help-17

[mint badge]

n o

wait

y e s

sorry

[marsh nexus]

okay thank you

[vocal sleet]

@marsh nexus Has your question been resolved?

[vocal sleet]

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[novel widget]

I've tried several times to prove it using induction, but I always bump into some obstacle that I can't resolve.

It seems to me that it is possible to prove as follows:
Base Case: ...
Induction Step: Let a set of 2(n+1) points in the plane with no three collinear be arbitrary. Using Lemma(that I dont know how to prove) we conclude that there exists a pair of point that would not have an intersection with any other segment. By Induction Hypothesis there exist such pairing of points for 2n other points. Since these two points do not have an intersection, we conclude that the statement is true for 2(n+1).

Maybe it is possible to somehow prove lemma using convex haul?

[edgy sapphire]

it's a really hard problem and induction won't be able to solve it

[novel widget]

Why not, logical form seems to work

[edgy sapphire]

instead of convex hull there's some way of looking at the 4 point version and comparing the crossed drawing with the uncrossed on

I only know a contradiction proof

[novel widget]

Can you share it with me, or at least give me a hint to prove?

[edgy sapphire]

oh yea here's a quote on it

It is easy to waste a lot of time failing to find inductive arguments (can we find a line with the same number of A-points and B-points on one side of it etc).

sure it's this putnam problem https://prase.cz/kalva/putnam/psoln/psol794.html
https://www.youtube.com/watch?v=AWspiqNvQfM for an explanation

[novel widget]

Thanks a lot

.close

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[gusty heron]

If 0 < p < q and 0 < r < s, then
A) s - q > r - p
B) q - s > p - r
C) pq = rs
D) ps > qr
E) qs > pr

[gusty heron]

How to use alegbraic in this problem?

[quiet echo]

uhm

you can multiply the inequalities

[gusty heron]

What?

[quiet echo]

i will show

[gusty heron]

Wait we can do that?

[quiet echo]

let 0<x<2 and 0<y<3

the maximum of xy would be 6, right?

and the minimum would be 0

since x can be at most 2 and y can be at most 3

so 0<xy<6

[gusty heron]

Ooo

Wait Im trying to

So the max can be pr, while the min is 0

Wait, how about the < sign

[quiet echo]

yes

so 0<pr<qs

[gusty heron]

I mean, x can't be equal to 2 so therefore I use 1,9999 and 2,9999

Wich 2,9999 × 1,9999

[quiet echo]

look at the answer choices

[gusty heron]

Ahh sorry

Max is pr, min is 0 hmmm. Therefore pr > q and s then

[quiet echo]

[gusty heron]

Yeah right lol

I think that makes sense

[quiet echo]

👍

[gusty heron]

How do you have high problem solving skill

Im in deficit state rn

[quiet echo]

i built my intuition

lmfao its that and practice

[gusty heron]

By doing what?

Well thanks anyway

Gotta lock in

.close

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[quiet echo]

idk tbh

you see something you notice someting

or just create it entirely on your own

like this

[gusty heron]

Does this tells me Im dumb

[quiet echo]

\begin{align}0<a<b \ 0<c<d\implies \ 0<ac<bd \end{align}

[twin meteor]

;(

[quiet echo]

oh lord

[gusty heron]

Yeah I think that makes sense

[kind light]

if you want to be cheaty just give p,q,r,s numbers

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[analog marlin]

how do I project points in 3d space onto a plane defined by 3 points in 3d space?

[vocal sleet]

Please don't occupy multiple help channels.

[gusty heron]

Indo??

Bjir it's rare to find fellow Indo here

[hushed pewter]

You'll need to use the outer product matrix

From your 3 points, you need to create an orthoronormal vector set that spans your plane

Then, you compute the outer product, which you can use for vector projections

[analog marlin]

How do you do that?

[vocal sleet]

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[vast shale]

Why when you add x to 2/5x it doesn’t become 2x?

[drifting jackal]

Why would it do that?

[vast shale]

Isnt x plus x=2x?

[drifting jackal]

Yes but that's not x + x

If you have 2/5 + 1, what would you do?

[vast shale]

1/1 and get a common denominator

[drifting jackal]

Yeah exactly, a common denominator, so it's the same process with 2/5x + x

You need a common denominator

[vast shale]

2x+x=3x right?

[drifting jackal]

How

It was (2/5), how did you get 2?

[vast shale]

No this is just a new example

[vast shale]

Actually I get it now

.5x+x=1.5x right

[drifting jackal]

Are you just giving examples of adding like terms?

[vast shale]

Yeah. Now I get it. For some reason the idea of adding like terms to a fraction didn’t make sense. I’m just slow

.close

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[hollow acorn]

that is a dime

what value does a dime have

[drifting jackal]

That's not even an answer choice

You should google it though

What do you mean how?

You were just told it's a dime, you can google something like, "what is the value of a dime"

[hollow acorn]

in google

or like any other search engine

huh

[drifting jackal]

What year are you in?

1st?

What does 1s mean

[kind light]

the first grade of secondary prob

so 7th?

[drifting jackal]

<@&268886789983436800>

[hollow acorn]

your mommy said you were special?

I speak french

[autumn trail]

How old are you?

[livid summit]

...

[autumn trail]

Okay cool. Discord tos requires you be 13 or older so I'd have to ban if you were younger.

[hollow acorn]

did you get held back 3 times

[rapid swift]

woah we have the same birthday

[livid summit]

obvious troll

.close

pls

[kind light]

whats nevuvel btw

[sharp lynx]

It's already closed

[vocal sleet]

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[woeful prawn]

Can someone please help me on this probability question

[bright niche]

Try mapping it into 2 dimensions maybe and then see how many paths lead to the bottom?

Idk

[woeful prawn]

love your name bro

[bright niche]

Thx

[woeful prawn]

ik you're not a helper but can you assume that the ant goes backwards (like he goes down a step and then goes up a step so at the end, he didn't really go anywhere)

[bright niche]

Probably

I mean that counts as 2 steps so I would say ye

[woeful prawn]

so is there 13 total possible steps he could take?

[bright niche]

Idk 🤷‍♂️

[woeful prawn]

i have the probability knowledge of a 1st grader bro

<@&286206848099549185> please help

[languid sparrow]

I got u bro

[woeful prawn]

thanks

[languid sparrow]

Let’s split this into two: first step and second step

First step has to be down obviously

[woeful prawn]

second step he could go sideways, down, or up again

[languid sparrow]

Just assume it’s at the middle left point

[woeful prawn]

yeah that's what i did

[languid sparrow]

He can either go back up, right, left, or down

We want down

[woeful prawn]

so there is a 1/4 chance of that happening?

[languid sparrow]

Yessir

See

You got this

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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.

[woeful prawn]

so the answer is 1/4 or am I not done yet

[willow iron]

u done

[woeful prawn]

oh ok

[languid sparrow]

Yeah

👍

[willow iron]

srry i just finished reading the question LOL

[woeful prawn]

i overthought the entire question lol

[languid sparrow]

It’s all good

[woeful prawn]

i thought it was going to be harder since it's aops

thanks

.close

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[languid sparrow]

Oh is that alcumus?

[woeful prawn]

nah it's homework

[languid sparrow]

Oh

Ok

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[candid tinsel]

Could someone explain why the first and last table are isomorphic?

[near geyser]

by considering the order of the elements, there is only one isomorphism to try

[vocal sleet]

@candid tinsel Has your question been resolved?

[candid tinsel]

Sorry, could you elaborate on that?

[vocal sleet]

@candid tinsel Has your question been resolved?

[half imp]

The order of an element is the number of times you need to multiply it by itself to get the identity

In an isomorphism, the order must be preserved

[vocal sleet]

@candid tinsel Has your question been resolved?

[lilac pebble]

e->e
a->b
b->a
c->c
use * for group a
we have f(a*b)=f(c)=c=ba=f(a)f(b)
show f(x*y)=f(x)f(y) for the remaining combinations

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[halcyon oracle]

hi i think im having a brain fart and i hope you can help me

I am reading a math paper and they have a frequency table where for the value of 0 there is 4 instances of it

but in the raw data on the left there are no instances whereh the value is 0

can someone explain how i might be misinterpreting it?

[whole zealot]

Add one to the "number served every 2 minutes" values on the right.

I don't know why, but that gives the proper value.

Could be an error.

[halcyon oracle]

?

[whole zealot]

Add one to each value in the "number served every 2 minutes" column.

[halcyon oracle]

oh ok ty

.close

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[primal hedge]

how do i find h(x+1) for h(x)=8x-6?

[mental egret]

plug (x + 1) in place of x ?

throughout in the given equation

[whole zealot]

Plug (x + 1) in place of x throughout (h(x) = 8x - 6).
h(x) = 8x - 6
h(x + 1) = 8(x + 1) - 6
= 8x + 2

[primal hedge]

why does it change the 6?

[vocal sleet]

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.

[mental egret]

Did you do as I said? plugging x + 1 in place of "x" in the equation?

[whole zealot]

h(x + 1) = 8(x + 1) - 6
= 8x + 8 - 6
= 8x - 2.

Sorry for the over-simplification.

[primal hedge]

yeah i got h(x+1)=8(x+1)-6

[mental egret]

Yes.

now expand the brackets

[whole zealot]

Wait, I made a mistake.

[primal hedge]

ah thanks i got it

.close

[mental egret]

gr8

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[keen kettle]

hey can someone help me find the perimeter this question came in my topical test

[vocal sleet]

@keen kettle Has your question been resolved?

[lost barn]

alright

so the first thing to notice @keen kettle is the segments each vertical length opposite of AB must add up to 11

the much harder part, however, is the horizontal part

i thought i had something going but realized it wasnt possible

could you send the question to make sure the diagram is correct?

[vocal sleet]

@keen kettle Has your question been resolved?

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[topaz haven]

How can we simplify this?

[topaz haven]

This is the answer btw

If someone can show me how using paper or smth, like the steps of it

[ornate terrace]

difference of squares

[topaz haven]

That would mean a lot 💕

[ornate terrace]

helpers will probs not do this and just walk you through it

[topaz haven]

I’m not sure how it’s done but the subject is “multiplying and dividing rational expression”

[ornate terrace]

ok uh

[topaz haven]

Hope so, it’s just I struggle with learning easily but whatever helps ngl

[ornate terrace]

do you know how to factorise a^2-b^2

[topaz haven]

Yes

It’s divided in two ( )

[ornate terrace]

yep can you write it out

[topaz haven]

(a-b) (a+b)

[ornate terrace]

yep

[topaz haven]

That yeah?

[ornate terrace]

this is the principle you use

first, factorise the 3 out of the denominator terms

[topaz haven]

I know but I got a different answer, lemme write it in a paper

[topaz haven]

Mhm I see

This is what I came up with 🫠

[ornate terrace]

the 3 is where you have trouble

[topaz haven]

It should be outside the ( )?

[ornate terrace]

yep

[fiery elbow]

,rotate

[fiery elbow]

this is wronge

[topaz haven]

This is how it’s supposed to be like?

[fiery elbow]

yep

[topaz haven]

I know lol ;(.

[ornate terrace]

one of em should be +

[topaz haven]

Okay thanks :D 💕

[fiery elbow]

(c-d)(c+d)

[topaz haven]

Oh shit yeah I forgot about the rule

[fiery elbow]

tiny mistake

[topaz haven]

Then I remove the similars

[ornate terrace]

ye

[topaz haven]

Mhm figured

[ornate terrace]

lmao

bro

the numerator is c+d

[topaz haven]

Okay okay I see

I just noticed the top one was +

I wrote it wrong on the paper

Anyways thanks so much for your help :D! 💕💕

[ornate terrace]

ye, thats your only mistake rn

remember to close when youre done

[topaz haven]

Thanks again!!!

.close

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[smoky pebble]

i got gamma fn as ans any easier way?

[mental egret]

Idts. $N = 4\pi n_0 \int_0^{\infty} r^2 e^{-\alpha r^4} \dd r$

[twin meteor]

Arya

[desert hornet]

You just need the proportionality between N and alpha so you don't actually have to solve the integral

[desert hornet]

Just substitute u = alpha r^4 here and make it so that the integral is a constant

[lost barn]

I would do u = r^2

[desert hornet]

the point is to get rid of the alpha from inside the integral

[lost barn]

Actually maybe not

[lost barn]

Yeah I think either way ur left with some weird integrand stuff

So u = ar^4 is better

[mental egret]

$N = C_1 \int_0^{\infty} \frac{u^k \cdot e^{-u}}{\alpha^{3/4}} \dd u$

@smoky pebble this helps :o

[desert hornet]

this doesn't look right

[mental egret]

Huh? (@_@;)

[lost barn]

With that substitution I also get the gamma function

Something proportional to gamma 5/4

[desert hornet]

yeah gamma 5/4 sounds about right

[twin meteor]

Arya

[mental egret]

smh ;-;

[desert hornet]

you didn't do the substitution properly

[mental egret]

Yeah I saw. The simplification was done hastily

[vocal sleet]

@smoky pebble Has your question been resolved?

[smoky pebble]

ik just wondering

how ud solve it

[desert hornet]

it's just the gamma function

you can't simplify Gamma(1/4) any further

it's just a constant the same way pi or any other number is a constant

[smoky pebble]

hm

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[glad bloom]

Hey, wanted to ask in general if someone knows how good Chat GPT is at creating some tasks? I have these topics right now (Im german, not sure if these are named like this in english):

Propositional logic, sets, relations, mappings, number sequences, convergence of number sequences & proof techniques such as complete induction

Or is there a specific ChatGPT Version / Model that is recommended?

Because i don't have any tasks from the university anymore and wanted to do some

[hard atlas]

get a textbook

!nogpt

[vocal sleet]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[glad bloom]

I see thanks unfortunately the stores a closed here sundays, i have a exam tomorrow. I just wanted to check how good i can solve some stuff, or is there at least some kind of website with tasks like these?

Because im already through all the stuff we got from university

[wraith python]

Google --> subject filetype:pdf

[silver tusk]

maybe go to youtube

[glad bloom]

Thanks i will try this one 👍

[glad bloom]

Ah yeah, will do this too thanks

[whole zealot]

Try looking up practice sheets for the subject.

[hard atlas]

there are probably thousands of exercises on the internet

also doesnt hurt to look up old exams

sometimes you can find some

[wraith python]

Course websites will sometimes have old exams available for download.

[glad bloom]

kk will do ty, did the old exams already unfortunately. Will look if i find more tho thanks

[wraith python]

What subject are you looking for?

[glad bloom]

A few, im not sure if those are also written the same way as in german: Propositional logic, sets, relations, mappings, number sequences, convergence of number sequences & proof techniques such as complete induction

[wraith python]

Discrete Math

[glad bloom]

Alright thanks 👍

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[wet oar]

for some background rest of the problem that I did before

[devout kindle]

f'(x) represents the slope of function

so you just have to see where slope is minimum

[wet oar]

could I have a little more help

[obsidian vigil]

do you know how to find minimas?

[wet oar]

yes

[obsidian vigil]

and how do we do that?

[wet oar]

f''(x)>0 at a critical point where f'(x) = 0 or DNE

[obsidian vigil]

yes but here we need the minima of f'(x) not just f(x)

[devout kindle]

(hint: f'(x) represents slope and slope is also determined by tan theta)

[obsidian vigil]

so if we wanna find the minima of f(x) we need to differentiate it right?

[wet oar]

so is it where f''(x) swaps from decreasing to increasing

[obsidian vigil]

it was correct before the edit haha

[wet oar]

oh lmfao

[obsidian vigil]

ok so we need to find the minima of f'(x) which is when that function goes from decreasing to increasing

that's just when f''(x)=0 and f'''(x)<0

[mental egret]

Yes

And you already evaluated when f"(x) = 0

[obsidian vigil]

yup

[wet oar]

since theres only one value of f"(x) = 0 if there is a rel min it has to be at 0

tysm

[obsidian vigil]

here yes, but generally you should check the double derivative too to make sure its not a maxima

cause both the maxima and minima would have the first derivative = 0

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@wet oar Has your question been resolved?

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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.

[sturdy venture]

how to identify the limit here

[sturdy venture]

correct me if I'm wrong for the first one the limit is +∞, for the second one its -∞, and for the last its -∞?

[obsidian vigil]

whi -inf for 3?

[sturdy venture]

huh

whi?

what is whi

[obsidian vigil]

why*

oh wait

nvm

ur right

i didnt see the - on the limit in the 3rd one

[sturdy venture]

because the leading coefficient is 6 and its exponent is 7 which is odd therefore its -∞

am I right?

[obsidian vigil]

yup

[sturdy venture]

additional question

[obsidian vigil]

sure

[sturdy venture]

using rationalization it gives me that the limit is 3

but when I checked it in app its DNE

why is that?

but if using direct substitution, you get 2/0 or indeterminate

[obsidian vigil]

what did u do

[obsidian vigil]

cause the denominator isn't irrational

[sturdy venture]

rationalization method

[obsidian vigil]

u multiplied w sqrt(x^2-4)+2 ?

[sturdy venture]

check if this makes sense

[sturdy venture]

yeah

[obsidian vigil]

how is (x^2-8)=(x-2)(x+4) ?

[sturdy venture]

conjugate

[sturdy venture]

factor

[obsidian vigil]

try multiplying out the terms in the LHS

and tell me if it equals to rhs

[sturdy venture]

what's LHS

and rhs

[obsidian vigil]

left hand side of the equation

right hand side of the equation

[sturdy venture]

idk that in limits

[obsidian vigil]

just distribute the brackets in (x-2)(x+4)

and tell me what u get

[sturdy venture]

which brackets

[sturdy venture]

use foil method in this?

is that what u mean

[obsidian vigil]

yes

[sturdy venture]

oh

[obsidian vigil]

so

what did u get

[sturdy venture]

oops its rotated

so it's wrong

[obsidian vigil]

yes

[sturdy venture]

here's the full question

ait

wait

I used Direct substitution and rationalization already but the rationalization turns out to be wrong and idek how to perform factoring with that

[obsidian vigil]

i think your best bet would be to factorise the x^2-4 as (x-2)(x+2)

then we get sqrt((x+2)/(x-2))+2/(x-2))

oh wait nvm limit doesn't exist, so try evaluating from 2- and 2+

youll find that when evaluating from 2-

we get a negative value

but from 2+ we get positive

[sturdy venture]

huh

what 2- and 2+ 😭

[obsidian vigil]

you know right hand limit and left hand limit?

[sturdy venture]

I dealt with it in trigo but not in limits

[obsidian vigil]

ok so a function's limit at a point DNE when it approaches 2 different values from the left and right

now try to evaluate this function as it tends to 2 from the left and the right

[sturdy venture]

what method should I use

the only method I could think of with left and right is table of values

[obsidian vigil]

you dont need to

[sturdy venture]

wdym "it tends to 2"

[obsidian vigil]

like the x value approaches 2

[sturdy venture]

just by looking at this only?

[obsidian vigil]

yeah

just look at the function

and the sqrt part

sqrt(x^2-4)

[sturdy venture]

it's 0

[obsidian vigil]

yeah yeah

but this can't exist when (x^2-4) is negative right

[sturdy venture]

yes

[obsidian vigil]

when is x^2-4 negative

[sturdy venture]

wdym

[obsidian vigil]

like the values of x

for which x^2-4 is negative

[sturdy venture]

there's none because it's 0..?

[obsidian vigil]

bro

i mean

in general

[sturdy venture]

I don't get it 😭

sorry

oh

is it -4

[obsidian vigil]

bro bro

in general

when is x^2-4 negative

like gimme a range of values

[sturdy venture]

is it like -∞ such?

I'm lost 💀

[obsidian vigil]

girl just tell me atleast 1 value for x where x^2-4 is negative

[sturdy venture]

oh

1

that gives -3

[obsidian vigil]

yes great

[sturdy venture]

its that simple??? 💀

[obsidian vigil]

nono

im trynna build on this

[sturdy venture]

no i mean ur question

[obsidian vigil]

yes

[sturdy venture]

how dumb I am

💀

[obsidian vigil]

so obviously there will be a range of values for which x^2-4 is negative right

[sturdy venture]

yes

[obsidian vigil]

or actually forget that if we approach x=2 from the left can u tell me if x^2-4 is positive or negative

like for numbers very close to but smaller than 2

example 1.9999

[sturdy venture]

ohh that

[obsidian vigil]

yes

[sturdy venture]

that's what I'm talking about earlier

[obsidian vigil]

ye

[sturdy venture]

table of values

[obsidian vigil]

ya but here itll be hard to caculate cause irrational

[obsidian vigil]

js tell me this fro now

[sturdy venture]

neither

[obsidian vigil]

what

bro bro

[sturdy venture]

I mean

[obsidian vigil]

dont evaluate at x=2

[sturdy venture]

it's both positive and negative

[obsidian vigil]

we're approaching x=2

[obsidian vigil]

w h a t

[obsidian vigil]

so some number very close to 2 but smaller than 2

[sturdy venture]

wait wdym by your question

ahhh

1.9999 such

[obsidian vigil]

yes

[sturdy venture]

positive

[obsidian vigil]

how

[sturdy venture]

bcs 1.999 is positive?

[obsidian vigil]

yes but im asking for x^2-4

not x

[sturdy venture]

x²-4 and is not approaching to 2 but smaller than 2 that is close to 2?

negative

[sturdy venture]

if this what u mean

[obsidian vigil]

yes

[obsidian vigil]

YES PERFECT

[sturdy venture]

OMG

[obsidian vigil]

so if we take the sqrt of that

will it exist

[sturdy venture]

yes

[obsidian vigil]

how can u take the square root of a negative

[sturdy venture]

can't

[obsidian vigil]

yeah so how will it exist

[sturdy venture]

I inserted √(1.999)²-4 in my calc it gave me -2.0.. something so I thought it's like that

it doesn't exist

[obsidian vigil]

yesyes

so now can we say that the left hand limit doesn't exist

[sturdy venture]

yes

[obsidian vigil]

yes so will the 2 sided limit exist?

[sturdy venture]

no

[obsidian vigil]

EXACTLY

NOW WE GOT OUR ANSWER

YAY

[sturdy venture]

waittt

we didn't use this -

😭

[obsidian vigil]

did we not substitute the left hand limit as x tends to 2

[sturdy venture]

you mean √(2)²-4 -2 such?

[obsidian vigil]

this

[sturdy venture]

ohhh

I can't use that in my paper 😭

[obsidian vigil]

have u not learnt LHL and RHL??

[sturdy venture]

only among this-

[obsidian vigil]

bro that IS substitution

[sturdy venture]

in our class? not yet

[obsidian vigil]

its the same thing as the table

[sturdy venture]

the substitution I have learned yet is literal replacing the value of X's

[obsidian vigil]

what is the definiton of DNE you learnt?

[sturdy venture]

0/0

[obsidian vigil]

general definiton is LHL≠RHL

[sturdy venture]

or 1/0

[sturdy venture]

yeah that too

but in table only

this is what the direction substitution I mean

[obsidian vigil]

could've told me this earlier substitute x=2 you get -2/0

[sturdy venture]

i didn't know 😭

[obsidian vigil]

ya

[sturdy venture]

let me put the full solution and tell if its correct

[obsidian vigil]

just so u know the actual definition of DNE is LHL≠RHL

not 1/0 or 0/0

[sturdy venture]

okay okay

[sturdy venture]

I can put this now in my paper?

[obsidian vigil]

indeterminate and DNE are different

[sturdy venture]

oh

[obsidian vigil]

just erase the indeterminate and write DNE

[sturdy venture]

what are their difference

[obsidian vigil]

these are all the indeterminate forms of limits

[sturdy venture]

how about dne form

[obsidian vigil]

a limit does not exist if and only if LHL≠RHL

[sturdy venture]

does this mean like any number that is the denominator is 0

[obsidian vigil]

no

[sturdy venture]

except 0

[obsidian vigil]

no

[sturdy venture]

then?

[obsidian vigil]

this is an exhaustive list anything other than this is NOT indeterminate

[sturdy venture]

how can I say whether it's indeterminate or not

just like here

-2/0

and is DNE

[obsidian vigil]

i just sent u a list

if u get anything thats in that list

its indeterminate

[sturdy venture]

i see

I HAVE 2 MORE QUESTIONS, is that okay?? 😭😭

[obsidian vigil]

sure

[sturdy venture]

I feel guilty

[obsidian vigil]

no its fine

[sturdy venture]

okay..

so in 4

this is what I did in my paper

canceled x³

[obsidian vigil]

who told u that the limit evaluated is the same as the horizontal asymptote

[sturdy venture]

for no. 5 idk but I searched it says it's ∞

[sturdy venture]

organic chemistry? idk if I did the same though

[obsidian vigil]

W H A T

W H Y are u applying organic chemistry here

[sturdy venture]

it's the name of a channel in YouTube

[obsidian vigil]

oh

[sturdy venture]

you don't know him?

[obsidian vigil]

i know him

organic chemistry is also a subject

hence the confusion

anyways

limit is correct

do u know whats an asymptote

[sturdy venture]

this guy

[sturdy venture]

yes

[obsidian vigil]

what is it

[sturdy venture]

in graph?

this is an asymptote right

[obsidian vigil]

yes

but mathematically

an asymptote is when a function approaches infinity right

[sturdy venture]

no

[sturdy venture]

ahh

[obsidian vigil]

remember this

[sturdy venture]

yes

[obsidian vigil]

so this function will approach infinity when the denominator approaches 0 right

the asymptote is at the zero(s) of the denominator

[sturdy venture]

wait

[sturdy venture]

i don't get this

[obsidian vigil]

bro

whats 1/0

[sturdy venture]

undefined

[obsidian vigil]

yes so

if i have a denominator gets smaller

the fraction gets bigger right

[sturdy venture]

yes

[obsidian vigil]

so itll be the biggest when denominatorn is 0 right

[sturdy venture]

yes

[obsidian vigil]

so

this function will tend to infinity

when the denominator is 0 right

[sturdy venture]

yes

[obsidian vigil]

when is the denominator 0

[sturdy venture]

here we go again with when(s)

[sturdy venture]

if its undefined

[obsidian vigil]

yes but when is the denominator 0

for what x

[sturdy venture]

any number except 0

[obsidian vigil]

BRO

[sturdy venture]

?

what-

[obsidian vigil]

the function here

3x^3-4x^2+7

when is this 0

graph it and tell me

[sturdy venture]

idk how to graph that 😭

can we skip complex parts

like making me understand DEEPLY

[obsidian vigil]

the asymptote is the x value for which the function tends to infinity, which is the x value for which the denominator tends to 0

For this particular function 3x³-4x²+7 that's x=-1

[sturdy venture]

for this one

wrong image

5/3 is correct for the limit?

for 4

I'm guessing for 5 its ∞

[obsidian vigil]

Yea

Yeah

[sturdy venture]

but how to get the asymptote

isn't the limit also the asymptote?

[obsidian vigil]

This is how

No

[sturdy venture]

so in 4, the asymptote is ∞

and in 5 is 3

[vocal sleet]

@sturdy venture Has your question been resolved?

[obsidian vigil]

5 is 3 yes

but how is 4 infinity

[sturdy venture]

because you said the value of x is the asymptote

4 has ∞

[obsidian vigil]

i said the value of x where the denominator equals 0 is the asymptote

[sturdy venture]

then what is the asymptote of 4

[obsidian vigil]

where the denominator equals 0 is the asymptote

[vocal sleet]

Channel closed

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Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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

[onyx spade]

.how do i solve this

[manic linden]

can someone solve this i already know the answer to it so you wont but helping me with my "home work"

[manic linden]

and it isnt my homework

[atomic jasper]

!occupied

[vocal sleet]

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).

[atomic jasper]

someone got to the channel before you, use a different one

[devout kindle]

it's his channel, actually

[atomic jasper]

!status

[vocal sleet]

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

[manic linden]

fr

[atomic jasper]

oh wait, youre right

XD

how come the other message is on top?

[devout kindle]

XD

idk

bot glitch

or divine intervention

[manic linden]

just solve it please ig

[atomic jasper]

!nosols

[vocal sleet]

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.

[dense cedar]

They can show you the way, but you'll have to walk on it alone.

[quiet echo]

do you know the inradius formula

[manic linden]

nope

[manic linden]

BRO LOOK WHAI I HAVE WRITTEN

[atomic jasper]

the intersection of the 3 perpendicular bisectors give you the center of the circumcircle

[quiet echo]

k

[atomic jasper]

!volunteers

[vocal sleet]

Helpers are just people volunteering their time to help you. Be polite and patient.

[quiet echo]

let me get my formula sheet rq

[atomic jasper]

im just trying to help you bro, calm down

[manic linden]

sorry

my bad

i said its not my homework

the answer is 5.06

the working is also given in the mark scheme

[mental egret]

inradius why?

[manic linden]

if i had to copy i could

thats why im asking for helps

[quiet echo]

i forgot the terminology

[manic linden]

well i add that

[dense cedar]

Circumcenter

[mental egret]

circumradius is being asked

[manic linden]

i divided the 360 into the ratios

as ik the side CB = 7.41

its given in a previous part

[quiet echo]

yeah thats why it looks wrong

k

R=abc/4A where abc are side lengths and A is the area

[mental egret]

cos x = 4/R, cos(47 - x) = 5/R, would probably look pretty tough to get rid of "x" and solve for R

[quiet echo]

area can be calculated using 1/2 absin(C) formula

[mental egret]

I was gonna type this ✅

[quiet echo]

u alr know the side length

[quiet echo]

oops

[manic linden]

why cant this work

[mental egret]

but again, you'll need "a" for it to work

[manic linden]

$$ \frac{10}{10 + 8 + 7.41} \times 360 = 141.7 $$
$$ \text{which is angle ABO} $$

[dense cedar]

Why do I feel like, if I considered coordinates and found the vertices sides to find the circumcenter, it would be nearly the same work !
(0,0),(10,0) and (8cos,8sin)

[devout kindle]

i think he said a is given as 7.41

[mental egret]

instead, if you're gonna be doing it, use cosine law and go $(2R)^2 = \frac{b^2 + c^2 - 2bc \cdot \cos A}{(\sin A)^2}$

[twin meteor]

hades

Arya

[manic linden]

i know CB its 7.41

[mental egret]

Yes, but is it given in the question?

[manic linden]

yeah

in an earlier part

[mental egret]

Then 2R = BC/sin 47°

you're done

,calc 7.41/(sin(47 deg))

[twin meteor]

Result:

10.131896486741

[mental egret]

R = 5.06 approx

[manic linden]

can u explain

[mental egret]

sine law a/sin A = b/sin B = c/sin C = 2R

You should be able to visualize it as well

[manic linden]

why 2R

whats R

[mental egret]

R is circumradius

[manic linden]

whats a circumradius

its not there in my syllabus

[mental egret]

the radius of the circle that passes through the point A, B, C of the triangle ABC

[manic linden]

oh

yeah so

i dont have that formula tho

this the ms

$$ \frac{10}{10 + 8 + 7.41} \times 360 = 141.7 $$
$$ \text{which is angle ABO} $$

[twin meteor]

hades

[manic linden]

why wont this work

[mental egret]

this image explains the deal

[manic linden]

then i can use sin rule

[mental egret]

because, it is not a circle that you can divide the internal angle in the ratio of sides

It is only in a circle that the ratio of arc lengths = ratio of internal angle

[manic linden]

wdym

ohh

yeah

arc length and length are diff

thanks yo

[mental egret]

^^"

[manic linden]

yo thing is we could have used circle theorems aswell

COB is 96

as 47 * 2 = 96

[mental egret]

Yes that's true. But BC is not the arc length of the circle. Instead, it is a chord

[manic linden]

.close

[vocal sleet]

Channel closed

Closed by @manic linden

Use .reopen if this was a mistake.

[manic linden]

ye ye got it

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[half turret]

cos(x +45degrees) = square root of 3 / 2

[half turret]

i get it to +- 15 degrees + n x 360 degrees

but text book says -15 and -75

since cos(square root of 3 / 2) = cos(30degrees)

[quiet echo]

just to be clear, this is $\cos(x+45^{\circ})=\frac{\sqrt{3}}{2}$, right?

[twin meteor]

;(

[half turret]

yes

[quiet echo]

show work

[half turret]

1 sec

[quiet echo]

note that $x+45^{\circ}=\frac{\pi}{6}+2\pi\cdot k,\frac{11\pi}{6}+2\pi\cdot k$ for $k\in\bZ$

[twin meteor]

;(

[half turret]

so far in this trig class ive not used radians or "kez" so im not very familiar

anwser in book is cos x = -15 + n x 360 (degrees) & cos x =-75 + n x 360 (degrees)

@quiet echo heres work

[mental egret]

You're correct with the pos: -15° + n360°
For neg -> -x - 45° = 30° + n360° => -x = 75° + n360° => x = -75° + n360°

[vocal sleet]

@half turret Has your question been resolved?

[half turret]

why -x and where does the offset 360-x go? is this the wrong use case and if so, how do i recognize that is it?

@mental egret

what are the formulas for pos x and neg x

ive thought it was 180-v for sin and 360-v for cos

• n360

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[half turret]

.reopen

[vocal sleet]

✅

[mental egret]

Because cos y = cos(-y)

so if cos t = cos 30°, then it is my duty to put both t = 30° and -t = 30°

[half turret]

alright i understand that but ive used 360-v +n360 and it has worked so far, is this wrong and should i just format it like you did?

[mental egret]

yes this is wrong because 360 - (-15) + n(360) as you can see here, is just 15 + (n+1)360°, and unfortunately, 15° doesnot satisfy the equation

[past knot]

could someone help me

[mental egret]

instead, you should just put cos t = cos k => t = ±k + 360n

[past knot]

im having trouble with parabolas

[mental egret]

!help

[vocal sleet]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[mental egret]

Use #help-33

[half turret]

im sorry but what does k stand for?

.close

[vocal sleet]

Channel closed

Closed by @half turret

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[terse fiber]

If we want to express log(1/200) with log(2), it becomes -2-log(2), however I was thinking it would've been 2-log(2), but does the 2 become negative because if we simplify log(1/200) we get -log(2*100) = ....?

[atomic jasper]

,tex .log rules

[twin meteor]

Bonk

[atomic jasper]

Power rule, yes

$\log\left(\frac{1}{200}\right)=\log(200^{-1})=-\log(200)$

[twin meteor]

Bonk

[terse fiber]

Since you'd get -log(2*100) = -log(2) + log(10^2) = -log(2) + 2log(10), but that's wrong

[gaunt sparrow]

-log(2*100) =-(log(2)+log(100))
=-(log(2) + 2)

You’re just forgetting parentheses

[terse fiber]

Do we always have to put parentheses when - comes?

Just a general question now

[atomic jasper]

well, the - is on the log

so if you split the log, then the - is on both the terms

[terse fiber]

Ah alright, that makes sense, thanks :)

.close

[vocal sleet]

Channel closed

Closed by @terse fiber

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[vast shale]

is there usually a way to elaborate on this or i just write it in the calculator

[oak magnet]

-2log of what

[vast shale]

3*

sorry

idk how that was left off

log(10)3

[oak magnet]

I don't think you can do anything more

[vast shale]

thanks

[outer warren]

second and third terms could be simplified

using power and product to sum laws

which will lead to the simplification of the whole thing without the need of a calculator

[vocal sleet]

@vast shale Has your question been resolved?

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Remember:
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[last pine]

i got this wrong

[last pine]

the equation is y=mx+b is
y = 3/-7x-3

i checked on a graphing calculator too

it said at least one of my answers are wrong but idk which one? 😭

[hollow acorn]

so

[solar cape]

What is -21/-3?

[last pine]

7, no?

[solar cape]

Yes

[hollow acorn]

y = (-3/7)x + 3

-21 / -7 = 3

not -3

[solar cape]

Sorry I meant - 21/-7

[solar cape]

But yes that is equal to 3

Not -3

[last pine]

wait lemme check my scrap paper

oh

im silly

thank you guys

literal life savers

.close

[vocal sleet]

Channel closed

Closed by @last pine

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[vocal sleet]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[gritty niche]

Someone pls help ai doesn’t even know

[quiet echo]

use subsitution.

!chatgpt

[atomic jasper]

!nogps

!nogpt

[vocal sleet]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[solar cape]

Please trust yourself over ai

[quiet echo]

thank u brudda

[gritty niche]

Bro I got a few min to send this in

[atomic jasper]

is this a test?

[gritty niche]

No

Hw

[quiet echo]

like i said, use subsitution

[gritty niche]

Alr

[quiet echo]

its sparx or whatevr you call it

u can see it clearly

[atomic jasper]

write x as y or vice versa and plug it in

[quiet echo]

it says "watch video"

[solar cape]

So uh if xy=8,can you express x in terms of y

[atomic jasper]

ive never used it, idk

[quiet echo]

they already did in the second eqn tho

😦

[solar cape]

Yea but for the substitution cuh💀😭

[quiet echo]

oh this isn't small math server i forogt

[quiet echo]

(4y+36)y=8

solve quad

🗣️

[solar cape]

Yea same thing as mine

8/y=4y+36

[gritty niche]

Is this right?

[quiet echo]

also its me exiled

[solar cape]

(4y+36)y=8

[quiet echo]

!show

[vocal sleet]

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

[solar cape]

Did you use ai?

[gritty niche]

I used ai

💀

[hollow acorn]

😭

[atomic jasper]

!nogpt

[vocal sleet]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[quiet echo]

no.

[atomic jasper]

please dont use ai

[quiet echo]

dude, just do ONE thing without ai

[gritty niche]

Ok

[hollow acorn]

this is the second time

[lost barn]

Lmao

[gritty niche]

Sry

Im rushing

[atomic jasper]

and if you use AI you dont learn

[lost barn]

It's ok ppl hate ai here

[atomic jasper]

dont rush then

so that you understand

[lost barn]

I mean if it's last minute then they don't have a choice at this moment

[solar cape]

If xy=8 then x=8/y yes?

[gritty niche]

Well the question changed

[quiet echo]

quick factoring

[hollow acorn]

ai? more like schmai

[quiet echo]

dawg 😭

[lost barn]

True

[atomic jasper]

shouldve thought of that before hand

[solar cape]

Ok calm down yall

[gritty niche]

Sorry bro

[atomic jasper]

¯_(ツ)_/¯

[quiet echo]

send the q

[hollow acorn]

substitute

same principal

[gritty niche]

Shouldn’t I rearrange 1st

[solar cape]

If y=x^2
Then sub y=x^2 into y-4x+3=0

[solar cape]

It's already rearranged for you

[hollow acorn]

you can just sub y for x^2

[solar cape]

It's prime real estate

[hollow acorn]

exactlyyy

this guy gets it

[atomic jasper]

you can directly substitute that

[solar cape]

Just cook

[gritty niche]

So x^2 - 4x =3

[flat whale]

,tex .quadratic formula

[twin meteor]

riemann

[quiet echo]

yes!

wait no!

[gritty niche]

What

[flat whale]

Oh does it factor

[quiet echo]

x^2-4x+3=0

[quiet echo]

yes

[flat whale]

Alright factoring is better

[atomic jasper]

i have a suggestion for an addition but i cant msg, need frq first

[quiet echo]

@gritty niche if i were you i would lowkey do practice problems on these

it seems like u do not understand something fundamentally and/or just confused by the question

[gritty niche]

So x^2 - 4x =-3 ?

[hollow acorn]

no

x^2 -4x +3 = 0

[solar cape]

Don't move the 3

[quiet echo]

just factor it.

[hollow acorn]

and factor

[quiet echo]

x^2-4x+3=0

[flat whale]

Realistically, I'm not updating it anytime soon.

[hollow acorn]

so what multiplies to get 3 and adds to get -4

[quiet echo]

(pls tell me you know factoring)?

[gritty niche]

Yeah I just hate it

[hollow acorn]

real

[quiet echo]

oh my lord good

now lets do it!

[gritty niche]

-3 and -1

[hollow acorn]

yep

[solar cape]

So your roots are?