#help-28
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@modest pulsar Has your question been resolved?
modest pulsar
and you can just google that?
no
modest pulsar
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rigid nexus
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rigid nexus
shouldnt it be 1/2 * 15/45 man
female or guy is 50 chance, 1/2, if its a guy then 15/45 like reading
i just get 0.167 though
ivory cairn
there aren't an equal number of males and females.
rigid nexus
oh shit
wait why is there not an equal amount of males and females
where does it say that
ivory cairn
shouldnt it be 1/2 * 15/45 man
and the probability of enjoying reading isn't correct
rigid nexus
for men it is?
ivory cairn
wait why is there not an equal amount of males and females
the last column, the total number of males, and the total number of females
ivory cairn
for men it is?
nope. That's the probability that someone who enjoys reading is male. Not the probability that someone enjoys reading
rigid nexus
yeah the question is for male
ivory cairn
If you're going to do this is multiplication principle you should do (probability of male) * (probability of enjoying reading)
hmm, wait nope, I'm wrong. I'm doing independence 🤦
rigid nexus
is the answer 0.261
ivory cairn
no
the easier way to do this is just do (males who enjoy reading)/(total number of students)
you don't need multiplication principle at all here
rigid nexus
so its 0.130
ivory cairn
yes
ember tartan
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ember tartan
Im having a bit of trouble solving this.
Using the remainder estimation for taylor series is confusing
$R_{n} = \frac{f^{(n+1)}(z)(x-c)^{n+1}}{(n+1)!}$
glossy valveBOT
beanbeanjuice
ember tartan
since we have a taylor polynomial of the second order
it should be
$R_{2} = \frac{f^{(3)}(z)(0.8)^{3}}{3!}$
glossy valveBOT
beanbeanjuice
ember tartan
since c = 0 and x = 0.8
but finding z is difficult
the third derivative of cos(x) is
sin(x)
and to my understanding
$c \leq z \leq x$
glossy valveBOT
beanbeanjuice
glossy valveBOT
beanbeanjuice
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beanbeanjuice
ember tartan
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unique gyro
Hi team, if I have the following function, is e^bx the argument of cos? i am used too seeing y = cox(x). but in this question there is a multiplication sign instead of brackets.
dusk inlet
Hi team, if I have the following function, is e^bx the argument of cos? i am use...
Yeah.
The period after the cos is something I haven’t seen before. Maybe it is a typo?
unique gyro
Prefect thank you! This is a practice SAC question for VCE, possibly could be a typo....which would suck. Thanks for the help!
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tepid basin
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tepid basin
how is this 210 and not 110
610-360=250
250+110= 360
because coterminal angle is the angle from the point to the x axis?
gritty rose
,w coterminal angle
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@tepid basin Has your question been resolved?
tepid basin
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tepid basin
i got h=13 a= -12 o=5
sec = h/a
sin = o/h
do you guys know what i mightve done wrong?
is it possibly the negative sign in my answer?
sonic marlin
Well, sin is o/h
now your o and h is 5 and 13 respectively
but you give your answer as sin is -5/13
tepid basin
so it should be positive?
sonic marlin
yes
sonic marlin
wlc
tepid basin
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eternal tusk
im supposed to find x for this but it wont let me intersect
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im supposed to find x for this but it wont let me intersect
red radish
ivory cairn
im supposed to find x for this but it wont let me intersect
you're looking for the answer to 6.9 = log(x) +7.9, and trying to intersect 6.9 with log(x) + 7.9?
ivory cairn
why don't you subtract 6.9 and find the zero of log(x) + 1?
or use log rules to solve log(x) + 1 = 0
eternal tusk
6.9 with what
ivory cairn
subtract 6.9 from both sides of the equation
eternal tusk
my teacher did this tho
I did the same thing
I even used what I got here
and it didnt work
ivory cairn
🤦 ok. My recollection of these is that you need to choose both functions. You should be able to use your arrow keys to move between your functions
eternal tusk
Why did u face palm lol
ivory cairn
at x=0 your y_2 = log(x)+7.9 isn't defined. I don't know if that matters for choosing your functions, but might be part of the problem.
eternal tusk
🤦 ok. My recollection of these is that you need to choose both functions. You s...
Did that already
ivory cairn
without seeing what buttons you're pushing I doubt anyone can help. You should look up videos on finding the intersection and make sure you're doing it correctly
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loud hinge
What’s The difference between a Stationary and turning point
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@loud hinge Has your question been resolved?
edgy cloud
where is a good place to learn how to do questions like these?
edgy cloud
rustic hamlet
edgy cloud
I really don't get taylor series
how would you go about doing one of these questions
gritty rose
I really don't get taylor series
what specifically don't you get
just calculate terms in the formula one by one and piece them together
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marble nimbus
Hi! i got a quick question about discrete maths. We saw in classes the demonstration that R is transitive iff R o R ⊆ R . With a friend we were thinking about transitivity as a concept (thinking about diagrams) and end up having the following question: R is transitive iff R o R is transitive ? thanks in advance
stark sky
Could you send your definition of $R \circ R$?
glossy valveBOT
Kimbomanjaro
marble nimbus
Oh sorry
R is a relation, so R o R is the composition of R and R
Let me look for the exact definition of composition
spice orchid
marble nimbus
Yeah that's it xD
stark sky
This is a good question, I cant think of a counter example but I think your back implication may not work
marble nimbus
I found a counter example but i need someone to tell me if it's really a valid one ahahha
I was thinking about R = { (a,b) , (b,c) } being a non-transitive relation
Then R o R = { (a,c) }
Which is, i guess, transitive????
So that would break the iff, but idk if R o R is really transitive
spice orchid
I think your question boils down to whether this statement holds: $R \circ R \circ R \subseteq R \circ R \implies R \circ R \subseteq R$
glossy valveBOT
iCaird
spice orchid
which i dont think is true in general
spice orchid
Then R o R = { (a,c) }
I think this relation is vacuously transitive, because there's nothing to check
marble nimbus
**iCaird**
I'll try demonstrating that
thanks a lot iCaird
how do i close this
xD
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primal seal
Could any lovely individuals help me find the covariance of this distribution?
glossy valveBOT
feather
primal seal
Is that right?
glossy valveBOT
feather
primal seal
Now to find the means of either variable individually
glossy valveBOT
feather
primal seal
...but that diverges so what do I do
(Trying to find the pdf of X so I can find E[X])
oh
hey
im a bit of a brainlet
y varies from 0 to 1-x hurb
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agile vigil
how to calculate intersection of y = arctan(sqrt(x)) and y = -(x^2)
agile vigil
?
torn jolt
how to calculate intersection of y = arctan(sqrt(x)) and y = -(x^2)
try drawing it
like a rough sketch
agile vigil
is there a way without drawing ?
torn jolt
like a rough sketch
u will notice that in y=arctan(sqrt(x))
the domain is x>=0
so its in the 1st quadrant
and y=-x^2 all the points satisfy y<=0
main ridge
main ridge
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maiden pike
how do i find the x-intercepts and the vertex of y=4x^2-12x+9
maiden pike
<@&286206848099549185>
static leaf
<@&286206848099549185>
💀
kind jay
<@&286206848099549185>
read rules
maiden pike
oops sorry gotta wait 15 mins
static leaf
how do i find the x-intercepts and the vertex of y=4x^2-12x+9
factor
maiden pike
i got y=(x-6)^2 is that correct?
static leaf
i got y=(x-6)^2 is that correct?
nope
static leaf
how do i find the correct answer?
lets first solve for vertex form
do you remember what that is
maiden pike
no
maiden pike
how do i find the x-intercepts and the vertex of y=4x^2-12x+9
i do but im not sure how to get there from here
runic bloom
@maiden pike instead of vertex form, you can simply use x = -b / 2a to find the x value of the vertex
and plug that into the equation for the y coodinate
maiden pike
<@486171952600580116> instead of vertex form, you can simply use x = -b / 2a to...
can i use that with any equation with a?
maiden pike
and plug that into the equation for the y coodinate
okk thank u
how do i find the x intercepts thou?
runic bloom
can i use that with any equation with a?
yeah as long as it is in the form y = a^2 + bx + c
runic bloom
how do i find the x intercepts thou?
well for this one.. the vertex is actually the x intercept
however the vertex is not always the x int, so you'd typically want to factor it.. have you learned about that?
maiden pike
however the vertex is not always the x int, so you'd typically want to factor it...
i dont think so
maiden pike
yeah as long as it is in the form y = a^2 + bx + c
ok so the x intercept is 1.5?
runic bloom
yes, (1.5, 0) to be specific
maiden pike
how do i know the y intercept is 0?
and how do i know if the x intercept is the vertex?
sorry im pretty confused 😭
runic bloom
how do i know the y intercept is 0?
the y intercept can be found by simply setting x to 0
so plug in 0 into the equation and you can find that it's just 9 (the c value)
runic bloom
and how do i know if the x intercept is the vertex?
well they're completely different things but first of all, I'd recommend this video:
https://www.youtube.com/watch?v=U6FndtdgpcA&ab_channel=TheOrganicChemistryTutor
factoring polynomials is quite important to understand
runic bloom
np
and factoring polynomials is the way you'll find the x intercept(s)
setting y to 0 and factoring 4x^2 - 12x + 9
maiden pike
setting y to 0 and factoring 4x^2 - 12x + 9
i did that and i got y=(x-6)^2
runic bloom
uhh could you send your work?
runic bloom
nvm i did my work again and got( 2x-3)^2
that's correct!
maiden pike
and because its (2x-3)^2 theres only 1
so theres only one x intercept which means the x intercept is the vertex?
torn jolt
I got a question for y'all
Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
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smoky creek
Hi
smoky creek
I have no idea how to factor this
I know it's 0/0 but I still don't know how to start factoring it, can you help me?
brave blaze
Maybe try to use this : cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
smoky creek
What do you mean? 🤔
brave blaze
use this formula
brave blaze
yea
brave blaze
try to transform sin(6x) too 🤔
brave blaze
2sin(3x)cos(3x)
yea
smoky creek
2sin(3x)cos(3x)
@sharp gyro Look
smoky creek
yea
I was trying to help out someone but I also didn't take calculus in a while, so I was confused and we both were asking in the same place lol
Sorry
brave blaze
and after that you will have :
$\frac{\frac{\sqrt{3}}{2} \cos(2x) - \frac{1}{2} \sin(2x)}{2\sin(3x)\cos(3x)}$
glossy valveBOT
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sharp gyro
according to wolfram the limit is 1/3
sharp gyro
I dont know how to continue after this
smoky creek
Ok, so then the pi/6 is converted into a normal fraction in the coefficient
Right?
And then I don't know
spice orchid
Any chance you guys have learnt l'hopitals rule yet?
smoky creek
Someone else said l'Hopitals too, I don't know if the teacher expects us to use it though
@sharp gyro
spice orchid
If you've learnt it, definitely use it, if not, you can probably still do it the way you're going
Just a bit more of a pain
brave blaze
I think I found how to do it (without l'Hopital)
sharp gyro
Any chance you guys have learnt l'hopitals rule yet?
I haven't, prof said we can't use if we know it too
sharp gyro
I think I found how to do it (without l'Hopital)
Do tell 🙏
brave blaze
instead of using sin(2a) = 2sin(a)cos(a)
I did that : sin(6x) = sin(2x+4x) = sin(2x)cos(4x) + sin(4x)cos(2x)
the numerator doesn't change
after that we will have :
$\frac{\frac{\sqrt{3}}{2} \cos(2x) - \frac{1}{2} \sin(2x)}{\sin(2x) \cos(4x) + \sin(4x) \cos(2x)}$
glossy valveBOT
Ｈｅｒｅｌｓ
brave blaze
we separate the fraction like this :
$\frac{\frac{\sqrt{3}}{2} \cos(2x)}{\sin(2x) \cos(4x) + \sin(4x) \cos(2x)} - {\frac{1}{2} \sin(2x)}{\sin(2x) \cos(4x) + \sin(4x) \cos(2x)}$
oups
I did a mistake with latex xd
$\frac{\frac{\sqrt{3}}{2} \cos(2x)}}{\sin(2x) \cos(4x) + \sin(4x) \cos(2x)} - \frac{\frac{1}{2} \sin(2x)}{\sin(2x) \cos(4x) + \sin(4x) \cos(2x)}$
oh my god
well lets type everything
spice orchid
Double dollar at end?
glossy valveBOT
Ｈｅｒｅｌｓ
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brave blaze
still
spice orchid
Rip lol
brave blaze
$$\frac{\frac{\sqrt{3}}{2} \cos(2x)}{\sin(2x) \cos(4x) + \sin(4x) \cos(2x)} - \frac{\frac{1}{2} \sin(2x)}{\sin(2x) \cos(4x) + \sin(4x) \cos(2x)}$$
glossy valveBOT
Ｈｅｒｅｌｓ
brave blaze
nice
and in the first term, we factor by cos(2x) and in the second by sin(2x)
$$\frac{\frac{\sqrt{3}}{2}}{\tan(2x) \cos(4x) + \sin(4x)} - \frac{\frac{1}{2}}{\frac{\sin(4x)}{\tan(2x)} + \cos(4x)}$$
glossy valveBOT
Ｈｅｒｅｌｓ
sharp gyro
😦
This is so complicated for starting calculus
We have not even solved anything like this in class yet
gritty rose
Is it still this problem?
gritty rose
Try sin(4x+2x) in the denominator instead
brave blaze
that's what I did xd
sharp gyro
what does that mean
brave blaze
it will be hell
sharp gyro
there is no way our prof expects us to to this if its so hard
there must be something wrong
brave blaze
he means sin(4x) = sin(2*2x) = 2sin(2x)cos(2x)
it will become way harder than it already is
daddy l'Hopital will save us I guess
sharp gyro
I cant use it tho 😦
brave blaze
I'm tired fr
sharp gyro
Should I ask my prof about this?
Doesn't make sense for it to be this hard if we are just starting to see limits
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@smoky creek Has your question been resolved?
sharp gyro
Should we close this for now?
smoky creek
Should we close this for now?
Do you want me to?
brave blaze
depends of you
sharp gyro
Sure, I already sent an e-mail to the prof and he probably won't answer soon so I'll wait and see what he says
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smoky creek
Ok
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thick dove
Too much for my brain here
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Too much for my brain here
faint dock
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tawny jolt
hello can anyone help m with lorenz curve?
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hello can anyone help m with lorenz curve?
@tawny jolt Has your question been resolved?
tawny jolt
<@&286206848099549185>
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orchid bear
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orchid bear
I specifically need help with B
but probably also C and D
Also, is my answer correct on A?
I wrote: DNE because (lim as x -> -1+) does not equal (lim as x -> -1-)
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orchid bear
<@&286206848099549185>
nova basin
I wrote: `DNE because (lim as x -> -1+) does not equal (lim as x -> -1-)`
for a), the values are going to 1 no matter whether you come from the left or the right
orchid bear
for a), the values are going to 1 no matter whether you come from the left or th...
but wouldn't the jump discontinuity make that not work?
nova basin
limits ignore the value itself
that's why you can (and do) define continuity as limit = actual value
nova basin
there's not really anything particular going on at x=1.5 so you can just read the values (because f and g are continuous at x=1.5)
orchid bear
there's not really anything particular going on at x=1.5 so you can just read th...
but the value of f(x) at 1.5 is not a whole number
nova basin
we're not working with integers here, but that's not a problem
orchid bear
we're not working with integers here, but that's not a problem
should I just guess then?
nova basin
you can just assume something like f(1.5) = 1/4 and use that (because it's safe to say it's a parabola of slope at x=2 equal to 2, hence y=(x-1)² in this region and f(1.5)=1/4)
orchid bear
you can just assume something like f(1.5) = 1/4 and use that (because it's safe ...
so Im kinda guessing at the function
And then just evaluating?
nova basin
if you can use a ruler if you want to be sure
orchid bear
limit of sum = sum of limits
so literally just .25 plus -.05?
nova basin
-0.25 yes
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spring horizon
Could someone help solve this without using inverse
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Could someone help solve this without using inverse
spring horizon
<@&286206848099549185>
spring horizon
is their a method without inverse?
rocky vale
If there is one, it's certainly not common knowledge
There are some values of sin and cos you could be reasonably expected to have memorized, but not anything like this
spring horizon
or like one without the advanced inverse applications like the K and E
rocky vale
K and E?
spring horizon
sorry I meant without using arcos
spring horizon
math
rocky vale
I know lol
spring horizon
10
rocky vale
I mean, like high school geometry?
spring horizon
we are doing a glimpse of trig functions
spring horizon
idk how to, could you show me a step by step solution?
rocky vale
🤷 It's all just calculator work
Calculate the expression on the right
And then take the arccos of that
spring horizon
but we didnt learn anything about arccos so I dont want to have the teacher think I cheated
like that
only the basics cos tan sin cos csc etc
rocky vale
There's really no other way to do it
Your teacher isn't going to expect you to calculate trig functions by hand
spring horizon
oh okay, so what would I punch into my calculator
spring horizon
okay let me try rq
im getting the same thing
like if I arccos the right side I get the correct answer
but would I need to show my work for that??
rocky vale
There's nothing to show except that you took arccos of both sides
on the left it cancels with cos
spring horizon
oh okay thanks a lot man! didnt know it was that simple lol
rocky vale
No problem
spring horizon
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spring horizon
but you know how to get beta?
if the answer is 81 degrees, do you do 360-81 and that gives beta with the same cosine ratio?
oh ok sick thanks!
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torn jolt
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fathom saddle
There's no complex numbers here, so can't be
dim wolf
I need help
Open a different channel
dim wolf
torn jolt
There's no complex numbers here, so can't be
oh riht
the i and j are just for vectors?
not omplexx
fathom saddle
Ye
torn jolt
is it just
wooden remnant
<#488120190538743810>
None available
dim wolf
None available
I can see that there are
fathom saddle
Perhaps someone can check the answer for you
wooden remnant
I can see that there are
Aren't*
dim wolf
There are 3 available
wooden remnant
Where.
fathom saddle
Some people man
wooden remnant
Dude this is urgent
wooden remnant
I forgot this sibject
torn jolt
@wooden remnant
wooden remnant
And ty
fathom saddle
Very nice of you pike. Fine I'll check your answer kek
torn jolt
the constant should be (sint+cost)
i think..
wait
u can do some trig identity stuff for this can't you?
actutally no nevermind
fathom saddle
,w magnitude of the derivative of (e^(-t)sin(t))(1,0) + (e^(-t)cos(t))(0,1)
fathom saddle
I'm getting sqrt(2)
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fathom saddle
haha yes
fathom saddle
What did you get?
torn jolt
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torn jolt
How do i determine if this is true or false?
stiff musk
what is your definition of "critical number"?
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@torn jolt Has your question been resolved?
torn jolt
crticality is based on the substance being identified
cursive summit
I solved part a and am now stuck on how to get part b I put part a bc u need it to solve part b
static leaf
hello
how is your day
uhm
do u know what algebra is
you usually learn this in algebra 1, taught anywhere from 7th to 9th grade
4x-9=11
4x=20
x=5
that's how you would solve it for example
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shadow parcel
how can i check if a decimal, when written in base 3, contains a 1 in any of its digits?
shadow parcel
i want to do it without converting to base 3 and checking the digits
onyx glen
p sure it's impossible without converting to base 3 or doing something equivalent to that
stiff musk
if the fractional part's base 3 expression only contains 0's and 2's then it's in the cantor set, so that's kinda fun
shadow parcel
thats where im coming from
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wet briar
Find the next three numbers in the following sequence: 3,8,19,46,111,268, ...
plush egret
Find the next three numbers in the following sequence: 3,8,19,46,111,268, ...
use oeis 
j/k, what have you tried?
stiff musk
questions like this are so ridiculous
scarlet dirge
stiff musk
there's not much mathematical content here, any three numbers are possible and viable
wet briar
Sorry for the stupid question. I've tried arithmetic sequences and geometric sequences but they dont work
plush egret
apparently its a ||second order recursive relation||
but these questions who knows
it could be anything you want
wet briar
alright
wet briar
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ember tartan
Given a vector $<-4, 5, 5>$, how do i find its direction?
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Given a vector $<-4, 5, 5>$, how do i find its direction?
glossy valveBOT
beanbeanjuice
ember tartan
I know it's magnitude will be
$\sqrt{4^2 + 5^2 + 5^2}$
glossy valveBOT
beanbeanjuice
ember tartan
OR LENGTH
sorry caps
but in terms of direction, im not sure
apparently the direction should be in terms of a vector
stiff musk
depends on how you want to specify direction
ember tartan
but doesn't that just mean the direction is the vector itself?
stiff musk
i mean one way is just to normalize the vector so you get a unit vector
ember tartan
normalising as in putting the vector in terms of unit vectors like the quake algorithm thingy
stiff musk
just divide the vector by its magnitude
glossy valveBOT
beanbeanjuice
stiff musk
yeah
stiff musk
pleasure
ember tartan
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formal breach
$mv=F\Delta t$
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$mv=F\Delta t$
glossy valveBOT
emily ✿
formal breach
this formula exists for momentum and impulse
is there an angular version of this formula?
$I\omega=\tau \Delta t$
glossy valveBOT
emily ✿
formal breach
something like this?
kind jay
delta w Yes
hollow wigeon
how would I solve y=4x^2 - 3
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how would I solve y=4x^2 - 3
dense mist
?
dapper forge
What do you need to find for the question?
amber sapphire
dense mist
ya
hollow wigeon
how would I do that?
hollow wigeon
idk how to get the vertex 😭
hallow flare
light sonnet
idk how to get the vertex 😭
Sounds like you need to do some more research on your own and learn the prior knowledge you need
hollow wigeon
Sounds like you need to do some more research on your own and learn the prior kn...
ye it does 😭
alright im gonna do some research
I'll be back in 10
alright I got it!
@light sonnet I was able to solve it
thank you guys for the help
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wild tundra
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wild tundra
I need help with these 2 sums
tight glen
do you know the laws of exponents?
wild tundra
do you know the laws of exponents?
multiplying the exponents??
tough garnet
May help
light sonnet
How does (10^5)^2 = 100?
wild tundra
the bracket means we multiply with the outer number so it becomes 10 so 10 x 10 = 100
wild tundra
I am even more confused than I was before
wild tundra
Im confused with what to do with the powers
tight glen
ok, have you learnt how to deal with powers before?
wild tundra
not really this is one our new topics
wild tundra
what are considering x for the product rule?
wild tundra
thank u, Ill watch it right now
supple jay
ž
supple jay
guys
i solved derivation like this
but my teacher also continued like
and made -6 = 4/1
hmm
oh w8
light sonnet
and made -6 = 4/1
Not how math works
light sonnet
case closed
Alright, then .close to close the channel
full forumBOT
@supple jay Has your question been resolved?
kind cypress
If $p_n$ is a strictly increasing sequence of positive numbers such that $\sum\frac1{p_n}$ converges, I want to prove that $\frac{n}{p_n} \to 0$
glossy valveBOT
Syst3ms
kind cypress
My first instinct was that if n/p_n didn't converge to 0, I could find a subsequence that is always above a positive number, and i'd get a contradiction because of the divergence of the harmonic series
The problem is, it could be that the appropriate subsequence is spread out enough that the reciprocal of the function that selects the indices has a convergent series
full forumBOT
@kind cypress Has your question been resolved?
full forumBOT
@kind cypress Has your question been resolved?
torn jolt
Headscratcher you have here
And not well formulated i think
Here is an equivalent problem
kind cypress
Oh yeah, that hint does it
That identity gives $0 \le 2na_{2n} \le 2\sum_{k=n+1}^{2n} a_k \le 2\sum_{k=n+1}^\infty a_k \underset{n\to\infty}{\to} 0$
glossy valveBOT
Syst3ms
torn jolt
That identity gives $0 \le 2na_{2n} \le 2\sum_{k=n+1}^{2n} a_k \le 2\sum_{k=n+1}...
nice one, I think you proved the subsequence $(a_{2n})$ converges
kind cypress
And $0 \le (2n+1)a_{2n+1} \le 2(n+1)a_{2n+1} \le 2\sum_{k=n+1}^{2n+1} a_k \le 2\sum_{k=n+1}^\infty a_k \underset{n\to\infty}{\to} 0$
kind cypress
Hence 2n*a_2n and (2n+1)a_(2n+1) both converge towards 0, so na_n converges towards 0
torn jolt
And $0 \le (2n+1)a_{2n+1} \le 2(n+1)a_{2n+1} \le 2\sum_{k=n+1}^{2n+1} a_k \le 2\...
I am not sure here, how did you prove that $a_{2n+1} \le \sum_{k=n+1}^{2n+1} a_k$ ??
glossy valveBOT
AimaneSN
kind cypress
No, i proved $(n+1)a_{2n+1} \le \sum_{k=n+1}^{2n+1} a_k$
glossy valveBOT
Syst3ms
kind cypress
And that's just using a_n being decreasing
torn jolt
No, i proved $(n+1)a_{2n+1} \le \sum_{k=n+1}^{2n+1} a_k$
how ?
kind cypress
$(n+1)a_{2n+1} = \sum_{k=n+1}^{2n+1} a_{2n+1} \le\sum_{k=n+1}^{2n+1} a_k$
glossy valveBOT
Syst3ms
kind cypress
But yeah, it's really tough without any hint
torn jolt
But yeah, it's really tough without any hint
yeah the hint is difficult to see honestly
kind cypress
I did have ideas of expressing n*a_n as a_n+...+a_n and using inequalities
but nothing really fleshed out
torn jolt
I did have ideas of expressing n*a_n as a_n+...+a_n and using inequalities
that's the way to go but the inequality in the hint is tricky haha
kind cypress
Anyhow
torn jolt
maybe a proof using the definition of a limit is possible
but may require the same trick
kind cypress
The actual question is even more opaque than this
torn jolt
The actual question is even more opaque than this
what is it
kind cypress
It's asking what the implications are between (na_n) converging towards 0 and the series of a_n converging
So also have to guess that the series converging actually implies na_n -> 0
(the converse isn't true, consider a_n = 1/n*ln(n))
torn jolt
(the converse isn't true, consider a_n = 1/n*ln(n))
yep nice example, $(a_n) \to 0$ definitely doesn't imply $(na_n) \to 0$
glossy valveBOT
AimaneSN
torn jolt
the converse seems true
but not sure how to prove it
if $(a_n)$ is nonnegative we can just write $a_n \le na_n \forall n$ and since RHS converges, LHS converges too
glossy valveBOT
AimaneSN
kind cypress
we just proved the converse
if the series of a_n converges, na_n converges towards 0
the series, not the sequence
torn jolt
if the series of a_n converges, na_n converges towards 0
no you only proved that if the sequence is decreasing
torn jolt
but sounds true in the general case
torn jolt
if $(a_n)$ is nonnegative we can just write $a_n \le na_n \forall n$ and since R...
my proof here can't be true, I didn't even assume a_n to be decreasing
but not clear to me where is the mistake
kind cypress
We're asking about the sum of the a_n, not the sequence
torn jolt
We're asking about the sum of the a_n, not the sequence
Ah I see
kind cypress
The result isn't true if a_n isn't decreasing
torn jolt
so you want to know if $(na_n) \to 0$ implies $\sum a_n \to 0$
kind cypress
Here's an example to boot
glossy valveBOT
AimaneSN
kind cypress
that's false, a_n=1/n*ln(n)
But, it is also false that $\sum a_n$ converges $\implies na_n \to 0$ if $a_n$ isn't decreasing
torn jolt
that's false, a_n=1/n*ln(n)
but here $(na_n)$ doesn't converge to 0
glossy valveBOT
AimaneSN
glossy valveBOT
Syst3ms
kind cypress
A simple example to boot
Consider a_n = 1/n if n is a perfect square and 0 otherwise
Then na_n = 0 if n isn't a perfect square and 1 otherwise, clearly doesn't converge towards 0
Yet $\sum a_n = \sum_{k=1}^\infty \frac1{n^2}$ which converges
void wedge
I'm new to integration and my teacher said that this function is non integrable, what does that mean?
tired tapir
I'm new to integration and my teacher said that this function is non integrable,...
it means that ine integral is impossible to evaluate, so no matter how hard you try you will never find a function such that its derivative = sqrt(sin(x))
void wedge
it means that ine integral is impossible to evaluate, so no matter how hard you ...
i get the literal meaning, but why is that
like you can find the derivative of any function
tired tapir
oh of you are looking for a proof of why this specific one is non integrable then idk lol
void wedge
not this specific but a general idea I guess
like is it impossible to find the area under this?
doesn't intuitively feel impossible
tired tapir
no, some functions can be evaluated between limits but finding an algebraic formula for any limits is impossible
for example $e^{-x^2}$ is non integrable but $$\int ^\infty _{-\infty} e^{-x^2} dx = \sqrt{\pi}$$
glossy valveBOT
Nathan_
void wedge
does -inf to inf mean indefinite integral?
tired tapir
yes
glossy valveBOT
AimaneSN
void wedge
.close
full forumBOT
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Available help channel!
lavish comet
Hi
static leaf
just look at the first term lol
then the second
then the third
to narrow answers to 1
using the logic of multiplying sets
neat bay
That is the most straightforward obvious definition lol
neat bay
shows up a lot in group theory
Why would someone want to compute {a^2b, ba} times {ab^k} though
Seems very random
stiff musk
i guess just to practice the concept
lavish comet
Its an assume qeustion
Question*
Is it hard?
Cause if not
I would love help with one like this please
All these questions have confused me very much
olive saffron
oh god it's formal language theory
okay
I assume this is from a computer science course?
olive saffron
I'll take a crack at it, though I haven't touched context-free grammars in several years
It is perhaps most enlightening to consider each possible answer in order
The first set of production rules can produce, for example, strings such as $10$ via $$S \rightarrow 1S \rightarrow 10S \rightarrow 10 \epsilon$$
glossy valveBOT
jckynaston
olive saffron
Where I have included the terminal $\epsilon$ for clarity
glossy valveBOT
jckynaston
olive saffron
The second rule fails for similar reasons, and also does not include an $\epsilon$-production
glossy valveBOT
jckynaston
random oracle
How to solve this im doing law of sines thing.
olive saffron
The third rule fails because it also does not include an $\epsilon$-production, leaving only the fourth rule
glossy valveBOT
jckynaston
olive saffron
Does that make sense @lavish comet ?
olive saffron
Yep
glossy valveBOT
jckynaston
lavish comet
So it will always be S TO 0A?
Thats a rule?
So, the top 2 are marked of cause they do not go to 0A
olive saffron
There are two possibilities when you start with $S$, either you follow the first rule $S \rightarrow 0A$ or the second rule $S \rightarrow 1B$.
glossy valveBOT
jckynaston
olive saffron
The top one is marked off because it generates the language ${0,1}^$, where $^$ is the Kleene star
glossy valveBOT
jckynaston
olive saffron
The second and third are mark off because they do not contain $\epsilon$-productions
glossy valveBOT
jckynaston
olive saffron
And therefore the strings in their languages do not terminate (if my memory serves - I'm a mathematician who took this kind of course like six years ago now)
olive saffron
Yes, iirc
That's the rule that basically says "stop making this string longer now"
lavish comet
Ok so
It has to start like S to 0A or S To 1B
No other way to start or go through
olive saffron
Yes
lavish comet
?
olive saffron
That's what the fourth grammar says, yes
lavish comet
Nice
And you say the top one is marked of because it
Generates the language 0,1
?
What does this mean?
olive saffron
The language ${0, 1}^$ is the language ${0, 1, 00, 01, 10, 11, 000, 001, 010, 011, 100, ... }$. Basically, all possible combinations of $0$ and $1$ - that's what the symbol $^$ means.
glossy valveBOT
jckynaston
lavish comet
Is it becuase it does 0S?
olive saffron
It's because you have the two rules $S \rightarrow 0S$ AND $S \rightarrow 1S$. So, you start with $S$ and can keep adding either $0$ or $1$ to the front until you stop.
glossy valveBOT
jckynaston
olive saffron
It's wrong because it lets you generate words like 10, which are not listed in the question
Do you understand how to generate a language given a set of rules?
olive saffron
Right, I see
Well that would be a good place to start
I assume you're doing these questions as part of a course?
If so, it may be prudent to read said course material
olive saffron
Generating a language from its grammar is pretty straightforward
Though it'll largely depend on the depth of the course
lavish comet
Also with this question. I know why it is 22. But why does it have with margin?
lavish comet
Though it'll largely depend on the depth of the course
Oh ok thank you
olive saffron
Also with this question. I know why it is 22. But why does it have with margin?
Erm not sure. I think it's probably just the test software saying "the answer is 22 with a margin of error of 0"
Some questions might be like "22 (with margin: 0.5)", so it'd also accept 22.2, for example
Just me guessing anyway
lavish comet
OH ok
Thank you
If you are willing to help with anymore I would apprieceate it
Its fine if not
I was gonna ask about this?
Is it the top because is got the E?
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@lavish comet Has your question been resolved?
hollow wyvern
Can someone help solve this rational equation?
full forumBOT
Can someone help solve this rational equation?
hollow wyvern
torn karma
you remember how to add fractions with unlike denominators, right?
do that to the right side
it will become very clear
although you have to watch for extraneous solutions(if they are there)
hollow wyvern
Ok
Could you just do it for me lmfao
I’ve been working on it all day
Cant figure it out smh
torn karma
Could you just do it for me lmfao
one part of solving equations is combining the fractions with different denominators. this makes it much easier to manipulate one side of the equation
how would you turn this into one fraction?
adding 2/5 and 1.3 requires you to do this:
I understand that it seems more frustrating to do it with variables, but the process remains the same
to add a/b and c/d
you would multiply a/b by d/d and multiply c/d by b/b to get a common denominator
you aren't changing the actual values, but you are representing them differently so you can actually add them
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@hollow wyvern Has your question been resolved?
lavish comet
Hi
lavish comet
homogeneous recurrence. Im confused on what this is can anyone help me with this topic please?
silent hedge
question about l,hopitals rule (analysis):
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question about l,hopitals rule (analysis):
silent hedge
in the example above, can we use the rule even if the bottom function is zero at x=2 ?
nvm the theorem states its derivative cant be zero
.close
copper sequoia
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copper sequoia
It's a h.w and i actually don't know where to start from..
plush egret
do you know how to distribute?
foggy tree
Well to start do you know what fractional exponents mean
copper sequoia
Yes i do