help-10

[sonic mantle]

so.. my plan here is to find the cross product of PQ and PR / PQ and PS and see if the vector that's result of the cross product have the same direction or not

[deep kraken]

consider the cross product is 0

[sonic mantle]

but is there any faster method than that?

[sonic mantle]

ohh right

so i can just find the cross product of PQ and PR / PQ and PS and if both results in 0 then they are parallel therefore on the same plane right?

[deep kraken]

not necessary parallel

[sonic mantle]

oh mb

[sonic mantle]

also could you elaborate a bit?

[obtuse pebble]

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[obtuse pebble]

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[quiet oasis]

if the question asked me to answer in the form of y=mx + c can I like simpfly it so it doesn't have fractions? in this case the ans will be 3y = 2x + 3 or should I just use the fractions answer

[high lily]

use the fractions

3y = 2x + 3
isn't in the specified form

[quiet oasis]

I see then thanks

.close

[obtuse pebble]

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[languid tinsel]

I want to prove that the topology on $\mathbb A^2(k)$ (Zariski) is not given by $\mathbb A^1(k) \times \mathbb A^1(k)$. Can someone do this with me; I havent had basically anything about the "diagonal of a topology" if that is helpful here

[warm shale]

ILikeMathematics

[languid tinsel]

.close

[obtuse pebble]

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[obtuse pebble]

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[tawny pecan]

guys

[tawny pecan]

are u trolling?

[trim portal]

what?

[tawny pecan]

they just joking

bro

they just can do that with chatgpt

huhcat

it more help

[tawny pecan]

but they not keeping in the same sub...

1 sec lol

[trim portal]

you can use chatgpt if you want, but I prefer using this server for most questions

[trim portal]

also, this discussion doesnt really belong here

[tawny pecan]

i mean

bro i know this server so help

but i mean

like

some ppl here

is just trolling

[trim portal]

some people are, most people arent

[tawny pecan]

yes

[trim portal]

and the people who are trolling are usually quickly dealt with by mods

[tawny pecan]

bro like when u try to help them

at last

u gonna find them was trolling u

[trim portal]

I've never experienced a question which seemed legit but turned out to be trolling

usually its either obvious troll or a legit question

btw ill close this channel now, if you wanna discuss this, you can move to #discussion

[tawny pecan]

like i'm bac

grade 12

3rd

i can just send u a photo of my book and that qu

and ill ask u in call

or

like

u gonna help me

but some ppl

[trim portal]

oh you have a math question to ask?

[tawny pecan]

not even study

they here

for troll

[tawny pecan]

no no

but if i have

ill ask

ill do my best first like chatgpt and youtube

and when i give up

ill back to this server

[deep kraken]

Dude is trolling

[trim portal]

lets just move this to #discussion , alright?

[tawny pecan]

he asked

i answear

[trim portal]

.close

[tawny pecan]

okok

[obtuse pebble]

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[obtuse pebble]

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[slim furnace]

Can anybody help me determine the galois group in ques 7th . I think its (Z/(2))^3 but on stack exchange it says Q8 (quaternion group) just a hint about finding image of u under any element of group would do . Thank you in advance

[obtuse pebble]

@slim furnace Has your question been resolved?

[slim furnace]

<@&286206848099549185>

[slim furnace]

.close

[obtuse pebble]

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[fathom meadow]

Evaluate 2cos^2 60° + 3sin^2 45° - 3sin^2 30° + 2cos^2 90°

[fathom meadow]

how to solve this

[high lily]

first term is missing the angle

[fathom meadow]

mb w8 rq

edited

[high lily]

but these all seem to be special angles
you should know their trig ratios
and then the rest is simplification

[fathom meadow]

alrighty leme try to solve

[fathom meadow]

5/4 coming ig correct thts wht given in textbook

im kinda new to trig so tryna prac problems :p

ty :D

.close

[obtuse pebble]

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Channel closed

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[flint verge]

hi
i not want to describe what exactly i do
but want confirmation for my precision issue

for f(x) = x^(-2)
    ( f(x+dx)-f(x) ) / dx
    ( 1/((x+dx)^2) - 1/(x^2) ) / dx
    ( 1/((x^2 + 2*x*dx + dx^2) - 1/(x^2) ) / dx
    #idk is it really correct to do, but seems so
    #since dx^2 is in second, and alter is dx in first
    #i can just remove it
    ( 1/((x^2 + 2*x*dx) - 1/(x^2) ) / dx
    .. getting result: 
    (-2*x*dx)/(x^4*dx)
   basically by dx^2 precision
  
   but if i do whole math with 'let a = (x+dx)^2'
   i getting this: 
   ( -2*x - dx ) / ( x^4 + 2*x^3*dx)

   and dx is finite
   i may drop dx^2, but not dx

   doing math with keeping entire equation is a lot of calculations
   can i use this 'bigger than pow 2 = remove' in other calculations?
   here i removed dx^2 when i have /dx
  
   can i safely do the same for any dx^n under /dx^h if 'n-h > required precision' ?   

[restive gorge]

What is dx precision?

[flint verge]

around 0.01 0.03, cant drop

may be higher

question in power
also i not yet sure that my code is correct, but anyway, there math question

[polar fossil]

Dropping dx^2 works in the limit case, but you may find that your approximation isn't good enough if you can't drop dx

[flint verge]

yeah, so it is fine for speeding up calculations if i not doing it wrong, thx
i may doing stuff wrong but its on me now, thx for confirmation

how to !solve?

[restive gorge]

.solved

[flint verge]

.solved

[obtuse pebble]

Channel closed

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[obtuse pebble]

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[olive isle]

how do I convert euler angles directly to axis angle without a quaternion in the middle
(I need >360° rotations represented for angular velocity)

[obtuse pebble]

@olive isle Has your question been resolved?

[olive isle]

<@&286206848099549185>

[dire moss]

What’s good brochacho?

[olive isle]

I need to convert euler angles to axis angle without clamping

[dire moss]

@olive isle, do you have any examples you want to go over?

[obtuse pebble]

@olive isle Has your question been resolved?

[obtuse pebble]

Channel closed

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[calm basin]

Hey I need help

[brazen gorge]

send your question

[obtuse pebble]

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

@calm basin Has your question been resolved?

[calm basin]

Hey I got a question

[calm basin]

Let
X

R
X=R with the usual topology, and let
A

(
0
,
1
)
⊂
R
A=(0,1)⊂R.
Find the closure of
A
A.
Find the interior of
A
A.
Find the boundary of
A
A.
Is
A
A open, closed, both, or neither in
R
R? Justify your answer.

[brazen gorge]

bro this ain't readable

you seem to be copying this from somewhere, maybe send a screenshot?

[calm basin]

Ok

I was trying this question from gpt but couldn’t understand how to get started

@brazen gorge

Do u understand the problem

[shut lagoon]

Are you able to define what the closure, the interior and the boundary of a set are?

[calm basin]

No

[shut lagoon]

Well that would probably be a good start. Are these not defined anywhere in the material you’re using?

[calm basin]

No

Just give the answer

Put the fries in the bag bro

[shut lagoon]

Oh that’s not how this server works unfortunately. You try and we help!

[calm basin]

Are u a bot?

Common Put the fries in the bag bro u got this

[shut lagoon]

You’re asking a question about topology and you can’t define the words in the question. I am having trouble believing that you’re being asked this with none of those concepts defined prior.

[calm basin]

That’s true

[shut lagoon]

In any case, my point still stands. The point of this server isn’t to get your work done by other people.

[calm basin]

So ur saying topology is not ment for me 🫩

How rude

One day I will become a better mathematician than you

[shut lagoon]

There’s plenty of people here willing to help you through the problem, but unfortunately we can’t do it for you.

[calm basin]

Why not

What’s the problem

[shut lagoon]

Good for you! We need good mathematicians!

[calm basin]

Bruh u can’t be for real

[shut lagoon]

Are you going to actually try or is this all you came for?

[calm basin]

I want the answer to my problem

I need help

Put the rice in the bag bruh

[shut lagoon]

I’ll ask again : are you willing to try or not? We don’t give out answers here.

[calm basin]

Why not what is the problem of not giving answers

Give me a reason at least

[shut lagoon]

It’s a server rule for one, and in any case it’s a disservice to you.

[restive gorge]

two reasons

[calm basin]

How is it a disservice

[shut lagoon]

Because you’re not learning anything and not putting in any work, hence it doesn’t help you understand.

If you’re not willing to try, then there’s nothing we can do for you.

[calm basin]

I don’t want to try I just want the answer and go to sleep

[shut lagoon]

And I’m telling you it’s not happening

[calm basin]

Common dude it’s not that deep

[shut lagoon]

<@&268886789983436800> entitled-ish? Will stop interacting for now.

[calm basin]

Take one for the bois

[karmic cedar]

we're not here to do your work for you, man

we're here to help

[mystic jetty]

This might actually be real arjun wtf

[karmic cedar]

who

[calm basin]

Who is real Arjun 😂😂

What did he do

[karmic cedar]

we don't talk about the moderation history of users here

anywho, since you don't really need help, I'm going to close this help channel

[calm basin]

Bruhhh

Do u play video games by any chance

DarQ

[karmic cedar]

next time you demand people give you the answers instead of working for it yourself it might be considered a cheating attempt and you'll be banned

.close

[obtuse pebble]

Channel closed

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[obtuse pebble]

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[weary pebble]

I don’t understand how this is at all possible

[mortal blade]

,rccw

[mortal blade]

Can you send an image of the question? The RHS isn't very readable

[weary pebble]

It’s the last one d

[gilded drift]

sin(x-y)=sinxcosy-sinycosx, -cosx(cosx-siny)=-cos^2 x+sinycosx
notice how the sinycosx get cancelled and you get sinxcosy - cos^2 x+1
you can rearrange the last 2 parts as 1-cos^2 x which as we know is sin^2 x because 1=sin^2 x + cos^2 x=> 1-cos^2 x=sin^2 x, so then it becomes sinxcosy+sin^2 x,

[gilded drift]

for the sin(x-y), you wrote down sinxcosy-cosysinx which are the exact same thing

[weary pebble]

Wait I thought it did not get cancelled cus they are both negatives

Does the - get distributed?

[gilded drift]

sin(x-y) = sinxcosy - sinycosx, not sinxcosy-cosysinx which is what you wrote, additionally
-cosx times cosx=-cos^2x, but -cosx times -siny is cosxsiny

[gilded drift]

also in the 3rd line you wrote, the 1 disappeared

[weary pebble]

Ik still getting the result with a - not a +

[gilded drift]

can you show a pic of what you currently have

[karmic bronze]

,rccw

[gilded drift]

cos^2x=1-sin^2x
-(cos^2x)=-(1-sin^2x)=-1+sin^2x

[weary pebble]

Wait I thought for proofs you can only work on one half of the equal sign

[gilded drift]

?

you have -cos^2x there not cos^2x

[weary pebble]

That’s just my bad handwriting

I’m still confused how to make the - a + tho

Like I realized I forgot the 1 but even after adding it I’m confused

So when I factor it or find the gcf whatever it is called I’ll get rhe right answer but it is not right because it is subtracting not adding

[gilded drift]

you have -cos^2x
-cos^2x is not equal to -1-sin^2x

[gilded drift]

^

[weary pebble]

Wait I’m so confused now 😅

I thought that is a pyth identity

[gilded drift]

cos^2x=1-sin^2x,,,
you did not take into accouont the sign of -cos^2x when you wrote 1-sin^2x in the 4th line

[gilded drift]

sin^2x+cos^2x=1
sin^2x=1-cos^2x
cos^2x=1-sin^2x

[weary pebble]

Now I have no idea what to do because I can’t factor now

Cus now I just have sinxcosy•
-cos^2x+1

But I need to factor out a sinx for the answer but there’s no sinx to factor

[gilded drift]

you wrote -1-sin^2x, -cos^2x is NOT equal to that

[weary pebble]

Yes but I fixed that

[gilded drift]

what is it now

[weary pebble]

Wdym

[gilded drift]

what is the value in there

yk it would be more beneficial here to substitute 1 as sin^2x+cos^2x here

[weary pebble]

Ohh that helps

Ty

I always forget u can do that

It feels like cheating

Any tips on how to figure out if I should use a reference angle on these type of problems I have no idea how I could tell on a test

I’m royalty screwed for this test cus senioritis is hitting me

[gilded drift]

210=180+30
150=180-30
120=180-60

etc etc

imagine the unit circle

and either 180 it(subtract 180 if it's greater than 180) and/or mirror it

[weary pebble]

I’m so confused how they got from this to that

Like I know that but I have never done a problem like this in class

wait

That’s phrased badly

I know sin is cos shifted but I never knew it could effect these problems

How would it look if it was cos to sin if that makes sense?

OH WAIT now I recognize them

I legit have a reference sheet of these next to me 😅

and I get it on the test so

But I did not study enough so 😀

How does that final row make sense tho how does that equal 1

I just don’t see how they got sin^2x+cos^2x from all that

[weary pebble]

Wouldent that fraction simplify to sin^2x-1

[obtuse pebble]

@weary pebble Has your question been resolved?

[weary pebble]

I don’t understand wth is going on here how can we cancel the two out it is a apart of the other expression next to it

Yea but it is attached to the sin^2x

Like I know other times in class people tried to cancel stuff but could not because it was attached

[warm shale]

BeautifulSoup

[weary pebble]

I don’t see anywhere else we can simplify

Yea

Oh wait

Sorry it’s like 12 am for me

I procrastinated😅

Cus I knew this stuff was going to stress me out so I get worried about being stressed out

Obviously now I’m on a time crunch so I have to get it done

Is that simple enough?

My test is tomorrow 😅

Like I care but then im a senior I’m accepted to college

so I could just get like a c this quarter and it would not matter but I don’t want to

Ok this one is about to have my crash out

Like-

WTH

[warm shale]

BeautifulSoup

[weary pebble]

I just have no where to even start it’s not even the writing

I would use a double angle idenity for the right expression but than that ^2 is in the way

[weary pebble]

Like I see how pyth identities could fit but I don’t know how with all the extra stuff

I have no idea what to do with the left stuff

We haven’t learned that

Oh wait

That’s the box

where would I do that tho?

But I don’t have a third variable

I would need another like sin variable without a ^2

[warm shale]

BeautifulSoup

[weary pebble]

Like there’s no way I can cancel the sins out so there is none don’t matches what’s in the problem

😀

I keep looking at the answer key I know I shouldent

I don’t understand this at all if I do I’ll fail this test

I’ve done like 3 problems in like 3 hours and it’s mostly by looking at the answer key 😭

like all of it I just don’t know what to do

I guess more with the more recent stuff

It just doesn’t click

Then I panic

The problem is most of the time I just don’t even know what to do first so then I cant ask questions since I just don’t know

Also this is an opinionated question are these simply challenge problems ? It just says extra pratice but idk. The left one is the study guide the right is the extra pratice

Oh-

say u where in like jury duty and they took away your phone

Welp I’m going to procrastinate until 1 am so 13 minutes and call it a break cus I’m in like panic mode so I’m not going to be able to get work done -_-

Im just going to pray my school fire alarm breaks again but during the test because that is far more likely to happen than me passing this test

[somber spear]

Don't lose hope gang try try ...

[obtuse pebble]

@weary pebble Has your question been resolved?

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[chilly reef]

hi i need helping doing \lim_{x \to 0} (\frac{1}{x^2} - \frac{1}{\sin^2(x)}) without using l'hopitals. i've gotten it to \frac{\sin^2(x)-x^2}{x^2 \cdot \sin^2(x)} but i dont know where to go from there
i hope this latex works out well im kinda new to it

[mild sandal]

latex indeed didnt work out

[chilly reef]

:(

uhhhhh

$\lim_{x \to 0} (\frac{1}{x^2} - \frac{1}{\sin^2(x)}) without using l'hopitals. i've gotten it to \frac{\sin^2(x)-x^2}{x^2 \cdot \sin^2(x)}$

[warm shale]

Diaso

[mild sandal]

im also trash at latex

[chilly reef]

oh

$\lim_{x \to 0} (\frac{1}{x^2} - \frac{1}{\sin^2(x)}) \text{without using l'hopitals. i've gotten it to }\frac{\sin^2(x)-x^2}{x^2 \cdot \sin^2(x)}$

[warm shale]

Diaso

[chilly reef]

thats kinda better

[mild sandal]

wait no

[chilly reef]

nevermind the hint gave me a good idea how to approach it from here

.close

[obtuse pebble]

Channel closed

Closed by @chilly reef

Use .reopen if this was a mistake.

[obtuse pebble]

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[weary stag]

We need help with Regions between curves, don't really understand the topic in general and would appreciate any help anyone can provide.

[shut lagoon]

Do you have any particular problem you're having trouble with?

[silver anvil]

hey bro do you know dot product?

[shut lagoon]

!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).

[weary stag]

Let R be the region bounded by the graph of y=2x+2 y=3x+3 x=4

Its AP calculus but we're in high school still

[shut lagoon]

And what's the question about? Computing the area of this region?

[weary stag]

Yeah

[shut lagoon]

OK. Well first thing in any of those kinds of problems is to sketch the region. Have you tried that so far?

[weary stag]

Yeah, I just turned the hw in. I gtg the student teacher got pissed.

[shut lagoon]

Oh ok

[weary stag]

Sorry.

I will def be back later

[obtuse pebble]

@weary stag Has your question been resolved?

[obtuse pebble]

@weary stag Has your question been resolved?

[weary stag]

Okay I'm back, so yes I did draw a picture

Its on my homework I turned in so I'll try to recreate it

[obtuse pebble]

@weary stag Has your question been resolved?

[obtuse pebble]

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[tacit plank]

What did I do wrong?

[brazen gorge]

.json? what about .yml

[restive gorge]

Should be -4b?

[weary stag]

damnit bro this was mine, I just had to drive home

.reopenm

.reopen

[fallow dust]

just get a new one bro

[obtuse pebble]

@tacit plank Has your question been resolved?

[obtuse pebble]

@tacit plank Has your question been resolved?

[neon vector]

@tacit plank you've been told what you did wrong

What's the point of reacting ❌ to the bot?

[tacit plank]

I changed it to -4b but the answer I got was still incorrect so I thought there was more that I did wrong

[neon vector]

Can we see the work

[neon vector]

Well maybe not 🙁

[obtuse pebble]

@tacit plank Has your question been resolved?

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[limpid fossil]

Hi so I have to find an answer to this differential equation, there is a bit in french but;
y(0) exists
y(1) = 0
So far what I am struggling with is just finding a general solution to the equation, without even starting the Sturm-Liouville problem, just the differential equation, I have tried solving it with Bessel's equation and a variable change t= sqrt(beta) * x but I am unable to simplify it
I appreciate any and all help T_T

ps: chatGPT did not help

[tardy epoch]

show your work

[limpid fossil]

1 min

[tardy epoch]

<@&268886789983436800>

[limpid fossil]

I did not go very far as I got stuck on it...

$\frac{1}{x}(t^2 u'' + t u') + (t^2 - 4) u = 0$

[warm shale]

nightfury

[limpid fossil]

would be the last line

but it does not work so I wonder what other way there is to solve this

[tardy epoch]

is there a typo in the differential equation? you said you're solving it for bessels, but does it say that in the question?

[limpid fossil]

It does not say bessel but i've tried it since that's all I could think of
but unfortunately there is no typo

$x y'' + y' - (4 - \beta x^2) y = 0$

[warm shale]

nightfury

[tardy epoch]

then what do the instructions say?

[limpid fossil]

find the eigen values and functions of the following sturm-Liouville problem
y(0) exists
y(1) = 0

the instructions are short
but to do so I have to solve this differential equation

and Beta is a real number

sorry I might've been unclear...

[tardy epoch]

if beta = 0, then you get a cauchy euler type equation

https://math.libretexts.org/Bookshelves/Differential_Equations/A_First_Course_in_Differential_Equations_for_Scientists_and_Engineers_(Herman)/02%3A_Second_Order_ODEs/2.05%3A_Cauchy-Euler_Equations

from there you could try to follow example 13.2.2
https://math.libretexts.org/Bookshelves/Differential_Equations/Elementary_Differential_Equations_with_Boundary_Value_Problems_(Trench)/13%3A_Boundary_Value_Problems_for_Second_Order_Linear_Equations/13.02%3A_Sturm-Liouville_Problems to get the general solution when beta != 0

[limpid fossil]

ah yes indeed I forgot about this equation but yes, if beta = 0 it isnt too bad
but then the real problem is when beta is not 0

[tardy epoch]

yes read this

[limpid fossil]

thx

Hum, this does not help much for the diff. eq. but I think I figured something out for when beta is not 0
thx for the help!

how do i tell the bot it's solved?

and sorry i just saw that this was a pre-uni channel

[obtuse pebble]

@limpid fossil Has your question been resolved?

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[obtuse pebble]

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[steel night]

im confused why they evaluated at f(1) and f(2) and made an inequality out of that

[proud geyser]

can you state the IVT?

rather, state what you understand about the IVT.

[steel night]

IVT is where there is a point c in a close interval a,b , where f(c) = some value z

[proud geyser]

very incomplete.

do you want to try again?

[steel night]

I said closed interval because that implies a continuous function within that interval right

[proud geyser]

no.

[steel night]

or its just the end points

thats continuous

[proud geyser]

the openness of an interval has nothing to do with the continuity of a function within it.

[sand roost]

(R is an open interval, and that last f(x) was continuous on it!)

[proud geyser]

now knowing this, would you like to retry stating the IVT?

[steel night]

yes sure

[proud geyser]

go ahead.

[steel night]

IVT is where there is a point c in the mid point of the closed interval a,b , where f(c) = some value z

[proud geyser]

still incomplete.

[steel night]

IVT is where there is atleast one point c in the mid point of the closed interval a,b , where f(c) = some value z

[proud geyser]

still incomplete!

[steel night]

assuming a,b, c and z are real numbers

[proud geyser]

unfortunately that does not save your definition.

[steel night]

ok I give up, what is it

[covert fjord]

you need to relate z with f(a) and f(b)

and involve continuity

[proud geyser]

IVT:
Suppose f is continuous over a closed interval [a, b]. If there exists a real z such that f(a) < z < f(b) or f(a) > z > f(b), then there is some c in [a, b] such that f(c) = z.

[steel night]

ok Ive seen the definition but i coudnt recall

[proud geyser]

recall is a different story, but the fact that you left out that f must be continuous over that interval is a big no-no. that is what allows the IVT to work!

[covert fjord]

yeah

[steel night]

but c has to be hte mid point of a and b right or not necessarily

[covert fjord]

not necessarily

[proud geyser]

not necessarily.

c only needs to be in [a, b] somewhere.

also, niche, do you intend to take over helping this channel?

[steel night]

there can be multiple right

[covert fjord]

try to understand it logically like if you have a function that goes from a y-coordinate like 2 to a y-coordinate like 6, then it must pass through all y-coordinates between 2 and 6 if it's continuous

[steel night]

multiple points

like c

[restive gorge]

-# you made a small typo

[covert fjord]

im just trynna help out here and there

[proud geyser]

then I will step back, since I think we're just repeating each other.

[covert fjord]

no it's fine

u started first u can continue @proud geyser

[covert fjord]

i'll step back in this case

[steel night]

I dont mind 2 helpers tbh

i dont really think u guys are repeating

but yeah

[sand roost]

another thing to note: for every possible z between f(a) and f(b), there is at least one c. if [f(a),f(b)] = [2,6] (so we're considering y-values), then there is c so that f(c) = 4, there is d so that f(d) = pi, there is k so that f(k) = 2.345634563456...

(c,d, and k are x-values)

[steel night]

for every possible z between f(a) and f(b), there is at least one c.

so every possible z can have multiple c?

[sand roost]

yes - think about cos(x), it attains -1 at pi, 3pi, 5pi, ...

so if i made my interval of x [0, 4pi], i could expect two points where cos(x) = -1

[steel night]

whats that z value again? is that the y value or its just value at that point?

[sand roost]

z is on the y-axis

c is on the x-axis, and f(c) = z

[steel night]

whats that z value again? is that the y value or its just value at that point?

edited

[sand roost]

it's a y-value, and it's in between f(a) and f(b)

[steel night]

so its not the value of the point?

its just some arbitary y value

[sand roost]

it's the value of the function for x=c

not sure what you mean by value of the point though

[steel night]

oh right

[sand roost]

but it is arbitrary, as long as it's in the endpoints! this is how we apply the IVT to the problem

[steel night]

and what does that tell us because that was pretty obvious that there is y values for every point

I mean its common sense right

or we just need it to prove some questions?

[sand roost]

yes i suppose, but we use it to answer the original question you had

[steel night]

yes

[sand roost]

so back to that question. $\sqrt{x} = x^2 - 1 \iff \sqrt{x} - x^2 + 1 = 0$. \
What we will do is let $f(x) = \sqrt{x} - x^2 + 1$, then $\sqrt{x} = x^2 - 1 \iff f(x) = ?$

[warm shale]

haseeb ♥

[steel night]

-1?

[sand roost]

0, actually. $\sqrt{x} - x^2 + 1 = 0 \iff f(x) = 0$

[warm shale]

haseeb ♥

[sand roost]

pretend you are substituting $f(x) = \sqrt{x} - x^2 + 1$

[warm shale]

haseeb ♥

[sand roost]

with me so far?

[steel night]

wait

[steel night]

how did u get this

im confused whats going on

[sand roost]

i defined a function, $f(x)$, which is conveniently equal to $$\sqrt{x} - x^2 + 1$$

now the problem has become, prove $f(x) = 0$ at some point in the interval $[1,2]$

[warm shale]

haseeb ♥

haseeb ♥

[steel night]

ah okay

[sand roost]

now, let's consider the IVT again, but this time z=0, and [a,b] = [1,2].
what is the statement of the theorem?

you can work off of Yukari's statement of the theorem:

Suppose f is continuous over a closed interval [a, b]. If there exists a real z such that f(a) < z < f(b) or f(a) > z > f(b), then there is some c in [a, b] such that f(c) = z.

[steel night]

yeah thats the thereoum

[sand roost]

okay, now modify it so that z=0, a=1, and b=2, like the problem

[steel night]

f(a) < z < f(b) or f(a) > z > f(b)

i dont understand this

[sand roost]

"if z is above f(a), and below f(b), on the y-axis"

and vice-versa

i.e. z is in between f(a) and f(b)

(hi yukari feel free to chime in ^-^)

[steel night]

wait do u mind if i can come back to this question

<@&268886789983436800>

[steel night]

Ill put it in my notes and come back to it

I have another question i wanted to ask

ill make a new channel

.close

[obtuse pebble]

Channel closed

Closed by @steel night

Use .reopen if this was a mistake.

[sand roost]

sure, we are 3/4 of the way there btw :)

[proud geyser]

as a fair reminder to OP.

[restive gorge]

necessary reminder

[steel night]

well lets continue in a new channel after I post a new question

it should be short

[proud geyser]

it may be short but jumping around probably hurts you more than you think, on top of possibly confusing helpers.

[steel night]

i just decided to do that later because its a bit harder

[proud geyser]

fair, but considering how close you are to the end...

[steel night]

ill make sure to continue from here

[proud geyser]

sure then, I'm not going to probe into why you won't finish it first since there is a risk you will run into a helper who didn't know what was discussed earlier.

but I will note the disadvantages of what you're doing.

[steel night]

Noted, Il try and complete right after this

[obtuse pebble]

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[steel night]

#help-10 message

my previous problem wasnt solved, I want to know why he evaluated at f(1) and f(2) and set them into inequalities

[dense yoke]

you have not done what hasseb has asked you to try. this is why I do not prefer you jumping between questions.

[high lily]

to show that z, in your case 0
lies between f(2) and f(1)

[tardy epoch]

Did you understand this theorem

[sand roost]

let's start here

(if you understood IVT)

[steel night]

yes

[steel night]

yeah I did

[sand roost]

okay, so what's the statement of IVT if z=0, a=1, b=2?

[steel night]

continuous function in the interval [a=1, b=2] where there is a c within that interval in which (fc) = 0

[sand roost]

there was also a bit about f(a) < z < f(b)

[steel night]

1 < 0 < 2?

the value at a=1 and b=2

oops

[sick terrace]

hm

@steel night what's the problem?

oh wait u where gonna make a new channel oops

[steel night]

here

[tardy epoch]

And what are those values

[tardy epoch]

.

[steel night]

well dont I need to know the function first?

[restive gorge]

You do

[tardy epoch]

Maybe you should reread the question

[steel night]

but f(x) is not the subject

[restive gorge]

Whats the subject then

[steel night]

0

[tardy epoch]

Are you saying 0 should be here instead of f(a) and f(b)?

[sick terrace]

okay

[steel night]

if i equate it to 0, is that the same f(x) being the subject

[sick terrace]

hm

[tardy epoch]

Equate what to 0?

[steel night]

i mean if i make everything on the lhs

to make the rhs = 0

[dense yoke]

what are you even working with though? you have a compound inequality; which side is the left/right? clarify.

[sick terrace]

yea I'm to dum for thi 🥀

gl ø

[steel night]

the lhs is f(a) and rhs is f(b)

[dense yoke]

why?

you were asked to restate the IVT given concrete values. what are you attempting here?

[steel night]

im not sure whta im required to do

oh

[dense yoke]

^

[dense yoke]

^

[steel night]

do i restate it with the value s in?

[dense yoke]

yes, as stated.

[steel night]

with the IVT, one has to be set below 0 and above 0 right?

[dense yoke]

no.

[steel night]

yeah I think im stuck

can I get a hint

[dense yoke]

literally put those values given into the theorem statement. there's no brainthink involved whatsoever

[steel night]

Suppose f is continuous over a closed interval [1, 2]. If there exists a real z such that f(1) < 0 < f(2) or f(2) > 0 > f(1), then there is some c in [1,2] such that f(c) = 0

[dense yoke]

you missed one z, but there we go. wasn't that bad, right?

[steel night]

yes it wasnt

thanks!

.close

[obtuse pebble]

Channel closed

Closed by @steel night

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[obtuse pebble]

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[weary pebble]

For this problem I understand the first couple steps, find the common denominator , then use a pyth identity but I’m confused on that third step of what happened

[boreal cliff]

which step specifically?

[high lily]

going from $\frac{s^2 \cdot s^2}{c^2}$ to $s^2 \cdot \frac{s^2}{c^2}$?

[warm shale]

ραμOmeganato5

[boreal cliff]

assuming you get it till $\frac{(\sin^2(x))^2}{\cos^2(x)}$, its just the definition of tan?

god my latex be rusty

[warm shale]

Περσυ

[weary pebble]

I understand the third but don’t know how we got to the forth

Oh wait no

[high lily]

witht he amount of things listed, its unclear which you're referring to as the third

best to clearly state
which expression to which expression

[polar fossil]

is the missing piece the fact that $\sin^2 + \cos^2 = 1$?

[warm shale]

professional attention seeker

[weary pebble]

I don’t understand where the cos^2x went

[boreal cliff]

i cant tell 'steps' when it's multiple equal signs in one line, but also new lines 😭

[boreal cliff]

whats tan(x)

[high lily]

best to clearly state
which expression to which expression

[weary pebble]

Sinx/cosx

I believe it is going from left to right not up and down

[polar fossil]

It is, yes. Can you please highlight the other expression you're confused about? Are you struggling to see where the blue thing came from, or what happens to it in the next step?

[boreal cliff]

blue?

[weary pebble]

So for the second to third step I don’t know where the cos^2x went since sin^2x turned into 1-cos^2x

[boreal cliff]

oh highlighted ok

[civic canopy]

sinx/cosx is tanx

[high lily]

combined into single fraction and factored out s^2

[civic canopy]

So sin squre x/cos squre x is tan square x

[polar fossil]

sin^2 did not turn into 1 - cos^2 from 2 to 3

[high lily]

pythag identity was actually applied from 3→4

[weary pebble]

Yea

[civic canopy]

Which step is he asking about

[weary pebble]

Wait

[weary pebble]

What happened then?

[high lily]

combined into single fraction and factored out s^2

[weary pebble]

OHHH

Oh I see thank you

[civic canopy]

".close" if no more doubts :)))

[obtuse pebble]

@weary pebble Has your question been resolved?

[obtuse pebble]

Channel closed

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[obtuse pebble]

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[tight gull]

chat help me with this question.....
if the 4 digit numbers greater than 5000 are randomly formed from the digits 0,1,3,5 and 7, then what is the probability of forming a number divisible by 5, when the digits are repeated ?

[spice inlet]

What have you tried

[tight gull]

i could not think of it yet

[spice inlet]

Ok well what is the divisibility rule of 5

[tight gull]

the number needs to have either a 5 or 0 in the last digit

[spice inlet]

Yep 👍

So now the question says greater than 5000

So what are the possibilities for the 1st digit

[tight gull]

could be 5 and 7

[spice inlet]

Yep

And the middle 2 digits can be any number

[tight gull]

yes

[spice inlet]

Yep so 2 possibilities for 1st digit, 5 possibilities for 2nd digit, 5 possibilities for 3rd digit and 2 possibilities for 4th digit

Can u find the no. Of favourable outcomes

[tight gull]

2.5.5.2 = 100 ??

is the answer 100?

[spice inlet]

Yes but also be careful that the question says GREATER than 5000

And we have included 5000 as a possibility

[tight gull]

so one possibility could be 5000 itself ??

[spice inlet]

No that's the possibility we need to remove

[tight gull]

so it is 99??

[spice inlet]

Yep (not the answer to the original question tho because they have asked probability)

[tight gull]

ok

[sour field]

it says digits are repeated

we have counted cases that dont repeat as well

eg 7305

[tight gull]

HAVE WE ?

IS IT WRONG ??

[sour field]

yeah 7 is possible for first digit, 3-0 for 2nd,3rd and 5 for last

so we need to subtract those

[spice inlet]

I think they just mean digits CAN be repeated

[sour field]

question mention digits are repeated so i'd assume they are asking for only those cases when digits must be repeated

are is a very strong word

idk though might be wrong

[spice inlet]

@tight gull could you send a picture of the original question

[latent thunder]

Can you show the original question

[sour field]

find answer that way too will be good for your concept this aint an exam

[latent thunder]

This reads more like allowed ngl

[spice inlet]

Yeah exactly

[sour field]

either way you need to find the cases when repetition is not allowed

so

[spice inlet]

When I did such questions it always meant allowed and not required

[latent thunder]

We can show him both ways ig

[sour field]

umm my book generally had language like "repetition is allowed"

[tight gull]

yess

[spice inlet]

Alright well first focus on allowed..coming back to this

[latent thunder]

Ok so there can be two interpretations

[tight gull]

guys can we move back to solving the first part

[spice inlet]

:/

[latent thunder]

That repetition must happen

[spice inlet]

Alright I'm dipping then too many cooks

[latent thunder]

And that the repetition may happen

[sour field]

i am really sorry

[latent thunder]

Alr kunal can handle

[sour field]

can you real quick check the answer of first part if your book has answers attached

check whether it is 99

[tight gull]

it is 99 indeed

[sour field]

oh so focus on the second part

now we need to compute cases when repetition is not allowed so we can either have 0 or 5 as the last digit

[tight gull]

i will solve the 2nd part myself, thank you

.close

[obtuse pebble]

Channel closed

Closed by @tight gull

Use .reopen if this was a mistake.

[obtuse pebble]

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[tall perch]

how do i solve i integrated the function but dont know how to check opetions

[tall perch]

got it

.close

[obtuse pebble]

Channel closed

Closed by @tall perch

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
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[barren pollen]

👀

<@&286206848099549185>

[velvet spoke]

ts imo problem

[barren pollen]

yep

[barren pollen]

u know how to solve ??

[velvet spoke]

no

[barren pollen]

@true solar

[barren pollen]

np 😄

[true solar]

!noping.

[obtuse pebble]

Please do not ping individual helpers unprompted.

[barren pollen]

-_-

!noping

[obtuse pebble]

Please do not ping individual helpers unprompted.

[barren pollen]

dem

/help

[inner sierra]

HOW IS THIS BOT IN HERE

😭

idk even know we had this bot

[barren pollen]

whos he

@frank cove

[inner sierra]

but anyways i see this is kinda recursive or some stuffs like that

if $P = x + f(y)$ then $f(P) = f(xy) + P$

[barren pollen]

how did u do that

[warm shale]

1 divided by 0 equals Infinity

[barren pollen]

if $P = x + f(y)$ then $f(P) = f(xy) + P$

[warm shale]

Doomslayer101

[brazen viper]

@barren pollen you mentioned that this was an imo problem, do you know which imo?

[barren pollen]

nah someone else mentioned

but he didnt knew how to solve

[errant spoke]

I saw a youtube video by prime newtons on it i think, lemme find it

[brazen viper]

So one technique you can do, if you don't know where else to start, is to hammer down one value for f(x) and see if it forces the rest of the function to behave a certain way or causes a contradiction.

Let's say f(0) = 0.

This would imply, if x = 0,

f(f(y)) = f(y)

In other words, this forces f to be a fixed point function

[uneven schooner]

yk i feel this method may work, follow at your own discretion. Let $x$ be a fixed point of $f$, and let $f(y)=0$. try to derive $f(1)$ from the given eq.

[warm shale]

Annie Maqionde

[brazen viper]

The only fixed point functions that pass through (0, 0) are f(x) = x and f(x) = 0

Or I guess any constant function

Hmmm, because the functional equation is f(f(y)) = f(y) it only needs to be fixed point after one iteration

[uneven schooner]

if you do have $f(1)$ you can write $f(x+1)$ in terms of $f(x)$.

[warm shale]

Annie Maqionde

[brazen viper]

.close

[obtuse pebble]

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[sour field]

.reopen

[sour field]

just to clarify this has no solutions right

[sour field]

cuz by substituting y=0 and using the property of functional eqn, i am getting f(x)=x+f(0) which on substituting in the original eqn yields xy=0 therefore there cant be any solution for all reals?

.close

[obtuse pebble]

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[civic socket]

why it says i got pinged here

[obtuse pebble]

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[eager wasp]

Alr

[quick nova]

hi

[eager wasp]

Hi

[quick nova]

do you have a question

[eager wasp]

Yeah are there actual professors here?

[quick nova]

yeah some here are

[eager wasp]

Alright thanks

Cuz i just joined

😭

[quick nova]

lol

[sly elm]

i am here

[quick nova]

if you don't have a question you need help, you can close the channel

[eager wasp]

Is there anything i should know about this?

[sly elm]

welcome

[eager wasp]

Hello

I will close it then

How do i do it...?

[quick nova]

type .close

[eager wasp]

.close

[obtuse pebble]

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[noble quarry]

Open

I don't get the logic

[hidden compass]

.you can't reopen it, because you are not OP

.reopen

[obtuse pebble]

✅ Original question: #help-10 message

[noble quarry]

How do I open my own?

Nvm I see

[hidden compass]

.close

[obtuse pebble]

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[proud tapir]

does this mean for 3a M1

[proud tapir]

u can

u can just put x^-2 instead of explicitly stating x^n -> x^(n+1)

i think that x^n -> x^(n+1) is kinda stupid to state

[restive gorge]

it is indeed

[proud tapir]

because ur integrating

[restive gorge]

seems to me it would suffice to just rewrite the expression 1/x^3 into x^(-3) to make the grader notice that you will use the power rule

[proud tapir]

ok

.close thanks

[obtuse pebble]

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[obtuse pebble]

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[proud tapir]

yo

[proud tapir]

here u gotta use H = mt + c

but how are u supposed to know that its linear

[meager breach]

hi

[proud tapir]

what if its a cubic or something

[meager breach]

hru

[proud tapir]

im ok

[meager breach]

good

[proud tapir]

oh it says use a linear model

[daring ravine]

they tell u to use linear

[proud tapir]

that sounds so vague tho

[daring ravine]

wt

[proud tapir]

lines can be curved bent whatever

[meager breach]

who

[daring ravine]

the problem asks for linear model goddamnit

just do it 😭

[proud tapir]

ok vro

im just saying a curved graph is still a line

[daring ravine]

no

lines are straight

curved lines dont exist

its called a curve

[proud tapir]

ah

[pseudo swift]

well yeah it's a contrived question for a contrived exam

the only way to know if the growth rate of a tree is linear or not is by planting some damn trees

and seeing what happens

[proud tapir]

ill get a cow or some animal to eat the tree

then i eat it

.close thanks

[obtuse pebble]

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[obtuse pebble]

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[spice inlet]

<@&268886789983436800> hello

Oh so 5 letters r allowed here

[obtuse pebble]

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[spice inlet]

That's crazy

[upbeat plinth]

ruh roh

[spice inlet]

Rocket launcher ❤️

[upbeat plinth]

baby yoda

https://tenor.com/biiZv.gif

[spice inlet]

https://tenor.com/view/here-have-some-wuv-bebe-yodie-gif-22520598

[obtuse pebble]

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[proud tapir]

yo uh

[proud tapir]

how do u get x >= cuberoot 4 ?

[shut lagoon]

I just depends on the specific definition of increasing used.

[proud tapir]

huh?

increasing is when the gradient is positive

[shut lagoon]

In some texts it's synonymous with strictly increasing, so derivative > 0
In some other it's synonymous with increasing or stationary, so derivative >= 0

[proud tapir]

o

[shut lagoon]

I suppose the key was made to account for both

[proud tapir]

ah it says "or" because of that

thank u

.close

[obtuse pebble]

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[obtuse pebble]

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[proud tapir]

what does it mean by sight

[wise dust]

you need help?

nvm i just read it

[wise dust]

it means if they see plus or minus those numbers, then they give you the mark

[proud tapir]

oh k

.close thanks

[obtuse pebble]

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[proud tapir]

.reopen

[obtuse pebble]

✅ Original question: #help-10 message

[proud tapir]

how do i differentiate that

for part b

[coarse marsh]

differentiate 3925e^(-0.25T)=500?

in terms of T?

[proud tapir]

ok uh i got confused

because i dint know about the e rule

[coarse marsh]

oh ok

you got it now?

[proud tapir]

yea

[coarse marsh]

kk nice

[proud tapir]

thanks ima close this now

.close

[obtuse pebble]

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[obtuse pebble]

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[agile totem]

oh my days im getting ptsd from a level maths

[ember frost]

hi i am traumatized too but do you have a question

[obtuse pebble]

@agile totem Has your question been resolved?

[obtuse pebble]

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[rich igloo]

<@&268886789983436800>

<@&268886789983436800> its in every help chanel

[obtuse pebble]

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[tired quest]

45

[obtuse pebble]

Please don't occupy multiple help channels.

[umbral jetty]

One message removed from a suspended account.

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[tired quest]

change of base formula and also im using ts chanel

[umbral jetty]

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[viscid bronze]

you can use ln2 divided ln1/3

or log10

[restive gorge]

hey guys thats my pinkg calculator and it's cute

[viscid bronze]

try substitution

[tired quest]

bro that doesnt work

i pick 2/x for u

i get du= 2lnx

how does that help me

[umbral jetty]

One message removed from a suspended account.

[oak glen]

Does it help if I write it as $t^{-2}tan(2t^{-1})$

[viscid bronze]

Yes

[restive gorge]

You should open your own help channel btw

[umbral jetty]

One message removed from a suspended account.

[warm shale]

astral

[viscid bronze]

seems you tried to differentiate u=2/t and got 2lnt which isn't correct, you can try rewriting u=2t^(-1) and finding du again

[tired quest]

you cant differenciate to -1 power i thought

[oak glen]

This is of form $f'(x) g(f(x))$

[warm shale]

astral

[viscid bronze]

this is possible too

[restive gorge]

<@&268886789983436800>

[obtuse pebble]

@tired quest Has your question been resolved?

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[steel night]

I got this q wrong

[viscid bronze]

check your direction

[steel night]

the diagram is wrong?

[viscid bronze]

diagram is okay, your first direction vector equations have issues

[steel night]

why does it have issues?

CD already implies that it is negative of AB

[viscid bronze]

check the second line

[steel night]

oh

it shoudve been OD- OC

also I wonder why I got this incorrect

max min thereoum states that there is a min and max given its a closed interval and continuous

[viscid bronze]

the function isn't continuous

[steel night]

why?

it is

those are elementary functions

[viscid bronze]

what happens when x=2

[steel night]

cos(2)?

im not sure

[viscid bronze]

try to imagine the graph

when x approaches 2 from left to the right

and when x=2 on the second function

[steel night]

as it approaches 2, the limit is -1

[viscid bronze]

what about for the top function

i didn't add the boundary [-5,4] but this is how the two functions look like

[steel night]

is there a simple way for me to know

because in the test, we are only going to be using the desms scientific calculator

on the computer

[viscid bronze]

i guess

for the piecewise functions like these you should always check continuity at the boundary points

like x=2 for this example

check the limit at both sides

[steel night]

how do i do that?

Ive been taught the table method by a helpee before

[viscid bronze]

not too sure what that is

but you can probably just plug in values

the first one just goes to 4e^2

second one is just 5cos(2)-2 when x=2

[viscid bronze]

they're not equal so you can tell there's a "jump" or break

[viscid bronze]

yeah something like this ig

it approaches 3 in that example

[steel night]

why did u choose x=2 specefically

[viscid bronze]

you don't really have an undefined in this case (since no division by 0) so it should be simpler

[viscid bronze]

the first function stops at x<2 and the second one is at x≥2

so the function changes at x=2 so it is possible for the continuity to fail there

[proud geyser]

if you have piecewise functions, always test continuity at the boundary points. that would be a good place to start.

[steel night]

i mean without a graph, how could we tell

[proud geyser]

isn't that why we test?

[steel night]

ok let me do that

Then?

[viscid bronze]

test the breakpoint

[proud geyser]

...what happened to testing at the boundary point?

[steel night]

Which boundary point

oh

[proud geyser]

the point at which the function changes definitions.

[steel night]

I plugged them wrong

It should be -5 and 4

[viscid bronze]

😭

[proud geyser]

that's somehow ten times worse.

[viscid bronze]

if you have the function
x+1 for x<2 and
x+999999 for x≥2

is this continuous

[proud geyser]

you're checking the wrong points again.

[steel night]

f(5)=593.652

ok there we go

[proud geyser]

it's quite amazing how you've managed to somehow miss a single message.

[steel night]

So we don’t sub the end points

[topaz zealot]

don't you just check the left and right limits? if they are equal, then it's continuous, if not, then it's not continuous?

[steel night]

Ok 2 is the point where it changes definitions

[proud geyser]

finally, some sense!

[viscid bronze]

Yes

[topaz zealot]

lim x->2- f(x) = 4e^(2)
lim x->2+ f(x) = 5cos(2) - 2
Evaluate those two one sided-limits
Are they equal?
Yes -> Limit exists -> is continuous on [5, -4]
No -> Limit as x->2 DNE -> discontinuity at x=2 -> not continuous on [5,-4]

@steel night

[proud geyser]

I was hoping to have him realize and do it himself, but sure.