isnt 1^2
#help-17
trail notch
but you missed the g
so itsj ust g/4pi^2
grizzled halo
yes
grizzled halo
,w 9.8/(4pi^2)
twin meteorBOT
grizzled halo
you want this?
trail notch
you want this?
i think so?
grizzled halo
then if you've got a calculator, you just put that in
trail notch
okk
grizzled halo
with g=9.8
grizzled halo
yeah
trail notch
so L=0.25
grizzled halo
sure
grizzled halo
it's a right angled triangle, so pythagoras' theorem would be good
trail notch
it's a right angled triangle, so pythagoras' theorem would be good
but how do i do that wiht just z
*x
grizzled halo
if you let the longest side be y, then y^2=(2x)^2+x^2?
(i would work on the area first though)
trail notch
(i would work on the area first though)
how tho?
grizzled halo
area = 1/2 x base x height?
trail notch
so x=square root of 30
grizzled halo
so that gives you the two shorter sides, and then you can use pythag for the longest side
trail notch
so that gives you the two shorter sides, and then you can use pythag for the lon...
so its 2*square root of 30?
so i right 2√30?
grizzled halo
yes, for the second side
trail notch
trail notch
yes, for the second side
can u check for me?
grizzled halo
,w sqrt150
twin meteorBOT
grizzled halo
looks good
trail notch
ok but it doesnt exactly equal 30
trail notch
round b and c to nearest tenth and you're done
how do i do that
grizzled halo
,w 2sqrt30
twin meteorBOT
grizzled halo
same way you rounded x?
wary mantle
For proving that gcd(m_1, n) = 1 and gcd(m_2, n) = 1 ==> gcd(m_1m_2, n) = 1, would you use Bezout's identity?
vocal sleetBOT
For proving that gcd(m_1, n) = 1 and gcd(m_2, n) = 1 ==> gcd(m_1m_2, n) = 1, wou...
wary mantle
It'd give us
1 = a_1m_1 + b_1n
1 = a_2m_2 + b_2n
Now multiply these two together?
But that wouldn't lead us where we want
tidal dock
if m_1 doesn't have any common factors with n, and neither does m_2, then their product can't have any common factors with n
lyric relic
if p is a prime s.t. p|n and p|m1m2 then p|m1 or p|m2 ...lets say p|m1 then we get a contradiction because p|m1 and n ...
now a common divisor of n and m1m2 will not have any prime factors... so only +-1 could be a common divisor
wary mantle
now a common divisor of n and m1m2 will not have any prime factors... so only +...
and so it's 1? Thanks
wraith venture
so all you need is actually Gauss's lemma
wary mantle
if p is a prime s.t. p|n and p|m1m2 then p|m1 or p|m2 ...lets say p|m1 then we g...
Wait, contradiction to p|n and p|m1m2 means not p |n or not p|m1m2
or, not and
cobalt ocean
you can also just do it constructively, it turns into letter salad but it works
if ar + bx = 1 and cs + dx =1
ars + bsx = s
ars = s(1 - bx)
acrs = cs(1-bx)
acrs = (1-dx)(1-bx)
(ac)rs + (b+d-x)x = 1
so we're done
wary mantle
you can also just do it constructively, it turns into letter salad but it works
...
Thanks!
.close
vocal sleetBOT
lyric relic
so all you need is actually Gauss's lemma
gauss have done a lot of lemmas in his life
wraith venture
Some call it Euclid's lemma too
vocal sleetBOT
Available help channel!
lime tartan
vocal sleetBOT
lime tartan
Im trying to understand how to go about this.
vocal sleetBOT
@lime tartan Has your question been resolved?
vocal sleetBOT
@lime tartan Has your question been resolved?
lime tartan
You know someone who can perhaps
lime tartan
chatgpt seems to get this stuff wrong
quiet whale
If you Will learn how to solve it I can help
I know how the thing works
But I cant solve it
woven gull
Okay I'm back, I found nothing else to do.
quiet whale
Bruh
lime tartan
Is that your uncle
woven gull
What?
woven gull
It's okay, and no, sorry, I'm not on that level of maths yet, though I am intrieged by it, in other words, I love maths.
quiet whale
I am trying but I cant understand how it works
lime tartan
this is discrete math / combinatorics if that helps
woven gull
And I'm only a Year 6 learner that does Year 7 maths ( by a small fraction).
lime tartan
i was doing algebra in 8th grade. wtf
woven gull
In the way of saying it from where I am, I'm a Year 6 pupil.
quiet whale
I am doing everything that I wnat in 8th grade
I can do algebfa
But I need to know
What is n!
woven gull
I have a strong intrest about algebra.
woven gull
But I like Pi more
lime tartan
n! = n * n-1 * n-2 * n-3 * n... * 1
quiet whale
I like n- infiniti
lime tartan
its n times every integer below n
woven gull
Ah, okay.
lime tartan
n factorial
quiet whale
I am really interest in goniometric funcitions algebra I am learning cyclometric functions I am trying to understand Quantum physics maxwells equations And More!
woven gull
In my school, I was the only one that realised my school has been doing algebra for YEARS.
lime tartan
i wrote a paper using maxwell equations
woven gull
Oooooooo~ sounds interesting.
quiet whale
Ayo young sheldon mindset
lime tartan
let me try to find it. i still need help though with my problem
woven gull
Who has the Young Sheldon mindset may I ask?
lime tartan
if you guys know someone id greatly appreciate
quiet whale
You
quiet whale
?
woven gull
not you too...
woven gull
My parents call me Young Sheldon all the time because I'm 'Too smart!'
woven gull
One of my classmates called me him aswell
quiet whale
Like I know it is a iracional number
But I think if you are good at it
It is good for you
woven gull
3.14159265358979323826460338327950288419716939937510582097494459230781640628620898628034825342117067
Is that right?
I hope so.
lime tartan
Remebering pi is useless. What does pi represent?
woven gull
Hold on, I have a book near me about this brb
quiet whale
It is 3.14159265359
lime tartan
You rounded that last digit
quiet whale
?
woven gull
Who?
lime tartan
Dominik
lime tartan
Its irrational.
lime tartan
Which means you cannot represent it in a finite sequence of digits
quiet whale
I dont know every english word
lime tartan
Its ok
quiet whale
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 ...
lime tartan
Yes it goes on forever
quiet whale
Like plank constant
woven gull
Oml
lime tartan
Yes
woven gull
My handy-dandy math book is MISSING.
quiet whale
Anthony
lime tartan
Actually no, it is not like planks constant. Plank constant is rational
woven gull
I SPENT A YEARS WORTH OF MATHS IN THERE AND IT'S VANISHED OUT OF THIN AIR...
quiet whale
BRO
woven gull
I will scream rn
quiet whale
I have my book And it is only 2 monhts old
lime tartan
At least you have the entire internet
lime tartan
No worries
quiet whale
I understand the operations but I cant do equations with it I am really sorry
Know the e And the !
lime tartan
Dont worry
lime tartan
Dont worry my quiz on this stuff is on monday so it will be too late by then
quiet whale
Show me pic
woven gull
I mean it'll do for now I guess
quiet whale
Anthony
@lime tartan
K! = 1 is it right
Anthony
I can help but I need your help too
Please
quiet whale
What are we solving for?
quiet whale
If k is arbitary n is too
lime tartan
Yes
lime tartan
No lol
quiet whale
But why is There k=1
lime tartan
What are you talking about?
lime tartan
Yes.
look up summation
This is a bit more advanced than what you know and thats ok. Dont worry
lime tartan
No
lime tartan
No
It represents the number of distinct subsets of size k of a set of size n
in other words, it is the number of ways you can choose k things from a collection of n of them
quiet whale
I am totally lost
But I know that if k is something n is something too
I think the solition might something do with the times two
lime tartan
No
quiet whale
But the set can be empty right?
quiet whale
What grade are you
lime tartan
University
quiet whale
Hmm
My brain is not braining but I Will help
Math is helping me get oit of my problems
lime tartan
its ok cause there is a lot of stuff you need to know to be able to understand this
you need to know summation factorials binomial theorem set theory combinators and number theory
quiet whale
When I am doing math I forgot that I am ridiculed
lime tartan
keep doing math math is good
quiet whale
I heard of every one of the teories
But I dont know what they are about
Oh
We need the binomial theorem to proof the equation
Am I right?
lime tartan
Yea its part it
quiet whale
It Will do something with the sets I think
We need the Pascal's triangle
But , sum of exponents is always equal to n
But in the equation There is subtracion
What Will we do?
Anthony what Will we do
lime tartan
No worries
quiet whale
N must be an sum of something
vocal sleetBOT
quiet whale
Nooo
vocal sleetBOT
Available help channel!
vast shale
what is 2+2?
vocal sleetBOT
what is 2+2?
vast shale
or 3+3?
bleak oak
what is 2+2?
depends on what group or ring ur working in
vocal sleetBOT
@vast shale Has your question been resolved?
sleek sluice
vocal sleetBOT
sleek sluice
why do they create another set C to solve this? none of any my other questions involved making a new set
or is C just an example for all A
tight rampart
You have to prove that B is a subset of the intersection of the elements of F. This is equivalent to saying that B is a subset of each element of F : C acts as an arbitrary element of F
If B is a subset of C, for C an arbitrary element of F, then B is a subset of the intersection of the elements of F
sleek sluice
okay, thank you for clarifying. i'll try to solve the question further because that confused me
.close
signal river
vocal sleetBOT
signal river
why isnt the answer for ycm 1?
lyric relic
wdym with ycm?
vocal sleetBOT
@signal river Has your question been resolved?
flat whale
why isnt the answer for ycm 1?
Why do you think it should be
vocal sleetBOT
@signal river Has your question been resolved?
signal river
Show the formula
flat whale
Your class doesn't have textbook?
signal river
not that i know of
flat whale
Then how are you learning formulas
flat whale
Like from here
signal river
signal river
do you happen to know it
flat whale
Calculus textbook should have it
signal river
what free textbooks
wow
i found it
you could have just told me i needed to add the 1/2
instead of telling me to google it
flat whale
you could have just told me i needed to add the 1/2
That's also wrong?!
flat whale
Working for one function doesn't mean it works for all
signal river
oh and squared to teh x
flat whale
Telling you the answer is against server rules
flat whale
Having a textbook means you won't get formulas wrong anymore
signal river
right
flat whale
Giving away answers usually isn't as helpful as guiding
flat whale
#book-recommendations also should have calculus book recommendations
signal river
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
stuck girder
Hi
candid mountain
hey 😄
stuck girder
Is the Stewart calculus 7th edition early transcendental book good
I am trying to pre learn calculus
So I was wondering if it is a good book
Hello?
tribal citrus
hey man i am learning calculus 3 now i have this book do know if it helps you
stuck girder
Ok
tribal citrus
hey man i am learning calculus 3 now i have this book do know if it helps you
THOMAS’
CALCULUS
blazing atlas
could someone help me with solving sin(1/x)=1/sin(x) i have no idea how i would do this
vocal sleetBOT
could someone help me with solving sin(1/x)=1/sin(x) i have no idea how i would ...
flat whale
could someone help me with solving sin(1/x)=1/sin(x) i have no idea how i would ...
is this a hw question
blazing atlas
its not
i saw it in a blackpenredpen vid and wanted to try but i didnt get very far
i got to this
e^{ix}-e^{-ix}=\left(e^{\frac{i}{x}}-e^{-\frac{i}{x}}\right)\cdot\left(e^{ix}-e^{-ix}\right)
idk how the bot works?
ebon rapids
put dollar signs on both sides
blazing atlas
$e^{ix}-e^{-ix}=\left(e^{\frac{i}{x}}-e^{-\frac{i}{x}}\right)\cdot\left(e^{ix}-e^{-ix}\right)$
twin meteorBOT
DaanHun
flat whale
,w expand (exp(i/x) - exp(-i/x)) * (exp(ix) - exp(-ix))
twin meteorBOT
flat whale
**DaanHun**
this is false
blazing atlas
hmm what
then im just trash
this should be true:
$\frac{2i}{\left(e^{ix}-e^{-ix}\right)}=\frac{\left(e^{\frac{i}{x}}-e^{-\frac{i}{x}}\right)}{2i}$
twin meteorBOT
DaanHun
flat whale
what are you doing
flat whale
yes those are right
blazing atlas
add those to each other
oblique saddle
try putting sin into exponential form
flat whale
try putting sin into exponential form
they did
oblique saddle
I remember trying this problem and I found that there were no solutions
blazing atlas
im just not sure how to get any further than this:
$\frac{2i}{\left(e^{ix}-e^{-ix}\right)}=\frac{\left(e^{\frac{i}{x}}-e^{-\frac{i}{x}}\right)}{2i}$
twin meteorBOT
DaanHun
blazing atlas
wolframalpha gives 6 solutions
flat whale
,w solve 2i / (exp(iz) - exp(-iz)) = (exp(i/z) - exp(-i/z)) / (2i)
twin meteorBOT
Requested by rie.mann
flat whale
wolframalpha gives 6 solutions
all complex
blazing atlas
right 4 answers that are like a square and some other points very far away idk how that even happens
flat whale
,w plot 1/sin(x) - sin(1/x) for -100 < x < 100
twin meteorBOT
flat whale
the difference never intersects the x axis
blazing atlas
but there are complex answers no?
flat whale
or maybe i have to increase the domain
,w expand (exp(i/z) - exp(-i/z)) * (exp(iz) - exp(-iz))
twin meteorBOT
flat whale
,w (exp(i/z) - exp(-i/z)) * (exp(iz) - exp(-iz)) = 2cos(z + 1/z) - 2cos(-z + 1/z)
twin meteorBOT
flat whale
**DaanHun**
from here you just need to solve $-4 = 2 \cos(z + 1/z) - 2\cos(z-1/z)$
,tex .sum diff trig
probably won't be helpful
blazing atlas
hmm
twin meteorBOT
riemann
blazing atlas
i can do that i think
so solving that would work?
ohh i know what i duid wrong i thjink
would this work? :
$-4=\left(e^{\frac{i}{x}}-e^{-\frac{1}{x}}\right)\cdot\left(e^{ix}-e^{-ix}\right)$
twin meteorBOT
DaanHun
blazing atlas
i meant i/x
$-4=\left(e^{\frac{i}{x}}-e^{-\frac{i}{x}}\right)\cdot\left(e^{ix}-e^{-ix}\right)$
twin meteorBOT
DaanHun
blazing atlas
i think i put down the exact same just exponential and not cos
vast shale
Is the 3 in front of the absolute value multiplying the inner contents of it?
blazing atlas
just 3 times whatever the output of that abs value is
so if x=1 the abs value of x-2 will be 1 multiplied by 3
i think
vast shale
So for the two equations it would be $3(x-2)-3$ and $-3(x-2)-3$
twin meteorBOT
Matt
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
vast shale
How am I supposed to know what the equations are
What exactly is f’’(x) on the graph there?
And how do I find f(0)
With no equation given
vast shale
How am I supposed to know that tho
pale perch
f'(x) is the gradients of f, the rate of change of f
vast shale
Yeah I understand the first derivative
pale perch
f''(x) is the gradients of f', the rate of change of f'
pale perch
because the gradient is negative yeah but its increasing
vast shale
???
pale perch
its negative (going down)
but its increasing, it eventually becomes 0 at B, then it goes up
it becomes less steep
vast shale
Then how is E negative for f’’(x)
pale perch
because the gradient is getting more negative, the graph of f is getting steeper downwards
pale perch
the gradients are negative yes, so f'(x) is negative
vast shale
Yeah
pale perch
its becoming more positive
it could be going something like
-5, -3, -2 ,-1, 0 (at B), 1, 2, 3
it was negative but it was increasing
vast shale
Ohh
pale perch
like look on f
at C f is negative but its increasing
vast shale
Yeah
pale perch
similar relationship with f' and f''
pale perch
youd be looking at the region by the y axis, we can tell f is p off the bat
i think f' being positive is also obvious
as for f'', you can see how f is getting less steep as it approaches D? That means the gradient is decreasing
pale perch
yeah
pale perch
,rcw
twin meteorBOT
pale perch
do you mean for c?
pale perch
it will be a point where f''(x)=0 yeah
vast shale
Not f’(x) = 0 right
pale perch
thats M
pale perch
maxima and minima occur when f'(x)=0
p.o.i occur when f''(x)=0 and the sign of f''(x) changes on each side
pale perch
sure, you didnt really need to do the second derivative test for finding M though,
the x most negative would be M just from the graph
but i like it
nice work
vast shale
So -5 is M and -2 is N?
pale perch
yeah, seems about right
pale perch
would you be able to get the gradient at x=3?
vast shale
I just plug it into f’(x) to get the gradient without variables right
And then use y - y1 = m(x - x1)?
pale perch
seems like a good plan to me
pale perch
looks good
vast shale
So f’(x) = 0 is for finding the x-cords of turning points?
pale perch
yeah
vast shale
And f’’(x) = 0 is for finding the x-cord of inflexion?
pale perch
p.o.i occur when f''(x)=0 and the sign of f''(x) changes on each side
dont forget the additional condition
pale perch
then its not a p.o.i
knotty kestrel
find range of : 3x^2/(x^2-25)
vocal sleetBOT
find range of : 3x^2/(x^2-25)
knotty kestrel
um x cant be 5?
frosty mural
so look at the demonimator
yes, actually x != +-5
it cannot be positive/negative 5
knotty kestrel
yea but isnt that for domain
frosty mural
oh wait mb
didnt see the question
sry
lets try again
so actually
there is a little trick
frosty mural
so basically you find the coefficient of the x^2's
knotty kestrel
3?
frosty mural
which, in this case, are 3,1
and you find the ratio of it, which should be 3
and then, you find the constant numbers
which is 0, -25
and the ratio of it is obviously 0
so, (3, 0]
knotty kestrel
uh huh
frosty mural
wait actually
[0, 3)
that might be wrong, however i use it
like the range of x^2+3/x^2+1 is (1,3]
frosty mural
well glad you got the right answer
knotty kestrel
.close
idle coyote
part c
idle coyote
the solution https://www.calcchat.com/book/Calculus-11e/10/3/91/
vocal sleetBOT
@idle coyote Has your question been resolved?
torpid kite
A cell phone manufacturer produces 145,000 phones a year. It costs $3.25 to store each phone for one year and $230 to produce each batch Find the number of batches that should be produced annually
vocal sleetBOT
A cell phone manufacturer produces 145,000 phones a year. It costs $3.25 to stor...
torpid kite
Status 1
flat whale
Is this the entire question?
torpid kite
Yea
torpid kite
So the total is 145,000
torpid kite
Its a calc problem
Anyways there’s definitely a way to find out what’s considered a batch
frosty mural
no i think there is actually formula of that
ive see similar questions before
lemme see
frosty mural
no
i think its like square root and something, there is definitely a formula for that
and im searching it in my memory
torpid kite
Same
frosty mural
and im just a poor middle school student. anyway im searching for it
torpid kite
Im like a 14 year old in college 😂
torpid kite
3.25(145,000)/2(230)
Im thinking since its
3.25 store for one year
And the total is 145,000 for the whole year
torpid kite
Yea im not sure about that one
Isn’t that to calculate the flow rate?
- Q represents the flow rate (in units of volume per unit of time, e.g., liters per second).
- D is the coefficient of discharge, which accounts for the efficiency of the orifice.
- S is the cross-sectional area of the orifice.
- H is the head, which is typically the height of the fluid above the orifice.
<@&286206848099549185>
frosty mural
D: Annual Quantity Demanded
Q: Volume per Order
S: Ordering Cost (Fixed Cost)
C: Unit Cost (Variable Cost)
H: Holding Cost (Variable Cost)
i: Carrying Cost (Interest Rate)
From web
im not actually sure
torpid kite
Yea i dont think thats the right formula
Cuz thats for
Liken
Ima kms
This problem seems so simple 😭
Idk why my brains struggling
A cell phone manufacturer produces 145,000 phones a year. It costs $3.25 to store each phone for one year and $230 to produce each batch Find the number of batches that should be produced annually
frosty mural
wait i think I found the right formula
torpid kite
Hm
frosty mural
N = EOQ/D
N should be stand for replenishment cycle
so, find EOQ, which is sqrt(2 * 145000 * 230/3.25), according to the formula EOQ = sqrt(2DS/H)
in this case D means demand rate, which is 145000 phones/yrs
S is 230dollars per batch
s means setup cost
frosty mural
and H(holding cost) is $3.25 phone/yrs
so we actually have D,S,H
and plug them in we have sqrt(20523076.9)
which is 4530.3
and its a rational number
and use the formula, N=D/EOQ, which is N=145000/4530.3
maybe that is the right answer, idk
torpid kite
Says its wrong rip😭
frosty mural
bruh I have no idea
torpid kite
Lmao yea no worries
frosty mural
those problems are tough to me
torpid kite
Definitely had me believing tho😂
torpid kite
Says the answer should be under triple digits
frosty mural
triple digits???
torpid kite
Under so double digits
😭
Tbh if u read the question it actually makes sense it wouldn’t be in the thousands 😭😭
Idkk ima kns
Kms
My last hope
Is
@zinc quail
torpid kite
Yk him?
Seems like he’s famous
<@&286206848099549185> someone help me before i end it all
frosty mural
yeah kinds
kinda
alight i gotta sleep, and I hope someone can answer ur question
cya
its 1:05 AM
vocal sleetBOT
@torpid kite Has your question been resolved?
torpid kite
<@&286206848099549185>
torpid kite
Idk thats the whole question
Someone got the right answer
But idk how they did it
They used the formula km/2(a)
torpid kite
Yea but a girl
Somehow did it
But she had to go
3.25(145,000)/2(230)
Idk what she used
native pagoda
I would ask your professor to clarify the question.
native pagoda
Tell them it’s not possible to solve without more information. For example
- What is a batch?
A batch has no meaning without numbers or substance
A batch could be mean 2 bats
10 cookies
Who knows
I know I am not giving any answers. But that problem is unsolvable without assumption.
torpid kite
Your saying the exact thing i told my teacher
Just said re read the question
About to kms
lyric night
did this jessica girl get her answer checked by the prof
native pagoda
Probably not considering this problem appears unsolvable
native pagoda
Well she must have assumed or used other information.
torpid kite
There’s something obvious that im not seeing
lyric night
There’s something obvious that im not seeing
i dont there is
native pagoda
Well my perfect record is about to take a hit
I would recommend talking to your professor again. I apologize for inconclusive solutions but I don’t see any way this is possible.
lyric night
yeah pretty much
i mean i guess theres a possibility the prof specified something beforehand
?
native pagoda
I am headed to bed. I hope you find a solution!
torpid kite
well i need any type of attempt
One of you guys makeup something
Thats gets me the answer 32
And hopefully he wont look at my work too carefully
.close
empty fern
how to solve this question?
vocal sleetBOT
how to solve this question?
pallid zenith
what is nice here is that youve been given two different x values where $f(x_1)+3 = f(x_2) + 3$
twin meteorBOT
jan Niku
twin meteorBOT
pallid zenith
well, actually, i guess even this isnt really necessary, but i think this makes it easier to visualize 
given 3 points you should be able to determine the quadratic anyways
actually, yea, using the thing i was talking about is fastest
say this was the unknown function
if you were told that f(-2)=f(2) = 0
and then some point precisely between these two
no its easiest to solve for the full quadratic
sorry im babbling, are you there @empty fern
empty fern
yeah
pallid zenith
so
you can write your function out
ax^2+bx+c
three unknowns
youre given 3 points
so for example, the middle one
it tells you that a(24)^2+b(24)+c+3=8
you can create 3 equations here
your points happen to give you the vertex though
empty fern
24,8 is vertex?
pallid zenith
well, 24,5
your table gives you f(x)+3
the thing is your general vertex form is what
empty fern
ahh
pallid zenith
$y=a(x-h)^2+k$
twin meteorBOT
jan Niku
twin meteorBOT
jan Niku
pallid zenith
so youre awful close on the y-intercept
but you need a
maybe you can get it from one of the other points 
f(28)+3=-72
@empty fern have i trailed off too much 
pallid zenith
hmm its not long i guess
pallid zenith
**jan Niku**
this is step 1
step 2 is solving for a
but thats fine, you can do it with any of the other pieces of information
honest heath
vocal sleetBOT
honest heath
is phi not almost trivially injective?
since for two matrices to be equal, each of their entries have to be equal, and if each of their entries are equal then the complex number that mapped to those entries under phi have to be the same?
paper depot
is phi not almost trivially injective?
it is not hard to show that it is injective.
honest heath
it is not hard to show that it is injective.
just assume phi(z1)=phi(z2) where z1=a+bi and z2=c+di
then (a,b; -b,a)=(c,d; -d,c), but matrices are only equal if each of their entries are equal, so a=c and b=d and so a+bi=c+di then z1=z2 ? or am i missing anything?
paper depot
no, you're not.
vocal sleetBOT
lapis marten
okay awesome, thanks for always helping!
An isomorphism is more than an injection though
honest heath
An isomorphism is more than an injection though
yes i know! thank you for making sure though!
lapis marten
okay
honest heath
I was just doing the bijectivity first and i was like, this seems way too easy lol
vocal sleetBOT
Available help channel!
wooden sphinx
When you have a tangent plane to a 2 variable function
vocal sleetBOT
When you have a tangent plane to a 2 variable function
wooden sphinx
And it’s equation is
P = F(a,b) + Fx(a,b)(x-a) + Fy(a,b)(y-b)
Is that just explaining how z changes in terms of x and y
Together
mental falcon
yes, z = F(x, y)
wooden sphinx
In a very local area of course
Near the point (a,b)
I’m only asking
Because apparently this is how you can understand differentials
Right?
Because if you wanna do df
You just say it’s equal to
mental falcon
yeah, its analagous to the tangent line for a 1 variable function approximating the function locally
wooden sphinx
(PDF/Dx)d/dx + (PDF/Dy)d/dx
And essentially df is just the change in height for a 2 variable function
mental falcon
yeah, just like if you zoom in really far into a 1 variable function, it starts to "look like a straight line" more and more, if you zoom in to a 2 variable graph it starts to look more and more flat
and the tangent plane becomes a good approximation
wooden sphinx
And when you say that df = Fx(DeltaX) + Fy(deltaY)
Are you basically finding
The change in Z in the x change
And the change in Z with the Y change
And adding together
Which then tells you how much Y chnaged overall?
wooden sphinx
Ah got it
I’m trying to visual this
And basically if I were to just compartmentalization
This
mental falcon
its a little funny because youre kind of looking at the change in z at point A by combining the changes at points B and C right?
wooden sphinx
Should I just see the height change in the direction
mental falcon
and if you travel diagonally instead of in straight lines in x / y directions, z can change differently
mental falcon
BUT the idea works of looking at as a linear combination IF you're talking about the limits as dx and dy -> 0
wooden sphinx
I consider how Z increases/decrease as you change X
So either z goes up or down
And then
Once I moved that point around
I then move it in the y direction
And see how much additional height has been gained
wooden sphinx
Appreciate it so much
mental falcon
the math kinda all magically works out to be like this when taking the limits as dx, dy -> 0 its quite beautiful
wooden sphinx
It really is
vocal sleetBOT
@wooden sphinx Has your question been resolved?
vast shale
Can someone explain me why the period Fourier series are represented with functions on a circle.
vocal sleetBOT
Can someone explain me why the period Fourier series are represented with functi...
@vast shale Has your question been resolved?
vast shale
Can someone explain me why the period Fourier series are represented with functi...
<@&286206848099549185>
vocal sleetBOT
@vast shale Has your question been resolved?
umbral snow
vocal sleetBOT
umbral snow
hello
river minnow
,w solve y = 300 + 0.9(y - 1000) + 200 + 2000
twin meteorBOT
river minnow
river minnow
Yeah how did you get 2410 there
river minnow
0.9 * 1000 is 900 so you had 300 - 900 + 200 + 2000
river minnow
i calculated 0.9 * (-1000) is -90 ?
No
umbral snow
oh wtf
river minnow
It's -900
vocal sleetBOT
radiant plinth
,rotate
twin meteorBOT
proven garden
(x-a)^2+(y-b)^2=r^2 have center of (a,b) and radius r
obtuse scroll
The center is just 0,6
vocal sleetBOT
@tepid fossil Has your question been resolved?
tepid fossil
(x-a)^2+(y-b)^2=r^2 have center of (a,b) and radius r
i’m asking how they find the centre @proven garden
do they subtract the radius from something
i remember doing something like that
im still quite confused @obtuse scroll
obtuse scroll
Hi stig
Did you see the 2 messages I sent
Just use that, that's pretty standardized
Gimme a sec let me log on my computer
oh god
We're given $x^2+y^2-12y-13=0$
twin meteorBOT
diaas_(yt)
obtuse scroll
Convert this to $(x-a)^2+(y-b)^2=r^2$
twin meteorBOT
diaas_(yt)
obtuse scroll
We get $(x)^2+(y-6)^2=7^2$
twin meteorBOT
diaas_(yt)
obtuse scroll
**diaas\_(yt)**
Alternatively you can just take the original equation and compare it with this
tepid fossil
can you teach me how to convert
also thank you for taking the time to help me
do we just square everything
obtuse scroll
can you teach me how to convert
Meh, In my board I only use the form in the first image
So I have no idea how to convert from form A to form B
form A being $x^2+y^2+2gx+2fy+c=0$
tepid fossil
like see how it’s -6 in the equation but in reality it’s 6 as the coordinate
twin meteorBOT
diaas_(yt)
obtuse scroll
No issues
obtuse scroll
when it looks cool
BTw
You want a trick for circles?
Trust me, JEE makes me study way more than a 11th grader should.
Bro you might wanna close the channel
tepid fossil
You want a trick for circles?
sure
obtuse scroll
So here's the thing
obtuse scroll
**diaas\_(yt)**
refer to this
If a circle is given to you in this form, the center is -g,-f