least 5 sf
bold topaz
over here you either use exact value or round to at least 5 sf
where at?
brazen hare
and only for final answers do you round to 1 d.p. or 3 s.f.
bold topaz
assuming you havent calculated anything wrongly
nah dont think so
brazen hare
,w (3863665 * 2 / 80) / (sin 50.6 deg)
clever fjordBOT
brazen hare
hmm
bold topaz
uhh
brazen hare
7725 / 80 isnt 90.5625
brazen hare
its 3863,665
bro i keep forgetting you're from a part of a world that uses commas for dots
you meant 3863.665 right
bold topaz
yes correct hahahah
brazen hare
omg
sorry lol everyone here uses commas to separate groups of three digits, like 1,000,000
bold topaz
sorry lol everyone here uses commas to separate groups of three digits, like 1,0...
yeah that makes sense
not your fault
brazen hare
once you get AE, can you see how to use that to get DE?
bold topaz
yeah
brazen hare
how?
bold topaz
alright i have no way to check it unfortunately but i got DE = 96.56
should be alright though
brazen hare
,w sqrt(124.96^2 + 80^2 - 2 * 124.96 * 80 * cos 50.6 deg)
clever fjordBOT
bold topaz
ah cool
brazen hare
yeah looks correct
brazen hare
thank you so much for the help
np
odd edgeBOT
odd edgeBOT
Available help channel!
graceful parrot
odd edgeBOT
graceful parrot
Can someone explain to me how you would get the bounds for theta and phi?
For this problem
graceful parrot
x^2+y^2+z^2 = 9 bounds a sphere of radius 3
Yes
graceful parrot
Spherical coordinates, right?
Yes*
graceful parrot
x^2+y^2+z^2 = 9 bounds a sphere of radius 3
Oh so that itself tells you it’s a sphere? That tells you for p phi and theta?
i thought it only told me the region for p
What about the y > 0?
What does that tell me
safe vapor
Well the triple integral over E says that you want to intergrate along the shape E
Shape E is a hemisphere defined by x^2+y^2+z^2 < 9 and y > 0
x^2+y^2+z^2 < 9 says "start with a full sphere"
And y > 0 says chop off the left (negative y) half of it to get a hemisphere
that's your bounds of integration
Now you want to represent that in terms of spherical coordinate bounds
graceful parrot
And y > 0 says chop off the left (negative y) half of it to get a hemisphere
Ahhh ok
That helps a lot
Thank you so much
odd edgeBOT
Available help channel!
latent cargo
Someone please help me to calculate this limit
odd edgeBOT
Someone please help me to calculate this limit
somber spoke
is that $\lim_{x \to \frac{\pi}{2}} (\sin(x))^{tgx}$?
clever fjordBOT
Hyacine
latent cargo
(I can’t use L’Hopital’s rule)
latent cargo
is that $\lim_{x \to \frac{\pi}{2}} (\sin(x))^{tgx}$?
Yeah
unkempt lichen
**Hyacine**
latent cargo
@somber spoke do you have any ideas?
somber spoke
not at the moment, unfortunately. sorry.
latent cargo
Ok
quasi falcon
sin(pi/2)=1
tan(pi/2) doesnt exist
eager wraith
where does tan come from
latent cargo
where does tan come from
Power
eager wraith
oh i haven't seen that notation before mb
somber spoke
that's how a tangent is notated?
latent cargo
I can show you what I tried to do
But there is a tiny problem
Ctg(t) lim_t->0 can’t be calculated
With this
eager wraith
i'll give this a proper go in a second but my intuition would be to use logarithms to remove the power
latent cargo
So I do exactly what I did but I use logarithm to remove the power?
eager wraith
no idea if that'd work, might be worth a shot though
i don't have paper on me at the moment
eager wraith
okay i just verified logarithms work
try letting $y = \sin(x)^{\tan(x)}$, then equate $\lim_{x\to \frac{\pi}{2}}\ln(y)=\lim_{x\to \frac{\pi}{2}}\ln(\sin{x}^{\tan{x}})$
clever fjordBOT
lucas
odd edgeBOT
@latent cargo Has your question been resolved?
fleet lake
6th and 7th
odd edgeBOT
6th and 7th
woeful briar
What did you try
fleet lake
For 6, what do you know about binomial coefficients
Remains untaught in school
We were just told to write answers due to some unsharable reason
woeful briar
Hmmm
Do you know binomial coefficient are symettric around n/2?
$\binom{n}{k}=\binom{n}{n-k}$
clever fjordBOT
ExpertEsquieESQUIE
tacit wasp
For example:
1 2 1
1 3 3 1
1 4 6 4 1
...
(Coeffs of the powers of a binomial)
fleet lake
.close
No useful
odd edgeBOT
odd edgeBOT
Available help channel!
shrewd pewter
odd edgeBOT
shrewd pewter
Is it ±15a⁸b¹⁸
shrewd pewter
ur confused abt +-?
A bit
shrewd pewter
thanks for the help
supple thunder
nw
odd edgeBOT
Available help channel!
autumn flare
odd edgeBOT
autumn flare
As you can see, the above 3 equations have been defined as a plane, but 2x-y =0 is not a plane is it, its just a straight 2D line, what am i missing here?
twin plover
2x-y+0z
strange aspen
As you can see, the above 3 equations have been defined as a plane, but 2x-y =0 ...
You are graphing it on a 2D-plane
strange aspen
Hell yeah 🔥🔥🔥🔥🔥
odd edgeBOT
odd edgeBOT
Available help channel!
humble sinew
i need help with this, i dont seem to under stand this math
regal nebula
i need help with this, i dont seem to under stand this math
do u not understand how they simplified it or is it the multiplication itself?
regal nebula
is it both
its okay if it is cause if you dont understand this now, youll be cooked later on lol
humble sinew
🥲
regal nebula
without the simplification, just do the multiplication as normal
multiply the top with the other top, the bottom with the other bottom
humble sinew
ohhhhhh okokokookokok wait nvm now i get it thanks
regal nebula
woohoo
mystic saffron
Integrate csc proof
odd edgeBOT
Integrate csc proof
tepid pelican
have u tried watching some vids?
this is something that should be easily googlable
mystic saffron
I don’t like this stupid poon. They all use that absurd trick
dapper canyon
what's poon
tepid pelican
wtf
nocturne mica
...what
dapper canyon
in what language??
mystic saffron
English
Someone on Reddit used it to refer to there lady part I assumed it was recognised slang
dapper canyon
,w integrate csc x
clever fjordBOT
dapper canyon
yeah so the integral is evidently a bit complicated. i don't think there's a direct "follow ur nose" approach
vernal yacht
maiden sierra
trig integrals are always "conjure something up idk man go fuck yourself"
stoic cloud
You have to use a 𝑢 sub
mystic saffron
I did that poon
odd edgeBOT
Helpers are just people volunteering their time to help you. Be polite and patient.
mystic saffron
Wait let me show you my working
maiden sierra
I did that poon
also poon is likely not the correct term here
whoever you heard it from is a r*dditor
so there's that
frigid canopy
whoever you heard it from is a r*dditor
excuse me
dapper canyon
oh maybe u could try weierstrass sub
clever fjordBOT
wai
mystic saffron
frigid canopy
oh maybe u could try weierstrass sub
This is actually very smart
It gives the answer directly
$\int \frac{ 1+\tan^2(x/2)}{ 2 \tan(x/2)}dx$
clever fjordBOT
wai
frigid canopy
you should be able to to this quite easily
frigid canopy
I did that poon
MInd your language
mystic saffron
I’m sorry it’s just such a naughty word
frigid canopy
This is a casual academic server sure, but uphold decorum
mystic saffron
I’ve been getting into saying words that sound naughty but don’t have a meaning
fair forum
at least not do it in a help channel....
mystic saffron
Weasteard
summer wave
a better sub would be u = cosx after multiplying top and bottom by sinx
hasty jacinth
autumn bolt
a better sub would be u = cosx after multiplying top and bottom by sinx
holy damn
how did i never see this sub
insane
odd edgeBOT
@mystic saffron Has your question been resolved?
summer wave
https://en.wikipedia.org/wiki/Bioche's_rules whenever you're out of options, but sometimes it's unnecessarily complicated
mystic saffron
can someone help me with this one
odd edgeBOT
can someone help me with this one
summer wave
can you use taylor expansions
mystic saffron
what kind of equivalence
like consequences of the first remarkable limit
mystic saffron
any big O/ small o?
idk what's that
summer wave
and l'hopital's rule?
mystic saffron
and l'hopital's rule?
nah, can't
thorny spindle
taylor is the best choice here like blou said
summer wave
my attempt: your expression is equal to $$\frac{1-\cos x}{x^2} + \cos (x) \frac{1 - (\cos 2x)^{1/2} (\cos 3x)^{1/3}}{x^2}$$
clever fjordBOT
bloubbloub
mystic saffron
taylor is the best choice here like blou said
i just can't use it because we haven't learned it yet
mystic saffron
can we apply that
yeah
summer wave
then we only need to find the limit of the last fraction, for that you can use formulas for cos 2x and then cos 3x
thorny spindle
i just can't use it because we haven't learned it yet
u haven't learnt taylor expansion too?
mystic saffron
u haven't learnt taylor expansion too?
yeah
summer wave
then we only need to find the limit of the last fraction, for that you can use f...
each time you can factorize by cos, at the end it should give you the result
ionic heart
can someone help me with this one
n(n-1)/4
Or +1
idk
use cosx = 1-x²/2 and (1-y)ⁿ = 1-ny
for all the terms
mystic saffron
each time you can factorize by cos, at the end it should give you the result
can you demonstrate i have no idea how to factorize by cos in this case
ionic heart
Now open all the brackets
summer wave
use cosx = 1-x²/2 and (1-y)ⁿ = 1-ny
@mystic saffron are you allowed to use this btw? it's actually taylor in disguise
mystic saffron
<@456226577798135808> are you allowed to use this btw? it's actually taylor in d...
i can use in case when x->0 1 - cosx ~ x^2 / 2 or sin ~ x and etc but the second which _kavin wrote - no
summer wave
ok
what I meant was that since $\cos 2x = 2 \cos ^2 x - 1$, then $$ \begin{align*} \frac{1 - (\cos 2x)^{1/2} (\cos 3x)^{1/3}}{x^2} &= \frac{1 - (2 \cos ^2 x - 1)^{1/2} (\cos 3x)^{1/3}}{x^2}\ &= \frac{1 - \cos (x)(2 - 1/\cos^2 x)^{1/2} (\cos 3x)^{1/3}}{x^2} \ &= \frac{1 - \cos (x)}{x^2} + \cos (x) \frac{1 - (2 - 1/\cos^2 x)^{1/2} (\cos 3x)^{1/3}}{x^2} \end{align*}$$
clever fjordBOT
bloubbloub
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
summer wave
hm now that I think about it
I'm not even sure it will work
it won't actually
sorry
I'm not sure how to do it since idk how to get rid of the roots without resorting to (1+x)^n ~ 1+nx
mystic saffron
I'm not sure how to do it since idk how to get rid of the roots without resortin...
yeah, that's the main trouble
odd edgeBOT
@mystic saffron Has your question been resolved?
odd edgeBOT
@mystic saffron Has your question been resolved?
orchid torrent
<@456226577798135808> Has your question been resolved?
orchid torrent
<@560122149126275093>
not my question
I was showing the op they could've googled it
safe bluff
ok
graceful parrot
Can someoen tell me what to do for problem 18?
odd edgeBOT
Can someoen tell me what to do for problem 18?
graceful parrot
this section really confused me
im unsure where to begin
i know theres like a jacovdian whatever
can someone break it down for me please
lethal spoke
Find out the region's boundaries in the uv plane first, then calculate the Jacobian J(u,v)
odd edgeBOT
@graceful parrot Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
hot glen
Question 4a and 4b
odd edgeBOT
Question 4a and 4b
hot glen
.close
odd edgeBOT
balmy stump
odd edgeBOT
Available help channel!
loud bough
odd edgeBOT
loud bough
This is a bit of a silly question, i got the answer as $2^{2y}$, but how exactly do a find a number?
clever fjordBOT
Yebba's Heartbreak
loud bough
i would need a specific value of y to find an exact number, unless by "should be a number" they mean not a set
but i mean, if i find the range, i could still express it as a set anyway
so what's the angle here?
this is from spivak's
amber schooner
i would need a specific value of y to find an exact number, unless by "should be...
i mean you’re already done
i think he used y on purpose
instead of x
to try and make you think of it as a number rather than a function
but regardless, there is nothing else to do
odd edgeBOT
odd edgeBOT
Available help channel!
proven relic
Can someone pls explain how do I prove beta to be 1? I am getting beta to be 0 if I substitute the function h to be sin(0), and I tried testing if transformation will help but idk if it helped
gritty spire
define h
odd edgeBOT
odd edgeBOT
Available help channel!
slow cradle
for this
slow cradle
what if we isolate
all the x and y terms
i did that
and on the denominator with 2cos theta+sin theta
but that can equal 0
so how come its a?
wooden python
wdym by "isolate all the x and y terms"? can you show exactly what you did, with full working?
slow cradle
i mean
i did it
in a book
and like
if i take a picture its gna be inverted
when i mean isolated i mean like factor out all x and ys
so 2nd equation =1 and the first equation =2 so the first equation = 2 of the 2nd equation
collect like terms, x and y
factor out
quasi falcon
!occupied
odd edgeBOT
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).
white bloom
ok ok
wooden python
idk how to take a photo on laptop
reproduce your work in like word equation editor or something
or Paint
slow cradle
reproduce your work in like word equation editor or something
ok
slow cradle
cosox-sinoy=2sinox+2cosoy
cosox-2sinox=2cosoy+sinoy
x(coso-2sino)=y(2coso+sino)
x(coso-2sino0)/(2coso+sino)=y
slow cradle
Are the notes here yours or from a prof?
thats a ms
worked solutions
thats not mine
random stranger
slow cradle
cosox-sinoy=2sinox+2cosoy
cosox-2sinox=2cosoy+sinoy
x(coso-2sino)=y(2coso+sino)...
i was trynna say
u cant divide by 0
so if 2coso+sino=0
sino=-2coso
tano=-2
defo has solutions between 0 and 2pi
quasi falcon
for this
goddam i just realized a really fast way to justify this one
anyways, from the algebraic standpoint
You should be able to find a way to use the identity $\cos^2\theta+\sin^2\theta=1$
clever fjordBOT
∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴
quasi falcon
defo has solutions between 0 and 2pi
From this conclussion, you can already see that somewhere you went wrong, given you already know that the correct answer is a
quasi falcon
cosox-sinoy=2sinox+2cosoy
cosox-2sinox=2cosoy+sinoy
x(coso-2sino)=y(2coso+sino)...
Havent really checked, but its probably here
specifically because you transformed all that into tanθ = -2
And already assumed that theres a problem for 2cosθ+sinθ = 0
Which, for the original problem, is not.
slow cradle
but u cant divide by 0?
quasi falcon
but u cant divide by 0?
That problem only comes from your way of operating sadly
If i can give you a hint, try squaring all 4 parts of the original system
Again, there is such a neat solution to this one, but we cant really call for it rn 🥀
slow cradle
That problem only comes from your way of operating sadly
If i can give you a hin...
i dont see any algebraic mistake though
slow cradle
Again, there is such a neat solution to this one, but we cant really call for it...
wdym
quasi falcon
wdym
It so happens that this system is really special, but you dont really have to know it to solve it.
dry lodge
You can't divide by 0, so you cannot get from x(coso-2sino)=y(2coso+sino) to x(coso-2sino0)/(2coso+sino)=y .
when tan o is -2
quasi falcon
If you do it, you are dismissing some solutions
slow cradle
You can't divide by 0, so you cannot get from x(coso-2sino)=y(2coso+sino) to x(c...
i see
thats weird
never thought abt it like that
quasi falcon
y=x is just a line
y/x = 1 is the same line, but without the center at (0,0)
cause 0/0 isnt a thing
slow cradle
i see
i dont know how to do it algebraically either
like the way the solution did it
the 2 simulatenous equations jst arent simplifying for me
quasi falcon
Again, try squaring the four parts of the system, youll soon arrive to an easy identity
quasi falcon
btw, ever heard of a rotation matrix? dont give it much thought either, just to know
slow cradle
erm
kinda
yh
kinda forgot though
matrices kinda stink
wait wait
i kinda rmbr the formula
what was it
2 by 2
sin theta
and cos theta
quasi falcon
this jst isnt going anywhere though
Have you solved it?
As in, done the full expansion
slow cradle
yes
quasi falcon
Hope you got something like this
quasi falcon
Add the two equations, yes
quasi falcon
Given you are working with trigonometric functions
Ill take it you already had your algebra basics
Does that equation ring a bell?
slow cradle
idk what your refering to
quasi falcon
Implicit of a circumference?
quasi falcon
By logic extension, there are infinite solutions between $0\leq\theta\leq 2\pi$
clever fjordBOT
∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴
quasi falcon
which is a)
Also, i just will get you the hint on why i was mentioning the rotational matrix
slow cradle
its the formula
quasi falcon
Our system is basically the linear system version of the counterclockwise rotational matrix
So, for each angle of rotation, there has to be an original point that will be (2,1)
slow cradle
yh
quasi falcon
Aka, if you get a random point in a circle of radius sqrt5, theres always an angle you can use to get to (2,1)
matrices are useful btw
slow cradle
bro matrices are so long
like
😭
was never much of a fan of it
even though
ive done very little on it
quasi falcon
Youll eventually realize they are one of the quickest forms of doing huge operations
anyways, hope that helped
quasi falcon
you can also write the fact that theres a solution for all thetas formally
by using this:
$\x= \sqrt 5 \cos\theta\
y= \sqrt 5 \sin\theta$
clever fjordBOT
∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴
quasi falcon
and replacing into the last equation.
You can see that it easily simplifies to 5 = 5
quasi falcon
yes, $C(t)=\left(\sqrt 5 \cos t ,\sqrt 5 \sin t\right)$
clever fjordBOT
∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴
quasi falcon
t represents essentially the same as theta
odd edgeBOT
odd edgeBOT
Available help channel!
livid juniper
I am little confused with this...i am having trouble rereading this and trying to learn
livid juniper
@wooden python
If anyone can understand my previous chats...then please help
i have one more question based on that
safe vapor
Dont ping helpers unless they've told you to do so.
safe vapor
I am little confused with this...i am having trouble rereading this and trying ...
Outline the question explicitly, the link you sent is to a latex from Ann
digital shore
whats the question
vernal yacht
odd edgeBOT
@livid juniper Has your question been resolved?
graceful wave
Suppose that there are sets $A_n$ and $B$ such that $ \bigcup_{n=1}^{\infty} A_n = B $
and another set $C$ such that $ C=B - \bigcup_{n=1}^{k} A_n$. What will $C$ equal to, as $k \xrightarrow{} \infty$?
gritty spire
well, whadya think
graceful wave
It makes sense to be an empty set but idk how to prove it
clever fjordBOT
Skrauzy
graceful wave
yeah
gritty spire
so in this case the seqwuense is monotone decreasing
and it makes sense to take the infinite intersection as the limit
graceful wave
yuppieee
gritty spire
ok
graceful wave
tyy 🙏
gritty spire
ok
graceful wave
.close
odd edgeBOT
odd edgeBOT
Available help channel!
topaz jewel
A wholesaler buys boxes of green tea from two suppliers. He buys 80% of his boxes from supplier A and 20% from supplier B. 10% of the boxes from supplier A show traces of pesticides, and 20% of those from supplier B also show traces of pesticides. A box is randomly taken from the wholesaler’s stock .It is observed that the sampled box shows traces of pesticides. Calculate the probability that this box comes from supplier B
warped cargo
What have you tried?
topaz jewel
Okay so the problem is boiled down to find P(S|Sb) which S is the probability what a box show traces of pesticides
But I'm not sure how to find P(S)
warped cargo
You mean, S is the event that a box shows traces of pesticides
topaz jewel
You mean, S is the **event** that a box shows traces of pesticides
oh yes mb
warped cargo
Also, what is Sb?
warped cargo
You didn't define correctly the events here, because P(S|Sb) = 1, as you defined them. If we are guaranteed that Sb happens (the way you defined it), then S is happening too by definition
warped cargo
You would rather define the events
A: The box comes from supplier A
B: The box comes from the supplier B
S: The box shows traces of pesticides
topaz jewel
it's supposed to be find the probability that SB happens knowing S happen
warped cargo
It's equivalent, but it's not needed to define SB the way you did.
You could also just say that you are looking for P(B|S), with B meaning the box comes from the supplier B
Anyway, regarding your original question, to find P(S), there are two favorable outcomes in your tree that satisfies the event S
topaz jewel
do I do like P(S_B)+P(S_A)?
topaz jewel
Anyway, regarding your original question, to find P(S), there are two favorable ...
I understand it's S_A and S_B right? but i'm a bit confused
warped cargo
By any chance, have you learned the law of total probability? I wonder if your teacher uses that or only uses trees as you drew above.
topaz jewel
sorry the material is in France so i'm not sure the term in english
warped cargo
Je parle français mdr
Avez-vous appris la formule des probabilités totales?
Sinon, dans ton arbre, il y a 2 chemins qui font en sorte qu'il y a des pesticides
Ce sont ceux-cis
Tu peux multiplier les probas sur ton chemin pour obtenir la proba que ce ''chemin'' se réalise
near spoke
Avez-vous appris la formule des probabilités totales?
ohh oui
Donc je devrais faire P(A) x P(S_A) + P(B) x P(S_B) ?
warped cargo
Es-tu la même personne?
near spoke
Non, @topaz jewel il a juste essayé de m’aider, ce sont mes devoirs ☺️
warped cargo
Ah, okay
topaz jewel
:p
warped cargo
Donc oui, l'expression que tu proposes te donnera bien P(S)
où S est l'événement qu'il y ait des pesticides dans ta boîte
near spoke
attendez, c’est sensé être pour la question b. Je l’avais déjà résolu
A: « la boîte provient du fournisseur A »
B: « la boîte provient du fournisseur B »
S: « la boîte présente des traces de pesticides »
-
Traduire l’énoncé sous forme d’un arbre pondéré.
-
a. Calculer la probabilité que la boîte choisie provienne du fournisseur B et qu’elle présente des traces de pesticides.
b. Montrer que la probabilité que la boîte prélevée présente des traces de pesticides est égale à 0.12.
-
On constate que la boîte prélevée présente des traces de pesticides. Calculer la probabilité que cette boîte provienne du fournisseur B. On arrondira à 10^-2 près.
-
Le grossiste affirme que parmi les boîtes ne présentant pas de traces de pesticides, plus de 80% proviennent du fournisseur A. Justifier l’affirmation du grossiste en présentant un calcul
l’énoncé: Dans cette exercice, les probabilités seront, si nécessaire, arrondieds au millième. Un grossiste achète des boites de thé vert chez deux fournisseurs. Il achète 80% de ses boites chez le fournisseur A et 20% chez le fournisseur B. 10% des boites provenant du fournisseur A présentent des traces de pesticides et 20% de celles provenant du fournisseur B présentent aussi des traces de pesticides. On prélève au hasard une boîte du stock du grossiste et on considère les événements suivants :
j’ai déjà répondu à la question 1, 2a et b. Je suis à la 3 haha 😅
warped cargo
Avez-vous appris la formule de Bayes?
near spoke
pas du tout, je suis seulement en première math spé ☹️. Je crois que c’est à partir de la Terminale?
topaz jewel
Donc je devrais faire P(A) x P(S_A) + P(B) x P(S_B) ?
N'est-ce pas déjà P(S_A)=P(A)*P(S_B|A) ? Je suis un peu confus à propos de cette partie
Alors, c'est comme, P(S_B) voici mon P(S_B|A).Si c'est le cas, cela aurait beaucoup plus de sens
warped cargo
En 3, on cherche alors $P(B \mid S)$ ou encore $P_S(B)$, dépendamment de la notation qu'utilise votre prof, et en utilisant les événements fournis par l'énoncé
clever fjordBOT
all matrices are invertible
near spoke
on utilise P_S(B), donc ça serait P(BnS)/P(S) ?
warped cargo
Ok, oui!
near spoke
la formule d’une proba conditionnelle
warped cargo
Ça revient au même que d'utiliser la formule Bayes dont je mentionnais plus tôt
et pour calculer P(BnS), ceci correspond à l'un seul de tes 4 chemins dans l'arbre : tu as calculé cette proba en 2(a)
near spoke
Woooo d’accord hahaha je savais pas du tout! Oui normalement c’est 0,04, mais comment trouve S ?
warped cargo
Tu l'as calculé en (b)