we take everything in C that is also not in A
#help-19
nocturne mica
the concept of elements that are not in a certain set is called?
(we've just talked about this)
graceful shore
Complement
nocturne mica
good
so that means that C \ A is really the same as C intersecting with the complement of A. agreed?
nocturne mica
with the complement of A
graceful shore
Oh
nocturne mica
not with A itself
graceful shore
Yes
nocturne mica
so now you have everything you need for Q1
you are given the proposition that A is a proper subset of B.
turn this proposition into another statement that involves the complements of A and B.
graceful shore
hmm
nocturne mica
we've gone through this already
odd edgeBOT
graceful shore
.reopen
odd edgeBOT
✅
graceful shore
We're Gone through it
nocturne mica
right here
graceful shore
But it's a bit hard to comprehend at first
yes
into another statement that is the same
nocturne mica
technically i've given you this part for free
but i want you to restate it in your own understanding
nocturne mica
hm?
nocturne mica
so what would the correct statement be?
graceful shore
I do not know how to include A as well
nocturne mica
complement B is a (what) of complement A
you don't need to include A
graceful shore
wait
nocturne mica
look at this statement and compare with the earlier conclusion we reached about the complements of A and B
graceful shore
shouldn't I find something that is equal with A proper set of B?
nocturne mica
you're already given that A is a proper subset of B
you want to work from that given statement to the conclusion
you're not trying to prove that A is a proper subset of B
graceful shore
what am I trying to do then?
nocturne mica
you are given the proposition that A is a proper subset of B.
turn this proposit...
^
this is the first step
you're building towards the conclusion that C \ B is a proper subset of C \ A
graceful shore
B complement is the subset of A complement
nocturne mica
there we go
next step - on both sides of the relationship, intersect each complement with C
this is where you bring C into the picture
graceful shore
intersect, so B^c intersection C is a subset of A^c intersection with C?
nocturne mica
yes!
last step. remember what we said about the intersection of a set complement with another set?
graceful shore
how do I draw C, a bigger circle that B? So B is the subset of C?
nocturne mica
so that means that C \ A is really the same as C intersecting with the complemen...
^
graceful shore
last step. remember what we said about the intersection of a set complement with...
yes
nocturne mica
how do I draw C, a bigger circle that B? So B is the subset of C?
C is any circle inside the universal set
if you wanna use circles
nocturne mica
yes
so that means, on the left side, we have the complement of B intersecting with C
change this to a set difference
do the same on the right side with the complement of A intersecting with C
nocturne mica
well C \ B, not C / B
nocturne mica
do you have another way to?
nocturne mica
i have no idea what question that is supposed to be
we'll tackle that in a bit
first, let's complete your proof
do the same for the complement of A intersecting with C
nocturne mica
do the same for the complement of A intersecting with C
well you haven't explicitly stated this as a set difference
just making sure we tidy things up
graceful shore
it's C\A
nocturne mica
correct
so we have that (C \ B) is a proper subset of (C \ A)
which is exactly what we need to prove
so we are now done
graceful shore
Got it, thank you
The second should be also solved like this?
No, all 3 questions should be solved it complement??
nocturne mica
no the second one is WAY more straightforward
graceful shore
if it's straightforward, then how do you prove it
nocturne mica
think of the definition of a set difference
graceful shore
it's feels like im provine 1+1=2
nocturne mica
what does A \ B mean?
graceful shore
It is what you cannot find in both
nocturne mica
more specifically?
graceful shore
A is a subset of B?
nocturne mica
no
graceful shore
It is not specified
nocturne mica
if I have an element in A \ B, which subset is the element in: only A, only B, both, or neither?
graceful shore
A
nocturne mica
correct
so A \ B are the elements that are in only A and not B
and the same goes for B \ C - these are the elements that are in only B and not C
agreed?
nocturne mica
ok now let's call A \ B set D and B \ C set E
so our main statement turns into D \ E
nocturne mica
D contains of only elements that are in A and not B. so D contains nothing in B
graceful shore
Yes
nocturne mica
and E contains those elements in B but not C
so every element in E is in B
but D contains nothing in B, so it can't possibly contain anything in common with E
so D \ E must still be D itself
and D was A \ B
so end of story
nocturne mica
thought you did it already
nocturne mica
i see you are trying the element method
nocturne mica
so if you want to use the element method, consider an element x, as you have
now, if x $\in$ A, there's nothing to prove
clever fjordBOT
Furina
nocturne mica
but if $x \in A \cap B$, then by definition x $\in$ A also
graceful shore
oh
nocturne mica
either way, $x \in A$, and so $A \cup (A \cap B) $\subseteq$ A
wooden python
now, if x $\in$ A, there's nothing to prove
$x \in A \cap B$
clever fjordBOT
Ann
wooden python
please dont leave math symbols outside of math mode, they will be cold and sad
graceful shore
Yes, I did that, and then put And between
clever fjordBOT
Furina
wooden python
$A \cup (A \cap B) \subseteq A$
clever fjordBOT
Ann
nocturne mica
now we have to prove the other way round, that $A \subseteq A \cup (A \cap B)$
clever fjordBOT
Furina
nocturne mica
well this one... do we have to say much about this? by definition a set is definitely a subset of its union with another set
even if the other set is a null set
clever fjordBOT
Furina
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
nocturne mica
ah i'll fix it later
nocturne mica
with this method
yeah?
graceful shore
I have to prove the first, and that A = A union (A intersection B)
Like, changing the places
no?
nocturne mica
wdym?
nocturne mica
that we do
graceful shore
nocturne mica
the first thing you need to prove is $A \cup (A \cap B) \subseteq A$
clever fjordBOT
Furina
graceful shore
cause for them to be equal, they should be included one in another?
nocturne mica
the second thing you need to prove is $A \subseteq A \cup (A \cap B)$
clever fjordBOT
Furina
graceful shore
yes
nocturne mica
if you're asking why we need to prove both
nocturne mica
?
long tinsel
cause for them to be equal, they should be included one in another?
Yeah it's a standard procedure to show sets are equal
graceful shore
My pair is starting, I'm at university... can we please continue later? Can I give you friends?
graceful shore
Yeah it's a standard procedure to show sets are equal
Oo, hiii
nocturne mica
you can open another channel later
nocturne mica
but we've pretty much reached the end of the proof
graceful shore
hm? How?
nocturne mica
**Furina**
we've done this by proving that an element in $A \cap B$ must be in A
clever fjordBOT
Furina
graceful shore
mhh
nocturne mica
**Furina**
and this is kinda by definition
if you union a set with any other set, the resulting set must at least have the elements of the first set, regardless of the elements of the other set
agreed?
nocturne mica
so if you union $A$ with ($A \cap B$), then even if ($A \cap B$) is empty, you still have A
clever fjordBOT
Furina
graceful shore
Thank you so much
nocturne mica
so that direction is proven too
graceful shore
I have so much to learn.
nocturne mica
all the best!
graceful shore
it can be empty?
nocturne mica
nps
graceful shore
.close
odd edgeBOT
odd edgeBOT
Available help channel!
shrewd trellis
I got the answer correct It was differently expressed to the answer solution
nocturne mica
what is x and y?
nocturne mica
there's no y in the image. why not simply state the dimensions as is?
you clearly have them
shrewd trellis
there's no y in the image. why not simply state the dimensions as is?
state the dimension as it is?
nocturne mica
yes
shrewd trellis
what would that be
shrewd trellis
yea but if x=1 and y=2, it satisfies the problem, right?
its the same thing but writtten differently
nocturne mica
are you asked for the value of x and y, or are you asked for the dimensions of the box?
because if i were you, i'd rather answer with something like:
(calculations)
Therefore, the dimensions of the box minimizing the cost is {final answer}.
why not write a concluding sentence when you're already this far into the question
communication matters as much as knowing the answer. if you can't communicate the answer, you might lose marks for no good reason
shrewd trellis
why not write a concluding sentence when you're already this far into the questi...
because I can just box it
which makes that a conclusion
nocturne mica
sure, but you found x and y... of which only x is defined in the question
unless you defined y as another length somewhere in the question, concluding that y = 2 means nothing in the context of the question
still again, it's not that much of a hassle to write one more sentence to make it clear anyway
shrewd trellis
Therefore, the dimensions of the box minimizing the cost is 1m by 2m by 2m
nocturne mica
there we go
shrewd trellis
why cant I just write 1m by 2m by 2m and box it
the calculations already speaks for itself
nocturne mica
an ultra-pedantic examiner can ask "what is 1m by 2m by 2m for?"
i prefer to leave the examiner no room for idiotic pedantry
if you wanna leave it out, by all means do so at the risk of your own marks
shrewd trellis
yeah I undersatnd u but I don't really think my marker is that strict
nocturne mica
then ask your marker?
shrewd trellis
yeah
nocturne mica
you're asking us, who are not your markers
all we can do is give best practice
if you want to know to what level you can cheap out on the answer, ask your marker and not us
odd edgeBOT
near scaffold
Hi
unkempt lichen
!redir
odd edgeBOT
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
Available help channel!
vapid rock
Hi, can i have help with understanding how to solve this?
"Decide the biggest possible domain and range to the function"
I only understand how to do it graphically and I have forgotten how to do it like this and I struggle to understand
Please note that I need everything dumbed down to understand, i will struggle to understand if it is not dumbed down, and that English isn't my first language, I may struggle using and understanding the correct mathematical words if google translate fails me.
crystal charm
Hi, can i have help with understanding how to solve this?
"Decide the biggest ...
Do you know what a domain and range is
vapid rock
Yeah, I have just forgotten how to solve them without a graph
And Google isn't dumbing it down enough for me to understand it and remember
crystal charm
Yeah, I have just forgotten how to solve them without a graph
graphing it is usually the easiest way since it gives some idea of what its domain and range would be, for example. sketching a graph for question a gives us this
crystal charm
Can you figure out the domain and range for it?
odd edgeBOT
@vapid rock Has your question been resolved?
vapid rock
Sorry had to do something rq. Actually I think I need more work figuring it out on graphs too, at least on linear graphs, im not quite sure where to look
and on graphs that don't have break point things (idk what they're called in English) like this graph has, I understand graphs like this one
warped glacier
Sorry had to do something rq. Actually I think I need more work figuring it out ...
a is a bit of a trick question, cause the domain and range is "all real numbers" and "all real numbers"
no matter what you sub in for x, you always get a valid number for y, and you can get any (real) number for y this way
but then questions b, c, d aren't like that: there's something stopping either the range or the domain from being all real numbers
and yes I'd encourage graphing the other functions too
vapid rock
Oh alright, how would i write the answer for something that is like question a?
My math book wants me to write domains and ranges in this format thingy ish
(Using random numbers example)
2≤y≤5
warped glacier
Oh alright, how would i write the answer for something that is like question a? ...
$x \in \mathbb R, y \in \mathbb R$
clever fjordBOT
south
warped glacier
yeah cause you can't zoom out infinitely, so honestly graphing doesn't really work in situations like part a
noble solstice
how are 11 and 12 the 50th and 51st value when the set only has 7 values, im so confused
mental lotus
the second row tells you the frequency
warped glacier
there are four 7s etc
mental lotus
like there are 4 things with value 7 etc
warped glacier
seven 8s
mental lotus
so in all I guess that sums up to a total of 100
noble solstice
that part i got
warped glacier
,calc 4+7+9+14+16
clever fjordBOT
Result:
50
just not sure how 11 and 12 are the medians
mental lotus
well, like they said, one of the 11s is 50th value
and one of the 12s is 51st
and when you got even number of objects, you take the two middle values and avg them to get the median
noble solstice
oh
wait
so
sigma f+1/n = 50.5
therefore
i need to count till 50 (and 51)
counting 4 times for t=7
etc..
therefore i reach 50 when t=11, and 51 when t=12
i finally get it
mental lotus
sigma f+1/n = 50.5
wdym?
mental lotus
yea, I got that, but whats n?
clever fjordBOT
woomy
mental lotus
okok
odd edgeBOT
odd edgeBOT
Available help channel!
near swan
Problem Statement: Given an array, print all the elements which are leaders. A Leader is an element that is greater than all of the elements on its right side in the array. how do i check if an element is greater than all of the elements on its right side?
near swan
#include <iostream>
int main()
{
int n = 4;
bool condition = false;
int a[4] = {4, 7, 1, 0};
std::vector <int> leader;
for(int i = 0; i < n; i++)
{
for (int j = i+1; j < n; j++)
{
if (a[i] > a[j])
{
condition = true;
}
}
if (condition == true)
{
leader.push_back(a[i]);
}
}
}``` does this work?
wanton bison
```cpp
#include <iostream>
int main()
{
int n = 4;
bool condition = fals...
What happens if it fails after the second neighbor?
You could have something like {1,2,1} and the condition would be still true even though it should fail
near swan
oh, yes; does not work unless the very last element is greater than it
wooden python
wouldn't it be easier to just scan thru the array BACKWARDS
wanton bison
I would rather check when the condition fails anyway
low locust
could you print the elements that are bigger than all preceeding elements?
wooden python
its last element is always a leader vacuously
near swan
could you print the elements that are bigger than all preceeding elements?
is not that kind of the same thing?
near swan
well
let me try
we will need an extra variable to store the maximum number "so far"?
low locust
yes
wooden python
vague sounding "philosophical" statement, check
what
near swan
isn't it just this: cpp int n = 4, max_so_far; int a[4] = {4, 7, 1, 0}; max_so_far = a[0]; for(int i = 1; i < n; i++) { if (a[i] > max_so_far) { std::cout << a[i] << std::endl; max_so_far = a[i]; } }
low locust
well that wouldnt print the first one which may or may not count
but yes
now solve the original problem
near swan
on it
#include <iostream>
int main()
{
int n = 4, max_so_far;
int a[4] = {4, 7, 1, 0};
max_so_far = a[n - 1];
std::vector <int> leader;
for(int i = n - 1; i > 0; i--)
{
if (a[i] > max_so_far)
{
leader.push_back(a[i]);
max_so_far = a[i];
}
}
for(int i = 0; i < leader.size(); i++)
{
std::cout << leader[i] << std::endl;
}
}```wait
right, this does not print 0
well
does the last element not always come in the list?
so we can just, print it?
late dust
You could but also, you don't need max_so_far
near swan
eh?
late dust
It's redundant
low locust
an easy way to fix it would be to set max_so_far as something smaller than the last element
near swan
but we gotta initialize it, right?
near swan
It's redundant
i do not see another way to do it
because we want to check all the elements
late dust
It's redundant
Not in your current code of course, but think about where max_so_far could be taken from
near swan
i will be back
okay so, what you try to mean is that rather than taking an extra variable to store the maximum element encountered yet, i can just do that by checking in-place?
low locust
what do you mean by in-place
near swan
{4, 7, 1, 0}
low locust
what comparison are you proposing
near swan
wait
can we do something like
we take an inner loop as well
well, let me write it down
low locust
no inner loop
near swan
oh
late dust
okay so, what you try to mean is that rather than taking an extra variable to st...
No I'm saying you are literally storing max_so_far in two places, hence the redundancy
near swan
where else does a[i] end up
in my code, the first element?
that probably does not make sense
near swan
No I'm saying you are literally storing `max_so_far` in two places, hence the re...
my question is
we still have to initialize the variable
how else do we do it
low locust
you are saving a[i] two times. one as max_so_far, the other time as the last element of leaders
so if you want to refer to it back later, what can you do
late dust
we still have to initialize the variable
Yes you do, but you can initialize the other thing that's storing max_so_far
near swan
we can use the last element stored in leader?
late dust
Exactly
low locust
no
late dust
Yes 
low locust
oh we are talking about different places
low locust
instead of max_so_far it should be the last element of leader
near swan
okay, let me modify my code
also
it does not really have an impact on the algorithm's time complexity, right?
low locust
no
as long as you dont use an inner loop you are fine
this is a pretty minor optimization
near swan
okay, thank you
#include <iostream>
int main()
{
int n = 4;
int a[4] = {4, 7, 1, 0};
std::vector <int> leader;
leader.push_back(a[n - 1]);
for(int i = n - 1; i >= 0; i--)
{
if (a[i] > leader.back())
{
leader.push_back(a[i]);
}
}
for(int i = 0; i < leader.size(); i++)
{
std::cout << leader[i] << std::endl;
}
}``` like this?also does the order matter?
low locust
in what sense?
the order of a of course matters
oh the order of leader
yeah thats the wrong way
late dust
The printing? The problem statement doesn't specify
low locust
probably not intended that way
late dust
Yes, you could just reverse (the vector, or the printing)
Still one mistake though, you aren't checking the first element of a
near swan
is it okay now?
late dust
No
low locust
you are never having i=0
late dust
By first element I mean last in your loop
near swan
oh
low locust
aka never checking a[0]
wide pollen
hey im trying to attack b and i would like your help on that
wide pollen
thats what ive tried so far :
summer flax
thats what ive tried so far :
cant understand your language sorry but i personally would use AM-GM
sonic flint
since you have got the result 0<=y_0<=sqrt(y_0y_1)<=y_1<=1
then cant u just use the intermediate value theorem?
theres another way to do it: define another function thats the log of f(x)
@wide pollen are u there?
odd edgeBOT
@wide pollen Has your question been resolved?
wide pollen
since you have got the result 0<=y_0<=sqrt(y_0y_1)<=y_1<=1
yep im here sry for not answering
wide pollen
then cant u just use the intermediate value theorem?
thats what i did in the last line but i wanted to know if my steps are correct
wide pollen
its all correct!
oh ok since my teacher did g(x)=f(x)-sqrt(y0y1)
sonic flint
so it is tricky to use IVT to do this
wide pollen
oh ok since my teacher did g(x)=f(x)-sqrt(y0y1)
i wouldnt think about it during a test
wide pollen
so it is tricky to use IVT to do this
yehh
sonic flint
theres another way to do it: define another function thats the log of f(x)
instead its better to do this.
wide pollen
so now only y0>y1 left right?
sonic flint
it could be any log
so ln works too yeah
bassically we wanna take that square root and turn it into a sum of sorts
and log is the way to do that
can u do it now or should I explain the whole thing?
wide pollen
bassically we wanna take that square root and turn it into a sum of sorts
can you explain it a little more
since english not my native lang
so sry for that..
clever fjordBOT
AlmondAxis987
wide pollen
yeh
sonic flint
we see that 0<f(x)<1, so g(x) is well defined for those values
(ie no negative values appear which would break the log)
wide pollen
we see that 0<f(x)<1, so g(x) is well defined for those values
f(x) not equal to 0 and 1
sonic flint
g(0) = ln(y0) and g(1) = ln(y1)
sonic flint
f(x) not equal to 0 and 1
ah sorry, my mistake
sonic flint
now see that the value $\ln\sqrt{y_0y_1} = \frac{\ln(y_0)+\ln(y_1)}2$
wide pollen
i think so just a sec
clever fjordBOT
AlmondAxis987
wide pollen
yeh basic log arithmetics
sonic flint
nice
now the RHS of this can be written as $\frac{g(0)+g(1)}2$
wait thats wrong
one sec
clever fjordBOT
AlmondAxis987
wide pollen
**AlmondAxis987**
i can see that
sonic flint
and thats the arithmetic mean of 2 g(x) values, which is guaranteed to fall between g(0) and g(1)
unlike the geometric mean.
so now IVT can be used!
there exists some s such that $g(s) =\ln\sqrt{y_0y_1}$
clever fjordBOT
AlmondAxis987
sonic flint
now u can surely complete the proof?
wide pollen
im still trying to figure out this just a sec
wide pollen
**AlmondAxis987**
ok theres ln(sqrty0y1) that equals to this
sonic flint
yes
wide pollen
and since g is cont on [0,1]
wide pollen
**AlmondAxis987**
then this one is correct by the IVT
wide pollen
hmm
lemme write it
btw thx for your patience and help
got it i think
lemme show you
its just that g(s)=everything we said so far
and g(s)=ln(f(s))
and g(s)=ln(sqrty0y1)
smth like that
bruh
sonic flint
you forgot to remove the ln.
wide pollen
its just that g(s)=everything we said so far
and g(s)=ln(f(s))
and g(s)=ln(sqrty0y1)
then
g(s)=ln(f(s))=ln(sqrty0y1) ------> f(s)=sqrty0y1
sonic flint
yep!
you should show this as taking exponent of both sides
that way its more clear
but thats correct
wide pollen
thats amazing but as a newbie i wouldnt think about it str8 fast like you do lol..
sonic flint
do you understand why we coudnt take IVT on f(x)?
wide pollen
its a question out of a test
wide pollen
thats what ive tried so far :
on here @sonic flint ?
wide pollen
do you understand why we coudnt take IVT on f(x)?
^
sonic flint
ok nice
are u done or theres sumthing else I can help with?
actually, since its on a test, u dont need the whole log thing.
its for clear use of IVT, so if u have a test and it comes up you can just use IVT directly/
on f(s)
also its given that f(x) > 0, so we dont need to care about square roots of negative values
that being said, taking logs is still cleaner formally
I hope I could help 👍
wide pollen
thats what ive tried so far :
btw if i would have written it on a test would it be ok?
i would also write for a y0>y1
with using the ivt
since the log thing is elegant but for a newbie its a little bit less comes up
sonic flint
yep! but makesure to add that the geometric means holds only cus the f(x) is always>0
sonic flint
wym the geometic means holds?
means that x<=sqrt(xy)<=y is true
but if one of them i negative
then the root will be of a negative number
wide pollen
its all positive so its ok
sonic flint
yep
wide pollen
thx!!!
sonic flint
since the log thing is elegant but for a newbie its a little bit less comes up
yeah, that is a bit overkill ngl
ok, close the channel if ur done!
wide pollen
.close
odd edgeBOT
odd edgeBOT
Available help channel!
golden totem
sweden 10th grade just started need help with this
odd edgeBOT
sweden 10th grade just started need help with this
golden totem
its -p but i cant for the life of me understand why
golden totem
So what will u do when denominators are same
I can put the nominators above the common denominator
Wow
It wasnt hard
Idk what i was doing wrong
-2p/2 = -p
mystic saffron
Exactly
mystic saffron
I can put the nominators above the common denominator
Its numerator tho
golden totem
Ok
mystic saffron
Use .close once u r done
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keen jackal
orchid torrent
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swift mist
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swift mist
Currently reviewing L'Hopital's rule before diving into calc 2 again. Whoever is performing this example took the natural log of both sides in that third step, but then sets the limit equal to the right side after taking the natural log. Didn't he just get rid of the ln on the left side of the equation? Am I missing a property of logs?
marble laurel
Currently reviewing L'Hopital's rule before diving into calc 2 again. Whoever is...
He didn't get rid of it
He kept in mind that ln(y) is equal to the limit of the right hand side
swift mist
wouldn't he be taking the limit of the natural log of y, and not the actual function of x though?
marble laurel
The limit of natural log of a function is the same as the natural log of the limit of the function
swift mist
ahhh okay. why does that work?
swift mist
so can you always just replace the limit of f(x) with the limit of ln(f(x))? do certain conditions have to be met?
of course 99% of the time it would set you backwards, but I just want to understand
marble laurel
$\lim_{x\to c} \ln( f(x)) = \ln ( \lim_{x\to c} f(x) )$
clever fjordBOT
VulcanOne
swift mist
oh i see what you are saying
i am still confused i think. When he goes from this top step to the bottom, he's not taking an additional ln of f, he's just getting rid of the ln on the left while keeping the right the same?
marble laurel
He's not getting rid of the ln(y)
He's focusing on the ratio
After he evaluates the limit on the rhs
He'll undo the ln(y) to find the actual limit
swift mist
welp, i should've watched the rest of the video before getting confused
That makes sense. Thank you for your help Vulcan! You are awesome
marble laurel
swift mist
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true silo
Help, I need help solving e and d I don't gett ittt
odd edgeBOT
Help, I need help solving e and d I don't gett ittt
deft spear
qualitatively, all D is asking for is which point (A,B,C,D) is the velocity vector parallel to the south-pointing arrow
true silo
ohh wait i knew that, I meant e and f sorryy
I feel like e has to do with the pythagorean therum but it i only have one side length sooo i'm llost
and f i don't even know where to begin
😭
brazen hare
Help, I need help solving e and d I don't gett ittt
for part e: where on the circle do you think he would be facing Northeast?
try to visualise it if you can
deft spear
e is similar, north-east means moving at a 45 degree angle (tangent to the circle), so you can look at the circle and deduce where that would be by observation, analyze the radian angle of that on the circle, then use that value to find solve the question
deft spear
f is almost the opposite process, you're given the "angle" (in the form of revolutions) and then you can find the tangent vector's direction using geometry or maybe some other method
deft spear
and we know that bc its a tangent to the circle??
you know you're looking for where the velocity vector is pointing at a 45 degree angle because it says "north-east" which means "45 degrees"
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opaque fog
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opaque fog
how would you prove this
odd edgeBOT
@opaque fog Has your question been resolved?
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@opaque fog Has your question been resolved?
charred granite
Hello, can someone help me with my geometry homework? I'm stuck on a question and i feel stupid.
faint knot
Hello, can someone help me with my geometry homework? I'm stuck on a question an...
the tickmarks tell you which sides are intended to be the same length
take a look at the ||s here
and here
the same symbol on both sides indicate that theyre congruent
same applies with the angles, these both have the same angle:
this symbol means something specific: it means that GJ and HI are parallel
charred granite
ohh so the tick marks dont mean congruence?
faint knot
Im not sure how you gathered that from what I said, lets restart
take a look at the tickmarks, the ||s, here
these things in the middle of the side are called tickmarks
because theyre ticked on the KI
and because theyre marked on the KI
charred granite
this symbol means something specific: it means that GJ and HI are parallel
ogm sorry i was talking ab this
charred granite
omg no wonder i got it wrong tysm
warm drum
Need help w a math question-
Can't really find a breakthrough
warm drum
I keep goin in circles
zinc glacier
personnaly, i would also draw the line from the incenter to right angle too
warm drum
instead, draw these lines
Ooo icic
faint knot
what I did after was to then find the tan of the blue angle here,
in terms of the tan of the red angle here,
which is made convenient with the tan subtraction identity
warm drum
what I did after was to then find the tan of the blue angle here,
Mind explainin what searching for tan does?
Idt my teach explained it yet
(Or they have and I forgot--)
faint knot
you can expand tan(angle - some other angle) to what it looks like below
the bottom needs the tan of each angle, which youll know
faint knot
what I did after was to then find the tan of the blue angle here,
to make use of this, you first have to solve for the blue angle in terms of the red angle
you wont know the angles themselves, dont calculate them
warm drum
Aa
But what to do after?
my class only reached the basics of trigono and haven't dive into the more complex things so I have no idea what's goin on--
faint knot
the math question you found isnt at your trig level?
warm drum
the math question you found isnt at your trig level?
It's supposed to be cause it's a practice sheet given from the teacher themselves
faint knot
do you know the tan subtraction identity?
warm drum
I only know the equation and not how it may be used-
faint knot
I cant tell you every step there is
heres the triangle again
do you see the red and blue angle in this triangle?
Im going to assume you can see them given you havent said anything
lets say the red angle is A
warm drum
do you see the red and blue angle in this triangle?
Yup
faint knot
and the blue angle is B
warm drum
Im going to assume you can see them given you havent said anything
Srry was doin sumn'-
faint knot
ok, what about if B is here instead
warm drum
Er is it right to assume A=B in terms of angles?-
faint knot
see if you can justify why that must be true
warm drum
ok, what about if B is here instead
Cause the length of the hypotenuse is the same and bc one of the perpendicular sides is the radius of the circle it must be the same too-
Bc 2 sides of the triangle are the same length and it's a right angled triangle then it can be summed down to just 2 triangles mirrored?
Also english is not my first language so it might not be correct mathematical terms and a bit clunky in explainin-
faint knot
thats essentially correct, youre using HL congruence
the radii are the same, so a leg of each are the same
they share the same side, so the hypotenuse of each are also the same
and theyre both right triangles since the circle is tangent to each side
by HL congruence, the triangles are congruent
and so A = B
faint knot
very nice that you spotted a way to justify this
to be honest, past me wouldnt have figured this out, and he's good at the usual triangle proofs
warm drum
Atp that's the limit of my abilities-
faint knot
yep, theres a weird trick to this, and that trick requires some trust
warm drum
Trust?
faint knot
yea, because if you think about it,
most of the times when you find another angle, the expression isnt very nice
and then to take the tan of it and expect something nice, or even rational, would be a major stretch
so youll have to trust that tan(B) is very nice here
now knowing that the angles next to A and next to B here are the same,
see if you can solve for B in terms of A
warm drum
so youll have to trust that tan(B) is very nice here
Oo ic
warm drum
see if you can solve for B in terms of A
180 = 90 + 2a + 2b
90 = 2a+2b
-2b = 90-2a
-b = 45 - a?
warm drum
180 = 90 + 2a + 2b
90 = 2a+2b
-2b = 90-2a
-b = 45 - a?
b = 45 - a
Did I mess up the positive and negatives
💀💀
faint knot
should be 2b and b instead of -2b and -b
warm drum
Aaa okok
faint knot
only the 2a was moved to the opposite side, the equation was then read RTL
warm drum
Ooo icic
warm drum
so then tan(B) = tan(45 - A)
So then solve it using the tan identity you mentioned?
faint knot
yes
you can see what tan(A) is by referring to the original diagram
fill in what you need then that will tell you tan(A)
using this, the tangent subtraction identity lets you find tan(45 - A) conveniently
that information then fills in this area of the diagram
warm drum
So then solve it using the tan identity you mentioned?
Then by using this, is tan (b) = -1?
Or did I miscalculate-
faint knot
tan(B) should be 1/2
heres where some foreshadowing pays off
the picture from earlier was really 45 - A
tan(45) = 1, and tan(A) you should be able to figure out
actually tell me what tan(A) is
warm drum
I got ⅓ 💀
warm drum
tan(B) should be 1/2
Mind tellin me where I got it wrong? Still stumped on tan(b)
faint knot
???
warm drum
Aa ic
faint knot
think about if you had (1 - 5) / (1 + 5)
are you saying thats 5/5 * (1 - 1) / (1 + 1)?
you can see that feels wrong
if you had (5 - 5) / (5 + 5), then by distributive property youd have 5/5 * (1 - 1) / (1 + 1)
warm drum
true-
warm drum
now go try putting that into there
Tan (45-a) = 1/2?
faint knot
yep
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heady meadow
ay i need help
odd edgeBOT
ay i need help
odd edgeBOT
ay i need help
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
heady meadow
anyone know how to do part B? Ik part A and C
Like I might be stupid or smth
But I've literally been trying on this 1 question for like 15 mins and I js typed in discord.gg/math and this came up 😭
I finished like all other 24 questions
just this one thats throwing me off
whole gyro
the easy way to know where a function is positive is to check where the line is above the x axis
by line i mean the plotted function
heady meadow
the easy way to know where a function is positive is to check where the line is ...
Ye I got that im talking about part B
The interval notation
I also got Part C
whole gyro
right how would you answer the question if you didnt have to use interval notion
heady meadow
right how would you answer the question if you didnt have to use interval notion
Just put the x values of the points f(x)>=0
whole gyro
also for your information the brackets tell us where the intervals lie. for example if i say [3,5], i mean all x such that 3<=x<=5. If I used open brackets like (3,5) then it would mean all x such that 3<x<5
heady meadow
Ohhhhhhhh
whole gyro
Just put the x values of the points f(x)>=0
uhh not really the function is not just positive for a few x, its positive for a whole range of x
and we can capture that range using interval notation
heady meadow
Ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Ye I understood it when my teacher taught it but now it js completely flew out of my head
whole gyro
so what do you think the answer is?
heady meadow
so what do you think the answer is?
Do you use all brackets?
whole gyro
as in?
heady meadow
]
whole gyro
again the [ mean im including that value like [3,5] is the range 3 to 5, with 3 and 5 included
and (3,5) means the range from 3 to 5 with 3 and 5 excluded
heady meadow
and (3,5) means the range from 3 to 5 with 3 and 5 excluded
Wait so
whole gyro
(these are examples btw)
heady meadow
do I include the [ for values not included and the ( for the values included
whole gyro
do I include the [ for values not included and the ( for the values included
the oppsoite
whole gyro
[ to include boundary values ( to exclude boundary values
heady meadow
@whole gyro alr so I entered this and this what it said
whole gyro
well why is it (-3,4] U (1,5] instead of [-3,5]
whole gyro
but did you understand?
heady meadow
Yes I got it
odd edgeBOT
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simple inlet
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simple inlet
How can I find an upper bound?
whole gyro
How can I find an upper bound?
see what happens when b|a and then see what happens when a = bq + r where 0<r< b
@simple inlet
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@simple inlet Has your question been resolved?
simple inlet
see what happens when b|a and then see what happens when a = bq + r where 0<r< b
Ok sire
simple inlet
see what happens when b|a and then see what happens when a = bq + r where 0<r< b
Thanks
.close
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faint knot
what solution did you get
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simple inlet
How to do these kind of quet
odd edgeBOT
How to do these kind of quet
robust storm
How to do these kind of quet
I'm not quite sure how to solve this but honestly I'd start with f(x^2+f(y))=f(xy) and then use f(4)=20
and see if I can get anywhere from there
simple inlet
I'm not quite sure how to solve this but honestly I'd start with f(x^2+f(y))=f(x...
Try put values?
simple inlet
Ok lemme try
robust storm
or maybe I'd try to set x=xy, then replace in the first half so I get f(x)=f(something)
simple inlet
or maybe I'd try to set x=xy, then replace in the first half so I get f(x)=f(som...
Hmm maybe
robust storm
if this is a textbook exercise, it's probably solved similarly to others from the same chapter
also I'd you can prove f is 1-1, then you get x^2+f(y)=x*y
@simple inlet I found something, set x=0 and see what you get
mental vigil
<@946729301036920832> I found something, set x=0 and see what you get
is the function constant 🤔 ?
robust storm
seems like it
mental vigil
let him try
odd edgeBOT
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uneven compass
Hello! I have to solve this line integral, where C is the frontier of the given D region. I have to solve it both directly and by using the Green formula. I’m trying to see if i understood properly how to solve exercises like this one
odd edgeBOT
Show your work, and if possible, explain where you are stuck.
uneven compass
oki wait
ok so for the green formula i think everything is right and there shouldnt be any issues in solving the new integral over the D area, but for the other method I guess im having issues on how to approach it? do i have to separate the curve into 3 different ones, as written in the bottom left corner?
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scarlet stratus
ok so for the green formula i think everything is right and there shouldnt be an...
Yes. Split it into three curves to evaluate the line integral
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uneven compass
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uneven compass
Yes. Split it into three curves to evaluate the line integral
could you help me with the parametrization of the 3 curves? from then on i should be fine
scarlet stratus
For clarity you could write it as a single curve which is traced once as t varies but it would probably be a messier way to do it which is why it's easier to just consider it as the c_1, c_2, c_3 as you have.
Your c_2 looks right so it's just the two line segments to paramaterise.
uneven compass
ok, great! and that would mean three separate integrals as well, no?
another issue with parametrization: shouldn’t they all be in a way connected? or it doesn’t matter since i’m separating them? also, for C1 i think the parametrisation is wrong since its going clockwise? or is that irelevant?
odd edgeBOT
@uneven compass Has your question been resolved?
scarlet stratus
ok, great! and that would mean three separate integrals as well, no?
another i...
Yep, you need to make sure the curves are going in the right direction
scarlet stratus
ok, great! and that would mean three separate integrals as well, no?
another i...
You can split up the line integral into 3 to make calculations either and add them together.
I can imagine without doing it myself that you could parameterise the entire boundary into one piecewise curve.
There's a situation where you might want to do it in one single piecewise curve to show certain conditions hold for theorems relating to transformation theorems of double integrals but most of the time it's not worth the trouble and better just doing it the way you did with 3 separate curves.
uneven compass
so then i would only have to change the direction of the parametrization
scarlet stratus
Yep. For the proof of Green's theorem it is mandatory that the curves are parameterised such that the boundary is parameterised to have the region on the left as you traverse the boundary.
That's why we must be careful that we parameterise the curves to go in the right direction 🙂
For C_1 I would instead use x = -2t, y = 0 as then then t interval for that line segments is from t = 0 to t = 1 which is often easy to use when evaluating the integral.
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scarlet stratus
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dreamy grotto
Hello guys! I have an extra homework that it is so difficult. I even don't know as much as about it. Can anyone help me please. Here it is : "Choose a convex polygon with 30 vertices. How many ways are there to choose 4 vertices of the polygon so that the 4 vertices form a magneton with 2 sides coinciding with 2 sides of the polygon? The 2 sides are the two diagonals of the polygon?"
dreamy grotto
magneton?
Given a convex polygon with 30 vertices. How many ways are there to choose 4 vertices of the polygon so that the 4 vertices form a quadrilateral with 2 sides coinciding with 2 sides of the polygon, the 2 sides are the two diagonals of the polygon?
here
signal yacht
i would recommend starting with a simpler example so you can develop concrete understanding
like a hexagon
signal yacht
alr
tender bloom
i have to go school now
use .close
vernal yacht
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vernal yacht
use .close
Roger that 🫡
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wide pollen
is it right that the domain of w(x) is every x except x=+-1
tender bloom
is it right that the domain of w(x) is every x except x=+-1
you are correct, the domain of w(x) is all real numbers exept x=+-1
i am unaware why your teacher might think the domain does not include only x=1 and not x=-1
odd edgeBOT
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agile umbra
We did this in class and instead of doing the entire integral for the y-coordinate, he said some stuff and concluded that it's the same as the x-value. How? For the center of mass
sour oyster
We did this in class and instead of doing the entire integral for the y-coordina...
ahh there was a very good formula, its releated to area
go google it
u can easily find out coords
agile umbra
Uh that's not my question, I know the formula
sour oyster
ohh
sour oyster
Uh that's not my question, I know the formula
im very confused on ur q
agile umbra
I'm saying, in class my teacher didn't use the formula for the y-coordinate he said some stuff about the function height or something and that concluded that it's the same as the x. Asking how he could conclude that without doing it all over
sour oyster
I'm saying, in class my teacher didn't use the formula for the y-coordinate he s...
what is the same as x..?
agile umbra
the y-coordinate for the center of mass
odd edgeBOT
turbid comet
What did you try
Also is this a test
@urban pelican you will need to open a new channel
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sterile fiber
Help
sterile fiber
Can someone tell me what im supposed to do here im confused. Do i just plug in calculator ? Im confused on what the question is asking
nocturne mica
i guess you're allowed to use a calculator for the whole thing? the mention of laws of exponents make it sound like only the numerical part should be calculated while the powers of 10 is done by hand
but it'd be silly if that was the stipulation
sterile fiber
Ok Im just gona use calculator
wooden python
Can someone tell me what im supposed to do here im confused. Do i just plug in c...
you're supposed to plug this stuff into a calculator but be smart about it
- convert all factors into scientific notation which are not in it already
- split up the powers of ten from the mantissas (ie the stuff that's not powers of ten)
- work out the mantissas separately (with your calculator), and the powers of ten separately (using exponent laws)
- put it back together and adjust if needed
@sterile fiber do you still need help w/ this and do you want to be guided through it
abstract epoch
1. convert all factors into scientific notation which are not in it already
2. s...
just wanna add here, you also need to follow appropriate laws of significant digits as mentioned in the question before multiplying/dividing as plugging it straight into a calc and finding singnifcant digits might give a slightly different answer
wooden python
you need to truncate your sigfigs to whatever the coarsest of your inputs is.
but that comes only at the very end
abstract epoch
you need to truncate your sigfigs to whatever the _coarsest_ of your inputs is.
i dont understand what that means
nocturne mica
think she means this.
wooden python
look at how many sigfigs each of your original numbers in the expression has. take the LOWEST of these. you need to round your result to that many sigfigs.
sterile fiber
I got it thanks
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opaque hearth
yo
strange aspen
can someone describe a method for this question
what do you mean by "describe"
odd edgeBOT
tacit wasp
opaque hearth
oo
strange aspen
https://youtu.be/wRy5ExEYEBE?feature=shared from 3:45
ok that was a cool vid tbh
opaque hearth
https://youtu.be/wRy5ExEYEBE?feature=shared from 3:45
ye i started to do it like him thanks i'll watch it after i get it right
or wrong
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strange aspen
it's already closed
opaque hearth
it's already closed
oh preciate it
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clever elm
Can someone tell me if there is any problem in this math?
"Prove that, sin78°19′cos18°19′ - sin11°4′ + sin18°19′ = (√3)/2"
clever elm
Anyone?
clever elm
Minute
opaque hearth
i probably don't know it
opaque hearth
never heard of it sorry bro
if i had to guess u can use products of sine and cosine though
clever elm
never heard of it sorry bro
Np thanks for coming tho :)
mystic saffron
Can someone tell me if there is any problem in this math?
"Prove that, sin78°19′...
is it supposed to be sin11⁰4' * sin18⁰19' ?
wooden python
$\sin(78\dg 19') \cos(18\dg 19') - \sin(11\dg 04') + \sin(18\dg 19') = \frac{\sqrt{3}}{2}$