we expressed b and c in terms of a
#help-10
tacit scarab
spark wasp
ok
so what does that even tell us
c = -a b =-2a
av1 -2av2 - av3 = 0 oooh
but how do we now from this if its linearly dependent
spark wasp
bruh what
its dependent if a b and c
are 0
we dont know if it is
so how can u tell that
tacit scarab
it's INdependent if a b c are 0
tacit scarab
..
we're not solving for a
we are proving the solution exist
the solution doesn't matter that much
for example let a = 1
then you get one solution
a = 2 is another solution
etc
spark wasp
this is killing my braincells
💀
my prof is solving for c1 c2 c3
to figure out if its depedent or not
you see?
timid silo
scalar triple product != 0
tacit scarab
the general solution is -2t,0,t
-2,0,1 is just one of the solution
again what's important is that a solution exist
spark wasp
-2,0,1 is just one of the solution
ik but i didnt get
where she got that from
like how can you tell if a solution exist
if you dont know the number
thats what i mean
tacit scarab
you don't know the value of x and y though
spark wasp
we need to know if the values are all 0 or if 1 of them is not 0
to determing if dependent
or independent
tacit scarab
bro
spark wasp
correct?
tacit scarab
they are not mutually exclusive
every system have the trivial solution
of all 0
s
we want to find if there are non trivial ones
btw I gtg
obtuse pebbleBOT
@spark wasp Has your question been resolved?
errant crane
How do I do this one?
obtuse pebbleBOT
How do I do this one?
obtuse pebbleBOT
@errant crane Has your question been resolved?
tawny birch
How do I do this one?
loss in ke = gain in potential energy
final locust
whats 2 + 2 ?
sterile trench
22
timid silo
4
sterile trench
The formula would be K.E= kq1q2/r, take r on one side and put the values
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
late chasm
is the first one a bijection? I am confused . since all of the negative integers would map to -2 which isnt in the codomain
obtuse pebbleBOT
is the first one a bijection? I am confused . since all of the negative intege...
latent walrus
even if you ignore the issue with the -2
it doesnt map to any positive even integers so its not surjective anyway
If it only maps to -2 for negative integers then its also not injective
timid silo
shouldnt here be a x<0 ?
latent walrus
it says x>=0 so the -2 is basically reserved for (else do this)
which would only be x<0
late chasm
oh yeah thank you
what about the third one
From what i figured out it maps between 0 and 1 only
@latent walrus I need your guidance
is it also not a bijection?
latent walrus
it doesnt map to any negatives or even 0 so it cant be a bijection
late chasm
as
nvm
real numbers
but somehow the question is asking
which one of these is not a bijection
latent walrus
the first one isnt even a valid function so it may not count that
late chasm
makes sense
thank you AZ empty set!
is there a way i could give you some sort of points?
also how do i close thsi channel
late chasm
.close
spring elk
.reopen
half acorn
How do i calculate and get the 0.12% between this two prices ? 🤔 most easy way
tacit scarab
(changed_price-original_price)/original_price
half acorn
when i do * 100 giving me then 0.1126307320997586
meaning it's exactly 0.112 % right ?
warm shaleBOT
half acorn
Thx ❤️
obtuse pebbleBOT
Available help channel!
timber pine
how would i do b?
obtuse pebbleBOT
how would i do b?
timber pine
,rotate
warm shaleBOT
echo knoll
i gotchu. lemme see what I can do for u.
timber pine
alright thanks!
timber pine
2 squares?
warm shaleBOT
Krispeh
timber pine
so what's the issue?
i got to 4integrate(sec theta tan^2 theta)
no idea how to continue
timber pine
**Krispeh**
isnt dx 2secutanu?
obtuse pebbleBOT
@timber pine Has your question been resolved?
obtuse pebbleBOT
@timber pine Has your question been resolved?
obtuse pebbleBOT
@timber pine Has your question been resolved?
obtuse pebbleBOT
@timber pine Has your question been resolved?
covert forge
Hey guys can anyone help me please?
-
How do I work out on a calculator? what is 2/3 thirds of [X meaning the total number].
-
how do I work out what is X% of amount.
-
how to I Calculate my currency to another at the BUY rate. and then how do I Calculate the buy / SELL. of the Foreign currency where I to SELL it. If you can give me an Example for each with the icons on a calculator. Thank you very much.
obtuse pebbleBOT
Hey guys can anyone help me please?
1. How do I work out on a calculator? what...
latent walrus
if you want 2/3 of x then do 2/3 multiplied by x
if you want x% then multiply by x/100
for 3 id assume its just the above two but youd have to see the exchange rates and calculate it
covert forge
if you want 2/3 of x then do 2/3 multiplied by x
if you want x% then multiply by...
cheers how do I do the 2/3 on the calculator
latent walrus
i see
- 2/3 of x will be (2÷3)*x
covert forge
i see
1) 2/3 of x will be (2÷3)*x
(2÷3)*x whats the *
latent walrus
the *?
latent walrus
thats multiplication, its the x above the -
covert forge
thats multiplication, its the x above the -
so times
latent walrus
yeah
latent walrus
it can always be used as a replacement for it yes
/ generally means fraction, but you can consider it ÷
they do the same thing
latent walrus
is / ÷ on a calculator on all sums.
what do you mean on all sums?
obtuse pebbleBOT
Available help channel!
eternal garden
Trying to write a sci-fi novel, and I'm having trouble with some math. Consider a galaxy 100,000 light-years in diameter. How fast would one need to go in order to traverse the entire length in one week? (This would likely be the max speed of the warp in my book)
obtuse pebbleBOT
Trying to write a sci-fi novel, and I'm having trouble with some math. Consider ...
tardy epoch
,w light year
warm shaleBOT
warm shaleBOT
obtuse pebbleBOT
@eternal garden Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
full crown
Yo can someone help rq
obtuse pebbleBOT
Yo can someone help rq
obtuse pebbleBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
Show your work, and if possible, explain where you are stuck.
tight patio
@full crown
full crown
idk where to begin
tight patio
aight
which part do u need help in?
Im pretty sure u just estimate this stuff but idk if thr is a formula for these
full crown
how do i find out how many people are between 120-150
tight patio
how do i find out how many people are between 120-150
its given in the question
240 ^^
full crown
no like
for part a
how many had a systolic blood pressure reading 120 and 150, including 120 but not 15
150
tight patio
how many had a systolic blood pressure reading 120 and 150, including 120 but no...
u have to find that
obtuse pebbleBOT
@full crown Has your question been resolved?
boreal otter
can anyone see what i did wrong?
obtuse pebbleBOT
can anyone see what i did wrong?
boreal otter
what
second like as in when i waa cancelling the 2x?
line*
here is the original question
obsidian estuary
Your variable should be canceled out on the third line
So it should be 2/1
On the second step of the third line
latent walrus
yeah, you cancelled $\Delta x$ but then its still there and the 2 is missing
warm shaleBOT
AℤØ
latent walrus
should have just been lim(2)=2
boreal otter
ooooooooh
i just cancelled it wrong
thank you
i’m not sure where to start
delta x towards zero ***
tardy epoch
Multiply the top and bottom by the conjugate
timid silo
What am I misunderstanding about Vectors? Ive watched about an hour if video and tried looking in my text book but I just cant seem to make any sense of what's the right way to do it
obtuse pebbleBOT
What am I misunderstanding about Vectors? Ive watched about an hour if video and...
timid silo
The question just wants the magnitude and direction of the resultant
What are the bearings relative to?
I see it as go 5 units on a 100° bearing like a compass and then go 6 units on a 60° bearing from that point
Last picture is horrible, I realised how wrong it is, but the first two I just cant understand whether its right or not
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
meager gale
ok
meager gale
ok
so
this is the hw
and
specificallty
i wanna understand how to do
9ab
i dont get it
because
ripe venture
Don’t dox urself homie
meager gale
idk
ripe venture
no but might not be impossible to figure out a location
meager gale
oh thats fine
ripe venture
Which one?
meager gale
start with the summation definition of multiplication
meager gale
wdym
serene fossil
do you go to stanford?
meager gale
its not stanford.edu
its ulo.stanford.edu
its like a program for highschoolers
for UG math
serene fossil
oh i see
meager gale
ye
meager gale
costed way too much for me to fail 😭
i think the midterm will have proofs so
i gotta get good at these
ima latex now.
$AB = BA$ \
$A^n = 0$\
$B^n = 0$\
For some $n \in \mathbb N$
warm shaleBOT
amukh1 | JS,Axler Fanboy
serene fossil
thats slightly incorrect
meager gale
as a first pass
meager gale
thats slightly incorrect
?
meager gale
yea ik
serene fossil
and you shouldnt assuem theya re
serene fossil
yeah but why bother tbh
meager gale
cuz it may be simpler?
warm shaleBOT
amukh1 | JS,Axler Fanboy
meager gale
😭
serene fossil
so you assume A^n=0 and B^n=0 and AB=BA
meager gale
yup
serene fossil
sure
serene fossil
what do you mean?
meager gale
is (AB)^n not B^nA^n
serene fossil
not in general
meager gale
then what is it
serene fossil
its actually just $ABABABAB\cdot AB$ n times
warm shaleBOT
llspacebarll
meager gale
right..
meager gale
aw
serene fossil
we have commutativity
serene fossil
yes
meager gale
which is 0 . 0
serene fossil
yeah
meager gale
= 0
serene fossil
so QED
serene fossil
now generalize tho
meager gale
um
oh yeah thats fine
A^n is 0
0 * B^k
is gonna be 0
and same the other way
A^n * 0
= 0
right
serene fossil
well yeah but you should write a formal proof i guess
serene fossil
i also think its worth noting that (AB)^n=A^nB^n
might not be taken for granted
meaning you could try to prove it as well
using induction is best
fleet quartz
I need to prove whether the set of all fractions p(x)/q(x), where p(x) and q(x) are polynomials with coefficients of complex numbers. (and q(x) is not the zero-polynomial q(x)=0 for all x). Is or isn't a field. I'm stuck deciphering the language of the question and I don't quite understand how to begin writing all the axioms. So far, I have been able to determine that q(x) cannot have a degree equal to 1.
obtuse pebbleBOT
I need to prove whether the set of all fractions p(x)/q(x), where p(x) and q(x) ...
polar fossil
why not?
fleet quartz
Because then q(x) is guarenteed to have an x value that causes it to be equal to 0.
warped scroll
so you need to prove the field axioms?
fleet quartz
Yes, I do.
polar fossil
Because then q(x) is guarenteed to have an x value that causes it to be equal t...
that's true for all polynomials
warped scroll
do you know the field axioms
polar fossil
what q can't be is identically zero
warped scroll
that's true for all polynomials
yeah
fleet quartz
Right! Oh my goodness, I forgot the fundamental theorem of algebra. I forgot that complex x values exist and can make q 0.
warped scroll
wow
fleet quartz
I feel like that I might have an idea on how to start.
warped scroll
give it a try
fleet quartz
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fathom flicker
obtuse pebbleBOT
fathom flicker
I was hoping someone could check my work for this
Since $2|xy|\leq (x^2+y^2)$ for all $x,y$ then we should have that
warm shaleBOT
Austin
fathom flicker
$$\frac{x^2y}{x^2+y^2}\leq \frac{x^2y}{2|xy|}=\frac{|x|^{2}y}{2|x||y|}=\frac{|x|y}{2|y|}$$
warm shaleBOT
Austin
fathom flicker
if $y<0$ then $y=-|y|$ and $y\geq 0$ then $y=|y|$ so either way we have that
warm shaleBOT
Austin
fathom flicker
$$\frac{x^2y}{x^2+y^2}\leq \frac{|x|}{2}$$ or $$\frac{x^2y}{x^2+y^2}\leq \frac{-|x|}{2}$$
warm shaleBOT
Austin
fathom flicker
which when we then take the limit as (x,y)->(0,0) then these go to 0 so so does our original function
so lim (x,y)->(0,0) f(x,y) =f(0,0) so it is cont at (0,0)
gilded needle
my only issue with this is that when you put |xy| in the denominator, you have issues if x=0 or y=0
what if instead of applying the hint to the denominator, you applied it to the numerator?
fathom flicker
what if instead of applying the hint to the denominator, you applied it to the n...
how can we rewrite x^2y into a form involving a factor of |xy| though
if we write |xy|x=x^2*y this is false
gilded needle
$|x^2y| = |xy||x|$
warm shaleBOT
Bungo
fathom flicker
$|x^2y| = |xy||x|$
then we immediately have |f(x,y)|<= |x|/2
taking limit gives us it goes to 0
gilded needle
yep
gilded needle
your way works too but you'd have to have special cases if x=0 or y=0
gilded needle
what the
obtuse pebbleBOT
Yes<@779131727338930196>
@astral aurora Has your question been resolved?
Available help channel!
low path
obtuse pebbleBOT
warped scroll
isn't it speeding up when the acceleration is positive
tacit scarab
yes s is displacement, v is velocity and a is acceleration
obtuse pebbleBOT
@low path Has your question been resolved?
sage dagger
how do I evaluate this?
obtuse pebbleBOT
how do I evaluate this?
tacit scarab
what's e^(-infinity)?
sage dagger
0?
formal inlet
confused on how this doesnt count as orthogonal
obtuse pebbleBOT
confused on how this doesnt count as orthogonal
formal inlet
any vector times an orthogonal vector of the original vector is 0
so taking one of the parallel vectors and finding values that would make the dot product 0 should work
civic zealot
that's not totally true.
you're vector isn't orthogonal to the other parallel line, for example
formal inlet
ok
with the info I currently have aka 2 points and 2 parallel vectors of a plan, how would I find an orthogonal vector
.close
timid silo
Ihello, I am learning the limits
To solve this I have to apply Identity lt x-> 0 Sinx/x = 1
I want to make x-> 0 as ax -> 0. can I equate x -> 0 as we do in equations
x-> 0
ax -> a*0
ax -> 0
So i can apply the identity
And what it is called I want to learn more about it
obtuse pebbleBOT
Ihello, I am learning the limits
To solve this I have to apply Identity lt x-> 0...
@timid silo Has your question been resolved?
weary heart
Solve the equation for :
x^n=n!
obtuse pebbleBOT
Solve the equation for :
x^n=n!
royal basin
!status
obtuse pebbleBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
also did you mean x^n = n! with a lowercase x?
weary heart
```
What step are you on?
1. I don't know where to begin
2. I have begun but got...
I think the answer is 1 and I want correction
weary heart
also did you mean x^n = n! with a lowercase x?
What?
old isle
the more i learn about math the more complicated it gets
royal basin
I think the answer is 1 and I want correction
the answer is not x = 1
old isle
ann, how many languages do you know
old isle
just curious cuz i feel like i remember you knowing polish and i saw someone mention you knew hindi
royal basin
perhaps we should move to #discussion if you want to talk about this further?
old isle
sure
weary heart
there is no (lowercase) x in
X^n = n!
What's the difference between X and x
royal basin
X is a capital letter, x is a lowercase letter
weary heart
How will it make difference in solving this equation
royal basin
solving X^n = n! (with big X) for x (small x) makes no sense
high lily
if the question was genuinely solve:
$$X^n = n!$$
for $x$,
its nonsense because there is no $x$ to solve for
warm shaleBOT
ℝam()n()v
weary heart
Solve the equation for x :
x^n=n!
old isle
yall are missing the invisible x
weary heart
Sorry I didn't notice
old isle
$x*0 + X^n = n!$, duh
royal basin
how'd you get x=1
warm shaleBOT
accialto
royal basin
note: "how did you get ___" does NOT mean " ___ is wrong, redo your work without showing it to us"
weary heart
I didn't do anything I thought of a stupid thing
Never mind that
How to even solve this?
@royal basin
royal basin
i mean raising both sides to the power of 1/n should do the trick, no?
warm shaleBOT
Hamdy Hisham
royal basin
$x = (n!)^{1/n}$
warm shaleBOT
Ann
weary heart
What's next
weary heart
The original one was $(x)^{2021-n}=(2021-n)!$
warm shaleBOT
Hamdy Hisham
weary heart
@royal basin
old isle
feels like some kind of 2021 olympiad problem
royal basin
like it was not just an equation
there had to have been something else written along with it
weary heart
Wait I'll give you what I've done
royal basin
i do not understand this, i'm afraid.
don't give me what you've done
give me a clear and understandable problem statement first
weary heart
Ah I wrote it wrong
It's $y=x^{2021}$ then ...... =2021!
a.$y^{(2019)}$
b.$y^{(2020)}$
c.$y^{(2021)}$
d.$y^{(2022)}$
warm shaleBOT
Hamdy Hisham
weary heart
@royal basin
royal basin
this is literally the same as before
oh wait
those things are derivatives are they
weary heart
Yup
royal basin
so you're asked which order derivative of x^2021 results in 2021!
weary heart
Yup
royal basin
this doesn't need any of that equation-solving bullshit
how many times do you need to differentiate x^n to make a constant
royal basin
yes
weary heart
I think I'm stupid
royal basin
and what's the n'th derivative of x^n?
weary heart
nPn?
royal basin
well maybe you could tell me what nPk is or admit you don't know
weary heart
I don't know
royal basin
if you start writing numbers from n and go down by 1 every time,
and you write out n numbers
what'll be the last number you write down?
obtuse pebbleBOT
@weary heart Has your question been resolved?
weary heart
what'll be the last number you write down?
Aha n!??
royal basin
no, the last number won't be n!.
weary heart
no, the last number won't be n!.
It'll be 1 so nPn=n!
royal basin
yes
royal basin
geogebra?
royal basin
dunno
soft pond
Hey guys
I need help to calculate and understand this
obtuse pebbleBOT
Hey guys
I need help to calculate and understand this
tacit scarab
find the endpoints and equations of the two lines
soft pond
yea, i know, but how do I find it?
cyan lark
Help each time this type of q come up I don't understand it
cyan lark
Oh did not saw that thanks
soft pond
what's the end points of the first line?
at (1,2), the line on the left is the first line
tacit scarab
that's the right end point
does it contain 1?
I mean does the line contain that end point?
soft pond
yes?
obtuse pebbleBOT
@soft pond Has your question been resolved?
soft pond
<@&286206848099549185>
heavy zephyr
is there any x you can't plug in here?
soft pond
i dont know
heavy zephyr
well, do you kind of know how the function looks like?
soft pond
no i do not
heavy zephyr
for these kind of questions you only have to think about whether or not there is a mathematical rule you're going against when plugging in certain values
rules like "can't divide by zero"
neat blaze
(a+b)^3
soft pond
for these kind of questions you only have to think about whether or not there is...
I am a freshman high schooler. I am trying to learn this stuff.
heavy zephyr
Is there a value for x you can't plug in here? Meaning: If you plug in 5 you will get an answer with h(5)=(5-3)^2=4. Is there an x so when you plug it in, you won't get an h(x) value
soft pond
I still don't know how to find the answer
heavy zephyr
Hmm okay. The answer is, the domain of the function is every x in the real numbers.
There is no number we can't plug in here so that h(x) is not defined. Why is this even important?
There are functions where we have fractions and x is in the denominator. So there x couldn't be 0 and therefore the domain would be all x in the reals but without x being 0
soft pond
Thanks
.close
devout shell
HELLO
inland thicket
⚔️ Guys
sage geode
Yes to both questions
inland thicket
woah
yo im confuse @sage geode just 1 more question
i know u not economic profesional but i also wonder why p*f(L,K) is also not that rule
sage geode
Is p a constant?
sage geode
Yes
sage geode
Even if you were to apply the product rule to p * f(L, K)
You would end up with the same thing
inland thicket
you expert
yo
yo wait can you just help with 1 more question
with your iq5000
sage geode
Sure
inland thicket
1min
this is perfect competition and diference is
there is no complex derivation there
but your probably cant use iq5000 for this
but i try wrap my head around this
first example i gave
second picture was first example
THIS FUNCTION IS MONPSONY (SECOND PICTURE)
first picture is without complex derivation
shiiii
so market supply in second picture ( Monopsony) is rising because it increases with wage and labour increases (each another worker hired, monopsony has to pay him more, but also pays every other worker more
that why w(L)??
but in first picture w is constant cos its perfect competition (firm cant affect wage)
so thats why no complex derivation in perfect competition
am i right?! 😮
sage geode
I don't know econ 
inland thicket
yo but
like does it make sense
from iq5000 perspective
its just lines and graph and math like
i gave like econ premise
but in math like does it connect
i make econ bold
just 2 rules
sage geode
I suppose it connects
inland thicket
woah
im enlightedn now
i used to look at those function and think damn
and thought i gotta memorise
in my brains
but now i knwo the truth
.close
frail depot
Try and use Newton-Raphson Method to compute all the zeros of f1(x) = 0.
frail depot
What would the steps be to compute all the zeros?
atomic hornet
have you studied the newton-raphson method yet?
royal basin
what is f_1
atomic hornet
also that yea
frail depot
have you studied the newton-raphson method yet?
Yes..^^
I know how to do it
I have also implemented it in python
atomic hornet
but what is f1(x)
polar fossil
I'd agree with that
atomic hornet
definetly has one
royal basin
you can even solve the eq explicitly without the use of any special methods
frail depot
I did
royal basin
which ig means you have a way to doublecheck yourself
frail depot
I got x=0
But, exercise is to use the method
So
But so would the idea be to find two values one negative and one positive
f(x)
and then you know by IVT that inbetween this there must be a value for f(x)=0
atomic hornet
oh sure then
frail depot
You find a negative f(x) and a positive f(x) and then you know by the intermediate value theorem that inbetween these two there must exists x such that f(x)=0
Because the assignments says "compute all the zeros of"
atomic hornet
but as you said,theres only one
frail depot
Yes, but how would I know that using the newtons raphson?
Or is that just not possible
Or not using that
but like without solving the equation
atomic hornet
not possible really
frail depot
f(x)=0
atomic hornet
its just a lot easier to do algebraicaly
frail depot
Ye, I did solve f(x)=0
i just don't feel like thats what the assignment is telling me to do
atomic hornet
thats true
frail depot
Try and use Newton-Raphson solver to compute all the zeros
atomic hornet
is that a given solution?
frail depot
But that does not furfill that tho
It's the question
2) Try and use Newton-Raphson solver to compute all the zeros of f(x)=0
Anyway, perhaps it's fine what i've done
thanks for the help
.close
graceful marten
Howdy
amber nest
!show
obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
graceful marten
I dont know where to start
I know they are parallel lines.
I know the formula (x-x)^2 + (y-y)^2 Root all this stuff
Is the shortest distance between two points
Its also not the Green Line (Difference in Y axis)
polar fossil
yeah you need the perpendicular line
proper verge
the shortest distance would be the perpendicular
there is also a formula for it
which always works
graceful marten
Alright?
I dont think ive done that formula before
and chat gpt isnt helping, usless as always 0/10 i rate out of the 5 times i used it
proper verge
try |C1–C2|/√(A^2 + B^2 )
graceful marten
what would A and B be?
proper verge
both equations can be written as ax + by + c = 0 and ax + by + c1 = 0
proper verge
and chat gpt isnt helping, usless as always 0/10 i rate out of the 5 times i ...
Also yes dont use chatgpt for maths questions, its gonna blurt out garbage and apologise when you tell it that its wrong every time
edgy cedar
hello
frank monolith
what's confusing you?
tight patio
!status
obtuse pebbleBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
Because I’m division when u divide anything by a fraction
U make the think ur dividing by its own reciprocal
And the signs becomes multiplication
edgy cedar
uhm
thin star
edgy cedar
can u explain simpler pls
if i divide fraction the second fraction go upside down and it become multiply
cooks told me that before
i remember now
thin star
$\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b} * \frac{d}{c}$
warm shaleBOT
TooManyCooks
graceful marten
obtuse pebbleBOT
@edgy cedar Has your question been resolved?
gilded ferry
Hi
obtuse pebbleBOT
obtuse pebbleBOT
Hi
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
Available help channel!
edgy cargo
for this I got 8y+6 for the width but im not sure what to do next to find the area
obtuse pebbleBOT
for this I got 8y+6 for the width but im not sure what to do next to find the ar...
edgy cargo
do i just do (8y+6)*2y
obtuse pebbleBOT
@edgy cargo Has your question been resolved?
edgy cargo
ty
runic void
For any integer n>2, Show that there are at least two elements in U(n) that satisfy x^2=1.
obtuse pebbleBOT
For any integer n>2, Show that there are at least two elements in U(n) that sati...
runic void
U(n) is the set of all least residues modulo n which are relatively prime to n
1 is element of U as 1 is always relatively prime to n
wide rose
and -1?
runic void
Different context
that’s one of my confusion too, if think they are taking solutions modulo m i guess
definitely -1 not in U(n), -1 cannot be a least residue aka remainder when divided by m.
<@&286206848099549185>
Question 20.
obtuse pebbleBOT
@runic void Has your question been resolved?
royal basin
definitely -1 not in U(n), -1 cannot be a least residue aka remainder when divid...
what number in U(n) is congruent to -1 mod n?
also what's m
thin oxide
Alpha is contained in irrational n.group. just how?
obtuse pebbleBOT
Alpha is contained in irrational n.group. just how?
royal basin
it doesn't matter that alpha is irrational
royal basin
Alpha is contained in irrational n.group. just how?
c'est vrai pour tout alpha réel
ça matière pas qu'il est irrationnel
pour le premier pas au moins
thin oxide
Can you speak English?
thin oxide
What I don't get is how `Alpha^(n+1)+Alpha^n = Alp^(n) * (Alp+1)
thin oxide
Alpha is contained in irrational n.group. just how?
This ^
alpine raven
alpha +1 = alpha²
royal basin
$\alpha^{n+1} + \alpha^n = \alpha^n \cdot \alpha + \alpha^n \cdot 1$
warm shaleBOT
Ann
alpine raven
si tu te souviens du polynome qui donne le nombre d'or
x²-x-1
x² = x+1
vrai pour alpha
warm shaleBOT
Ann
royal basin
agree or disagree?
thin oxide
agree.
thin oxide
Thanks but without this info, it is impossible?
royal basin
i mean...
sure?
like alpha was INTRODUCED as one of the roots of that equation
so it's a strange question to ask
thin oxide
Well, this will take me to another topic rather math that if you want to know.
which is I'm going to learn math using French in Uni while I'm not that cool with the language.
Anyway, thank you.
.close
copper citrus
hello guys! I think that the correct answer from the book to the challenge question 20 was totally unclear for me (didn't even visualize or get the first requirement that scalars should be positive)
obtuse pebbleBOT
hello guys! I think that the correct answer from the book to the challenge quest...
@copper citrus Has your question been resolved?
copper citrus
<@&286206848099549185>
obtuse pebbleBOT
@copper citrus Has your question been resolved?
tacit sorrel
anyone can explain me the sum of sequences formula ? the 1-q^n+1 / 1-q ?
tacit sorrel
on geometrical sequences
warm shaleBOT
A Lonely Bean
sage geode
Then $qS = q + q^2 + q^3 + \dots + q^{n+1}$, right?
warm shaleBOT
A Lonely Bean
sage geode
@fickle flame If you have any questions about what I am writing/saying, just ask
fickle flame
yes, until now i didn't study that, so i'm a bit confiosing
sage geode
You will understand the proof once I am finished, I hope, but for now I shall wait for the helpee's response
tacit sorrel
for what u said yes
but then saying that my sequence start at u1 = 1
does it change something to the formula
sage geode
Once you know the formula for 1 + q + q^2 + ... + q^n, you can just multiple it by u1 and you will get the formula for any geometric sequence
But let's first be done with simplifying S
Alright, so, you may notice that these two sums (S and qS) share a lot of terms in common
tacit sorrel
yes
sage geode
In fact, every term is shared except for 1 and q^{n+1}
What would happen if we were to subtract S from qS?
tacit sorrel
just q ?
tacit sorrel
yes
sage geode
No no q gets cancelled out as well
sage geode
**A Lonely Bean**
It's present in this sum
sage geode
**A Lonely Bean**
And that sum too
sage geode
Alright, so, you may notice that these two sums (S and qS) share a lot of terms ...
I mentioned this fact because all of those shared terms will cancel out when we subtract the sums
tacit sorrel
I mentioned this fact because all of those shared terms will cancel out when we ...
how tho i m interested
sage geode
So q, q^2, q^3 and so on up until q^n disappears when we take qS - S
sage geode
how tho i m interested
\begin{align*}
S &= 1 + q + q^2 + q^3 + \dots + q^n \
qS &= \phantom{1 + } q + q^2 + q^3 + \dots + q^n + q^{n+1} \
S - qS &= 1 + \cancel q - \cancel q + \cancel{q^2} - \cancel{q^2} + \cancel{q^3} - \cancel{q^3} + \dots + \cancel {q^n} - \cancel {q^n} - q^{n+1}
\end{align*}
Ugh wait
warm shaleBOT
A Lonely Bean
tacit sorrel
okay i see and how does it give the 1-q^n+1/1-q formula tho
sage geode
So the last equation is just the same as S(1 - q) = 1 - q^{n+1}
And you just divide both sides by (1 - q)
sage geode
1 - 2 is -1
tacit sorrel
knowing first term is =1
sage geode
So 1 - 2^64, when divided by -1, becomes 1/(-1) - 2^64/(-1)
Which is -1 + 2^64
Or just 2^64 - 1
sage geode
Because the formula gives us $\frac{1-2^{64}}{1-2}$, everything up until this makes sense, right?
warm shaleBOT
A Lonely Bean
tacit sorrel
the why we do this no but ig it s just applying formula
like i could get there too by just following the formula
but then the after for results i don t get it
do u think i should understand the formula?
like the why
sage geode
Well I have shown you the proof of the formula already
tacit sorrel
**A Lonely Bean**
can you explain why there is 1 in the beginning of S
sage geode
That's just how I defined S to be
tacit sorrel
so wait instead of putting the 1 at the beginning u just put it in qS ?
to explain it s q^next one always?
i m sorry i lack a lot in some stuffs in maths i m trying to figure out
so i can understand the exercice better
and why it gives 2^64 -1
sage geode
No I defined S to be 1 + q + q^2 + ... + q^n because any geometric sum can be evaluated by knowing the formula for 1 + q + q^2 + ... + q^n
sage geode
Let's say we have some geometric sequence with the first term and the common ratio given as $u_1$ and $q$ respectively
warm shaleBOT
A Lonely Bean
sage geode
The $k$th term of the sequence can be calculated using $u_k = u_1q^{k-1}$, right?
warm shaleBOT
A Lonely Bean
sage geode
Ah, so you start with 0
tacit sorrel
it s another system that might be the reason as well
sage geode
Alright one moment I'll fix that
tacit sorrel
in my today exercice it starts from u1
but i would like to understand the difference
of what it does to the formula
tacit sorrel
oh
sage geode
The end result is the same no matter what you call your variables
tacit sorrel
and no matter from when does it start?
the sequence
no matter like first term is ?
sage geode
Yeah, as long as you have done everything else correctly, there should be no problem
So u0 or u1, which one shall we start with?
tacit sorrel
So u0 or u1, which one shall we start with?
u1
sage geode
Let's say we are given some geometric sequence starting with $u_0$ and the common ratio as $q$. The $k$th term of the sequence can be aclculated using $u_k = u_0q^k$, right?
warm shaleBOT
A Lonely Bean
tacit sorrel
yes
sage geode
So if we were to add up some amount of first terms in the sequence, we would have [ u_0 + u_1 + u_2 + u_3 + \dots + u_n ] For some natural number $n$. According to the formula for the $k$th term, we are able to rewrite that as [ u_0 + u_0q + u_0q^2 + u_0q^3 + \dots + u_0q^n ] Can you see anything that can be factored out?
warm shaleBOT
A Lonely Bean
tacit sorrel
u0?
sage geode
Yes, when we factor it out, we get $u_0(1 + q + q^2 + q^3 + \dots + q^n)$
warm shaleBOT
A Lonely Bean
sage geode
And that sum in the parenthesis is some geometric sequence starting with 1 as its first term
This is why you can calculate any geometric sum by knowing how to calculate geometric sums whose first term is 1
Hence I defined S to be 1 + q + ... + q^n
tacit sorrel
oh my god