Height will decrease in future
#help-33
serene spoke
slim nest
Guys, do I close the ticket?
serene spoke
Tectonic movements
serene spoke
Guys, do I close the ticket?
Yeah ofc
slim nest
Alrightyyy
scenic path
cairo casually jumped from mathematctics to geology
slim nest
Byesss
scenic path
bye
marsh citrusBOT
slim nest
Btw are you guys arab?
serene spoke
Btw are you guys arab?
No
serene spoke
go to my ticket
Wherr ?
scenic path
near india
serene spoke
No any link ?
scenic path
near maldives
serene spoke
To your ticket ?
marsh citrusBOT
Available help channel!
astral jungle
A = (pi r^2 • Ta/360) - (r^2 - (sin(90 - Ta/2) • r)^2 ) • (sin(90 - Ta/2) • r)
astral jungle
Can someone help me simplify this equation
I can change the • to * if it is easier to read
marsh citrusBOT
@astral jungle Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
still temple
usually when its a U sub dont you have to do du / dx why are they doing dx / du
marsh citrusBOT
@still temple Has your question been resolved?
twilit grove
because they are replacing dx in the integral
prisma mason
how to continue? am I do it right?
marsh citrusBOT
how to continue? am I do it right?
prisma mason
btw, had = lim
stuck crater
Dont multiply top and bottom
Leave them as is
X-4 on top cancels with x-4 on the bottom
prisma mason
Leave them as is
what?
prisma mason
X-4 on top cancels with x-4 on the bottom
but its √x - 2?
stuck crater
stuck crater
X-4 on top cancels with x-4 on the bottom
^
prisma mason
x/y = x(y)/x?
stuck crater
Hm?
stuck crater
Ye
stuck crater
Get what
prisma mason
this
stuck crater
Thats what you did
prisma mason
(x-4)(sqrtx + 2)/x-4
prisma mason
You multiplied on the top
OH LOLLL
i just realized
but why?
wait
nevermind
i see
tytytyty
so i suppose to do it step by step
stuck crater
marsh citrusBOT
marsh citrusBOT
Available help channel!
spring stratus
Find the minimum of the expression
marsh citrusBOT
Find the minimum of the expression
spring stratus
Where x y and z are real
What ive did is complete to square for x and y
And then i got stuck
Ive added and substracted 9/4
<@&286206848099549185>
still temple
And then i got stuck
Where?
late geode
we're you able to determine the mins of
x^2 - 3x
y^2 - 3y
spring stratus
we're you able to determine the mins of
x^2 - 3x
y^2 - 3y
I havent really tried to
I was thinking we could have three squares equal to 0
which would be amazing
late geode
what do you have after completing the square
spring stratus
for x and y?
late geode
for the x and y terms
light tree
Hello
light tree
I am in need of help for geometry B lol
spring stratus
Open a channel
light tree
How do u do that
late geode
missing the ^2 for the ys
spring stratus
My mistake, yes that is squared
late geode
what's the min of (x-3/2)^2
late geode
what's the min of (y-3/2)^2
late geode
as for the min of
z^2 + 1 + 1/(z^2 +1)
you can apply amgm
marsh citrusBOT
@spring stratus Has your question been resolved?
spring stratus
as for the min of
z^2 + 1 + 1/(z^2 +1)
you can apply amgm
Minimum of that is 2
marsh citrusBOT
@spring stratus Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
lyric kelp
marsh citrusBOT
crystal lintel
yes
lyric kelp
why did they write so much just for that
crystal lintel
"at the point x = a" and the likes usually makes me cringe
lyric kelp
okay so
it goes as e^2x, 2e^2x , 4e^2x , 8e^2x
and since x a = 1/2
2^k e^1
and taylor series so 2^k e^1(x-1/2)^k /k!
is it this?
omg i actually got it
i mean i totally expected
crystal lintel
do note e^1 = e
lyric kelp
totally
lyric kelp
do note e^1 = e
yuppp
normal sky
void elm
normal sky
its evaluated at a = x0 = 5
glass silo
[well, define "basically" 
]
lyric kelp
[well, define "basically" <:RooThink:532310138439073792>]
you can ignore when i say basically
its an escape path
crystal lintel
basically
void elm
essentially
glass silo
effectively 
normal sky
fundamentally
lyric kelp
its evaluated at a = x0 = 5
but they put it as x=x_0 so isnt x=a?
crystal lintel
manifestly
normal sky
principally
void elm
isnt this bascially a maclaurin serie?
it's only called a Maclaurin series when x_0 = 0, iirc
whole thorn
rhetorically.
lyric kelp
it's only called a Maclaurin series when x_0 = 0, iirc
oh yeah true
normal sky
but they put it as x=x_0 so isnt x=a?
mclaren series are just taylor swift series when you're evaluating them at a = x0 = 0
whole thorn
mfw x-a is surjective
lyric kelp
so no (x-a) is not just 0 <:despairjj:1102006876687847545>
Oh yeah oops 😭
normal sky
lyric kelp
It’s funny how every help channel I open becomes an emoji con
void elm
syrex is a helpee favourite, it seems 
normal sky
lyric kelp
syrex is a helpee favourite, it seems <:catthink:526983414226747393>
Maybe people just like series
crystal lintel
and the fun community of every syrex channel
whole thorn
thanks to chartbit we have emojis to react with
glass silo
And of course @crystal lintel 
normal sky
lyric kelp
but f(x) = 1/x-4 since x is always 5 whatever derivative its always going to be 1 no?
glass silo
You're saying the derivative of f evaluated at 5 is going to be 1, or?
normal sky
well the 1/(x-4) part is going to be 1 yes, but you're missing something else from the derivatives
lyric kelp
well the 1/(x-4) part is going to be 1 yes, but you're missing something else fr...
uhm
second derivative is -1/(x-4)^2
that would be -1
and then 1 and then -1
normal sky
$-(x-4)^{-2}$
elfin berryBOT
chebyshev's infinite pee norm
normal sky
are you sure 
normal sky
glass silo
[also 
the art of using series you know 
]
lyric kelp
wait but how do i put this into series since
it goes from 1 1 2 3
i included alternating signs arleady
normal sky
well it goes from $1, 11, 112, 1123$
elfin berryBOT
chebyshev's infinite pee norm
normal sky
do you recognize that pattern
lyric kelp
its n! on crack
normal sky
lyric kelp
oh wait its just k!
since k = 0
starts at 0
aye its greeb
my sanity is restored ty
normal sky
greeb
lyric kelp
yes
glass silo
Also 
glass silo
[also <:nyaSparkles:733578218514284625> the art of using series you know <:nyaaS...
note that $\frac1{x - 4} = \frac1{1 + (x - 5)}$, of course, soooo
elfin berryBOT
@glass silo
glass silo
if you remember either how 1/(1 - u) or 1/(1 + u), there's a shortcut you can use there
i mightve forgotten
glass silo
Replace u = -(x - 5)
normal sky
do you remember what geometric series are
normal sky
so $\frac{1}{1-u} = \sum_{n=0}^\infty u^n$
elfin berryBOT
chebyshev's infinite pee norm
normal sky
basically
lyric kelp
**chebyshev's infinite pee norm**
is it bad that i dont recognize this
oh
wait thats
okay nvm
i just write in terms of a and r
normal sky
normal sky
Replace u = -(x - 5)
.
crystal lintel
you don't really care where it converges for these problems anyway
but this one does converge in some places
glass silo
but this one does converge in some places
(and, if anything, r is supposed to be -(x - 5) in this case, hence-)
lyric kelp
(and, if anything, r is supposed to be -(x - 5) in this case, hence-)
ah is it 0
oops
wait why not
if x = 5
normal sky
you're trying to determine all the possible x values so that the common ratio is < 1
the series does converge when x = 5, but that's only a single point for which it converges
normal sky
lyric kelp
marsh citrusBOT
Available help channel!
lament silo
Find the equations of the tangent and the normal to the graph of:
marsh citrusBOT
Find the equations of the tangent and the normal to the graph of:
elfin berryBOT
Zachy 🌸
lament silo
at the point:
elfin berryBOT
Zachy 🌸
lament silo
and I got that:
tangent -> y=0
normal -> x=pi/4
mighty gyro
What's the problem?
broken dome
Hippy funk function fr
quasi apex
Your answers are correct
marsh citrusBOT
@lament silo Has your question been resolved?
lament silo
Hippy funk function fr
I had a seizure when I first looked at it lol
lament silo
Your answers are correct
Thanks
tropic summit
Hello i need some help with Trigenometry problems
marsh citrusBOT
Hello i need some help with Trigenometry problems
quasi apex
ask away
tropic summit
thank you Mr bean. i am getting my images together
were doing wuestions 17 and 16. Ive shown work for 16, adn the graph of 17 in DESMOS. I am stuck and the solutions ive gotten are not acepted
marsh citrusBOT
@tropic summit Has your question been resolved?
marsh citrusBOT
@tropic summit Has your question been resolved?
hushed crest
Hello! I have a question about the Graceful Tree Conjecture. I am reading about it at the moment and I saw that it was proven for a lot of special cases and tree configurations (most of which are not very popular such as bananas or firecrackers)
Do you guys know of any other special tree configurations where the conjecture is still unproven? Looking online is not really helpful since those obscure trees are not really talked about.
Thank you!
marsh citrusBOT
Hello! I have a question about the Graceful Tree Conjecture. I am reading about ...
hushed crest
(I will try to prove some of these cases because I think it could be a fun exercice and it could perhaps help the conjecture)
marsh citrusBOT
@hushed crest Has your question been resolved?
marsh citrusBOT
@hushed crest Has your question been resolved?
marsh citrusBOT
@hushed crest Has your question been resolved?
hushed crest
Hello! I have a question about the Graceful Tree Conjecture. I am reading about ...
<@&286206848099549185>
ivory mica
<@&286206848099549185>
youre probably better off asking in #discrete-math
hushed crest
Alright, thanks!
marsh citrusBOT
@hushed crest Has your question been resolved?
keen reef
yo
marsh citrusBOT
@hushed crest Has your question been resolved?
brisk totem
Question 21
marsh citrusBOT
Question 21
brisk totem
Noticed it looked like this
It’s a test over integral so I assume I need to use that somehow here?
Does it involve the definition of an integral in terms of sigma notation
tired oxide
it’s a riemann sum!
tired oxide
yeah, factor out a 1/n from the summand
brisk totem
huh
tired oxide
and try to imagine it like a riemann sum
brisk totem
Yeah
serene spoke
<Imagine>
latent coral
yeah, factor out a 1/n from the summand
am i stupid, how would you factor 1/n out from 1/(n+k)?
brisk totem
Yeah
latent coral
1/n * 1/(1 + k/n) ?
serene spoke
am i stupid, how would you factor 1/n out from 1/(n+k)?
No she says
To bring it in general form
brisk totem
How does that help
serene spoke
k/n = x
brisk totem
As n approaches infinity
tired oxide
so the first step here (and i will sleep after because i’m sleepy) is $$\sum \frac{1}{n} \frac{1}{1 +(k/n}$$
elfin berryBOT
smay
brisk totem
X would approach 0
tired oxide
sorry i’m slow at typing
serene spoke
so the first step here (and i will sleep after because i’m sleepy) is $$\sum \fr...
Better than who cant type like this 🙂
elfin berryBOT
Nathan
brisk totem
Am I looking at it right
tired oxide
yes the size of the intervals get small
tired oxide
okay, someone else will come help, because this is a fun question, but i have to sleep i’m sorry
brisk totem
It’s only 1:30 am
tired oxide
it’s 3 am here ;P
brisk totem
Even better 😭
no help ever came
Ln(2)?
@serene spoke
Looking at the definition of an integral
Let $$\frac{b-a}{n} = \frac{1-0}{n}$$
elfin berryBOT
Nathan
marsh citrusBOT
@brisk totem Has your question been resolved?
upbeat sable
marsh citrusBOT
marsh citrusBOT
Available help channel!
woeful shadow
how do i do question 6
marsh citrusBOT
how do i do question 6
woeful shadow
atomic geyser
first write sum of first 10 terms of ap according to formula
then again make a equation of first 5 terms
solve 2 eqn
you will get a and d
first term and common diff
atomic geyser
hm
woeful shadow
marsh citrusBOT
@woeful shadow Has your question been resolved?
woeful shadow
.close
lilac siren
is there some exponential rule comprehension here, maybe as command
marsh citrusBOT
is there some exponential rule comprehension here, maybe as command
knotty trellis
,tex .exp rules
elfin berryBOT
MethIsAlwaysRight
knotty trellis
I think you need preamble for this though
marsh citrusBOT
marsh citrusBOT
Available help channel!
marsh citrusBOT
still temple
So all of those scaling factors you get
[
\norm{\vv r_u \cross \vv r_v} \qq \4{\norm{\grad F}}{\norm{\grad F \vd \vc p}} \qq\3{f_x^2+f_y^2+1}
]
should be just the Jacobian of the coordinate transformation that happens doing this right?
marsh citrusBOT
So all of those scaling factors you get
\[
\norm{\vv r_u \cross \vv r_v} \qq \4...
elfin berryBOT
still temple
if so, is there a way to derive them directly using a Jacobian-based argument?
I have been trying to figure that out
marsh citrusBOT
@still temple Has your question been resolved?
outer lodge
So all of those scaling factors you get
\[
\norm{\vv r_u \cross \vv r_v} \qq \4...
Which scaling factors?
still temple
the one i highlighted
outer lodge
The cross product?
still temple
these
they are just scaling factors to the coordinate transformation that happens between the integrals
aka the Jacobian
and i want to figure out how you are meant to figure out those formulations FROM the Jacobian
outer lodge
No, they are the length of the normal vector at the given points on the surface
Which corresponds to some small area enclosed by the tangents I believe
still temple
what you just said is not making sense to me
also how could it not be the Jacobian when this is the defining feature of what it is?
outer lodge
The Jacobian deals with scaling issues caused by a change in coordinates, whereas the term you highlighted is the area of a small, flat patch on a curved surface
still temple
well yeah but still its a mapping between submanifolds and we have the chart that defines this mapping no?
like im just trying to see why not this wouldnt work out
outer lodge
R is a projection of S, right? The patch element on S has a z component which changes the scale compared to the corresponding small area on R. But this is not due to a change in coordinates, it’s due to the curvature of S
outer lodge
@still temple does this help?
marsh citrusBOT
@still temple Has your question been resolved?
foggy mantle
marsh citrusBOT
foggy mantle
I need some hints
foggy mantle
Yea that's easy
still temple
for the leftover terms
quasi apex
Till where were you able to reach
still temple
i think you can
foggy mantle
Ok
quasi apex
Now what do you think you should do next
foggy mantle
Well x^2 +4x+4 is (x-2)^2
foggy mantle
Ok just a sec
quasi apex
Also note that x HAS to be positive
foggy mantle
yea
quasi apex
What are you getting now?
foggy mantle
last time -4
foggy mantle
(log2(x^2+4/x))^2 = (-(x-2)^2+2)^2 *
quasi apex
No
Okay, lets go a step back
We had
$$ \log_2{ \frac{x^2 + 4}{x} } + (x-2)^2 = 2$$
elfin berryBOT
fukwerint
quasi apex
Let it be like that
foggy mantle
yes
elfin berryBOT
fukwerint
quasi apex
For x > 0
foggy mantle
**fukwerint**
I still don't understand how to continue from
quasi apex
Wait sorry, I forgot you were there
Tag me if I don't respond
Do you know AM-GM inequality?
@foggy mantle
foggy mantle
I remember it
marsh citrusBOT
@foggy mantle Has your question been resolved?
quasi apex
@foggy mantle any issues?
foggy mantle
so 4<x^2+4/x
quasi apex
x^2?
Just x + 4/x >= 4
And the minimum value is attained at x = 2
(x + 4/x)/2 >= sqrt(4) = 2
So x+4/x >= 4
@foggy mantle bro with me?
foggy mantle
(x + 4/x)/2 >= sqrt(4) = 2
So x+4/x >= 4
yea but x + 4/x is equal to (x^2 + 4)/x
that's what i meant
quasi apex
Oh okay, yeah
So its minimum value is 4
So whats the minimum value of log_2(that expression)?
foggy mantle
2*
foggy mantle
So i solve the ecuation with the minimum value?
quasi apex
No
You know that LHS has to be greater than or equal to 2 + 0 = 2
But RHS is 2
So the only way this equation works is if both the terms on LHS attain their minimum value
For (x-2)^2, its 0 at x=2
And for the other one its 2, coincidentally at x=2 only
If it was (x-3)^2, this equation wouldn't have a solutino
quasi apex
Yup
foggy mantle
.close
marsh citrusBOT
serene spoke
It means
Log (3x+2)² = log 121
Or (3x+2)² = 11²
By removing log
?
,w solve (3x+2) = ±11
elfin berryBOT
serene spoke
,calc -2/3+11/3
elfin berryBOT
Result:
3
cobalt aspen
If it takes a men b hours to dig c holes, how many holes can be dug by d men in e hours?
Hi Please help.
marsh citrusBOT
If it takes a men b hours to dig c holes, how many holes can be dug by d men in ...
worn sluice
proportionality
cobalt aspen
proportionality
I have the answer keys but I don't understand it.
worn sluice
calculate it in man hours
ab man hours dig c holes
then 1 man hour will dig c/ba holes
cobalt aspen
yes, i got that
cobalt aspen
then 1 man hour will dig c/ba holes
wait hold up
why c/ba
a men -> b hours -> c holes
so it must be
worn sluice
men and hours are inversely proportional
worn sluice
men and holes are directly proportional
cobalt aspen
then 1 man hour will dig c/ba holes
so a/b man 1 hour will dig c/ba holes?
worn sluice
no
cobalt aspen
then 1 man hour will dig c/ba holes
so what is this? 1 man or 1 hour?
worn sluice
1 man for 1 hour
cobalt aspen
a (man) -> b (hours) -> c (Holes)
1 (man) -> ba (Hours) -> ??? (holes)
Ok i get the inverse proportion
worn sluice
a (man) -> b (hours) -> c (Holes)
1 (man) -> ba (Hours) -> ??? (holes)
c/ba
cobalt aspen
c/ba
but isn't man and holes proportional? y=kx
same applies to hours and holes right?
cobalt aspen
because we're finding the no. of holes
yeah yeah ok I get that
and a = k/b, correct?
worn sluice
yeah
still temple
yo
still temple
how do i solve this
still temple
wait
jaunty portal
whats the question
normal sky
whats the question
"how do I solve this"
jaunty portal
didnt she already get x=1/4
still temple
still temple
"how do I solve this"
so rude of u to assume that ngl
i was boutta send my question
ok so
idk how to solve
normal sky
I made no such assumptions
jaunty portal
wait isnt this turkey problem
serene spoke
9 slices weigh 1 pound
still temple
guys
elfin berryBOT
Result:
2.25
GUYs
i didnt ask for answers or for u to calculate
i said how to cross multiply those
oof
those things
still temple
ok so like
thats one equation
how do i like
combine those two equations
to form one
this is question
jaunty portal
so
still temple
2 equations
jaunty portal
your first equation
u should rephrase it
because 3 is not equal to 1/3
its 3 slices
so use x to mention that
jaunty portal
how much does 1 slices weigh
then
still temple
thats what i meant
jaunty portal
ignore the other equation for now
jaunty portal
$3s = \frac{1}{3}$
elfin berryBOT
Amby
jaunty portal
find s
still temple
oh
marsh citrusBOT
marsh citrusBOT
Available help channel!
hearty dust
marsh citrusBOT
hearty dust
i dont understand why they did 12sin30 to get the h
sin30=h/12 would mean that PQ is 12 no? But 12 is given at PR
quasi apex
Just draw it now as I speak
hearty dust
yes I did it
quasi apex
Now at the end of P
Create a line starting from P and at an angle of 30 degrees to PR
Make that line very long
hearty dust
okay done
quasi apex
Now can you visualise what would be the shortest length from R which just reaches that long line you just drew?
hearty dust
yes
quasi apex
What would be it, can you draw and show me
quasi apex
PR is 12 cm
Then we draw a long line PR' at an angle of 30
Do you see that the perpendicular to PR' from R would be the shortest possible line
quasi apex
You are trying to choose a point Q on PR' so that PQR can be a triangle
But I am saying, that if you choose A as that third point of your triangle
Then the resulting length of AR will be the shortest
marsh citrusBOT
marsh citrusBOT
Available help channel!
prisma cypress
I think I solved the Riemann hypothesis.
-
We begin by defining the Riemann zeta function as ( \zeta(s) = \sum_{n=1}^\infty n^{-s} ) for ( \text{Re}(s) > 1 ).
-
The Riemann hypothesis posits that all non-trivial zeros of ( \zeta(s) ) lie on the critical line ( \text{Re}(s) = \frac{1}{2} ).
-
To investigate the behavior of ( \zeta(s) ) near this critical line, we focus on the value at ( s = \frac{1}{2} ).
-
Evaluating ( \zeta(\frac{1}{2}) ) involves understanding the convergence of the series ( \sum_{n=1}^\infty n^{-1/2} ).
-
By examining the real part of the sum at ( s = \frac{1}{2} ), we gain insights into the behavior of ( \zeta(s) ) near the critical line.
While analyzing the behavior of ( \zeta(s) ) at ( s = \frac{1}{2} ) is informative, proving or disproving the Riemann hypothesis requires a more comprehensive approach that considers the behavior of the zeta function across the complex plane.
marsh citrusBOT
I think I solved the Riemann hypothesis.
1. We begin by defining the Riemann ze...
elfin berryBOT
ika
prisma cypress
Here is the full try at the Riemann hypothesis
-
We begin by defining the Riemann zeta function as ( \zeta(s) = \sum_{n=1}^\infty n^{-s} ) for ( \text{Re}(s) > 1 ).
-
The Riemann hypothesis posits that all non-trivial zeros of ( \zeta(s) ) lie on the critical line ( \text{Re}(s) = \frac{1}{2} ).
-
To investigate the behavior of ( \zeta(s) ) near this critical line, we focus on the value at ( s = \frac{1}{2} ).
-
Evaluating ( \zeta(\frac{1}{2}) ) involves understanding the convergence of the series ( \sum_{n=1}^\infty n^{-1/2} ).
-
By examining the real part of the sum at ( s = \frac{1}{2} ), we gain insights into the behavior of ( \zeta(s) ) near the critical line.
While analyzing the behavior of ( \zeta(s) ) at ( s = \frac{1}{2} ) is informative, proving or disproving the Riemann hypothesis requires a more comprehensive approach that considers the behavior of the zeta function across the complex plane.
-
Investigating the real part of ( \zeta(\frac{1}{2}) ) sheds light on its behavior near the critical line. However, proving the Riemann hypothesis necessitates exploring the distribution of non-trivial zeros across the entire complex plane.
-
Techniques such as analytic continuation, functional equations, and the properties of prime numbers play crucial roles in understanding the deeper implications of the Riemann hypothesis.
-
While your exploration of ( \zeta(s) ) at ( s = \frac{1}{2} ) is a valuable starting point, it's essential to delve further into the complex dynamics of the zeta function to address the full scope of the Riemann hypothesis.
-
Additionally, studying the behavior of the zeta function in regions near the critical line, such as the critical strip (0 < \text{Re}(s) < 1), provides valuable information about the distribution of its zeros.
elfin berryBOT
ika
prisma cypress
what will you do with your one million dolla
Invest it or sum.
normal sky
I hear gme is a safe investment
prisma cypress
Already got 200 on it loll
normal sky
you could have 1 million more sir
crystal lintel
sorry you will have to hand over the 1 million dollars to the creators of chatgpt
prisma cypress
sorry you will have to hand over the 1 million dollars to the creators of chatgp...
Wait lemme try putting the text into chat gpd maybe he will help
Ah yes. The classic "wow. Unraveling the Riemann sequences..." Man gpd cannot even give a good opinion
normal sky
man Gpd is so useless
marsh citrusBOT
@prisma cypress Has your question been resolved?
mortal badger
I feel like I have a proof that is flawed in some way but I cannot find where that flaw would be.
Statement: The set of discontinuities of a a regulated fuction (a function that is the limit of a uniformely convergent sequence of step functions) is countable.
Proof:
Let f be a regulated function defined on the interval [a, b], then there exists a uniformely towards f convergent sequence of step functions t_n.
Let N be the set of discontinuities of f and M be the set of discontinuities of t_n for every n, then M is countable.
We proof that N is a subset of M.
Let x be in N. Since uniform convergence preserves continuity, by contraposition, there exists a step function t in our sequence t_n such that t is discontinuous in x, therefore x is in M.
marsh citrusBOT
I feel like I have a proof that is flawed in some way but I cannot find where th...
whole sleet
Why does every step function in the sequence have countably many discontinuities?
mortal badger
the definition we got defines a step function as a function with finitely many jumps
spark otter
the main problem is that the following part is to me not enough explained:
if x is a discontinuity point of f, why would it be a discontinuity point of some t?
on second thought, nvm that
whole sleet
Why do you think the proof is flawed?
mortal badger
if x is a discontinuity point of f, why would it be a discontinuity point of som...
hmm i was thinking since uniform convergence preserves continuity if every t_n was continuous at x then so would f be
mortal badger
Why do you think the proof is flawed?
at least the way the theorem is stated and framed in material we got it seems to imply that the proof should be a consequence of the alternative characterization of regulated functions as functions that have single sided limits in every point or at least use that characterization so im inclined to believe a relatively short proof that doesn't do so is very probably flawed
marsh citrusBOT
@mortal badger Has your question been resolved?
marsh citrusBOT
@mortal badger Has your question been resolved?
marsh citrusBOT
mortal badger
oh after some thinking i dont think the proof is flawed anymore
marsh citrusBOT
Available help channel!
tawny bane
marsh citrusBOT
still light
I meant to send that elsewhere sorry 😅
tawny bane
Please help
marsh citrusBOT
@tawny bane Has your question been resolved?
marsh citrusBOT
@tawny bane Has your question been resolved?
chilly plank
is anybody able to help with physics
marsh citrusBOT
Available help channel!
bronze osprey
marsh citrusBOT
bronze osprey
So far, I've calculated the height of the triangle which is 9cm
however I'm not sure how to find the base
bronze osprey
yes youve realised🥲
maiden frost
there excessive lengths XD
bronze osprey
yup🥲
winter smelt
split the triangle ABC in half like this
call this midpoint of AB as M
and the point where the line AC intersect Circle 1 as T
since AC is a tangent to circle 1 at T, you know the angle MTC is a right angle
and you have MT = 5, MC = 9. So using trig, work out the angle MCT (denoted as theta), and then work out AM
marsh citrusBOT
marsh citrusBOT
Available help channel!
old wren
marsh citrusBOT
old wren
this is calculus 2 please help and let me know what i am doing wrong
twilit grove
I asked you this before, but what object are they referring to? and how can what is shown in the graph have a volume? is there additional context?
old wren
I asked you this before, but what object are they referring to? and how can what...
Does this help
<@&286206848099549185> plssss
marsh citrusBOT
@old wren Has your question been resolved?
turbid oracle
why cant i use s = 1/2(u+v)*t here
marsh citrusBOT
why cant i use s = 1/2(u+v)*t here
turbid oracle
where s = 100, v = 25, u = 10, t = 5
my answer is wrong and the book uses the s = ut + 1/2at^2
whole thorn
why cant i use s = 1/2(u+v)*t here
for part c?
desert dirge
it has uniform acceleration, its speed is 25 after 5 seconds
you do not know thats how fast it is moving after moving 100m
so you cannot use any formula with v in it
as you dont know what v is
you only know u, a and s
turbid oracle
ohhh
ok thanks
makes sense because displacement at v= 25 was already more than 100 metres
ok gotcha tq
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
still temple
marsh citrusBOT
still temple
Did I make a mistake
late geode
yes
late geode
its supposed to be in both those lists
still temple
late geode
and not irrational
late geode
yes
still temple
Ty
late geode
The book said irrational means the numbers never stop
non repeating, not the same as "doesn't stop"
late geode
sqrt of non square integers are irrational
marsh citrusBOT
still temple
.reopen
marsh citrusBOT
✅
still temple
For 3-10 I can look in the book and find the answers but is it good for me to memorize the names
Yes, it's not that hard is it?
turbid galleon
hi
turbid galleon
i got the first sub- question answer
how do i solve the second
The Answer for the first one is (2x−3)(4x−21)
<@&286206848099549185> can someone Help?
late geode
!15m
marsh citrusBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
tame lintel
how do i solve the second
well there is obviously some way to use the first one for the 2nd right?
spark siren
i got the first sub- question answer
try x = (3y^2+2) and use the first.
turbid galleon
i can convert 3y^2 + 2 to X
tame lintel
i can convert 3y^2 + 2 to X
indeed
turbid galleon
try x = (3y^2+2) and use the first.
but to use the first i need to make both of them match
they aren'y matching up
spark siren
they aren'y matching up
are you sure?
tame lintel
by putting 3y^2+2 in the place of x in the first you get the 2nd one
turbid galleon
by putting 3y^2+2 in the place of x in the first you get the 2nd one
wdym
spark siren
try x = (3y^2+2) and use the first.
thats what i said
tame lintel
thats what i said
are you gonna explain or should i because its confusing when we are 2
spark siren
i said that same like you, replacing x by 3y^2+2
turbid galleon
i said that same like you, replacing x by 3y^2+2
then what?
like what should i do next
tame lintel
i said that same like you, replacing x by 3y^2+2
yeah but he obviously doesnt get it so someone needs to explain
will you do it or shoulld i
alr i will so we arent wasting time
turbid galleon
have you tried replacing x in the 1st one with 3y^2+2?
but why should i change the first one
i got the answer for the 1'st sub question
now for the second i am trying to make it the same as the 1'st to substiture the values
spark siren
8x^2-50x+63 -> replacing x by 3y^2+2 -> 8(3y^2+2)^2-50(3y^2+2)+63 = second one. then you know you can use the factorizing of the first.
tame lintel
now for the second i am trying to make it the same as the 1'st to substiture the...
yes. try adding 100 and subtracting 100 from the 2nd one
turbid galleon
yes. try adding 100 and subtracting 100 from the 2nd one
why add and then subtract
tame lintel
why add and then subtract
to create the 63 you have in the first one
or elseways
write -37 as 63-100
turbid galleon
Oh i get it now
tame lintel
Oh i get it now
do you get all of it or the 63 part
turbid galleon
but how are we allowed to add 100 to -37
tame lintel
but how are we allowed to add 100 to -37
we arent just adding it though. we are substrating it too. Like we write -37 as 63-100. its the same as -37=63-100
tame lintel
so the 2nd one is 8(3y^2+2)^2-150y^2-100+63 right?
tame lintel
so now if i substitute the values i will get the answer right?
wait
turbid galleon
yes
turbid galleon
-50(-3y-2)
tame lintel
-50(-3y-2)
are you sure?
turbid galleon
are you sure?
yes
tame lintel
-50(-3y-2)
are you sure
spark siren
you missed the square from y^2 somewhere on the way.
turbid galleon
-50(-3y^2-2)
tame lintel
-50(-3y^2-2)
try expanding this. do you get the same as -150y^2-100?
turbid galleon
oh i get it
spark siren
there is no need to do all the "try this, try that" if you do it this way: #help-33 message
turbid galleon
-50(3y^2+2)
spark siren
would be jsut straight forward.
tame lintel
-50(3y^2+2)
good
tame lintel
so it becomes 8(3y^2+2)-50(3y^2+2)+63
which is like the first one and you can factorize it
turbid galleon
where did the -100 go?
tame lintel
-50(3y^2+2)
you factorized it here
tame lintel
np
marsh citrusBOT
marsh citrusBOT
Available help channel!
simple creek
marsh citrusBOT
simple creek
how do you know that the angle is 225
like
how am i supposed to reach that conclusion
spark otter
how do you know that the angle is 225
you got tan theta = 1
so theta = pi/4 or 5pi/4 if you're solving on [0,2pi[
since c > 0, check which one has negative sin and cos...
spark otter
?
spark otter
yes
marsh citrusBOT
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
Available help channel!
marsh citrusBOT
quasi patrol
Take the derivative wrt to height
marsh citrusBOT
@daring panther Has your question been resolved?
proven geyser
Looks like A, a, and h are functions of t so it is: A(t) = (1/2)(a(t) + 3)h(t)
So we need to take derivative of both side wrt to t first
after that just plug in some numbers and solve for dh/dt
I don't know what you are doing
Do you know how to take derivative wrt to t 
with respect to
This is a related rate problem so you should be able to take derivative, though?
it is similar to implicit differentiation if you know it
earnest sundial
Let there be a function $f: \mathbb{R}^2\setminus{0}\to \mathbb{R}^2\setminus{0}$ \
with $f(x_1,x_2) = (\frac{x_1}{x_1^2+x_2^2},\frac{x_2}{x_1^2+x_2^2})$.
marsh citrusBOT
Let there be a function $f: \mathbb{R}^2\setminus\{0\}\to \mathbb{R}^2\setminus\...
elfin berryBOT
Bob Goldham
earnest sundial
(there's a bunch of exercises here, I'll only post the parts I'm struggling with)
earnest sundial
$0\in\mathbb{R}^2=(0,0)$
elfin berryBOT
Bob Goldham
earnest sundial
is the definition we use
earnest sundial
In a previous exercise, I've determined the total derivative of f to be
$\frac{(x_2^2-x_1^2, -2x_1x_2)}{(x_1^2+x_2^2)^2} dx_1 + \frac{(-2x_1x_2, x_1^2-x_2^2)}{(x_1^2+x_2^2)^2}dx_2$
elfin berryBOT
Bob Goldham
earnest sundial
now the part I don't think I understand is the following
"Show that $df$ (the total derivative of f) has the property that $df_x(df_x)^T$ is a scalar multiple of the identity matrix for any $x\in\mathbb{R}^2\setminus{0}$"
elfin berryBOT
Bob Goldham
elfin berryBOT
Flappie
earnest sundial
a vector
times the same vector transposed
is a scalar (which importantly is not a matrix)
What am I not understanding here?
leaden monolith
Huh?
earnest sundial
df_x is df at point x I think?
earnest sundial
what's df_x
ivory turtle
$f_x=\begin{pmatrix}\frac{\partial f_1}{\partial x}\\\frac{\partial f_2}{\partial x}\end{pmatrix}$
leaden monolith
That’s the derivative of f at point x
elfin berryBOT
Flappie
earnest sundial
df_x = ... no?
ivory turtle
**Flappie**
or its the tranpose of this, i forget
leaden monolith
No df_x is the total derivative of f at x
earnest sundial
f at x is not its derivatives
leaden monolith
The directional derivative of f in the direction x is f_x
There’s no d in that notation
leaden monolith
**Flappie**
This is correct but not what is asked of us
earnest sundial
The directional derivative of f in the direction x is f_x
okay interesting, but I'm trying to prove something about the total derivative
leaden monolith
$df_{\vec x} =\left.\left(\frac{(x_2^2-x_1^2, -2x_1x_2)}{(x_1^2+x_2^2)^2} dx_1 + \frac{(-2x_1x_2, x_1^2-x_2^2)}{(x_1^2+x_2^2)^2}dx_2\right)\right|_{(x_1, x_2) = \vec x}$
elfin berryBOT
Frosst
earnest sundial
what's the meaning of dx1 dx2 here?
leaden monolith
That’s the coordinates of vec x
leaden monolith
Where
earnest sundial
I don't know
leaden monolith
df_x?
earnest sundial
dx_1
leaden monolith
df is a vector, its components tell you how much f changes wrt x₁ and x₂ respectively
And each component is also a function of the point to evaluate at, ie the rate at which f changes wrt x₁ and x₂ depends on where you evaluate this f at
leaden monolith
👍
earnest sundial
so now I just do component-by-component matrix multiplication on these and should hopefully get a multiple of the identity matrix?
leaden monolith
Yes
marsh citrusBOT
earnest sundial
so now I just do component-by-component matrix multiplication on these and shoul...
isn't this still a scalar?
.reopen
marsh citrusBOT
✅
earnest sundial
a row vector
times a column vector
makes a scalar
is it "a multiple of the identity matrix" in the sense of "The 1x1 identity matrix, aka the number 1 and since this is scalar it is a multiple of 1"? Is that what they're getting at?
.close
marsh citrusBOT