so it goes 1, -1, 1, -1
#help-27
timber pebble
woven radishBOT
jan Niku
timber pebble
so this is the last part we need to build
how do we write 1, -1, 1, -1, 1, .... in terms of m?
floral badger
-1^m
woven radishBOT
jan Niku
floral badger
so we wanted the 1s?
timber pebble
the 1s?
floral badger
oh -1^m makes it flip between 0 and 1
timber pebble
well theres 2 big pieces here
one is that we realized our coefficients were going to be 0 half the time
0,1,0,-1,...
so, we reindexed.
that created all these 2m+1 pieces
when we did that, we created this term $f^{2m+1} (x)$
woven radishBOT
jan Niku
floral badger
so we ignored the 0s
floral badger
ye
timber pebble
the (-1)^m just makes it alternate
floral badger
thats what i asked
timber pebble
oh 
well okay anyways
if youd like you can believe me that this is convergent for all x
if you dont you can do the ratio test
lets go ahead and use it for your problem
you wanna write $7 \sin (5x)$ as a series
floral badger
so here we need to ignore the 0 case
Order f(x) f(0)
0 7sin5x 0
1 35cos5x 35
2 -175sin5x 0
3 -875cos5x -875
4 4375sin5x 0
woven radishBOT
jan Niku
timber pebble
so here we need to ignore the 0 case
Order f(x) f(0)
0 ...
oh, you mean 0 as in order = 0
floral badger
no
timber pebble
yea we need to ignore every other term
floral badger
when f(0) = 0
timber pebble
right, yea
we need to reindex to avoid those terms
is that alright? were almost done but i dont wanna move on if youre still curious about the process
floral badger
**jan Niku**
so this applies to 7sin5x basically
timber pebble
it does, yea
the series is convergent for any input
so, we can just input 5x
and, we can multiply both sides of f(x) = series by 7
floral badger
for x
timber pebble
to get 7 f(x) = 7 series
timber pebble
for x
yea
youll get $7 \sin (5x) = 7 \sum _{m=0}^\infty \frac{(-1)^m (5x)^{2m+1} }{ (2m+1)! }$
woven radishBOT
jan Niku
timber pebble
again exercise is use the ratio test to make sure this is actually convergent
floral badger
(-1)^m (7sin5x)^(2m+1) / (2m+1)!
timber pebble
well you cant bring the 7 inside the power like that
the way to think of this is maybe to write like
$\sin (5x) = \sum _{m=0}^\infty \frac{(-1)^m (5x)^{2m+1} }{ (2m+1)! }$
woven radishBOT
jan Niku
timber pebble
now, multiply both sides by 7
floral badger
7(-1)^m * 5^(2m+1) *x^(2m+1) / (2m+1)!
timber pebble
yea
floral badger
what do we do now?
floral badger
cant be
timber pebble
why not?
floral badger
it wants it as n
timber pebble
swap m for n
floral badger
oh
timber pebble
its just a variable of summation
you can make it anything you want
other than x i guess
floral badger
floral badger
oh i forgot it
fierce cedar
devout snowBOT
fierce cedar
Can someone explain to me how they got those numbers in AD
silver fjord
are you talking about the 1 and 4?
fierce cedar
Yes
silver fjord
you see the small triangle on the bottom left of the drawing?
it's base is 1 unit, it's height is 2 units
you see that?
fierce cedar
Yea
silver fjord
Good. Now since that is a right triangle, you can use the Pythagorean theorem
fierce cedar
But I see 4
woven radishBOT
TooManyCooks
fierce cedar
Can you show it
silver fjord
here, c would be the line AD
fierce cedar
It goes up four
fierce cedar
Yes
silver fjord
those are just grid lines
what matters are the numbers associated to them
the coordinates that are relevant here are 3 and 1
to get the length of the side, you just subtract 3 and 1, which is 2
does that make sense?
fierce cedar
Length is height ?
silver fjord
i'm not sure i follow. what do you mean
fierce cedar
You said height is 2units and length of side is 2
silver fjord
length is just another word for distance
height is just another word for "vertical" distance
fierce cedar
It would be better if you drew
silver fjord
so yes i guess
fierce cedar
Ok nvm I got it
silver fjord
cool
silver fjord
if you draw a right triangle with CD as the hyptonuse, what are the length of that right triangle's sides?
fierce cedar
8,3
devout snowBOT
@fierce cedar Has your question been resolved?
short barn
devout snowBOT
woven radishBOT
keen nacelle
How would I solve b^x +b^(1-x) = b+1
devout snowBOT
How would I solve b^x +b^(1-x) = b+1
keen nacelle
where b is a positive constant
i tried rearranging and using logs, but did it wrong and got nowhere
$b^x +b^{1-x} =b+1$
ugh, kinda that but the 1-x is raised
yes that
woven radishBOT
UsingApp
gleaming socket
Can you make 1 base b
gleaming socket
Write 1 as b^something
devout snowBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #βhow-to-get-help for instructions.
keen nacelle
!status
devout snowBOT
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
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
Right so b^(1-x) can be b/b^x ?
gleaming socket
Write 1 as b^something
Forget this step
keen nacelle
yes
keen nacelle
Right so b^(1-x) can be b/b^x ?
yes
gleaming socket
After converting that, multiply both sides by b^x, see what you get
keen nacelle
u get b^2x +b = b^x+1 +b^x
i figueed it out , but idk hoe to justify its exhaustive
x= 0 or 1
gleaming socket
How b^(2x)?
keen nacelle
i rhink
gleaming socket
Oh yeah
keen nacelle
<@&286206848099549185>
gleaming socket
So like (b^x)^2 + b = (b+1)b^x
gleaming socket
What if you try subbing b^x as m?
woven radishBOT
Blue Guilmon
rigid vapor
Replace $b^x$ by a dummy variable say $y$ and you get the polynomial in $y$, that is, $y^2-(b+1)y+b=0$ solve for zeros of $y$ then substitute back in and you get two separate equations of $b^x$ which may or may not have solutions depending on what the zero is
woven radishBOT
Blue Guilmon
rigid vapor
Try this
rigid vapor
**Blue Guilmon**
I am on my phone so I can't do it myself but this should work unless I messed up this step somehow
You can even use the qaudratic formula tbh
Your solution will be $x=\log_{b}(\frac{b+1\pm\sqrt{(b+1)^2-4b}}{2})$
woven radishBOT
Blue Guilmon
rigid vapor
This will depend on two things, if $(b+1)^2-4b>0$, if $b>1$, or if the inside of the log is >0 as well for whether or not real solutions exist
woven radishBOT
Blue Guilmon
rigid vapor
Complex solutions are a bit more complicated it's been a while since I've used the full logarithmic function on the complex plane so I can't help you there from my phone
Sorry I guess I didn't see you had already done it lol, my bad
Just keep in mind polynomials are very versatile, you can always substitute in portions of an equation for a dummy variable and sometimes retrieve a polynomial equation which may be simple enough to solve independently to come up with conclusions on solutions
devout snowBOT
@keen nacelle Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
solar goblet
Solve $\log_3x\log_9x\log_{27}x\log_{81}x = \frac23$
devout snowBOT
Solve $\log_3x\log_9x\log_{27}x\log_{81}x = \frac23$
woven radishBOT
FungusDesu
vapid nest
Solve $\log_3x\log_9x\log_{27}x\log_{81}x = \frac23$
put it under a common based
solar goblet
So after simplifying everything I get $\log_3x = 2$ and found x = 9, but what I don't get is why there is also $x = \frac19$
woven radishBOT
FungusDesu
past scaffold
$\log_3x=-2$ is possible as well
woven radishBOT
sirus
solar goblet
oh right, before that I got $\log_3^4x = 16$
woven radishBOT
FungusDesu
past scaffold
So -2 is also a solution
devout snowBOT
devout snowBOT
Available help channel!
solar isle
I'm currently facing a difficult situation and I could use some guidance. I'm feeling lost and unsure of how to proceed, so any assistance you can provide would be greatly appreciated.
devout snowBOT
I'm currently facing a difficult situation and I could use some guidance. I'm fe...
@solar isle Has your question been resolved?
devout snowBOT
@solar isle Has your question been resolved?
solar isle
<@&286206848099549185>
crisp adder
Let's look at 3 first to see whats happening
Each A_n is a subset of real numbers for various values of n
for example, when $n=1$, we have $A_{1}=\left{ x \mid x>2-\frac{1}{1}\right}$. This is the subset $(1,\infty)$ in interval notation.
woven radishBOT
pencentre
crisp adder
Would you be able to figure out the interval for n=2 in part 3?
devout snowBOT
@solar isle Has your question been resolved?
rigid vapor
Which part do you need help with @solar isle , the expanding/contracting part or evaluating the limit? The previous person gave you a good way of determining if it is expanding or contracting, look at successive steps in the sequence by evaluating consequetive values of n starting from n=1 and draw a conclusion (very quickly) from the behavior you see in the outputting intervals, so is it the overall limit you need help with?
When deciding if the interval is contracting or expanding instead of the $\leq$ and $\geq$ symbols, for intervals these are almost synonymous with $\subseteq$ and $supseteq$ between intervals
woven radishBOT
Blue Guilmon
rigid vapor
So a set is "getting bigger" if consequetive intervals in the sequence contain the previous, and it is "getting smaller" if the previous contains the next
The tex here doesn't seem to support the reverse subset command I know sadly srry about that
solar isle
Which part do you need help with <@697894092910100530> , the expanding/contracti...
All but, specifically the #1 so after that i to asnwer independently the rest
rigid vapor
For n=1 what is the interval?
In the first one
Plug in one and write it here
Do you know how to read set builder notation?
That's essentially the whole {x| blahblahblah } format
solar isle
That's essentially the whole {x| blahblahblah } format
i dunno po
rigid vapor
So the notation is as follows { all the variables declared to be in the set | relationships/rules these variables have to follow to be in the set}
solar isle
our just give that assignment without any explanation and i also dont have a background anout that
rigid vapor
So essentially
solar isle
our just give that assignment without any explanation and i also dont have a bac...
prof.
rigid vapor
${x | 1 + \frac{1}{n} \leq x \leq 4 - \frac{1}{n} }$
woven radishBOT
Blue Guilmon
solar isle
So the notation is as follows { all the variables declared to be in the set | re...
so how i would construct a full answer regarding that problem?
rigid vapor
This is read in words as "The set of all x, such that, 1 + 1/n is less than or equal to x which is less than or equal to 4 - 1/n"
Or simply
"The set of all x, such that, x is between 1+ 1/n and 4- 1/n"
A sequence is a list indexed (counting by) a natural number, so literally just counting 1, 2 , 3, 4, etc.
The index is determined by the subscript on the sequence
So the indexing variable here is n
solar isle
This is read in words as "The set of all x, such that, 1 + 1/n is less than or ...
yass this is was actually i read this but the problem is i dont know how to contruct a solution or answer about this
rigid vapor
So start with n=1
Plug in n=1 and tell me what the interval is
For the first entry
The goal here is to check if the intervals are getting smaller or larger
As we plug in larger and larger values for n
solar isle
Plug in n=1 and tell me what the interval is
what do you mean?
rigid vapor
So the set builder notation tells you that for every value of n you get a specific interval
Given by that inequality equation
Start with n=1, then n=2, and so on
n=1 is the starting point in the sequence
rigid vapor
**Blue Guilmon**
In here what happens if n=1
solar isle
Plug in n=1 and tell me what the interval is
how about if the interval is (1,infinite)?
rigid vapor
That's problem 3 but you wanted help on problem 1
rigid vapor
So we have that the sequence of intervals is given by $1 + \frac{1}{n} \leq x \leq 4 - \frac{1}{n}$
woven radishBOT
Blue Guilmon
rigid vapor
What happens when n=1?
rigid vapor
So a set is "getting bigger" if consequetive intervals in the sequence contain t...
I gtg to bed now but if you compare consequetive terms in the sequence namely , n and n+1 in this manner you can conclude if it is expanding or contracting, that is how you show this
solar isle
I gtg to bed now but if you compare consequetive terms in the sequence namely , ...
x is between 2 and 3? if n = 1?
solar isle
.close
devout snowBOT
devout snowBOT
Available help channel!
timid bane
Can someone help me: "Prove: for any π β R, π, π β R with π < π, π β πβ²+ β© πβ²β and π : π ββ R function monotonically increasing, if π (π) is dense on the closed interval [π, π], then limπ₯βπβπ (π₯) = limπ₯βπ+π (π₯)."
πβ² is the set of all accumulation points of π
devout snowBOT
Can someone help me: "Prove: for any π β R, π, π β R with π < π, π β πβ²+ ...
timid bane
I know that there are (xn) and (yn) sequences that converge to c from left and right
My main problem is to prove that limπ₯βπβπ(π₯) = M and = limπ₯βπ+π (π₯) = L are equal
I know I need to assume they are different and find a contradiction
The function is increasing, so M <= L
devout snowBOT
@timid bane Has your question been resolved?
devout snowBOT
@timid bane Has your question been resolved?
ionic parrot
How many ways can we draw eight cards from a deck of 52 cards if the eight cards must contain exactly three aces?
devout snowBOT
How many ways can we draw eight cards from a deck of 52 cards if the eight cards...
topaz axle
which three times what else
devout snowBOT
@ionic parrot Has your question been resolved?
ionic parrot
which three times what else
@topaz axle i got its C (4,3) * C (48,5)
topaz axle
i like it
ionic parrot
now I need to do may contain a maximum of three aces
topaz axle
that's the same as not containting four
devout snowBOT
devout snowBOT
Available help channel!
astral reef
devout snowBOT
astral reef
I need help with this question
On the right is how far I've gotten, but I'm super lost
devout snowBOT
@astral reef Has your question been resolved?
lone plaza
so you don't know calculus right? let me think another way
astral reef
Found a video π
I don't understand what he's saying but math is a universal language
lone plaza
I don't understand what he's saying but math is a universal language
He first calculates the area of the sector and then subtracts the area of the triangle to get a portion of it. The same is true for the other part. In the end, it adds up to it.
astral reef
.close
random crypt
$\sum_{k=1}^{\infty} x_k$ is a convergent series of only positive numbers. Show that $\sum_{k=1}^{\infty} \frac{1}{x_k}$ diverges.
devout snowBOT
$\sum_{k=1}^{\infty} x_k$ is a convergent series of only positive numbers. Show ...
woven radishBOT
severed_toast
random crypt
not sure where to start with this
rich summit
Intuitively x_k has to keep getting smaller right?
random crypt
yes
random crypt
Do you have to prove this with epsilon-delta?
doesnt say but im guessing yeah you do
random crypt
So 1/x_k sort of gets bigger
yeah this makes sense intuitively
rich summit
How would you express this more rigorously?
rich summit
Intuitively x_k has to keep getting smaller right?
this part first
random crypt
$\forall \epsilon > 0, \exists N, \forall m > n > N : \sum_{k=n+1}^m x_k < \epsilon$
rich summit
since all x_k are positive
use proof by contradiction if you want
or take m = n + 1
random crypt
$\forall \epsilon > 0, \exists N, \forall m > n > N : \sum_{k=n+1}^m x_k < \epsi...
so if i did proof by contradiction i would assume this holds for 1/x_k
uhh
rich summit
**Jelle**
I meant to use it for this statement
but m = n + 1 works
So for every $\epsilon_2 > 0$, there exists $\epsilon = \frac{1}{\epsilon_2} > 0$
woven radishBOT
Jelle
random crypt
how did you get that?
rich summit
this is the start of the proof for divergence
this is just a true statement, if you have e_2 > 0, then e = 1/e_2 > 0
and because $\epsilon > 0$ there is an $x_k < \epsilon = \frac{1}{\epsilon_2}$
woven radishBOT
Jelle
random crypt
okayokay
rich summit
How would you rewrite the last inequality to prove that x_k will always be "big enough"
also, the divergent sum is at least as big as one of its terms
random crypt
How would you rewrite the last inequality to prove that x_k will always be "big ...
not sure what you mean by this
big enough for what?
woven radishBOT
Jelle
rich summit
So for every e_2, there is an 1/x_k that's bigger than e_2
random crypt
ah, so from that we get that 1/x_k is unbounded?
rich summit
yeah
random crypt
im still confused about the e and e_2, you use them both for the same series, but what do each represent?
im guessing e is still just a small number > 0
rich summit
Yeah, it might not be the best notation, but e_2 is something that can be arbitrarily big, and e is something that can be arbitrarily small (it's the same one as in the convergent series, I reused it)
random crypt
ah yeah
the e = 1/e_2 makes sense then
okay great that helps a lot
thank you
.close
daring sparrow
so this is the notation for integrating over all the reals from -β to +β on both x and y and i want to know the notation for integrating from 0 to β in a similar form to this
devout snowBOT
so this is the notation for integrating over all the reals from -β to +β on both...
meager sequoia
Single integral, over R
$\int_{\mathbb{R}^{+}$
stone stump
$\int_0^\infty\int_0^\infty$
meager sequoia
Oh 0 to infinity
woven radishBOT
Denascite
LayneTheAndroid
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
stone stump
or $\iint_{[0,\infty)\times [0,\infty)}$
woven radishBOT
Denascite
rich dagger
Just help
rich dagger
Well, now you have to listen. I need help with my assignment.
Task c) Determine the angle o the circle section BC2D
I have used the distance formula to find their distance
So what know?
brisk totem
thatβs not enough to solve
you need at least one more value
gleaming lava
So what know?
Jeg tror du har den forkerte tilgang til problemet.
Prov at tegne en trekant fra B,D og C_2
Det er nemmere at finde vinklerne i en trekant
rich dagger
Jeg tror du har den forkerte tilgang til problemet.
Prov at tegne en trekant fra...
Det har jeg ogsΓ₯?
rich dagger
thatβs not enough to solve
you need at least one more value
What is it?
gleaming lava
Det har jeg ogsΓ₯?
Okay sΓ₯ herefter skal du prΓΈve at finde lΓ¦ngderne i denne trekant
rich dagger
.
gleaming lava
sΓ₯ er der nemlig en relation du kan bruge til at finde vinklen
rich dagger
Okay sΓ₯ herefter skal du prΓΈve at finde lΓ¦ngderne i denne trekant
Det har jeg ved at bruge afstandsformlen?
C2D og C2B
gleaming lava
Det har jeg ved at bruge afstandsformlen?
Har du alle længderne i trekanten B,D og C_2
rich dagger
Har du alle længderne i trekanten B,D og C_2
Ja, se billederne...
@brisk totem what do you mean
gleaming lava
Ja, se billederne...
Okay godt, sΓ₯ er der en relation du kan bruge, hvor du sΓ¦tter trekanternes tre sider ind, og kan isolere vinklen
rich dagger
Okay godt, sΓ₯ er der en relation du kan bruge, hvor du sΓ¦tter trekanternes tre s...
Ja, hvordan
gleaming lava
Ja, hvordan
okay...
prΓΈv at bruge cosinusrelationerne
rich dagger
Er det ikke tangens?
gleaming lava
Er det ikke tangens?
Nej, fordi man kan ikke bare antage, at det er en retvinklet trekant
rich dagger
min ven sagde: 6c. Bestem de to hældninger først,
a1 = fra punkt B til punkt C2
a2 = fra punkt D til punkt C2
sΓ₯ har du vinklen; v = ( tan-1(a1) - tan-1(a2) ) ΒΊ
rich dagger
Nej, fordi man kan ikke bare antage, at det er en retvinklet trekant
Det er ogsΓ₯ rigtigt.
gleaming lava
Det er ogsΓ₯ rigtigt.
Jeg tror din ven har lavet to linjer, y=ax+b, og fundet vinklen mellem dem
det kan man ogsΓ₯ gΓΈre
gleaming lava
Til det skal du bare bruge de to rette linjers hældning
rich dagger
vi bruger bare cosinusrelation
hvordan sΓ₯ formlen ud nu?
derefter den formel, sΓ₯ bruger vi cirkeludsnits formel
gleaming lava
gleaming lava
hvad for en af dem skal vi bruge?
de er egentlig alle de det samme, det kommer bare an pΓ₯ hvordan du navngiver punkterne, og det er vilkΓ₯rligt
Okay sΓ₯
rich dagger
C2B = 4,38 og C2D = 4,29
gleaming lava
I tegningen vil cosinusrelationen eksempelvis beskrive, at
gleaming lava
Er det de tal der skal sættes ind?
i formlen kan du sætte trekantens sidelængder ind, og isolere C_2
rich dagger
i formlen kan du sætte trekantens sidelængder ind, og isolere C_2
Er det den formel helt ΓΈverst?
Hvor jeg putter ind
gleaming lava
Er det den formel helt ΓΈverst?
den formel som jeg har skrevet til dig
rich dagger
SΓ₯, hvad skal Γ¦ndres? BC2? hvad skal der stΓ₯ der?
gleaming lava
Den kommer bare ud fra alle de andre formler jeg sendte tidligere, men jeg har bare Γ¦ndret pΓ₯ punkterne og sidernes navne, sΓ₯ de passer med din tegning
rich dagger
Jeg har kun fundet C2B og C2D
gleaming lava
C2B og BC2 er det samme
gleaming lava
hmm
rich dagger
Hvordan vil du sætte dem ind i formlen?
gleaming lava
4,29 og 4,38
NΓ₯r der i formlen jeg skrev eksempelvis stΓ₯r |C2D|, betyder det lΓ¦ngden fra C2 til D.
gleaming lava
Ja, men hvad med BC2?
Længden fra punktet B til punktet C_2
gleaming lava
er det stadig det samme?
Ja det er det samme.
Længden fra C2 til B er det samme som længden fra B til C2
rich dagger
Okay, vent lad mig putte pΓ₯.
rich dagger
Ja det er det samme.
Længden fra C2 til B er det samme som længden fra B til C2
men vil du fortælle mig, hvad jeg skal ændre?
ogsΓ₯ det der |BC|^2
gleaming lava
ogsΓ₯ det der |BC|^2
Det vil sige længden fra B til C2 sætter du i anden
SΓ₯ f.eks. hvis lΓ¦ngden er 6, sΓ₯ bliver det 6^2
gleaming lava
men skal der stΓ₯ 4,29 heletiden
Ja hvis lΓ¦ngden fra C2 til D er 4,29, sΓ₯ skal der stΓ₯ 4,29 her:
rich dagger
Ja hvis lΓ¦ngden fra C2 til D er 4,29, sΓ₯ skal der stΓ₯ 4,29 her:
Se
| 4,38 |^2 + | 4,29 |^2 - 2 * | 4,38 | * | 4,29 | * cos(c2)
Hvad skal der stΓ₯ i c2?
gleaming lava
Hvad skal der stΓ₯ i c2?
C2 er den vinkel som du skal finde.
SΓ₯ efter du har sat alle vΓ¦rdierne ind i formlen, er det C2 som du skal isolere
p.s. du kan godt fjerne de lodrette streger efter du har sat længderne ind
gleaming lava
ja
gleaming lava
Hvad med det der 4,38^2
det kan du bare beregne. Det giver 19,1844
gleaming lava
SΓ₯ hvordan isolerer vi sΓ₯
Har du i øvrigt længden fra B til D?
rich dagger
Har du i øvrigt længden fra B til D?
Nej.
Hvordan vil du skrive tallene op og isolerer...er lidt forvirret nu.
Ved ikke om det er rigtigt er skrevet
gleaming lava
Nej.
Den skal vi ogsΓ₯ bruge, fordi den eneste ubekendte vΓ¦rdi vi vil have tilbage er C2, for ellers kan vi ikke isolere det og finde ud af hvad det er
gleaming lava
Hvordan vil du skrive tallene op og isolerer...er lidt forvirret nu.
Jeg kan prΓΈve at skrive det op for dig
1s
rich dagger
Jeg kan prΓΈve at skrive det op for dig
1s
Takkk
rich dagger
Den skal vi ogsΓ₯ bruge, fordi den eneste ubekendte vΓ¦rdi vi vil have tilbage er ...
Hvor skal B til D stΓ₯ henne?
Bar vis, det er nemmere tror jeg
gleaming lava
Hvor skal B til D stΓ₯ henne?
Der hvor der stΓ₯r |BD| i formlen her
gleaming lava
BD = 6,202
Okay, sΓ₯ nu har vi det her
SΓ₯ skal man bare isolere ligesom nΓ₯r man skal finde x
men her er det bare C2 man skal finde
rich dagger
Okay, sΓ₯ nu har vi det her
Skrev prΓ¦cis det samme. Og ja, hvordan vil du sΓ₯ isolerer
Skal C2 ikke rykkes pΓ₯ venstre side og 6,202 pΓ₯ hΓΈjre side
gleaming lava
Skrev prΓ¦cis det samme. Og ja, hvordan vil du sΓ₯ isolerer
Okay fΓΈrst er der mΓ₯ske lΓ¦ttest at regne ud hvad 6,202^2, 4,38^2 og 4,29^2 er
rich dagger
Okay fΓΈrst er der mΓ₯ske lΓ¦ttest at regne ud hvad 6,202^2, 4,38^2 og 4,29^2 e...
Tjek om de er rigtige
gleaming lava
Tjek om de er rigtige
ja de er rigtige er jeg rimelig sikker pΓ₯
Nu har vi sΓ₯ det her
rich dagger
Yes.
gleaming lava
nu kan vi f.eks. lægge 19,1 og 18,4 sammen
rich dagger
37,5
rich dagger
nu kan vi f.eks. lægge 19,1 og 18,4 sammen
Hvad nu?
rich dagger
Ehm
rich dagger
Yes, what know
gleaming lava
Nu er det tid til at isolere
gleaming lava
37,5 - 37,4?
Nej det kan man ikke gΓΈre, for 37,4 er ganget ind i cos(C2)
Vi kan minus begge sider med 37,5
SΓ₯dan her
rich dagger
Hvad nu?
gleaming lava
Hvad nu?
Du kan se pΓ₯ billedet, at 37,5 og -37,5 gΓ₯r ud med hinanden, for 37,5 minus 37,5 giver bare 0
rich dagger
Ja, sΓ₯ hvordan vil den se ud?
rich dagger
Yes, hvad nu
gleaming lava
SΓ₯ kan man regne ud hvad 38,4 minus 37,5 er
rich dagger
0,9
gleaming lava
Fordi gange og dividere er modsatte, vil det gΓ₯ ud med hinanden
rich dagger
Eller ud af siderne
gleaming lava
1s
rich dagger
yes
rich dagger
Yes what know
rich dagger
π
gleaming lava
π
SΓ₯ vil -37,5 gΓ₯ ud med -37,5
Fordi den i toppen er ganget ind i cos, og hvis vi sΓ₯ dividere det med det samme, vil de gΓ₯ ud med hinanden fordi at gange og at dividere er modsat hinanden
rich dagger
SΓ₯ vil -37,5 gΓ₯ ud med -37,5
Ja, og hvordan ser den sΓ₯ ud efter det?
gleaming lava
Nu har vΓ₯ altsΓ₯
rich dagger
Nu har vΓ₯ altsΓ₯
Skal cos ikke pΓ₯ den anden side nu?
gleaming lava
Skal cos ikke pΓ₯ den anden side nu?
Jo, vi vil gerne have cos over pΓ₯ den anden side, sΓ₯ vi har C2 for sig selv.
For at gΓΈre dette, skal vi bruge det modsatte af cosinus. Ved du hvad det modsatte af cosinus er?
rich dagger
Jo, vi vil gerne have cos over pΓ₯ den anden side, sΓ₯ vi har C2 for sig selv.
Fo...
arcos
sΓ₯ hvordan vil den se ud
rich dagger
Yes. What know
gleaming lava
Og igen vil arccos og cos gΓ₯ ud med hinanden, fordi de er modsat hinanden:
Nu har vi det her tilbage
gleaming lava
Nu ved vi hvad C2 er, og for at lave det om til en vinkel, kan vi bare sætte det her ind i en lommeregner
rich dagger
Nu ved vi hvad C2 er, og for at lave det om til en vinkel, kan vi bare sætte det...
Hvas giver det sΓ₯?
91,38 grader?
gleaming lava
91,38 grader?
jep, og nu har vi vinklen
gleaming lava
og vΓ¦r lige obs pΓ₯ at det mΓ₯ske vil vΓ¦re lidt uprΓ¦cist, fordi vi har afrundet hele tiden
rich dagger
og vΓ¦r lige obs pΓ₯ at det mΓ₯ske vil vΓ¦re lidt uprΓ¦cist, fordi vi har afrundet he...
Hvad mener du?
I stedet for 360 er det sΓ₯ ikke 180?
gleaming lava
Hvad mener du?
de 91,38 grader kan i virkeligheden f.eks. godt vΓ¦re 91,39 eller 91,37, fordi vi har smidt nogle tal ud som stΓ₯r bagved imens vi regnede det ud
rich dagger
de 91,38 grader kan i virkeligheden f.eks. godt være 91,39 eller 91,37, fordi vi...
Ahhh
gleaming lava
I stedet for 360 er det sΓ₯ ikke 180?
Nej, hvis du skal finde cirkeludsnittet nu, skal du sΓ¦tte 91,38 grader ind det hvor der stΓ₯r v
gleaming lava
Hvad er vores radius sΓ₯?
Radius vil vΓ¦re lΓ¦ngden fra centrum til et af punkterne pΓ₯ udkanten, B eller D
rich dagger
Radius vil vΓ¦re lΓ¦ngden fra centrum til et af punkterne pΓ₯ udkanten, B eller D
Ja, sΓ₯ hvilken af de to?
gleaming lava
Ja, sΓ₯ hvilken af de to?
Det er lige meget.
Det burde vΓ¦re den samme, fordi lΓ¦ngden fra centrum af en cirkel til et punkt pΓ₯ kanten er de samme ligegyldigt hvad for et punkt man tager
rich dagger
Det er lige meget.
Det burde være den samme, fordi længden fra centrum af en cir...
Ja, sΓ₯ hvad for et tager vi?
gleaming lava
Ja, sΓ₯ hvad for et tager vi?
det bestemmer du selv
rich dagger
4,29?
gleaming lava
6,202
6,202 er ikke lΓ¦ngden fra centrum til et punkt pΓ₯ kanten. Det er lΓ¦ngden fra B til D
Vi skal bruge længden fra C2 til B
eller længden fra C2 til D
rich dagger
Okay 4,29 sΓ₯
gleaming lava
Okay 4,29 sΓ₯
Ja du kan godt bruge 4,29
gleaming lava
3,42102 hvad?
SΓ₯ sΓ¦tter du det ind for radius
gleaming lava
SΓ₯dan, tak.
sΓ₯ lidt
hΓ₯ber du har lΓ¦rt noget af det her
rich dagger
Det har jeg i hvert fald π - det kan vΓ¦re, at jeg kontakter dig igen.
devout snowBOT
@rich dagger Has your question been resolved?
calm maple
devout snowBOT
next parrot
the first one can be done by rewriting it into (1+1/f(n))^g(n) form and apply definition of e
wooden veldt
Try rationalise the numerator
calm maple
How?
next parrot
the second one can is easy with stolz, since n is increasing divergent with n+1 - n =1, and (e^(1/ n+1)+1 - (e^(1/n)+1)))=e^(1/ n+1) - e^(1/n) which goes to 0
calm maple
the second one can is easy with stolz, since n is increasing divergent with n+1 ...
so bn = n
an = e^1/n -1
?
Stolz is meant to be for an/bn
?
@next parrot
next parrot
yeah
next parrot
e^1/n -1 is an -->0, bn is 1/n decreasing and --> 0
o wait
yeah sorry
i was wrong
calm maple
So any other advice?
Maybe if we look for sandwich theorem, but i cant see any estimations
π¬
<@&286206848099549185>
Please
devout snowBOT
@calm maple Has your question been resolved?
devout snowBOT
@calm maple Has your question been resolved?
sick pond
can someone just solve the answer and explain it to me instead of just ignoring or dispearing after one message its just 3 questions ill send oen by one
devout snowBOT
can someone just solve the answer and explain it to me instead of just ignoring ...
devout snowBOT
can someone just solve the answer and explain it to me instead of just ignoring ...
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
timber pebble
I could help walk you through one question
sick pond
ok thank you
appreicatei t
everyone else
just ignoring
or disappearing
after one message
i have a due date for this
timber pebble
i reserve the right to disappear
so, all you need to find the equation for a circle is the center and radius
then you can just write it down
sick pond
yea go fuck urself bitch
timber pebble
? for what
near stone
ain't no way
smoky nimbus
Lmao I think they got booted for that
near stone
they left the server
hazy quail
lmao
timber pebble
word
hazy quail
thereβs no way thatβs real
timber pebble
.close
devout snowBOT
smoky nimbus
? for what
Probably because you said you had the right to disappear
timber pebble
also
bot
what the heck
youve been saying the owner disappeared all weekend
on every other channel
smoky nimbus
they left the server
I think it was an auto boot for the language or something, because that person has been here for a while I think
smoky nimbus
I can now see their profile
I mean it might not be them leaving the server but them getting bot booted
near stone
oh okay
devout snowBOT
Available help channel!
vivid torrent
1 The angle between the height and the base of the cone
2 The angle between the generator SN and a plane base of the cone
3 The angle between the base radii AO and ON, if the angle BN=100 degrees
4 The angle between lines SO and ON
A)90 degrees
B)80 degrees
C)30 degrees
D)40 degrees
E)60 degrees
I don't understand how this can be done
devout snowBOT
1 The angle between the height and the base of the cone
2 The angle between the ...
wheat pawn
- the height of the cone would be line OS. The base of the cone is the circle (surface). What's the angle between that vertical line and the circle?
- The generator SN is that line. A plane base of the cone would be the plane that contains the circle (surface). What's the angle between that plane and that line?
- Wrongly stated. It should read "the angle BON=100 degrees". What's the angle AON, if BON=100ΒΊ, considering AB is a diameter?
- SO is the height of the cone. ON is a radius on the circle. What's the angle between those lines?
vivid torrent
1) the height of the cone would be line OS. The base of the cone is the circle (...
- Π‘
- Π
- Π
- Π
??
wheat pawn
1 is incorrect
vivid torrent
hmmm... but why?
vivid torrent
1 is incorrect
I don't see any other options
wheat pawn
because the base of the cone is a horizontal (piece of a) plane. OS is vertical. What's the angle between them then?
vivid torrent
because the base of the cone is a horizontal (piece of a) plane. OS is vertical....
It sounds like 90 degrees
wheat pawn
there you go
vivid torrent
but can 2 options be the same?
1 and 4
oh I wrote the condition wrong
I need this corner
.close
bitter kraken
Hello, i am stuck on this exercise.
Let f $\in \mathbb{C}^2(\mathbb{R}_+^*, \mathbb{R})$ such that $\forall x > 0$, $f(x + 1) = x\times f(x)$ and $f''(x) > 0$.
1Β° Show that $\exists \alpha \in ]1, 2[$ such that $f'(\alpha) = 0$. Deduce the sign of $f'$ and variations of $f$.
2Β° Find $lim\ f$ when $x \rightarrow +\infty$
I did the 1 but cant do the 2
woven radishBOT
michelson prime
devout snowBOT
@bitter kraken Has your question been resolved?
devout snowBOT
@bitter kraken Has your question been resolved?
devout snowBOT
@bitter kraken Has your question been resolved?
dapper tiger
note that lim f can't be a real l, otherwise, take the limit in the equality f(x+1) = xf(x), it's a contradiction
so either the limit doesn't exist, or it's an infinite, use 1. to conclude
gloomy valve
devout snowBOT
gloomy valve
Can anyone guide me with a strategy on how to prove this?
A part of me was thinking induction but like
im not sure if thats a correct approach or not
devout snowBOT
@gloomy valve Has your question been resolved?
sullen island
A part of me was thinking induction but like
sounds good
grave acorn
when solving for domain, is there a reason why 0 was included in the bracket?
trail eagle
Is there a reason why they specifically want -x/2 + 4 >= 0?
Because just like that -x/2+4 has domain R.
devout snowBOT
@grave acorn Has your question been resolved?
devout snowBOT
brisk totem
you mean x?
(-2)^2 = 4.
oh i didnβt scroll up
your bounds are incorrect
they also come bundled with a restriction that x^2-4 is either positive or negative
itβs not false, but itβs not the best bound
they also come bundled with the restriction that x^2-4 is either positive or negative
yup
no, you have to consider both
or otherwise you construct bounds that are too strict like you did
,w |x^2-4|<0.5
woven radishBOT
lament cradle
,w graph |x^2-4|<0.5
woven radishBOT
brisk totem
eh thatβll do
lament cradle
they show the same thing in diff ways
brisk totem
desmos coloured the region in which the x values satisfy the inequality
the wolfram graph graphs the function and the constant and the area bounded by those 2 functions where y=0.5 is on top are the x solutions
(probably needs to zoom in a bit)
desmos equivalent
brisk totem
short answer is
if the stuff inside the abs value is even or odd (and x^2-4 is even) and nothing else is done with the abs value, then yes
it would work but then itβs mirrored about x=1 or 1 respectively and you need a bit more work
which one?
itβs x^2-4 not (x-4)^2
so no horizontal translation
brisk totem
then |f-L|<0.02 implies |6-2x|<0.02
whatβs wrong with c?
i guess you forgot a minus sign
L is -3 and you have f(x)-L = f(x)-(-3)=f(x)+3
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
lucid rock
How to get value of K? ππ
devout snowBOT
How to get value of K? ππ
lucid rock
Help please
wheat pawn
,rotate
woven radishBOT
brisk hare
K^(2c)=1?
brisk hare
Is there anything related to c given
wheat pawn
Do they consider 0 as positive?
brisk hare
Who would
wheat pawn
a solution would be c=0, k!=0
wheat pawn
another solution would be k=1, c any (positive, given restriction) real
lucid rock
I will send better the entire exercise xD
Statement gives me a Distribution function
wheat pawn
send full instructions always, not just a part
wheat pawn
ni siquiera se molestan en escribirlo bien T.T
lucid rock
ni siquiera se molestan en escribirlo bien T.T
Hablas espaΓ±ol jaja
In which language should I talk anyway
wheat pawn
english probably
lucid rock
Ok
Well I will explain what Ive done
If we derivate the distribution function we would get density function and it has a Characteristic that if the integral between (-infinite) and infinite of density function adds up all mass of probability (1)
So if we get density function and we do integral we equal that to 1 as it must be 1 the result
And we have to get somehow
K and C
π€π€π€
Ignore the second part of exercise
It isnt really difficult it just other integral and really easy
But the problem
Is I got as result k^2C=1
So how I make it
π
pulsar sand
First of all, whoever wrote that assignment should be chastised for swapping capital letters so often. Second, you wrote CK^C(K^-C/C)
Then you simplified it incorrectly
lucid rock
Now yes
Proven it is a density function so as we checked it is a density function it must be a real distribution function since it is Obtained from integrating
lucid rock
First of all, whoever wrote that assignment should be chastised for swapping cap...
π btw sorry for my letters haha
pulsar sand
No I meant the person that made the assignment
pulsar sand
F(x) with a domain restriction as a function of X. Defining a constant K and C and using a k and c in the function. This is just ridiculous for an instructor
devout snowBOT
@lucid rock Has your question been resolved?
visual maple
devout snowBOT
visual maple
why is the answer (d)
okay so its eight books
shared between two people
where each person has to get AT LEAST 1 book
so wouldn't we do something like 8C8 * 8C0 * 2 (8 books for person x, 0 books for person y and vice versa)
which would give us 2
then we would do 8C2 to find like all possible selections? if that makes sense
and then essentially we would do
8C2 - 2
visual maple
so wouldn't we do something like 8C8 * 8C0 * 2 (8 books for person x, 0 books fo...
this gives us 2
so we take from the sum
i thought it would be C
topaz axle
we wouldn't do 8C8 * 8C0 * 2 at any point
oh you mean you subtract it
yeah
every possible selection is 2^8
and there's no reason to think it's 8c2
topaz axle
8c0 + 8c1 .. + 8c8 is every possible selection, and 2^8 is short for that
visual maple
yeah that makes more sense
for this question
so we're selecting 4 numbers
that make up a four-digit number
and it needs to be divisible by 5
visual maple
and it needs to be divisible by 5
this means there's no remainder left or like a decimal
right?
so if we were to usually answer this question WITHOUT THE restriction of the number being divisible by 5
it would be
5 * 5 * 4 * 3
Where it is 5 possible numbers for the first box (5, 4, 3, 2, 1),
5 possible numbers for second box, say you got 5 in the first box (4, 3, 2, 1, 0)
4 possible numbers for third box, say you got 4 in the 2nd box (3, 2, 1, 0)
and so on
now to apply this restriction
the number needs to be divisible by 5
oh
so
0, 1, 2, 3, 4, 5
make up four digit number
so
first box = 4, 3, 2, 1, 5
second box = 3, 2, 1
third box = 2, 1
fourth box = 0
so essentially it'll be 5x3x2x1
never mind
ok so last number has to be 5 or 0
π i dont know
help
drifting sierra
Separate the cases
How many numbers that end with 0, then how many that end with 5
visual maple
0, 1, 2, 3, 4,5
how many numbers end with 0?
first box = 5 choices (5, 4, 3, 2, 1)
second box = 4 choices (4, 3, 2, 1)
third box = 3 choices (3, 2, 1)
fourth box = 1 choice (0)
5x4x3x1 = 60
60 numbers end with 0
How many numbers end with 5
First box = 4 choices (4, 3, 2, 1)
second box = 4 choices (3, 2, 1, 0)
third box = 3 choices (2, 1, 0)
fourth box = 1 choice (5)
4x4x3x1 = 48 choices
48 + 60 = 108
so its (e)
woohooo
drifting sierra
visual maple
mmm
so I know the answer is (b)
because of the 8!
cause like
if the adults are to remain together
they count as 1 essentially
meaning 7 children and then 1 group of adults
so 8!
but why is it multiplied by 5!?
to rearrange the adults?
cause 5 adults
and then they can be arranged 5 different times
or idk
whats the reasoning
drifting sierra
Seems correct to me
visual maple
devout snowBOT
visual maple
how do I solve this
so
is it permutation or combination
cause it says arrange
so i think its permutation
and like I dont know what to do
someone hint me in the right direction
ive tried a lot of different things but it doesn't result in any of the multiple choice
dark sable
someone hint me in the right direction
uh are the boys and girls identical or different
visual maple
uh are the boys and girls identical or different
i mean
with these question's
id say identical?
well
they arent the same
but like
girl girl girl
is identical
dark sable
id say identical?
that would lead to bbgggb, bgbggb, bggbgb, and bgggbb being the only answers
dark sable
that would lead to bbgggb, bgbggb, bggbgb, and bgggbb being the only answers
also these are the main formations of the people, now you just have to multiply to 4 the number of times you can interchange between the girls and the number of times you can interchange with the boys which is 6 for both so 4 * 6 * 6
dark sable
also these are the main formations of the people, now you just have to multiply ...
which is 144
visual maple
that would lead to bbgggb, bgbggb, bggbgb, and bgggbb being the only answers
like this way
in terms of letters
and it'll help4
thank you
visual maple
.close
devout snowBOT
devout snowBOT
Available help channel!
cunning mica
Im confusedd
devout snowBOT
Im confusedd
cunning mica
Is this correct?
mild sail
what?
winter patrol
what are you being asked to do?
mild sail
yeaas
pine lance
he probably needs to factorize it or something
brittle burrow
it's factorisation yeah
mild sail
ohk
winter patrol
consider grouping them like
$$\red{ac + 3ad} + \blue{2bc + 6ad}$$
then proceed with factorisation by grouping
woven radishBOT
βΞ±ΞΌΞ©βΟβ €
winter patrol
what type of way are you expecting?
pine lance
Is tjere another way?
yeah you could group ac+2bc and 3ad+6bd
cunning mica
So then ull have to factorise again right?
pine lance
So then ull have to factorise again right?
its not "again", we are just showing how to group them, we havent done any factorisation yet :>
pine lance
yeah you could group ac+2bc and 3ad+6bd
If I factorise this I will get c(a+2b)+3d(a+2b)
cunning mica
yeah you could group ac+2bc and 3ad+6bd
Ohh so after this what happens
cunning mica
If I factorise this I will get c(a+2b)+3d(a+2b)
Yep. So it will be (a+2b)(c+3d) as the answer right?
pine lance
Yep. So it will be (a+2b)(c+3d) as the answer right?
Yeah
cunning mica
Ohhh oki thanksss
pine lance
Check it again to make sure, I might have missed a letter or something. Yw
cunning mica
Oki so for this the 16th one is the same case
winter patrol
yeh
devout snowBOT
devout snowBOT
Available help channel!
heady remnant
drawing a venn diagram for this, does the circle of A intersect through all the other 3?
devout snowBOT
drawing a venn diagram for this, does the circle of A intersect through all the ...
heady remnant
wait I'll take a picture
does A have it's own part
so does 1/40 + 1/10 + 3/5A = A or is there something in the middle of A?
small quartz
observe that P(R)+P(S)+P(T) = 1
So the circles of R S and T should cover everything
heady remnant
alright thxs π
small quartz
and the fact that P(A|T) = P(A)
heady remnant
.close
drowsy kite
Let sn=1+1/2+...+1/n
Prove that sn>=1/2(1+log2(n))
I tried to prove this by induction, by proving s(n+1)>=1/2(1+log2(n+1))
s(n+1)=s(n)+1/(n+1)>=1/2(1+log2(n))+1/(n+1)=1/2(1+2/(n+1)+log2(n)) and im stuck from there.
devout snowBOT
Let sn=1+1/2+...+1/n
Prove that sn>=1/2(1+log2(n))
I tried to prove this by indu...
rich summit
Induction might not be possible, you can compare the series to the area under the curve y = 1/x though
drowsy kite
Explain it further, I think it implies integrals, something that I have not studied in my class
yet
rich summit
hmm, in the induction step it is enough to prove that $$n\cdot2^{\frac{2}{n+1}}\ge n+1$$
woven radishBOT
Jelle
