damn
#help-10
azure lark
i though i could just find the distance between distance travelled north and south
but cos the person travelled north east, idk what difference that would make for finding the difference between south and north when east is in the mix
azure lark
cant blame
yo idk if like you're being rude or nah
twin sorrel
yo idk if like you're being rude or nah
not being rude
im confused too
help should arrive
well goodluck
obtuse pebbleBOT
@azure lark Has your question been resolved?
azure lark
<@&286206848099549185> could i get some help
oblique sage
azure lark
?
compact shadow
If ground is considered flat, (5,0)+(2sqrt(2),2sqrt(2))+(0,-6)=(5+2sqrt(2),-6+2sqrt(2)) so distance is sqrt((5+2sqrt(2))^2+(-6+2sqrt(2))^2) expand yourself
If earth is considered as a sphere, distance varies with respect to original position, and the direction “north-east” will be tricky, involving local coordinates
azure lark
this question is from a physics course btw, but its not that realistic
cos the next part of that question is
Draw a scaled diagram of these vectors and use this to determine the magnitude and direction of the person’s resultant displacement
tardy epoch
this question is from a physics course btw, but its not that realistic
Physics server is in #old-network
azure lark
yea im in that server, this server is hella active though.
bro ong i have no clue how to do this lol, ik i need to use like vectors or sm
patent shell
Hi, can someone please help on this? I know that form(L) is countable, and therefore Σ is countable.
obtuse pebbleBOT
Hi, can someone please help on this? I know that form(L) is countable, and there...
slim cove
Hi, can someone please help on this? I know that form(L) is countable, and there...
what are the results in section 2.6?
patent shell
some theorem of countable, 1 if x is countable then y∈x is countable
If X and Y are sets with X countable and there is a bijection from X to Y then Y is also countable.
If X and Y are countable then so is X ∪ Y
slim cove
also what's form(L) btw
patent shell
form(L) are the set of all wffs of L
slim cove
ah okay
hmmm are there any more details about L? because this seems wrong because we can just choose Sigma = {} and then there are no derivations from Sigma, no?
or are we requiring that Sigma be nonempty
slim cove
what's the name of the textbook?
slim cove
ahhh okay
is there a link anywhere
or no
I just want to check what all the terms they are using here formally mean lol
patent shell
slim cove
okay awesome
slim cove
okay first of all, form(L) is countable by theorem 2.31; then, use the fact that every line of the derivation is in form(L); use proposition 2.30 to confirm then that the set of all derivations is countable
conclude that the set of all possible derivations is countable
I think this should work?
patent shell
how can you say that every line of the derivation is in form (L)?
like is there any proof needed here
slim cove
how can you say that every line of the derivation is in form (L)?
do you recall the definition of derivation
slim cove
no problem! :D
slim cove
oh wait actually quick note @patent shell that only proves that the set of all derivations is countable, not the set of all derivations from Sigma
obtuse pebbleBOT
oh wait actually quick note <@756062513011097610> that only proves that the set ...
slim cove
but luckily you can use the fact that all the axioms of L are valid lines of a derivation
which will prove that the set of derivations from Sigma is at least countable
(whereas what we proved before was that it is at most countable)
I'll let you flesh out the details since it shouldn't be too hard to figure out given what we already did, but if you can't figure it out then open another help channel
.close
timid silo
Oh i see, thank you. I did 0 -8 because that's the height of the cone but the integral from 3-8 of the parabola would obviously overlap the cone and leave extra. Quite a silly mistake from me but thanks :)
obtuse pebbleBOT
Oh i see, thank you. I did 0 -8 because that's the height of the cone but the in...
merry girder
hi
merry girder
mossy arch
Area = (base*height)/2
Rationalise denominator by multiplying by √27/√27
maiden radish
$area=\frac{base \times height}{2}$
warm shaleBOT
عزالدين لقام
obtuse pebbleBOT
@merry girder Has your question been resolved?
toxic mulch
obtuse pebbleBOT
toxic mulch
hi so I was making this excersize
and I was wondering
why didnt they include 2 options
and not write k * 2pi
timid silo
maybe theres a range given
toxic mulch
hmm
we are only given the max and the min
of the fonction
and the period
maybe bcs it is a problem?
oh nvm
they are equal to each other i just noticed
pi/2 = pi - pi/2
.close
patent shell
Can somebody help with part c please?
obtuse pebbleBOT
Can somebody help with part c please?
patent shell
what I already have is that odd number of negation symbols is equivalent to 1 negation symbol and I proved that this is complete set
.close
dense viper
i forgot how to do basic trig 🗿
obtuse pebbleBOT
i forgot how to do basic trig 🗿
high lily
consider drawing a right triangle where tan(theta) = sqrt(3)/2
obtuse pebbleBOT
@dense viper Has your question been resolved?
high lily
and from that triangle you should be able to determine sin(theta)
obtuse pebbleBOT
@dense viper Has your question been resolved?
tall tusk
how to solve this
tall tusk
finite product instead of sum
dense viper
and from that triangle you should be able to determine sin(theta)
yea dw i was dumb didnt use my brain
timid silo
how to solve this
ok if u mutltiply the first three terms u will see
haughty coyote
I think there's only 1 way to get each power of x
haughty coyote
I think there's only 1 way to get each power of x
You mean about that divyansh ?
cerulean pine
how to solve this
do you have to simplify ?
tall tusk
do you have to simplify ?
yeh
haughty coyote
It may help to think in binary
timid silo
and the last term is x^(1+2+4+......+2^n)
it would be very lenghty nasty calculations
lol
tall tusk
ok if u mutltiply the first three terms u will see
isnt first 3 terms just (1+x)^5
timid silo
what
timid silo
how are u understanding 2 questions at the same time lol
haughty coyote
and the last term is x^(1+2+4+......+2^n)
As I said, think in binary
timid silo
no
haughty coyote
Makes it trivial
tall tusk
ok u sum up the powers
compact shadow
how to solve this
Multiply by 1-x
tall tusk
and use binomial theorem?
haughty coyote
You can express every power
compact shadow
Then divide by 1-x in the end
haughty coyote
Multiply by 1-x
Also this yes
timid silo
lol
timid silo
Then divide by 1-x in the end
apply this for a small value of n to guess the general expression, then prove it by induction
tall tusk
what😭
timid silo
Multiply by 1-x
how u thought that i mean what was the motivation
tall tusk
<conjugation>
tall tusk
ptsd
ok let me try
bruh can anyone also help chris hu in help-9
hes very desperate for help
im sobbing rn
ive class at 2
still 5 hours still fine
whoops this meant to go to the other chris hu
help one
humble quest
how to solve this
more context
warm canopy
.
timid silo
just multiply and divide by sin(x/2^n) in b
obtuse pebbleBOT
@tall tusk Has your question been resolved?
fervent locust
I think this is pretty simple but I cant find an answer how can I find the coefficenets from the pruduct mutiplication
obtuse pebbleBOT
I think this is pretty simple but I cant find an answer how can I find the coeff...
fervent locust
or is it just trial and error
warm canopy
Give an example of what you mean
fervent locust
Give an example of what you mean
what 2 numberes multiplies to 20
kind hawk
do a prime factorization of 20
then any factor of 20 has to contain a subset of those primes as its prime factorization
so by going through all these subsets we find every factor of 20
obtuse pebbleBOT
fervent locust
.reopen
obtuse pebbleBOT
✅
fervent locust
then any factor of 20 has to contain a subset of those primes as its prime facto...
one more question, i need this to a code I am writing to a floorplan generator thing, what if the area result in 23 becasue 23 is already a prime number
kind hawk
then the only factors of 23 are 23 and 1
fervent locust
but then the floorplan i am generating will look weird
kind hawk
well that's the thing with prime numbers
can only put them into rectangles 1xp
(assuming you only allow integer side lengths)
fervent locust
no It will problely be floats
kind hawk
well then you could always just take sqrt(23)xsqrt(23) or something
distant plank
Hello, need another help
obtuse pebbleBOT
Hello, need another help
distant plank
how to determine $m = inf \int_{0}^{2\pi} (asin(t) + bcos(t) - e^t)^2 dt$
warm shaleBOT
Pako
distant plank
i'm stuck here, don't know where to begin
distant plank
$(a,b) \in \mathbb{R}^2$
warm shaleBOT
Pako
haughty coyote
What have you tried ?
distant plank
produce a scalar product
timid silo
how to determine $m = inf \int_{0}^{2\pi} (asin(t) + bcos(t) - e^t)^2 dt$
probably you need to use an orthogonal projection
I don't remember this well to give the details
distant plank
yes
I have to look for a basis then orthonormalize and use the orthogonal projection
ok i will try thx
timid silo
I have to look for a basis then orthonormalize and use the orthogonal projection
not sure orthonormalizing is necessary, but you won't go wrong doing it
that's a different example but applies the same technique
distant plank
https://math.stackexchange.com/questions/219592/finding-the-min-of-an-integral
oh thx a lot
timid silo
Yw
wanton dagger
So I’m trying to find the original point of (2,-4)
obtuse pebbleBOT
So I’m trying to find the original point of (2,-4)
wanton dagger
So I did:
(2,-4)
(2,-4/3)
(0,-4/3)
And then (0,-4/3-1)
=(0,-7/3)
But the answer says (0,-5/3) and I’m not sure where I’m wrong
I simply did the reverse of everything since we’re finding the original point but I’m not sure where the problem is at
Is the answer wrong or what?
Nvm I got it
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
opaque siren
A worm is at the bottom of a 12m wall. Every day the worm crawls up 3m, but at night it
slips down 2m. How many days does it take the worm to get to the top of the wall.
How do I go about solving this
obtuse pebbleBOT
> A worm is at the bottom of a 12m wall. Every day the worm crawls up 3m, but at...
tired skiff
> A worm is at the bottom of a 12m wall. Every day the worm crawls up 3m, but at...
do (3-2) + (3-2) + ... until you get to 12
then count how many times you repeated that step
in order to get to 12
opaque siren
do (3-2) + (3-2) + ... until you get to 12
do i just keep adding (3-2) ?
high lily
not quite
tired skiff
then stop
? how so
it starts at 0, you add 3 for the day and subtract 2 for the night
high lily
but you don't slip back down on the crawl up that gets you to 12
high lily
you would instead consider how many times you repeat until you get to 12-3 = 9
and then add one more day for the last crawl
tired skiff
just continuously add 3 and subtract 2 until you get to 12 then just stop
opaque siren
(3-2) + (3-2) + (3-2) + (3-2) + (3-2) + (3-2) + (3-2) + (3-2) + (3-2) +(3-2) + (3-2) + (3-2)
that'd = 12 tho
tired skiff
well at some other point you get to 12 beforehand
opaque siren
wym
high lily
but you don't slip back down on the jump that gets you to 12
i.e. by considering the whole net change
when you're at 9m
you crawl up, but then be completely oblivious that you're already at the 12m top and slip back down to 10m
and on top of that, you're somehow crawling on thin air the day after to get to 13m above the ground where there is no wall
when what's supposed to happen is when the worm was a 9m, the night before,
the climb up 3m to get to the 12m top and then stop
opaque siren
so at the final day of climbing the worm needs to be at 9m
1st day the worm starts at 0m, climbs 3m and slips down 2 so now it's 1m up
2nd day the worm at 1m, climbs 3m to 4m and slips down 2 so now it's 2m up
3rd day the worm at 2m, climbs 3m to 5m and slips down 2 so now it's 3m up
4th day the worm at 3m, climbs 3m to 6m and slips down 2 so now it's 4m up
5th day the worm at 4m, climbs 3m to 7m and slips down 2 so now it's 5m up
6th day the worm at 5m, climbs 3m to 8m and slips down 2 so now it's 6m up
7th day the worm at 6m, climbs 3m to 9m and slips down 2 so now it's 7m up
8th day the worm at 7m, climbs 3m to 10m and slips back 2 so now it's 8m up
9th day the worm at 8m, climbs 3m to 11m and slips back 2 so now it's 9m up
10th day the warm at 9m, climbs 3m to 12m and slips out
would that be correct
tired skiff
yeah probably
obtuse pebbleBOT
@opaque siren Has your question been resolved?
opaque siren
can anyone fully confirm if it is
winged delta
> 1st day the worm starts at 0m, climbs 3m and slips down 2 so now it's 1m up
> ...
it's correct ya, but I don't think it's the point of the exercise
say that on day 'n' the worm reaches the goal
to get there, it took 3n meters climbing up, and 2(n-1) meters slipping down
so essentially you are trying to solve 3n - 2(n-1) = 12
3n - 2(n-1) = 12
3n - 2n + 2 = 12
n + 2 = 12
n = 10
so that day is the 10th day, as you've also shown
obtuse pebbleBOT
@opaque siren Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
shut stirrup
obtuse pebbleBOT
shut stirrup
Yeah most probably
fierce lagoon
You can probably do some elimination jank
wooden cipher
gilded needle
if it has one solution it'll have infinitely many, as there are more variables than equations
obtuse pebbleBOT
@shut stirrup Has your question been resolved?
tranquil dust
this is a regular one to one functionn in which x2 is codomain and the domain consist of 1234
obtuse pebbleBOT
this is a regular one to one functionn in which x2 is codomain and the domain co...
tranquil dust
is this possible ? in the set of domain a unmapped variable ?
so in this case what is the domain ?
or like ignoring repeated numbers in a set we should also ignore the D and only write abc in the set ?
slim cove
this is a regular one to one functionn in which x2 is codomain and the domain co...
yes that is a one to one function function
slim cove
is this possible ? in the set of domain a unmapped variable ?
no this is not possible because all of the points in the domain have to have an arrow coming out of it
tranquil dust
@slim cove lets say you got a set of abcd and inputing d gives you D/0 which undefined and it is not in the co domain
slim cove
if you cannot input d to the function, then d cannot be in the domain of the function
shut stirrup
.close
south flame
I was wondering how I could solve this using degree measures.
obtuse pebbleBOT
I was wondering how I could solve this using degree measures.
fierce lagoon
There's a couple of ways
Uh
You can find the minimum and maximums
Or you can set the derivative to any number and solve for x
south flame
but like I haven't been taught the derative of tan values and how can I find the minimum and maximums in degrees when x has to be the same as the tangent value
fierce lagoon
are you familiar with derivatives
south flame
yes
south flame
I can do like equations but not tangent and that stuff
fierce lagoon
Well are you aware that all these trig functions are cyclical
south flame
yes
fierce lagoon
Which means that any tangent on any iteration is the same on the same spot on any other iteration
So start by setting tan(2x) = 0
And solve for x
fierce lagoon
all x values
south flame
x = pi/2n
fierce lagoon
Not quite
south flame
I mean pin/2
fierce lagoon
Remember your periodicity of tangent
south flame
(pi*n)/2
fierce lagoon
$$x = \frac{\pi}{2}n, n\in\bZ$$
warm shaleBOT
Umbraleviathan
fierce lagoon
So just plug any 5 values of n
south flame
yes thats what I was tryinng to say
fierce lagoon
That fits within its domain set
south flame
ok but like 1 wehn i plug in to equation gives me undefined
fierce lagoon
You sure?
south flame
like into tan(pi) cause that the equation I have to plug in x to
wait nevermind
I reread the question and saw that all 5 values of tangent have to be equal
i understand the question now.
thanks mate
.close
slender kindle
Am finding a relation such that
F is minimum when n.sin theta+n.cos theta is maximum
obtuse pebbleBOT
Am finding a relation such that
F is minimum when n.sin theta+n.cos theta is ma...
upbeat island
you just want the max of sin t + cos t then?
you can take the first derivative and find when that's zero
gilded needle
you could use the cauchy schwarz inequality here if you know it
tardy epoch
how do i find the max value of that
Take a derivative and set it equal to zero
Or write it as a single sinusoidal and use equation for peaks
obtuse pebbleBOT
@slender kindle Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
leaden shoal
what is wrong with my calculations?
obtuse pebbleBOT
what is wrong with my calculations?
upbeat island
line three should be subtracting 16
leaden shoal
hmm im confused
upbeat island
(a - 4) (a + 4) = a^2 - 16
leaden shoal
-4*4 = -16
upbeat island
yee
upbeat island
think of it more like difference of squares, so a^2 - b^2
leaden shoal
its always -
upbeat island
the classic
stoic sleet
What were the name of these terms called? @upbeat island I forgot. They can cancel each other out and just square a and b
upbeat island
which ones?
stoic sleet
the (x - a) (x + b)
leaden shoal
its a formula
stoic sleet
Right but the terms, didn't they have a name?
upbeat island
umm there's conjugates
stoic sleet
Yes!!!!!
upbeat island
😄
leaden shoal
ye
stoic sleet
thank you
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
opaque rain
can someone help me with some determinants properties?
obtuse pebbleBOT
can someone help me with some determinants properties?
opaque rain
I'm trying to "prove" some of them and I got stuck at the one that says that when you add a multiple of a row to another row the determinant stays the same
I don't find my mistake, and if there isn't, I don't know how to factor that to get the same answer
obtuse pebbleBOT
@opaque rain Has your question been resolved?
upbeat island
i'll look lol but it might be easier to expand on first row instead of first col
opaque rain
maybee, but it should be ok anyway : c
upbeat island
oh, can't tell from the pic quality, but looks like middle row last column should be f + kc, but you expand that as d + kc
🪦
if you track that through your first two lines of expansions maybe you can salvage lol
opaque rain
oh, can't tell from the pic quality, but looks like middle row last column shoul...
well
seems like my problem is not math but the alphabet
lmao
thank you very much <33
upbeat island
np fam
opaque rain
.close
obtuse pebbleBOT
idk what to do next
compact shadow
Doesn’t converge
leaden shoal
Doesn’t converge
hmm what does this mean?
stoic sleet
it diverges
leaden shoal
so it approaches a number
pallid flame
no
leaden shoal
if its infinity then the limit doesnt exist
pallid flame
diverges towards positive infinity
leaden shoal
diverges towards positive infinity
how did u calculate that?/ how do u know that
pallid flame
bottom is cos^2
which is never negative (cuz it’s squared)
so 1/ε for ε being a positive number really close to 0 (infinitesimal)
which is positive infinity
leaden shoal
so 1/ε for ε being a positive number really close to 0 (infinitesimal)
hmm i dont understand this
pallid flame
do you know what the actual definition of a limit is
timid silo
why do some people find ratios hard
pallid flame
what
timid silo
ratios
pallid flame
to find what y value as it approaches that x value from both sides
yes and no
leaden shoal
which part is no
timid silo
sorry-
pallid flame
also limits don’t have to be of functions
timid silo
there is one question on which the discussion is on going
leaden shoal
also limits don’t have to be of functions
ok
timid silo
ill add my question later
pallid flame
but the type of problem u see will be mostly like what u described
leaden shoal
mhm
stoic sleet
ill add my question later
timid silo
use another help channel <#903430333096132618> <#903430333888884736>
okay i was new to this so couldn’t understand
there are like many channels related to mathematics
pallid flame
however a limit that diverges to positive infinity is really:
for sufficiently large M > 0, there exists 0 < |x - a| < δ such that f(x) > M
leaden shoal
wha--
stoic sleet
there are like many channels related to mathematics
yes, go to #❓how-to-get-help it should help you understand where to get help
Sorry for the interruption jnmwn and atomic.
leaden shoal
but the limit isnt approaching infinity. Its approaching to pi/2
timid silo
alright, thanks!
pallid flame
that’s what a is
pi/2
$$(\forall M > 0) \text{ }0 < |x - \frac{\pi}{2}| < \delta \implies \dfrac{\sin^2(x)}{\cos^2(x)}> M$$
leaden shoal
however a limit that diverges to positive infinity is really:
for sufficiently l...
hmm i dont understand this. I'm learning limits and continuity, like the basics
pallid flame
looks very confusing i know
warm shaleBOT
jnmwn
pallid flame
for example imagine delta is 1
leaden shoal
ok
pallid flame
then x is from pi/2 - 1 to pi/2 + 1
excluding pi/2
because we dont look at the exact point we’re taking the limit towards
leaden shoal
ye like decimals
pallid flame
(a limit can be defined approaching a point where it’s not defined)
like lim{x->0} x/x
anyway we look at the minimum value on the interval
aka tan(pi/2 - 1) and tan(pi/2 + 1)
the graph looks like this
y is about 0.4
not very impressive
we only get it proven for all M <= 0.4
leaden shoal
ow
pallid flame
but what if delta is 0.1
now we get it for all M <= 99
the graph is above all values under 99 over the entire interval
as delta goes to 0, m goes to infinity
so every M > 0 works
thus it diverges to positive infinity
i only showed this graphically but it’s intended to be proven through actual algebra
anyway the concept allows you to identify a limit diverging to infinity
past fog
what can i do here?
I’d have left the bottom alone; made it
1-cos^2/1-sin^2
then did some cancelling and simplifications there
because that simplifies to what, sin^2/cos^2
which is tan^2(x)
and then tan^2(pi/2) = UD
@leaden shoal
obtuse pebbleBOT
@leaden shoal Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
edgy needle
hi i need some heklp
obtuse pebbleBOT
hi i need some heklp
timid silo
Do you just want to simplify it
edgy needle
expand and simplifly
edgy needle
yes
timid silo
what is it
edgy needle
i got x^2 - 1
devout sable
So you get x^2 -(x^2-1)
timid silo
So you get x^2 -(x^2-1)
jinx
edgy needle
oh i got it...
i thought it was on difference of perfect squares
cuz this chapter is on difference of perfect squares
edgy needle
oh fax...
then i did the working wrong
can u do it for me
and show paint
ig ot this
haughty coyote
That's not a simplification
haughty coyote
Take line 1 and get rid of the parentheses. It should be more obvious
devout sable
Is it?
haughty coyote
If the question is to simplify, then no
edgy needle
wait whats the difference
devout sable
Also it is x^2 ** - ** (x^2-1)
cedar lichen
The original question had (x + 1)(x - 1). Expanding that to x² - 1 was using difference of squares. You don't need anymore than that
haughty coyote
Which is x^2 - x^2 + 1
haughty coyote
Take line 1 and get rid of the parentheses. It should be more obvious
Is what I meant
edgy needle
omg tysm guys
obtuse pebbleBOT
@edgy needle Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
stoic sleet
Things fall at the same time, but this only applies when there's air resistance, correct?
obtuse pebbleBOT
Things fall at the same time, but this only applies when there's air resistance,...
stoic sleet
God, I was so confused, I was like "how would they if there's resistance?"
stoic sleet
see the famous dropping of a feather and a rock(maybe a hammer) on the moon
I forgot that! Always coming in with good examples, nice man
warm canopy
rocky cosmos
Give an example of a function f(x) that has a vertical asymptote at x=4 and a horizontal asymptote at y=6.
obtuse pebbleBOT
Give an example of a function f(x) that has a vertical asymptote at x=4 and a ho...
rocky cosmos
This is what I thought:
One example of a function with these asymptotes is:
f(x) = (6x - 24)/(x - 4)
To find the vertical asymptote, we set the denominator equal to zero and solve for x. This gives us x=4.
To find the horizontal asymptote, we take the limit of the function as x approaches infinity. This gives us:
lim f(x) = lim (6x - 24)/(x - 4)
= lim 6x/x - 4
= 6
haughty coyote
,w plot (6x-24) / (x-4)
warm shaleBOT
haughty coyote
does that look like a vertical asymptote to you ?
the problem is it's just a removable discontinuity. It mustn't be
rocky cosmos
How do we determine a function with both a vertical and horizontal asymptotes?
rocky cosmos
$\frac{6x}{x-4}$
rocky cosmos
This?
warm shaleBOT
haughty coyote
it doesn't show it on the right but yes
rocky cosmos
literally anything
Why is -24 Stopping us?
haughty coyote
because it allows for the factorisation by x-4
rocky cosmos
So we can say 6x/(x-4)?
haughty coyote
then you can write: when x != 4, x-4 != 0 so we can simplify by x-4
(6x - 24) / (x-4) = 6 (x-4) / (x-4) = 6
with a discontinuity at x = 4, where it isn't defined
haughty coyote
So we can say 6x/(x-4)?
yes
snow peak
obtuse pebbleBOT
devout sable
Either is fine(assuming it is correct)
pine sail
You just wrote down the question. Just in a not so good looking way.
I mean, what you wrote is presented better in the image anyway. And I think what deep meant was that it doesn't matter if you use decimal or fractions for your final answer as long as they are equivalent, and more importantly correct answer to your problem.
So if you solved it, then write it in whatever form you like.
obtuse pebbleBOT
@snow peak Has your question been resolved?
snow peak
ok thanks so much guys
obtuse pebbleBOT
obtuse pebbleBOT
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craggy elbow
How do you explain square root or fractional power.
Power means 2^5 = 2x2x2x2x2
Square root 5√2 or 2^(1/5) = ?
I am not looking for the solution but the extraction of like i did in power
obtuse pebbleBOT
How do you explain square root or fractional power.
Power means 2^5 = 2x2x2x2x...
native nexus
are you saying the fifth root of 2?
we use fractional powers to describe roots yes, but there isnt necessarily an extraction like how we describe powers normally
obtuse pebbleBOT
@craggy elbow Has your question been resolved?
tepid fulcrum
Hey guys, working through this differential equation and I feel like I've gone wrong somewhere but I'm seriously unsure where... I'm very new to these. Is anyone able to help me find where I went wrong?
obtuse pebbleBOT
Hey guys, working through this differential equation and I feel like I've gone w...
tepid fulcrum
I'm not sure I understand why
lofty jay
Hey guys, working through this differential equation and I feel like I've gone w...
this looks correct to me
compact shadow
Yeah
Don’t know why you think you did something wrong
Perhaps the only thing is that you forgot absolute value
Even though in this particular case you can take it off since y(0)>0
tepid fulcrum
Well, what form should the solution for such a question... asking for the solution to a differential equation, be in? Should the answer be an equation? Like, the reason I thought I did something wrong was because it seemed off, as an answer?
tepid fulcrum
oh..
haha
alright
thanks guys, sorry for wasting your time 
have a good one <3
lofty jay
np
tepid fulcrum
.close
warm shaleBOT
RFish
warm shaleBOT
RFish
compact shadow
Again
Do it by definition
How do we show a set is contained in another set?
Do it by definition
warm shaleBOT
RFish
compact shadow
So do it
warm shaleBOT
RFish
compact shadow
Already told you, whether you do it is your choice
warm shaleBOT
RFish
cerulean pine
no, your function is defined as f : A —> B
that means for all x∈A, f(x) ∈ B
okay then x is in the set on the right
warm shaleBOT
RFish
cerulean pine
np
noble kindle
idk how they used lagrange theorem
obtuse pebbleBOT
idk how they used lagrange theorem
noble kindle
specifically why (gH)^4 = H
compact shadow
?
Any group A of order k
Any x from A
<x> is a subgroup of A so order of <x> which is order of x, divides k
Now
A=G/H
x is gH
kind hawk
maybe first question should be, how many elements does G/H have
solar trellis
Any group element raised to the order of the group is the identity
As the order of the element divides the order of the group, by Lagrange's theorem
compact shadow
?
noble kindle
|G| / |H| = 4
compact shadow
Order of group G/H is 4
solemn nacelle
oblique sage
!15min
obtuse pebbleBOT
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.
solemn nacelle
.close
half wren
obtuse pebbleBOT
half wren
Any advice on this?
obtuse pebbleBOT
@half wren Has your question been resolved?
half wren
<@&286206848099549185>
timid silo
Any advice on this?
lets take the paths along y = 0 and x = 0
half wren
Its both 0
timid silo
yes
what you have to notice is that the function is not continuous at $(0,0)$ (which is due to division by zero), however this doesn't mean that it cannot be computed
warm shaleBOT
Aude
timid silo
however since there's no obvious factorization method, there is a chance the limit does not exist, the good news is that lim (0,y) = lim(x, 0)
compact shadow
It equals $(\frac{x^{6}}{x^{6}+y^{3}})y$, notice that $\frac{x^{6}}{x^{6}+y^{3}}$ bounded when $(x,y) \to (0,0)$
warm shaleBOT
Cogwheels of the mind
compact shadow
Do you want me to show why it’s bounded?
half wren
Yes please
compact shadow
When x=0, this is zero, when x doesn’t equal 0
$x=r\cos(t),y=r\sin(t), \frac{x^{6}}{x^{6}+y^{3}}=\frac{1}{1+\frac{\sin^{3}(t)}{r^{3}\cos^{6}(t)}}$
warm shaleBOT
Cogwheels of the mind
compact shadow
For $|\frac{x^{6}}{x^{6}+y^{3}}|<1$ we need $|1+\frac{\sin^{3}(t)}{r^{3}\cos^{6}(t)}|>1$
warm shaleBOT
Cogwheels of the mind
compact shadow
So when sin is negative we need $r^{3}<\frac{-\sin^{3}(t)}{2\cos^{6}(t)}$
warm shaleBOT
Cogwheels of the mind
compact shadow
We find the minimal of $-\frac{\sin^{3}(t)}{2\cos^{6}(t)}$ for t from $(π,2π)$ it’s done
warm shaleBOT
Cogwheels of the mind
half wren
Thankss
compact shadow
Not finished yet
half wren
Lol
compact shadow
Still thinking
tardy epoch
cog going ham on this problem
compact shadow
I thought sin^3/cos^6 > some positive number for t from (0,π)…
compact shadow
**Cogwheels of the mind**
So we need to find a r smaller than all $\frac{\sin(t)}{\cos^{2}(t)}$ for t from $(0,π)$
warm shaleBOT
Cogwheels of the mind
compact shadow
Shit.. failed…
half wren
Don't worry
Maybe we can prove it by writing the full function in polar coordinates and makien r tend to 0
compact shadow
I don’t think it has limit :
Any x doesn’t equal zero
No matter how small its absolute value might be
We can find t such that
|t/(1+t^3)|>1/x^2
Since t/(1+t^3) approaches infinity when t approaches -1
Then we let y=tx^2
|f(x,y)|=|x^6y/(x^6+y^3)|=x^2|(t/(1+t^3))|>1
And since t approaches-1 let’s say -1.5<t<0.5
x^2+y^2=x^2+t^2x^4<=x^2+2.25x^4 indeed can be arbitrarily small
So it doesn’t have limit 0 at all…
Does it make sense? @tardy epoch
half wren
compact shadow
Not valid
cos^6sin/(cos^6+sin^3)
Isn’t bounded
That’s how I constructed counter example
t=sin/cos^2
compact shadow
cos^6sin/(cos^6+sin^3)
This is cos^2(t/(1+t^3))
When sin/cos^2 approaches -1 this doesn’t necessarily approaches 0
For any cos, we can find t such that |t/(1+t^3)|>1/cos^2
compact shadow
|t/(1+t^3)|>1/x^2
That’s exactly my point here
compact shadow
What you proved is that
Lim (t goes to 0) f(tx,ty)=0
You proved limit is 0 when approaching (0,0) on any line passing origin
tardy epoch
,w plot x^6 * y / (x^6 + y^3)
warm shaleBOT
compact shadow
Yeah
y=-x^2 nearby
That’s exactly why I don’t think it has limit 0
Anyway I think my argument was rigorous
tardy epoch
yea just set y=-x^2 + eps for eps > 0
then numerator remains finite and denominator = eps approaches 0
compact shadow
Yeah
half wren
Well, thanks for taking your time to help me
tardy epoch
Anyway I think my argument was rigorous
i think i followed the logic and looks good. i didn't follow all the algebra since i don't have pen and paper on me.
compact shadow
Ic
half wren
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
round ember
Wikipedia states, that Cauchy product of two holonomic functions is also a holonomic function ( https://en.wikipedia.org/wiki/Holonomic_function ), but it does not show how given holonomic functions a(x), b(x) as ODE calculate c(x) = a(x)b(x) also as ODE. I have tried to find it but most sources omit the proof, and a few ones that do not omit the proof give only existential one (from what I understood). I have picked simple (in my opinion) example b(x) = a(x) = sigma i: 1/(i!) ^2 * x^i, (a - a' - xa'' = 0 as ODE) but I still find it really hard. Can someone help me?
obtuse pebbleBOT
Wikipedia states, that Cauchy product of two holonomic functions is also a holon...
round ember
Sorry, didn't read that only pre-university stuff should be asked here
my bad
.close
obtuse pebbleBOT
nocturne minnow
Sorry, didn't read that only pre-university stuff should be asked here
You can technically ask anything, but you'll get less replies if it's too advanced
warm shaleBOT
Ippo
obtuse pebbleBOT
Available help channel!
wraith vapor
Two right cylinders are similar. If the larger cylinder has a diameter of 5 cm
and a surface area of 75 pi, what is the surface area of the smaller cylinder if
it has a diameter 3 cm?
obtuse pebbleBOT
Two right cylinders are similar. If the larger cylinder has a diameter of 5 cm
a...
wraith vapor
This is a bit more urgent..I kinda need help like rn...
cedar lichen
What have you tried @wraith vapor
obtuse pebbleBOT
@wraith vapor Has your question been resolved?
obtuse pebbleBOT
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Available help channel!
prime spade
hello! i was wondering if the stuff i circled in the bottom is the answer? can quadratic equations have more than one inverse? lets say if i would get something like this in a test are both of them the answer? im a littel confused, i hope the question isnt too dumb
obtuse pebbleBOT
hello! i was wondering if the stuff i circled in the bottom is the answer? can ...
slim cove
quadratics are not one-to-one so they don't have an inverse per se
you can get around this by restricting the domain to make it one-to-one
prime spade
so one of the answers is the inverse on half of the parabola? im sorry i dont fully understand
slim cove
yeah
that's exactly right
one of the answers is the inverse for the left side and the other is the inverse for the right side
prime spade
so do i need to restrict the domain or range in the answers for them to be functions?
i thought i can just restrict any side, but if each answer if specific to a side that confuses me.. i might be mixing terms?
gilded needle
just like a function needs to pass the vertical line test in order to be a function, if it is going to have an inverse it needs to pass a horizontal line test
and quadratics don't pass that test, which is why you need to restrict the domain
prime spade
how do i know what side to restrict? if i get 2 answers can i just restrict any side i want in both of them? im confused
gilded needle
if you restrict the domain of the quadratic to only the right of its vertex, you get one of the inverses, and if you restrict it to only the left of its vertex, you get the other inverse
if the domain includes points on both sides of the vertex then there is no inverse
prime spade
if i restrict the domain on both sides to one of the answers i got in photomath it could be an inverse function to the left and right side? im still confused how thier could be 2 inverses
gilded needle
have you tried plotting the quadratic?
geometrically it's fairly easy to understand
prime spade
ill rephrase my question juist amin ill send a sc
gilded needle
sure
slim cove
yep
gilded needle
yes
prime spade
wait so i do not need to restrict the answers i got in photomath for them to be a function? i was taught that i always need to restrict them but it dosent look like i need to..?
gilded needle
now try drawing a horizontal line somewhere above the x axis
it intersects y = x^2 twice
in order for there to be an inverse function you need to restrict the domain so every horizontal line intersects the restricted version at most once
note that sqrt(x) is a valid inverse only if the domain of the original function is restricted to positive numbers
and -sqrt(x) is a valid inverse only if you restrict the original domain to negative numbers
prime spade
if my answer for the inverse function of a quadratic function isn´t a quadratic function like what i got in symbolab i dont need to restrict it? since the answers are already ¨restricted¨? like each answer if for each half of the parabola?
gilded needle
if your proposed inverse is actually a function (passes the vertical line test) then you're ok
prime spade
if the answer i got was in rhe form of a quadratic function id need to restrict it to get each side? right
gilded needle
in the example above it does not, you have a parabola that faces in the +x direction, and every vertical line to the right of the origin intersects that parabola twice
prime spade
so there is like 2 ways of writing the answer if they ask me to show the inverse of a quadratic function that is a function....? like if my answer is a quadratic formula ill need to restrict it, and if it not not?
gilded needle
if your answer gives two or more y values for a given x value then you need to restrict
prime spade
right, but for the same question i can write a function that dosent have 2 or more values for given x and not need to restrict it ...? like the sc i sent before of the symbolab answer
nocturne minnow
The synbolab answer is showing 2 possible answers as the inverse. Because the function was a quadratic, for it to be a valid inverse, you can only plot one of the solutions, which is restricting the domain of the quadratic
prime spade
yes that is what i meant, like one answer is for right side and other for left, but those answers could be also written as an equation that ISNT a function but the restricted?
nocturne minnow
Graphing both at the same time, makes it not a function so you have to plot either solutions
prime spade
so basically answer 2 ill need to to limit for it to be a function?
but they are theoretically the same thing...?
i dont understand how to get to the second answer tho, the one which isnt a function
nocturne minnow
I honestly don't understand what exactly you are asking
If you are trying to find the inverse of a quadratic, then it's possible, only if you restrict the domain
prime spade
im confused why i got 2 different answers in the last 2 screenshots ive sent, and how did they solve it differently to get those 2 different answers.
nocturne minnow
Which screenshot specifically?
prime spade
these two
nocturne minnow
The top screen shot is a quadratic, hence the two solutions, the bottom screenshot is not a quadratic
prime spade
im just confused about in what situation will i need to restrict the the equation for it to be a function (i always get 2 answers that are already functions, but i was taught that ill need to restrict the equation for it to be a function), how do i get the answer that is not a function, that is needed to be restricted.
nocturne minnow
When the original function, meaning not the inverse function, does not pass the horizontal line test
If the function does not pass the horizontal line test, then you need to restrict the domain
woeful spruce
Yes or just check for injectivity
nocturne minnow
Yes or just check for injectivity
I don't think they know what injectivity means
prime spade
how do i get the answer x=y² and not √x an -√x. in a a form of y=. if that makes sense..? is that possible like is there a way to represent √x and -√x in one equation
nocturne minnow
If they learn about inverse functions they should know?
Not those kind of terms, that more advance terms
nocturne minnow
how do i get the answer x=y² and not √x an -√x. in a a form of y=. if that m...
Most equations are in the form of y = ... so you can't have it in one equation. If you were to have it in one equation then you have x = y^2
prime spade
so in x = y^2 the only way of showing the answer for solving for y is √x or -√x , like there isnt another way to reprsent the answwr except(y=±√x)
nocturne minnow
That's correct, there is no other way except for $y = \pm \sqrt{x}$
warm shaleBOT
dldh06
prime spade
That's correct, there is no other way except for $y = \pm \sqrt{x}$
oh thank that clarifies everything..im sorry it took so long, thank you so much for you help
.close
austere tree
Find all possible values of ab given that a + b = 2 and a^4 + b^4 = 16.
obtuse pebbleBOT
Find all possible values of ab given that a + b = 2 and a^4 + b^4 = 16.
austere tree
I got 0 and -4 but I don't believe -4 is a valid answer
when I solve for a and b with ab = -4, I get 1 + sqrt5 and 1 - sqrt5
which don't satisfy the equations
so my real question is why is -4 not an answer
now I will lay out my steps for you to tell me where a "wrong" answer sneaks in
(a+b)^2 = a^2 + b^2 + 2ab
a^2 + b^2 = 4 - 2x
x is ab
(a+b)^4 = a^4 +b^4 + 6(ab)^2 + 4ab(a^2 + b^2)
16 = 16 + 6x^2 + 4x(4 - 2x)
-2x^2 + 16x = 0
(x)(x-8) = 0
give me a moment the answers appear to actually be 0 and 8
alright nvm just a simple math error, those roots check out
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
heady kiln
Can anyone help me solve this question, I just need to know the steps on how to solve it
obtuse pebbleBOT
Can anyone help me solve this question, I just need to know the steps on how to ...
high lily
do you know labelling conventions for shapes?
heady kiln
Not really
high lily
the vertices of your rectangle will go from A→B→C→D going in either a clockwise or anticlockwise direction
heady kiln
Ok
obtuse pebbleBOT
@heady kiln Has your question been resolved?
timid silo
can you explain the highlighted question
obtuse pebbleBOT
can you explain the highlighted question
floral canopy
because its (2^3)^5/3 ---> 2^(5/3*3) ---> 2^5
floral canopy
after you get 2^2 x 2^5 = 2^k
you can use exponent rules
2^2 * 2^5 is actually..?
timid silo
but my answer isn’t coming
floral canopy
what did u get
timid silo
it’s 7 and i was getting 20
floral canopy
How 20..?
floral canopy
after you get 2^2 x 2^5 = 2^k
What did u do after this step?
timid silo
did the similar steps but
i tried canceling all 2s
oh nooooo
now we can see that bases were same so the powers would be added
floral canopy
yess
floral canopy
np! if you are done u can close this channel with .close
obtuse pebbleBOT
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worthy notch
Hey there! I have a problem I'm trying to solve concerning 3D coordinates. I have a point X that I want to keep in the same position relative to three other points (A, B, and C). These other points are moving. This sketch illustrates the starting position of the points (in 2D to simplify drawing it)
obtuse pebbleBOT
Hey there! I have a problem I'm trying to solve concerning 3D coordinates. I hav...
worthy notch
In this starting situation all coordinates are known and I can calculate vector angles, vector lengths, etc.
Then, points A, B, and C are moved and I want to calculate the new position of X
compact shadow
Easy:
worthy notch
Like this. As you can see the shape of the A,B,C triangle doesn't stay the same
compact shadow
You calculate X-C=r(A-C)+s(B-C)
For r and s
Then they remain
X’-C’=r(A’-C’)+(B’-C’)
worthy notch
Can I ask what r and s stand for? My math knowledge isn't what it used to be