Pretty much the last one b4 i go on to samplings and estimations
#help-33
hasty wasp
hasty wasp
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
raven wren
For this I'm just wondering how u go from the second last line to the last line? (The top part is just integrating one part of it)
marsh citrusBOT
For this I'm just wondering how u go from the second last line to the last line?...
dapper socket
For this I'm just wondering how u go from the second last line to the last line?...
which one is the variable here? Z or R
raven wren
which one is the variable here? Z or R
I think theyre both variables in this context but its a partial derivative in r
This is the context
dapper socket
This is the context
So you increasing the radius of disk from 0 to inifinity? that doesn't feel right
Also are you sure the integration is correct ? I am too tired to check it
raven wren
Also are you sure the integration is correct ? I am too tired to check it
This is my lecturers notes and i checked it in wolfram alpha
raven wren
So you increasing the radius of disk from 0 to inifinity? that doesn't feel righ...
Well thats just the last part, im just wondering abt the algebra
dapper socket
So you increasing the radius of disk from 0 to inifinity? that doesn't feel righ...
probably you are checking electric field at a point Z units away from the disk from 0 to infinity
raven wren
probably you are checking electric field at a point Z units away from the disk f...
Ya and theyre all the same cuz the equation doesn't depend on z
dapper socket
Ya and theyre all the same cuz the equation doesn't depend on z
$$
\frac{\sigma z}{4 \epsilon}[\frac{-2}{z} - \frac{2}{\sqrt{z^2 + R^2}}]
$$
is this your second last line?
elfin berryBOT
notwish
raven wren
is this your second last line?
Yes
$$
\frac{\sigmaz}{4\epsilon_0}
(
\frac{-2}{z} \frac{-2}{\sqrt{z^2+R^2}}
)
$$
To
$$
\frac{\sigma}{2\epsilon_0}
(
1 \frac{-2}{\sqrt{z^2+R^2}}
)
$$
elfin berryBOT
Hemesfere
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
dapper socket
Yes
you made a mistake copying the notes then
as you can see there is no z in the denominator of right most part
you still removed the z ourside the paranthesis
which is not possible
dapper socket
**notwish**
$$
\frac{\sigma z}{2 \epsilon}[\frac{-1}{z} - \frac{1}{\sqrt{z^2 + R^2}}]
$$
elfin berryBOT
notwish
raven wren
you still removed the z ourside the paranthesis
Ya thats what im confused about😭
raven wren
you made a mistake copying the notes then
These are his
dapper socket
Ya thats what im confused about😭
yea that was a mistake
when copying the notes
the last thing you should be getting is
raven wren
Im guessing its 1 - R²/z² in the sqrt
raven wren
when copying the notes
No his notes r just wrong
dapper socket
$$
\frac{\sigma z}{2 \epsilon}[\frac{-3}{z} + \frac{1}{\sqrt{z^2 + R^2}}]
$$
elfin berryBOT
notwish
dapper socket
this is what i get if I put the lower and upper limits of R as R and 0
raven wren
That doesn't seem right
dapper socket
These are his
is that z on top of the sqr root
or is it 2
is it is z then i need to make changes
raven wren
is that z on top of the sqr root
Idek, would it work if it was z?
dapper socket
These are his
mate you wrote something else than this
raven wren
mate you wrote something else than this
Whatd i write different
dapper socket
why is there -2/z or simply -1/z instead of +2/z or +1/z
raven wren
the -1/z will be +1/z
Why would it be +?
dapper socket
These are his
cause here your prof. wrote +1
not -1
you took z outside not -z
so it'll be 1/z not -1/z
raven wren
cause here your prof. wrote +1
How would it be +1 there tho
dapper socket
These are his
also you didn't have to take the z outside in the first place
dapper socket
How would it be +1 there tho
well idk your prof. wrote it
raven wren
also you didn't have to take the z outside in the first place
U did, u had to cancel with the z outside
dapper socket
$$
\frac{\sigma}{2 \epsilon}[1 - \frac{z}{\sqrt{z^2 + R^2}}]
$$
elfin berryBOT
notwish
raven wren
well idk your prof. wrote it
Ya, well im wondering how he got his answer so?😭
dapper socket
**notwish**
This is what your prof. last wrote before putting the limits from 0 to R
now when you put the limits
inside the []
raven wren
now when you put the limits
No man, thats not how do u a definite integral
He had already put in the limits at that stage
dapper socket
i mean if he put the limits already
he skipped not only taking out the integral of whatever was there
but even calculated the whole thing
even einstein wouldn't be doing such jumps my lord
i can't help i am sorry
I am too tired to do the integration
raven wren
For this I'm just wondering how u go from the second last line to the last line?...
All I'm wondering is how to get from the 2nd last step to the final step, no limits just algebra
I'm guessing now as u said that the denominator is z
dapper socket
All I'm wondering is how to get from the 2nd last step to the final step, no lim...
you can't go from 2nd last to last directly you are making some mistake there
oh you can
wait wait
wait
so you take -2 outside the paranthesis
and z inside the paranthesis
so z/z becomes 1
raven wren
Ahhh right
dapper socket
and there is z/square root(z^2 + R^2)
dapper socket
Ahhh right
sorry for the time waste TvT improve your handwriting mate I can't differentiate between your 2 and z tbh
raven wren
Still doesn't explain the signs tho, the - isn't outside the brackets
raven wren
sorry for the time waste TvT improve your handwriting mate I can't differentiate...
Lol thx for explanation
dapper socket
Still doesn't explain the signs tho, the - isn't outside the brackets
-ve sign in electric field is just its direction so your prof probably ignored it
raven wren
Ya true
dapper socket
"usually" that is the case with -ve signs in physics
modern hedge
i need help, sorry if i use incorrect terminology or are asking a stupid question. I am fairly sure my formula is wrong, the p pronumeral is our factorial count & f is the number that we are factorializing. The inconsistency is that if an even number is input as f when p=2 then it will because zero because e.g. 6 * 4 * 2 * 0 = 0.
i could not figure out what would need to be added in order for it to not attempt to multiply by zero.
marsh citrusBOT
i need help, sorry if i use incorrect terminology or are asking a stupid questio...
@modern hedge Has your question been resolved?
upbeat raft
Please, if anyone can help, I need applications of Hurwitz's theorem for a presentation on complex analysis. All the applications I found were in algebra
marsh citrusBOT
Please, if anyone can help, I need applications of Hurwitz's theorem for a prese...
spark otter
Please, if anyone can help, I need applications of Hurwitz's theorem for a prese...
I mean if you haven't seen this already :
take (fn) holomorphic and injective that converge uniformly on compact subsets to f holomorphic. What can we say about f? Note: the domain must be open and connected
Answer : ||f is either constant or injective||
Or if you want stronger, it is one of the theorems involved in proving that any open and simply connected non-empty proper subset of C is biholomorphic to the unit disk
if you haven't seen "simply connected", let's just say that it means "a set that contains no holes"
marsh citrusBOT
@upbeat raft Has your question been resolved?
upbeat raft
thank you 🙏
lyric kelp
marsh citrusBOT
urban bobcat
"Determine the largest and smallest value of the function"
marsh citrusBOT
"Determine the largest and smallest value of the function"
@urban bobcat Has your question been resolved?
marsh citrusBOT
@urban bobcat Has your question been resolved?
neat timber
"Determine the largest and smallest value of the function"
the largest value must be talking x = 5 and y = 5
while will be equal to 125
the lowest value x = 7 and y = 3
while will be equal to 85
i'm not sure though
urban bobcat
hmm yes okay maybe
urban bobcat
how do i show that tho?
red nimbus
how do i show that tho?
I think one way to do would be to solve for one variable and plug in your constraint function into f(x,y) so that it gets to either f(x) or f(y) and then you investigate the extreme values.
Anotherway would be Lagrange-Multiplicators
urban bobcat
Yes okay, I am back again with another 8 questions haha
red nimbus
what are you yapping
urban bobcat
Do I like start with finding the partial derivatives for x and y?
red nimbus
Do I like start with finding the partial derivatives for x and y?
What method do you wanna do?
urban bobcat
i am not sure, what do you think is easier?
red nimbus
it's important
because in order to do what i suggested
we will check if there are any extreme values on the border of the region
red nimbus
yea
urban bobcat
and xy = 21 implies that y = 21/x?
red nimbus
yes if x not 0 but we can ignore them anyway
red nimbus
yea
keep in mind we are assuming there are no relative extrema in the inner region
n
also wait
you can do 21/x = 10-x
and solve for x
I think the better way
y = 10-x into yx = 21
(10-x)x = 21
x = 3 or x = 7
urban bobcat
yes i got that too
if we put x=3 into y = 10-x we get 7 and if we put in x=7 into y =10.x we get 3?
so are the two points (3,7) and (7,3)?
red nimbus
oh no bruh
oh yea
we only considered the borderes!
hence we had this system:
x+y = 10
xy = 21
urban bobcat
yes
red nimbus
also I checked
f has no extreme value in the region
it only has a minimum at (0,0) which is not of itnerest
urban bobcat
hmm okay
red nimbus
yea sorry that you are disappointed
urban bobcat
no i am not, but what does that mean that is does not have a buggest and smallest value?
red nimbus
In the region it has
urban bobcat
dont we get the smalles and bigges if we put in the points (3,7) and (7,3)?
red nimbus
well these are the only possbile points
probably
if you plug in your constraints into f and then f' = 0
you will notices that both dont share a common solution
urban bobcat
hmm okay
red nimbus
f(x) = x² + 4(10-x)² and f(x) = x² + 4(21/x)²
Like for example I founf (8,80) is a minimum
but it doesn't satisfy xy = 21
urban bobcat
no stop its fine haha
red nimbus
life is not so yummy for you anymore
red nimbus
do that
marsh citrusBOT
marsh citrusBOT
Available help channel!
cyan plinth
graphical solution of systems of linear equations, i don't understand how to get to the answer, i dont understand how there is a minus before x, then + changed to - behind 2 and - appeared behind 6??
marsh citrusBOT
graphical solution of systems of linear equations, i don't understand how to get...
cyan plinth
the answer is supposed to be (2,2 ) i also dk how to get to that
blazing plover
graphical solution of systems of linear equations, i don't understand how to get...
just multiply both sides of the equation by -1
cyan plinth
just multiply both sides of the equation by -1
where'd we get the -1
blazing plover
You can do whatever you want to an equation, as long as it applies to both sides of the equation.
cyan plinth
ah
I forgot to put it
how do we know when there's a -1
in other ones we don't need to do that
but this one just confuses me
blazing plover
When we added the two equations together, we multiplied the first equation by -1 so that -x and +x cancel each other. Now you can add them together and find y
x+2y=6
And
-x-2y=-6
is same thing just multipled by -1
cyan plinth
how do we find the other one (2,2)
do we have to multiply it by -1?
oohh
then what do we do after
if you know
blazing plover
🧐
cyan plinth
do we?
blazing plover
I dont understand you
cyan plinth
the first one
cyan plinth
x+2y-6=0
blazing plover
Lets put y=2
blazing plover
All
blazing plover
You can try
cyan plinth
would it be correct if it was 2y=
blazing plover
Can you explain
cyan plinth
in my notebook it says 2y=-x+6
now half of it is gone since the teacher wiped the table and my friend is dumb just as me and is failing 3 classes
and she didnt write anything
blazing plover
in my notebook it says 2y=-x+6
Yeah its same thing
cyan plinth
will it be the same as your way
im gonna go your way since idk what is going on in my notebook
what do we do next
blazing plover
Adding or subtracting things from either side of the equation doesn't change anything.
There is nothing wrong
cyan plinth
the other one?
we go from 2y=-x+6
bruh ngl i feel as if im gonna fail madly on the exam , our teacher said that this one gives the most points
and we literally didnt practice it at all
i only have 2 of the same ones unfinished
blazing plover
Don't give up, math is a very easy subject
cyan plinth
thank you, in 8th grade did you study math after you've done a lection or
how long did you study before an exam? or did you practice even before an exam
blazing plover
I start studying a week before I take school exams
I usually get full marks from all of them
cyan plinth
my friend went to instructors n stuff
she still failed
thing is i studied like 2 days before
you have no idea how much she paid for them
and i still got a grade higher than her
blazing plover
Be assured that this question you asked me is actually so simple that in my opinion, solving this question using a pen would be disrespectful to myself.
cyan plinth
let's switch places on the exam
blazing plover
😅
cyan plinth
what grade are you in?
blazing plover
Im 12
cyan plinth
highschool?
blazing plover
Yes
cyan plinth
im in 8th grade
blazing plover
Yes you said
cyan plinth
i feel a bit embarassed to ask questions here since it seems simple
i asked my friend and she called me autistic
cyan plinth
how do we do this
blazing plover
i feel a bit embarassed to ask questions here since it seems simple
Do not hesitate, you can ask any question here, it is not a shame not to know, it is a shame not to learn.
Lets solve
Wait 1 min
cyan plinth
are you busy ? since you're in 12 grade
my friend is in her first year of highschool and very busy sometimes
blazing plover
Yes but no problem
cyan plinth
thank you for helping me it really means a lot
blazing plover
@cyan plinth
I usually study for my exams by watching videos on YouTube, I recommend it to you too
cyan plinth
thank you
that's actually so simple but
I still can't understand how we got the -1 from im sorry
cyan plinth
When we added the two equations together, we multiplied the first equation by -1...
can't they cancel eachother without adding -1?
blazing plover
It's possible, let me solve it for you with another method
cyan plinth
thank you bro
blazing plover
Don't be afraid because it's long, I just extended it for your understanding.
I hope it will be helpfull
If there is something you don't understand, ask
cyan plinth
I dont know how to thank you
i have a small question
when we add 6
do we only add numbers that are simple, like that don't have x or y infront of them
blazing plover
You can add whatever you want, a simple number or a complex expression. That's the beautiful thing about math.
cyan plinth
if it was like x+5y-8=0 we could've done it like x+5y-8+8=+8
blazing plover
Yeah its the same thing
blazing plover
would we do x-y+4+4=+4
It wouldn't be wrong to do that, but it would also be useless to us
Remember our purpose in doing these operations is to leave the unknown number alone.
So we should add -4 not +4
cyan plinth
x-y+4-4=-4?
Hold on i'm writing down what you've sent me
i have to remember that
thank you very much again
blazing plover
No problem
blazing plover
x-y+4-4=-4?
Yes
cyan plinth
Don't be afraid because it's long, I just extended it for your understanding.
then I do the same as this method?
also how do we know if it goes with - or +
blazing plover
x-y+4-4=-4
x-y=-4
x-y+y=-4+y
x=-4+y
As you can see x was left alone, that was our goal
cyan plinth
or is it the same and doesnt matter which one we used
blazing plover
Both methods are correct, valid for every problem
cyan plinth
phew thank you
blazing plover
also how do we know if it goes with - or +
You pour water to extinguish the fire, right? If we subtract itself from a number, the number disappears. For example, add +7 to eliminate the number -7. Add -43 to eliminate the number 43. Add -452y to eliminate the number 452y.
cyan plinth
which one's easier?
i will try going with - always, it goes for the same one and is always correct
i mean hopefully
blazing plover
which one's easier?
Both methods are very easy
cyan plinth
but doesn't matter which ones i pick? Can i always pick -
blazing plover
No
You have to understand the logic of this or you can't move forward
An example
a+6b-3=0
Lets make "a" alone
Lets add +3
a+6b-3+3=+3
a+6b=3
Lets add -6b
a+6b-6b=3-6b
a=3-6b
Very simple
blazing plover
wdym by a has to be alone
I'm talking about having only "a" on one side of the equation
blazing plover
it can't be a=3-6b+4c?
It can, its only a example
blazing plover
You must have learned something now, go to the first question and try to solve it on your own
cyan plinth
It wouldn't be wrong to do that, but it would also be useless to us
also wdym it wouldnt be wrong to do that
could it work? Would it give me the same results?
blazing plover
I just have to work on when it's - and when +
Add the inverse sign of the number you want to destroy, that's all.
blazing plover
also wdym it wouldnt be wrong to do that
Its not wrong, but will not help you solve the question
cyan plinth
it wont give the correct answer?
blazing plover
it can
cyan plinth
Add the inverse sign of the number you want to destroy, that's all.
- and - eliminates, + and + doesnt,, - eliminates idk 332
blazing plover
+ and - eliminates, + and + doesnt,, - eliminates idk 332
- and + is friend
- and - is friend
- and - is enemy
- and + is enemy
cyan plinth
and that's how i know when it comes with - and when with +?
blazing plover
Yes
cyan plinth
i will note that down
blazing plover
👍
cyan plinth
+ and + is friend
- and - is friend
+ and - is enemy
- and + is enemy
by the enemies we choose which ones the -?
blazing plover
You must choose the enemy of whoever is in front of you to kill him
still temple
graphical solution of systems of linear equations, i don't understand how to get...
this isn't a graphical solution lmao
still temple
graphical solution means you graph them and find the intersection point
blazing plover
this isn't a graphical solution lmao
She is new to math 🤫
still temple
do you have any worked out example problems of the same wording
cyan plinth
what do you mean?
blazing plover
Check out other solved questions
cyan plinth
yes but he writes fast and then erases the table
we have to draw a graph also
and like add something on it
i will study that tomorrow
then practice everything i've studied
then exam
still temple
we have to draw a graph also
that's what a graphical solution is
cyan plinth
that's what a graphical solution is
then I was right i guess
still temple
i mean no
cyan plinth
i put what it said in the google translate
still temple
graphical solution means you use the graph to find the solution
blazing plover
Like this graphs?
still temple
you don't find the solution and then graph
still temple
Like this graphs?
worst graph in my life lmao
cyan plinth
you don't find the solution and then graph
i guess it translated wrong
it isn't even my fault
blazing plover
worst graph in my life lmao
Why bro i drew it
@cyan plinth You should watch math exam videos on Youtube
cyan plinth
<@1210236825172443147> You should watch math exam videos on Youtube
i did
still temple
ngl
still temple
when is your exam
cyan plinth
this week
still temple
what is it on
still temple
no sorry i meant what material is being tested
blazing plover
equations, powers and squareroot i guess
blazing plover
Squareroot
still temple
oh
tbh @cyan plinth you're not totally cooked
yesterday i helped somebody who didn't know what an exponent was
and then another person who didn't know how to plug numbers into an equation
cyan plinth
graph of linear function and line equation,implicit equations and explicit,zero point of a linear function, equations of the line through one and two points
still temple
oh
cyan plinth
and then another person who didn't know how to plug numbers into an equation
not sure what that is
still temple
well that's ez
still temple
yeah nvm you're cooked
cyan plinth
i know it's easy since you're possibly older
blazing plover
Bro wait
cyan plinth
i remind myself of my little cousin who's crying over basic multypling
multiplying
mutli
,ti
wersklgtjrebgfdtrw
elfin berryBOT
You haven't set your timezone! Set it using the interactive timezone picker with ,ti --set.
cyan plinth
by the enemies we choose which ones the -?
blazing plover
graphical solution of systems of linear equations, i don't understand how to get...
Then this is not an equation, the intersection of two lines
blazing plover
Yes xd
still temple
she's supposed to look at the graph
cyan plinth
what country are you from plas
blazing plover
Turkey
cyan plinth
she's supposed to look at the graph
we're supposed to solve the equation or whatever
then do the graph
still temple
that's stupid
cyan plinth
that's stupid
it's not really
there's another way around
but we do it the other way
still temple
either your teacher doesn't know what the problem is asking or just translation error
cyan plinth
i have a quick question
how'd he know my gender immidiately
the sexism in this world☹️
cyan plinth
oh
blazing plover
Yes xd
still temple
when you joined the server you clicked on a button that said you were a girl
cyan plinth
yeah don't mind that
still temple
claiming sexism
cyan plinth
I was joking
still temple
no you weren't
cyan plinth
ya i was
still temple
i think you're just trying to save face
cyan plinth
☹️
still temple
tbh you're a child so this behavior is expected
cyan plinth
how old are you
still temple
instead of taking responsibility for the mistake you act like you didn't make it
cyan plinth
I sincerely apologize, I was not intended as a serious thing.
blazing plover
There is no serious problem, we are just kidding
still temple
There is no serious problem, we are just kidding
lmao and now you're doing the same thing
still temple
saying he's joking
still temple
gl in your exam and don't accuse people of assuming your gender when you freaking told them what your gender is
cyan plinth
gl in your exam and don't accuse people of assuming your gender when you freakin...
i was joking i'm serious
i didn't tell anyone my gender, i forgot i put it even
blazing plover
saying he's joking
She took it seriously and I didn't want her to be upset
still temple
i was joking i'm serious
Damn you upgraded from moron to oxymoron
cyan plinth
She took it seriously and I didn't want her to be upset
i wasn't being serious
cyan plinth
Damn you upgraded from moron to oxymoron
☹️
still temple
She took it seriously and I didn't want her to be upset
tbh she should take it at least semi-seriously bc ppl might take that accusation harsher than we did
blazing plover
Anyway, let's close the topic...
still temple
also the childish behaviour trying to say it was a joke on top of that
cyan plinth
are you being serious
still temple
.close
blazing plover
:d
cyan plinth
i have a pokemon collection
blazing plover
i have a pokemon collection
Cool
cyan plinth
plas sorry if you took it seriously
I didn't really mean anything of it , my friends and me joke around like that
blazing plover
No problem 👍
cyan plinth
Also thank you for helping me with the math stuff, I really appreciate you 😄
how do i close this
.close
marsh citrusBOT
still temple
Also thank you for helping me with the math stuff, I really appreciate you 😄
yeah you're cooked tbh
marsh citrusBOT
Available help channel!
edgy frigate
marsh citrusBOT
edgy frigate
idk if this is right
these are my options btw
im pretty sure last one is def right idk abt first
idk if its that or maybe algebra
quasi patrol
First 1 isnt pythagorean
edgy frigate
ok so its def algebra?
thick junco
y
edgy frigate
ok wait
it cant be quotient
or pythagorean bc of the parenthesis
and it cant be reciprocal
so its either even/odd or algebra
but i can kinda see it being even/odd more
or am i wrong completely
yea i think its odd/even
quasi patrol
yea i think its odd/even
What even is even/odd
edgy frigate
quasi patrol
What does it mean
edgy frigate
its one of the options
quasi patrol
Ohh
edgy frigate
and its the closest i think
quasi patrol
and its the closest i think
Dont look at formulas
Look at your mind
Use brainpower
Does that look like a trig identity
At all
edgy frigate
im learning this first time tdy 😭
edgy frigate
Does that look like a trig identity
no
quasi patrol
Brainpower > eyes
edgy frigate
ok ok
it cant be quotient
def not even/odd
not pythagorean
so its either reciprocal or algebra
quasi patrol
Its just binomial expansion
edgy frigate
so algebra
ok thats what i thought of first but i just wanted to make sure
ill use my brain for now on
thick junco
isn't step 3 just algebra
since ur just dividing cos(x) by cos^2(x)
and moving where the brackets are
edgy frigate
oh
yea
ok
how do these look
im still trying to figure out the 4th and 5th one
edgy frigate
algebra again
thick junco
ye
thick junco
eh, u might just be tired
thick junco
i got all the other ones down at least
incl 5?
edgy frigate
i would think its reciprocal
thick junco
that's the intention
edgy frigate
no worries
thick junco
i probably won't
edgy frigate
LMAO
thick junco
i would think its reciprocal
how would you describe the change between the two steps?
brb gotta take my meds
thick junco
not quite
edgy frigate
and sin^2x is basically taking over both sinx on the 5th
thick junco
look here. we start and end w/ a cosx on the top
thick junco
would what be squared
edgy frigate
actually wait no nvm
wait wait
i think i got it one sec
wait
is this actually quotient
thick junco
no
edgy frigate
yea ok im so lost
thick junco
think about it this way: we're expanding out q (=sin(x)) in the sense of q^2 = q * q
and then moving one of those q's to its own fraction
edgy frigate
yea and the only thing that like pops up with that is just algebra now
no way its algebra again
i needa review this more oml 💀
edgy frigate
this is the last unit for my class and honestly i already have a decent grade so im not too worried
so it was algebra
?
@thick junco
marsh citrusBOT
outer pewter
how do i use percentage again
my area for the half circle is 20,444... m2
but how do i add 12%
marsh citrusBOT
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harsh vine
Can someone please help with question 1b
marsh citrusBOT
Can someone please help with question 1b
hazy lion
try writing: $u-x = (\sqrt u)^2 - (\sqrt x)^2$
elfin berryBOT
jan Niku
harsh vine
try writing: $u-x = (\sqrt u)^2 - (\sqrt x)^2$
does the same apply to question c?
hazy lion
hmm maybe you can try $x^{3/2} = \qty( \sqrt x ) ^3$
elfin berryBOT
jan Niku
hazy lion
np
harsh vine
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lyric kelp
marsh citrusBOT
lyric kelp
how did the thing above become the thing under
fervent rampart
finding a common denominator of 4-x^2 and adding
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glass locust
Alright so
marsh citrusBOT
Alright so
glass locust
The formula for the number of reflexive relations is 2^(n²-n)
Could someone elaborate
As to how the formula is given
And how am I supposed to use it in questions?
For example
There's a set A with elements {1,2,3}
How many reflexive relations will it have?
Nevermind I got the second part
But yeah I do need the derivation of the formula and also what's a universal set
tired hawk
umm hi?
slim spire
idk what universal set would be here, usually it's just the biggest set possible
tired hawk
what is this server? mathematics?
slim spire
for counting relations you have to ask for each pair of elements, is there a connection, like a=b
slim spire
you might wanna go to #discussion lol
dry prawn
can u give me devide but not hord? plz?
!help
marsh citrusBOT
can u give me devide but not hord? plz?
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slim spire
in general there are n^2 pairs, so the total number of relations is 2^n^2, but with the reflexive property you already know some connections, a=a, b=b, c=c,...
so the exponent is a bit less which gives you the number
glass locust
I'm sorry I didn't quite understand
slim spire
you can see it by drawing out a table, and you know the diagonal is all 1's, so count the rest of the squares
ignore the checkmarks
glass locust
Oh
For a set A with elements {1,2,3}
The number of relations containing (1,1) , (2,2), (3,3) would be three?
slim spire
way more
slim spire
oh I'd have to look up what the rest of those are
for reflexive you can choose 0 or 1 for the blank squares, so 2^6=32
glass locust
I know what those are
glass locust
for reflexive you can choose 0 or 1 for the blank squares, so 2^6=32
I'm sorry but isn't 2^6 equal to 64?
slim spire
aaaa yes
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echo pivot
hello
sick needle
well, you need to find the values for x
such that tan x = 0.61
where is tan positive?
in which quad?
echo pivot
wait i dont know if tan is positive
sick needle
oh okay
echo pivot
but that one is negative
sick needle
yes its negative
Now, look at the bounds
Where is it bound to?
in between what exactly
sick needle
mhm
echo pivot
silliness has caught me
echo pivot
how does it go again?
1st quad is on the right and 2nd is left?
third is bottom right and fourth is bottom left?
sick needle
no
1st quad is top left
no wait
1st quad is top right
2nd is top left
3rd is bottom left
4th is bottom right
So, it goes anticlockwise from 0 to 360
echo pivot
gotcha, so counterclockwise
sick needle
yes
sick needle
Now, do you know A S T C?
sick needle
ahah
Okay, s
A S T C refer to which values of what trig are positive
So, in the first quadrant, A is positive
A stands for all
Sin, tan, cos are all positive in the first quadrant
S stands for sin, which is positive in the second quadrant, whereas tan and cos are negative
T stands for tan, which is pos in 3rd quad, and sin and cos are negative
C stands for cos, which in pos in 4th quad, where sin and tan are negative
sick needle
YES
echo pivot
that is easy to remember
echo pivot
a for all, s for sin where its only pos, t is tan and only pos, and c is cos and only pos
echo pivot
sick needle
thats where its positive !!
echo pivot
uhhh i dont know where t is positive
sick needle
A S T C
T is Tan, and third quadrant
remember that
tan is negative in S AND C
because thats where only sin and cos are positive
You with me so far?
I'm teaching you how to do these types of questions in itself, not that one particularly
sick needle
alright, good
Now, we deduced that tan is negative in 2nd and 4th quadrant
but, we also have a interval
which limits us to which quadrant?
echo pivot
interval?
sick needle
yes
echo pivot
yes?
echo pivot
it is in the S, 2nd quad
sick needle
GOOD
So, steps you need to follow to do these questions
- look at the sign, is it positive or negative? look at the trig function? where is that function positive or negative
- look at the bounds/interval. where does it limit us to? using that info, in which quadrant does the angle lie?
you with me so far?
echo pivot
2. look at the bounds/interval. where does it limit us to? using that info, in w...
well you said 2nd and 4th
sick needle
well you said 2nd and 4th
correct
echo pivot
1. look at the sign, is it positive or negative? look at the trig function? wher...
its negative but i dont know what you mean by trig function or function thats positive or negative
echo pivot
its tan
sick needle
and if it is, is it negative or positive
echo pivot
tan is postive?
echo pivot
oh on the chart
echo pivot
OHHH
sick needle
YESEYS
and the interval, it limits us to 2nd quad
Now you know where the angle lies
Now simply find arctan(-0.42) to find the angle
And find what value that angle would be in the 2nd quadrant
echo pivot
and the interval, it limits us to 2nd quad
whys that?
sick needle
whys that?
because the interval says that the answer lies between
90 degrees and 180 degrees
which quadrant lies in that section?
echo pivot
2nd
sick needle
see
echo pivot
i think im starting to get it
echo pivot
thank you
echo pivot
Now simply find arctan(-0.42) to find the angle
how do i do this?
sick needle
mhm
echo pivot
oke
elfin berryBOT
echo pivot
yes
sick needle
or degrees
echo pivot
oke
echo pivot
:> yaaay
echo pivot
its -0.39
sick needle
ah
yes
my bad
-0.39, you're right
however, that angle exists in
the second quadrant
Its value in the second quadrant would be different
In the second quad, the angle you find is subtracted from pi
So your final angle would be pi - 0.39
What does that give you?
echo pivot
3.531
elfin berryBOT
echo pivot
oh crap
sick needle
its okay
echo pivot
i did pie--0.39
sick needle
remember
tan (-x) = - tan(x)
consider angle to be positive when you're dealing with it
Its kind of confusing rn, isn't it?
echo pivot
okay ill note that down
sick needle
Lets try doing it in degrees first
echo pivot
i think whats more confusing to me is the pie
echo pivot
.999
sick needle
nopedy nope
sick needle
nope
echo pivot
wait what?
sick needle
there we go
For now, ignore the negative sign
Where do you think the angle 22.78 would exist?
echo pivot
probably where the acute side is at which is maybe quad 1?
echo pivot
echo pivot
yes 90 degrees is bigger than 22.78
echo pivot
but didnt we do that already?
sick needle
between pi/2 and pi
sick needle
but didnt we do that already?
not yet
we only found the negative angle for the value
Which is basically negative of tan (22.7 degrees)
so therefore you consider the angle as positive
,w tan (-30 degrees)
elfin berryBOT
sick needle
,w -tan(30 degrees)
elfin berryBOT
sick needle
see that?
echo pivot
where did you get 30 degrees from?
sick needle
its just an example
echo pivot
okok
sick needle
I'm proving to you that tan(-x) = -tan(x)
now, we need to find the value of the angle iN THE 2ND QUADRANT, which lies between 90 degrees and 180 degrees, such that its value is -0.42
How do we do that?
subtract the angle you got in first quadrant, from 180
echo pivot
180-22.7?
sick needle
So an angle in the first quadrant, would be 180-(x) in the second quadrant
echo pivot
157.3
sick needle
perfect
echo pivot
echo pivot
5 pie/6?