help-27

[wild spindle]

And ping me when you respond bcs I'm currently making capcut edits and not lurking here 😅

[hushed drift]

@wild spindle did u get 120º?

[wild spindle]

No

X isn't 120

Huh I wonder why my ping didn't work 😭

[wild spindle]

X isn't 120. Because DOC is 180-4x

And DOE is also 180-69=111

And COE is x

So DOE is 180-3x

So 111=180-3x

So 3x=69

[devout snow]

@hushed drift Has your question been resolved?

[hushed drift]

okay ty

[devout snow]

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[atomic idol]

I have a vector space X with a finite dimension
There’s a projection P for which P * P = P is true
The range of the projection consists of all vectors x so that P(x) = x and the intersection of Ran[P] and Ker[P] is only the zero vector

Now how do I show that there’s a basis V for which the matrix looks like this:

[atomic idol]

,rccw

[atomic idol]

This condition also applies to the diagonal matrix

[devout snow]

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[restive river]

im stuck pls helppp
i tried using 30 60 90 and bunch of stuff but it doesnt work?
idk how im supposed to get the radius

[rotund umbra]

have you drawn a diagram of this?

[devout snow]

@restive river Has your question been resolved?

[rotund umbra]

👋

[devout snow]

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[restive river]

.reopen

yo why aint this working

[restive river]

yesss

.reopen

[devout snow]

✅ Original question: #help-27 message

[restive river]

helppppp

[sturdy solstice]

You need to find the circumcenter (prob spelled wrong who cares) which will be the center of the circle since it is equilateral triangle. Using this, you can then determine the length from the center of the circle to the edge, set that equal to w√3, and solve for w

[restive river]

oho so like i find the distance from one of the vertices to the center

cuz thats the radius

i think i can do this

i was confused on what to do

[sturdy solstice]

Basically you need to use the circumcenter equation to get the central point of the triangle. This will then allow you to get the distance from the center to the edge of the circle.

Then go from there

[restive river]

wait i tried to solve without that eq cuz like its for sat and no way im memorizing that like is ther way to solve without using it

i did allat back in alg and trig but i fogor

[sturdy solstice]

The way I said is by far the easiest way to do it

There are likely other ways but not easy ones

[restive river]

ok imma just memorize

no biggie

thanks

.close

[devout snow]

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[sturdy solstice]

Actually

[sturdy solstice]

Actually

Yeah there is another way actually

Thats prob easier

idk how I missed this

break the triangle into 3 equal triangles

then go from there

[devout snow]

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[strong igloo]

I'm havinga brain aneurysm trying to understand this

[strong igloo]

Isn't this true by definition?

The orthogonal complement W^ortho of some subspace W of V consists of all vectors of the V that are orthogonal to the basis vectors of W

[devout snow]

@strong igloo Has your question been resolved?

[cinder bobcat]

well the definition i'm familiar with is that the orthogonal complement is the set of all vectors whose inner product with anything in W is 0

[lyric hornet]

or dot product if you're unfamiliar with the term "inner product"

[devout snow]

@strong igloo Has your question been resolved?

[north grail]

Hint : Differences

[strong igloo]

.close

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[soft umbra]

I need someone to verify my work

[vital edge]

👀

[soft umbra]

n = 1\
$1 = 1^2$\
n = 2\
$1 + 3 = 2^2$
n = k\
$1+3+5+....+(2k-1) = k^2$\
n = (k+1)\
$1+3+5+...+(2k+1) = (k+1)^2$\
Because $(k+1)^2 - (2k+1) = k^2$\
Hence proven

[woven radish]

Acknowledged Scumbag

[vital edge]

Would be good to expand and show the last statement

And a statement that the kth odd number is 2k-1

[soft umbra]

Alright, sounds like a great idea

tysm, I'll keep that in mind

[vital edge]

Also you don't need to show n = 2 usually

[soft umbra]

just wanna verify my understandings so far

[vital edge]

Yeye

[soft umbra]

Alright, appreicate it

[vital edge]

The case of n = 2 only becomes relevant when your induction step involves some form of overlapping intersection

As an example, look up the proof that all horses are the same colour

[soft umbra]

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[lusty reef]

if g and h are elements of infinite order in SL(2,C), show that g and h commute iff g and h have the same fixed points

[lusty reef]

here, SL(2,C) is acting on C

and fixed point means that for any z in C, gz = z and hz = z

im trying to show just the forwards direction right now - ive already tried showing that the fixed pts of g is a subset of the fixed pts of h and vice versa, but its really hard to do both at the same time

a useful fact is that h stabilizes fixed pts of g and vice versa

[lusty reef]

and this comes from g and h commutative, so i still havent used that g and h are infinite order

[devout snow]

@lusty reef Has your question been resolved?

[lusty reef]

i know this is not the place to be venting but man. ive spent way too many hours going over the same elementary computations in the hopes of making a slightly different proof by contradiction

[hidden star]

I'm pretty much sure you already did the hardest part

Are we not going to swap h and fixed points of g rather than fixing them individually?

[lusty reef]

what do you mean by this :0?

[hidden star]

Let's say let's make use of the definition of commutativity

Let me write it down rq

So let's define a few things here

Let's say
S -> set of fixed points of g
P -> point in the set S

So, we can say g(p)=p

So, what happens to the point h(p)? Does g "fixes" h(p)?

Let's say we test it by plugging h(p) to g so smth like

g(h(p))

Since, we already know h and g are commute so we can swap it, right?

h(g(p))

Then we know p is a fixed point of g so we know that g(p) = p

So, that's h(p)

Meaning we have
g(h(p)) = h(p)

[lusty reef]

yup so hp is a fixed point of g as well

[hidden star]

Doesn't this prove that h maps the set of g's points to itself

Fixed points in this case but yes

[lusty reef]

yes

[hidden star]

Well, that's how I view this so far

[lusty reef]

yeah :'D

i appreciate the help regardless ^^;;

[hidden star]

Yea, I'll tell you if I figure something out 😭

[devout snow]

@lusty reef Has your question been resolved?

[lusty reef]

so actually theres been partial progress

[hidden star]

What's your current progress?

More like what did you do after?

[lusty reef]

so transformations in SL(2,C) have the form of being rotations around an axis (elliptic, 2 fixed pts), rotation around one point at infinity (parabolic, 1 fixed pt), and some kind of directional flow (loxodromic, 2 fixed pts)

[hidden star]

I can agree to this

[lusty reef]

if g is loxodromic and has fixed points x- and x+ where the transformation is going from x- towards x+, then for any x =/= x-, you have lim g^n (x) = x+

however: suppose for contradiction that h maps x- to x+, ie those fixed pts of g are not fixed pts of h

so in this case, lim g^n h^-1 x is both equal to x- and x+, contradiction

[hidden star]

That should be right

That might mean we need to fix x+ and x- individually, right?

[lusty reef]

i forgot i was missing some info lol, i just added it in but h is assumed (for contradiction) to swap x- and x+

[hidden star]

Right, so I assume you assumed that h(x+) is x-?

And vice versa?

Though, shouldn't it not equal? Since loxodromic should have two distinct points?

So x+ ≠ x-

Then, we might have to debunk the statement that h swaps them

😭 I see now why this has got you stuck for hours

So, with that we can somewhat conclude that h cannot swap the fixed points since it'll cause the loxodromic transformation to stray away from it's required two distinct points.

Somehow, need to map x+ to x+ and x- to x-

Wait hold on

We could just say that h must fix each point individually then conclude that h and g share the same fixed points

[lusty reef]

heres a more clearly written version lol

[devout snow]

@lusty reef Has your question been resolved?

[devout snow]

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[stoic crystal]

why is the solution taking time for second half as 5(1.2x)

it's supposed to decrease by 20%

[silk panther]

well when u slow down, does the time taken to finish increase or decrease?

[stoic crystal]

oh

wow didn't think of it that way

[silk panther]

haha, try to tie it up with irl examples and u got it

[fossil locust]

agree, so if his pace is 10 minutes per kilometer, it increases to 12 minutes per km

so he goes from 6 km per hour to 5 km per hour: that's a reduction of 1/6th

you can think of it like this instead: should work out to the same

[stoic crystal]

it seems like they are taking pace as 1/speed

[fossil locust]

yes

[stoic crystal]

I see

thanks

[fossil locust]

no worries!

[stoic crystal]

wow I just realised we have mutual friends

also can I model this as:

t=d/v

and as pace=1/v
then v=1/pace

t=d*(pace)

and then $5(x)+5(0.8x)<55$

[woven radish]

Jug

[devout snow]

@stoic crystal Has your question been resolved?

[hidden star]

It looks great

[young spade]

the problem was probably meaning to say "minimum pace"

[devout snow]

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[glass zephyr]

Can anyone help with (2)

[glass zephyr]

(this is a 3d space problem, so part (1) dont really effect the problem at all)

[errant harbor]

What have you tried?

[glass zephyr]

I have tried to calcualte the relation of AB like this:

AB^2 = AC^2 + BC^2 - 2 AC BC cos(ACB)

Since BC^2 =BD^2 + CD^2

AB^2 = AC^2 + BD^2 + CD^2 - 2 AC BC cos(ACB)

My teacher says i'm on the right trach

But i'm not sure how to correlate ACB with the dihedral angle

Hang on lemme retype my writing a bit

Here

From what i see i should be able to connect ACB to the required angle

But it doesnt make sense at all

Oh nvm i think i know how to solve this now

.colse

.close

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[honest lion]

I think part a to this problem is false. Am I correct? In particular, consider a f to be a piece wise linear (table looking) function starting at 0 with slope $n$ for $x \in [0,1/n]$, then horizontal, then slope $-n$ for the last $1/n$ interval. I’m not quite sure if a piece wise linear function is in $H^1_0$ but if not a smooth approximation should still be a counter example. What am I doing wrong?

[woven radish]

Owen

[honest lion]

When I say f here I mean u

[devout snow]

@honest lion Has your question been resolved?

[devout snow]

@honest lion Has your question been resolved?

[devout snow]

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[atomic idol]

How do I show that there’s a basis for the vector space X (with a finite dimension N) that looks like this

Delta is 1 if the condition applies and 0 if not

[atomic idol]

P is a projection with the property P = P * P

I’ve shown two things for this problem already but they seem unrelated so I didn’t add them

[violet wind]

can you start with a basis for ker(P)?

or maybe you actually want to start with a basis of Im(P)

[atomic idol]

I’ll add the other things I’ve already shown just in case

[atomic idol]

Do you mean the range?

[violet wind]

image means range, yes

[atomic idol]

Do these help?

[violet wind]

they look useful, yeah

start with a basis for Im(P)

or Ran(P)

where do those basis elements get mapped?

[atomic idol]

P(v)=v

[violet wind]

right

that should give you a few columns for your matrix

[atomic idol]

Im confused

Where would I get the basis of Ran(P)

[violet wind]

every vector space has a basis

you can just choose one

you have that Ran(P) is a subspace, right

[atomic idol]

Do you mean the first thing I’ve proven?

Also I’ve had this as an idea for the basis
Would this work?

[violet wind]

idk what that is

[atomic idol]

A sum of all standard basis vectors up to the dimension N

[violet wind]

do you have a theorem that says every vector space has a basis

[atomic idol]

Im not sure honestly

Im working with a terribly formatted extremely long script

I think i might’ve found sth

[violet wind]

it's not terribly difficult to prove for finite dimensions

you just keep choosing independent vectors

when you run out of independent vectors, that's your basis

[atomic idol]

How do you know how many dimensions p has

[violet wind]

p has a basis of size N

[atomic idol]

I just know that X has a finite dimension
But not that p has the same dimension

[atomic idol]

Why?

[violet wind]

wait what

is that at the bottom

of the summation

n = n?

$n = \cap$?

[atomic idol]

That’s how I write a 1

[woven radish]

Dreyuk

[violet wind]

oh

[atomic idol]

Handwriting

[violet wind]

yeah ok

[violet wind]

e_1, ..., e_N

[atomic idol]

It’s just all standard basis vectors from 1 to N scaled and added together to span P

If dim(P) = N that should be the basis correct?

[violet wind]

that is the basis, which is how you know dim(P)=N

dimenison of N is defined as having a basis of size N

[atomic idol]

Yes but I don’t know the dimension of P nor do I know what the basis looks like at first

Or do I get the information implicitly somewhere

Does P inherit the dimension of X?

[violet wind]

the basis is e_1, ..., e_N

[atomic idol]

The only thing I know is that dim(X) = N =< infinite

Just fyi
The variable N is already used by the task
In case you’re just calling it that for P without knowing about it

[violet wind]

oh

can some of the a_n be 0?

i think i see why i was confused then

[atomic idol]

Technically yeah
n is just an index
You could start by counting at 0
But I thought 1 would be nicer

[violet wind]

no like the alpha_n coefficients

[atomic idol]

They could be 0 yes

Depending on how you want to scale the basis vectors

[violet wind]

ok this is strange

inside that thing is only one vector?

you're taking span of a signle vector

[atomic idol]

No wait
I rewrote the basis earlier

Forgot to show you sorry

[lyric shard]

Just chiming in because this problem interests me as well
Would it be possible to start solving this by saying that we're picking some arbitrary basis of Ran[P] that we just call V? And then because P(V)=V (by definition of Ran[P]) our matrix representation would end up looking like the one given to us?

[violet wind]

that's what i want to do yeah

[lyric shard]

Oh ok I see

[violet wind]

ok so on the left you're leaving out some like set notation then?

P is the set of vectors that result from that sum for all a_1, ..., a_N in F

[lyric shard]

I'm just not exactly sure how I'd personally write that as a proof since my linear algebra skills got a bit rusty

[atomic idol]

I am saying P is just the linear combination of all standard basis vectors up to the dimension N

[violet wind]

and N is the dimension of X?

[atomic idol]

And that this is equal to the span of all bask vectors

[atomic idol]

P is a projection with the properties from the beginning of the conversation

[violet wind]

if P is a projection then it's a function, not a set, it isn't the "span" of anything

[atomic idol]

Would the range of P be the span of the basis then?

[violet wind]

is N the dimension of X, as you said earlier?

because then no

[atomic idol]

Yes N is the finite dimension of a vector space called X

P is a projection so that P = P * P

[violet wind]

...a projection from X to X?

[atomic idol]

Yes seems like it

[violet wind]

right ok

[atomic idol]

Says this

[violet wind]

so e_1, e_2, ... e_N is a basis for X

[atomic idol]

Yes

[violet wind]

so it's span will be all of X

not Ran(P)

[atomic idol]

And also for P if dim(P)=dim(X)

[violet wind]

yes

but it probably doesn't

[atomic idol]

How would I get a basis for P in that case

Do I just take my sum from earlier and rename the upper limit to D = dim(P)

[violet wind]

P is a function, so it doesn't have a basis

only vector spaces have bases

[atomic idol]

Can you not give a basis for the image of said function?

[violet wind]

you can

you'd call that a basis for Ran(P)

[atomic idol]

I see

Alright then

[violet wind]

you can get it because all vector spaces have bases, and Ran(P) is a vector space

but if you don't have that fact given

[atomic idol]

How would I show that there’s a basis v of X with these properties

[violet wind]

Start by finding a basis for Ran(P)

or asserting it's existence

[atomic idol]

What about this

,rccw

[atomic idol]

I’ve defined the dimension of that range to be D

And changed the sum to only combine all standard basis vectors from 1 to that dimension

Does this work?

[violet wind]

if i saw that in a paper, i would probably fill in the gaps myself, but I don't imagine you know what the gaps are

[atomic idol]

No clue

[violet wind]

if your basis for X is already chosen, you can't just choose the first D elements and hope that they happen to span Ran(P)

there are likely lots of other dimension D subspaces that aren't Ran(P)

and it would probably span one of those instead

[atomic idol]

So it’s like saying we have 3 dimensions in X and 2 in P (for example)

And pretending that every subset of 2 dimensions will span P

Despite it being one specific option

[violet wind]

yeah like if i'm working in R^3

and my Ran(P) is {x+y+z = 0}

i can't just choose like <1,0,0> and <0,1,0> as my basis for Ran(P)

[atomic idol]

Because it could be <0,0,1> instead

[violet wind]

no

because none of those vectors are even in Ran(P)

<0,0,1> isn't either

so it's not even like i can just choose the right subset and have it span Ran(P)

i have to start from scratch and specifically choose a new basis of Ran(P), rather than starting with an arbitrary existing basis of X

[atomic idol]

Alright

How do

[violet wind]

So we need to choose a basis of Ran(P), from scratch

If we know that every finite-dimensional vector space has a basis, we can just use that fact

otherwise, we need to make our basis by choosing linearly independent elements one by one until we span all of Ran(P)

[atomic idol]

Which we can’t do because we don’t know anything about RanP

Can we just say let there be
V = Base(Ran[P]) = { v_1, … , v_D}

[violet wind]

Probably

don't say Base() though, unless somehow that's actually established notation in your course

just say let V be a basis of Ran(P)

[atomic idol]

alright I’ll change it

Got rid of it

Can you write @violet wind the basis of a vector space as the reunion of the basis of both the kernel and the range

[violet wind]

not usually

but in this case your kernel and range dont intersect

[atomic idol]

So?

[violet wind]

so you can make it work

[devout snow]

@atomic idol Has your question been resolved?

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[devout snow]

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[cursive hazel]

question related to advent of code day 2:

what are numbers like 11, 22, 3434, 567567 called? what do they have in common? i feel like there must be some mathematical way to go about this so if someone could tell me what to google that would be great

[pseudo basin]

567567 is not a palindrome

[sage ibex]

my fault 🤦

serch in oeis

[cursive hazel]

the what

[sage ibex]

online encyclopaedia of integer sequences

[cursive hazel]

ohhh
ok ty

[sage ibex]

11,22,3434,567567,891011891011?

[pseudo basin]

anyway

[cursive hazel]

for example

[pseudo basin]

the best way to describe these is like... numbers that consist of two copies of the same number stuck together

[sage ibex]

i think there halfway 567|567 2|2

[cursive hazel]

basically if you split the number in 2 you get 2 of the same
if its a word that is
123123 => 123|123 => 123 and 123

[cursive hazel]

yeah
using strings this is easy but inefficient

[pseudo basin]

how against the rules is it to share the original advent of code problem

[cursive hazel]

uhhh idk if anyone cares since its yesterdays problem

[pseudo basin]

can you share it then

so that we have a clearer picture of what you're trying to do

[cursive hazel]

basically
given some number ranges, find all such numbers in them
11-22 has 2: 11 and 22
95-115 has 1: 99
1188511880-1188511890 has 1: 1188511885

x mod (10^half of digit count of x) == floor(x/10^half of digit count of x)

maybe?

[devout snow]

@cursive hazel Has your question been resolved?

[devout snow]

@cursive hazel Has your question been resolved?

[cursive hazel]

<@&286206848099549185>

[devout snow]

@cursive hazel Has your question been resolved?

[devout snow]

@cursive hazel Has your question been resolved?

[tender cobalt]

I dont think they have a name

youre better off using strings, there isnt really anything mathematical I can see here other than being numbers of the form 11 * single digit, 101 * double digit, 1001 * triple digit, 10001 * quadruple digit, etc.

for example think about printing the first 100 numbers of this form, you can go through all of them with strings and easily compare their sizes by how many digits they have

also, day 2 of advent of code and youre already trying to find answers online instead of trying the problem on your own? sort of defeats the purpose

[devout snow]

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[peak tiger]

i need help

[peak tiger]

how to find height of triangle ABC if the yellow shadded area are the same

[hidden star]

Do you have the original question?

Hold on, let me make sense if this

[peak tiger]

here is better drawing

this problem my dad gave me

if i solve it, i get to play my video games

btw the height is not 16

[hidden star]

Isosceles?

Right but I'm confused how this is looking right now 😭

[peak tiger]

is my drawing too chopped?

[peak tiger]

yes

[hidden star]

Hold on, let me see

Am I understanding this right?

[peak tiger]

yes

the height of the red triangle is 11

the height of the trapozoid on the bottom is 5

help find height of abc

[hidden star]

Okay so, the trapezoid and triangle are supposed to somehow form a big triangle?

[peak tiger]

trapezoid + triangle does not equal the entire triangle

but the two shaded parts have same area

[hidden star]

Right, so do they have space in between?

[peak tiger]

they have space inbetween

[hidden star]

Let me see

[deep abyss]

so we have another trapezoid in between?

(Is trapezoid and trapezium the same?)

[hidden star]

Something like this then?

[peak tiger]

yes

[hidden star]

Right just to be sure, it's not measuring the shaded area but rather the height?

[peak tiger]

yes

[hidden star]

An isosceles triangle
AB = AC

[peak tiger]

yes

[hidden star]

Right, what have you tried so far?

[peak tiger]

no clue what to do

but my dad said something about similar tiangles

[hidden star]

Similar triangles?

so far I find the information insufficient but let's see I might've overlooked something

No I can't link this in any ways with similar triangles unless I'm missing something that I shouldn't 😭

[peak tiger]

my dad taught me

its very goofy

[hidden star]

I don't know if I can help you on this so, I'm just going to pass this to someone who might know how to deal with this cause my brain is not picking anything up 😭

[devout snow]

@peak tiger Has your question been resolved?

[devout snow]

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[real sail]

Hello, I'm requesting help with an exponential function formula problem, please!

[real sail]

So far I wrote out 2 functions:
f(71) = ab^2
f(83) = ab^6

Then used the ratio method to get

71/83 = 1/b^4

Not sure what to do next

[drifting sierra]

That makes no sense

I'm guessing you meant "71 =" and "83 ="

[pseudo basin]

those are not "two functions" btw

also yeah definitely 71 not f(71), and 83 not f(83)

71/83 = 1/b^4
Not sure what to do next

if you had b^4 = (number) instead, would you know what to do

[real sail]

ah, yes that's what I meant

so 71/83 = 1/b^4

I remember being taught this recently, but my memory is failing

I think I got it, thanks

.close

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[rare kernel]

dy/dx = (x+y-2)/(x-y)

[rare kernel]

how to solve this

[pseudo basin]

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[rare kernel]

i just cross multiplied

and stopped there

[glossy dew]

convert to homogenous form..

X = x + h and Y = y + k

and find h and k such that equation has only X and Y in numerator and denominator

[rare kernel]

is there a better method?

i use homogenous only if theres no other option

[glossy dew]

idk this is a common approach though

[fiery pivot]

Idk what is this abt but my mind telling me, do integral on both sides

[rare kernel]

?

[glossy dew]

... maybe you need to wait 2 more years and come back to this...

[fiery pivot]

Nah. I'm wrong. Pardon me

[rare kernel]

alr well if homogenous is the only way then

fine

.close

[devout snow]

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[cedar briar]

I need help as fast as possible, i need to find the domain of these functions, could someone write to me the steps that i have to write and the solution to help me u guys can skip the n1 if u want

[long pasture]

,rcw

[cedar briar]

Need help its for something important

[vital edge]

What is it for

[cedar briar]

To be accepted into the next year

If u want to know

[vital edge]

Well the domain of a function is the region in which it's defined

[mental forum]

You just have to find the domain of values that are "legal to use". So for example, for a division, you can't have 0 in the denominator. Just do the same for the others

[vital edge]

Possible places where it might not be are divisions by zero, square root of a negative, and tangent of an odd multiple of π/2

Or log of a negative number

[cedar briar]

The first one i did - 3, 0, 3 as the result idk if its thr correct number

[mental forum]

Seems correct

[deep abyss]

all real except these yeah

[cedar briar]

The thing is i used ai to do that if im honest bro and i dont want to seem like its blatant copying

And i dont trust ai that much

And theres no one with me too

[mental forum]

Just do denominator = 0 and find all of the values that solve this. These values are what you are searching for, at least for everything that is a division

[cedar briar]

Bro thats like speaking a foreign language to me like i unxerstand what u sayinh but idk the zteps i gotta zo to find that yk im not asking u guys to do my homework and ifbu dont want thats fine guts i still apprecciste for the concern

[mental forum]

So, every function has a domain where they are defined, meaning they have a value. For function that have a fraction, so for example "y = 1/x", the denominator, in this instance "x" must not be equal to 0, because dividing by 0 is not defined.

So for 1. you have to find the values for x that solve the denominator = 0, meaning x³-9x = 0

[mental forum]

So, to sum it up, you each function you have to first, see which for which values this function is not defined (1/x, log(x), e^x, √x, tan(x), sin(x)), and then you can solve equations while being mindful of the domain of definition of each function, so for example
1/log(x²-9)
So there is 2 function here
one being similar to 1/x, and another being similar to log(x). So you have to solve log(x²-9) ≥ 0, because log(x²-9) must not be less of equal than 0 because of how log is defined, and also not equal to 0 because of how 1/x is defined

[cedar briar]

The fiert is -3, 0, 3 the second - infinite - 2 U (1,5) thats what i pur at least

the third R / { 1,0,1} the other two its fine if dont do em

[deep abyss]

sounds abt ryt

[mental forum]

there is something missing in the 2nd one

[cedar briar]

whats the answer bro

[mental forum]

you got some rights, but you forgot the roots of x²+x-5 after factorising x³-6x+5 = (x-1)(x²+x-5)

after that, you have to see for which values of x the whole thing is negative, because the square can't be negative in R

[mental forum]

also, do you have to put it in inverval ?

[devout snow]

@cedar briar Has your question been resolved?

[mental forum]

you want the answer out right, or do you want more time ? i can also give you a pic with all of the steps

[devout snow]

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[misty folio]

Pls help

[mental forum]

Traduction ?

[misty folio]

No dis 1

Help me please

Help

[gloomy aurora]

Could you maybe translate?

[devout snow]

@misty folio Has your question been resolved?

[cedar briar]

i guess

[devout snow]

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[mild plaza]

Hello

[rain summit]

post your question

[mild plaza]

So basically I wanna ask why this is include instead of belong (sets)

Well that’s what ai told me atleast

This is a segment and a line

I don’t see a set in it for it to be includ

Or subset

Wtv u wanna call it

[uncut crow]

i know things about line segments and sets but i have no idea what the notation in that image means

[faint zinc]

I have also never seen that notation.

[mild plaza]

Basically they are asking if the sets given are belong or subset

And

That was one of them

[mild plaza]

Same

I have an exam tomorrow

Fucking alien shit

[uncut crow]

i can’t say anything without more context tbh

[mild plaza]

That’s everything I have on it

[uncut crow]

lol

[faint zinc]

Well, ok so AB is a line segment?

[mild plaza]

The question says to choose between belong doesn’t belong subset no subset

[mild plaza]

Idk I think so

[faint zinc]

!original

[devout snow]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[uncut crow]

this is a long shot but is [AB] a line segment that includes endpoints and (AB) is a line segment that does not include endpoints

[faint zinc]

I was also thinking that it might be the case.

similar to how [min, max) includes min but does not include max.

[mild plaza]

I don’t know

What that means

I’m gonna be honest

[uncut crow]

😭

[faint zinc]

So let's consider a concrete example.

Let's say A = (0, 1) and B = (4, 0), so AB is a line segment from (0, 1) to (4, 0)

[mild plaza]

…

[faint zinc]

[AB] includes the points (0, 1) and (4, 0), but (AB) does not include these points.

[mild plaza]

I have a question

Don’t kill me

Is a segment a non ending line

From both sides

[faint zinc]

https://www.desmos.com/calculator/b8tuqlepq1

Here was what I was talking about

both [AB] and (AB) contain the green line, but (AB) doesn't contain the red and blue points.

[faint zinc]

A line segment is a part of a line between two particular points, it doesn't go off to infinity. A ray is part of a line that starts from a point and goes off to infinity in one direction. A line goes to infinity in both directions.

[mild plaza]

Oh

[faint zinc]

this is my guess anyway

[mild plaza]

I understand now

So it has an end

Basically

[faint zinc]

line segments have 2 ends.

[mild plaza]

Yes

That’s what I meant

It’s limited

I’m slow

Okay.

[faint zinc]

You're not slow

[mild plaza]

Math is hard

[faint zinc]

Yes, math is hard.

[mild plaza]

Ur a genius tho so

[faint zinc]

Nah

[mild plaza]

I don’t think that effects you a lot

Did u ever fail math

I took 2/10.

[faint zinc]

Yes, I have failed a math class before.

[mild plaza]

…

Wow

[native gyro]

Bruh

Math is easy

I learnt the whole calculus in 8th grade

[faint zinc]

Math is difficult. And it takes work, and demands thinking in particular, very organized, kind of alien ways.

[mild plaza]

How old are yall

[faint zinc]

41

[native gyro]

16

[mild plaza]

Yeah

Wth

[native gyro]

What

[mild plaza]

I see

[faint zinc]

But the good news is

I'm a moron, so if I can do it, anyone can.

[mild plaza]

Are u like

Married

[native gyro]

Doubt it

[faint zinc]

yeah, I'm married.

[mild plaza]

Sorry I just had to ask

[native gyro]

My classmates can do much worse

[native gyro]

Also how old are you

[mild plaza]

I’m 15.

[native gyro]

Yea dc normally has teenagers

[uncut crow]

wow that’s so impressive

[mild plaza]

Ur one of them

[native gyro]

Yep

[native gyro]

Ty

[mild plaza]

I’m stuck in sets

I hate this

[native gyro]

I hate geometry

[uncut crow]

i guess i didn’t make that message sarcastic enough

[mild plaza]

I love geometry.

[native gyro]

Xd

[native gyro]

Bruh

[mild plaza]

Algebra is hell

Well

[native gyro]

FYI, i wasnt trying to flex

[mild plaza]

Is sets considered algebra

Or

Geometry

[native gyro]

Nope

[mild plaza]

I see

[native gyro]

Its neither

[mild plaza]

Oh

[native gyro]

Its sets

[mild plaza]

Gulp

I knew that

[native gyro]

Also, whats the original question

Or are we finished

[mild plaza]

Is this subset or belong

[native gyro]

Wth is this

[mild plaza]

Idk

Ur the genius here

Basically

They gave me a lot of sets

And I have to say

Belong

Doesn’t belong

Subset

Not subset

[native gyro]

Aha

[mild plaza]

This shit was one of them

[native gyro]

What is even [AB]…(AB)

[faint zinc]

that's was our question

[native gyro]

Is this some marking that i dont know????

[faint zinc]

It's some marking that I don't know either.

[mild plaza]

Idk

I don’t know aswell

[native gyro]

Because sets are defined as A:= {something}

[mild plaza]

I came here for help

I have an exam tomorrow

[native gyro]

Woops

[mild plaza]

Am I cooked

[faint zinc]

Sets are defined in many different ways, set builder notation is just one method of notating a definition.

[native gyro]

Gl youll need it

[mild plaza]

Thanks

I took 2/10

[native gyro]

Aha

[mild plaza]

Last time

I had freaking vectors

[native gyro]

Oh wow thats impressive

[faint zinc]

angy, can you take a picture of the rest of the page please?

[mild plaza]

Isn’t builder notation

Comprehension

And

Roster is

Uh

Extension

[mild plaza]

Yes

I can

[faint zinc]

I'm not sure what you mean by comprehension (list comprehension from python?) or roster and extension.

[mild plaza]

Uh

Uh

This is comprehension

Rotate it

[faint zinc]

,rccw

[faint zinc]

oh, AB are probably two sets not a line segment, and the () vs [] notation is probably intersection and union? Not sure, I haven't encountered this notation either, but it would make more sense in context.

[mild plaza]

Idk what that is

We usually say

Intersection and union

In like

u

But also u flipped

Upside down

[faint zinc]

$\cup \cap$

[woven radish]

OmnipotentEntity

[mild plaza]

Yes

This

[faint zinc]

what book is this from?

[mild plaza]

My school book

[faint zinc]

what I'm asking for is the name of the book

so I can look it up

[mild plaza]

It’s called mathmatics

My teacher made it

It’s a booklet

[faint zinc]

oh well, then I really don't know lol

can you contact your teacher and ask the meaning of this notation?

[mild plaza]

Do u think ill fail

[mild plaza]

I did he didn’t answer

He’s bald

Sorry

[faint zinc]

I don't see how that's relevant?

[mild plaza]

I’m just joking

[native gyro]

Wait these notations are pretty normal

[faint zinc]

are they?

[rain summit]

Save those jokes for this

[rain summit]

!redir

[devout snow]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[uncut crow]

definitely not normal

never seen it in many years of looking at sets

[faint zinc]

same

[rain summit]

$A = B$?

[woven radish]

1 divided by 0 equals Infinity

[faint zinc]

$[AB]$ vs $(AB)$

[woven radish]

OmnipotentEntity

[heavy current]

I have no idea what the notation [AB] or (AB) means

[faint zinc]

with A, B presumably sets

[mild plaza]

My bad

[faint zinc]

if I had to guess I'd say $[AB] = A \cup B$ and $(AB) = A \cap B$, but this is just a guess from context.

[woven radish]

OmnipotentEntity

[native gyro]

Ok now these are not normal

The ones you sent earlier is

[heavy current]

when in doubt, ask your teacher

[faint zinc]

yup

[mild plaza]

I did tho

[faint zinc]

if they don't answer ask again.

[native gyro]

In*

[mild plaza]

He didn’t answer

[native gyro]

Lol

[faint zinc]

Chances are no one here is going to be able to help if you're working from a bespoke book with non-standard notation.

Maybe the notation is defined somewhere earlier in the book

but that would be something you'd need to search for in that case.

[mild plaza]

I’ll try to check

Thank you so much tho

Please wish me luck

Thanks guys

I hope yall never fail math

.close

[devout snow]

Channel closed

Closed by @mild plaza

Use .reopen if this was a mistake.

[uncut crow]

,w bespoke

[faint zinc]

best of luck

[woven radish]

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[devout snow]

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[stiff karma]

a) is 7/2

[rain summit]

solution set

[native gyro]

Ahh sets to sets

[rain summit]

So should be $\left{ \frac72 \right}$

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

They said solution set

Now try b)

[stiff karma]

Yeahvrhays the only dolution

B) is {sqrt(7)}

However it must be in Q.

So idk..

So it isn’t possible

[rain summit]

No

[rain summit]

Have you ever heard of an empty set?

[deep abyss]

So null set

[stiff karma]

Why is it {}

What*

[rain summit]

It's a set with 0 elements

[stiff karma]

Because there isn’t a solution that fits Q, so we put empty?

Oh okay

[deep abyss]

Yes

[stiff karma]

Ok ok that makes sense

[rain summit]

Glad

c) should be a breeze

[stiff karma]

x^2 + 3x = -2

I can’t do that…

[deep abyss]

Factorization of a quadratic

[faint zinc]

quadratic formula, or just factor it

[stiff karma]

I did these recently

y = ax^2 + bx + c

And what now

[faint zinc]

The thing about math is it's cumulative, so once you learn something you're going to need to use it for things later on.

[stiff karma]

@faint zinc

[faint zinc]

0 = x^2 + 3x + 2, what are a, b, and c?

[stiff karma]

It’s -2 or -1

So {-1, -2}

EZZZZ!!!

[rain summit]

Try d now

[stiff karma]

It will just be

sqrt(9/4)

[rain summit]

Nuh uh

[stiff karma]

Why

[rain summit]

negative

[stiff karma]

sqrt(9/4)

Or

-(sqrt(9/4))

[rain summit]

Yesss

Now write that in set form

[stiff karma]

It’s just 2 1/4

Right

And square

[devout snow]

@stiff karma Has your question been resolved?

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[stiff karma]

Is this correct?

[cold haven]

,rotate

[pseudo basin]

(3/2)^2 - 4×1×(-1) gives (3/2)^2 + 4

so no, there's a sign error you made

[stiff karma]

25/4

Ok

.close

[devout snow]

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[lilac pelican]

Is this

[lilac pelican]

Equal to this?

[leaden obsidian]

Prob yea

[lilac pelican]

Probably?😭😭

[leaden obsidian]

Yea I think so

[lilac pelican]

Why can I sawp these

[brisk raptor]

yes, unless the limit DNE or is infinity because ln(DNE) or ln(inf) doesnt exist

in this case it isnt

[supple knot]

the logarithm is a continuous function so you can swap lim log = log lim

same for any other continuous function

[leaden obsidian]

Isn't lim(1+1/x)^x=e?

[lilac pelican]

Yes

There's this video that's asking to spot where the proof of this limit is wrong

😅

Well thanks for answering my question

.close

[devout snow]

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[willow helm]

As $x \to \infty$ yes

[woven radish]

USS-Enterprise

[devout snow]

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[devout snow]

@light hazel Has your question been resolved?

[devout snow]

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[cursive hazel]

this happens to be available so let me respond

my idea abt the mod and digit count and stuff turned out to be correct

yes its a trivial task with strings but strings are very slow

and i wasnt looking for an answer to the problem just a potential way to solve it with maths english isnt my first language and idk math vocab so googling smth like this is difficult

[ebon coyote]

I mean, given the actual question, you can literally just check for them, I would imagine

Like, if you've got a range 2491XXXX - 2491YYYY, it should be pretty obvious that the invalid ID should be 24912491, provided that's in the range itself

[devout snow]

@cursive hazel Has your question been resolved?

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[devout snow]

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[lofty verge]

Is this impossible?

If so, why?

Can it be approximated without recursion?

$\int (1+(cos(x))^2)^\frac{1}{2} dx$

[woven radish]

UCYT5040

[acoustic leaf]

,w integrate sqrt(1 + cos^2(x)) dx

[woven radish]

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[acoustic leaf]

it's an elliptic integral

[lofty verge]

What does that mean?

Never learned that

E is a function???

[supple knot]

https://mathworld.wolfram.com/EllipticIntegral.html

[devout snow]

@lofty verge Has your question been resolved?

[devout snow]

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[deft flower]

how do i properly use feynman's integration technique

[uneven coral]

You'd likely have better luck in #math-discussion

[deft flower]

i just don't know what to do after calculating an image of the derivative of the function we set so i thought i might get help here

especially since it's quite a difficult integral

[supple knot]

[deft flower]

integral from 0 to pi/4 of cubic square of tanx

[uneven coral]

If you've got a particular question then you can share it here

cubic squares? Didn't get that

can you share an image of the question please

[deft flower]

uhh the power of 1/3

[deft flower]

yeah sure

[uneven coral]

Have you tried the approach for √tanx?

[deft flower]

not really

wait imma show you the whole progress

[uneven coral]

Sure mate

[deft flower]

sorry for the messy paper

[uneven coral]

Okay I haven't done that before

Let me try this question

[deft flower]

alright sure !

[uneven coral]

Can do solve this integral

$\frac {3(u)^(3)}{1 + (u)^(6)}$

[woven radish]

doctorstrangejr

[uneven coral]

Whoops, I hope you get it

[deft flower]

are the 3 and 6 powers ?

[uneven coral]

Yes

wait just take u^4 as t

3u^3du = dt

dt/1 + t^2

arctan(t)

Checks out?

Whoops no

It'd be dt/(1 + t^(3/2)

Ohhhh wait

Just take u^3 as t, and then do partial fraction

[deft flower]

oh mb i went to watch a youtube video to help rq

[deft flower]

what is this going to help with with the original integral tho

[uneven coral]

Well multiply numerator and denominator with sec^2x, take tanx = t, then expand the sec^2x at the denominator to 1+t^2

That's how we do √tanx

[uneven coral]

Here, I was left with t^(1/3)/(1 + t^2)

So take t^(1/3) as u

That gives 3u^3/(1 + u^6)

[deft flower]

ahhhhhhh i'm lost

so after i use u substitution i do partial fraction decomposition. is that right ?

[uneven coral]

Yes, now take u^3 as w

[deft flower]

like this ?

[uneven coral]

Wait I'll do it and send a pic until that step

[deft flower]

thanks cuz this is midnight and my head is burning out 😭😭

[uneven coral]

Sorry for the delay

Damn there must be a method shorter than partial fraction after this, if anybody finds it then do message here

[deft flower]

exactly it's gonna be so long imma crash out

[uneven coral]

I'm doing it

[deft flower]

alright please send when you do !

[uneven coral]

Sure mate

@deft flower

[deft flower]

yeah

[uneven coral]

Just put in the 0 and 1s

Let me check from the integral calculator if this is correct or not

, w integrate cbrt(tanx)

[woven radish]

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[uneven coral]

What in the world

[deft flower]

what the hell is this

[uneven coral]

Wait wait

Let me check from another one

[deft flower]

youtube might be our only hope to check

but i think i was pretty close to getting it

with feynman's technique

[uneven coral]

Wait let's check the final answer

[deft flower]

i calculated I'(0)

[uneven coral]

,w arctan(-1/sqrt3)

[woven radish]

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[deft flower]

indefinite form

[uneven coral]

Dude

I got -3/8 log(8) + √3 pi/4

Calculator says -log(2)/2 + pi/2√3

[deft flower]

rip

what did i get myself into

[uneven coral]

Wait looks like he did the same stuff as I did

Yo wait

WHAT

[deft flower]

where did u get it wrong

[uneven coral]

Even I'm not sure

We're same until partial fraction, after that we're different

[deft flower]

oh well...

imma check the answer using desmos

[uneven coral]

Dude

[uneven coral]

you see my working here

See how I smudged out the +Bx and wrote +Bw in the partial equation

[deft flower]

0.56

[uneven coral]

I skipped it when finding the values of A,B and C

That changes the values

[deft flower]

LMAO

[uneven coral]

Holy shit, let me do this again

[deft flower]

alrrr

i just noticed that i used feynman's technique COMPLETLY wrong 💔

and ended up integration ln(tanx) for absolutly no reason

[uneven coral]

Dude

I got it

Holy shit

[deft flower]

NO WAYYYY

what did u do

[uneven coral]

Log(1) is just 0

Wherever I've underlined is when that integral is finished

[deft flower]

you're so goated for actually getting this monstrosity correct

[uneven coral]

Thanks man

[deft flower]

i can now sleep in peace now that its solved

goodnight and thanks man !

[uneven coral]

Anytime man, this was both fun and a headache

[deft flower]

.close

[devout snow]

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[simple grotto]

$P+(VC-P)t+(VX-VO)x+(VY-VO)y=Q$ where VC is where on plane P x and y=0. This is proven correct. All collections of upper case letters are points as one together and lower case are variables. I would like to not have Q much and this is 4d+ projection. Another formula states $P+(VO+(VX-VO)x+(VY-VO)y-P)t=Q$, t is similar but x and y scaled by t here directly relate to the other x and y with subtracting VC x and y. See the program for interesting stuff. X E.

[woven radish]

maybeJosiah

[simple grotto]

Basically, I want to find some relation for x, y, and t. X E.

The file is Javascript. X E.