help-10

[warm shale]

SWR

[timid silo]

its x + y = 85 btw my bad

i forgot to multiply the 2 that i got from the 4 square root with the 2 from the formula

oh

now i just do the thing

ok

ok now i have (x-y) . 85

i know that √ x - √ y is 9

ohh

its 85 squared?

the answer

can u solve it real quick and verify my answer

√x - √y = 9
And x . y = 4

Find √x³ - √y ³

i mean 85 . 87

not 85 squared

i looked at the wrong side of paper

wait i just want to know something

is (√x - √y)² equal to (x-y)

oh its not

dang

i really got it messed up

[timid silo]

im stuck here

can i relate (x-y) with the information √ x - √ y = 9

.close

[obtuse pebble]

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[old wadi]

can someone help solve this

[obtuse pebble]

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@old wadi Has your question been resolved?

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[old wadi]

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[violet vine]

aw u coulda just used cosine rule

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[sacred siren]

Hi! Trying to find the exact place Frechet constructs this embedding, a couple searches through the referenced paper yielded nothing
https://en.wikipedia.org/wiki/Kuratowski_embedding

[sacred siren]

paper in question is https://link.springer.com/article/10.1007/BF03018603

Have seen multiple sources refer to this paper, but annoyingly not with any more specific locator (so this is probably not a wiki problem)

And lecture notes for a different course I'm taking refers to the finite-dimensional version of this as the "Frechet embedding"

Checking mathscinet yields two reviews by Hahn, checking if he mentioned anything

Nope, not as far as I can tell

<@&286206848099549185> , do you mind?

[obtuse pebble]

@sacred siren Has your question been resolved?

[sacred siren]

Possible sighting: Item 51, part 2 of the theorem

We consider $\epsilon_p=\inf_kd(A_p,A_k)$ for a sequence $A_k\in E$ a metric space

[warm shale]

gesh (on break)

[sacred siren]

hrm. doesn't seem to be going anywhere near an embedding

OK, so Item 62 defines a sequence space with a weighted pointwise bounded l1 metric

Item 68 seems to be defining $\ell^\infty$, and not liking it:

• because for the norm to be well-defined we need to limit ourselves to bounded sequences
• because it is very incomplete -- the subspace ${0,1}^\mathbb{N}$ has no limit points in it

[warm shale]

gesh (on break)

[sacred siren]

Nope

No dice

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[forest lake]

Calc 2

[forest lake]

Find the area of the shaded region

I dont know where to start

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[forest lake]

#help-32

[obtuse pebble]

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[gritty bloom]

I just need a reminder on how to get the derivative, we started introduction to differentiation recently

[fossil crag]

(f(x+h) - f(x))/h

and then make h->0

[gritty bloom]

What does the h stand for again?

[fossil crag]

a small change in x

that small change becomes infinitely small

(f(x+h) - f(x))/h is the 'steepness' in y, for that small change in x

[gritty bloom]

Thank you!

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[abstract solstice]

need help with simple integration

[abstract solstice]

how to integrate (x^3)e^(x^2)

x^2=u, and u(e^u)xdx

but why does xdx = du/2

[abstract flame]

du/dx=2x

just rearrange that

[abstract solstice]

u=x^2 and du=2dx

is that correct?

so du/2 = dx

[abstract flame]

this is not correct

remember power rule

[abstract solstice]

oof ok let me think about this on my own its been a while since i did calc

[abstract solstice]

power rule as in int (x^2)dx = (x^3)/2 +c

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[warm quarry]

I need help solving this question. I am aware of a solution that uses Schwarz's Reflection Principle but I believe that I am expected to solve it without that result. I have deduced that f(0)=0 and am trying to show the coefficients of all even powers in the power series expansion is 0 but am having no luck

[warm quarry]

<@&286206848099549185>

<@&286206848099549185> pls

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[zenith raft]

i'm prolly being stupid here but... if we just take the n=1 case (so f(x) = Qx^2 with Q>0) the inequality is equivalent to ||2Q(x-y)|| <= Q||x-y|| right? but that's false?

[drifting roost]

[zenith raft]

[drifting roost]

I can help if you wait for me to study real analysis

[zenith raft]

ok i'll keep it open until then

[forest sinew]

i think in this case, youd have to take Q = L > 0

to my head that a constant is its own eigenvalue seems ... right

oh wait

i see what you mean

[zenith raft]

i noted Q > 0 already in my original message but that doesn't even matter

[forest sinew]

yea i get the problem youre saying

[zenith raft]

[obtuse pebble]

@zenith raft Has your question been resolved?

[brisk matrix]

is that L in the question meant to be the eigenvalue or just the lipschitz coeff

[zenith raft]

the eigenvalue

it's not just prove there is some lipschitz coefficient

[brisk matrix]

then certainly that's just wrong

[zenith raft]

should be f(x) = 1/2 x^TQx or something

welp the deadline already passed and i'm doing this so late so not sure how nobody pointed this out already and it didn't get corrected

[brisk matrix]

probably. if not that then maybe the square root. but what's up there looks wrong fs

[brisk matrix]

this is odd lol

[zenith raft]

then i like how this part has a 1/2 when it's completely unnecessary

like there's no issue with it there but the problem would make just as much sense and the answer be just as significant without it

but now idk if i should answer this one as if f(x) = 1/2 x^TQx or as it is written in the problem

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[ripe hazel]

tried 56/98 * 42/97

[obtuse pebble]

@ripe hazel Has your question been resolved?

[drifting wraith]

maybe round more?

24.7?

[ripe hazel]

huh ill try

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[surreal bone]

Help

[obtuse pebble]

Please don't occupy multiple help channels.

[tacit pewter]

What's the problem?

[surreal bone]

O ok

Um right here

Times should be equal right?

[tacit pewter]

No

[surreal bone]

What?

Why

He drives 6km/hr faster to make up for the time

[tacit pewter]

The route is same and the driver goes faster than usual so don't u think it will take less time than usual?

Assume he goes with a speed of xkm/hr usually

[surreal bone]

Ooooo yes i didnt think of it like that

[tacit pewter]

Then the time he takes usually is t1 = 270/x

U understand till here? So i proceed

[surreal bone]

Ok

[jaunty wadi]

I’m doing same question yeah that makes sense

[tacit pewter]

Write the second equation

[surreal bone]

270/x+6). + 1/2?

[tacit pewter]

t2 = t1-1/2 = 270/x+5

6*

[surreal bone]

Can I do this: 270/x= 270/(x+6)+1/2?

[tacit pewter]

Exactly

[surreal bone]

Alr alr

Cause time keeps going

Ok ol

Ok

Thx

So much

[jaunty wadi]

What happens from here @tacit pewter

[surreal bone]

I think @jaunty wadi has a question

[jaunty wadi]

Help if a pipe can empty a swimming pool 20hrs and another pipe can fill the pool in 32 hours would it be -x/20 +x/32

[tacit pewter]

Ask where didn't u understand it

[jaunty wadi]

Sorry my wifi cut out I get the other question

[tacit pewter]

Lemme think

[tacit pewter]

What's the equation for?

[jaunty wadi]

Solving rational equations

[tacit pewter]

What's the complete question

[jaunty wadi]

That is it

Oh wait it’s not but I’m just asking

The question is the part before

Can I do -x/20 + x/32 = 1

How long would it take for the pool to drain

[tacit pewter]

Oh

[jaunty wadi]

Is it right

[gaunt shore]

It seems that you posted this question twice, but I don't know if you looked but I gave you the answer for it, and I am convinced it's right.

Were you not satsified with my answer, or do you think that it's stupid?

[obtuse pebble]

@surreal bone Has your question been resolved?

[tacit pewter]

x+y=12 implies that x=y-12

[surreal bone]

Why is it 1/x - 1/(12-x) and not 1/(12-x) - 1/x

[tacit pewter]

It's considered

U can use both

[surreal bone]

U can use both?

[tacit pewter]

Yes

[surreal bone]

Wdym its considered

?

If x is 12

[tacit pewter]

If you do the first equation that means x>y

Sorry x<y

[surreal bone]

What is y?

[tacit pewter]

That's not possible

It'll be 1/0 if y do that

[surreal bone]

So I got to do both ways if I get like a negative first time?

[surreal bone]

Wdym

[surreal bone]

Wdym

[solar meadow]

$a + b = 12$\
$\frac{1}{a} - \frac{1}{b} = \frac{2}{9}$

[warm shale]

Roman_Garland

[surreal bone]

B+a = 12

I wont get the same answer tho

[solar meadow]

$a, b = ?$

[surreal bone]

If i do b+a

[warm shale]

Roman_Garland

[surreal bone]

Wdym

[solar meadow]

$a + b = 12$\
$\frac{1}{a} - \frac{1}{b} = \frac{2}{9}$\

Here, find a and b

[warm shale]

Roman_Garland

[surreal bone]

K

[tacit pewter]

When u solve it

U get a quadratic?

[solar meadow]

Yes.

[surreal bone]

One sec

Okay i got answer

For doing 1/x first

Answer key says two pairs possible

[tacit pewter]

Because it's a quadratic equation

And some get rejected

[surreal bone]

Ok

[last pilot]

@surreal bone

!done

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[swift valve]

i need help with fractions

[swift valve]

hello?

[knotty thorn]

[high lily]

i have yet to see said fractions

its hard to help if you don't post specific questions

[obtuse pebble]

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[delicate tartan]

what's the difference between y = kx + m and y = mx + k?
i see people use both and i dont understand the difference

[azure willow]

there is no difference, they are just different choices of which letters represent which numbers

[quasi tree]

there's also even y = ax+b in some places

they're the same thing, just with different variables

[delicate tartan]

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[west sierra]

Can a circular motion occur without jerk?

[west sierra]

Because I heard centripetal acceleration is always towards centre which means it has to be changing direction continuously which means jerk ≠0

[warm canopy]

Acceleration can be constant in circular motion

[west sierra]

Do you have an example

[warm canopy]

Acceleration is change in velocity, that includes changing direction

[west sierra]

but if velocity changes direction, the one responsible for the change is centripetal acceleration and I was taught that it's always toward the centre, so being a vector, won't the direction of centripetal acceleration be changing as well?

[marsh geyser]

what about earth orbiting the sun? assuming it's always same speed

[west sierra]

It's changing direction

Because gravitational force is acting as centripetal force

[warm canopy]

The force (hence acceleration) is always acting towards the center of the circle of the motion

[west sierra]

And if at any one instance I draw centripetal acceleration, I would draw it towards sun and at another instance I would do same...I would notice that centripetal acceleration is changing direction

[west sierra]

Yes

[marsh geyser]

acceleration is constant in magnitude

always directed to the center

[west sierra]

But acceleration is vector so it's not constant in direction

[warm canopy]

From the frame of reference of the moving body its always in the same direction

[west sierra]

Ohh

That's true

Wait, from the reference of moving body, I would see the sun instead revolving around earth and again it will not be in same direction

So does that mean acceleration can never be constant in circular motion ?

[warm canopy]

Non inertial reference frames are whack from whatever I remember. Acceleration in one frame may not appear as acceleration in another

[marsh geyser]

correct

they don't follow newton's law of motion

[west sierra]

Yeah

So I have studied they applied pseudo force

Still I can not imagine how would it be like

Thank you both btw

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[silent furnace]

how did they get A=1/4

[severe juniper]

dividing the equation 1 = 4A by 4

[silent furnace]

no coefficient of x4 is only A

where did the 4 come from

[severe juniper]

(1+1²)² = 2² = 4

[silent furnace]

☠️☠️☠️☠️☠️

i know basic maths buddy

[severe juniper]

Then i dont understand your question buddy

[silent furnace]

how are they putting 1 in equation number 2

1-x=0…. x=-1

oh

☠️

btw how did they write A-B with x4 when x4 is only with A

[azure willow]

there is also the term Bx^4 by expanding the second term

[silent furnace]

alright got it

thanks

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[dark hedge]

Hi

[dark hedge]

I need help

[versed stratus]

[dark hedge]

close.

.close

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[tacit pewter]

Trapezium is all u going to do in the exam tmrw?

[dark hedge]

Ohh wow hi

[dark hedge]

And midpoint

[tacit pewter]

It's a unit test?

[dark hedge]

No

Midpoint is from the graph chapter

[obtuse pebble]

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[shell oar]

what does the notation in yellow mean?

[tacit pewter]

Ok

[undone yoke]

Are you sure this a math oriented question ?

This feels a computing question

[shell oar]

oh

[shell oar]

yh it is im sure

[undone yoke]

Do you have an idea about coding ?

Like what are for loops, while loops ?

[shell oar]

yes i do

[undone yoke]

And about the expansion of sin(x) ?

[shell oar]

taylor series expansion?

if so, yes

[undone yoke]

Okay. So O(N) is called as the big O notation which determines the speed at which a code (or generally, a proces) is being run. When we use a for loop, the big O will be O(n), a linear rate, due to the for loop being a linear function (it executes one iteration at a time).
Now if you expand sin(1/n) in terms of taylor series, the first term is 1/n. So you use the definition of limits to prove that it converges at a rate of O(n).

Note here that O(n) does not have anything to with the value of N in it. O(N) simply indicates what behaviour a process is following. If it is logarithmic, it will be O(logn). That's it. Nothing much

[shell oar]

oh i see

ok so does O(whatever) just tell as how quickly something coverges basically?

so O(1/n) would converge faster than O(logn)?

[undone yoke]

Yes

Exactly correct

[shell oar]

perfect

that makes sense

thanks alot

[undone yoke]

👍

[shell oar]

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[astral grove]

something just doesnt work for big numbers here. maybe there is no limit but im having hard time to prove it

[native inlet]

,w lim n-> inf of ((n+4)^n-(n-4)^n)/(n^n+3^n)

are you allowed to use l'Hopital's?

[astral grove]

nope

and tried it still and it made it so much worse

wait

maybe I can make it work for the denominator

[native inlet]

well you could make it easier

x^x+3^x is about x^x for large x (i.e infty)

[astral grove]

no nvm it doesnt work

[astral grove]

yup

but the numerator is also approching inf but still after about 140 it starts to break for some reason

[native inlet]

okay I think I got it

so you have $\frac{(x+4)^x-(x-4)^x}{x^x}$, right?

[warm shale]

PajamaMamaLlama

[astral grove]

im listening

[astral grove]

not exactly

the denominator is wrong

ad 3^x

add

[swift stream]

The point is you can ignore the 3^x

[native inlet]

for signficiantly large x x^x+3^x -> x^x

[astral grove]

ok not a problem. it approches infinity either way

[native inlet]

After some algebra what you have is $\left(\frac{x+4}{x}\right)^x-\left(\frac{x-4}{x}\right)^x$

[swift stream]

To formalise this notion, just factor out an x^x and do whatever you want to do

[warm shale]

PajamaMamaLlama

[astral grove]

yes i see this

[native inlet]

this is simply the limit definition of e^x

[astral grove]

oooooooh i under stand i think

[native inlet]

$\left(1+\frac{4}{x}\right)^x-\left(1+\frac{-4}{x}\right)^x$

[warm shale]

PajamaMamaLlama

[astral grove]

i cant remember the limit definition by heart though

[native inlet]

$e^x=\lim_{n\to\infty}\left(1+\frac{x}{n}\right)^n$

[warm shale]

PajamaMamaLlama

[native inlet]

so your limit is e^4-e^(-4) :)

[astral grove]

yes thats more or less what I remembered

[minor anvil]

for significantly large x, (x+4)^x - (x-4)^x is also infinity so just because it approaches infinity is not a reason to believe this, you have to see that while it is true it approaches infinity, which infinity it is

x^x + 3^x not just approaches infinity, but it's an infinity that in itself approaches x^x is what you should think

[astral grove]

yes ofc. just because the numeretor and denominator approach infinity that doesnt say much about the limit of the whole function

its a little more complex

.close

[obtuse pebble]

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[elder vortex]

Which is the answer for the question 6?

My reasoning was to subtract the number of possibilites that may contain queens with the number of possibilities that doesn't contai queens, so I arrived at the solution: (52!/47!)-(48!/43!)

Is it correct?

[undone yoke]

Do you know the actual answer ?

[undone yoke]

Of course this is wrong

[elder vortex]

No the book doesnt show it

For somereaso the book just show the answers for the odd numbered questions

[undone yoke]

52!/47! is all the cases possible ($52C5*5!$)

[warm shale]

Solomaniac

[undone yoke]

and 48!/47! is all the cases when there is NO queen.

This means the subtraction will yield all the cases when there is ATLEAST one queen

We want EXACTLY one queen

That is $4C1 * 48C4 * 5!$

[warm shale]

Solomaniac

[elder vortex]

What is C

[undone yoke]

permutation and combination symbol

Basically, $48!5!/3!4!$

[warm shale]

Solomaniac

[undone yoke]

Do you want me to explain it properly ?

[elder vortex]

No need

Imma figure it out on my own

Thx

[obtuse pebble]

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[ornate merlin]

hi

[ornate merlin]

pls help

[obtuse pebble]

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[queen sand]

i need help with task d

here is the c task

[obtuse pebble]

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[queen sand]

.close

[obtuse pebble]

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[quaint bone]

whats the limit as x approaches 0 of tan^2 3x / sin^2 2x? you're only allowed to solve it using trig limits

[quaint bone]

every time i do it i get 1/4 and the actual answer is 9/4

[timid silo]

!showwork

[obtuse pebble]

Show your work, and if possible, explain where you are stuck.

[rotund bolt]

for tan^2(3x)

divide and multiply with 9x^2

lim x to 0 tan x/x is 1

similarly for sin^2(2x) , divide and multiply with 4x^2

lim x to 0 sin x/x is 1 too

9x^2/4x^2 = 9/4

[quaint bone]

@rotund bolt what did i do wrong here to keep getting 1/4?

[rotund bolt]

how did you make 3x/cos 3x tend to 1?

[quaint bone]

i used the denominator of 3x/3x for the sin3x to make it equal 1 and i used the numerator of that fraction to get 3x/cos3x

[rotund bolt]

ye so what happened to 3x/cos(3x) then?

how did it turn to 1?

[quaint bone]

the 3x cancelled the 3x and then it was 1/cosx

and cosx is equal to 1

[rotund bolt]

...

which 3x cancelled which one?

[quaint bone]

wdym?

[rotund bolt]

how did it become 1/cos x?

[karmic ridge]

Bro did u solve it or need help?

[rotund bolt]

solved it but he has issue in his solution

[karmic ridge]

Skill issue

Gg

[rotund bolt]

here's his solution

[quaint bone]

when i multiplied sin3x by 3x/3x i used the denominator of the fraction for sin3x and then i used the numerator of 3x/3x for 3x/cos3x

[quaint bone]

yeah my calculus teacher sucks

i've been teaching it to myself

[karmic ridge]

Refere to books

Cover and try all solved expamples

[rotund bolt]

yes , then what happened to the 3x/cos(3x) next?

[karmic ridge]

Examples

[quaint bone]

i don't have any text books

my high school can't afford them i think lol

[karmic ridge]

Bruh don’t rely on internet buy books hard printed

Mark your mistakes using pencil

[quaint bone]

i cancelled the 3x of the 3x/cos3x to get 1/cosx

[karmic ridge]

So u don’t repeat it

[quaint bone]

i dont money for that stuff

[rotund bolt]

🤦

[quaint bone]

is that haram

[karmic ridge]

Bro

[quaint bone]

does allah not allow you to do that

[rich otter]

or u can just "find" pdfs of books :)

[karmic ridge]

Oh no

Bro

[rotund bolt]

Haram

not halal

[karmic ridge]

U need trigonometry

[rotund bolt]

you can't cancel the arguments of a trignometric function with a function outside omg

[quaint bone]

math allah is not proud rn

[rotund bolt]

its an angle

[karmic ridge]

Nah there’s a reason libraries still exist

[quaint bone]

ITS BEEN A LONG TIME SINCE I DID MATH OK

[rich otter]

yeah but he just said he doesnt have the money to buy books

[rotund bolt]

chill

[quaint bone]

why can i cancel the sin3x with 3x then!?!

[rotund bolt]

it doesn't work like tha

you don't cancel them

[quaint bone]

oh

[karmic ridge]

There’s a reason you read the Quran from a book not a pdf while praying

[quaint bone]

i've been doing this completely wrong then

[karmic ridge]

Use library

[quaint bone]

i whip out my amazon kindle and start reading from there

[rotund bolt]

Ayush , what college are you in?

[karmic ridge]

Oh nooo😭

Bro

How

How 😭

[quaint bone]

how do you make sin3x/1 equal 1 then?

[karmic ridge]

I’m not in college

[rotund bolt]

lim x tending to 0 sin(x)/x is 1

[karmic ridge]

They teach use calculus

Most of it

In last year of school

[rotund bolt]

your profile says undergrad

[quaint bone]

ik but what about the 3x?

[karmic ridge]

In which I am

[rotund bolt]

abbey

nvm

[quaint bone]

because its sin3x/x not sinx/x

[karmic ridge]

Do u know u can expand sin 3 x and take sin x common

@quaint bone

[quaint bone]

wdym?

[karmic ridge]

Oh no 😭

[quaint bone]

my math teacher is horrible

[rotund bolt]

bhai tu shaant hoja @karmic ridge

[quaint bone]

i know nothing

[rotund bolt]

chill

[quaint bone]

i learn calculus from the organic tutor on youtube

[rotund bolt]

listen

[karmic ridge]

Tu hi bata de

[karmic ridge]

He’s good

[rotund bolt]

for your question

which is lim x tending to 0 tan^2(3x)/sin^2(2x)

you see the tan^2(3x) part?

[quaint bone]

mhm

[rotund bolt]

lim x to 0 tan x/x is 1

so

(tan (3x))^2

[native oasis]

yo guys can someone help me with a question please

[rotund bolt]

we need to divide and multiply with (3x)^2

i.e. 9x^2

[karmic ridge]

Yes

[karmic ridge]

Open a new help room

[rotund bolt]

so that tan^2(3x)/(3x)^2 tends to 1

[native oasis]

Question 8 a i

[rotund bolt]

and the 9x^2 remains intact

[native oasis]

How do I open a new help room

[rotund bolt]

similalry for the sin^2(2x)

we divide and multiply with (2x)^2 i.e. 4x^2

when sin^2(2x)/(2x)^2 tends to 1

[karmic ridge]

Go to suggested channel section send a hi

[rotund bolt]

and the other (2x)^2 remains intact

so now its 9x^2/4x^2

now as x tends to 1

its 9/4

[native oasis]

Wait what I can't find it 😆

[karmic ridge]

Skill issue

U want to do it by substituting?

[native oasis]

Just tell me what you got please

[karmic ridge]

Take the one in side the root = t^2

[native oasis]

yes please

thats what I did

@karmic ridge

[quaint bone]

how do i write all of this out?

i understand the math now but idk how to write it

[karmic ridge]

U can proceed from here

Understand “

?

[native oasis]

oh I used u instead of t

[karmic ridge]

Same same but difflent

[native oasis]

and also I made the entire square root equal to u (or t)

[karmic ridge]

Same thing

Square both sides BOOM =u^2

[native oasis]

I got 2u^5/2/45 + 8u^3/2/27

[karmic ridge]

Bro I don’t read that way

Can u write it

Or send ur solution

[native oasis]

ok one sec

its taking a long time

@karmic ridge sorry bro it's taking a long time

[obtuse pebble]

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[fickle nymph]

hi help

[fickle nymph]

i dont get how we can deduce the 8 in camping and the 6 in hotels

ping me when you answer

[native oasis]

@karmic ridge forget it, my computer is too slow

[fickle nymph]

nuh uh 😠

[karmic ridge]

Bro

[native oasis]

sorry bro -- maybe tommorow

because my computer is very slow bro, very sorry indeed

[fickle nymph]

bro get out of my help channel, delete your messages

@native oasis

@karmic ridge

now the pictures are far away

[karmic ridge]

Lol

NUH uhh

[native oasis]

yo bro how do you make a help channel in the first place

[fickle nymph]

wdym

just chat in the help channels that are available

[native oasis]

oh ok

[fickle nymph]

those are available

as soon as you send a message it will be put at your name

now help me

@native oasis

https://cdn.discordapp.com/attachments/903430332324405288/1210705422437326928/Screenshot_2024-02-23_184747.png?ex=65eb884a&is=65d9134a&hm=7d7b4899af6dba61945f3e8f1d2c8e1a74d8edec6bb4ef1074a679f696ed96be&

https://cdn.discordapp.com/attachments/903430332324405288/1210705349007376466/image.png?ex=65eb8839&is=65d91339&hm=dedee8d695e3646a9788b5ff37ee6452818faba01dc6991bcd83896432d7a450&

how we can deduce the 8 in camping and the 6 in hotels

[rough perch]

no

[obtuse pebble]

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[wispy acorn]

Need helping determing how much more Markos made

[wispy acorn]

box plot

I know markos made more

but it seems like I'm having trouble caculating how many more markos made

[obtuse pebble]

@wispy acorn Has your question been resolved?

[karmic ridge]

Lmao

[obtuse pebble]

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[obtuse pebble]

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[kindred basalt]

sorry for blurry image

i cant figure out what the guys head is blocking

[proud coyote]

ok its like a big curly bracket { bc EC^2 - CD^2 is DE^2 (pythagoras)

apologies for the even blurrier image

[obtuse pebble]

@kindred basalt Has your question been resolved?

[proud coyote]

what else was the question?

[kindred basalt]

so de^2 = ec^2 - cd^2 bc of pythag

and then i just swap around with the equation abovei

to prove the question

[proud coyote]

yeah the triangle above shows that ec^2 - cd^2 = de^2

so you can replace it

and then it is the equation you need to prove

[kindred basalt]

ok thanks

.close

[obtuse pebble]

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[kindred slate]

I got the wrong roots

Did I do I calc error

[obtuse pebble]

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[long hedge]

$x^2+x-2$

[long hedge]

factor

[warm shale]

putridplanet

[long hedge]

$x^2+2x-1x-2$

[warm shale]

putridplanet

[long hedge]

$x(x+2)-1(x-2)$

its not working

[dark stirrup]

maybe review how you got to this

[warm shale]

putridplanet

[long hedge]

ok i see

yo have to separate them

[versed pier]

Dyk about vieta’s

It’s super overkill

But could be good if you wanna expand past deg 2

Polynomials

[obtuse pebble]

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[maiden trail]

the textbook says the answer is false and I'm not sure how to prove it

[brisk matrix]

if this is false then all you need is a counterexample

consider the definition of D_vf

[maiden trail]

D_vf = gradient f . v

im not sure if thats right

[brisk matrix]

check the definition in your textbook

[maiden trail]

I can't find a definition for either of those in the book

[brisk matrix]

that is surprising

[maiden trail]

as far as I understand Du_f = the dot product between the gradient at a point and (v/IIvII)

but Dv_f and Dv/IIvII are completely new to me

[obtuse pebble]

@maiden trail Has your question been resolved?

[obtuse pebble]

@maiden trail Has your question been resolved?

[obtuse pebble]

@maiden trail Has your question been resolved?

[brisk matrix]

you should consult the definitions in the textbook (assuming this is a question from the textbook)

this kind of question is wholly dependent on the definition they use

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

MINE

[timid silo]

2x3

so 3 is the multiplicand

and 2 is the multiplier

[marsh geyser]

No

3 is the multiplier

[timid silo]

no

[upper cobalt]

Wtf

New math?

Wth is this

[iron edge]

It doesn’t matter actually

The results are the same

[timid silo]

cause of the commutative property ik

but

order still matters

[upper cobalt]

💀💀

[timid silo]

like sometimes, u can calculate faster

with a specific order

thats why im confusec

[marsh geyser]

Multiplicand comes first

[timid silo]

like how much does the order matter

[marsh geyser]

I think i know whats happening

Maybe its because of the country

[timid silo]

how much does the order matter, coz when i think it matters, i get confused since it shouldnt matter coz of the commutative property but u can calculate faster sometimes w a specific order so it does matter?

[marsh geyser]

The order never matters in absolute terms

Only relative to you

[iron edge]

True

[timid silo]

https://en.wikipedia.org/wiki/Multiplication

it is second

[timid silo]

wdym

it does matter cause u can calculate faster sometimes w a specific order

[marsh geyser]

Who is “you”

“You” is relative

Maybe you calculate faster 25x7 doing one direction and i do faster the other direction

[timid silo]

..

bro samuel u just macde me more confused and i dont trust u anymore as u got the order wrong

[timid silo]

wdym

noo

like, 77x5x2 is faster calculated as 77 x 10, not 385 x 2 (not my eg)

[marsh geyser]

I didn't get the order wrong

Your country has different order of calling the things

[timid silo]

it was wiki

wikipedia

[marsh geyser]

again, it depends on the country

anyways, that's not the important thing about your question

[timid silo]

yes

[timid silo]

^'

[marsh geyser]

as I told you, your capabilities to multiply faster in a specific order depends on you

[timid silo]

wiki is same for everyone doe

[marsh geyser]

ok sir, keep with the non-important question if u want

have a nice day

[timid silo]

i mean 385 is a bigger number

oooooook

.close

[obtuse pebble]

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[fallow widget]

If the determinant is = 0 in a 3x3 matrix. Does that imply that there exists no inverse?

[fathom flicker]

yes

[fallow widget]

1 0 1
0 1 1
1 1 0

This was the matrix i was given but i got the determinant to 0

However the book says it's possible to find the inverse of that

[fathom flicker]

the determinant is not 0

[fallow widget]

$1(10-11) -0(00-11)-1(01-11)$

[warm shale]

Merineth

[fallow widget]

= 0

[fallow widget]

https://youtu.be/YvjkPF6C_LI?t=89 I tried applying this method to find the determinant

[fathom flicker]

yes

in that method the signs alternate

so that should be a plus

where I drew

[fallow widget]

oooh

So the determinant is actually 2?

[fathom flicker]

-2

[fallow widget]

Ah ok!

thanks

[fathom flicker]

this matrix

transforms the standard basis vectors in R3

scales them all by sqrt(2)

[brisk matrix]

don’t trust these christian matrix propaganda videos

[fallow widget]

why?

[brisk matrix]

never mind that video is fine

[fathom flicker]

so the effect on the volume of the parallelopiped that they form is going to scaling by 2

[fallow widget]

that is too advanced for me to understand lol

[fathom flicker]

dont mind my buddy he is a little paranoid

[fallow widget]

but thanks for the help

.close

[obtuse pebble]

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[brisk matrix]

the thumbnail looks like they are blessing the matrix or something

[fathom flicker]

it goes to a different size cube

one that is 2 times bigger

that's the idea

the matrix takes it there

[obtuse pebble]

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[inner basin]

uh

[inner basin]

i am no math expert

but can i get a yes or no

this, is the equation i copied and gave to ai

and it solved it while the website said its unsolvable

idk if it made any mistakes ( i am dumb )

[kind hawk]

AI says a lot of stuff which seems reasonable

doesnt mean that it is correct

you cannot trust it

[inner basin]

i know, i am a dev.... testing it

[kind hawk]

your AI will not have solved an unsolved problem within 5 seconds

it doesnt help that you wrote 2(2^127)-1 instead of 2^(2^127)-1

your AI probably just looked at the first one. which isnt prime obviously

because its a difference of squares

[obtuse pebble]

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[slate wharf]

not sure how to show 5c

im not too sure if i can use this formula specifically for c

[median yacht]

Is tan^-1 arctan or cot?

[slate wharf]

arctan

[median yacht]

$$\tan^{-1}(\frac{1}{7}) + \frac{1}{4}\pi = \tan^{-1}(\frac{1}{7}) - \tan^{-1}(\frac{-1}{1})$$

$$\theta_u = tan^{-1}(\frac{4}{3})$$

[warm shale]

Rub05

[median yacht]

You have to proof that $\theta_u = \theta_z - \theta_w$

[warm shale]

Rub05

[median yacht]

u = z/w

z = 7 + i ; w = 1 - i

[slate wharf]

should i use the same formula

[median yacht]

No

Put every complex number in $pe^{i\theta}$ form

[warm shale]

Rub05

[median yacht]

And solve z/w

z/w = u, make conclusions and done

[slate wharf]

oooooo

thanks

yo thanks alot

how do i close this

[candid yarrow]

.close

[obtuse pebble]

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[lofty hare]

(V) please

[swift stream]

!occupied

[obtuse pebble]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[timid silo]

Sorry

[candid yarrow]

what does this set look like?

when you draw it

[lofty hare]

It looks like dots that slope towards the x axis

[candid yarrow]

slope?

they should all be inside the real line

[lofty hare]

Its for 1/k where k are integers

[candid yarrow]

Yes

[lofty hare]

So they would have discrete representation on each integer value

[candid yarrow]

well, this is what I get

[lofty hare]

yeah

[candid yarrow]

so, is it open?

[lofty hare]

no

[obtuse pebble]

@lofty hare Has your question been resolved?

[candid yarrow]

and is it closed?

[obtuse pebble]

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[hardy gale]

Hi

[hardy gale]

Could I please get help with this

Why is the answer that

Shouldn’t it be 3x + 2y = 20

[civic sapphire]

You need 4 strips of length y because there are 4 vertical strips in the diagram?

[candid yarrow]

Why 20?

[civic sapphire]

Because there are 20m of strips total (first two words of problem)

[candid yarrow]

where did you get this answer from?

[candid yarrow]

Oh, I see now

[obtuse pebble]

@hardy gale Has your question been resolved?

[hardy gale]

Why isn’t it 6x then

[candid yarrow]

where did you get this answer from?

[civic sapphire]

It's 3x because there are 3 horizontal strips

[candid yarrow]

no, there are 6

[hardy gale]

There’s 6

There’s also 2 vertical strips

[civic sapphire]

OK, I'm not seeing 6 in that diagram, just 3.

Well, 4 vertical strips since you count the ones on the left and right side

[hardy gale]

Then shouldn’t it be 6 instead of 3

3 on top

3 on bottom

[civic sapphire]

Oh, a strip goes all the way across. The thing where it says x refers to the entire strip going across, not just the middle section

[hardy gale]

Wdym

[civic sapphire]

The top strip goes across three windows per row

[hardy gale]

And what about y

[civic sapphire]

each strip goes from top to bottom (2 windows) and there are 4 of them

[obtuse pebble]

@hardy gale Has your question been resolved?

[obtuse pebble]

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[chilly scroll]

Mr x can walk up either 1 step or 2 at a time , he needs to walk up to 16th step but should not step on the 8th one how many ways

[chilly scroll]

[honest forum]

totally, how many ways can he go up the stairs

how many ways can he get to the 8th step?

[chilly scroll]

uh

[honest forum]

how many ways can he get from the 8th step to the 16th?

[chilly scroll]

im laying out the number of ways and it gets messy

[honest forum]

see if you can put all of that together

[chilly scroll]

ok

the total

i think im doing it long way

Case1 16 1 steps 0 2 steps

Case 2 14 1 steps, 1 (2 steps)

And permuting so so

This is too lengthy

ok is ir

It

The 1st one

1 + 15c1 + 14c2 + 13c3 + 12c4 + 11c5 + 10c6 + 9c7 + 8c8

Idk how to sum these is there a formula

[obtuse pebble]

@chilly scroll Has your question been resolved?

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[twilit meteor]

i got d(lnx)/dx as ln(1+1/x) using first principle, is it correct and is there any other way to solve it?

[fervent cradle]

that's not right

how did you get that

[rotund bolt]

if you used the first principle , you forgot to do something with the h in the denominator

that's why it's wrong

[fervent cradle]

ngl i think they got multiple things wrong

[rotund bolt]

I guess yes

can you show your work? @twilit meteor

[twilit meteor]

yea one seec

@fervent cradle @rotund bolt

sry for the image quality

[fervent cradle]

hmm

i'm not sure binomial approximation necessarily works if the power is changing

lemme think

because the second coefficient would be like

(1/h)(1/h - 1)/2 * (h/x)^2 which doesn't go to 0

non-trivial

so i don't think you can use binomial approximation here

[twilit meteor]

makes sense

but how else do u find it

[fervent cradle]

hint: (1 + 1/x)^x

[twilit meteor]

i dont get u

[fervent cradle]

do you know what $\lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x$ is

[warm shale]

Kaisheng21

[twilit meteor]

e

right?

[fervent cradle]

ok

does that look similar to anything you got

[twilit meteor]

but i have an x multiplied to the 2nd term

[fervent cradle]

sure

but try and make it into something of the same form

for example

$\left(1 + \frac{h}{x} \right)^{\frac{1}{h}} = \left(1 + \frac{1}{\frac{x}{h}} \right)^{\frac{1}{h}}$

[warm shale]

Kaisheng21

[fervent cradle]

anything?

[twilit meteor]

oh

raise it to the power x

and take 1/x outside ln

damn

[fervent cradle]

yeah i don't think i would have necessarily gotten that if i hadn't seen it before

well, maybe

[twilit meteor]

thank u @fervent cradle

.close

[obtuse pebble]

Channel closed

Closed by @twilit meteor

Use .reopen if this was a mistake.

[twilit meteor]

.reopen

[obtuse pebble]

✅

[twilit meteor]

wait can u allso give me a hint on how tofind indefinite integral of lnx

[versed stratus]

IBP

[fervent cradle]

for that one you just IBP

[twilit meteor]

i havent learnt that

[timid silo]

by parts

[twilit meteor]

is there another way

[twilit meteor]

yea i havent learnt that yet

[fervent cradle]

yeah idk then

[versed stratus]

all methods, would eventually require IBP

afaik

for instance, let $x=e^y$

[warm shale]

Why am. I here

[timid silo]

maybe it is possible without ibp let me cook

yup possible

sending sweet solution

[twilit meteor]

no

gve me a hint

idt u r allowed to send sol anyway

!nosols

[obtuse pebble]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[timid silo]

oh okay xd

so

[twilit meteor]

lmao funny that the prrson asking the doubt sends this

[timid silo]

😆

so

[twilit meteor]

yea

[timid silo]

first substitute

tru getting rid of lnx first

try*

[twilit meteor]

x = e^y

u get y.e^y

[timid silo]

yeah that would work

[twilit meteor]

dy

[versed stratus]

that requires IBP

[timid silo]

can be done without that, i just did

so you know whats special about e^x
derivative of e^x is itself so integration is too

[twilit meteor]

yea

oh

i got it

[timid silo]

?

say it

[twilit meteor]

d/dy (y.e^y - e^y) is exactly what we have

[timid silo]

mhm

take e^y common

so its e^y(y-1)

[twilit meteor]

yea

[timid silo]

and you got e^y y in your question

[twilit meteor]

so u get x(lnx-1)