help-36

[tardy goblet]

Thats the issue, I don't see a next step, and cubed quadratic seems to be out of course parameters

[real needle]

Yea

[tardy goblet]

Is there some correlation between the long equation at the end and h of x?

The long one seems to be h(x) +2

[real needle]

There seems to be

That would mean (h^-1(2)) = x

[tardy goblet]

Yes

[final saddle]

@tardy goblet Has your question been resolved?

[real needle]

If you factor the long equation then maybe you get a quartic equation or something but idk if that's helpful

[tardy goblet]

<@&286206848099549185> anyone know how i could do this?

[outer current]

@tardy goblet I don't think you screenshot the whole problem. but shouldn't you just find the inverse function of that h(x) given, and find the values for these points? it seems unrelated to previous context

[tardy goblet]

That's the entire question 10, no extra stuff. We're stuck at trying to find the inverse, can't seem to do it

[outer current]

woah haha what is that

[tardy goblet]

Bruh moment

There's gotta be some trick to this question, no way this is so difficult

[outer current]

why not just do it that way?

[tardy goblet]

How is this hinverse tho, isn't this just h

Also i think its gonna be 1-y^3

[outer current]

oh yeah my b

there

you are right, I messed up

I guess?

basically I'm starting to doubt the whole maneuver I did here, BUT

[tardy goblet]

Ohh

[outer current]

something like this?

now question if this is hard to solve

yeah seems to have a reasonable solution

[tardy goblet]

This is exceedingly difficult

Final answer's 4 btw

[outer current]

yeaah there has to be a trick somewhere here this is too sus

xD

wait I almost had it but it flew away

[real needle]

For the long equation?

[final saddle]

@tardy goblet Has your question been resolved?

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[stark needle]

im stuck how do i find theta?

[stark needle]

<@&286206848099549185>

.close

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[tiny forge]

topic: permutation and combination

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@tiny forge Has your question been resolved?

[tiny forge]

<@&286206848099549185> am getting 96
idk what's answer

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@tiny forge Has your question been resolved?

[dense cargo]

Is it mentioned that in a dictionary ( as per ncert language)?

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[hushed sonnet]

I don't quite get this question so if someone could help that would be awesome. Would f, g ∈ M in this case? And the bounds be from -1 to 1? Am I then correct in thinking this reduces to the integral of f(x)g(x) from -1 to 1 and f and g only being orthogonal if f(x)g(x) = x^k with k odd since when then get an odd function?

[hushed sonnet]

Or should I be looking at two maps being orthogonal and am I headed completely in the wrong direction lol

[desert mantle]

remember gram schmidt

you have the linearly independent set ${1, x, x^2, x^3, x^4}$ and an inner product $\langle f, g\rangle = \int_{-1}^1 f(x) g(x) dx$

[soft zealot]

Denascite

[desert mantle]

from there apply gram schmidt. you won't just get the odd monomials, that would be too easy

[hushed sonnet]

Right I didn't quite get the question tbh

We have the inner product like you gave yes

But then what's with the set M?

My English fails me at times

[desert mantle]

do you know gram schmidt

[hushed sonnet]

Doesn't ring a bell sadly no

[desert mantle]

does googling it ring a bell?

[hushed sonnet]

Oh yes it seems familiar indeed

[jolly widget]

anyone have any idea

[hushed sonnet]

So what I really have is how I define the inner product here, which is the integral right?

[desert mantle]

read #❓how-to-get-help and get your own channel

[hushed sonnet]

And I want to obtain the orthogonal set of M?

[desert mantle]

an orthogonal set which spans the same subspace of M, but yes

[hushed sonnet]

Awesome could you also help me out with the calculation perhaps

[desert mantle]

no sorry don't have the time for that

[hushed sonnet]

That's fine :)

.close

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[barren olive]

Yo

[barren olive]

Did I do the 2sin(2theta)+1=0 correctly

4th problem on the page

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@barren olive Has your question been resolved?

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@barren olive Has your question been resolved?

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[grim fox]

.reopen

[fathom venture]

I'm having some weird errors in maple. It worked perfectly fine, before pressing "Execute the entire worksheet".

[fathom venture]

lmao. After closing and pressing "Execute the entire worksheet" it works

.close

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[odd rivet]

Why does the geometric series not converge for x equals one

[grand bronze]

1+1+1+1+1+1+1+....=?

[odd rivet]

Oh

Ofc

.Close

.close

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[distant wraith]

Had quick linear algebra theory question

[distant wraith]

If let’s my prof said this is true

Since the denominator value is lambda and the coefficient bfr the identity matrix is 1 therefore it’s just K=Lambda

If we were to say 2 * identity matrix - 1/4 * A would the lambda value be 2*4=8=lambda?

Assuming that the determinant of A is 0, not invertible.

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[tranquil pine]

pls help

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[shut ether]

help

[shut ether]

<@&286206848099549185> how do i find x or y

[carmine cargo]

only ping helpers after 15min

[shut ether]

<@&286206848099549185> how do i find x or y

<@&286206848099549185> how do i find y

[grim badger]

Don't abuse the helper ping, you used that 3 times in 25 mins. Ping only once, which you did, and wait patiently for help

[shut ether]

no

[grim badger]

Why no? What's the rush?

[shut ether]

its due in 10 minute

[grim badger]

And that's not really our problem that you waited last minute to do your hw

[shut ether]

no i been stuck for a rlly long time

[grim badger]

Then wait patiently for help and don't abuse the helper ping

[shut ether]

<@&286206848099549185>

[grim badger]

Really, stop abusing the ping

[shut ether]

can you help me

[grim badger]

No

[shut ether]

<@&286206848099549185>

where helper

[vital crag]

.

[opaque ember]

@shut ether pls only ping helpers once

[shut ether]

can u help me

janpu

[flint mist]

LMAO

[shut ether]

yes

[flint mist]

Bro j got pentuple teamed

[shut ether]

they are rude

[flint mist]

You are rude

[shut ether]

no i need help

[flint mist]

then don't be a dick about asking for help

[shut ether]

<@&286206848099549185>

[grim badger]

.

[shut ether]

what

i just need y then im gone

[flint mist]

Yeah

helpers r done w u

[shut ether]

nahhh

[flint mist]

figure it out bro

[grim badger]

Then don't abuse the helper ping

[shut ether]

i think they got me

<@&286206848099549185>

[grim badger]

Seriously, don't abuse the helper ping

[shut ether]

i wonder where they are

ok i wont

[flint mist]

wow this guys hilarious

im actually guffawing rn

[grim badger]

Not in the mood to help you since you used the ping 7 times in 30 min

[shut ether]

<@&286206848099549185>

[flint mist]

<@&268886789983436800> hey can one of u guys ban this dude

[opaque ember]

@shut ether asked u to not abuse helper pings, come back in 24h

.close

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[fathom stream]

Am I right?

or did I do it wrong

[grim badger]

<@&268886789983436800>

[fathom stream]

ai brah

why did u have to choose dis channel doe

[opaque ember]

ty

[fathom stream]

oh dub

[light wren]

this looks so painful

[fathom stream]

yeh sorry my handwriting sucks

😢

but like the answer they got is diff

its this

r both of these answers ==?

[light wren]

I think your just missing the 01

-1

oh

you keep the x on denom

yeah I think its the same

[fathom stream]

but still

even if they did move the x up right

where is it

in their answer

[light wren]

when they move the x up

its just $\frac{x^a}{x^b}=x^{a-b}$

[soft zealot]

Clarkie

[light wren]

we all got the same

😄

[fathom stream]

ohhhhh

I see

[fathom stream]

oh u solved it too lol

tysm man

Im such an idiot

[light wren]

but you got the right answer

[fathom stream]

yeh but

I wasted over 10 mins

comparin my answer

with theirs

[light wren]

over an exponent rule

[fathom stream]

: ( lol

exam szn

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[polar wing]

how did this get simplified

[polar wing]

after you multiply both by b^2

$(x^2 b^2)/a^2 - b^2$

[soft zealot]

i love to boki

[polar wing]

square root gets you

$xb/a - b$

[soft zealot]

i love to boki

[polar wing]

which is no where near what the picture is showing

[royal gust]

Square root does not break over -

When you take the square root, you actually have:

$±\sqrt{(x^2 b^2)/a^2 - b^2}$

[soft zealot]

Kaynex

[royal gust]

We can factor b² from that, which can come outside of the sqrt if we drop its square

$±b\sqrt{x^2/a^2 - 1}$

[soft zealot]

Kaynex

[royal gust]

And we can do the same with 1/a²

Might be clearer how, if I write it like this:

$±b\sqrt{x^2/a^2 - a²/a²}$

[soft zealot]

Kaynex

[royal gust]

Factoring out that 1/a²:

$±\frac{b}{a}\sqrt{x^2 - a²}$

[soft zealot]

Kaynex

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@polar wing Has your question been resolved?

[polar wing]

ahhh thxxx!

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[onyx basin]

how can I know if the function is decreasing or increasing ?

[final saddle]

Please don't occupy multiple help channels.

[polar wing]

whats the definition of increasing function

[final saddle]

@onyx basin Has your question been resolved?

[restive falcon]

you take the derivative and then plug in a random number, mostly 0 and see if the result is positive if it is then it is increasing if not it is decreasing

[polar wing]

no need for that, just plug in a few numbers

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[onyx basin]

what about this ?

[final saddle]

Please don't occupy multiple help channels.

@onyx basin Has your question been resolved?

[final saddle]

@onyx basin Has your question been resolved?

[vital crag]

@onyx basin you have a channel. stick to one

.close

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[unkempt horizon]

https://media.discordapp.net/attachments/326138737606262786/1050307223206768701/image.png
Please find the domain of the expression

[unkempt horizon]

4y^2-9x^2 not = 0 does not work

[ashen pewter]

Yeah I figured

Because you want the x

[unkempt horizon]

neither does saying first term equal to second term

[ashen pewter]

Set the bottom equal to 0 but then isolate y

4y^2=9x^2

4y=3x

Y=3x/4

[unkempt horizon]

y not 3/4x

[ashen pewter]

X>4/3

[odd rivet]

If you Take the root on both Sides IT would be 2y = 3x

[ashen pewter]

Shit my bad

y=3x/2

x>2/3

Thank you for fact checking me

[unkempt horizon]

nope

[ashen pewter]

Also it seems you can simplify the numerator

[odd rivet]

This is the original question right?

[ruby bramble]

you can

[unkempt horizon]

yes

[ruby bramble]

(3x-2y)^2

oops

[unkempt horizon]

i dont need the simplified equation

i need the domain for the big fraction

no simplifying

[ashen pewter]

(3x-2y)^2/(2y+3x)(2y-3x) ->3x-2y/-(2y+3x)

This makes it easier to solve

[unkempt horizon]

separate answer

its two different answers

[magic gyro]

have you already tried y not 1.5x

[unkempt horizon]

yes

[magic gyro]

have you tried y and x not 0

[unkempt horizon]

yes

[magic gyro]

can you tell me what answers have worked

[unkempt horizon]

none

[magic gyro]

wait but isnt y not -1.5x a solution

[unkempt horizon]

for the simplified one

oh

wait

shit

im fucking stupid

im a fucking retard

.close

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[supple storm]

One message removed from a suspended account.

[trail lance]

Algebras

[topaz yacht]

You could plug them into symbolab and see if it gives you a more direct answer

[supple storm]

One message removed from a suspended account.

[topaz yacht]

isolating for a variable?

[trail lance]

Solving algebraic equations would be my definition

[topaz yacht]

@supple storm https://www.sparknotes.com/math/algebra1/expressionsandequations/section4/

[supple storm]

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[topaz yacht]

Well if you have any questions feel free to ask and I can explain how to solve it

[supple storm]

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[iron needle]

hi bence

i can help u

[supple storm]

One message removed from a suspended account.

[iron needle]

lemme solve it in easy steps

these equations are called linear equation in one variable

you have to isolate the variable

[supple storm]

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One message removed from a suspended account.

[iron needle]

yes

[supple storm]

One message removed from a suspended account.

[iron needle]

cross multiply

and then isolate

it

if we put y=1/-5 the Left hand side equation becomes equal to Right hand side of equation

so in all the equations you have to find the value of variable so that the left hand equation will be equal to right hand equation

[supple storm]

One message removed from a suspended account.

[iron needle]

thats means

[tranquil pine]

math is cool

[iron needle]

you ahve to divide the under arrow equation by -5

both side

[supple storm]

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[iron needle]

do u understood now?

[supple storm]

One message removed from a suspended account.

[iron needle]

ohh thats a relief

for me

now

🙂

[supple storm]

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One message removed from a suspended account.

[iron needle]

no

i must be bad for

expressing

[supple storm]

One message removed from a suspended account.

[iron needle]

learn math from yt

if you dont get it

[supple storm]

One message removed from a suspended account.

[iron needle]

ohh

thats linear equation in one variable

[supple storm]

One message removed from a suspended account.

[iron needle]

ok

just

beleive in your sslef

self

you can do it

its a time

to learn

not blame

[supple storm]

One message removed from a suspended account.

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[iron needle]

and my teacher said that once "losers always give excuses"

dont be a losers

go ahead

solve next one

?

did you

try?

[supple storm]

One message removed from a suspended account.

[iron needle]

ok np

you can dm me

[supple storm]

One message removed from a suspended account.

[final saddle]

@supple storm Has your question been resolved?

[final saddle]

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[spiral epoch]

find the sum of all natural solutions of the inequality 3x - 2-x/3 ≤ 10

so is the solution:

[spiral epoch]

oh wait I wll write, acc pressed enter

[iron needle]

hi

can i help?

[spiral epoch]

yeah u can, I will write the solution and I dont know if its good one. 1sec

3x - 2-x/3 ≤ 10 | * 3
9x - 6 - 3x ≤ 30
6x ≤ 36 |: 6
x ≤ 6

[spiral epoch]

this is the answer good?

[iron needle]

mistake in second step

if are multiplying with 3 then x/3 multiplied by 3 will give x not 3x

[spiral epoch]

9x - 6 - x ≤ 30
8x ≤ 36 |: 8
x ≤ 4,5

[iron needle]

x is less than or equal to 4

why you write 5 there

its means

[spiral epoch]

because 36 / 8 = 9/2

[iron needle]

x belongs to (-infinity,4]

[spiral epoch]

aa

[iron needle]

ohh

[spiral epoch]

so x ≤ 4

[iron needle]

srry

[spiral epoch]

np, so x ≤ 4,5

but now i need to find a sum. I know the answer is 6, but how to get it

[iron needle]

ohh

you have to find

the sum of all natural solutions

[spiral epoch]

if I do 1 + 2 + 3 + 4 = 10

[iron needle]

yes

i am getting same

[spiral epoch]

but in answer lap, answer is 6

if I do 1 + 2 + 3 = 6, haha I think things doesnt work like that

[iron needle]

ohh

you get it right

if you put 4

in equation

you will see

a magic

[spiral epoch]

10 - 4 = 6?? XD

[iron needle]

3x - 2-x/3 ≤ 10

3*4 -2 -4/3<=10

12-2-4/3<=10

10-4/3<=10

26/3<=10

its 7.1

<=10

i dont think

4 have to involve

so 1+2+3 =6

[spiral epoch]

Okey ty

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[fallen reef]

How can I check my work for SAS and SSS triangles? To make sure I got the correct answers?

[iron needle]

you can

check

it by

finding the area

of both traingles

because

two triangles are congruent then they have same area

[fallen reef]

What if I am only solving for one triangle @iron needle ?

Like here, solving for one triangle that is either sss or sas

[iron needle]

well you cant say one traingle to be sss and sas

its comparison between two traingles

[fallen reef]

I don't think I understand

If you're asking to solve a triangle. What are the two triangles being compared?

[amber belfry]

well there is only one trianfle, so you wouldnt use SSS or SAS

since similarity needs to be between two triangles

have you heard of the sine rule and cosine rule?

[fallen reef]

Yes

Sorry I should've been more clear. After using law of sin and cosine to solve for the missing the angles and sides, how can I double check my answers to make sure they are correct?

[amber belfry]

i guess you could use the rule you didnt use at first to see if the answer matches

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[wary bramble]

Hey! I understood from the internet that the number in the () are called vectors, right?

4y in the first one and 2 in the second one correspond to X

-2x and 1 correspond to Y

I would first like to ask if I understood that correctly 🙂

[boreal bluff]

yeah

[wary bramble]

Then, how do I calculate everything together to fix X euler 1? I don't know which mathematical operations are allowed in this case

[wary bramble]

Thank you!

[boreal bluff]

v(x_0) is basically v(2, 1)

so you have v(x_0) = (4, -4)

uh I'm not sure what the ! is doing there but I assume h = 1/2

[wary bramble]

Yes I think so

[boreal bluff]

so multiplying a vector by a number is multiplying each entry by that number

and adding two vectors means adding the entries

$\begin{pmatrix} a \ b \end{pmatrix} + \begin{pmatrix} c \ d \end{pmatrix} = \begin{pmatrix} a + c \ b + d \end{pmatrix}$

uh bot down

from there you can do the rest I guess because I'm not sure what the Euler means in the exponent

[wary bramble]

Thank you very much!

I will try to redo it myself following your instructions to see if I got it

Appreciate it!

[wary bramble]

Here, did you maybe mean x_0 = v(2, 1)?

[boreal bluff]

no

v(x_0) = v(2, 1)

[wary bramble]

Ok got it! Thank you

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[foggy ether]

Im confused with this problem

[foggy ether]

I thibk i have to write it as

[iron needle]

hi

what help u need

[foggy ether]

Whoops wrong image lmao

Pretty sure i write this as

0<5x+3<58*?

i was able to write this as 0<2x-6<108 and then solve it by adding 7 to both sides

Is it the same formula for the top one too?

[iron needle]

dude

its simple

dont complicate

it

lemme hold my beer🍺

[foggy ether]

I do have a problem with overthininking things tbh

Lol okay

[iron needle]

the value of x is 39

[iron needle]

in this ques x=39

2x-6=180-108

2x-6=72

2x=78

[shell mountain]

What's your fascination with giving away answers

[iron needle]

x=39

gamer

he asked the top one

not this

[shell mountain]

Then why bother answering it when they already solved it?

Or wait am I high

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[foggy ether]

.reopen

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✅

[foggy ether]

Wait but whats the top one

The reason im confused with it is cuz idk what to do with the two values

[tranquil pine]

Which one?

[foggy ether]

Top picture

This one

[tranquil pine]

Show

What to find?

[foggy ether]

X

Well i think i qrite it like 0<5x+3<58

[tranquil pine]

@foggy etheryou can use here trigo

But it will be complicated

[foggy ether]

Trigo? Trigonometry?

But this is for geometry

Im in 10th grade

[tranquil pine]

@foggy ether yep it would take 2 pages

[foggy ether]

I dont think ive learned trigonometry yet

[tranquil pine]

Ok so

Um

Is that two sides equal?

[foggy ether]

Its hinge theorm

I think thats what its called

[tranquil pine]

@foggy ether the one you marked a line?

[foggy ether]

Yeah we had to draw a median

[tranquil pine]

@foggy ether yes after proving it congruent you will use here hinge theorem

:))

[foggy ether]

How do we prove its congurence tho?

[tranquil pine]

I would give you a hint 🙃

[foggy ether]

I like to know the steps

[tranquil pine]

Aren't there two triangles?

[foggy ether]

Yeah technically

[tranquil pine]

So if there are two triangles at each other there's a common side

[foggy ether]

Would that ve the middle?

The middle line?

But may i ask, how does the middle line factor into the equation?

[zenith lintel]

Any other info given?

[tranquil pine]

Um without proving congruent you can't use hinge theorem

Btw it's easily being prove no worries

One is common side other is both 90° and

The side is equal that you have marked

So by sas it's congruent

Now use the hinge theorem

[zenith lintel]

Wait do we have ti find the range of x?

[tranquil pine]

By separation of two triangles@foggy ether

It will be easier for you

@zenith lintel ya

[zenith lintel]

X<7

[foggy ether]

Alrigjt

Then do i

Plug it in

0<5(7)+3?

So 0<38?

[tranquil pine]

No it's x= 7

@foggy ether wait see this

[zenith lintel]

Hmm ok

[tranquil pine]

@zenith lintel @foggy ether if you want to know the congruency tell me

[zenith lintel]

Its 53 angle bro and other one is 58

In here angle will be in inequality

So does x

[tranquil pine]

@zenith lintel see the question properly the sides marked with a line are equal

AB and DC are equal

[zenith lintel]

But not the angles

[tranquil pine]

@zenith lintel so by Side angle side it's congruent so the sides are equal

[zenith lintel]

Ita 53 and 58

[tranquil pine]

@zenith lintel the angles is not req. 🗣️

[zenith lintel]

Why

[tranquil pine]

See the perpendicular, common side, and the equal side is making the two triangles congruent so by congruency the base of the first and second triangle are equal

And finally solve it

Finished

[tranquil pine]

. @zenith lintel

[zenith lintel]

Ok

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[foggy ether]

sorry was busy in class

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[willow otter]

Given a gradient, how do you find the direction of steepest ascent

[willow otter]

i don't get what it means when they say that the direction of the gradient is the direction of steepest ascent like how do you find the direction

[iron needle]

can u send question

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[vital crag]

what's cnf

this?
https://en.wikipedia.org/wiki/Conjunctive_normal_form

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[tranquil pine]

(Proof its not a test, but test prep)

f(x)=x^7+2x^6-23x^5-24x^4+144x^3; zeros include x=3 with multiplicity 2.

[tranquil pine]

Just full struggle, really need a guide through this

The zeros included i read as “x=3^2” where the exponent represents a quadratic on the graph

(w/o a calc!) is written as a note from the teacher, she wants us to do it by hand

I factored the equation and got
X^3 ( x^4+2x^3-23x^2-24x+144 )

That means x^3=y y=0
So
X: 3^2 , 0^3
And i need to find 5 more x’s

Does x=3, mult 2 mean 0=x^2 -3?

Thats what i thought so i used that to factor the factored form of the original question

[shell mountain]

x = 3, mult 2 means (x - 3) is a factor twice

Or (x - 3)², which you can expand and do long division

[tranquil pine]

Ah!

So would that be(x-3)(x-3) or x^2 -3^2

[shell mountain]

No

(a + b)² ≠ a² + b²

Use FOIL

Or remember (a + b)² = a² + 2ab + b²

[tranquil pine]

So (x-3) * (x-3)

X^2 -6x +9

[shell mountain]

Yes

[tranquil pine]

I FOUND MY PEN

So the right division problem would be correct

[shell mountain]

,rotate

[shell mountain]

It should be + 144, but yes

[tranquil pine]

Shoot your right

Ok so factoring the factor gave me x^2+8x+16

I wish there was a root sign emoji

-b +- (squareroot) b^2 -4(a)(c)
——————————-
2(a)

Now right?

Quadratic formula

I got 3 as the answer for that

(Imma use [] for square root just for convenience)

• -6 +- [36 -4(1)(9)
  ———
  2(1)

+6 +- [36-36
———
2

6 +- [0
———
2

3

When im listing my x’s i use that number on the list the amount of times that it has as an exponent?

So i need 7 x’s cause 7 is the highest exponent.
The question gave me x=3 with multiplicity 2
So is that
X: 3, 3, -, -, -, -, -

And x^3 = 0 so

X: 3, 3, 0, 0, 0, -, -, -

And my answer was quadratic answer was another 3?
But if use 4*4=16 and 4+4=8 then (x+4)(x+4) or -4^2

<@&286206848099549185>

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[tranquil pine]

<@&286206848099549185>

[radiant flame]

wait why are you redoing what the problem gave you

the problem already told you it has solutions at x = 3

from that you derived that x^2 - 6x + 9 must be a factor of the polynomial literally because it is the polynomial with two solutions at x = 3

why are you recalculating, and using the quadratic formula if you already know its solutions 💀

[radiant flame]

thats good

[radiant flame]

no you got the right factorization, just (x+4)(x+4)

for everything on the left side, if the x you find is a solution, if you plug it in it has to make something 0. For example if x = -4 is a solution, then if you plug in -4 into your polynomial you're supposed to get 0. In this case, you know that actually -4 IS a solution because the (x+4)(x+4) part gives 0 if you plug in -4 since (-4+4) is literally just 0. and then the rest of the polynomial doesnt matter because 0 times anything is 0.

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[abstract mica]

can someone show me how they solved x pls

[main saddle]

Does anyone know how to define this derivative

[grand bronze]

too disgusting equation to do with latex, they probably just put this in a calculator or something tho

note that you could simplify stuff a lot along the way but i just didnt feel like bringing out a calculator all the time so i just treated all the numbers as variables till the very end

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[drifting ginkgo]

how can i show that this series diverges?
$$
\sum^n_{k=1} \frac{(-1)^n}{\sqrt{n-k}\sqrt{k}}
$$

[vital crag]

by showing it doesn't converge

[soft zealot]

Levens

[drifting ginkgo]

i think one of the criteria for series is that the sequence of it should converge to 0

could that be helpful or is there another way?

Or how is this true for $$c_n := \frac{(-1)^k}{\sqrt{(k+1)(n-k+1}}?$$ Based off $\sqrt{ab} \leq \frac{1}{2}(a+b)$ btw... but i dont understand how that middle part is true

[soft zealot]

Levens

[main saddle]

#1021175428326633542 Prove with an epsilon - delta*proof that f(x)=x^2 +x is continuous at xo

[abstract mica]

would you be able to show me the simplified version with the calculator

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[grand bronze]

literally just google solve for x calculator and the first results should all be able to input that

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[arctic vine]

this one is just gross and I seem to keep screwing up the derivative.

[arctic vine]

.close

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[tribal turtle]

I'm trying to prove triangle inequality for integrable complex function, but i'm stuck on where to go from here

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[tribal turtle]

<@&286206848099549185>

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[vital crag]

thats just one function.

do you have the original question?

[vital crag]

Your proof is complete for this problem. There is no triangle inequality involved anywhere

[tribal turtle]

But my proof has a square. I can't seem to get it into the form in the question

[vital crag]

Oh you're right. My bad

Skip the square in the first step

The rest is simpler

Should be like 3 lines

[tribal turtle]

Oh ok, i'll give it a go thanks

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[mellow owl]

Hi all,

I am wondering whether Popoviciu's inequality on variances ( https://en.m.wikipedia.org/wiki/Popoviciu's_inequality_on_variances ) also holds as a bound for (the magnitude of) the covariance of two random variables. Is this known?

Let’s say random variables x,y can take outcomes both in [a,b]. Then, per the above inequality, can one show that

-1/4 * (b-a)^2 <= cov(x,y) <= 1/4 * (b-a)^2

? 🙂 I am not familiar with the literature (and this is not so much my field of expertise, sorry), so any references to bounds on this would be great! Thanks all!

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@mellow owl Has your question been resolved?

[vital crag]

https://arxiv.org/pdf/2106.10037.pdf

[mellow owl]

Thanks a lot 😊 Equation (9) exactly is what I have been curious about! This answers „Yes“ to my original questions.

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[supple jolt]

Why is the square root of a number always positive?

[vital crag]

the domain of square root is nonnegative numbers

[supple jolt]

Why

How

[wispy pilot]

the square root is defined to be positive

[supple jolt]

Is there any other way to prove it?

[wispy pilot]

you don't prove definitions

[vital crag]

squares of numbers are nonnegative

[supple jolt]

Ok and

[oblique portal]

the guy inventing complex numbers be like

[supple jolt]

Nonna just type already

😭

[chrome cove]

[supple jolt]

Wait ur a guy

[chrome cove]

Indeed, Nonna is a nickname lol

[supple jolt]

Wow

Ok

So?

[wraith crater]

Wdym so

[supple jolt]

So i was hoping for Donna to explain

[oblique portal]

donna

[vital crag]

@supple jolt what is your updated question now that you've been told by Zef and me some properties of square root function

[oblique portal]

donna da eplonna

[supple jolt]

So

If i told you

1+1=3 by definition

[vital crag]

define +

[supple jolt]

Then

[vital crag]

define 3

[oblique portal]

define =

[supple jolt]

I cant just accept it

[oblique portal]

define 1

define numbers

[supple jolt]

Give me some other proof

[vital crag]

that's a you problem

[wispy pilot]

well for every mathematician out there, the square root of a positive number x, is the unique positive number y such that y² = x

[supple jolt]

And theres no proof

[wispy pilot]

there is nothing to prove

[supple jolt]

We just accepted it

[oblique portal]

its the definition man

[supple jolt]

?

[vital crag]

definitions don't require proving

[wispy pilot]

except maybe existence and uniqueness ?

[oblique portal]

there was this one book that tried to write all of msthematics from like 5 axioms or something

if you wanna read that ur choice

[vital crag]

understand this

[oblique portal]

they got to adittipn on page 200 tho its unreasonable and stupid

[supple jolt]

Ok

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[chrome cove]

For some reason I struggled a lot with this too

It's just a definition, when you take the square root of a number, you find the positive number that multiplied by itself gives the original number

You can always make up a function that gives you the negative number that multiplied by itself gives the original number, or something that gives both the positive and negative numbers, but that won't be the square root, it would be something you made and you defined

Lol I type so slow

[wraith crater]

a = sqrtb = -a => a=-a

Break maths

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[delicate hinge]

can anyone help? I've tried like every notation and I'm so sure it's correct

[tulip coyote]

Did you try including the endpoints of those intervals? (e.g. Like $(-\infty, -1], [1, \infty)$)

(also bear in mind this note)

[delicate hinge]

Yeah I've tried different notations with the note

[soft zealot]

chartbit

[delicate hinge]

It worked tysm

Why would it be included though?

[tulip coyote]

T'was a guess 😉 does their definition of increasing have to be strict?

I also took a look at my notes and tried applying this lol

[delicate hinge]

That'll do it

Thx again~

[tulip coyote]

No problem!

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[wanton sentinel]

from:
sin^2x + cos^2x = 1
How to proof that :
sin^2x = 1/2(1-cos2u)

[wanton sentinel]

so i can just memorize sin^2x + cos^2x = 1 and from it get the other identities

[rare halo]

You know cos2x=1-2sin²x?

[wanton sentinel]

yes ik but is there is a way to get all those from
sin^2x + cos^2x = 1

?

instead of memorizing them all

or is it just not possible ?

[rare halo]

I guess it's not possible

[wanton sentinel]

ah alright thanks

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[polar wing]

how can well seperated be phrased in more formal math jargon

without using math notations

is there a specific noun for that in other word?

[final saddle]

@polar wing Has your question been resolved?

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

[lapis raven]

Hello

[lapis raven]

I am a 7th grader (obviously above 13), and I am doing Algebra 1. I was practicing for Mathcounts, and I was doing the mock tests.

But I had a few questions.

First off, how would we solve this?

Next question, how would we solve this?

Second-to-last last question, how would we solve this?

And finally, my last question is, how would we solve this?

Sorry, if it is too much 🤣

[cinder sinew]

Have you done any work in any of those?

[lapis raven]

I have no idea where to start, that's the thing 😦

[young ravine]

For the first one make an equation

[cinder sinew]

For all of them actually lol

[young ravine]

Haha very trye

Think like people who own only dogs plus people who own only cats equals what

[lapis raven]

That equals 85

And then divide by 5?

[young ravine]

Yes

And what else

[lapis raven]

So cats would be 17?

?

[young ravine]

Yeah

[lapis raven]

But the answer key says its 23

[young ravine]

Hmm maybe its not people who only own cats and only own dogs

[lapis raven]

There was no explanation, so I decided to ask

[shell mountain]

The number of people who own dogs is, in general, 4 times the number of people who own cats

It does not say the number of people who own just dogs is 4 times the number of people who own just cats

[lapis raven]

Oh

So that means that the 15 would be included

[shell mountain]

Let's say x people surveyed own a cat

[lapis raven]

yes

[shell mountain]

How many people own a dog?

[lapis raven]

4x

[shell mountain]

And 15 people own both

[lapis raven]

ok

[shell mountain]

How many people own just dogs, if 4x own dogs and 15 of those also own cats?

[lapis raven]

4x-15

[shell mountain]

And how many own just cats

[lapis raven]

x-15

Oh wait

So

Now we know just dogs

just cats

and both

so we can add them

[shell mountain]

Yes

[lapis raven]

So 4x-15+x-15+15=100

So 5x=115

and x=23

[astral basalt]

Can you help me, I am first year Bsc Mathematics student. On 22 there is exhibition in our college, can anybody suggest a working model in mathematics which can be showed as exhibit

[shell mountain]

#❓how-to-get-help

[lapis raven]

Ok, I finally get the first question

Now the second one

[shell mountain]

What's the opposite of flipping at least 3 heads?

[lapis raven]

flipping at least 3 tails?

[shell mountain]

In terms of heads

Actually, ignore me

If you're flipping at least 3 heads, that means you're either flipping 3 or 4, right?

[lapis raven]

yes

[shell mountain]

What's the odds of flipping exactly 3 heads?

[lapis raven]

1/8?

[shell mountain]

Not quite

That's the odds of a specific combination of 3 heads, like HHHT

But there's also HHTH, or HTHH, etc

[lapis raven]

Oh, ok

[shell mountain]

How many of these combinations are there?

[lapis raven]

4

so 1/2?

[shell mountain]

Yes

[lapis raven]

ok

[shell mountain]

Now, what's the odds of flipping exactly 4 heads?

Wait

[shell mountain]

It's not 1/8

[lapis raven]

Ik its 1/2

[shell mountain]

It's not 1/2 either

[lapis raven]

What?

THHH

[shell mountain]

I knew it seemed too large

[lapis raven]

HTHH

[shell mountain]

There's 4 combos, yes

But the odds of a particular combo, like HHHT, is not 1/8

[lapis raven]

It is 1/16?

[shell mountain]

Yes

[lapis raven]

Yes

So, 4 combos

So it is 1/4

[shell mountain]

Yes

Now, what about 4 heads

[lapis raven]

That is 1/16 because there are no orders of anything

it is HHHH

[shell mountain]

Yep

[lapis raven]

So 1/4+1/16

is 5/16

[shell mountain]

Yep

[lapis raven]

Ok

Halfway done 👍

Thanks

Third problem

[shell mountain]

Can you post the problem again so I don't need to scroll up

[lapis raven]

of course

[shell mountain]

Let's name a variable. Let's say Gracie poured out x gallons

[lapis raven]

ok

[shell mountain]

So how many gallons of 50% juice were left?

[lapis raven]

1-1/2x

[shell mountain]

Howd you get that?

[lapis raven]

Because 50% juice of 2 gallons

So 1 gallon juice

And we pour out x

[shell mountain]

No, it's 2 gallons

Of punch, my bad

[lapis raven]

Ok, so 2-x were left

[shell mountain]

Thinking about it in terms of juice is definitely better, actually

[shell mountain]

So there was this much juice left

[lapis raven]

yes

[shell mountain]

How much juice was added to that?

[lapis raven]

uhh

one sec

Wait, same amount that was poured out

so x

because 100%

[shell mountain]

Yes

So how much juice was there after mixing?

[lapis raven]

65% of 2 gallons so 1.3 gallons

[shell mountain]

Yes, but what about in terms of x?

[lapis raven]

1+1/2x?

[shell mountain]

Yes

[lapis raven]

ok

[shell mountain]

1 + x/2 gallons of juice were in there

[lapis raven]

yes

[shell mountain]

But there was also 1.3 gallons

So?

[lapis raven]

theyre equal

so 1+x/2=1.3

x=0.6

[shell mountain]

Yep

[lapis raven]

Ok

So she poured out 3/5 gallon

Ok got it

75% done with all qeustions

Last question

I will post it again

so you dont have to scroll

[shell mountain]

Let's start with the cylinder

If the radius is r, what's the height?

[lapis raven]

3r

[shell mountain]

And thus, what's the volume of the cylinder?

[lapis raven]

pi 3r^3

[shell mountain]

Yep

Now for the cone: if the cones radius is R, what's the height?

[lapis raven]

6r

[shell mountain]

*6R. Variables are case sensitive

[lapis raven]

Oh yes,

6R

[shell mountain]

Now, what's the volume of the cone?

[lapis raven]

I dont know how to find the volume of a cone

Ill write it down somewhere can u tell me

wait

isnt it cylinder except 1/3

[shell mountain]

Yes

[lapis raven]

oh then it is pi 2r^3

[shell mountain]

2πR³