I GOT IT
#help-33
digital spindle
*1:3
H8 to break it to you
You still have 5 mins remaining but that one is wrong
@upper anchor hey listen
I actually messed up
So sorry
digital spindle
We have $\frac{AD}{DC}= \frac{1}{3}$
elfin berryBOT
Lelouch
upper anchor
uh huh
digital spindle
Surely u understand this
upper anchor
yea
digital spindle
With this we have $\frac{CD}{DB}=\frac{1}{3}$
elfin berryBOT
Lelouch
upper anchor
yea
digital spindle
Now we take this equation again
upper anchor
uh huh
digital spindle
We multiply both sides by $(DC)$
upper anchor
y
elfin berryBOT
Lelouch
digital spindle
There is the correction
upper anchor
ok
digital spindle
We multiply both sides by DC
upper anchor
uh huh
digital spindle
So we have $(AD)=\frac{(DC)^2}{DB}$
elfin berryBOT
Lelouch
elfin berryBOT
Lelouch
digital spindle
Now divide both sides by $(DB)^2$
elfin berryBOT
Lelouch
digital spindle
No wait
upper anchor
ok
digital spindle
$\frac{AD}{DB}= \left ( \frac{CD}{DB} \right )^2$
elfin berryBOT
Lelouch
digital spindle
We know that $\frac{CD}{DB}$ is 1/3
elfin berryBOT
Lelouch
upper anchor
im 13
digital spindle
Japan or sum shit
upper anchor
georgia
upper anchor
yea
digital spindle
I did this when i was 15 but anyways
digital spindle
No 13 year old should be given to do this wtf
upper anchor
No 13 year old should be given to do this wtf
remember my parents are asian too
digital spindle
I thought so , this isn't from your school, it's from ur parents
digital spindle
Tell me, do you really like learning math? Or r u being forced?
upper anchor
yea
digital spindle
I think you will learn this in 10th grade
upper anchor
but im tryna get everything done
so i can take a break
and wont have to worry bout this
digital spindle
That's a good mindset but remember to not force urself to learn , that's a grave mistake and is the worst way of learning cuz u will eventually understand nothing
digital spindle
:3 srsly tho
digital spindle
Well if the sides are in ratio 1 is to 3 then what about the areas?
upper anchor
also 1:3?
upper anchor
I think you will learn this in 10th grade
im in 8th grd so according to my mom im gonna learn it soon
digital spindle
No more hints after this, AOD is similar to COB
upper anchor
yep
digital spindle
No more hints after this, AOD is similar to COB
@upper anchor if i give u any more info , then there is no point so...
I think you should play with equations in this one , for a good 30 minutes
Like don't stop untill u solve
Without help
I am going to eat dinner now
I will take a look at this after that
digital spindle
I think you should play with equations in this one , for a good 30 minutes
I used to be stuck on problems for a good week , and still not look at the solution or any hints , cuz it would hurt my ego , and that will build skill in math
upper anchor
oh
i understand
thank you for ur wise words great Lelouch
@digital spindle
GREAT LELOUCH
I GOT IT
ITS 9
TYSM FOR UR GREAT WORDS
digital spindle
Well done !
digital spindle
ty for ur great words
:3
upper anchor
bye lelouch :))
digital spindle
i will take a break now
As u should
digital spindle
bye lelouch :))
Bye,
marsh citrusBOT
@upper anchor Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
safe crescent
I need help to prepare for my exams
astral pagoda
can you just send all of your question/doubts in here so that everyone can help?
marsh citrusBOT
@safe crescent Has your question been resolved?
radiant abyss
marsh citrusBOT
radiant abyss
Condition 3 should say f(x) > x
instead of f(x) < y
does this transformation exist?
if so what is it?
if not why?
marsh citrusBOT
@radiant abyss Has your question been resolved?
marsh citrusBOT
@radiant abyss Has your question been resolved?
still temple
marsh citrusBOT
bright jay
Did you try anything?
still temple
yup
leaden monolith
what did you try
bright jay
Are you posting your work?
still temple
leaden monolith
9^(1/2) is √9
bright jay
They did that
leaden monolith
oh
bright jay
They didn't show that part
still temple
is my working out incorrect
leaden monolith
so is it wrong then
bright jay
Assuming that's a multiplication sign, then everything looks correct
still temple
hmmmm i somehow messed up
leaden monolith
im kinda confused what you needed help with
leaden monolith
surely you didn't mess up 3 * 16
iron meadow
did you multiply 3x16 correctly?
still temple
now I did but before i did it wrong
iron meadow
what did you get?
lean flame
,calc 3*6
elfin berryBOT
Result:
18
👍
leaden monolith
lol haha all good
lean flame
,calc 3*18
elfin berryBOT
Result:
54
✅
iron meadow
....
still temple
.close
iron meadow
:\
marsh citrusBOT
lean flame
, calculate 3"16
elfin berryBOT
The following error occured while calculating:
Error: Unexpected operator " (char 8)
lean flame
💀
iron meadow
do they not teach multiplication table anymore these days?
lean flame
Why use brain cells when there is bot calculator
burnt abyss
fr
iron meadow
good question, ponder that one for a while 😄
bright jay
do they not teach multiplication table anymore these days?
Not the 16 times table
I only know up to 12
iron meadow
3x10 + 3x6, surely you can add those together : )
burnt abyss
,w \frac{9^{\frac{1}{2}}}{4^{-2}}
elfin berryBOT
Requested by Mike Oxbig#0599
bright jay
,w \frac{9^{\frac{1}{2}}}{4^{-2}}
Don't think it likes the latex part
elfin berryBOT
burnt abyss
there we go
marsh citrusBOT
Available help channel!
plucky anvil
I'm trying to understand Markov chains, is this a correct Markov chain for the sentence "hello how are hello you"? (p means probability)
marsh citrusBOT
I'm trying to understand Markov chains, is this a correct Markov chain for the s...
@plucky anvil Has your question been resolved?
plucky anvil
<@&286206848099549185> maybe someone who knows markov chains?
proven timber
Looks right, though I don't know if "you" loops back to "hello," but I haven't done Markov chains in forever
plucky anvil
Looks right, though I don't know if "you" loops back to "hello," but I haven't d...
if it wouldn't, then what would happen if the current state is "you"?
proven timber
if it wouldn't, then what would happen if the current state is "you"?
Terminate? Idk, you're probably better off ignoring me in terms of the ending bit. I'm fairly certain everything else is correct though
plucky anvil
I think I'll keep it like that to take into account this "edge case". Thank you for your help!
narrow jetty
i already did the first part. how can i get the second part?
marsh citrusBOT
i already did the first part. how can i get the second part?
narrow jetty
wait i think it's 10654.50 is that right?
glad topaz
yup
frosty wraith
marsh citrusBOT
frosty wraith
For 14 do I just put e-3 in my calculator
Or do I use ln
Fuck math finals on the last day of school
Help
marsh citrusBOT
@frosty wraith Has your question been resolved?
tall scaffold
Guys, I need to prove that
∃x ∈ N ∀y ∈ N, x ≤ y
marsh citrusBOT
Guys, I need to prove that
∃x ∈ N ∀y ∈ N, x ≤ y
tall scaffold
I know x=0
Since every number is greater than 0
But I have no idea how to out it into words
Put*
sharp mortar
you just did
marsh citrusBOT
@tall scaffold Has your question been resolved?
spiral cedar
tiny acorn
marsh citrusBOT
tiny acorn
<@&286206848099549185>
i need help
on this question
i need to make a algebra equation
marsh citrusBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
@tiny acorn Has your question been resolved?
fiery junco
marsh citrusBOT
fiery junco
Can someone explain 1d
still temple
well what'd you get for 1a,b,c?
still temple
you sure that (2,0,2)x(-4,0,-4)=16?
still temple
You are right, I ignored those bars. But anyways if you noticed the 2 normal vectors you get from axb and bxc are parallel which tells us that all three lie on the same plane since they share a normal vector.
fiery junco
i dont understand how you know they are parralel
is it because they are both on the xz plane
still temple
if you took the cross product of the normal vectors you'd get the 0 vector further telling you that they are parallel. But also vectors are parallel if they are just a scalar multiple and -2(2,0,2)=(-4,0,-4)
fiery junco
ahhh okok
still temple
and it can be logically see that a,b,c are coplanar because if axb forms a plane and bxc forms a parallel plane then both planes must share vector b. So, they're coplanar
marsh citrusBOT
@fiery junco Has your question been resolved?
snow sun
can someone give the solution for this the red text is the answer
marsh citrusBOT
can someone give the solution for this the red text is the answer
proud oxide
Why do you have answers next to the question
anyways
you should be aware of what sin, cos, and tan do
@snow sun
snow sun
you should be aware of what sin, cos, and tan do
i do but i can't make the solution cause i have class in 5 mins and im supposed to be doing a presentation
halcyon spire
i do but i can't make the solution cause i have class in 5 mins and im supposed ...
soh cah toa
snow sun
the opposite adjacent side
snow sun
soh cah toa
what
omg i have to go
i have the other ones i just need 1 more but ill just do them on the bus
THANKS FOR HELPING THO
.close
marsh citrusBOT
proud oxide
the opposite adjacent side
And we are looking for opposite and know adjacent
marsh citrusBOT
Available help channel!
summer kayak
What is 98 in z13
marsh citrusBOT
What is 98 in z13
mystic minnow
either do the division to find the remainder or subtract 13 until you get to a value in Z13
marsh citrusBOT
@summer kayak Has your question been resolved?
ashen pivot
marsh citrusBOT
hasty cliff
Observe $$\left(1 + \frac{1}{x^2}\right)^{3x-4} = \frac{\left(1 + \frac{1}{x^2}\right)^{3x}}{\left(1+ \frac{1}{x^2}\right)^4}$$
elfin berryBOT
BenJr
ashen pivot
Yea
lean flame
"good morning world" what a generic ass name
hasty cliff
Now for the top, how should we approach it?
lean flame
"BenJr" is your father Benjamin Franklin?
hasty cliff
We know lim((1+1/x)^x) = e.
ashen pivot
Yes
hasty cliff
Observe $$\lim((1+\frac{1}{x^2})^{3x}) = \lim(e^{3x\log(1+\frac{1}{x^2})})$$.
elfin berryBOT
BenJr
ashen pivot
Okay
hasty cliff
To evalue the right side lim, we just need to e^lim(…) instead.
Where … is the stuff on top of e.
We have infinitely times 0 when evaluating the limit.
Do you see that?
I switch over to laptop to make this easier.
ashen pivot
Alright tks
hasty cliff
I know
blissful berry
that is log to the base e
ashen pivot
What will happen when” infinity” times 0
blissful berry
What will happen when” infinity” times 0
0
ashen pivot
So it will be e^0
Which is 1
So 1/1
=1
But it is weird seeing infinity times 0
hasty cliff
$$\lim_{x\to\infty}\left(1+\frac{1}{x^2}\right)^{3x} = \lim_{x\to\infty}e^{3x\log\left(1+\frac{1}{x^2}\right)$$.
proper zodiac
But it is weird seeing infinity times 0
It's not always, different fields of maths take different conventions
blissful berry
if not then the question is simply wrong as log requires base
elfin berryBOT
BenJr
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
hasty cliff
**BenJr**
Compile Error! Click the <:errors:504266556054962196> reaction for mor...
the right side follows from power rule of log.
proper zodiac
the question arises that the log here is really ln or not
They are using log for ln, nothing more going on here
hasty cliff
$$\lim_{x\to\infty}e^{3x\log\left(1+\frac{1}{x^2}\right) = e^{\lim_{x\to\infty}3x\log\left(1+\frac{1}{x^2}\right)$$.
elfin berryBOT
BenJr
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
hasty cliff
$$\lim_{x\to\infty}e^{3x\log\left(1+\frac{1}{x^2}\right) = e^{\lim_{x\to\infty}3...
3x goes to infity and log(1+1/x^2) goes to 0 as x goes to infinity. So we have an indeterminate form.
Applying lhopital rule we have.
hasty cliff
$$\lim_{x\to\infty}e^{3x\log\left(1+\frac{1}{x^2}\right) = e^{\lim_{x\to\infty}3...
$$e^{\lim{x\to\infty}3x\log\left(1+\frac{1}{x^2}\right) = e^{\lim_{x\to\infty}\frac{\log\left(1+\frac{1}{x^2}\right)}{\frac{1}{x^2}}$$
elfin berryBOT
BenJr
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
hasty cliff
Sorry about my latex.
when you take the derivative of top and bottom of right side and we evalute the limit we have e^lim(...) = e.
so $\lim_{x\to\infty}\left(1+\frac{1}{x^2}\right)^{3x} = e$.
elfin berryBOT
BenJr
hasty cliff
@ashen pivot
hasty cliff
yep.
ashen pivot
But Answer is 1 I think
It comes out with this
hasty cliff
for which one?
hasty cliff
**BenJr**
Sorry, the whole latex mess was me trying to this ^.
I look for a link online that explains it clearly.
Here, the idea I used is basically what the 2nd person answered.
You have to scroll down to see it. Not talking about the comments to the questions.
ashen pivot
I see
I found the answer of the question should be 1
Anyway thanks for your help
.close
sullen valley
.help
marsh citrusBOT
Commands:
clopen: .close, .reopen
factoids: .tag
help: .help
Type .help <command name> for more info on a command.
sullen valley
.help me
marsh citrusBOT
No command called "me" found.
sullen valley
.reopen
still temple
Why is sinx times 1+cosx equal to -1? And why is 1-cosx times 1+cosx equal to sinx
marsh citrusBOT
Why is sinx times 1+cosx equal to -1? And why is 1-cosx times 1+cosx equal to si...
still temple
Not sure how they arrive at that. lol
swift cypress
Why is sinx times 1+cosx equal to -1? And why is 1-cosx times 1+cosx equal to si...
where do you see that
still temple
the red box
blissful siren
yh
marsh citrusBOT
@still temple Has your question been resolved?
raven wasp
We're playing a game, if I flip heads you give me $30 if I flip tails I give the coin to you, then you go. How much would you pay to go?
marsh citrusBOT
```We're playing a game, if I flip heads you give me $30 if I flip tails I give ...
raven wasp
i said 15$ because the P(H) = 1/2, and the probability of P(T) = 1/2. the outcome of flipping H is $30, so I multiplied that with 1/2 and the outcome of flipping tails is 0 since i am giving the coin to my opponent so i multiplied that by 0. i than add both events together (30*.5) + (0*.5) and got $15.
wanton wing
The person who flips heads wins on the spot. If tails is flipped, the game continues.
Scenarios in which opponent wins: H, TTH, TTTTH, TTTTTTH, etc
Scenarios in which I win: TH, TTTH, TTTTTH, etc
What is the probability that opponent wins? Sum of probabilities of all those cases. 1/2 + 1/8 + 1/32 +... = 2/3 (infinite geometric series formula)
So there's a 2/3 chance I lose $30
And similarly, a 1/3 chance I gain 30$
So on the whole I expect to obtain 2/3 x (-30) + 1/3 x (30) = -10$
So you'd have to pay me $10 to play
raven wasp
the question is asking how much would you pay?
raven wasp
not me paying you
raven wasp
Scenarios in which opponent wins: H, TTH, TTTTH, TTTTTTH, etc
Scenarios in which...
are those scenarios
where the opponet flips?
wanton wing
Yeah, I assumed the opponent flips first
Ohhh wait
"pay to go" means I get to go first right?
raven wasp
yeah
wanton wing
Okay sorry my bad
I misunderstood that part haha
Then the roles of 'me' and 'opponent' are flipped in my analysis, and I expect to win $10
So I'd pay $10 to go
wanton wing
If I flip heads I win. That's 1/2 chance
If I flip tails and you flip tails and I flip heads I win. That's a 1/8 chance
You can see where this is going?
raven wasp
how 1/8?
wanton wing
TailsxTailsxHeads, 1/2 x 1/2 x 1/2
raven wasp
ah
raven wasp
as long as you flip H at the end you win right?
wanton wing
This forms an infinite geometric progression, there's a nice formula to find the sum for that
wanton wing
as long as you flip H at the end you win right?
Yeah, and as long as the number of tails until then has been an even number
raven wasp
even number because it would mean that the opponent was the last person to give you the coin right?
wanton wing
Yep
raven wasp
is this the formula?
wanton wing
Although in this case n is infinity
And since r is smaller than 1, r^n basically gets smaller and smaller until it vanishes. So the formula reduces to a/1-r if n is infinity
wanton wing
the prob is r right?
r is the ratio between successive terms
The series goes like 1/2, 1/8, 1/32, etc
Each time we're multiplying by 1/4, so r=1/4
And the first term a=1/2
raven wasp
i can only have 1 H not 2 H
since 1 H is enough for me to win right?
how did you get the 1/3 than?
raven wasp
And the first term a=1/2
a1 right?
wanton wing
since 1 H is enough for me to win right?
Yeah
wanton wing
how did you get the 1/3 than?
First I calculated probability I win by doing 0.5/(1-0.25) = 2/3
Then the probability I lose is just 1 minus that
raven wasp
First I calculated probability I win by doing 0.5/(1-0.25) = 2/3
which equation is that?
raven wasp
r still the same
wanton wing
So the first term a1=0.25. R is same
wanton wing
Yeah
raven wasp
why did you multiply 1/3 by 30?
we would pay the amount we are expected to lose so we cant be in debt?
wanton wing
Yeah, that makes sense
raven wasp
if i pay $10
and i lose
i lose all my money but wont be in debt
but if i win
i gain the money i initally spent so i wont really gain money either
wanton wing
Yeah, it's like a break even
raven wasp
why do we do this?
wanton wing
Well um
So there's something called the expectation value
Also known as the mean
If I played the game a million times, how much in average would I expect to win?
That sounds like a fair idea of how much I should pay to go
(ideally I'd like to pay less but yeah)
raven wasp
im asking why do we pay an amount for me to gain profit every time?
wanton wing
If I pay more than that, I expect to lose
If I pay that much or less, I expect to gain
So I'm willing to pay up to 10$
raven wasp
ah
so i would either pay up to $10 since i wouldnt lose any money right?
either no gain or gain
no loss
wanton wing
Yeah
I mean if you only play a few times you could be unlucky
But with probability it's about hypothetically doing it lots of times and seeing the average
wanton wing
Np
glass viper
$1+sin(x)=\sqrt{3}cos(x)$
marsh citrusBOT
$1+sin(x)=\sqrt{3}cos(x)$
elfin berryBOT
Mohad
glass viper
any ideas?
marsh citrusBOT
@glass viper Has your question been resolved?
thorny jungle
Is the center of symmetric group and alternating group S4 and A4 only the identity?
marsh citrusBOT
Is the center of symmetric group and alternating group S4 and A4 only the identi...
marsh citrusBOT
@thorny jungle Has your question been resolved?
marsh citrusBOT
@thorny jungle Has your question been resolved?
proud pawn
Yes
If you take a non identity permutation σ in S4, then σ(i)=j for some i,j in {1,2,3,4}. (We could assume without loss of generality and by symmetry that i=1 and j=2, but no problem). But i≠j so σ(j)=k for some k≠i≠j, k≠j.
Now, if we consider (ij) we have that (ij)σ(i)=i but σ(ij)(i)=k, so σ and (ij) does not commute.
I think that suffices
rough plank
marsh citrusBOT
rough plank
iam at the radical rn
i need help on what to do next <@&286206848099549185>
what is the equation for the radical
so i have (90,50) and (130,30)
i just need help with the function now
marsh citrusBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
rough plank
sorry
but can u help me @proper zodiac
just what is the radiacl function
and where can u substitute my points
rough plank
y = x^(1/a)
so will it be 90^(1/a)=50
rough plank
y = -(x^(1/a))
-(90^(1/a))=50
glad topaz
yup
wait
ergh
forgot that every new function you add
needs translation from origin
so
it will be
y = -((x-90)^(1/a))+50
hopefuly you get a back that is positive
even better when integer
rough plank
y = -((x-90)^(1/a))+50
what is this
glad topaz
btw radical function means that a should equal 2
so it will wind up into
y = -sqrt(x-90)+50
rough plank
rough plank
y = -sqrt(x-90)+50
that didnt work
rough plank
ok
rough plank
glad topaz
there are 2 options from here to get it to work
rough plank
thats still wrong its not touching y=30
glad topaz
either you add parameter a before sqrt
as in
y = -a*sqrt(x-90) + 50
and the other
you change degree of a root
rough plank
what are you saying i dont understand
glad topaz
so
y = -((×-90)^(1/a))+50
but I dunno if this qualifies as radical function
I need to check literaturr
one moment
rough plank
<@&286206848099549185> ?
rough plank
what is the *
rough plank
so it became 50=sqrt(90)
glad topaz
if you plug x-a instead of x
rough plank
if you plug x-a instead of x
here why did u do this
glad topaz
you just move it to the right by value of a
so that it would atart from point 90
then I knew for value 90 it will be just 90-90
so 0
so it needs a little push to the up
by a 50
then for the final I stretched it a bit by just multiplicating term with x
and solved for second point
it was suppossed to be
y = -a*sqrt(x-90)+50
30 = -a*sqrt(130-90)+50
simplifying
a*sqrt(40) = 20
a = 20/(2*sqrt(10)) = sqrt(10)
then I knew that
sqrt(m)sqrt(n) = sqrt(mn)
so final formula was made
ping if you need any more help
rough plank
can we go on a vc @glad topaz
rough plank
wait vc doesnt work for me could u joine this instead https://zoom.us/j/96266401935?pwd=NTJXYnFabGYxNzZEaDgvUmZGZXgxUT09
@glad topaz
glad topaz
I'll try
marsh citrusBOT
@rough plank Has your question been resolved?
marsh citrusBOT
@rough plank Has your question been resolved?
flat aspen
in this khan academy limits course it says this
marsh citrusBOT
in this khan academy limits course it says this
flat aspen
i don't get how it knows what the function looks like when approaching from the right?
could you please explain this too me?
<@&286206848099549185>
dusky wing
When it approaches -6 from the right, we're looking at the values of x -5.9, -5.99, -5.999, and the value that h(x) gets close to. h(-5.999)=-1.02, that's close to -1.
flat aspen
When it approaches -6 from the right, we're looking at the values of x -5.9, -5....
i still don't get it? it said to also see what it is on the right side?
dusky wing
-5.999 is on the right side of 6, and is close. h(-5.999)=-1.02 is close to -1
flat aspen
.close
marsh citrusBOT
flat aspen
thanks
marsh citrusBOT
Available help channel!
glass viper
marsh citrusBOT
glass viper
Shouldnt it be -a/1+a^2?
bright jay
One, don't ping specific people, and two read #❓how-to-get-help
And open your own channel
fossil brook
Greetings!
Can someone tell me if I did the right thing? A negative answer seems wrong to me so I'm wondering if I solved it correctly or not
next ravine
You can graph the function on Desmos to see if the function is below the x-axis
It actually is in this case
Although if you don't want signed area, then positive is the way to go
fossil brook
So it's fine?
next ravine
If you'd like you can check the integral in Desmos
You can just give Desmos the integral and it'll give you the signed area
next ravine
yup!
marsh citrusBOT
untold brook
How would I do this
fiery path
can you quote your nth term for me please
wet zenith
Write the formula for Tn
Then equal it to the options i think, see for which one it works🤔
fiery path
the nth term is a + (n-1)d
untold brook
8n-5
fiery path
they will appear in teh sequence if n is an integer
marsh citrusBOT
marsh citrusBOT
marsh citrusBOT
noble nebula
nope.
noble nebula
It should get deleted any moment
ivory sundial
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main idol
,rotate
elfin berryBOT
merry plaza
im given (x1, x2, ..... , xn) thats a set of Rn dimensions, where n is the set of all positive integers, that satisfy (cosx1 + cosx2 + ... + cosxn = 0)
marsh citrusBOT
im given (x1, x2, ..... , xn) thats a set of Rn dimensions, where n is the set o...
marsh citrusBOT
@merry plaza Has your question been resolved?
normal oracle
I assume you're familiar with the notion of continuity -- what it means for a function to be continuous -- right? What definition for continuity are you using?
I think there's something confused in how you phrased the question -- probably you mean that for any fixed positive integer n, you must show that the points (x1, ..., xn) in R^n satisfying (cos x1 + ... + cos xn) = 0 are closed. Is that right?
(And non-compact)
hasty cliff
It’s clear for n = 1 that the set for this n is closed. Suppose it’s closed for some n >= 1, we want to show for n+1 the set is closed. Take any fixed points (x_1,…,x_n) such that cos(x_1) + … + cos(x_n) = 0. Let S be the set of real number x such that cos(x_1) + … + cos(x_n) + cos(x) = 0. It follows S is just the set of real numbers x such that cos(x) = 0. Clearly S is closed. The set for n is closed, so the product for the set for n and S is the set for n+1, which is closed. Since the product of closed set is closed. I think this is a way to do it.
It might be wrong, never done a problem like this before.
This is one attempt.
I will take it up with #real-complex-analysis for confirmation.
normal oracle
That doesn't quite work -- cos(x_1) + ... cos(x_n) + cos(x) = 0 has solutions where cos(x) is not zero. So S is a bit more complicated than you've said.
hasty cliff
That doesn't quite work -- cos(x_1) + ... cos(x_n) + cos(x) = 0 has solutions wh...
x_1,…,x_n is fixed. That is point (x_1,…,x_n) for the set n.
We have cos(x_1) + … + cos(x_n) = 0.
So we just left with dealing with cos(x) = 0 for S.
normal oracle
Again, if @merry plaza is still around, I'd start with what definition of continuity you're using. If it's that the preimage of any open set is open, your life is very easy for this question.
merry plaza
@normal oracle i need to show the set (x1…xn) is closed
merry plaza
I think there's something confused in how you phrased the question -- probably y...
Oh yea
This
My bad
normal oracle
Ok. And you know cos(x) is a continuous function from R to R?
normal oracle
Ok. If you can show cos(x_1) + ... + cos(x_n) is a continuous function from R^n to R, then you can appeal to the fact that {0} is a closed set of R, so its preimage in R^n will also be closed.
(So for example -- you must know or show that adding finitely many continuous functions together results in a continuous function)
merry plaza
Would I do that through the limit definition?
normal oracle
If that's your definition of continuity, then yea. There are many definitions of continuity though -- using limits, epsilon-delta stuff, or open/closed sets.
Do you define a closed set as one that contains all its limit points?
merry plaza
Wait I think this might be referring to being closed under different linear combinations
normal oracle
Hmm, that's an entirely different question, if so. But odd to ask about non-compactness in that context.
merry plaza
It’s supposed to be linear alg and multivar calc
normal oracle
Are you familiar with the notion of a closed set (in the multivariable calculus sense?)
merry plaza
Not rlly
normal oracle
It's a famous fact, for example, that any compact set in R^n must be both closed (in this sense) and bounded (meaning doesn't contain points that get arbitrarily far away from the origin). So if a set is non-compact, it's either not-closed (but your set is closed!) or else not-bounded (so that's what you'd have to show in this problem).
merry plaza
Oh cause the cosines of all the elements converge?
normal oracle
Ok -- lemme take a stab; see if this clicks. A set of points $S$ is closed if, whenever you have a sequence of points $s_1, s_2, \ldots$ in $S$ that converge, meaning that $\lim_{i\to\infty} s_i = s$ for some $s$, then the limit point $s$ is also in the set $S$. Does that ring any bells?
elfin berryBOT
daveamayombo
normal oracle
So what you'd have to show is that, if $S$ is the set of points $(x_1,\ldots,x_n)$ for which $\cos(x_1)+\cdots+\cos(x_n)=0$, and you have a sequence of points $s^1, s^2, ...$ in $S$ that converge to a point $s$, then $s$ is also in $S$.
elfin berryBOT
daveamayombo
normal oracle
(The superscript isn't meant to be exponentiation, by the way -- just an index into the sequence of points)
merry plaza
I see
normal oracle
If this is seeming like a bit too much -- I'd say maybe see if your teacher can point you in the right direction. The issue I'm facing is just that there are many different ways of defining all these things ("closed", "continuous" etc) that all turn out to be equivalent. In an intro class you might only see one definition, and I'm not sure which ones you're using.
Also, the baby's waking up so I gotta run!
merry plaza
Alright ty for the help
normal oracle
Yah, sorry couldn't get you across the finish line this time.
merry plaza
.close
marsh citrusBOT
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astral oyster
Considering the determinant of a 2x2 matrix - What is the signature of the quadratic form representing the determinant? I want to say (1,1) because we have ad-bc -> xˆ2-yˆ2 but i'm not sure if this reasoning is correct. Can someone help?
marsh citrusBOT
Considering the determinant of a 2x2 matrix - What is the signature of the quadr...
@astral oyster Has your question been resolved?
main idol
Considering the determinant of a 2x2 matrix - What is the signature of the quadr...
i'm not sure, but this might help https://math.stackexchange.com/questions/3193710/on-the-signature-of-a-quadratic-form
sonic juniper
integrate (lnx)^2, why is the method using u = (lnx)^2 and dv = dx ? isnt first logical attempt to use u = lnx and dv = lnx ? also what is the theory behind why you are able to use dx as one of the variables when integrating by parts such as the first method in this example, and why do you not need to include dx in either u or dv in other integration by parts questions?
marsh citrusBOT
integrate (lnx)^2, why is the method using u = (lnx)^2 and dv = dx ? isnt first ...
main idol
integrate (lnx)^2, why is the method using u = (lnx)^2 and dv = dx ? isnt first ...
not really theory, just something that works by finding patterns in the product rule
sonic juniper
not really theory, just something that works by finding patterns in the product ...
ah ok. but why then do you use dx in one of either u or dv in some questions but not in others? what makes you able to dismiss it?
main idol
ah ok. but why then do you use dx in one of either u or dv in some questions but...
at this point for you, just trial and error
sonic juniper
at this point for you, just trial and error
just so i know, is there a way to know and you are saying that for my level i should just trial and error or is that what everybody does?
sonic juniper
https://math.berkeley.edu/~ehallman/math1B/IntByParts.pdf
this is good, thanks
main idol
it's what everybody should do yes
marsh citrusBOT
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iron owl
number 4 please. I understand that revenue=(sales)(price) so I get 52000= (2.00+0.05x)(6500-5x)
marsh citrusBOT
number 4 please. I understand that revenue=(sales)(price) so I get 52000= (2.00+...
iron owl
but I dont know where to go from here to find the new price and the #sold
marsh citrusBOT
@iron owl Has your question been resolved?
marsh citrusBOT
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echo kernel
What are the solutions of this equation?
marsh citrusBOT
What are the solutions of this equation?
echo kernel
can someone please confirm?
if my reasoning is correct then its A the correct answer
echo kernel
This equation has 2 real solutions when...
marsh citrusBOT
This equation has 2 real solutions when...
echo kernel
i believe the correct answer is E
because if we take 2 then we will get two results that are equal
can someone please confirm?
fiery path
Do you know how to use the discriminant
echo kernel
its b^2-4ac
fiery path
And for what values of the discriminant are there 2 solutions?
echo kernel
when its positive
because if its equal to zero, then we would have two equal solutions
echo kernel
Yes, but i wanted to be sure that the answer was indeed E and not D
I belive its not D because if we take -2 then the statement becomes not true
the discriminant would become equal to 0
fiery path
Correct
echo kernel
Perfect, thank you 🙂
I have another question if you dont mind
can i post it here in the same thread?
fiery path
Sure
echo kernel
Two concentric circles delimit a circular circle whose area is half the area of the larger circle. The ratio of the radius of the larger circle to the radius of the smaller circle is...
fiery path
Could you draw it out?
elfin berryBOT
echo kernel
this is what i tried to do
I used r for the radius of the small circle, while R for the bigger one
The problem tells us that the area of the bigger circle is equal to half the area of the "circular crown" (dont know if this term exist in English)
from there i tried to something but i didnt work out in the end
marsh citrusBOT
@echo kernel Has your question been resolved?
echo kernel
<@&286206848099549185>
echo kernel
<@&286206848099549185>
marsh citrusBOT
@echo kernel Has your question been resolved?
marsh citrusBOT
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still temple
marsh citrusBOT
fiery path
can you divide by 0?
still temple
no
fiery path
correct
it is undefined so h(t) won't have a value when the denominator is 0
that's why we find the t values for when the denominator is 0 so we can say it is not continous for those values of t
still temple
so i would always have to equal it to zero
fiery path
if you have a function of t on the denominator, yes
still temple
so equal it to 0 then factor it
why cant i just factor it instead of equaling it to zero
fiery path
because you need to check when the factors = 0?
fiery path
yes
fiery path
you have your factors?
still temple
yes
ohhh ok i get it
the instructions were werid
so just factor it out first then equal it to zero
fast coyote
In Figure 8, are represented, in Cartesian reference,
of origin at point O, the lines defined by the equations
Point I is the point of intersection of two of these lines.
What is the system of equations that makes it possible to determine the
point I coordinates?
marsh citrusBOT
In Figure 8, are represented, in Cartesian reference,
of origin at point O, the ...
fast coyote
i have already ruled out option A
because the slopes are opposite of eachother
so there needs to be a negative and positive slope
bright jay
So you know that the general equation for a line is y = mx + b
You already identified that one line as a positive slope and the other has a negative slope
For the line that has a positive slope, what is the y intercept?
fast coyote
which one
bright jay
The line with the positive slope
fast coyote
there are 2
bright jay
You're looking for the lines that goes through point I, aren't you?
fast coyote
oh ye
bright jay
So would the line that does not go through point I make sense to use?
fast coyote
but they dont associate the equations with the lines
so i dont know which equation represents that line
bright jay
Well, I'm asking, there are two lines that goes through point I
As you stated, one line as a positive slope and the other has a negative slope
fast coyote
yes
bright jay
For the line that has a positive slope, what is the y intercept?
fast coyote
-2
bright jay
Can you use what you know about the slope and the y intercept to determine the proper choice?
fast coyote
yes
cerulean kindle
does the identity permutation of $S_n$ have length 0 or length 1 ?
marsh citrusBOT
does the identity permutation of $S_n$ have length 0 or length 1 ?
elfin berryBOT
Rœmer
cerulean kindle
(and why ?)
plucky shoal