help-26

[trail trench]

It always equals 1

[chrome hinge]

cool

so

$\frac{a}{a}\cdot\frac{a}{b}$ is equal to..

[thorny flame]

.,..

[trail trench]

1

[chrome hinge]

times what

[trail trench]

Times a/b

[chrome hinge]

oh damn

so $\frac{(x-2)(x-2)}{3x(x-2)}$ would be equal to..

[thorny flame]

.,..

[trail trench]

1

[chrome hinge]

times what

[trail trench]

1 * 2/3

[chrome hinge]

how is this even lol

[chrome hinge]

so lets go back here

[trail trench]

Ok

[chrome hinge]

lets say that a=x-2 and b=3x

[trail trench]

Ok

So it would be 1*x-2/3x

[chrome hinge]

yes

[trail trench]

But then what happens? Doesn’t that just keep x-2/3x the same?

[chrome hinge]

wdym

[trail trench]

Ok so 1 times anything is that number

So 1 times 2 is 2

So this fraction stays the same

[chrome hinge]

so what you are saying is that $\frac{(x-2)^2}{3x(x-2)}=\frac{x-2}{3x}$?

[thorny flame]

.,..

[trail trench]

Well I know that (x-2)^2/3x(x-2) = 1

[chrome hinge]

no

[trail trench]

Wait hold

(X-2)(x-2)/3x

[chrome hinge]

What about that

[trail trench]

I’m confused about 1 * a/b

[chrome hinge]

ask

[trail trench]

And if a/b

Equals

[chrome hinge]

a/b is 1 only when a=b

a/a is always one

[trail trench]

Ok

Yes

I’m a little confused

So

I cancelled out the x-2s

I got 3x

That was equal to 1

And now we have 1 * a/b * a/b

Where do I go from there?

[chrome hinge]

wait

[trail trench]

What about the fraction at the bottom?

Is that what I’m supposed to do?

[chrome hinge]

your numerator is wrong

[trail trench]

Which one

The left one?

[chrome hinge]

read the bottom one first

[trail trench]

Ok I read them

But if you have x-2/3x

How will you get x/3?

[chrome hinge]

you multiply $\frac{x-2}{3x}$ by $\frac{x^2}{x-2}$

[thorny flame]

.,..

[trail trench]

Where is x^2/x-2 coming from?

[chrome hinge]

the original question

[trail trench]

Oh I see

Ok

I have a question

Won’t I get a negative from this?

[chrome hinge]

what

[trail trench]

Ok so for example

3x and X-2

There is like an invisible 1 next to the x

So 1-2 = -1

3x * -1

-3

[chrome hinge]

whens your exam

[trail trench]

I’m homeschooled

I’m following a curriculum

It’s called allinonehomeschool

[chrome hinge]

who teaches you math?

[trail trench]

Myself because I have no teacher

Sometimes my brother and I work together but he’s just as confused as I

[chrome hinge]

and you both are homeschooled

[trail trench]

Yes

[chrome hinge]

makes sense

I gotta ask you something

what do you think the x is in these

[trail trench]

X is a variable

[chrome hinge]

yes

and you cant do shit like 4x+5=9

[trail trench]

I see how what I said above doesn’t make sense tbh it was a shot in the dark

[chrome hinge]

math dont work like that

4x+5 is 4x+5 unless we know what x is

Why dont you go to public school btw

[trail trench]

Well

My family travels a lot

Long story but that’s it basically

[chrome hinge]

ok so anyways I think I gotta guide you more through this

[trail trench]

Ok thank you for sticking with me for so long

[covert lion]

Hi

[chrome hinge]

$\frac{x-2}{3x}\cdot\frac{x^2}{x-2}=\frac{x^2(x-2)}{3x(x-2)}$

[thorny flame]

.,..

[chrome hinge]

hi

[trail trench]

I see

[covert lion]

How are you

[chrome hinge]

im good how hi are you

[trail trench]

So do I cancel the x-2s?

[chrome hinge]

Yes

[covert lion]

I am good too

[chrome hinge]

what do we get

[trail trench]

And now I have x^2/3x

[chrome hinge]

yes

and the what

[covert lion]

What is the question

[chrome hinge]

this

[covert lion]

Ok

[trail trench]

And x^2 is equal to x*x

[chrome hinge]

yes

[trail trench]

So then I cancel the Xs

?

[chrome hinge]

yes

[trail trench]

So then I have 3

[chrome hinge]

ehh

You should think about what we did here

[covert lion]

Is ur friend coping well

[chrome hinge]

what friend

[covert lion]

@trail trench

[chrome hinge]

coping or copying

[trail trench]

So I cancel the x on the denominator of the left fraction and the numerator of the right fraction

[covert lion]

I simply mean if he is following along

[trail trench]

I keep the x numerator on the left and then combine it with the 3

Hmm

[chrome hinge]

getting us what

[trail trench]

X/3

[chrome hinge]

good job mr rooster2005

[trail trench]

So I only cancel the 2 x’s

[chrome hinge]

somewhat

[pliant bobcat]

hello im kind of new but I need help to study for an exam, anyone here can help me out?

[chrome hinge]

atleast he seems to be trying

[chrome hinge]

#❓how-to-get-help

[covert lion]

Ok

[trail trench]

So that’s how we solved the problem?

That’s it?

[covert lion]

Is it a maths exam

[pliant bobcat]

yeah but not cheating at all

[covert lion]

Ok

[pliant bobcat]

just studying

[chrome hinge]

yeah but you gotta work on those

[covert lion]

Have u been studying past questions

[trail trench]

Thank you ..,..

[chrome hinge]

eh

close enough

[covert lion]

So which topic seems hard for you

[chrome hinge]

probably some math stuff

not sure

[covert lion]

mmmmh

[pliant bobcat]

binmoio raised to the power N

Pascal's triangle

language translation

1st degree equations

second degree equations (quadratic, factorization or general formula)

application problems

[covert lion]

Ok

[pliant bobcat]

I dont know if you can kind

of test me or sum

[chrome hinge]

so 1st degree equations are y=ax+b?

[pliant bobcat]

ye

[covert lion]

I will try my best

[pliant bobcat]

thank u

[chrome hinge]

you should ask specific questions

[covert lion]

I will start with Pascal triangle

[pliant bobcat]

ok

[chrome hinge]

its just 1s outside and then you add the numbers above

closest 2

[covert lion]

1
1. 1
1. 2. 1
1. 3. 3. 1

As u still move forward

[pliant bobcat]

hmm

ok

[covert lion]

Thanks

[sweet shard]

@trail trench are you done with this channeL?

[chrome hinge]

yes

[covert lion]

The main thing guiding Pascal triangle is that,1 stays out side for both sides

And also to get 1. 3. 3. 1
1+2= 3
2+1= 3

[pliant bobcat]

and which problems involve pascal triangle?

[chrome hinge]

no idea never used

[covert lion]

Also for 1. 4. 6. 4. 1
1+3= 4
3+3= 6
3+1 = 4

[covert lion]

When it comes to binomials

[pliant bobcat]

ooh

what about second degree equations

can u help me with those?

[covert lion]

Yes

It is when the variable x is squared
E.g x² + 2x+6

Which is also the quadratic equation

[topaz sinew]

@trail trench Has your question been resolved?

[pliant bobcat]

ok

thanks

but can u explain a bith more? @covert lion

[topaz sinew]

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[floral rampart]

How do I show that a sphere cannot have a nonzero vector field?

[floral rampart]

I tried taking a point P on the manifold and cutting a disc out of it and looking at the complementary disc

but i think im missing something

[ashen eagle]

Yes, I think that's one of the most famous proofs

I'm sure it's explained in the Internet

Maybe if you find a source we all can try understanding it together

[floral rampart]

i see this which is trying to take the same approach as me

[ashen eagle]

Maybe we have to look at the actual Lefschetz's proof

[floral rampart]

https://www2.math.upenn.edu/~pjmcgrat/research/hairy-ball.pdf

something like this

i cant find the actual proof online

i do not

[ashen eagle]

Which part

[floral rampart]

most of it, the proof is far beyond what i know. i only really know about it since my teacher mentioned it and im looking into it

[ashen eagle]

Oh

[floral rampart]

mostly this part is confusing

[ashen eagle]

Have you ever studied homotopy?

[floral rampart]

i have not

well sorta i have not

like not formally

[ashen eagle]

okay

Its like a continuous transformation of a function to another function by a parameter continuously

That mantains a lot of topological properties

Since curves are functions one can apply homotopies to them

Well, but turning back to the photo

Take s in (-1,1) the plane given by <q,p>=s is like cuting the sphere with different angles

q1x+q2y+q3z=s

[floral rampart]

oh i see

[ashen eagle]

when s=0 the intersection is a great circle

[floral rampart]

yea, where is n coming from though?

[ashen eagle]

(it dives the sphere in two semispheres)

Because the curves have a rotation number

The number of rounds they do

[floral rampart]

so when s = 0, all thats being said with the n = -n = 0 is that we have two hemispheres, and if its approaching one, it barely cuts?

[ashen eagle]

with respect to the orientation

Well that part i don't perfectly understand

The orientation in one side of the sphere is opposite to the other

because of the election of the orientation in the sphere

It's like the right-hand rule

[floral rampart]

ah yea

[ashen eagle]

The normal vector in the opposite semispher is opposite

so the relative rotation of the curve is oppsite

I think it is something like that

I should read the proof with pencil and paper but I don't have here now

[floral rampart]

i think it mostly makes sense

[ashen eagle]

You have the same great circle but with two diffeerent parametrizations

which have opposite orientation (direction of rotation with respect to fixed orientation of the basis)

so in one hand the rotation number is n and on the other hand it is -n

but bc of homotopy the rotation number must be equal n=-n because one can homotopically pass from one parametrization to the other

n=-n implies n=0

[floral rampart]

ah yea

and i see the approach -1 and 1

when s approaches 1

so that leads to a range of n that cant happen

so we have an issue

which means there needs to be a place with a zero vector?

[ashen eagle]

yes

because you supposed there's no zero

and that gaves you n=0 and n=-1 or n=1 at the same time

[floral rampart]

mhm, thanks! this is so much more fun than functions class is, i cant wait to do more of this

[floral rampart]

yea

[ashen eagle]

Sorry

The <p,q>=s I don't understand well because I don't have a piece of paper now but I hope I have helped you understand more the proof

maybe not perfectly since neither I do

[floral rampart]

i think they want p to be the positive normal

which is why they have it like that

[ashen eagle]

Yes i think so

[floral rampart]

alright that makes sense, ill try to work through it with pen and paper now. thank so much!

.close

[topaz sinew]

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[tulip coyote]

Can I get some help with this pls, I am really confused

[neon iron]

similar shapes have the same angles but their sides are increased or decreased according to a coefficient

[topaz sinew]

@tulip coyote Has your question been resolved?

[tulip coyote]

what would that be

[neon iron]

you can determine the ratio by dividing the sides that are in front of the same angles

[tulip coyote]

15.3/10.2?

1.5?

[neon iron]

yeah

[tulip coyote]

So what would I do with 1.5

[neon iron]

you can then multiply the 13 with it

and you find X

[tulip coyote]

13.6?

[neon iron]

ye

[tulip coyote]

20.4

x = 20.4

[neon iron]

yep

[tulip coyote]

y° = 46.5?

@neon iron

[neon iron]

angles remain the same

[tulip coyote]

sorry what do u mean?

[neon iron]

the angles remain the same

so the y = 31

[tulip coyote]

How come they remain the same

[neon iron]

it is what it is?

[tulip coyote]

oh okay haha

Ty

[neon iron]

and how do i get it

[topaz sinew]

@tulip coyote Has your question been resolved?

[topaz sinew]

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[slim folio]

I have a question. Is it 15 days from now to June 28 at 5pm or is little over or?

[worthy storm]

depends on the time zone

[slim folio]

I’m in USA in EST

[worthy storm]

so it's 11:08pm there yes?

[sweet shard]

Type ,w 15 days from now

[worthy storm]

nice, wolfram knows everything 😀

[slim folio]

Yea

15 days from now is 11:09pm on June 28th and I wanted 5pm on 28 so I think it would be 14 days and like 6 hours or so

So I guess I have to do is do the 29th at 5pm to have 15 days (little over it but it will work)

Ok I got the time now. So I’ll choose June 29 at 10pm and it will be 15 days 22 hours. Ok thanks for the help

[topaz sinew]

@slim folio Has your question been resolved?

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[orchid crow]

A social studies class has 20 girls and 15 boys in it. If 3 girls and 2 boys are selected to form a five-member team to participate in a competition, how many possible teams could be created?

[orchid crow]

So what I did was

20 nCr 3 = 1140
15 nCr 2 = 105

1140*105 = 119700

is that correct?

[mental remnant]

Wouldn’t u add them?

[orchid crow]

Oh wait that would make sense

yeah

Yeah that makes a lot of sense

.close

[topaz sinew]

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[orchid crow]

6. Our three administrators want to take a group picture with twelve math teachers. If they all line up on a straight line and the administrators must stand next to one another, how many different arrangements are possible?

[orchid crow]

Would this be 3! * 12!

[neon iron]

yes

[orchid crow]

Thank you so much

[neon iron]

i think

[mental remnant]

@orchid crow I think it would be 3! x 13!

[orchid crow]

13! or 12!

[mental remnant]

13!

I belive cause the group of admin becomes one claim

Clump

In the 12 teachers

[orchid crow]

Yes that does seem

correct

[mental remnant]

So 13 groups

[orchid crow]

That does make sense

Okay thank you

.close

[topaz sinew]

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[neat flume]

i dont understand how this works

[neat flume]

nvm

im dumb

.close

[topaz sinew]

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[hoary acorn]

can anyone help with these 2 past paper question pleaseeee

[winged roost]

yes

do you know what trapezium rule is

[hoary acorn]

yes but struggle .. a lot

[winged roost]

can you quote it for me please

[hoary acorn]

it’s a method of estimating integrals . it’s usually done by splitting the area under a curve into trapezium shapes .

[winged roost]

ok can you tell me the width of your stripes

[hoary acorn]

that’s what i’m not sure of

[winged roost]

I suggest you try to find that out

[hoary acorn]

great help buddy 🙂

[winged roost]

hint: you are given h

and 4 seconds

you can determine it from that

what is h in this case

can you tell me what it represent

[topaz sinew]

@hoary acorn Has your question been resolved?

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[versed moat]

How to define matrics of real number?

[versed moat]

$A\in \mathbb{R}^{M,N}$

or

$A\in \mathbb{R}^{M \times N}$

which one is correct?

[oak sequoia]

Matrices containing real numbers?

[versed moat]

yes

[thorny flame]

BeatriceBernardo

[tulip light]

both should be fine as long as you clarify what it is

[thorny flame]

BeatriceBernardo

[versed moat]

er... which one don't need clarification haha?

[tulip light]

I'd seen this one before

[versed moat]

huh, where is it from?

[tulip light]

https://math.stackexchange.com/questions/412200/what-is-the-notation-for-the-set-of-all-m-times-n-matrices just googling

there seems to be multiple but that's the one I'd seen before

[versed moat]

I see, thanks!

[tulip light]

as with every single notation

[versed moat]

can't wait until Chineese characters become part of the standard notations lol

thanks!

[topaz sinew]

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[silver valve]

dy/dx is an operator or fraction?

[silver valve]

can you take dx to the other side?

of an equation

[neon venture]

yea you can, physicist love to do that lol

[knotty ledge]

it is an operator, in one dimensions it acts like a fraction

[silver valve]

yeah yeah in the context of phy

[neon venture]

d/dx is an operator indeed

[silver valve]

how does that work?

if it is an operator, how can you take dx to the other side?

and integrate over different bounds?

[knotty ledge]

its basically notational shorthand for what is really going on behind the scenes

[silver valve]

what is?

the limit thing?

[knotty ledge]

moving around dy/dx like a fraction

[silver valve]

whats going on behind the scenes?

in this case

omega is a constant

[neon venture]

dx is an infinitesimal value, thats all i can say

dv too

[silver valve]

ok?

[neon venture]

so i think thats why you can move them

[silver valve]

i see -

but what about the integration?

why would that retain the equality?

[knotty ledge]

really youre integrating both sides wrt x from the start

the dx on the LHS "cancels" with the 1/dx

[neon iron]

its a simple trick used by physicists and linear DEQs

[silver valve]

wont another dv and dx come into picture when you apply integral?

[neon iron]

but its quite powerful

[silver valve]

what is the trick?

[neon iron]

to treat dv / dx like a fraction

[silver valve]

how do ik what the start is?

[silver valve]

so dv and dx are just variables?

to integrate (v)(dv) i do int( (v dv) dv)?

[neon iron]

no you just integrate

when you get vdv

[silver valve]

what does that mean?

to just integrate?

nvm

.close

[topaz sinew]

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[topaz sinew]

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@inner stump Has your question been resolved?

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[lapis lava]

Is 1.999... different from 1.999...99?

[topaz sinew]

Please don't occupy multiple help channels.

[inner oracle]

Ye

[dire laurel]

Yes.

[restive inlet]

the latter implies a terminating decimal with an unspecified amount of 9s

[lapis lava]

How are they different?

[worthy storm]

how many digits are represented by the ... in the second one?

[lapis lava]

Aren't both with infinite 9?

Is there notation to specify #of 9s?

[worthy storm]

no, there is no terminating fractional part with infinitely many digits...

[lapis lava]

Like (23) 1.999...99

Then you put 23 9s in the ...?

[worthy storm]

not sure if there is any standard notation for that, you could always define your own if needed. one way that would be recognized by anyone is $1 + \sum_{n=1}^{28}\frac{9}{10^n}$

[thorny flame]

OurBelovedBungo

[worthy storm]

where 28 is the 5 displayed 9's and the 23 represented by the ...

[lapis lava]

That evaluates to something different though

[worthy storm]

what does it evaluate to

[lapis lava]

That's 1.9... with 27 9s

[worthy storm]

28 9s, no?

[lapis lava]

It's not 1.999...99

[worthy storm]

it's 1.999...99 assuming there are 28 9's

[lapis lava]

With finite numbers they are the same

But with infinite then they are different

[worthy storm]

there is no number of the form 1.999...99 that has infinitely many digits and terminates

those two requirements are conflicting

if there are infinitely many digits then by definition of "infinite" there is no "last" digit

[lapis lava]

In a previous question I asked someone said this:

saying the error is 0.00...01 means you're truncating the number at 1.999...99, which is different than 1.999...

I didn't understand the meaning of it

[worthy storm]

both 0.00...01 and 1.999...99 have meaning only if ... represents finitely many digits

so presumably in that context, by ... in those two numbers they meant some unspecified but finite number of digits

[lapis lava]

@woeful drift

[worthy storm]

whereas for 1.999... they meant the non-terminating number with infinitely many 9's

which btw equals 2

[lapis lava]

Can you do other stuff with it if it didn't terminate?

[worthy storm]

like what?

[lapis lava]

Like 1.999...888...

[worthy storm]

you have to specify what you mean by those ...'s

[lapis lava]

See no termination

Infinite

[worthy storm]

the first ... in particular cannot represent infinitely many digits

the second ... could mean infinitely many 8's but I wouldn't automatically assume that unless the author said so

[lapis lava]

Ohhh

Interesting

Is there another notation that allows it?

[worthy storm]

allows which?

an 888 to follow some infinite number of unspecified digits?

[lapis lava]

Like .777...888... where infinite 7 and infinite 8

[worthy storm]

no, there's no "after" when it comes to an infinite number

(different cardinalities of infinity aside, which doesn't apply here)

[lapis lava]

What about if I flip it the other way and do infinite left string digits in p-adic numbers?

777...888... .0

[worthy storm]

as soon as you put that ... after the .777 and you mean it to represent infinitely many 7's, you can't put other stuff after that

i don't know enough about p-adic numbers to comment on that, but if we are talking about real numbers then there's no real number of the form 777...888...0 if the dots represent infinitely many digits

there's not even a 888...0 if there are infinitely many digits represented by the dots

[lapis lava]

Is there infinity in real numbers?

I don't think there is

Not sure

[worthy storm]

no, there is a notion of the extended real number system which allows +infinity and -infinity as "endpoints" of the real line

but that's not really relevant here

[hot furnace]

real numbers can have infinitely many decimal points if that's what you mean?

[worthy storm]

there is a notion of infinitely many fractional digits of course

but not of infinitely many digits to the left of the decimal

[lapis lava]

I never seen anyone do 1.777...77 before. Is stuff like that common in math text books?

[hot furnace]

sure

[worthy storm]

you have never seen it because it's not defined if ... is supposed to represent infinitely many digits

[hot furnace]

what if the number is 1.777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777?

[worthy storm]

you can't have a fractional part that has infinitely many digits and terminates

[hot furnace]

then 1.777...77 would be a compact form for it

basically we know there are a lot of 7's inbetween the decimal and the last digit

[lapis lava]

Do they normally use ... or can they use .. or .?

So like 1.77..77

Or 1.77.7

[hot furnace]

ive never seen anything like that

using just one would be really confusing

[lapis lava]

So it's always 1.7...7

[hot furnace]

... is standard for "lots of stuff i'm not writing here"

[lapis lava]

Ok 👍

Makes sense

@worthy storm @hot furnace thanks

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[short spoke]

Bamboo Plants Grow 91 centimeters per day what is the approximate growth of the plant, in inches per hour ?

[topaz sinew]

Please don't occupy multiple help channels.

[chrome hinge]

how many hours are in a day

[short spoke]

It don't really know it doesn't tell me how many hours it wants me to know the approximate growth per hour

[chrome hinge]

what

[short spoke]

It grows 91 centimeters per day I cant Figure out the approximate growth per hour is

[chrome hinge]

well you have to convert 91cm to inches

[short spoke]

358.27 Inches right

[chrome hinge]

no idea

so you have how many hours in a day?

[short spoke]

24

and per hour must be 1 hour right

[chrome hinge]

no shit

[short spoke]

Im stupid ok

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[worldly temple]

I nedd to factor this

I tried

But im not sure

If its right

[topaz sinew]

@worldly temple Has your question been resolved?

[worldly temple]

NOOOOOO

it hasnt

<@&286206848099549185>

.close

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[worldly temple]

If you want, help me,

[empty sail]

That question makes no sense

[worldly temple]

Which one

[empty sail]

The one you provided

[worldly temple]

Ik

I hate my life sometimes

Anyways

I have no clue how to do this

[empty sail]

Apply the concept of the discriminant, I believe is what you need to do

[worldly temple]

Ok

If i knew what that was

[empty sail]

Then look it up

I'm not Google

[worldly temple]

Discriminate prolly sperate

Do you get paid for this

?

[empty sail]

Nope

[worldly temple]

Thats sad ngl

Helping random losers solve shitty problems for nothing

[empty sail]

This server is all volunteer based

[worldly temple]

You seem like a post sec student

[empty sail]

What does that have to do with anything?

[worldly temple]

Life

Here you go

Not sure what i did

[empty sail]

That's valid, if your teacher wanted an equation that had no real roots

[worldly temple]

What did i do?

Like what did i use

[empty sail]

You used math

[worldly temple]

Acc

Like descrimative

Or like

[sturdy oracle]

Take your parent function and translate it real fuckin high

there

[worldly temple]

Product and sum

[sturdy oracle]

and show that its discriminant is less than 0

[worldly temple]

What

[empty sail]

You mean discriminant ?

[worldly temple]

Yes

[sturdy oracle]

take, for example, $x^2+278929200892009022092902$

[thorny flame]

Umbraleviathan

[sturdy oracle]

that's never gonna touch the x axis

[worldly temple]

Look man i have 3 exams and work tmrw and just tryna pass

[sturdy oracle]

you can do that

then show that its discriminant is less than 0

[worldly temple]

Whats the discrimate

Discriminate

[sturdy oracle]

$$b^2-4ac$$

[thorny flame]

Umbraleviathan

[worldly temple]

O ya

Taht

[empty sail]

Okay, still don't understand why you need to provide this, because everyone has life things, you're not the only one

[worldly temple]

Ik

[empty sail]

Could have Googled that, and would have given you the same exact thing

[worldly temple]

Im just lost hope

[worldly temple]

Prolly not

Ok

[sturdy oracle]

it will

[worldly temple]

So i gotta make

[worldly temple]

4ac = 0

[empty sail]

Proof

[sturdy oracle]

no

[empty sail]

Google is useful

[sturdy oracle]

make $$b^2-4ac < 0$$

But then like

[thorny flame]

Umbraleviathan

[sturdy oracle]

Dont even need to think about a, b and c

you remember your parent function for a quadratic?

[past kayak]

Gonna be honest, of all the things google will pull from "discriminate," I don't think the discriminant is one of them. The power of a single letter...

[worldly temple]

Yes?

[sturdy oracle]

remember how it only touches the x axis at (0, 0), and that's its minimum?

[worldly temple]

Yes

[sturdy oracle]

Simply just move that function away from the x axis

by moving it up

[worldly temple]

Do make it postive

[sturdy oracle]

So you can literally have $x^2+298769087690707689289082818828$ and itll be fine'

yes positive

[worldly temple]

Instead of neagtive

[thorny flame]

Umbraleviathan

[worldly temple]

So like

[empty sail]

But it didn't as I proved

[worldly temple]

X^2 + 377382919383783

And thts rught

[past kayak]

Because you googled discriminant, not discriminate, lol

[sturdy oracle]

yeah

[worldly temple]

Wow

[sturdy oracle]

or even just x^2 + 1

[empty sail]

Because discriminant is the proper spelling

[worldly temple]

U ppl are smart

[empty sail]

Not discriminate

[sturdy oracle]

you just need to show that the discriminant is less than 0

[sturdy oracle]

1950s moment

[worldly temple]

Im acc retarted

In have a 57 in math

[sturdy oracle]

dont use that word

[past kayak]

Ah, but if someone doesn't recall the spelling of discriminant, like the op, then googling may not be helpful, especially if how you think it's spelled turns out to be another actual word

[sturdy oracle]

So jadn just use $x^2+1$. What's its discriminant?

[worldly temple]

👍🏾

[thorny flame]

Umbraleviathan

[worldly temple]

Anything postive

[sturdy oracle]

No. Solve for it

and also I literally said this before

b^2 - 4ac < 0

[worldly temple]

X^2+100000030292929292929192992929292

Right?

[sturdy oracle]

it has to be less than 0 for the quadratic to have no real zeroes

[sturdy oracle]

just solve this

make your life easier

[worldly temple]

1

[empty sail]

Then be more specific, more specific the better and Google will figure it out

[sturdy oracle]

buddy use the formula $b^2-4ac$

[thorny flame]

Umbraleviathan

[past kayak]

Ah yeah I didn't think of that lol

[sturdy oracle]

Im asking for its discriminant and I feel like youre not even using the formula I gave you

[worldly temple]

4ac

wait

[worldly temple]

its anything over 0

[sturdy oracle]

no

[worldly temple]

wtf

[sturdy oracle]

for the quadratic to have no zeroes, the discriminant must be less than 0. That is what b^2-4ac means

[worldly temple]

so any neagtive

[sturdy oracle]

okay i think youre confused

take the function $x^2+1$

[thorny flame]

Umbraleviathan

[worldly temple]

ye

[sturdy oracle]

I want you to find the discriminant of THAT function

the numerical value of it

[worldly temple]

1x^2

[empty sail]

Aka, identify a, b, c and plug it into

[worldly temple]

o

[empty sail]

And then simplify

[sturdy oracle]

ahsfosfjlfjlfjlaskjflkfaasfasf

[worldly temple]

a= x^2 b=1 c=0

[empty sail]

No

[worldly temple]

im so confused

[empty sail]

The general form of a quadratic is ax^2 + bx + c

[restive inlet]

a,b,c refer to certain coefficients and constants of your quadratic

[worldly temple]

yea

[worldly temple]

standard form

[restive inlet]

and NOT the terms in the order that is written

[empty sail]

For the function, x^2 + 1, what is a, b, and c?

[worldly temple]

1 would be c

a would be x^2

[empty sail]

No

[worldly temple]

wtf

but it lines up

[empty sail]

a,b,c refer to certain coefficients and constants of your quadratic

As Ramonov stated

[restive inlet]

The general form of a quadratic is ax^2 + bx + c
look carefully at where a is and what it represents

[empty sail]

Is x^2 a coefficient or constant?

[worldly temple]

co

efficiant

[sturdy oracle]

no

[restive inlet]

no

[sturdy oracle]

wait no

[worldly temple]

wtf

[sturdy oracle]

i thought you meant a was a coefficent

[worldly temple]

i said that

[sturdy oracle]

a would be a coeffeient of x^2

[worldly temple]

co............................eficiant

[sturdy oracle]

but x^2 is not a coefficient

[worldly temple]

why

[sturdy oracle]

because x is a variable

[worldly temple]

ts has 2

[sturdy oracle]

its the independant variable

[worldly temple]

i thoiught it was 1

[sturdy oracle]

the power to which x is raised has nothing to do with it being a coefficient or not

a is 1

[empty sail]

Read carefully, and understand
The general form of a quadratic is ax^2 + bx + c
a,b,c refer to certain coefficients and constants of your quadratic
For the example, x^2+1, what are a, b, and c?

[worldly temple]

x^2 = a cause ax^2 and 1 = c

[empty sail]

No

[worldly temple]

isnt that hw tis works

[empty sail]

$a \neq x^2$

[thorny flame]

dldh06

[worldly temple]

why

cause

ax^2

[empty sail]

a,b,c refer to certain coefficients and constants of your quadratic

[worldly temple]

is in the quad formual

[empty sail]

x^2 is not a coefficient or constant

[worldly temple]

its dependeant

on 2

[empty sail]

Do you know what a coefficient or constant is?

[worldly temple]

yes

[empty sail]

What is it?

[worldly temple]

number

before varibale

[empty sail]

So is there a number before x^2?

[worldly temple]

1

x=1

[empty sail]

So then what is a?

[worldly temple]

coeff

[empty sail]

The value for a

[worldly temple]

a is 1

^2

[empty sail]

Where is the ^2 coming from?

[worldly temple]

x^2

[empty sail]

Is ^2 a coefficient or constant?

What is the coefficient or constant that is with x^2?

That coefficient or constant is a

[worldly temple]

constant

[empty sail]

The value for a

[worldly temple]

is 1

cause

1 time 1 is

1

[empty sail]

Why are you doing 1 times 1?

[worldly temple]

2****

^2

sq

mean

times its self

[empty sail]

Seriously, are you even reading what I am telling you?

[worldly temple]

YES

[empty sail]

Is ^2 a coefficient or constant?
What is the coefficient or constant that is with x^2?
That coefficient or constant is a

[worldly temple]

i swaer

[empty sail]

What is a?

[worldly temple]

1

[empty sail]

Why are you doing ^2?

[worldly temple]

cause its part of the eq

[empty sail]

There is zero purpose for that

[worldly temple]

sorry

[empty sail]

I stated that the general form of a quadratic is ax^2 + bx + c

You were given x^2 + 1

[worldly temple]

ya

[empty sail]

Then you were told to find a, b, and c

[worldly temple]

ya

[empty sail]

So what is a, b, and c?

[worldly temple]

a is 1

[empty sail]

Are you continuing?

[worldly temple]

yea

im thinking

b is 1

c is 1

right?

[empty sail]

No

[worldly temple]

b is 2

[empty sail]

No

[worldly temple]

WTF

b is 3

[empty sail]

Where are you even getting these numbers from?

[empty sail]

Still no

[worldly temple]

wait tell me the right answer

[empty sail]

ax^2 + bx + c
x^2 + 1

[worldly temple]

ill connect them

[empty sail]

No

[worldly temple]

there no b

wait

(x)(x)+1

a,b,c =1

[empty sail]

No

[past kayak]

[empty sail]

My suggestion, please review everything

[worldly temple]

if x is a variable

[past kayak]

Consider that x² + 1 = x² + 0x + 1

[worldly temple]

o

so

a= 1

b= 0

c=1

[empty sail]

Wasn't trying to spoonfeed this, OP needed to understand what was wrong

[past kayak]

I know, I'm an advocate of trying to get op to find the answer on their own as much as possible, but I feel as though there's a point where there's an impasse and progress wont be made unless we give a slight nudge in the right direction.

[worldly temple]

do you think im dumb?

tell me the answer

trust me

[empty sail]

If you want my honest opinion, yes, because if you could not identify a, b, and c given x^2 + 1 and the general form of ax^2 + bx + c, where all you needed to do was line up the variables and determine what the coefficients are, after lining it up. It means you need to study basic equation forms again

[worldly temple]

which gard is this from?

grade

[worldly temple]

Just tell me the answer

was a= 1 b=x =1

TELLLL MEEE THE ANSWER

[empty sail]

Doesn't even make sense

[empty sail]

No

[worldly temple]

yes it does

[empty sail]

What does a= 1 b=x =1 mean?

[worldly temple]

like

a=1

cause if x

[empty sail]

I think middle school so about 12 - 14 year old material

[worldly temple]

oml

im in grade 10

geez im truly stuipd

[empty sail]

https://www.khanacademy.org/math/algebra-home/alg-quadratics/alg-solving-quadratics-using-the-quadratic-formula/v/quadratic-equations-in-standard-form

That will help you identity a, b, c

[worldly temple]

ik where AB C

is

im not retarted

a= x^2

b=x

and c= number

[empty sail]

Then why are you having trouble identifying a, b, and c for the expression x^2 + 1?

[worldly temple]

cause there is not three damn numbers

there two

[empty sail]

It's not any different when there's 3 number and two. One term is just not there

[worldly temple]

yes it is

[empty sail]

No it's not

[worldly temple]

so the b = 0

[empty sail]

Concept is still the same

[worldly temple]

c=1

a= 1

RIGHT

[empty sail]

Is it?

[worldly temple]

I DONT KNOW

i believe you want to be some type of tutor or teacher when you grow up

with the amount of patience u have

but understand one thing\

not everyone's brains work the same

for example

giving me the answer

i will easily find out what i did wrong

how i should get there

[empty sail]

By learning

Relearn everything

[worldly temple]

OML

tell me the answer

please

[empty sail]

Anyways, good bye

[worldly temple]

No

[empty sail]

Still no

[worldly temple]

no

plz

answer

[empty sail]

Someone can if they feel like it but I'm not

[worldly temple]

no

[empty sail]

I'm done

Bye

[worldly temple]

no

wait

[topaz sinew]

@worldly temple Has your question been resolved?

[topaz sinew]

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[warm crest]

<@&286206848099549185>

[topaz sinew]

@warm crest Has your question been resolved?

[topaz sinew]

@warm crest Has your question been resolved?

Channel closed

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[rare isle]

given a start vector and a target vector, as well as 2 axis vectors i,j. the start vector rotates about axis i, then about axis j, such that it moves onto the target vector. what are the angles of rotation?

[rare isle]

i've been thinking about this problem for a while, and heres one of the solutions i have found:

assume all vectors are unit length. consider the 2 circles swept by the start and target vector when rotated about the axes, if they do not intersect, there are no solutions. if they do intersect then the intersection points mark valid stopping points of the starting vector around axis x, before rotating again around axis y. these points can be found by intersecting 2 planes with the unit sphere, then the angles may be measured to give the final solutions.

[warm sandal]

If Y=-2x+3, find the covariance of (X, Y)

[rare isle]

i dont know what that is. explain?

ok youre just in the wrong channel

read #❓how-to-get-help @warm sandal

[rare isle]

while this solution is elegant in theory, not in practice. it takes way too much code to do this, and i feel like the answer to my problem should be simple.

what i've tried: algebra with rotation matrices, quaternions.

they seemed promising, but the issue is that my problem seems quadratic in nature due to the intersecting circles

i would be delighted to find if quaternions can be used to find intersection points of 2 circles on a sphere, but i doubt it is the case

<@&286206848099549185>

[topaz sinew]

@rare isle Has your question been resolved?

[topaz sinew]

@rare isle Has your question been resolved?

[topaz sinew]

@rare isle Has your question been resolved?

[topaz sinew]

@rare isle Has your question been resolved?

[topaz sinew]

@rare isle Has your question been resolved?

[sweet shard]

.close

[topaz sinew]

Channel closed

Closed by @sweet shard

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[topaz sinew]

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Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[topaz sinew]

Please don't occupy multiple help channels.

[dusty perch]

before

and then after looks like

but i still apparently got something wrong

can someone please help

[ashen latch]

polynomials are infinitely differentiable

so f'' at D exists

[dusty perch]

but how do i know if its concave up or down

its just a increasing linear line

[ashen latch]

lets say that section was something like f(x)=2x

then what would the second derivative be

[dusty perch]

well the first derivative would be 2

second wouldnt exist

[ashen latch]

derivative of a constant is zero

[dusty perch]

oooooooooooohhhhhhhhhhh

omg wait that makes so much sense

ahhh tysm!!

@ashen latch its apparently still not right

i understood what u said so far and i put that in

but something is wrong still apparently

open to advice or help from anyone!! ^^

[ashen latch]

E doesn't seem like an inflection point mb

f'(x) is still increasing before E and after E

since f'(x) is increasing f''(x) should be positive

[dusty perch]

kk makes sense

ty

!!

.close

[topaz sinew]

Channel closed

Closed by @dusty perch

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[topaz sinew]

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[neon iron]

hello i wanted to know what is the difference saying that Polynomial of degree n is not a vector space
but when its a subspace it is a vector space with respect to V

[odd pagoda]

of degree exactly n or degree at most n

[drifting swift]

this is word salad.

[neon iron]

exactly N

lets say 7

[odd pagoda]

the 0 polynomial does not have degree 7

so it is not in your space

[neon iron]

let me link the 2 videos

https://www.youtube.com/watch?v=OK3Wn_47QPY&list=PLW3u28VuDAHJNrf3JCgT0GG_rjFVz0-j9&index=21 examples of vector spaces is F [x]
But then he writes a remark at 38:06 for polynomials of degree n that is not a vector space

[drifting swift]

yes, the set of polynomials of degree exactly n is not a vector space, and denascite gave one reason above: the zero polynomial is not in it

[neon iron]

but here at https://www.youtube.com/watch?v=RG3DVZ6pQGc&list=PLW3u28VuDAHJNrf3JCgT0GG_rjFVz0-j9&index=22 3:50 he says its a subspace of V of F [x] And the subspace itself is vector space with respect to V but the previous video he said its not

[odd pagoda]

difference between =n and <= n

[neon iron]

i think im confusing something

[drifting swift]

yeah there is a big difference between 'polynomials of degree EXACTLY n' vs. 'polynomials of degree AT MOST n'

[neon iron]

oh i see so the 0 polynomial is IN the subspace of at most 7

but its not IN 7

[drifting swift]

it's not in the set of all polynomials of degree exactly 7, yes.

[neon iron]

thank you guys ❤️

.close

[topaz sinew]

Channel closed

Closed by @tough osprey

Use .reopen if this was a mistake.

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Remember:
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lunar pond]

guys

i dont understand how to solve it

[winged roost]

this is an inequality

you want to find the range of values of x for which this is satisfied

[lunar pond]

yes

but idk how to solve it

[winged roost]

do you know how to add fractions?

[lunar pond]

yes

i did

but it made stuff wors

e

[winged roost]

show what you have so far

[lunar pond]

okay

1-X/X*X + 3X + 2 <= 0

X*X is X power 2

[winged roost]

how did you start

$\frac{2(x+2) - 3(x+1)}{(x+1)(x+2)}$

[thorny flame]

IntelligentCake

[winged roost]

this what you did?

[lunar pond]

made same denominator

[winged roost]

did you do this first?