Channel closed
Closed by @pine schooner
Use .reopen if this was a mistake.
#help-42
calm coralBOT
graceful dust
also just to be clear you want the set to contain the partial sums and the whole sum
pine schooner
also just to be clear you want the set to contain the partial sums and the whole...
well i was going to do ${\sqrt{2}, \sqrt{2}(1+\frac{1}{4}), \sqrt{2}(1+\frac{1}{4}+\frac{1}{9}),...}$
does that work?
potent lotusBOT
goobybalooby
pine schooner
oh really? isnt the other notation just explicitly writing out the terms of that summation though?
graceful dust
**goobybalooby**
this doesn't include the infinite sum itself
just its partial sums
pine schooner
this is what i have: ${\sqrt{2}, \sqrt{2}(1+\frac{1}{4}), \sqrt{2}(1+\frac{1}{4}+\frac{1}{9}),...}=\sum_{n=1}^{\infty} \frac{\sqrt{2}}{n^2}$
potent lotusBOT
goobybalooby
pine schooner
oh i didnt know
graceful dust
is just a number
it's sqrt(2)*pi^2/6
it's not equal to that set, and it's not in that set
pine schooner
oh okay
so what if i did
${\sqrt{2} + \frac{\sqrt{2}}{4} +\frac{\sqrt{2}}{9}+...+ \frac{\sqrt{2}}{n^2} : n \in \mathbb{N} }=\sum_{n=1}^{\infty} \frac{\sqrt{2}}{n^2}$ ?
whoops
graceful dust
.reopen the channel
pine schooner
.reopen
calm coralBOT
✅
graceful dust
$\{\sqrt{2} + \frac{\sqrt{2}}{4} +\frac{\sqrt{2}}{9}+...+ \frac{\sqrt{2}}{n^2} :...
whatever that is, no
no
potent lotusBOT
goobybalooby
pine schooner
still no?
graceful dust
no
pine schooner
okay
graceful dust
this part is fine
pine schooner
but i just cant say it equals the summation, is that it?
graceful dust
you can write ${\ldots}\cup \left{\sum_{n=1}^\infty \frac{\sqrt{2}}{n^2}\right}$ or something
potent lotusBOT
chmonkey #1 simp
harsh belfry
goobybalooby
pine schooner
oh so that makes it contain the partial sums and the whole sum like you said before?
harsh belfry
i have a question
graceful dust
yes
pine schooner
i have a question
yea?
graceful dust
pine schooner
do you believe peoples dreams have an end?
troll?
drifting seal
do you believe peoples dreams have an end?
drifting seal
im stoned asf rn
look up a philosophy discord
harsh belfry
anyway remember A MANS DREAMS, WILL NEEVR DIE!
yo ur speaking facts
calm coralBOT
calm coralBOT
Available help channel!
daring kraken
calm coralBOT
daring kraken
untold compass
how about exactly at x=0?
calm coralBOT
calm coralBOT
Available help channel!
wanton fiber
for b and c 😭
calm coralBOT
@wanton fiber Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
zealous hawk
calm coralBOT
zealous hawk
how do you do this
median bluff
Just calculate it normally
median bluff
It's just a normal
steel mason
Yep its normal
halcyon rock
we can pair positive and negative numbers
zealous hawk
what
median bluff
Lolll
zealous hawk
ok
calm coralBOT
@zealous hawk Has your question been resolved?
strange summit
How should I approach this? Am I supposed to Utilize trig properties?
strange summit
It's split into two sections, ask the question in the section that says available. There should be a green check next to it
You can also tell if a chanel is open by the available help channel message at the bottom. Also would appreciate it if you deleted your questions. thanks.
zenith island
oooh oh thanks, im sorry for any hindrance
strange summit
How should I approach this? Am I supposed to Utilize trig properties?
I don't know how to tackle this
<@&286206848099549185> I just need something to work with
please
<@&286206848099549185>
<@&286206848099549185> Someone please help me
strange summit
It's differentiation, so he probably won't accept it, also I don't really know what that is
zenith island
It's differentiation, so he probably won't accept it, also I don't really know w...
no diffrentiation
strange summit
No I mean like, the problem set focuses on differentiation, so I have to use it
zenith island
but how can u apply differentiation here, when its a formula based question
do u have the solution
??
strange summit
that's what I'm not sure about
zenith island
try using w(omega)=2(pi)f
just use this formula
zenith island
that's what I'm not sure about
is it a subjective question?
strange summit
No, I think it's trig, but I don't know what equation
median bluff
I think...
zenith island
i even checked the question's answer, seems pretty right
median bluff
It's about using differentiation through the distance huh
strange summit
I'm sure it's correct, but if wants it a specific way, he'll dock points, and will probably know I didn't do it
strange summit
It's about using differentiation through the distance huh
yeah I need to find the rate of change of the angle
Like I need a equation that I'll differentiate
help please
someone help me]
@sly geyser
It's something like this
please help me
@sly geyser
It's called related rates I think
<@&286206848099549185> please. I just need something to work with, not even the answer
remote mural
What grade are u in?
strange summit
12th. It is AB calc
strange summit
How should I approach this? Am I supposed to Utilize trig properties?
this is the problem
remote mural
are u in school rn or can u use internet?
strange summit
I'm working on it at home
strange summit
Oh okay
strange summit
It'll take a look at it. Thank you.
I'll just call it a day in this channel while i'm still online too
.close
amber wedge
Lara hat sich eine Faustregel erstellt, um von einer Funktion auf Eigenschaften der Ableitung schließen zu können. Dabei soll N Nullstelle, E Extremstelle und W Wendestelle bedeuten. Hat z. B. die Funktion f eine Extrem- stelle, dann hat f' eine Nullstelle. „Abwärts" gilt die Regel immer, aufwärts" oft, aber nicht immer. Geben Sie anhand der Funktion f mit f(x) = x^4 eine Folgerung an, welche „aufwärts" nicht gilt.
amber wedge
Lara has created a rule of thumb to be able to infer properties of the derivative from a function. N should mean the zero point, E the extreme point and W the turning point. For example, if the function f has an extreme point, then f' has a zero point. The rule always applies downwards, and often upwards, but not always. Using the function f with f(x) = x^4, state a conclusion which does not hold “upwards”.
tender coral
Lara hat sich eine Faustregel erstellt, um von einer Funktion auf Eigenschaften ...
Was hast du bisher versucht?
amber wedge
Um ehrlich zu sein, nichts
Bei x=0 gibts eine Nullstelle
Und auch ein Extrempunkt
x^4 hat keine Wendepunkte
tender coral
Bedeutet g'(x) = 0 immer Extrempunkt?
tender coral
x^4 hat keine Wendepunkte
Das kann man z.B auch angreifen. Dann würde ich das nehmen, wenn du eh schon selbst draufgekommen bist
tender coral
Doch es gibt VZW bei x=0
Nein, g'(x) = 0 heißt nicht notwendigerweise, dass es einen Extrempunkt gibt. Es kann ja eine Nst. ohne VZW sein. g'(x) heißt es gibt entweder einen Extrempunkt oder einen Sattelpunkt
tender coral
x^4 hat keine Wendepunkte
Aber vergessen wir, was ich gesagt habe und machen das so wie du vorgeschlagen hast:
Mit dem Wissen, dass f keine W besitzt. Kannst du einen Widerspruch in der 3. Spalte finden?
amber wedge
Na die 3. Stalte gibts bei x hoch 4 gar nicht
tender coral
Wie meinst du das? Bzw. was ist überhaupt f' und f'' in dem Fall?
tender coral
Na die 3. Stalte gibts bei x hoch 4 gar nicht
Ah, jetzt verstehe ich. Wir wollen ja von unten nach oben gehen. Vielleicht gibt es ja das N da unten?
graceful dust
Wie meinst du das? Bzw. was ist überhaupt f' und f'' in dem Fall?
das ist überhaupt nicht lustig.
tender coral
das ist überhaupt nicht lustig.
It's you again
amber wedge
??
graceful dust
oh hi oogway long time no see
amber wedge
layla??
graceful dust
graceful dust
She's cyber bullying me 😂
what did i do
tender coral
Making fun of me
graceful dust
tender coral
Are you actually german?
graceful dust
no i’m just a comedian
tender coral
Anyways, let's continue with this problem. We're almost done
tender coral
Ok, was ist f''(x) dann und f''(0)?
amber wedge
Ohhhh
I got it
x=0 is a zero
x=0 is a minima
x=0 ain't an inflexion point
Booyah
tender coral
Yeah
graceful dust
Anyways, let's continue with this problem. We're almost done
i’ve been helping oogway with math since you were in diapers. don’t anyways me
amber wedge
True dat
tender coral
i’ve been helping oogway with math since you were in diapers. don’t anyways me
Ah, that's why when you arrive he immediately solves the problem
graceful dust
you got it
tender coral
i’ve been helping oogway with math since you were in diapers. don’t anyways me
You mean since yesterday?
graceful dust
since an eternity ago
tender coral
since an eternity ago
How do you know? 😂
graceful dust
i was there on that fateful day
calm coralBOT
amber wedge
graceful dust
you’re not supposed to close other people’s channels…
is this your first day on the job
do i have to call eric
amber wedge
Spaßbremse
calm coralBOT
Available help channel!
spring ravine
just want to make this clear
calm coralBOT
just want to make this clear
spring ravine
they took the conjugate of 1/(x-1) to get the x+1/(x^2 - 1), right?
but do you not have to do the same with 2/(x^2-1)? Or can you just pick and choose what fraction to use the conjugate of
I'm not the best at algebra so this may be a dumb question
calm coralBOT
@spring ravine Has your question been resolved?
fleet verge
x-1 and x^2-1 are related
The common factor in both are x-1
x^2-1 = (x-1)(x+1)
Thats why they take x+1
It is like you have 1/2 + 1/4 = 2/4+1/4
Because 4 = 2 * 2 and in the fisrt fraction we have a 2
Which is common with the second
So we only need one of the 2 to multiply the one
But in the numerator of the second fraction we do nothing
tranquil meteor
$$19/25/3/5$$
calm coralBOT
$$19/25/3/5$$
potent lotusBOT
cricketislife
azure willow
(19/25) / (3/5) = (19/25) * 1/(3/5) = (19/25)*(5/3) = (19/5)/3 = 19/15
lunar meteor
how does it become 5/3
because you flip them
like when you want to switch from dividing to multiplying
tranquil meteor
OHHH
im so dumb
how did i not see that
so then it would be 19x5/25x3
and 95/75 = 19/15
sorry for this
waste of time for you guys
thanks anyways
.close
crystal forge
$\int\frac{dx}{\ln x}$
calm coralBOT
$\int\frac{dx}{\ln x}$
potent lotusBOT
Soosh
inner delta
!status
calm coralBOT
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
1
celest bluff
integration by parts
inner delta
You can take it as 1(dx/lnx)
crystal forge
and differentiating that helps, you sure?
celest bluff
u can use LIATE to help u choose what to differentiate and what to integrate
crystal forge
u can use LIATE to help u choose what to differentiate and what to integrate
after integrating by parts for one step i get $\frac{x}{\ln x}+\int\frac{dx}{\ln^2 x}$
potent lotusBOT
Soosh
crystal forge
i used u = 1/ln x and dv = dx for first step, but now i still don't see how this integral is doable, @inner delta @celest bluff
celest bluff
try u=lnx
crystal forge
i don't have a 1/x to build the du
inner delta
i used u = 1/ln x and dv = dx for first step, but now i still don't see how this...
Hmm I should've looked into it a bit more deeply
Lemme try again
The answer to it may not be as simple
potent lotusBOT
crystal forge
https://en.wikipedia.org/wiki/Logarithmic_integral_function
ok apparently it's a whole special thing i guess it just is not trivial to integrate so no wonder i was having trouble
.close
blazing coyote
if $\cos\left(x\right)-\sin\left(\alpha\right)\cos\left(\beta\right)\sin\left(x\right)=\cos\left(\alpha\right)$ find tan(x/2)
potent lotusBOT
Why am. I here
blazing coyote
don't see a way foward tbh
blazing coyote
yeah
upbeat venture
I thought it was being multipled lol
blazing coyote
but the LHS is a mess
upbeat venture
hmm
fringe reef
if $\cos\left(x\right)-\sin\left(\alpha\right)\cos\left(\beta\right)\sin\left(x\...
is that the original problem
blazing coyote
yeah
the OG problems states then find tan(x/2) which is basically the same thing
maybe I solve for cos(x)
That's doable
but it ain't going to be pretty
cos(x)=u
mortal orbit
quick tip: you're gonna have to use double angle formula at some point
blazing coyote
hmm
gusty steeple
Maybe try cosx=cos(x/2+x/2)
blazing coyote
that's cos^2(x/2)-sin^2(x/2)
blazing coyote
$\cos\left(x\right)-\sin\left(\alpha\right)\cos\left(\beta\right)\sin\left(x\right)=\cos\left(\alpha\right)$when I divide this?
potent lotusBOT
Why am. I here
mortal orbit
ok so we're almost there, I see a solution but not pretty so hang on
use that cos(x) = cos^2(x/2)-sin^2(x/2) and sin(x) = 2sin(x/2)cos(x/2)
factor the LHS by cos^2(x/2)
what do you get?
blazing coyote
working on it
$\cos^2\left(\frac{x}{2}\right)\left[1-\tan\left(\frac{x}{2}\right)\sin\left(\alpha\right)\cos\left(\beta\right)\right)=\sin^2\left(\frac{x}{2}\right)+\cos\left(\alpha\right)\ $
$\cos^2\left(\frac{x}{2}\right)\left[1-\tan\left(\frac{x}{2}\right)\sin\left(\alpha\right)\cos\left(\beta\right)\right)=\sin^2\left(\frac{x}{2}\right)+\cos\left(\alpha\right)$
potent lotusBOT
Why am. I here
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
mortal orbit
no you should have left sin^2(x/2) on the LHS
blazing coyote
ah, to get tan^2(x/2)?
mortal orbit
yes
blazing coyote
I can still get that here, right?
blazing coyote
ok, so that gives
$\cos^2\left(\frac{x}{2}\right)\left[1-\tan^2\left(\frac{x}{2}\right)-\sin\left(\alpha\right)\cos\left(\beta\right)\tan\left(\frac{x}{2}\right)\right]=\cos\left(\alpha\right)$
potent lotusBOT
Why am. I here
blazing coyote
please do
mortal orbit
write cos^2(x/2) in terms of cos(x)
blazing coyote
$\cos\left(\frac{x}{2}\right)=\ \sqrt{\frac{\left(1+\cos\left(x\right)\right)}{2}\ }$
potent lotusBOT
Why am. I here
blazing coyote
now cos(x)=
mortal orbit
no need for roots since we're working with cos^2(x/2)
blazing coyote
so that would be
mortal orbit
(and sometimes cos(x/2) = -that)
blazing coyote
$\frac{\left(1+\frac{\left(1-\tan^2\left(\frac{x}{2}\right)\right)}{\left(1+\tan^2\left(\frac{x}{2}\right)\right)}\right)}{2}$
potent lotusBOT
Why am. I here
blazing coyote
which is
mortal orbit
let t = tan(x/2), we better simplify notations
potent lotusBOT
Why am. I here
blazing coyote
so $\frac{1}{1+t^2}$
potent lotusBOT
Why am. I here
mortal orbit
great
mortal orbit
**Why am. I here**
now solve for t
blazing coyote
$\frac{1}{1+t^2}\left(1-t^2-\sin\left(\alpha\right)\cos\left(\beta\right)t\right)=\cos\left(\alpha\right)$
potent lotusBOT
Why am. I here
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
mortal orbit
sure
blazing coyote
.close
calm coralBOT
calm coralBOT
Available help channel!
analog heart
Let v_t be the speed of the troop and v_s be the speed of the soldier. If x is the distance travelled by troop till the soldier reaches the head of the column, then v_t = (x)/t and v_s = (x+5)/t because the soldier covered x + length of troop in time t. Now the soldier turns around and starts moving at the same speed as before, now the troop covers 5 - x meters distance, v_t = (5 - x)/t' , v_s = y/t' , we know 5 - x + y = 5 => x = y, but I'm stuck here
analog heart
I guess I need to find the value of x but there are too many variables
Ohh nvm got it
.close
analog heart
Can someone help me with (2)?
calm coralBOT
Can someone help me with (2)?
exotic blaze
Can someone help me with (2)?
You’ll want to use the original equality, take the reciprocal of everything then square and square everything on the original equality too
The use these two equalities to look at the given statement
analog heart
You’ll want to use the original equality, take the reciprocal of everything then...
Take the reciprocal of everything? you mean square of 1 over a+b+c+d = 1 over 4 squared?
Or take reciprocal of individual terms?
exotic blaze
Individual terms for now
(1/a + 1/b +1/c +1/d)^2 = (1/4)^2
And also (a+b+c+d)^2= 4^2
analog heart
(1/a + 1/b +1/c +1/d)^2 = (1/4)^2
How's that even true? we can't distribute the denominator over numerator
1/(a+b+c+d) = 1/4
exotic blaze
1/(a+b+c+d) = 1/4
Sorry yeah that’s what I mean
calm coralBOT
@analog heart Has your question been resolved?
analog heart
Nah I'm unable to extract anything out of these literally same equalities
dusky flax
wait i think i can solve this
calm coralBOT
@analog heart Has your question been resolved?
calm coralBOT
@analog heart Has your question been resolved?
calm coralBOT
@analog heart Has your question been resolved?
calm coralBOT
@analog heart Has your question been resolved?
inland sphinx
I'll try another approach
potent lotusBOT
7aman
inland sphinx
,w expand (a+b+c+d)^2
potent lotusBOT
calm coralBOT
@analog heart Has your question been resolved?
glad tartan
Can someone help me with (2)?
Apply AM GM HM inequality and apply Titu’s lemma and then simplify
analog heart
Apply AM GM HM inequality and apply Titu’s lemma and then simplify
I'm pretty new to inequalities, can you explain a bit more
We can apply AM-GM only if all numbers are non-negative, but here that's not the case
flint condor
Can someone help me with (2)?
But that's not true if we take big by module a and small b,c,d if a,b,c,d can be negative
glad tartan
We can apply AM-GM only if all numbers are non-negative, but here that's not the...
Excuse me
glad tartan
I'm pretty new to inequalities, can you explain a bit more
Don’t worry
I gotchu
U can’t do those cuz you’re saying they can be negative
analog heart
Wait I'm not even sure if the question is even correct
analog heart
They’re asking u to prove it right?
Yes
But take the case a = 3, b = 3, c = -1, d = -1 , it doesn't hold true
glad tartan
Can someone help me with (2)?
a+b+c+d = 4
Divide by abcd on both sides
Now apply AM GM inequality
glad tartan
But take the case a = 3, b = 3, c = -1, d = -1 , it doesn't hold true
Abcd are all positive then
analog heart
Abcd are all positive then
Yeah
glad tartan
a+b+c+d = 4
Divide by abcd on both sides
Now apply AM GM inequality
Apply AM GM inequality normally and for this also
AM>_ GM
You will get AM = GM
THEREFOR A=B=C=D
a=b=c=d=1
analog heart
You will get AM = GM
How?
glad tartan
Can someone help me with (2)?
All of them = 1 is the only solution
Bcoz if a or b is a fraction the following won’t hold true
analog heart
Apply AM GM inequality normally and for this also
On what elements you're applying AM-GM?
glad tartan
a+b+c+d=4 and 1/bcd+1/cda+1/bca+1/abd = 4/abcd
analog heart
.close
calm coralBOT
calm coralBOT
Available help channel!
normal wasp
1,8,22,43 ... sequence diffrenc to the next member makes a aretmatic sequence so like 8-1 is 7 then 22-8 is 14 and so on i need to find the original sequences what member would be 35351
amber bolt
uh
so it's like you add 7,14,21,28... and you get 35350
you probably make a quadratic equation
and that's all
inner delta
1+7=8
8+14=22=1+(7+14)
22+21=43= 1+(7+14+21)...
amber bolt
i guess you start at 0
inner delta
The sequence starts from 1
inner delta
What starts from 0?
inner delta
Oh you mean the sum of terms(7,14,..)? Then yes
I thought you meant the starting term of the sequence (which is 1 as it's given)
normal wasp
Nono
The original sequence
I need to find what member that number is in the original sequence
inner delta
Yes ik
amber bolt
that's what we're doing
inner delta
1+7=8
8+14=22=1+(7+14)
22+21=43= 1+(7+14+21)...
Do you see the pattern here?
amber bolt
@normal waspit means you want to find the point where the sum of 0,7,14... is 35350
at that point the orginal sequence will hit 35351
you make an equation for the sum of arithemtic sequence
normal wasp
Pls tell me quick i gtg in 5 mins
Do i use the sum formula?
Of the arethmatic sequence?
@amber bolt
amber bolt
🐸
normal wasp
So sn?
calm coralBOT
@normal wasp Has your question been resolved?
boreal ravine
I know the answers, I just need to understand how to get the first answer using sigma because when I used $$ \frac{\left(\sum _{i=1}^{999}:i\right)}{2} $$ it seems to be off by 250
potent lotusBOT
itzaine
boreal ravine
the answer is 250k, the answer i got was 249750
winged smelt
$\frac{1 + 2 + 3 + 4 +...+999}{2}$
potent lotusBOT
ColdTee
winged smelt
How does that relate to $1 + 3 + 5 +....+999$?
potent lotusBOT
ColdTee
winged smelt
Was there any reason for you write it like that?
boreal ravine
well i figured maybe it was $\frac{1 + 2 + 3 + 4 +...+999}{2}$ but after you get that answer you divide by 2 to get it without the numbers in the middle for ex 2,4,6, etc. but it didnt work so i just need to tweak it more until its closer
potent lotusBOT
itzaine
boreal ravine
i know i could use sn but i think the work wants me to use sigma
winged smelt
So according to you if you divide the result by 2 the numbers in between 2,4,6... should disappear or sth?
boreal ravine
So according to you if you divide the result by 2 the numbers in between 2,4,6.....
supposedly just a quick formula which didnt work so at this time no.
umbral condor
i know i could use sn but i think the work wants me to use sigma
As in this?
Sum of odd numbers
2x-1 represents the odd numbers
boreal ravine
As in this?
true but it needs something done to it i suppose because
i was also going for that $\left(\sum _{i=1}^{999}:2i-1\right)$
potent lotusBOT
itzaine
winged smelt
Well that's just $2\sum_{i = 1}^{500} i - 500$
potent lotusBOT
ColdTee
winged smelt
i was also going for that $\left(\sum _{i=1}^{999}\:2i-1\right)$
The upper limit is not correct in this case.
umbral condor
As in this?
If you solve this you'll get 250000
boreal ravine
The upper limit is not correct in this case.
i see
like how do I go about getting 500 from
boreal ravine
understandable
i think ill move on to question 2 as soon as i get this written down
thank you both 
.close
calm coralBOT
calm coralBOT
Available help channel!
wild quail
what does this mean
calm coralBOT
what does this mean
unkempt rain
¹⁰C5
calm coralBOT
calm coralBOT
Available help channel!
dense mason
We can't say for sure can we?
calm coralBOT
We can't say for sure can we?
fleet pine
yes
unkempt rain
Yea
dense mason
yes
If the intersection was equal to the product of the individual probabilities, that would mean they're independent right?
fleet pine
yes
calm coralBOT
fleet pine
np
calm coralBOT
Available help channel!
bright cape
I feel like I have to write up the balance equations but I am not sure how to include the probability that someone leaves. I am confused when the structure does not exactly follow the M/M/2
bright cape
I am also confused because $\frac{\lambda}{c \mu} = 1$
potent lotusBOT
williaaam.
bright cape
<@&286206848099549185>
calm coralBOT
@bright cape Has your question been resolved?
calm coralBOT
@bright cape Has your question been resolved?
calm coralBOT
@bright cape Has your question been resolved?
calm coralBOT
@bright cape Has your question been resolved?
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mighty meadow
how do I evaluate monomials?
calm coralBOT
how do I evaluate monomials?
graceful dust
mighty meadow
graceful dust
!original
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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.
graceful dust
darn you beat me
mighty meadow
darn you beat me
rahhh
graceful dust
,rotate
potent lotusBOT
graceful dust
this question is a bit
graceful dust
personally i do not know what someone asking me for if they ask me to evaluate y^4 when x=5
oh
mighty meadow
oh wait
mighty meadow
wait im good
idk this is stupid I just realized that the formulas for the variables are up there
idk why they aren't on the question
. close
.close
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mighty meadow
I'm the real slim shady
graceful dust
nah
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ruby goblet
is the answer
calm coralBOT
is the answer
ruby goblet
97 or 98
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ruby goblet
<@&286206848099549185> \
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ruby goblet
<@&286206848099549185>
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ruby goblet
one of these
idk which one tho
spark stratus
is the answer
how did you get 97 or 98
ruby goblet
how did you get 97 or 98
my friend got 98 i got 97
spark stratus
how did you get 97
spark stratus
for next time, dont write 2100 - 2000 = 100/4 = 25-1 = 24
write 2100 - 2000 = 100
100/4 = 25
25 - 1 = 24
ruby goblet
okay
spark stratus
2004, 2008, 2012, ... 2100 are 25 years
2004, 2008, 2012, ... 2096 are 24 leap years
2104, 2108, 2112, ... 2196 are 24 leap years
2204, 2208, 2212, ... 2296 are 24 leap years
2304, 2308, 2312, ... 2396 are 24 leap years
2000 and 2400 are both leap years
24 + 24 + 24 + 24 + 1 + 1 = 98
it looks like you forgot that both 2000 or 2400 are leap years, so you should 25 + 24 + 24 + 25 instead of 24 + 24 + 24 + 25
ruby goblet
it looks like you forgot that both 2000 or 2400 are leap years, so you should 25...
okay yeah i forgot the 2000
thanksp
spark stratus
np
ruby goblet
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lucid oxide
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lucid oxide
Help expand this please
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lucid oxide
<@&286206848099549185>
pseudo wedge
!status
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2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
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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
Expand
Like yea expand
I know double angle, I used
Then ok, still can't figure out how to expand into that
pseudo wedge
Maybe try starting from the right hand side
lucid oxide
Help expand heh
I mean from right-hand side doesn't make it easier to expand for me
Well, I know it's still double angle formula but it's so long that idk how to simplify back
lucid oxide
Try taking the 1/2 to the other side, that will simplify things
This refers to show that they both equal btw
lucid oxide
You mean you wanna prove it via showing that they sum to 0?
God, I hate this expanding stuff, tho its better then Metric space topology XD
pseudo wedge
Honestly you could just replace $$\sec^2\frac{\theta}{2}=\frac{2}{\cos\theta+1}$$
potent lotusBOT
kheerii
pseudo wedge
And a similar thing for the tan term
And do the simplification
It shouldn’t be that hard, just some algebra
lucid oxide
It shouldn’t be that hard, just some algebra
Annoying tho, haven't gotten in touch with actual brute force long after learning Honor mathematical analysis
pseudo wedge
There probably is a better way tbh
I just can’t see it
I don’t see where the (1-a/1+a)^2 term would come from
lucid oxide
I don’t see where the (1-a/1+a)^2 term would come from
Tbh i find it more relaxing to see brute force then seeing these shits XD
But equally bad XD
Anyways, ok I try again
wide anchor
Did I do 11 right?
calm coralBOT
Did I do 11 right?
surreal patio
Did I do 11 right?
?
derivative of x is 1 , y(x) should be just (y(x))' , no?
also u need to seperate the (y(x))' and have them all at 1 side
half sparrow
No idea on (b)
calm coralBOT
No idea on (b)
half sparrow
This leads me nowhere
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half sparrow
<@&286206848099549185>
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sharp burrow
Is there any way I can compute the maximum number of "zero" elements in the inverse of a nxn matrix (non singular)? as well as the special case in which the matrix is symmetric
glass heart
you can look at the adjugate matrix I suppose
but unless you know more about the matrix I doubt you can gain much information
sharp burrow
all I know is this
glass heart
obviously the inverse is also nonsingular, so can have at most n^2-n zeros
sharp burrow
yes
glass heart
and there are examples where you have n^2-n zeros. so you cant make a better general bound
sharp burrow
altho that doesnt seem to be the case when the matrix is known to be symmetric
sharp burrow
identity matrix
has the most number of zeroes possible if it is invertible, it makes sense where the n^2 - n comes from
how would it change if the original matrix is symmetric tho
sharp burrow
oh, so you say it'll still be n^2 - n?
glass heart
yes
sharp burrow
yes
https://math.stackexchange.com/questions/4244205/maximum-number-of-zero-elements-entries-in-a-1 this post says otherwise and my textbook answer key agrees with it
spare beacon
That says real positive elements. You can't just arbitrarily drop key words.
glass heart
if the entries of A arent allowed to be zero that changes things
sharp burrow
ah, yea
why does the OP use that very specific example?
with only 2 distinct elements
glass heart
because it works
sharp burrow
without the loss of generality?
glass heart
this has nothing to do with loss of generality
they are given an example to show that the inverse can have n^2-2n zeros
and then they prove that this is indeed the max
so there is no better bound you can give
sharp burrow
they are given an example to show that the inverse can have n^2-2n zeros
The cofactor of any other entry in the same column in A−1 is zero.
How does having exactly one non zero entry in a row explain this?
nvm got it, thank you for your help and time
!close
.close
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tough tide
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summer herald
hi, everyone i was looking at an example problem but cannot figure out where the upper bound 10 is coming from
vivid vine
when you substitute bounds changes
u= 5+x upper bound x= 5 upper bound u =5+5=10
same with lower bound
summer herald
then does the lower bound 0 is from the origin right?
vivid vine
lower bound for x was 0 lower bound for u is 5 cuz 0+5=5
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sly crane
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sly crane
Just wanted to ask why there’s no reaction force going up vertically for object P
^^ diagram above is the worked solutions diagram
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crystal forge
$\int\sqrt{3+2\cos\theta-2\sin\theta}d\theta$ hm how does one approach this integral?
potent lotusBOT
Soosh
blazing coyote
weistress sub probably?
crystal forge
no idea what that is
it's from like a high school calc BC problem so i don't think it should need anything too advanced
blazing coyote
use the half angle formulae
first
and then maybe multiply and divide by sec^2(x/2)
crystal forge
like these?
blazing coyote
I mean like sin(x)=2tan(x/2)/(1+tan^2(x/2))
blazing coyote
!original lol
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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.
crystal forge
part d)
blazing coyote
can you convert that into it;s cartesian form( I don;t know polar maths ) so I can't help with that part
crystal forge
so have r = 1 + cos t
dr/dt = 1 - sint
so i think the integral would be
$\int_0^{\frac{5\pi}{3}}\sqrt{(1+\cos t)^2+(1-\sin t)^2}dt$
potent lotusBOT
Soosh
crystal forge
can you convert that into it;s cartesian form( I don;t know polar maths ) so I c...
well this is formula for arc length between 2 thetas, so im really just plugging into that
blazing coyote
hmm
crystal forge
oh wait
the problem is just "write an expression that represents the distance traveled" i guess it doesnt actually expect you to evaluate it maybe
blazing coyote
maybe, yeah
crystal forge
so maybe just wants you to write the integral 🤷♂️
blazing coyote
,w $\int\sqrt{(1+\cos t)^2+(1-\sin t)^2}dt$
potent lotusBOT
blazing coyote
almost surely
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cedar ether
Consider the following series $\sum _{k=1}^{\infty }\frac{\left(-1\right)^k}{\ln k+\frac{\left(-1\right)^k}{k^2}}.$ Is it convergent? For large enough $k$, it looks like we get an alternating $1/\ln k$ series and it looks tempting to apply the alternating series test. However, for that I need to verify that the terms are decreasing and I'm stuck on that. I don't know where to go from $$\frac1{\ln k+(-1)^k/k^2}\geq \frac1{\ln(k+1)+(-1)^{k+1}/(k+1)^2}.$$ Any ideas on how I can proceed?
potent lotusBOT
Philip
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cedar ether
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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
tender pelican
hmmm
they share a side, AB
@potent lotus
so
[|AB| \times |BC| = 4 \times |AB| \times |BM|]
potent lotusBOT
General_Jacob
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onyx quiver
my homework is to find a romantic comedy tagline for a movie that is related to calculus
onyx quiver
so far i have
"you're out of my range"
does anyone know how i can continue this ?
I dont have enough math logic
dull wagon
make up your own or find an existing one
austere spoke
are you the square root of -100? Because you are a 10 but too good to be real
onyx quiver
are you the square root of -100? Because you are a 10 but too good to be real
THATS GOOD
austere spoke
😂
onyx quiver
Are you a complex number
onyx quiver
are you the square root of -100? Because you are a 10 but too good to be real
DID YOU COME UP WITH THAT??
austere spoke
DID YOU COME UP WITH THAT??
nah one of my friends told me that a while ago lol
austere spoke
fax
onyx quiver
Im writing that down
kind wagon
do you want calculus pick-up lines?
kind wagon
i don’t need to take derivatives to see how our relationship is changing
onyx quiver
i don’t need to take derivatives to see how our relationship is changing
LOOL
IM USING THAT
Did you come up w that on the spot?
kind wagon
or if you want a super nerdy one, you must be the result of a complex conjugation because you have a real part that’s positive
onyx quiver
Im scared if i win hes gonna google it and see if i copied it
onyx quiver
or if you want a super nerdy one, you must be the result of a complex conjugatio...
LOL
kind wagon
Did you come up w that on the spot?
yeah i have a talent for this
onyx quiver
amazing
kind wagon
are you a definite integral? because you add meaning to my area
onyx quiver
LOL
can you make one about this
"you are out of my range"
like something a silly nerdy boy would say
I cant figure out how to end it
You are out of my range so i'll stay in my domain
Ugh its too corny
kind wagon
hmmmmm
out of range huh
are you a graph of a function? because every time i try to plot my feelings for you, they are out of range
onyx quiver
oooooh good one
kind wagon
nah this doesnt make much sense
onyx quiver
Its too lovey tho
we need to be able to laugh
because its so stupid
ur first one was #1
kind wagon
if you want a simple one
are you a pi/2 angle? because you look just about right
or 90 instead of pi/2
onyx quiver
LOL
So far in calc we've learned
Limits, derivatives, related rates, and proofs
OOH so one ab proofs
kind wagon
cant really do much with proofs
topaz raft
my homework is to find a romantic comedy tagline for a movie that is related to ...
what
onyx quiver
Are you a derivative because our relationship is changing and ___
topaz raft
kind wagon
try something about constant love and derivative is 0
topaz raft
are you a derivative because I wanna be tangent to those curves
kind wagon
our love’s derivative must be 0 because its constant or something like that
onyx quiver
yes
kind wagon
BRO
onyx quiver
yes
kind wagon
i have the best one yet
kind wagon
can we be like $f(x) = \sin(x)$ and $g(x) = \arcsin(x)$
ok this sounded better in my head
onyx quiver
LMAOOOOO
potent lotusBOT
dqvidutzul
potent lotusBOT
dqvidutzul
onyx quiver
OMG
THERE WAS THIS ONE INEQUALITY THAT IF YOU SOLVE YOU GET I ❤️ U OR SOMETHING
9x-7i>3(3x-7u)
kind wagon
oh yeah
onyx quiver
but is that really calculus related
kind wagon
there is also a graph for a heart
potent lotusBOT
kind wagon
huh
kind wagon
how tf do i solve this
yeah but this is not full
if x is 0 you cant divide by x
but lets skip that
wait you subtract it my bad
yeah at the second line you should add |(-1)
multiplying it all by -1
and changing the sign
then dividing by 7
onyx quiver
okok
lucid knot
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vagrant quiver
helpppppppppppp
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helpppppppppppp
heavy bough
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steel tide
calm coralBOT
vivid vine
<@&268886789983436800> hes spaming the same question on multiple help channels
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@steel tide Has your question been resolved?
vagrant quiver
@vivid vine
steel tide
.reopen
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graceful dust
210 is a weirdly worded question (i would say it has infinitely many constant subsequences lol) but yea i agree with b
for 211 why c?
vagrant quiver
5 6 7 and 8 please helpp
graceful dust
5 6 7 and 8 please helpp
!occupied
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5 6 7 and 8 please helpp
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).
graceful dust
210 is a weirdly worded question (i would say it has infinitely many constant su...
not that it matters much but what it should say is like, how many real numbers x are there for which there is an x-constant subsequence
and the answer to that would be 2
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graceful dust
incase this times out you can take {1/2^n} as counterexample for c
steel tide
Yes that is what i was saying when limit n tends to infinity an=1/2
Oh it will be A
@graceful dust
graceful dust
yea me thinks so too
steel tide
210 is a weirdly worded question (i would say it has infinitely many constant su...
It can have infinite subsequence then. Why are we choosing only 2 subsequence (0,0,0,0,) and (2,2,2,2)
graceful dust
i wouldn’t worry about it
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restive dove
How would I do this
restive dove
<@&286206848099549185>
restive dove
Ive
untold compass
so like 10*.5^2 + 10*.5^2, and that'll get the answer
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turbid iris
guys how do i graph this?
calm coralBOT
guys how do i graph this?
turbid iris
i mean i can find x and y intercepts just fine but how do i find the vertex?
atomic idol
i mean i can find x and y intercepts just fine but how do i find the vertex?
the vertex will occur at the x-value which makes the inside of the square root be 0
turbid iris
wdym
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winter elbow
guys how do i graph this?
Have you squared both sides?
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turbid iris
Guys I’m about to goon 😩😩
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lucid oxide
Help with b please, I tried integrate it normally then it turned out really ugly ( Which I cant do anything about it to prove part c, and tangent(x/2) exists )
lucid oxide
Idk how to deal with it
neon sage
why dont you just u sub u = tan t/2
lucid oxide
why dont you just u sub u = tan t/2
I integrated whole thing and its not even usable lol
neon sage
what did you get
lucid oxide
Normal apporach is just u = tan t/2 , then you trigo sum tan
This is easy to find out
But then it turned out something real ugly
And i cant even use it
Cus its not even defined XD
Normally you should get
$$tan^{-1}(\dfrac{tan{\frac{tan\beta}{2}}}{L} -tan^{-1}(\dfrac{tan{\frac{tan\alpha}{2}}}{L}$$
potent lotusBOT
Catto Saint
lucid oxide
Where
lunar lotus
Hello
potent lotusBOT
Catto Saint
lucid oxide
So yea
I integrated this shit
But then its not even usable
In part c
And its undefined too
Denote $L = \dfrac{1+a}{1-a} $
$$tan^{-1}(\dfrac{tan{\frac{tan\beta}{2}}}{L} -tan^{-1})(\dfrac{tan{\frac{tan\alpha}{2}}}{L})$$
potent lotusBOT
Catto Saint
lucid oxide
I mean this
XD
A damn, mistyped
Anyways yea, idk how to continue after getting this shit
potent lotusBOT
Catto Saint
