1 Being probability of clearing stage 1
#help-19
paper onyx
inner ore
so a 2/3 chance of passing stage 2 by itself
paper onyx
You got 5/6
Because you did 1-1/6
But forgot about the 1/2 chance of not clearing stage 1 I'm the first place
So it should be 1 - 1/6 -1/2 +1/3
Which again coincides with our result of 2/3
Wait
No I'm right
Anything else?
@inner ore
inner ore
Umm so it is 2/3?
paper onyx
Yes
paper onyx
So it should be 1 - 1/6 -1/2 +1/3
This I got through de Morgan's law
If you are wondering
inner ore
Thank you morgan
🙏
33% chance by pure odds of passing stage 1 and 2, those are good odds ngl
paper onyx
True
inner ore
absolutely
summer cradle
my algorithm can handle that
inner ore
In case you wanna make a casino game
Something similar haha
paper onyx
Business is essential
inner ore
If I wanted to get really good at this stuff, what exactly would I need to study
statistics?
paper onyx
Screwing people over is needed in order to fulfill that essential
inner ore
Screwing people over is needed in order to fulfill that **essential**
Is your last name luthor by any chance
paper onyx
Close enough
paper onyx
statistics?
This is moreover probability
Other than that
Basic stats will be know
To make a good hold of data
summer cradle
just changing move left probability to 1/3 makes a huge difference
paper onyx
Unfair coin
Lol
It's a converging series
Stuff like this makes sense
And it being exponential
Makes being unfair even easier
Knowing stuff like this
Somehow people still think gambling is a good idea
Kinda cool
If you think about it
summer cradle
pretty significant for -5, 5
vast wasp
If three pipes are opened, they can fill an empty swimming pool in 3 hours. The largest pipe alone takes one third the time that smallest pipe takes and half the time the other pipe takes. How long would it take the smallest pipe to fill the pool by itself?
static totem
that looks wrong i think
the first pipe is 3 times better
should be 3x, (3/2)x, x
i can't tell if yours is right in some way tbh
it must be
yeah, you turn them upside down now
time to fill the pool, upside down becomes how many pools it fills in 1 time unit
which makes it additive
paper onyx
The time taken 1st pipe is a
The time taken 2nd pipe is x
The time taken 3rd pipe is y
a= 1/3 * x = 1/2 * y
3y= 2x
The time taken 1st pipe is 1/3 * x
The time taken 2nd pipe is x
The time taken 3rd pipe is 2/3 *x
Now try and do it
static totem
you renamed the pipes
paper onyx
Largest is 1st
Smallest is 2nd
The other one is 3rd
Sorry I didn't mention that
@vast wasp see if you get anywhere now
odd edgeBOT
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topaz moth
need to solve this using line integral
odd edgeBOT
need to solve this using line integral
topaz moth
the final integral i am getting is definitely wrong because it doesnt seem normally solvable
the part under the root is equal to 1 + t^2 + 2t upon simplification
but i am missing something because this aint right
odd edgeBOT
@topaz moth Has your question been resolved?
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@topaz moth Has your question been resolved?
gray plover
I don't understand this bit, where they make x/2 equal tan y
gray plover
feral scaffold
here it's stated that x = 2 tan y
so x/2 = tan y
odd edgeBOT
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spice brook
Could someone help me troubleshoot an Overleaf project? My .sty files are not loading into it and i suspect my ordering with which packages compile is the culprit.
spice brook
I've asked in #latex-help already
mossy tinsel
did u checkto make sure ur .sty file is in the root folder and not in a subfolder
spice brook
did u checkto make sure ur .sty file is in the root folder and not in a subfolde...
yep
i'm now checking if there is an unclosed group lurking somewhere
spice brook
ye i checked that
spice brook
i'm now checking if there is an unclosed group lurking somewhere
wouldn't you know it there was
mossy tinsel
also go to the dropdown that says recompile and click recompile from scratch
also create a new .tex file and make sure the .sty works on its own in there, if so its probably a problem with how the .sty file interacts with other parts in that og document
spice brook
omfg
i did it
only 12 errors now
thank you a lot
it was just weird unclosed groups that overleaf didn't inform me of for some reason
you saved me a headache
have a nice day ^^
.close
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ancient rampart
sin2x=2cos2x
odd edgeBOT
sin2x=2cos2x
noble obsidian
double angle
mystic saffron
tan(2x) = 2
ancient rampart
arent we assuming stuff about its domain then
odd edgeBOT
@ancient rampart Has your question been resolved?
exotic sail
No clue where to start pls help
odd edgeBOT
No clue where to start pls help
exotic sail
Can i use table of values even if its logarithm?
quartz trellis
odd edgeBOT
@exotic sail Has your question been resolved?
rose drift
Can someone help me with Inverse Trig Functions?
odd edgeBOT
Can someone help me with Inverse Trig Functions?
rose drift
obtuse raven
Pretty sure you can use SOH CAH TOA
warped glacier
square 23 and square 16
wtf you don't
mystic saffron
alr so you gotta find the hypotenous mb
mystic saffron
the opposite of the angle is called the opposite
you have the opposite and adjesent
use SOH
wait shit im blind
nimble blaze
alr so you gotta find the hypotenous mb
you don't
mystic saffron
bruh
steep mantle
toa??
mystic saffron
im blind
mystic saffron
toa??
yeah adjesent and opposite ;-;
i will show myself out have a good one gentlemen
uneven sable
TOA (tangent = opposite over adjacent)
odd edgeBOT
@rose drift Has your question been resolved?
somber isle
The antibiotic penicillin is produced from the fermentation process involving penicillin precursors:
C16H18N2O5S→C16H17N2O4S+H2O
If you start with 0.50 moles of penicillin precursor, how many grams of penicillin (molar mass = 334.4 g/mol) can be produced?
help plss T__T
uneven sable
Ooo science math yay
somber isle
yesyes, how do i get the one after 0.50?
My equation is 0.50/1 x ___ blank
uneven sable
I’m sorry someone else has to help you 😭 I just realized the time and I gotta get to an exam
somber isle
I’m sorry someone else has to help you 😭 I just realized the time and I gotta g...
omgo kayy!! goodluckk hope u pass !!
warped glacier
The antibiotic penicillin is produced from the fermentation process involving pe...
the mole ratio is 1 : 1 from the chemical equation coefficients
hence you also have 0.50 moles of penicillin
somber isle
the mole ratio is 1 : 1 from the chemical equation coefficients
hence you also ...
thank youu, may i ask how u got the mole ratioo?
warped glacier
thank youu, may i ask how u got the mole ratioo?
there's an invisible 1 in front of C16H18N2O5S
and an invisible 1 in front of C16H17N2O4S
hence 1 : 1
somber isle
thank youuuuu!!!!
warped glacier
no worries!!
odd edgeBOT
@somber isle Has your question been resolved?
cold tapir
honestly so freakin confuse
odd edgeBOT
honestly so freakin confuse
cold tapir
what are we comparing?
if were talking about series why do they write as a sequence
weary pelican
if were talking about series why do they write as a sequence
this I don't understand
It's written as a series
a sum from n=1 to infinity
though the series obviously diverges
weary pelican
why does it obviously diverges?
1 + 1 + 1 + ...
regal leaf
$a/a = 1$
clever fjordBOT
tobi
cold tapir
so it divereges because it just goes to infinity without an acutal answer?
weary pelican
what do you mean "without an actual answer"
cold tapir
yea like a finite answer
weary pelican
well you're adding infinitely many 1s together
I doubt your result would be finite
especially when adding another 1 would change it
regal leaf
you can also have a series, where all the partial sums are always bounded, but the series could still not be convergent
green elm
the terms don't converge to zero, end of story
weary pelican
(e.g $\sum (-1)^n$)
clever fjordBOT
rafilou is not not born in 2003
green elm
all series go on forever
weary pelican
you keep adding stuff, and the terms you add never go to 0
green elm
that's not a justification
weary pelican
if the terms you added converged at some point to 0 then we wouldn't be able to know just from that analysis whether it diverges or converges
regal leaf
$\sum_{n=1}^{\infty} 1 = \lim_{N \to \infty} \sum_{n=1}^{N} 1 = \lim_{N \to \infty} N$
weary pelican
starts at n=1
cold tapir
im say ok though I dont understand the whole test thingamajigy
clever fjordBOT
tobi
cold tapir
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long tinsel
sub x = π/2 - u
nimble blaze
king's rule/property
normal plume
heady plover
sub x = π/2 - u
Thx!!
spark wolf
I'm not entirely sure how to prove this. I attatched the question that it was referring to here as well
obtuse yoke
bruhhh what is this
spark wolf
my homework lol
obtuse yoke
this is on another level lol
spark wolf
its multivariable and vector calculus
obtuse yoke
meanwhile i m trying to get answer on my little question for my tomorrow exam
can ya actually help me with this you would need like 1 sec to solve this
spark wolf
maybe. did you post it in a channel?
spark wolf
post it and ill try and take a look and see if i can help
spark wolf
I'm not entirely sure how to prove this. I attatched the question that it was re...
i would think that I would have an integral with (1/2x-1)dA, but im not really sure where to go from there
obtuse yoke
post it and ill try and take a look and see if i can help
i posted it here #help-13
obtuse yoke
oh i thaught my massage didnt send
spark wolf
i would think that I would have an integral with (1/2x-1)dA, but im not really s...
oh wait no hold on
so
we're given the vector F
in problem 4
yeah no that doesnt really work
im kinda lost here
oh wait no im not supposed to be using the actual numbers from 4, ok
prime basalt
I'm not entirely sure how to prove this. I attatched the question that it was re...
Are they asking to prove Green's theorem or what
spark wolf
Are they asking to prove Green's theorem or what
i think? I'm not really sure myself either
prime basalt
Green's theorem is this, and the difficulty of the task depends on whether they ask you to prove it or not
This equality is almost obvious
(I can explain it if you want)
spark wolf
sure
prime basalt
You can write $\mathbf{n}$ as $(\cos\theta(s), \sin\theta(s))$, where $\theta(s)$ is the angle of rotation of the normal vector after we travelled distance $s$ along the contour.
Hence $\mathbf{F}\cdot\mathbf{n} \ ds = P\cos\theta(s)ds + Q\sin\theta(s)ds$
clever fjordBOT
EQUENOS
spark wolf
ok, that makes sense
prime basalt
(forgot to clarify that theta is the angle with Ox, counterclockwise direction is positive)
spark wolf
I'm not certain I see how that leads to Pdy-Qdx though
because if we just had F
it would be Qdx-Pdy right?
prime basalt
(forgot to clarify that theta is the angle with Ox, counterclockwise direction i...
Due to this cos(theta)ds = dy, sin(theta)ds = -dx
prime basalt
spark wolf
right
prime basalt
yeah so the first equality is easy
The second equality in (a) is just Green's theorem, but the question is whether they ask you to prove it or just use it
spark wolf
so now we have Pdy-Qdx
would I just apply green's theorem again, and end up with a double integral of...-Qdy-Pdx. Which would be equal to Pdx+Qdy?
spark wolf
The second equality in (a) is just Green's theorem, but the question is whether ...
yeah im not sure if theyre asking me to prove green's theorem. I'd assume no?
prime basalt
so now we have Pdy-Qdx
would I just apply green's theorem again, and end up with...
If you apply Green's theorem you simply get this:
spark wolf
hm
prime basalt
It's precisely the statement of the theorem
spark wolf
ok, now im confused
ok let me try this again
i feel like i just did it wrong
we have Pdy-Qdx
I apply green's theorem again, and end up with a double integral of (Px+Qy)dA
yeah, youre right, i think i was getting confused by the dx and dy
prime basalt
alright
spark wolf
and this would leave part b now
prime basalt
Yeah part (b) becomes a short calculation
spark wolf
would I convert to polar coordinates here?
F=<2(x+y),2(x+y)>
so we would have a double integral with
2+2dA.
Since the curve is a circle of radius R, could I have 4(pi(R)^2) as my answer?
odd edgeBOT
@spark wolf Has your question been resolved?
odd edgeBOT
@spark wolf Has your question been resolved?
prime basalt
F=<2(x+y),2(x+y)>
so we would have a double integral with
2+2dA.
Since the curve...
Correct
Sorry I forgot about this thread
mystic saffron
Struggling to understand a formula
odd edgeBOT
Struggling to understand a formula
mystic saffron
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@mystic saffron Has your question been resolved?
odd edgeBOT
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swift heron
why does the bounds of integration go from 0 to 1, to 0 to x
odd edgeBOT
why does the bounds of integration go from 0 to 1, to 0 to x
@swift heron Has your question been resolved?
odd edgeBOT
@swift heron Has your question been resolved?
odd edgeBOT
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untold cypress
What do i do?
odd edgeBOT
What do i do?
neat scaffold
What do i do?
well first find $\alpha$ and $\beta$
clever fjordBOT
Carter
open root
looks like you need to do roots of polynomilas
pmt has a great cheat sheet
so alpha + beta = -3/2 and alpha x beta = 4/2 = 2
untold cypress
pmt has a great cheat sheet
Thanks
untold cypress
so alpha + beta = -3/2 and alpha x beta = 4/2 = 2
But what do I do after this?
untold cypress
or just do (x-2alpha)(x-2beta)
Could you show me how?
open root
x^2 - (2alpha + 2 beta)x +4alphabeta
open root
so alpha + beta = -3/2 and alpha x beta = 4/2 = 2
then just sub in these :))
odd edgeBOT
chilly ridge
What do i do?
vietas
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Available help channel!
shy galleon
odd edgeBOT
shy galleon
This is the work I've done so far
I'm a bit lost on D
I solved a b and c no problem but am now stuck severely
odd edgeBOT
@shy galleon Has your question been resolved?
shy galleon
<@&286206848099549185> Plz i really could use some help here (i can provide solutions to A, B and C if you think it might be relavant)
lime light
let me check
unreal remnant
hey im trying to prove a work theorem for my EM hw. The entire equation should converge to just the first term as "a" approaches infinity, but the second integral diverges when I do so. I thought I did the second integral right, as it's supposed to be a surface integral of a sphere at a radius "a". What am I doing wrong?
https://imgur.com/a/hj0xGRV
oh
shy galleon
We still good?
odd edgeBOT
hey im trying to prove a work theorem for my EM hw. The entire equation should c...
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).
shy galleon
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odd edgeBOT
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burnt gazelle
Had an exam today that asked me to find a counterexample for:
Suppose R and S are rings, then any ideal of R x S is of the form I x J where I,J are ideals of R,S respectively.
Hint: S is not necessarily unital
burnt gazelle
Any counterexample/ideas for what I should be trying to do?
odd edgeBOT
@burnt gazelle Has your question been resolved?
burnt gazelle
<@&286206848099549185>
odd edgeBOT
@burnt gazelle Has your question been resolved?
warped grove
Had an exam today that asked me to find a counterexample for:
Suppose R and S ar...
I don't know the answer off the top of my head, but since the hint suggests considering rings that are non-unital, let's say R = 2Z and S = 2Z, and then consider the ideal generated by (2,2). Could you write that as a product of ideals? I don't think you could, but maybe I'm missing something.
toxic shale
I'm supposed to solve for the angle using law of sines
rose radish
toxic shale
Almaot done
Uh I can't plug it in the calculator
Is arc sin different from the -1 sin
toxic shale
But if I do arcsin(24sin(59) over 14) it doesn't work
mossy tinsel
yeah because the equation the other guy gave is not correct.
it shouldnt matter tho, now that you know the formula you should be subbing it in urself
the side a is directly opposite angle A
same for b and c
use this to redo the question
odd edgeBOT
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nimble sail
guys, help
odd edgeBOT
guys, help
nimble sail
they're asking me to find hmm
the points where it is not derivative.
but, how can I find that?
thick shell
when its not defined
nimble sail
is that it?
tiny sandal
when its not defined
wouldnt u find the derivative and the points its undefined there is no derivative?
thick shell
wouldnt u find the derivative and the points its undefined there is no derivativ...
when the original function is not defined
thick shell
oh yes
tiny sandal
but not differential
so u would need to take the derivative
then see where the derivative is defined
thick shell
yeah
nimble sail
then see where the derivative is defined
but like
when is that
I heard if my derivative is = 0
then tha's a point where's not derivative
twin quarry
I heard if my derivative is = 0
isn’t that relative min and max tho
tiny sandal
isn’t that relative min and max tho
yes
tiny sandal
then tha's a point where's not derivative
it is a derivative
twin quarry
when is not derivative
where the original function is not defined, the original function is not continuous anyways if u look at the denominator
if u set the denominator equal to 0
2x-1=0
nimble sail
where the original function is not defined, the original function is not continu...
is that it?
twin quarry
what is x
twin quarry
is that it?
uh basically
nimble sail
well, that should be 1/2
nimble sail
I do not know how is it called in english
twin quarry
ur gonna get whatever #/0
nimble sail
but like
twin quarry
and anything divided by 0
nimble sail
they're asking me
twin quarry
is undefined
tiny sandal
uh basically
nooo
twin quarry
singular points??
tiny sandal
ur forgetting
tiny sandal
vertical continuous
twin quarry
my Spanish classes kicking in
tiny sandal
when the graph is vertical and continuous
the derivative is still undefined
cause slope cant be vertical
tiny sandal
so u take the derivative of the function
then see where the derivative is undefined
and that is where the funcion is not differentiable
and ofcourse if its not continuous over a point its not differentiable
so 1/2 is one
tiny sandal
take the derivative of the function
thick shell
when the derivative is undefined
tiny sandal
and when is the denominator 0
tiny sandal
i think 1/2 is the only one
nimble sail
and, well
tiny sandal
but like usually u need to check for the vertical ones
nimble sail
yeah, only that one
tiny sandal
but for this one 1/2 is the only one
tiny sandal
just dont automatically assume there is only one
twin quarry
yes
nimble sail
so, only 1/2
twin quarry
when were talking abt rational functions that is
twin quarry
so, only 1/2
ye
twin quarry
derivative is undefined or does not exist at x=1/2
thick shell
what about when it's not rational
same thing
twin quarry
what about that then
depends on what type of functions we’re looking at I suppose
twin quarry
same thing
omg poopoo is that u
nimble sail
okay hmm
soo
what about this then
this doesn't have a derivative at 0
why tho
twin quarry
there’s a corner/cusp going on here
twin quarry
where there’s like sharp corners
nimble sail
why does that matter tho
tiny sandal
u can only have a tangent line if its a turve
twin quarry
also EW ABSOLUTE VALUES
odd edgeBOT
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Available help channel!
restive lynx
I just need to make sure im not missing something bc ive been struggling in calc
runic swift
there is
restive lynx
wait how 😭
runic swift
you know the first derivative of that?
runic swift
cancel the 2s
restive lynx
so js -x/y
restive lynx
y*xy'/y^2
runic swift
?
restive lynx
wait am i wrong
restive lynx
ok so y+xy'/y^2
runic swift
you sure you not missing a sign anywhere?
runic swift
and y' was?
restive lynx
or x(-x/y)-y/y^2
runic swift
ok good
then refer to the original equation
make either x² or y² as a subject
sub that in
restive lynx
wait wdym
runic swift
but still wouldnt it be -x^2+y^2/y^3
small mistake its -x² - y²
restive lynx
yeah the left one
shoot i dont know how i went off track on what i did
thank you so much for your help ill go back to studying implicit differentiation more 🙏
queen wind
if you do get truly stuck on implicit differentiation, you can verify your answer by solving for one variable (not always possible) and just taking the derivative like you're familiar with
so here d^2/dy^2 of sqrt(15 - y^2)
its not always a good idea but a good thing to have in your back pocket
restive lynx
wait so like solving sqrt of 15-y^2 when do I verify it with the differentiation i get
restive lynx
i dont mean to sound dumb but i still kinda dont get it 😭
OH WAIT NVM
it clicked in my head after I wrote it all out
thank you everyone who helped!
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kindred sparrow
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kindred sparrow
hi this problem has given me hell
it’s apparently very easy but I cannot find the intersection points with my usual algebraic methods
warped glacier
a few different methods exist, but note that $y - \frac{3}{2} = \frac{x^2}{8}$
clever fjordBOT
south, just south
warped glacier
you can then multiply both sides by 8
and sub in $x^2$ into equation $2$: you get a quadratic in $y$
clever fjordBOT
south, just south
odd edgeBOT
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odd edgeBOT
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jade obsidian
Hello. If I have a hollow sphere with 30cm inner diameter and I want to fill it with lead shot , how much would that inner volume of 3mm balls of lead shot weight?
If it would have been a 30cm lead ball, that would weight +-160kg.
For the air around the 3mm lead balls can there be done a fast calculation of getting the weight of full volume of lead and extracting +- 5 - 10% of weight due to the air?
Bigger balls inside = more air = less weight.
Would there be more than 2kg difference if I take 4mm lead shot instead of 3mm ?
Thanks!
stable needle
the diameter doesn't matter
It will matter right?
static totem
no, it's not like you're like approaching zero with smaller balls
stable needle
It won't converge but the difference can be substantial
static totem
viscid flint
boundary effects will take over if the ball is a significant fraction of the space (imagine a ball which is more than half of the diameter)
static totem
i understand that they have to be small and not big
viscid flint
these seem like the numbers you care about
static totem
between 0.6 and 0.64 yeah
odd edgeBOT
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lime vortex
for question c how is the answer 5.45 mins
odd edgeBOT
for question c how is the answer 5.45 mins
lime vortex
.close
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cyan plume
forgot how this worked
odd edgeBOT
forgot how this worked
cyan plume
if i had ()() without a sign does it mean addition or multipication?
and this question too
mossy tinsel
if i had ()() without a sign does it mean addition or multipication?
multiplication
mossy tinsel
and this question too
for this one, the exponent 7 applies to only the x whereas the exponent 3 applies to the whole thing (everythin withing the brackets)
odd edgeBOT
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distant crow
A group consists of 8 females and 13 males. Excluding 2 males, the rest are arranged in such a way that no females are seated together. How many ways can this be done?
The answer in the book says 12P8 * 11!
But shouldnt it be 13P11 * 12P8? cause 2 males can be excluded in 13C2 = 13C11 ways; again the order needs to be taken into consideration so the answer would be 13P11 * 12P8?
Can anyone kindly tell me if im wrong?
odd edgeBOT
@distant crow Has your question been resolved?
celest acorn
yes
so
there are 8! ways to arrange tge 8 girls first right?
no
siiting boys first will be easier
distant crow
Finally, someone
celest acorn
so 13P11 ways of sitting boys
distant crow
Yeaahh
celest acorn
and for the girls we have 12 gaps
distant crow
Multiplied by 12P8 then?
celest acorn
13!/2! * 12!/4! is the asnwer for certain
yes
the asnwer in the book seems wrong
unless it asked a slightly different qn
distant crow
13!/2! * 12!/4! is the asnwer for certain
Appreciate it
celest acorn
thanks
distant crow
unless it asked a slightly different qn
I tried to translate it as accurately as I could TwT
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ripe jolt
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ripe jolt
does the series converges ?
knotty oasis
you can use the property |sin(x)| < |x|
ripe jolt
how can this help me can you explaine please?
lime flume
lunar hedge
I think so, since the summands just approach 0 as it goes to infinity. It would converge
ripe jolt
yes but i must prove it
i though about using it as p-series
sense its similar to Σ(1/n^5/2)
and the lnn doesnt have a lot of impact to the series for large numbers
plus 5/2>1 from the p-series theory it means that it converges
odd edgeBOT
@ripe jolt Has your question been resolved?
summer cradle
I think so, since the summands just approach 0 as it goes to infinity. It would ...
this isn’t good reasoning
summer cradle
sense its similar to Σ(1/n^5/2)
do you mean n^3/2?
ripe jolt
do you mean n^3/2?
yes yes sorry
summer cradle
you can use the property |sin(x)| < |x|
then you can use this
ripe jolt
how can this help me can you explaine please?
.
summer cradle
consider the series $$\sum_{n=1}^\infty \frac{\pi}{n\sqrt{n}}$$
clever fjordBOT
slayla
ripe jolt
yes great
summer cradle
compare the two
summer cradle
this one and the one i wrote
ripe jolt
so that makes it π/n^3/2
π gets out of the series
so we have 1/n^3/2
this is a p-series now i guess
and in p-series we know that if 1/n^p and p>1 then the series converges
3/2>1
so it converges
thats what i did
summer cradle
that sounds relevant yes
ripe jolt
ok thanks but i must find a reason to remove sin
summer cradle
do you know comparison test
ripe jolt
i think no
am still in calc 1
same for this 2
but i must find a reason to remove ln(n)
ln(n) grows much slower so i can avoid it
but idk if there is a better way to do so
lunar hedge
this isn’t good reasoning
Why not?
clever fjordBOT
slayla
lunar hedge
no
ripe jolt
bros started beef in the middle of help needing 💀
summer cradle
but the summands approach 0 as n goes to infinity
lunar hedge
makes sense
ripe jolt
yo guys can you help me XD
summer cradle
yo guys can you help me XD
if you have two series of positive terms, and one of them converges, and the other has smaller terms, they both converge
are you familiar with this?
summer cradle
lol ok
summer cradle
you can use the property |sin(x)| < |x|
that’s why this is helpful
ripe jolt
ok so by this i can remove the sin
summer cradle
**slayla**
yea. this one converges, and the original one has smaller terms
ripe jolt
ok
something else
can i do that when ever i see a series of a sin
and the denominator is bigger than the numerator
ripe jolt
ok ig
on this 2 can i just say that lnn grows much slower so
its almost the same as 1/n^p
summer cradle
grows much slower than what
summer cradle
no, i wouldn’t just say that
ripe jolt
then which property can i use for those 2
wraith zealot
then which property can i use for those 2
this is pretty intuitive
if you are adding many terms that are smaller than the ones of a sum that converges
the new sum must also converge
odd edgeBOT
@ripe jolt Has your question been resolved?
leaden plover
that the ones of the sum that converges wdym
You have two sets of infinite sets of numbers. {a1, a2, a3, a4...} And {b1, b2, b3, b4...}
- If you add all the "a_n" and they "converge" (go towards) to a specific number.
- If all the "b_n" are less than or equal to "a_n".
you can logically deduce that if adding all a_n is giving me a number and all the b_n are smaller or equal to a_n then adding b_n should converge to a number too.
You understand? (:
ripe jolt
i already solved it with the lnn<n
odd edgeBOT
odd edgeBOT
Available help channel!
nimble sail
guys
latent scaffold
What do you want to know?
nimble sail
well, if my answer is correct?
latent scaffold
And what were you tasked to find to begin with?
latent scaffold
Are singular points like critical points?
If so I'm pretty sure you need the initial function to be defined there
nimble sail
When the function is not derivative
latent scaffold
The function is differentiable at x=pi/2, but its derivative is 0
nimble sail
wdym
odd edgeBOT
@nimble sail Has your question been resolved?
magic wasp
I have this homogeneous solution for a system of differential equations. I need help with how i find the constants A and B? Initial values are x(0) = 1 and dx/dt = 0.
low locust
plug t=0 in and you get an equation for A and B
differentiate and plug t=0 in again and you get a second equation
then solve those
odd edgeBOT
@magic wasp Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
radiant shore
Hiii, I have to do this equation and I’m stuck, I either do something wrong or I’m not aware of something
pastel steeple
i cannot read that 😭
winter berry
Hiii, I have to do this equation and I’m stuck, I either do something wrong or I...
Seems correct so far
radiant shore
okey, I’m going to rewrite it
radiant shore
log ab = log a + log b
and what about this 1/2
pastel steeple
log_5 x^3/2 * sqrt3 = 0
radiant shore
yes, i’ve got it and what is next step here because I should get 3^-1/3
winter berry
yes, i’ve got it and what is next step here because I should get 3^-1/3
There's a couple of ways you can continue you can either sum all the logs or set two remaining logs equal to each other
winter berry
Yeah
odd edgeBOT
odd edgeBOT
Available help channel!
long jetty
Quick question: is this how you say that x is a positive integer that has a value of at least 3?
ember oak
You can do just $\bZ$ you don't need $\bZ^+$
clever fjordBOT
SWR
ember oak
Hmm yes but if I wanna be explicit
It is unnecessary
long jetty
It is unnecessary
But is that the correct way to use curly brackets?
ember oak
Sorta
You wrote the set of all integers of at least 3, you did not say that x is an integer of at least 3
long jetty
How do I say that x is?
low locust
$x\in{x: x\in\bZ^+ \land x\geq 3}$
clever fjordBOT
Denascite
low locust
if you wanna stick with your set
long jetty
So the x belongs to before is necessary?
karmic umbra
when u write the curly braces thing you are defining a set
low locust
or just say $x\in\bZ$ with $x\geq 3$
clever fjordBOT
Denascite
karmic umbra
$x$ is an auxiliary variable that does not exist outside of the braces
clever fjordBOT
rain
karmic umbra
you happen to have an x outside of it that means something else
so you need to declare $x \in A$ for your set $A$
clever fjordBOT
rain
karmic umbra
what are you trying to say
are you just trying to define a set
or are you trying to say something you know (like a variable) is in that set
long jetty
Let's say I have a physics equation where the diameter needs to be an integer and must be at least 3. How is this done?
And I need to imply that x is that
karmic umbra
ok if the diameter is $d$ you write $d \in {}$
clever fjordBOT
rain
karmic umbra
whatever ur set is in that
but often in technical writing it is much more clear to say "Let $d \geq 3$ be a positive integer"
clever fjordBOT
rain
long jetty
And you need to put like {x: x \in Z}, you can't just put like {x \in Z}, right?
You need the x:, right?
long jetty
but often in technical writing it is much more clear to say "Let $d \geq 3$ be a...
That's true.
long jetty
You need the `x:`, right?
Basically like this??
But I'm wondering, isn't it redundant to put x : after the first curly bracket or?
long jetty
Ooh all right just feels redundant
karmic umbra
i assume you just want to learn how to do this notation bc I wouldn't write this in a question
your set is also $A = {x\in \bZ: x \geq 3}$
clever fjordBOT
rain
karmic umbra
I don't need the and symbol
please read this
the thing before the colon is defining the set where x lives
if it just says $x$ it is implicity $\bR$ or $\bC$
clever fjordBOT
rain
karmic umbra
depending on context
long jetty
https://www.mathsisfun.com/sets/set-builder-notation.html
Thanks a lot
And the difference between C (complex) and I (imaginary) is that complex can be written as a mixture of both imaginary and real numbers, while imaginary numbers are solely like 5i, right?
clever fjordBOT
rain
karmic umbra
oh wait
im not sure what convention you have, it may be different, but if I see I, i assume C\R
long jetty
And "such that", i.e. | means?
clever fjordBOT
rain
long jetty
Here I mean
clever fjordBOT
rain
long jetty
**rain**
But why isn't it $A \in {x\in \bZ: x \geq 3}$
I mean why is there an equal sign instead of a belongs to?
clever fjordBOT
Elliot Pixel
long jetty
Whoops I missed the braces
karmic umbra
i am saying $A$ IS that set
clever fjordBOT
rain
karmic umbra
not that it is a member of it
i just defined A that way bc i didnt wanna write it all out
long jetty
Oh and you should mostly always use x for the variable within a set?
long jetty
But A is a variable here, right?
long jetty
A is a "variable" but its a set
What is the difference? Stupid question but this is a new concept to me
karmic umbra
usually when people say variable they mean something that represents a number
there is no precise math definition for a variable
long jetty
But in what situations should you use sets?
signal oar
But in what situations should you use sets?
What do you mean?
odd edgeBOT
@long jetty Has your question been resolved?
remote token
Four circular disks of radius 1 are placed in a box
as shown. Some of the circular discs are partially covered
other circular disks. What is the total area of the
hidden parts of the circular discs?
remote token
this is no help/aid btw
i have literally no clue
i guessed e because i calculated that to be roughly 2-2.5
strange ginkgo
usually i write $\bC \setminus \bR$ but sure
is \b just \mathbb?
steep mantle
could you draw on all the circles so you can see the form of the hidden areas?
remote token
and then i thought about how it covered a bit less than a fourth, maybe a 6th of each. and thats 4 of them so (4/6)*pi= about 2-2.5 so i thought yup that suffices
karmic umbra
is \b just \mathbb?
yeah
strange ginkgo
oh thats cool
strange ginkgo
i guessed e because i calculated that to be roughly 2-2.5
what is the question`?
shaded area?
remote token
yup
steep mantle
like this shows the area where its covered
steep mantle
if you were to draw them how would they look like?
remote token
bro ion got a drawing thing
steep mantle
the key is to split it in half and try to find this shaded area
outer osprey
my bad i did not know
odd edgeBOT
@remote token Has your question been resolved?
terse mauve
What am I doing wrong here?
odd edgeBOT
What am I doing wrong here?
karmic umbra
,w sum (-1)^(n+1) * 3/2^n from n = 1 to infinity
clever fjordBOT
karmic umbra
the first term is not $-3$
clever fjordBOT
rain
karmic umbra
so you should have the top being $-3/2$ as well
clever fjordBOT
rain
terse mauve
Huh?
karmic umbra
the formula you used is a/(1-r) right
where a is the first term of the sequence
you incorrectly put a = -3
when a = 3/2
terse mauve
hmm
i see
so I need to keep the default first term in mind when evaluating even if the re-arranged sum suggests otherwise?
karmic umbra
i don't knwo what you mean by suggests otherwise
but
the formula needs the first term
thats it
terse mauve
i mean looking at my last sum there it really looks like its -3
atleast to me
nvm
im just being stupid
I see
thank you
.close
odd edgeBOT
odd edgeBOT
Available help channel!
uneven panther
I need help
odd edgeBOT
I need help
rapid reef
You flipped the derivative
steady tide
fill in the blank: if f'(x) < 0, then f(x) is .......
A. increasing
B. decreasing
C. flatline
D. doing your mom
steep mantle
D
clear current
It says where it’s decreasing not increasing
uneven panther
You flipped the derivative
meaning?
steady tide
fill in the blank: if f'(x) < 0, then f(x) is .......
A. increasing
B. decreasi...
@uneven panther
answer this question first
steady tide
you see where your mistake at here?
uneven panther
Oh Im STUPIFD
rapid reef
meaning?
Meaning the question asks for negative derivatives but you highlighted positive
steady tide
Oh Im STUPIFD
hi STUPIFD im fungus
uneven panther
uneven panther
Meaning the question asks for negative derivatives but you highlighted positive
I misread it
uneven panther
So is this correct?
clear current
-3 in closed brackets
uneven panther
mb
odd edgeBOT
Available help channel!