help-23

[vapid anvil]

How

About this?

[safe radish]

@vapid anvil Has your question been resolved?

[safe radish]

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[split fulcrum]

I don’t understand, where does the inequalities come from

[quasi bison]

which one(s)?

[split fulcrum]

All of them

[quasi bison]

well, inequality #1 comes from Appendix F, wherever that is.

inequality #2 comes from rewriting tan as sin/cos in #1,

and the left half of inequality #3 comes from multiplying both sides by cos(θ) and dividing both sides by θ in inequality #2

the right half of inequality #3 comes from sin(θ) < θ.

[split fulcrum]

But why does sin theta < theta = 1?

[quasi bison]

nobody said theta was equal to 1.

did you mean "But why does sin(θ) < θ lead to sin(θ)/θ < 1?"

[split fulcrum]

Yeah

[quasi bison]

look at these two inequalities yourself and see if you can answer your own question.

[split fulcrum]

I don’t get it am I supposed to solve for something there?

[quasi bison]

no, you're not supposed to solve for anything.

i mean ok fine you don't see it

But why does sin(θ) < θ lead to sin(θ)/θ < 1?
dividing both sides by θ

[split fulcrum]

But if you divide both sides by theta doesn’t the sin(theta) cancel out and just become sin = 1

[quasi bison]

no

no it does not

$\sin(\theta)$ is not the product of a magical number called ``sin'' and $\theta$

[flat frigate]

Ann

[split fulcrum]

ok so I shouldn’t treat it like a normal variable

[quasi bison]

idk what "it" is

[split fulcrum]

The sin(theta)

[quasi bison]

you should treat it as an indivisible unit perhaps

[split fulcrum]

ok

and when it says the limit of theta as it approaches 0 of 1 = 1 is that given by the inequality

[quasi bison]

limit of theta as it approaches 0 of 1 = 1
bad wording

the limit, as theta approaches 0, of 1

is 1

because 1 is a constant

[split fulcrum]

I don’t follow

[quasi bison]

$\lim_{\theta \to 0} 1 = 1$

[flat frigate]

Ann

[quasi bison]

the limit of 1, as theta approaches 0, is 1

if only because wtf else is it gonna approach, 42069?

[split fulcrum]

I thought it was gonna be like 0.99999 or 0.9 or something like 1.000001

[quasi bison]

so you think that the number 1, a constant, could be somwhere beside itself.

1 is a constant. a CONSTANT!!!

A CONSTANT!!!!

[split fulcrum]

dayum alright

But how do we know the limit of cos(theta) as theta approaches 0 also = 1

[quasi bison]

is cos continuous?

[split fulcrum]

Yes

[quasi bison]

what's cos(0)?

[split fulcrum]

1

Why do we input 0 into cos tho

[quasi bison]

as theta approaches 0

[split fulcrum]

Oh right

So what does lim x-> 0 (sin(x)/(x)) = 1 actually mean?

Is that just a step to help differentiate it

[quasi bison]

are you asking about meaning or are you asking about applications

[split fulcrum]

Both I guess

[quasi bison]

$\lim_{x \to 0} \frac{\sin(x)}{x} = 1$ means $\lim_{x \to 0} \frac{\sin(x)}{x} = 1$

[flat frigate]

Ann

[quasi bison]

like, it is a statement of the limit of a function

the closer x gets to 0, the closer sin(x)/x is to 1

this limit is useful for finding other, more complicated limits, and also comes up in the proof of the derivatives of trig functions.

[split fulcrum]

Alright

Sin is the y value right and cos is x?

Or is it the other way around

So as x approaches 0, sin or the y value approaches 1?

[safe radish]

@split fulcrum Has your question been resolved?

[split fulcrum]

Grrrrrr

[quasi bison]

OH YEAH SORRY FOR NOT RESPONDING IN AN IMMEDIATE MANNER AND INSTEAD HAVING 20 MINUTE DELAYS

Sin is the y value right and cos is x?
sure but that notation is gonna be treacherous

[split fulcrum]

Apology accepted

[quasi bison]

the x you mentioned isnt the same as the x i wrote

here is the graph of sin(x)/x

[split fulcrum]

so as the limit approaches 0 on the x axis, sin approaches 1 on the y axis

[quasi bison]

hhghjskdgj

bad wording bad wording

im out of energy to fix your bad wording sorry

dont ping me

[split fulcrum]

Oh ma lord you can’t just abandon me that’s not very Ann like

Actually it is but still

[hot thistle]

@split fulcrum where are you at with this

[safe radish]

@split fulcrum Has your question been resolved?

[safe radish]

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[chilly summit]

hi guys just a simple question. if i had to write up a polynomial required to have roots of a different multiplicity. is a multiplicity of 1 valid, probably not but i want to be lazy 💀

[split ether]

Sure, but you can't have all of the multiplicities be 1

[quasi bison]

as stated, you can have multiplicity 1 but for at most 1 root

[safe radish]

@chilly summit Has your question been resolved?

[chilly summit]

alright thanks. im just scared our teachers are implying certain criterias without outright stating

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[safe radish]

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[proper canopy]

Hello, this is proving trigonometric identities

I wonder what should identity should i use to change 1-sec z

[tall bough]

try putting them in same denominator

[misty blade]

Do this

[tall bough]

Do that

[proper canopy]

How

[misty blade]

Take the LCM?

[tall bough]

just like how u add fractions

[proper canopy]

I’ll copy the denominator to the numerator?

[misty blade]

Exactly this

[tall bough]

Exactly that

[misty blade]

What is a/b+c/d?

[tall bough]

$\frac{a}{b} + \frac{c}{d}$

[flat frigate]

Fucktalogist

[misty blade]

Or a/b-c/d=?

[proper canopy]

Hmmm i don’t get it

[tall bough]

Whats $\frac{1}{5}+\frac{1}{10}$

[flat frigate]

Fucktalogist

[proper canopy]

3/10

[tall bough]

how did you do it

[proper canopy]

By adding them 1/10 and 2/10 = 3/10

[tall bough]

do same thing to your question now

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[woven garden]

help

[woven garden]

I need to know if i did this correctly

can someone check

[tall bough]

No

expand and see if youre correctr

[fleet condor]

It's wrong

but like above said you should be able to expand it back out to check your work

[woven garden]

what!

how is it wrong

can someone help me with it

is this the right answer???

[fleet condor]

it looks better, but you should try multiplying it back out to check your work

[woven garden]

is this better?

@fleet condor

[fleet condor]

its the same answer

I'm not telling you your answer is wrong

[woven garden]

but are the steps fine?

thats all i care about

[fleet condor]

I guess they are, although it looks weird to write it out like that

[woven garden]

how is it weird?

can you elaborate please

@fleet condor

[safe radish]

@woven garden Has your question been resolved?

[woven garden]

No

[safe radish]

@woven garden Has your question been resolved?

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[spring horizon]

grey= 20%
white=12.5%
black=30%
blue=37.5%

if 12 students chose black as their top choice and students could only choose 1 colour each, how many chose each of the other colours

[spring horizon]

pls help

[spice grove]

So if total number of students is say, T. You know that 30% of those people chose black, and you're given the value for that number.
Are you able to figure out T from here?

[safe radish]

@spring horizon Has your question been resolved?

[spring horizon]

so is there 100 students??

[spice grove]

How'd you get that? Show all your steps.

[spring horizon]

idk i guessed

i know u shouldnt but

[spice grove]

Let's try this again.
30% of some number T is known to be 12.

Can you write an equation for this?

[spring horizon]

T-12 = 70%

does that work

oh wait

nvm

it doesnt

[spring horizon]

wait this could work

wait nvm

@spice grove i need help

im so confused

[spring horizon]

<@&286206848099549185>

[mortal pawn]

Yeah

That’s how it is

No one is there

No one will help me either

[spring horizon]

oof

[mortal pawn]

I can help you tho

If 30% of a T is 12

of means multiply

that means you multiply 30% by T and set that equal to 12

[spring horizon]

oh

[spring horizon]

but what about the other ones

[mortal pawn]

You can set up the same equation

except now that you know T

You replace T with the number

[spring horizon]

oh so its 40?

[mortal pawn]

and set that equal to the variable you want to find

What

[spring horizon]

oo ok

[mortal pawn]

Yeah the total

[safe radish]

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[trim marlin]

8 x 1,3 x 1,3 x 1,3 x 1,3 x 1,3... I have n number of 1,3, how to write that as power (or any constistent way where the formula does not change as here by adding 1,3 for each of n)? 8^1,3n does not work.

[tepid walrus]

It should be 8(1.3)^n. You multiply 1.3 n times to itself, and then multiply by 8

[trim marlin]

Yes...

Thank you.

[tepid walrus]

no worries

[trim marlin]

I would think that that would also make some insane big number therefore not what I want, but actually you are right.

.close

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[pallid nymph]

Find the family of curves suc that the projection on the x axis of the part of the normal between (x,y) and the x-axis is 1

[pallid nymph]

Im thinking I need to find a nice differential equation in terms of -dx/dy, but am kinda struggling

[hot thistle]

what do they mean by that normal

[pallid nymph]

orthogonal to the tangent

[hot thistle]

are you sure? what’s with the “normal between (x,y) and the x-axis”

[hard crest]

yeah that doesn't make sense to me

[pallid nymph]

i thought it was like the segment of that length is projected onto the xaxis idrk

thats what the exercise says verbatum

[raven heart]

"the projection (...) is 1" what is that thing

[pallid nymph]

this is what ive been able to come up with, it's 3 b)

[hot thistle]

oh i think i might understand it

[raven heart]

,rotate

[raven heart]

fu

[pallid nymph]

,rotate

[raven heart]

has length 1

ok ok

[hot thistle]

ok no nvm i still don’t know

[raven heart]

the drawing zander made seems fine to me

[pallid nymph]

yea, im just struggling to set up an equation

is there any advice you've got?

actually wait, i can get an equation of normal and the x intercept

and the difference if x coordinates should be one

[raven heart]

the slope of that normal is y when you think about it

[pallid nymph]

oh shoot

yea

so then i solve -dx/dy= y and im done

[raven heart]

yea ig

[pallid nymph]

cool thx

.close

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[mighty sigil]

i got the answer, but im struggling to see why we make the vector field <0, x> or <y, 0>

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@mighty sigil Has your question been resolved?

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[lean otter]

i need help. pls

@whole acorn

<@&286206848099549185> pls

thx

[austere spade]

bruh

[hardy lion]

bruh

[lean otter]

@austere spade @hardy lion

these are qualifying questions my professor sent me to complete if i want to get into the Indian institute of science
he said these are baby stuff compared to what question we get in Indian Institute of Science

for me i can

it is under the mathematical troops act quote

[broken yew]

<@&268886789983436800> troll

[lean otter]

wtf?

@white umbra glory to russia

i am joking

i need help on question

now!

i used a lot of methods

[heady sphinx]

My gosh

What is that?

[lean otter]

non linear partial differential equations

[lean otter]

qualifying question for indian institute of science

[heady sphinx]

Bro noway they are qualifying questions

Bro how the hell Are you supposed to solve that

[lean otter]

indian institute of science is extremely hard to get into

what u mean?

these are baby question said my professor

[hardy lion]

Sounds like a troll professor

[heady sphinx]

Is it IISC u talking about

[lean otter]

yes

[heady sphinx]

Bro that shit is hard asf

[lean otter]

yeah... they are

[hardy lion]

Im pretty sure theres some stupid trick

[lean otter]

my professor said if i cant do this, i will not be allowed into the college

[heady sphinx]

Yea sure there is

[hardy lion]

But also like look at MIT integration bee if you want some legit "hard" integrals or something

[heady sphinx]

Ofc u can

[hardy lion]

This is just a stupid time waste

[lean otter]

for me yes. i have political connections. kinda sounds corrupt but still i gotta solve this crazy shiiit question

[heady sphinx]

Nah bro

Solve the entrance paper bro

U can get in that way

Bro gotta sleep

[lean otter]

i get to skip that step of i can show all the work to this question and get it 100 percent correct

or else i have to give entrance exam

[hardy lion]

Then its cheating to ask for help

[heady sphinx]

Yeah

[lean otter]

they dont know i am "cheating"

[heady sphinx]

Yeah it is somewhat cheating

[hardy lion]

We know

[lean otter]

i mean i dont think any of the around 1 million ppl in this server can solve this tho. but still i have a little hope in case.... just in case

[hardy lion]

<@&268886789983436800> "cheating"

[lean otter]

bangalore

the best one

[heady sphinx]

Yeah

[lean otter]

cheating? lo;

[heady sphinx]

Thats why it is hard asf

[lean otter]

i bet no one in here can solve this. so how can it be cheating until i get an answer

that makes sense?

[heady sphinx]

<@&268886789983436800> cheating

[lean otter]

ahhh. shhh.

can any of yall 1 million ppl solve this?

pls?

1 million ppl... stil cant solve a "simple baby" math question?

my professor said this was easy

and baby problem

me? i dont know. that is why i am asking!

yes saaaar

pls solve someone

thx

<@&286206848099549185>

these ppl cant help lol

[hardy lion]

Good luck in iisc or whatever

[lean otter]

ok thx

[tall bough]

you wont get into iisc

this too easy

[lean otter]

to get wrong? yes

[tall bough]

its pi

[lean otter]

can u show work pls?

if i dont show work, my professor will kill me

literally

he told me this ahhhhhhhh

or i can quit and get back to eating trash on the streets with the dogs

[white umbra]

Did your professor mean you to solve the problems by yourself?

[lean otter]

mo

no

i can ask anyone

i have to solve it within 1 dya tho

day*

[tall bough]

https://admission.aglasem.com/iisc-admission-sample-paper-research/

[lean otter]

i get to skip this process if i can solve the above question

[white umbra]

Don't ping helpers until after 15 minutes have passed.

[lean otter]

ok sir

or ma'am

[tall bough]

ur boring

go troll somewhere else

[lean otter]

troll? i need this answer!

[slate herald]

sigh

[broken yew]

@white umbra they're an obvious troll - see their msg history

across like 5 channels or some shit

[lean otter]

i need help

i have 1 damn day to solve this crap

[white umbra]

Also stop mentioning this question outside this channel.

[lean otter]

my professor is crazy mad

[lean otter]

ok sorry

my professor hates me bro

[tall bough]

whos your professor

[lean otter]

i cant mention his name.. might be security risk

all i can say is he is in india

lol

[lean otter]

i even asked a chinese person. even he got scared of the question. i asked a random one tho. so i think i was a little racist

lol

[white umbra]

Okay that's enough

.close

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[livid pebble]

why did they add cos?

[lean otter]

Sin(A+B) = sin(A)cos(B) + cos(A)sin(B)

A = arcsin(1/8)

[livid pebble]

ohh okk that makes sense. i have been learning that

[lean otter]

B = arcsin(3/4)

[livid pebble]

thanks a ton

.close

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[carmine pulsar]

how to do this someone <@&286206848099549185> pls

[carmine pulsar]

ive alr tried i dont get it

[safe radish]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[hidden quail]

I'm sorry, I haven't learned this concept yet, please be patient and I'm sure someone will come

Thankyou

[dense prism]

tan(theta+alpha)=4/x
tan(alpha)=1/x

Take tan inverse in both equations

[willow bone]

are you giving test???

[light shoal]

what part are you stuck on?

[safe radish]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[light shoal]

classic, ask for help, ping helpers, and then disappear

[carmine pulsar]

na

i had emergency

but its fine now

thanks for help

[carmine pulsar]

i got it now

.close

[safe radish]

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[gleaming oriole]

i know how to do this for right triangles?

[gleaming oriole]

but im a little lost

[delicate bobcat]

Im not sure what your class defined as "Triangle Inequality Theorem" for you, but basically

For any triangle, the largest angle is opposite from the largest side

The middle side is across from the middle angle

[static hedge]

this is very similar to ur worksheet

[delicate bobcat]

The smallest side is across from the smallest angle

[static hedge]

remember the 2nd blank for the 2nd questoin?

[gleaming oriole]

zedzilla connected the dots! i was in the right direction i think, but i was missing part of the theorem

thank u!

.close

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[round parrot]

I need help with this. Idk the slope or y-intercept because there's 3 points

[light shoal]

well it's definitely not a line

otherwise the guy's temperature would be a lot higher than 102.4 after 2 hours

[round parrot]

exponential function?

[light shoal]

not enough info to say

[round parrot]

How i proceed

[royal kiln]

they want the line of best fit, probably

do you have notes on regression lines?

[round parrot]

I learned the best fit lines but i forgot how to do them

So Which points do I use

[royal kiln]

all of them

they only gave you three

you need those notes

[round parrot]

ok

[royal kiln]

here are the formulas:

https://www.varsitytutors.com/hotmath/hotmath_help/topics/line-of-best-fit

[round parrot]

ty

[royal kiln]

by the way in real life you would almost never use all the points and would certainly want more than 3. You would discard points that fall outside two standard deviations from the mean (outliers)

[round parrot]

i see

Thanks, Have a good day or night(idk which timezone ur in

[royal kiln]

you got it then?

[round parrot]

yeah I think I got the first questions but ill come back if I have anymore questions

[royal kiln]

ok, goodnight

[round parrot]

gn

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[wraith prism]

It says if this value is 0 then find x

[wraith prism]

Any short idea?

[final plinth]

C1 -> C1+C2+C3

[tiny patrol]

well did u take the determinant?

[final plinth]

and if you put 0 then determinant is clearly 0

[quasi bison]

i'm getting big brain linear algebra ideas

[wraith prism]

Please share

[wraith prism]

0 where to which value?

[quasi bison]

you're asked to give the eigenvalues of the matrix $\bmqty{-a&-b&-c \ -a&-b&-c \ -a&-b&-c}$

[tiny patrol]

if x is 0

[flat frigate]

Ann

[tiny patrol]

the determinant is 0

[final plinth]

put X=0

[tiny patrol]

so 0 has to be one of the answers, which rules out two of them

and then guess and check for positive a+b+c or negative a+b+c

[quasi bison]

ok nevermind i do not know how to phrase my idea without complications

abort

[final plinth]

after putting x=0, do this then you can factor x+a+b+c

[split ether]

With visual understanding of what this matrix does to R^3, the nontrivial eigenvalue becomes clear

[wraith prism]

I checked for x =0 it determinant is 0

[wraith prism]

I'll come to your method soon.

[quasi bison]

don't

[split ether]

Why though, you could just ask them what happens to the (1, 1, 1) vector for example

[wraith prism]

How to do it?

[final plinth]

do C1->C1+C2+C3

[wraith prism]

I have done it

And got this

X=0 del is 0

Still 2 options remaining

[final plinth]

you should get x+a+b+c in each element of column 1 by c1_>c1+C2+C3

[wraith prism]

Yes got it

And taken out common and determinants values is 0

But still 3,4 options remaining

[final plinth]

x+a+b+c * det =0

x+a+b+c=0

x=-(a+b+c)

[wraith prism]

Ohh this one

Gotcha

I got another method this question

A=b=0
C=1

. close

.close

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[wraith prism]

.reopen

[safe radish]

✅

[wraith prism]

Can we talk about this?

I want to know how it works

[split ether]

Basically, since each basis vector goes to (-a, -a, -a), (-b, -b, -b) and (-c, -c, -c) respectively

The entirety of R^3 gets mapped to the line x = y = z

And the vectors that lied on x = y = z even before the transformation are essentially eigenvectors

Meaning you could pick any vector from the line x = y = z, look at what happens to it when multiplied by the matrix, and figure out the nontrivial eigenvalue

Let's pick the vector (1, 1, 1)

[split ether]

Multiplying it by this matrix yields (-a - b - c, -a - b - c, -a - b - c)

Or simply -(a+b+c) * (1, 1, 1)

Hence -(a + b + c) is an eigenvalue

[safe radish]

@wraith prism Has your question been resolved?

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[wraith prism]

1 isoceles triangle
2 equilateral
3 right angle triangle
4 rightangled isoceles

[split ether]

The determinent would be zero when there's a pair of linearly dependent column/row vectors, think about this

[wraith prism]

How to check they are linearly dependent?

A+kb

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[wraith prism]

Any short method to solve?

[wraith prism]

C3 is linearly dependent on c2

[vivid stone]

haan bhai

ek method aur hai @wraith prism

[wraith prism]

Batao

Aage kya karna h vaise isme

[vivid stone]

determinat pata hai?

english mai bolte hai?

[wraith prism]

0

[vivid stone]

ye jo hai

hindi mai nahi pata kya bolte hai

toh kya hai

[wraith prism]

Ha malum h bhai

[vivid stone]

ase determinat mai

tu kya kar sakta hai ki

jo last walli row hai na

jisme +1 hai

ruke karke photo bhejta hu

[wraith prism]

Thik h bro

[vivid stone]

hogaya

[vivid stone]

@wraith prism bhai ho ?

[wraith prism]

super

ye determinant yad kiya hoga????

[vivid stone]

bhai g**d lagti hai isme toh

merko bhi thode bhut yaad hai

ez hai hai vase i take my words back

ek pattern mai yaad kar

tu jee wala?

[wraith prism]

ni yar

pr jee wala man lo

[vivid stone]

😂

hmmmmm

[wraith prism]

[vivid stone]

koi na

[wraith prism]

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[lean otter]

Rounding of to the nearest significant digits is a concept mixed with other concepts, is there any question of a level of International math olympiad, which involves this concept. Probably a concept of number theory or sequences and series...

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[karmic hedge]

No. Sig figs don’t come in Olympiad, Olympiad is proof questions

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@lean otter Has your question been resolved?

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[solemn vault]

Hi

[solemn vault]

Is this ok

?

[hot thistle]

the right term, you assumed x = 3q+1?

[solemn vault]

And x=3q

x²=9q² = 3×3q²= 3k

[hot thistle]

you should be saying x^2 = 3q or x^2 = 3q+1

not x

[solemn vault]

[hard crest]

i don't understand this step

these steps (either one)

[solemn vault]

3x(x²+5)

I assumed x=3q (which I'm wrong)

x² -> 3q

9q(3q+5)

[hard crest]

don't assume anything about x

just work with x^2 = 3q

[solemn vault]

OK but If I say that then I'll end up with
$$3x(3q+5), 3x(3q+6)$$

[flat frigate]

_basudev

[solemn vault]

So second one is divisible by 9

3x(3(q+2)) => 9x(q+2(

[hard crest]

ok you might have to do some things with x for the first one

[solemn vault]

But what about the the first ons?

[hard crest]

if x^2 = 3q what's going on with x

[solemn vault]

X is a positive number...and divisible by 3

[hard crest]

yeah so x isn't 3q but x is 3 times something

[solemn vault]

Ahhh...no Ig

x²=3q only if x is in the form of 3r

x²=3q+1 only if x is in the form of 3r+1

[hard crest]

don't use q for the same thing twice like that!

use r or something

you've already shown it for the x^2 = 3q+1 case

all you have left is the x^2 = 3q case

[solemn vault]

Yes
$$9 \nmid 3x(3q+5)$$

[flat frigate]

_basudev

[hard crest]

uhh

didn't you say x was 3r in this case?

[solemn vault]

.

[hard crest]

yeah but you showed that

[solemn vault]

So I'm right then

?

[hard crest]

it's the right idea i guess

but you're using q to mean two different things in the same equation

if you just want to say you're working mod 3 that's fine

[solemn vault]

there's x=3q+2

But
x²= 9q²+4+12q
x²=3(k)+4 (not possible)

So only case that remains is

x=3q or x=3q+1

Which is belive should do it...

[hot thistle]

why is x^2 = 3k+4 not possible?

[solemn vault]

a number divided by 3 can't leave a remainder of 4??

[hot thistle]

a remainder of 4 is the same as a remainder of 1

[solemn vault]

So not possible m

[hot thistle]

3k + 4 = 3k + 3 + 1 = 3(k+1) + 1

[solemn vault]

Oh

So it's the same case

Mb I thought its not possible

So is my idea right?

Or wrong?

[hard crest]

if you have x = 3q + 2
then we established that x^2 = 3k + 1
which you already took care of, it was the stuff on the right

you original paper was largely correct except some of the q's should have been r's

[solemn vault]

Alr then

Thanks for the help

I Appreciate the time

.close

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[wraith prism]

I am having difficulties with decimal to binary/hexadecimal,octal conversion

[wraith prism]

If someone knows easy way please share

[worthy hemlock]

Google videos

[solemn vault]

Decimal to binary

Continueously divide by 2 and collect the remainder from bottom to top...

[lean thorn]

yeah tbh this is the best way to learn. Organic Chemistry Tutor has all conversions in videos

[worthy hemlock]

Definitely easier to follow and watch the videos then explain by text

[wraith prism]

I tried this Youtube

[worthy hemlock]

What video did you use

[wraith prism]

Some videos in Hindi

[worthy hemlock]

https://www.youtube.com/watch?v=rsxT4FfRBaM&ab_channel=TheOrganicChemistryTutor

https://www.youtube.com/watch?v=QJW6qnfhC70&ab_channel=TheOrganicChemistryTutor

https://www.youtube.com/watch?v=ayul1fmZd0Y&ab_channel=TheOrganicChemistryTutor

[worthy hemlock]

Tbh this is primarily the one you need, because if you group binary into groups of 3, that's 1 oct

And 4 bits in bin is a hex

[wraith prism]

Both methods he explained very easily

First method is new one

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[wraith prism]

Elementary Number Theory:
Peano’s Axioms, Principle of Induction; First Principal, Second Principle, Third Principle, Basis
Representation Theorem, Greatest Integer Function, Test of Divisibility, Euclid’s algorithm, The
Unique Factorization Theorem, Congruence, Chinese Remainder Theorem, Sum of divisors of a
number. Euler’s totient function, Theorems of Fermat and Wilson.

[wraith prism]

Can anyone link any book/pdf for these topics?

[worthy hemlock]

Google them yourself, we aren't google

And use #book-recommendations

[wraith prism]

Bro you didn't understand the question actually

I can find these topics separately in google

[hot thistle]

...Test of Divisibility, Euclid’s algorithm, The
Unique Factorization Theorem, Congruence, Chinese Remainder Theorem, Sum of divisors of a
number. Euler’s totient function, Theorems of Fermat and Wilson
all of these you will find in any introductory algebra book

e.g. dummit & foote, or fraleigh

Peano’s Axioms
this you can easily find in a set theory book
e.g. naive set theory by halmos

Principle of Induction; First Principal, Second Principle, Third Principle, Basis
Representation Theorem, Greatest Integer Function
no idea, but probably in any random introductory number theory book

[wraith prism]

Yes. This is helpful thank you maximo

[lean otter]

For the last bunch, I recommend Kenneth rosen's "Discrete Math and its Applications"

[wraith prism]

Hard to find this one

[hot thistle]

here's one

oh induction will be in any set theory book as well

[quasi bison]

third principle what even is that

[hot thistle]

what are the first 2

[solemn vault]

@wraith prism
For number theory

The book called Modern olympiad by Aditya Khurmi is also gud

All the things you've mentioned has been covered in that buk

[safe radish]

@wraith prism Has your question been resolved?

[solemn vault]

You want other books as well

?

Structures, Examples, and Problems by
Titu Andreescu & Dorin Andrica

[wraith prism]

Yes

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[split fulcrum]

Need some help on question 8 part h

[split fulcrum]

Not sure what to do first

And I don’t know if it’s the log base 10 of x or if the - 2 is included

Like log base 10 of x-2?

[hot thistle]

try isolating the log first

[split fulcrum]

Or is it separate

[hot thistle]

log_10(x) - 2

[split fulcrum]

What do I do with the other numbers like the 3 in front of the log

[hot thistle]

let me ask you a similar question

solve for y:
3y - 2 = 10

[split fulcrum]

3y = 12

y=4

[wraith prism]

Nice

[hot thistle]

notice the similarity between that

and 3(log_10(x)) - 2 = 10

[split fulcrum]

oh

yeah

[wraith prism]

Question number?

Oh H

[split fulcrum]

Like this?

[hot thistle]

yes

[wraith prism]

Yes

[split fulcrum]

Oh

[wraith prism]

No no

[split fulcrum]

I keep forgetting that basic algebraic operations still exist in logs

So what do I do from there

[wraith prism]

$10^x =4$

[flat frigate]

arjunn5589

[hot thistle]

now use
a^(log_a(x)) = x

[split fulcrum]

I don’t follow

[hot thistle]

10^(log_10(x)) = x

do 10^both sides

[split fulcrum]

Do I raise both sides to 10

[hot thistle]

no

do 10^(left side) = 10^(right side)

[wraith prism]

Xlog 10 = log 4
X=log4 / log 10
X = ?

Is this wrong?

[split fulcrum]

Like this ?

[hot thistle]

yes

[split fulcrum]

So does the log on LHS cancel out?

[hot thistle]

yes

[split fulcrum]

o

Wait but the x still stays right

10^x = 10^4

[hot thistle]

no

[wraith prism]

No no

X=10 ^4

[hot thistle]

10^(log_10(x)) = x

your LHS becomes x

[split fulcrum]

Why

[hot thistle]

(10^{\log_{10}(x)} = x)

[flat frigate]

maximo

[split fulcrum]

Oh okay

x = 10^4??

10000

[wraith prism]

Is this wrong?@hot thistle

[hot thistle]

yes

[hot thistle]

yes

[split fulcrum]

So we raised both sides of the equation to the base of 10 to cancel out the log on the left?

[hot thistle]

yes

[wraith prism]

It should be $ 10 ^4 =x $

[hot thistle]

yes

[split fulcrum]

For part e should I rewrite it as log base 5 of 5^-1 = x

[hot thistle]

yup

[wraith prism]

Yes

[split fulcrum]

and do we do that raising both sides to the base trick so 5 becomes the base of both sides?

[hot thistle]

you don't need to do that

once you have log_5(5^-1) = -1 * log_5(5)

[split fulcrum]

Oh

[split fulcrum]

and then because of log base 5 of 5 that becomes 1 and then multiplied by -1 so LHS is -1 = x?

[wraith prism]

Yes

[split fulcrum]

👍

[wraith prism]

U can feel it directly

What can be the power which can make 5 to 1/5

Only (-1) power so x=-1

[split fulcrum]

Oh yeah true

[wraith prism]

Any more doubt?

[safe radish]

@split fulcrum Has your question been resolved?

[safe radish]

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[lean otter]

are hessians of polynomials always symmetric?

[devout shale]

not to come off as rude or anything, but have you tried googling this?

[lean otter]

i tried chat gpt

[devout shale]

try google instead

[hot thistle]

consider not asking gpt

[devout shale]

chatGPT is bad

it will just lie to you

[lean otter]

ok lol

[devout shale]

and be very convincing

[lean otter]

even gpt4?

[devout shale]

yes

[hot thistle]

also mathew, note that the hessian is symmetic if the second partials are continuous

[lean otter]

okay lmaoooo

ok thanks sounds good

[devout shale]

all chatGPT does is gather text off the internet, and try to 'guess' how to best put those most common words together to answer your question

[hot thistle]

this should be easy to check for a polynomial

[devout shale]

it has no idea how to do math

[hard crest]

this is also, like, a fairly well-established thing there are many people who have talked about this online before and have prepared lessons etc

[lean otter]

is there anything similiar for math or no?

[devout shale]

I mean there are lots of great calculators that can do suprisingly complex math

[hot thistle]

,w

[devout shale]

as for like answering word questions? not really?

[lean otter]

yea proof questions

[devout shale]

If you know how to fit the word question into a calculator

it could

[hot thistle]

there's proof checkers out there

[hard crest]

there are proof verifiers and to an extent generators

[devout shale]

like you

[lean otter]

[lean otter]

whwhere

[devout shale]

I'd just refer you to @hot thistle

[hard crest]

they don't read english they're more like programming languages

[devout shale]

just DM him as much as you'd like anytime of the day. treat his DMs like chatGPT and he will do it all for you

[hot thistle]

dont be mistaken

i will just say wrong stuff

[lean otter]

like gpt?

[hot thistle]

even moreso

[devout shale]

precisely

[lean otter]

okay

[devout shale]

pro tip

put GPT into GPT and ask if it is right

and then put that into GPT and ask if that is right

infinitely many times

and you will surely get a correct answer

it will converge

[lean otter]

it doesnt

yea it always says the last step wrong

-1^k

type thing

[devout shale]

alternating

XD

[lean otter]

.close

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[slow cobalt]

I've found out C to be 1.7 and I'm not sure if that's correct.
I'm not sure what's the point of all of this so if anyone can explain the question that would be great too.

[slow cobalt]

My "working"

[safe radish]

@slow cobalt Has your question been resolved?

[safe radish]

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[little cipher]

how do i find the circumfrance and area of this?

[little cipher]

i know the area of the half circle and triangle, but i don't know how to solve the circle segment

triangle + circle/2 = 49.2

[pseudo scroll]

Area of a sector is $\frac 12 \theta r^2$

[flat frigate]

neonperseus

[pseudo scroll]

Where θ is in radians

[little cipher]

what is a radiant?

[pseudo scroll]

Subtract the area of a triangle from this measure

[pseudo scroll]

Well it's the SI unit for measuring angles

180° = π rad

Can you tell me how much 60° would be

[little cipher]

60= pirad/3?

[pseudo scroll]

yes π/3

So what is the area of that sector

[pseudo scroll]

Using this

[little cipher]

what is rad equal to?

[pseudo scroll]

nothing, it's just a unit like degrees

[little cipher]

1/2*25?

[pseudo scroll]

θ = π/3

[pseudo scroll]

Uh, no

What's the value of the radius?

[little cipher]

its not 5?

[pseudo scroll]

It's 10

Imagine that arc being extended into a whole circle

What would the radius of that cirlce be?

Talking about arc CB

[little cipher]

why is it twice as large?

[little cipher]

when extended into a whole circle?

[pseudo scroll]

Draw a circle containing CB, with A as the center

What would the radius of that cirlce be

[little cipher]

ahh

[pseudo scroll]

yes so the value of r in this formula is the radius of such a circle

So now you know θ and r can you find the area

[little cipher]

so pi/3*50?

[pseudo scroll]

yes

You need the area of what exactly, the shaded bit?

[little cipher]

the circumfrance and area of the figure

[pseudo scroll]

This is the area of sector ABC btw not triangle ABC

[karmic hedge]

You’re still confused?

Remember the picture

[pseudo scroll]

Now add 50π/3 to the area of the semicircle then

[little cipher]

so 52.3598775+15.7

[little cipher]

roughly 68.1

[pseudo scroll]

alright

[little cipher]

but how do i find the circumfrance of the segment?

[pseudo scroll]

Length of an arc is $r\theta$

[flat frigate]

neonperseus

[pseudo scroll]

You know θ and r

[little cipher]

10*pi/3?

[pseudo scroll]

yes

Now add that to the base of the triangle and circumference of the semicircle

[little cipher]

wait how come it's so easy?

[pseudo scroll]

wdym lol

[little cipher]

i didn't even finish this before i had to go to sleep, yesterday.

[pseudo scroll]

The definition of an angle $\theta = \frac{l}{r}$

[flat frigate]

neonperseus

[little cipher]

what is l?

[pseudo scroll]

Where l is the arclength and r is the radius

So we're just going backwards, finding the arclength using the angle and radius

[little cipher]

pi/3=x/10?

[pseudo scroll]

yes

[little cipher]

10.4719755?

[little cipher]

damn thank you

[pseudo scroll]

you're welcome

[little cipher]

.close

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[lean otter]

For $\ds W = \braces{\begin{bmatrix} a \ b \ 1\end{bmatrix}, a, b \in \R}$. Is $W$ a valid vector space

[lean otter]

I believe this should be closed under multiplication but not for addition, right?

[dull radish]

a valid vector space with unusual vector addition and scalar multiplication but not a vector subspace of R^3

[lean otter]

Oh it is valid?

How can you guarantee that the addition will be closed

well if it was a 0 instead of a 1 it would be easy right? the third element would always be just 0, so how could you handle this 1 then?

[dull radish]

Define (a_1, b_1, 1) + (a_2, b_2, 1) = (a_1 + a_2, b_1 + b_2, 1)

[lean otter]

Wait

[lean otter]

1+1 = 1?

[dull radish]

No

A vector space requires a set, a vector addition, and a scalar multiplication

You only specified the set

[lean otter]

Oh I see fair enough

[dull radish]

So it's not clear which vector addition and scalar multiplication is meant

[lean otter]

dont think about this addition as regular R³ addition, its a modified version

[dull radish]

If you regard it as a subset of R^3 with the usual vector addition and scalar multiplication, it's not a vector subspace

[mortal sandal]

yeah you can basically make any set a vector space with the right operations (unless the number of elements is finite and not a prime or power of a prime)

[lean otter]

hmmm okay thank you guys

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[lone arch]

By Gaussian elimination, we'll get a $k \in \mathbb N$ and a bijective mapping $\Phi \ : \ \mathbb{R}^k \rightarrow \text{Sol}(A, b) \subset \mathbb{R}^n$. \[5pt] Before this, it was defined that [A = \begin{pmatrix} a_{11} + & \dots & + a_{1n} \ \vdots & & \vdots \ a_{m1} + & \dots & + a_{mn} \end{pmatrix}, \hspace{1cm} x:= \begin{pmatrix} x_1 \ \vdots \ x_n \end{pmatrix}, \hspace{1cm} b:= \begin{pmatrix} b_1 \ \vdots \ b_m \end{pmatrix}.] \[5pt] Why does $k$ get introduced here?

[lone arch]

<@&286206848099549185>

[plucky elk]

You're conflating a few concepts. If you have a problem you're working on or a text you're reading, show it

[lone arch]

This is about a passage from my book. It says "By Gaussian elimination, we'll get a $k \in \mathbb N$ and a bijective mapping $\Phi \ : \ \mathbb{R}^k \rightarrow \text{Sol}(A, b) \subset \mathbb{R}^n$". I showed what was defined for $A, x$ and $b$ above. My question is why $k$ is introduced, what does it mean that by Gaussian elimination, we'll get a k with that mapping?

[hard crest]

you are in a much better position to answer this than we are since you have the rest of the book

my guess is that it has to do with underconstrained or overconstrained solutions

[lone arch]

So you would just continue reading?

Alright

[hard crest]

or I would look at stuff before

[lone arch]

It seems that they set $x_{r + 1} = \lambda_1, x_{r + 2} = \lambda_2, \dots x_{n} = \lambda_k$ later.

so they do a parametrization for all x except x_r

[plucky elk]

Just show the whole page or pages

[lone arch]

It seems k is only needed later. Thank you!

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[lean otter]

is this correct?

[lean thorn]

looks great!

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

okay, thanks!

[safe radish]

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[untold river]

Hello, I am trying to answer some of this

[untold river]

And while this is accurate for the year 1, on year 2 and 4, the answers are wildly off

(I have calculator screenshots if necessary)

[safe radish]

@untold river Has your question been resolved?

[untold river]

Some additional info, I strongly suspect the chart on the worksheet was created before the Google Sheets problems...questions...one of those

[safe radish]

@untold river Has your question been resolved?

[untold river]

I'm gonna use my one <@&286206848099549185>

[plucky elk]

which question are you talking about

[untold river]

So c) right now

My issue is the huge discrepancy between what google sheets is giving me, and the initial table at the top of the worksheet

[plucky elk]

show the answers

and how you know they're off

[untold river]

So that at the top is the equation

and I double checked it to make sure it lined up with the table

So if this is Year 1, rounded up, it matched

Year 2, but it's off by 0.04

[plucky elk]

...

that's fine

[untold river]

Okay, but when we get to year 4, which on the table is 67

This is what happened instead

[plucky elk]

models be like that

[untold river]

Hm

I'm also learning this on the fly

We also don't 100% understand what e^k is, and I can't seem to parse it from their lecture notes

[untold river]

I know what k is now

.close

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[mint cipher]

I'm confused about how to integrate it

[mint cipher]

Thats what ive tried

yup nope I tried by u-sub instead of ibp and just got a longer equation when doing it for terms of y

[safe radish]

@mint cipher Has your question been resolved?

[hard crest]

IBP looks good

then angle sum formulas

you might try doing the y integral first, that might make the numbers less annoying

[mint cipher]

oh okay bet

ty

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[strange fog]

What do I do with the factorials on the right?

I can’t figure out how to simplify it in order to find the limit as n -> infty

[plucky elk]

Doesn't matter what k is, could be 2,3, pi, etc.

Just don't change it

Then take the limit as n goes to inf

[strange fog]

I know that k is supposed to be a constant, but I don't know how I'm supposed to factor out the expression on the right such that it cancels out the factorials

If I expand it like $\frac{(k+1) \cdot 1 \cdot (k+1) \cdot 2 ... (k+1)n}{(k+1) \cdot 1 \cdot (k+1) \cdot 2 ... (k+1)n \cdot (k+1)(n+1)}$ will it work?

[flat frigate]

supah_x

[strange fog]

So will I be left with $\frac{1}{(k+1)(n+1)}$ for the expression on the right?

[flat frigate]

supah_x

[safe radish]

@strange fog Has your question been resolved?

[safe radish]

@strange fog Has your question been resolved?

[plucky elk]

Well can you take the limit of this if k=2

[safe radish]

@strange fog Has your question been resolved?

[safe radish]

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