Well do what south said
#help-4
hazy pivot
snow thunder
do you know the product rule
spare salmon
Prompt: Find the derivative of e^2
Why is the derivative of e^2 0?
(I missed like 2 months of calculus, so I am really behind)
rocky lotusBOT
Result:
7.3890560989306
shut mirage
another way you can think of it is that the first derivative of a function is the slope of the function at a point
but if a function is the same number everywhere, then it's a horizontal line, which has 0 slope
spare salmon
another way you can think of it is that the first derivative of a function is th...
Yeah, I remember. It’s the same reason why derivative of pi is zero right? It is a number.
shut mirage
yup
spare salmon
I feel so dumb now. lol but anyways, Thank you for explaining!
shut mirage
don't feel that, it's a part of learning
spare salmon
I love when I forget how to math.
spare salmon
don't feel that, it's a part of learning
I know. I just feel like I should have already known that.
shut mirage
it happens mate
spare salmon
Something tells me my teacher reminded me of that rule a thousand times.
vale dockBOT
vale dockBOT
Available help channel!
candid ledge
sig digs but scientific notation how would i know how many numbers so put
candid ledge
like 42 515
stark wedge
!xy
vale dockBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
stark wedge
if the number was just given to you directly like this (and DIDN'T come from a calculation) then don't round unless asked to. so 42515 would be 4.2515 * 10^4
if it DID come from a calculation, then show us how the original data for it were given and what the calculation was
candid ledge
it says to round to the correct number of sig digs, hold on
stark wedge
show the full thing please
candid ledge
if it was from a calculation, for example 2 numbers with decimals are given, the number that has the least ammount of decimals is the same ammount of decimals to round to?
stark wedge
,rccw
rocky lotusBOT
stark wedge
if it was from a calculation, for example 2 numbers with decimals are given, the...
yes, you see how many sigfigs each one is given with and then use the LOWER number of sigfigs for the answer
candid ledge
yes, you see how many sigfigs each one is given with and then use the LOWER numb...
ok
butfor 4.25 how do they know to stop at 4.25 and not continue with 4.251 or so
stark wedge
nope it should be 4.2515
<@&268886789983436800> advertising
& this channel is occupied anyway
ancient prism
<@&268886789983436800> advertising
How is it adverysing when I can’t make money.
stark wedge
ask that to the mods not me.
ancient prism
ask that to the mods not me.
It’s non profit I’m
Just trying to help
I ain’t finna make money
stark wedge
dude you fucking spammed it across every channel, knock it off
ancient prism
dude you fucking spammed it across every channel, knock it off
Damn bro ma fault didn’t know it was that deep
stark wedge
was it written as 3.780000
stark wedge
Damn bro ma fault didn’t know it was that deep
don't call me bro
ancient prism
don't call me bro
Ma fault ma fault
vocal hatch
this problem is so hard to solve , did i do this right ? + i dont really familar with chain rule on this one
vocal hatch
oh ok let me try again
copper stump
(also this is quotient rule, not chain rule)
vocal hatch
(also this is quotient rule, not chain rule)
yea, my professor do chain rule for every derivate
hey for the -5x^-1/2
do i put x^1/2 in the bottom or just the 1/2
copper stump
wdym?
its from the numerator, keep it there
or you can divide both the numerator and denominator with it, to make it disappear from the top
up to you
copper stump
then it would become positive exponent there
but that affects the -5x^(5/2) too
so your last step, as it appears rn is wrong
robust lynx
bro
copper stump
this would be right
vale dockBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
copper stump
if you wanna move it to the denominator, then the numerator's x^(5/2) would become x^3
vocal hatch
if you wanna move it to the denominator, then the numerator's x^(5/2) would beco...
😓 why would it become x^3 .....
is it factor
copper stump
well, the numerator has more than a one term
so, you cant ignore the rest of the numerator
copper stump
😓 why would it become x^3 .....
well, after the most horrid paint session ever, I present to you
copper stump
well, you want sqrt x in the denominator
copper stump
so you can multiply and divide the answer in line 2 by sqrt x
vocal hatch
so you can multiply and divide the answer in line 2 by sqrt x
i have a question why would you multiple sqrt x?
copper stump
coz the numerator has the term 1/(sqrt x) that you wish to eliminate
and ofc sqrt x * 1/(sqrt x) = 1 removes it
robust lynx
just slide anyone who can solve computing maths
sand panther
vale dockBOT
copper stump
where are you stuck?
sand panther
On 3 and 4
copper stump
you might wanna use the fact that TEAM is a rectangle
sand panther
Yea
Im confused on how i can like get the angle for like Arc TE
Since the angle could be M or A
shut mirage
aren't they subtended by the same arc?
copper stump
measure of an arc is the angle at the center
sand panther
aren't they subtended by the same arc?
I'm sorry I don't know what subtended mean
sand panther
measure of an arc is the angle at the center
Our lesson is inscribed angle so we can't use the central angle
shut mirage
Our lesson is inscribed angle so we can't use the central angle
the measure of an arc is its central angle
sand panther
the measure of an arc *is* its central angle
I meant like we need to solve it without the involvement of the central angle?
shut mirage
(or rather, is the same as its central angle)
copper stump
Our lesson is inscribed angle so we can't use the central angle
inscribed angle theorem is just that the central angle is 2x the angle formed by the chords
wdym you cant use central angles? thats like half the statement
shut mirage
ok OP, how was the inscribed angle theorem stated to you?
sand panther
ok OP, how was the inscribed angle theorem stated to you?
Uh
Inscribed angle is one half the measure of intercepted arc
And vice versa
copper stump
yea, and the measure of the arc is just the central angle
its the same thing, just two names depending on context
sand panther
Still I don't know if we can use the central angle in getting the measurement
copper stump
well, thats fine. It still should stop you from 3 & 4
you already know TME and TAE are the same coz they are on the same arc
copper stump
Since the angle could be M or A
i dont get whats the confusion here
both the angles measure half the intercepted arc
sand panther
both the angles measure half the intercepted arc
So A and M have the same measurement?
sand panther
Aren't they angles?
copper stump
TME and TAE are angles
copper stump
angle is defined by the two arms TA and AE and the vertex A. So you call the angle TAE, and the arc TE
sand panther
Uh what
copper stump
bro you got 5 things to find
sand panther
bro you got 5 things to find
We only need 3 and 4
copper stump
so is this 3?
sand panther
Yes
copper stump
then its called angle MEA
not A anf M
use the names properly
wrong names indicate different things
shut mirage
maybe you can just draw on the diagram and take a picture of which angles you meant
sand panther
maybe you can just draw on the diagram and take a picture of which angles you me...
We can't
shut mirage
?
sand panther
I can edit tho
shut mirage
whatever method you can use then
copper stump
thats not an angle tho??
I'll show you an example
the entity drawn in blue is the arc AE (as asked in part c of the question). It corresponds to the angle ABE as I drew in red
junior ore
what is that semi circle over these letters?
shut mirage
what is that semi circle over these letters?
arc
shut mirage
just so we're on the same page, which subquestion are you on rn, and what info do you have?
sand panther
3
copper stump
my guy, the pic you have posted is of question 5, which has parts a, b, c, d, e
please pick one of these
sand panther
C
copper stump
then yes, you need to find not use the angle EBA or ABE
sand panther
They are divided right
copper stump
wdym divided?
sand panther
Since TEM is 58 degree
sand panther
wdym divided?
There's like a cut in their angle kind of
sand panther
There's a theorem that state opposite angle are supplementary?
sand panther
TEM + AEM = 90 (coz all angles of rectangle are 90deg)
Sort of
sand panther
There's a theorem that state opposite angle are supplementary?
This is true right
copper stump
just show them in the figure pls?
coz based on what you said as explanation, it seems wrong
the angles are not supplementary
supplementary means the sum is 180
the angles TEM and AEM are complementary (their sum is 90)
sand panther
Wait for my pic
Imma explain it
So essentially like this
It says TEM=58 right
copper stump
yes...
sand panther
If MTE is 90° then ANGLE TEM-MTE=TME
That means ANGLE TME IS 32 THEN
We could also say the same for ANGLE EAM but we can't since 58 +58 aint 90°
So flipped and boom
So now
There's a formula that state Measure of inscribed angle is 1/2 of intercepted arc
Theorem igs
copper stump
We could also say the same for ANGLE EAM but we can't since 58 +58 aint 90°
that seems overly laboured and not very mathematical argument
sand panther
Since we already know that TME is 32 we can safely say that 64÷2 did equal it
sand panther
that seems overly laboured and not very mathematical argument
I suck at writing in math terms
I dont even know the diff between arc chord or others
shut mirage
copper stump
arc is a part of the circle
sand panther
Oh wow
Angle TAE is 32 degree?
YES
SO THAT MEANS THAT TME AND TAE IS BOTH 32 DEGREE
Both are also facing the arc with measured 64
sand panther
There's a formula that state Measure of inscribed angle is 1/2 of intercepted ar...
From this theorem
copper stump
yep, correct till here
sand panther
I can safely conclude that the theorem is right then?
copper stump
well, theorem is supposed to be right all the time
sand panther
Wait
copper stump
if it isnt, then whats the point
shut mirage
conjectures?
shut mirage
conjectures are not 50/50. conjectures are unproven theories (could be wrong)
sand panther
conjectures are not 50/50. conjectures are unproven theories (could be wrong)
So 50/50 then since it could be wrong or right
shut mirage
many conjectures are actually highly stacked one way (towards or against being right), but that's a story for another time
copper stump
conjectures are true for all the observed cases, but if a its wrong is not yet found
sand panther
many conjectures are actually highly stacked one way (towards or against being r...
This is already a story lmfao
I really suck at math
copper stump
once you find a counterexample, you dont consider it conjecture anymore
shut mirage
let's not say that
sand panther
Anyway
copper stump
once you find a counterexample, you dont consider it conjecture anymore
it becomes proved false
sand panther
Does TE and MA have the same measure?
Is this correct?
sand panther
it becomes proved false
Until proven false then
copper stump
Is this correct?
yes
copper stump
you need to state why tho
sand panther
Wdym
sand panther
I don't think degree are needed for arcs right
copper stump
a sufficient reason would be that the arcs TE and MA are equal in measure coz the chords TE and MA, present in the same circle, form the opposite side of a rectangle and hence are equal in length
copper stump
I don't think degree are needed for arcs right
if you write a value, then its needed
sand panther
if you write a value, then its needed
Wait fr?
copper stump
you dont need to mention arc TE degrees
sand panther
I thought only angles neede arc
sand panther
I thought only angles neede arc
Degree*
copper stump
degree is a unit of measure, so as long as you mention the quantity, you need the unit
sand panther
So no degree
copper stump
arc TE is fine on its own, but you need to say arc TE is 64 degree
sand panther
mTE=64°
vale dockBOT
vale dockBOT
Available help channel!
vale dockBOT
shut mirage
are you to solve for x?
crimson turret
Yea, I want to find x
pure mirage
WA doesn't seem to give an exact form
Which might be a pretty good indicator that there is none
crimson turret
i think this was the exact thing
this is what my friend said it is but just so i am sure i will send the original
marsh forge
i think this was the exact thing
this and the expression you put earlier are different, btw
pure mirage
i think this was the exact thing
Right, that's better
crimson turret
this and the expression you put earlier are different, btw
yeah i am literally oblivious to this algebra math, my friend said they are the same I am sorry
vale dockBOT
crimson turret
didnt know it worked like that
shut mirage
it's ok, just take another channel
pure mirage
It's fine, forget about this channel and open a new one where you send the original right away
It might even be better like this
The first expression you gave is not equivalent
vale dockBOT
Available help channel!
spring estuary
Hello can you help me to do the b) : traduction :
1)P is a 3rd degree function on R : …..
b)Show that P can be written … with a, b and c to define
spring estuary
Thanks for help
shut mirage
,rccw
rocky lotusBOT
shut mirage
they are telling you that (x - 3) is a factor of this cubic
or rather, I think they want you to test that
then factor the cubic
spring estuary
Ok so there is already the answer, thanks you but then how I do the sign table ?
spring estuary
Yeah
shut mirage
one important rule about signs
a polynomial can only change signs when it crosses its roots
so first find all three roots of this cubic
spring estuary
Ok but I’m learning 2nd degree so I think I must write the function in 2nd degree
shut mirage
part b already has 2nd degree, if that's what you mean, but P(x) is referring to the original 3rd degree polynomial
spring estuary
Ok thanks I’ll try later thanks you it’s and have a good lunch
shut mirage
you too monsieur/madame
spring estuary
.close
vale dockBOT
vale dockBOT
Available help channel!
atomic pewter
vale dockBOT
marble arch
They have said that Market equilibrium occurs when Inverse supply = Inverse Demand
And you've been given the equation for both
Ps = 8q + 8
Pd = q^2 - 14q + 48
So Ps = Pd
You'll get a quadratic after equating them
atomic pewter
so i do both equations equal each other and then simplify it to one side and solve the quadratic that you get?
marble arch
Yes
Also be careful of the (0<=q<=6) they've written, you'll get two values of q, but you have to select only the one that follows this condition
marble arch
One second
atomic pewter
alright
marble arch
Yes it's correct
atomic pewter
so wat do i do after
marble arch
Not sure dude, the economics wording is something I'm not familiar with
Maybe they just need the value of Market equilibrium (just plug q = 2 in either of them and that'll give you that)
atomic pewter
i cant find the answers unfortunatly
let me see if i can use ai to solve it
and see if thats all i need
i think all u need to do after
is plug it back in
the equation
for q=2
so 8(2)+8
vale dockBOT
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Available help channel!
willow atlas
How do i solve for I? (Sorry if i make grammatical mistake)
vale dockBOT
How do i solve for I? (Sorry if i make grammatical mistake)
@willow atlas Has your question been resolved?
vale dockBOT
@willow atlas Has your question been resolved?
golden atlas
How do i solve for I? (Sorry if i make grammatical mistake)
What is wroten on the 3th line
Is it x² f'=f²
willow atlas
Yes
Yes
Im gonna have dinner and do housework wont reply for the next 3 hours sorry guys
sturdy sigil
I have this function that represents the average solar efficiency per year, where f(x) u(x) are functions.
l represents a variable that can go from -90 to 90, and i want to figure out what l will make the efficiency be the higest.
I know that I can just change l manually to find the highest point, but that's not very "mathematical"... What could I do to figure out which l returns the highest number in this function?
I believe that i need to make a function where x-axis is the l value and y-axis is the efficiency value and then I do the derivative to find the highest point
sturdy sigil
So currently, this formula gives me a value for each value for l, but I want to make it a curve
vale dockBOT
@sturdy sigil Has your question been resolved?
vale dockBOT
vale dockBOT
Available help channel!
willow atlas
Guys how do i solve for I (asking again because timed out)
vale dockBOT
Guys how do i solve for I (asking again because timed out)
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
2
I tried integrating f prime by integrating f squared over x squared but it gives stupid thing
verbal badger
Provide the original question and explain your work
willow atlas
Provide the original question and explain your work
The original question is written in language not in english sorry
vale dockBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
hazy pivot
Which language is it in
willow atlas
Vietnamese
hazy pivot
There's a possibility someone here knows it
shut mirage
it's fine. post it anyway
willow atlas
And it was a question from a book that i now temporary dont have access to, so ill have to try and contact the book owner
willow atlas
Guys how do i solve for I (asking again because timed out)
Its not possible to solve if i wrote it like this?
Here it is in vietnamese
A rough translation would be "let there be a function f(x) not equal to zero, continuous on [1, 2] and sastisfy f(1) = 1/3; x^2 × f'(x) = f^2(x) with all x on [1, 2]. Calculate the definite integral I = that thing"
vale dockBOT
@willow atlas Has your question been resolved?
vale dockBOT
@willow atlas Has your question been resolved?
distant galleon
Here it is in vietnamese
isn't this a standard diff eq 
$\frac{f'(x)}{f(x)^2}=\frac{1}{x^2}$
rocky lotusBOT
Civil Service Pigeon
distant galleon
now integrate both sides with respect to $x$
rocky lotusBOT
Civil Service Pigeon
distant galleon
||and use f(1) = 1/3 to compute the constant of integration||
jovial edge
isn't this a standard diff eq <:hmmcat:831508801646755850>
He hasn't been taught DE yet I believe
willow atlas
whats DE?
distant galleon
He hasn't been taught DE yet I believe
tbf you don't need to explicitly say DE
willow atlas
oh differential equations
willow atlas
Civil Service Pigeon
yeah i know how to rewrite this so that it shows df(x) over dx and calculate the integral
if thats what you mean
jovial edge
if thats what you mean
Not really..
willow atlas
yeah i thought that too
jovial edge
Học phương trình vi phân chx
willow atlas
Học phương trình vi phân chx
?
jovial edge
DE là phương trình vi phân đs
willow atlas
tưởng nó là kiểu viết thêm dy/dx thật
vale dockBOT
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Available help channel!
haughty jackal
Best way to integrate this? I've tried using substitution, but that's getting messy(?)
(I haven't formally done integration in Math; this popped up in a Physics problem I was solving.)
ashen prawn
Best way to integrate this? I've tried using substitution, but that's getting me...
trigonometric substitutions work beautifully here
R=r*tan(θ) or smth else too
ashen prawn
yes these methods work elegantly tbh
but @haughty jackal change the lower and upper limits carefully
dont forget them
haughty jackal
but <@884338559018999808> change the lower and upper limits carefully
$$\frac{1}{R^2}\left[\frac{r}{\sqrt{R^2+r^2}}\right]_{-\frac{L}{2}-x}^{\frac{L}{2}-x}$$
rocky lotusBOT
Will
haughty jackal
Assuming I did everything correctly
vale dockBOT
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Available help channel!
zenith lantern
Hi I need to determine if this series is convergent or divergent. I tried the divergence test (if the limit as n -> inf of the general term is not 0, the series diverges) and I got the limit is 0. I'm not sure what piece of information I'm missing to determine convergence/divergence
neat locust
Hi I need to determine if this series is convergent or divergent. I tried the di...
If you think the series diverges, show that your sum is greater than a divergent sum
If you think the series converges, show that your sum is less than a sum that converges
vale dockBOT
@zenith lantern Has your question been resolved?
zenith lantern
I'm trying to think of a bigger sum that converges
light saddle
do you know the limit comparison test?
zenith lantern
No
light saddle
what are you allowed to use?
zenith lantern
Anything I guess
light saddle
I'm trying to think of a bigger sum that converges
this will work actually
think of an inequality involving sin
zenith lantern
sin x <= 1
light saddle
that won't be enough though
light saddle
recall what the graph of sin looks like
zenith lantern
Waves
light saddle
another hint would be that pi/n goes to 0
so you need an inequality involving sin(x) for x close to 0
(but it will hold even when x is not close to 0)
zenith lantern
Why do we need an inequality involving sin x for x close to 0, how does that look like
light saddle
what does the graph of sin look like near x=0?
zenith lantern
Not sure
neat locust
Take a look
zenith lantern
y = x
neat locust
,w plot y=sin x, y=x
rocky lotusBOT
light saddle
can you think of an inequality involving sin x for x>0, then for x <0 now?
zenith lantern
Why x < 0
light saddle
did you do it for x > 0?
zenith lantern
No
light saddle
you should try it first
zenith lantern
Okay
you want an inequality involving sin x for positive x
But that's kind of vague
sin x < x
light saddle
yeah
light saddle
ok now you can show that your series is absolutely convergent
zenith lantern
(sin(pi/n))/n < pi/n^2 ?
light saddle
yup
zenith lantern
and pi / n^2 bc n is at a power higher than 1
do we ignore the numerator in the p series?
light saddle
you can think of it as factoring the numerator across the entire sum
since it's a constant
native kayak
can someone explain to me why cosh and sinh are (e^x+e^-x)/2 and (e^x-e^-x)/2 respectively
wraith heart
definition
native kayak
what
wraith heart
cosh(x) and sinh(x) are defined to be the formulas you posted
native kayak
I was more so asking how those definitions came to be
but maybe thats a lot now that I think about it
wraith heart
that's a historical question not a math question
wraith heart
what is "the identity"
wraith heart
can someone explain to me why cosh and sinh are (e^x+e^-x)/2 and (e^x-e^-x)/2 re...
these are just definitions
native kayak
so proving the definition then?
wraith heart
definitions do not require proof. they are given as assumed to be true
native kayak
assumed to be true
wraith heart
like e is defined to be the limit of (1+1/n)^n as n goes to infinity
wraith heart
you gotta start somewhere with math
native kayak
is there no mathematical way to prove it?
vague turtle
quick question when you don with laurina problem can you help mine ?
wraith heart
proving definitions is not a math thing
definitions are given
there's nothing to prove
light saddle
quick question when you don with laurina problem can you help mine ?
claim a channel
native kayak
definitions are given
given by who though
light saddle
vague turtle
i did
native kayak
thats what I don't get
you mean someone came along
and said this is how it is
it works
wraith heart
by people smarter than us
native kayak
and thats it?
wraith heart
if you don't want to accept definitions, ignore it
native kayak
smarter than us
you mean to tell me someone came to the conclusion that cosh = (e^x+e^-x)/2
because they felt like it?
with absolutely no reasoning
or proof
wraith heart
i didn't say there was no reasoning
definitions do not require proof, no
theorems/lemmas/propositions require proofs
fleet burrow
you mean to tell me someone came to the conclusion that cosh = (e^x+e^-x)/2
it isnt a conclusion, it's more like a premise
wraith heart
but those also have some starting point involving definitions
wraith heart
you mean to tell me someone came to the conclusion that cosh = (e^x+e^-x)/2
again, that's a historical question, not a math question
native kayak
isn't it a bit odd that there's not proof for it?
It may be true but knowing why it's true also matters does it not
wraith heart
definitions do not require proof, no
.
wraith heart
you're looking for a historical answer, not a math answer
native kayak
im looking for the mathematical proof as to why that definition works
light saddle
what "works"
gleaming kindle
in logic, a definition is a statement taken to be true without proof. what you may be seeking instead is the MOTIVATION of a definition
native kayak
right
guys I get that
i know proof is not needed
in the slightest
I'm saying is it not odd no one has proved it just because?
light saddle
guys I get that
sure?
gleaming kindle
a popular motivation of the limit definition of e is continuously compounded interest
fleet burrow
i know proof is not needed
A proof of a definition isnt possible
native kayak
why not
you mean to tell me there
is no mathematical way to prove the definition
proof may not be needed
but not needed doesnt equal not possible
light saddle
it's not that it's not needed, it just doesn't make any sense to prove it
fleet burrow
is no mathematical way to prove the definition
Suppose you defined x to be 2: "Let x = 2". How would you go about proving x = 2?
you cant
native kayak
isnt it more like x = 2 now prove how x = 3-1?
e existed before the definition did it not
oops
wraith heart
e existed before the definition did it not
again, this is a historical quesiton, not a math one
gleaming kindle
what does "existence before definition" mean?
native kayak
the defintion of cosh could not have come about without e being defined as what it is yes?
light saddle
yes
native kayak
so the definiton of cosh is using some sort of building block
light saddle
just like buttons were invented before keyboards
native kayak
a mathematical building block
im sure you can prove that a bunch of buttons = a keyboard can you not?
gleaming kindle
are you asking about e or cosh?
native kayak
if e is a button and cosh is the keyboard
like\
i dont see how its not possible to mathematically prove the definition
sure it doesnt ened one
need
but its possible is it not
light saddle
im sure you can prove that a bunch of buttons = a keyboard can you not?
you could argue that no, because in fact, a bunch of buttons IS a keyboard
if they are arranged correctly
gleaming kindle
there are multiple equivalent definitions of cosh
do you know what equivalent means in that sense?
vale dockBOT
@native kayak Has your question been resolved?
tiny torrent
alpha isnt necessarily a lower bound of x_n right
vale dockBOT
alpha isnt necessarily a lower bound of x_n right
tiny torrent
from n = 1 to infinity
keen tundra
yeah it wouldn't be a lower nor upper bound
keen tundra
notice its a partial limit
tiny torrent
whats a partial limit
keen tundra
how did you define limsup
tiny torrent
how did you define limsup
keen tundra
I see
tiny torrent
what ive done so far
is created a sequence $r_n = sup{x_k \mid k \geq n}$ which is decreasing and converges to $\alpha$
keen tundra
inf?
keen tundra
this is sequence is decreasing
tiny torrent
yeah mb
rocky lotusBOT
Branshi
tiny torrent
ok so I need to change my proof since I was using lim inf
right now I get $x_n \leq \alpha + \varepsilon$ from the fact $r_n$ converges
rocky lotusBOT
Branshi
tiny torrent
so now I need to figure out how to get the other half
tiny torrent
Branshi
I dont think this would imply that the interval (a - e, a + e) contains infintiely many points @keen tundra
my internet is dying my messages arent being sent
ok
keen tundra
rn converges to alpha and is decreasing
so for large enough n sup{x_k | k >= n} is at most alpha + epsilon
tiny torrent
rn converges to alpha and is decreasing
I dont understand
we need to show x_n is contained in the interval right
right
which implies x_n is at most alpha + epsilon
tiny torrent
ok that makes sense
keen tundra
this tells you there eventually x_m >= sup{x_k | k >= n} - epsilon >= alpha - epsilon
keen tundra
notice here n is not fixed and m is variable
I will be going to sleep
bye @tiny torrent
tiny torrent
ok ty for help
vale dockBOT
@tiny torrent Has your question been resolved?
tender saffron
whats 37 x 12 im asking here because my calculator is blocked
hardy olive
how do I simplify radicals with exponents fractions and also negative fractions
wraith heart
,tex .exp rules
rocky lotusBOT
riemann
hardy olive
like how do I use these ?
unborn sable
got a specific example?
hardy olive
like sqrt72y^3
unborn sable
$\sqrt{72y^3}$?
rocky lotusBOT
AℤØ
final adder
could you latex it?
hardy olive
yes like that
unborn sable
does 72y^3 have any square factors?
final adder
would you know how to start with this?
unborn sable
what would the factor be?
hardy olive
36 x 2
unborn sable
nice
36 * 2y^3
any other square factors i could split?
hardy olive
3 x 24
hardy olive
why is that ?
unborn sable
because 36 is the largest square factor of 72
unborn sable
theres another square factor in 72y^3
hardy olive
how are you finding these perfect sqaured
Im looking at perfect squared chart and Im not seeing the same thing
unborn sable
what are the factors of y^3?
hardy olive
I have no clue
unborn sable
y^3 = y * y^2
hardy olive
what is that ?
unborn sable
$y^3 = y \cdot y^2$
rocky lotusBOT
AℤØ
unborn sable
its just splitting y^3
hardy olive
oh
unborn sable
y^2 is a square number
hardy olive
how ??
unborn sable
well, y^3 is y*y*y is it not?
hardy olive
oh wait so if you are doing something like y^2 you are doing it twice just to split it ? correct ?
unborn sable
thats just the definition of an exponent
unborn sable
2^4 = 2 * 2 * 2 * 2 etc
hardy olive
oh ok cool I get it
unborn sable
so we now have sqrt[(36y^2) * (2y)]
where 36y^2 is our largest square factor of the argument
hardy olive
ok ok
hardy olive
Im gonna say no beacuse I dont see a proptery that 36y^2 can plugged in to
unborn sable
ah mb, are you aware that square roots are exponents of 1/2?
eg $$\sqrt{x}=x^{\frac{1}{2}}$$
rocky lotusBOT
AℤØ
hardy olive
I did not know that
unborn sable
so exponent laws apply
ill just give you the property then
$$\sqrt{ab}=\sqrt{a}\cdot \sqrt{b}$$
is what we will be making use of
hardy olive
ok
rocky lotusBOT
AℤØ
unborn sable
any thoughts on how we'll apply it?
hardy olive
Absolutly not my only guess is to put repalce ab with 36*2
unborn sable
so we now have sqrt[(36y^2) * (2y)]
think about how I framed the argument of the sqrt
hardy olive
36 = sqrt2 * y3 ?
unborn sable
nono
remember we split the inside into the square factor and the non square factor
now we want to split the sqrt into two
keep in mind the reason we are doing this is because the square factor will simplify from a square root, so we want it to have its own
hardy olive
nice
36 * 2y^3
any other square factors i could split?
look man to be honest Im lost at how this turn in to 36 * 2y^3
and everything else after
when you say split the sqrt
im lost
lyric sundial
AℤØ
Try to identify the a and b in your case, so that you can use this to split in a smart way
hardy olive
so
unborn sable
look man to be honest Im lost at how this turn in to 36 * 2y^3
and everything ...
you noted that the largest square factor of 72 was 36
so 36 *2
and the y^3 was already there, so 36 * 2y^3
hardy olive
A 36y^2 B 2y
hardy olive
sqrt72y^3 = sqrt36y^2 x 2y ?
unborn sable
yeah, now split the root
hardy olive
sqrt36y^2 x sqrt2y
unborn sable
also try not to use x for multiplication, and use brackets 
hardy olive
oh ok
hardy olive
I have no clue what to do after
unborn sable
36y^2 is a perfect square right?
hardy olive
yea
unborn sable
then what would its square root be
hardy olive
so it would be sqrt36 * sqrt y^2 = 6y ?
unborn sable
you didnt really need to split it again, but youre correct si
so whats the end result?
hardy olive
6y sqrt 2y
unborn sable
and we're done
hardy olive
👍
midnight pier
guys i can’t find the pattern for #1, #3, #7, and #8
vale dockBOT
guys i can’t find the pattern for #1, #3, #7, and #8
midnight pier
it wont let me send the photo lol
so ill just type it
- 18, 46, 94, 63, 52, 61, _
- 1, 4, 3, 16, 5, 36, 7, _
- 2, 3, 6, 1, 8, 6, 8, 4, 8, 4, 8, 3, 2, 3, 2, 3, _
shut mirage
is this some logic math question?
and you should have photo permissions in this channel
midnight pier
is this some logic math question?
yea
fickle lake
1) 18, 46, 94, 63, 52, 61, _
for #1, reverse the digits, they're squares
midnight pier
nvm
shut mirage
oh there we go
midnight pier
for #1, reverse the digits, they're squares
omg tysm
fickle lake
3) 1, 4, 3, 16, 5, 36, 7, _
for #3, there're odd num in odd position, and squares in even
shut mirage
I was about to prompt OP to realize that relationship herself
midnight pier
for #3, there're odd num in odd position, and squares in even
wdym
OH
so 3 is 64
fickle lake
so 3 is 64
yep
woeful trench
for #3, there're odd num in odd position, and squares in even
Please try not to give out too much of the solutions to questions where you can 
we want to guide people to find the solutions themselves as much as possible 
fickle lake
Please try not to give out too much of the solutions to questions where you can ...
oh
alright
didnt know
im new here
midnight pier
sorry didn’t mean to get you in trouble ㅠㅠ
woeful trench
didnt know
Don't worry, you're all good (and not in trouble at all, just letting you know!)
fickle lake
but not #7
same bro
fickle lake
3x6 = 1, 8
6x1 = 6
1x8 = 8
fickle lake
6x1 = 6
1x8 = 8
6x8 = 4, 8
midnight pier
4x8=32
shut mirage
I mean you've basically figured out the pattern
shut mirage
try reconstructing the sequence yourself
midnight pier
2x36, 3x6=1,8, 6x1=6, 8x1=8, 6x8=48,
so you multiply the numbers one before the next
so the next one would be 2,3
or just 2
shut mirage
more appropriately stated, you take each pair of digits starting from the 1st and 2nd, moving one digit to the right each time, multiply them, and add the individual digits of the product to the sequence
also, there's only one blank
midnight pier
oh
shut mirage
this sequence is part of the OEIS for some reason too
midnight pier
whaaa
shut mirage
ah you can ignore that. it's just an online listing of various integer sequences
shut mirage
anything else?
fickle lake
#8 please if you have time
u said u figured it out
shut mirage
i think i get #8
thought you had it? what was your intuition about it?
midnight pier
😭
shut mirage
Where do the X, Y, and Z go?
-> in elementary algebra books
it's more towards pattern finding
which is quite a good skill to have come number theory
midnight pier
the x goes before the B
shut mirage
in a help channel, what makes you think I took that as a joke first lol
shut mirage
the x goes before the B
reason being?
midnight pier
reason being?
so every 8 letters you skip 5 letters in the alphabet
shut mirage
ahhh ok I see the pattern now
shut mirage
this has nothing to do with skipping letters
midnight pier
oh
shut mirage
that's the first hint I will give you
shut mirage
instead, I will clue you in to how the letters are written. compare the letters in the first line and the second.
midnight pier
instead, I will clue you in to how the letters are written. compare the letters ...
oh
thanks
fickle lake
instead, I will clue you in to how the letters are written. compare the letters ...
OOH
but thats not maths
OR IS IT
midnight pier
does XYZ all go in the top row
shut mirage
absolutely
shut mirage
reason?
midnight pier
the top row has all straight lines for the letters
shut mirage
well spotted
vale dockBOT
fickle lake
night
prisma vale
Can anyone help with my physics assignment?
vale dockBOT
Can anyone help with my physics assignment?
prisma vale
ohld up
river shale
Just post it here
prisma vale
uplaoding
photo
friends notes
but i don’t understand
how to get the answer to the last part
river shale
prisma vale
How can u find speed on this graph?
and also how would I find velocity btwn 1-3s
🙏
shut mirage
the average velocity between two periods is just (v - v_0)/t, but I don't see that question anywhere in your paper.
I do see the question asking for the velocity only at 3s though. did you mean that?
prisma vale
Ahh, the avg velocity question is on a diff page i can upload here
But I also need help with the velocity at 3s
shut mirage
do you know what a derivative is? (just to check, though you should know because I see the tangent line in the above question)
prisma vale
yea, i do
thats how I got the other two parts
wait I am sorry, I didn't mean velocity at t=3
I figured that by plugging 3 in
I meant speed
thought that speed is js distance/time but i dont know how to tell distance
from this problem
shut mirage
I'm guessing the speed of the particle is the magnitude of its velocity vector?
prisma vale
I'm not sure, but I would assume so
shut mirage
would that be wrong? I don't think the magnitude of 27j + 18i would be as low as 32.45
oh and btw, since this is physics, remember your units!
well actually even in math
prisma vale
xd
well
thing is I am not sure how to calculate speed off this
idk if there was a diff equation i missed but idk
shut mirage
you have the velocity vector
shut mirage
I'm guessing the speed of the particle is the *magnitude* of its velocity vector...
and this
prisma vale
I'm sorry but I am not quite able to understand what you mean, i'm pretty bad at maths
but how does the velocity vector fall into the speed equation?
thought it was distance/time
shut mirage
the magnitude of the velocity vector is the speed
shut mirage
oh and that answer down there is right, if that's your answer
prisma vale
Im so sorry to ask this dumb question but what is the velocity vector here?? in the graph?
shut mirage
what do you mean?
prisma vale
As in where do u see the velocity vector?
What formula are u using to figure out the magnitude of the vector
shut mirage
part c)
prisma vale
ohh, the whole function
shut mirage
use the magnitude formula for a vector (which is just a fancy rebranding of the distance formula) for the speed
shut mirage
exactly
prisma vale
ohh
shut mirage
,calc sqrt(18^2 + 27^2)
rocky lotusBOT
Result:
32.449961479176
npnp, glad to help
prisma vale
.close
vale dockBOT
vale dockBOT
Available help channel!
wooden dune
can someone help me with this? i asked earlier but the person left the chat and i still need help
earnest dew
you took the derivative of the right side wrong
wooden dune
bruh
i asked you how to take it and you kept beating around the bush and told me to figure it out💔
wooden dune
3
earnest dew
6x
wooden dune
6
earnest dew
7x
wooden dune
7
earnest dew
1/190 *x
wooden dune
1/190
wooden dune
1/190 dx/dt
earnest dew
now look at what you wrote down
wooden dune
yeah you gave me an equation and told me to use it you didnt say this before lol
i had never seen that before
?
earnest dew
the equation is me saying it. it is more precise and inclusive than what i just did and it can be proven true by other known formulae. Part of learning math is not just being able to get a number answer to some random problem but to be able to speak the language and translate meaning both into math and out of it. There is so much information out there that is written in math one cannot understand until one obtains this skill. please consider attempting to learn standard algebric / calculus notation.
Also include units in your final answer , but yes that is a correct number.