help-38

[long basin]

$$(a^b)^c = a^{bc}$$
$$(10^{\log(a)})^x = ? $$

[solid kiln]

Umbraleviathan

[heady nimbus]

10^log(ax)

?

[heady nimbus]

is that right?

[heady nimbus]

^

[long basin]

No

[heady nimbus]

log((10^(x*log(a))))

[long basin]

Well yeah, holistically it would become the third step

[heady nimbus]

what is it then

i understand nothing

[long basin]

The problem is that you don't even understand the fundamentals of exponents and logarithmics

It would take a lot of my time to go through them

I'd say to review them on Khan Academy

[heady nimbus]

can u maybe give me the result for each step? im with a math teacher tomorrow that can explain everything further to me i just need the result

[trim jolt]

@heady nimbus Has your question been resolved?

[heady nimbus]

<@&286206848099549185>

[heady nimbus]

.close

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[merry viper]

Where does the -1 come from?

[merry viper]

.close

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[lean thunder]

Is the answer 4t+45?

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[vocal bison]

I keep getting wrong answers

Isn't this the area?

Or.. should i change the bounds to 0 to pi/2?

[stoic iron]

It's a circle

[vocal bison]

Ah ok

I used the area of a circle formula

and my answer was correct

Thanks for reminding me of that one

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[vague plaza]

Any help pls

@wise cipher 30 wasn't right for some reason😭

U got any other ideas?

[trim jolt]

@vague plaza Has your question been resolved?

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@vague plaza Has your question been resolved?

[trim jolt]

@vague plaza Has your question been resolved?

[stuck sable]

use the Thales's theorem to solve it

try to find BF and DF in terms of BD and x

[solid kiln]

Mehdi_Moulati

[stuck sable]

and since BF + DF = BD
replace BF and DF by their value

you will find at the end an equation you have to solve

[vague plaza]

Is that what you typed in?

[vague plaza]

This?

[stuck sable]

i use it two times

in the triangle ADB and BCD

[vague plaza]

Never heard of it😭

[vague plaza]

What is their value??

We don't know it

[stuck sable]

the Thales theorem says that :
let's a triangle ABC , and two point D and E in the lines AB and AC
if DE is perpendicular with BC then :
$\frac{AD}{AB} = \frac{AE}{AC} = \frac{DE}{BC}$

[solid kiln]

Mehdi_Moulati

[vague plaza]

Ahhhh

OK that makes sense

[stuck sable]

Intercept theorem or Thales theorem

[vague plaza]

Hmm

[vague plaza]

So can I equate them together?

[stuck sable]

yeah

DB is a common segment between ADB and BCD triangles

in the triangle ADB we will have
$\frac{DF}{DB} = \frac{DE}{DB} = \frac{EF}{AB}$

[solid kiln]

Mehdi_Moulati

[vague plaza]

But i get x = 30 which is wrong 😭

[stuck sable]

how did you get it ?

[vague plaza]

By equating them together

$\frac{\sin x}{\cos x} = \frac{1}{2\cos x}$

[solid kiln]

Candor.

[stuck sable]

this is not true

[vague plaza]

Oh it's not ☠️

Where did I mess up?

[stuck sable]

$\frac{EF}{DC} = \frac{sin(x)}{cos(x)}$

[solid kiln]

Mehdi_Moulati

[stuck sable]

and $\frac{EF}{AB} = \frac{sin(x)}{sin(2x)} = \frac{1}{2cos(x)}$

[solid kiln]

Mehdi_Moulati

[vague plaza]

Ah

[stuck sable]

$\frac{DC * sin(x)}{cos(x)} = \frac{AB}{2cos(x)}$

[solid kiln]

Mehdi_Moulati

[vague plaza]

Ahhh

OK ok

We have DC and AB too

Wait

[stuck sable]

you will get at the end : sin(x) = sin(x)

so it's not useful

[vague plaza]

Oh yeah true😭😭

[stuck sable]

just follow me

[vague plaza]

Alrr

[stuck sable]

by applying the Thales theorem in DBA triangle we will have :
$\frac{DF}{DB} = \frac{EF}{AB} = \frac{sin(x)}{sin(2x)} = \frac{1}{2cos(x)}$

[solid kiln]

Mehdi_Moulati

[vague plaza]

Yep

[stuck sable]

so $DF = \frac{DB}{2 cos(x)}$

[solid kiln]

Mehdi_Moulati

[stuck sable]

by applying the Thales theorem in DBC triangle we will have :
$\frac{BF}{DB} = \frac{EF}{BC} = \frac{sin(x)}{cos(x)}$

[solid kiln]

Mehdi_Moulati

[vague plaza]

Yeah

[stuck sable]

so $BF = \frac{DB sin(x)}{cos(x)}$

[solid kiln]

Mehdi_Moulati

[vague plaza]

Yep

[stuck sable]

and because BF + DF = DB

we will have :
$\frac{DB sin(x)}{cos(x)} + \frac{DB}{2 cos(x)} = DB$

[solid kiln]

Mehdi_Moulati

[stuck sable]

we can simplify by DB

[vague plaza]

We can cancel it out, yeah

[stuck sable]

so $\frac{sin(x)}{cos(x)} + \frac{1}{2 cos(x)} = 1$

[solid kiln]

Mehdi_Moulati

[vague plaza]

Alr lemme try this

,w solve sinx/cosx + 1/(2cosx) = 1

Oops

[solid kiln]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Candor.#5224

[stuck sable]

and since x between 0 and pi/2

so n = 0

[vague plaza]

Yeah it was between 30 and 45

I got it to that

Alr wait

[solid kiln]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[vague plaza]

Wait

,w solve -2*(tan((2+sqrt(7))/3))^(-1)

[solid kiln]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Candor.#5224

[stuck sable]

it's not 1/tan(x)

[vague plaza]

Tan^-1?

[stuck sable]

arctan(x)

[vague plaza]

Oh right

[solid kiln]

The following error occured while calculating:
Error: Unexpected type of argument in function pow (expected: number or Complex or BigNumber or Fraction or Unit or Array or Matrix or string or boolean, actual: function, index: 0)

[vague plaza]

,w solve 2(tan^-1(1/3(sqrt(7) -2)))

[solid kiln]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Candor.#5224

[vague plaza]

That's 24.56 in degrees

I'll try that

[stuck sable]

i got 24.295188945364570330759748906537 °

[vague plaza]

Yahh that's right

Thanks a lot!

[stuck sable]

gladly! 😉

[vague plaza]

.close

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[wraith hinge]

Describe the set of points whose distance from x-axis equals the distance from the yz plane

[shrewd ridge]

the distance from the yz plane is the x coordinate

the absolute value i guess

[sturdy leaf]

lets get some examples

(0,0,0) is obviously true

(x,y,z)
distance from yz plane is the x component
distance from x axis is via pythagoras: sqrt(y^2+z^2)

so our points are:
(sqrt(y^2+z^2),y,z)

$(\sqrt{y^2+z^2},y,z)$

[solid kiln]

~Martin

[trim jolt]

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[wraith hinge]

@sturdy leaf ok, so what kind of a figure do we get?

Seems like a cone, right?

@sturdy leaf also, so you know any book to learn 3d geometry, let me know please.

[sturdy leaf]

no sry

but yes it is a cone

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[wraith hinge]

@sturdy leaf thanks

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[timber perch]

.close

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[wraith hinge]

when doing related rates

when doing this part exactly, i have to put 0 i know but, do i keep the dZ/dt?

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[wraith hinge]

Two cars depart from the same point. One is heading south at 30 km/h and the other is heading west at 72 km/h. How fast does the distance between the cars increase two hours later?

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[clear thistle]

Helo

[clear thistle]

I'm given a 2nd degree homogeneous equation which is x²-kxy-6y² and the angle represented by this equation which is 45°. I've to find the +ve value of k.```

Here's my work

Is this correct??

<@&286206848099549185>

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@mystic sapphire Has your question been resolved?

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[tranquil junco]

What's the simplest way to prove that given some amount of string (say 100 cm), that the ellipse that encloses the biggest area is a circle?

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[astral mortar]

I’m not sure how to approach this

[trim lichen]

try to start small

[astral mortar]

If n=0 then we have 8 which is 2^3

[trim lichen]

and if n=1?

[astral mortar]

n=1 then we have 7^7 +1

I mean

[trim lichen]

can we get from 7^7 + 1 to a product of five primes in a way that, hopefully, generalizes somehow?

also like

i think induction would help us greatly here.

since 7^(7^(n+1)) = [7^(7^n)]^7

[astral mortar]

Ah yes

It suffices to show that if we have p=7^(2m-1) then (p^7+1)/(p+1) is a composite number

But how do I show this

Hm

[trim lichen]

well p^7 + 1 factors

[astral mortar]

Oh yeah

It’s

$p^6 -p^5 +p^4-p^3+p^2-p+1$

Bot dead

[trim lichen]

p, not x.

but yes

and... i think this can be factored further in turn?

probably not, actually.

[astral mortar]

[edgy cedar]

this can be rewritten as (p+1)^6 - 7p(p^2+p+1)^2

[astral mortar]

How?

I mean what’s the logic

[trim lichen]

well, you expand (p+1)^6 and see what's missing

supposedly

[edgy cedar]

pretty much

[astral mortar]

Okay so 7p is just 7^2m

(p+1)^6 - 7^2m^2

Hm

[edgy cedar]

what is your goal?

[astral mortar]

To show this is composite

[edgy cedar]

Right so can you write this as a product of 2 brackets?

[astral mortar]

Ooh difference of two squares

[(p+1)^3 - 7^m] [(p+1)^3 + 7^m]

so just check the smaller one

[(p+1)^3 - 7^m]

How do I deal with the m?

[edgy cedar]

7^m = sqrt(7p) we can argue that p>=sqrt(7p)

[astral mortar]

Yes

[edgy cedar]

[(p+1)^3 - 7^m] >= p^3+3p^2+3p+1-p^3-p^2-p

[astral mortar]

=2p^2 +2p+1

=113

[edgy cedar]

[astral mortar]

Thanks @edgy cedar and @trim lichen

.close

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[astral mortar]

I don’t really know how to do this

Hm

[amber python]

[edgy cedar]

@astral mortar you have lots of inequalities

[astral mortar]

Lol

[amber python]

chris literally did this the other day

no it was the exact same

[astral mortar]

Which

[amber python]

homogeneity + summing tangent line

[astral mortar]

Pure told me how to do it

This morning lol

You’re asking for inequalities so I’m just posting them

[amber python]

ugh typing this thing out is taking too long

[astral mortar]

Anyway this is the main q I’m doing

[twin swan]

is faq chris lol wtf

[amber python]

no

faq is not chris

[twin swan]

oh wait these are just usamo problems

are you grinding them out @astral mortar

[astral mortar]

Someone sent me lots of these problems

Im preparing for interviews

[edgy cedar]

what interviews

lol

[astral mortar]

Cambridge

[twin swan]

yeha what kind of interview ask for usamo questions

oh

[edgy cedar]

wtf

no

stop

[twin swan]

even so i think usamo is overkill

[sharp arrow]

[amber python]

bruh

[astral mortar]

@twin swan why

[twin swan]

just practice tmua

why are you doing usamo questions

[amber python]

theres no way you need usamo qs

[sharp arrow]

this is just cs

cauchy shwarz

no?

[amber python]

cauchy schwarz

[twin swan]

i remember snow broke it up into like 6 sub sums

[edgy cedar]

don't do any mos questions for cambridge

[twin swan]

no need for CS

[edgy cedar]

even trinity asks you basic maths

[twin swan]

they just did AM GM that’s it

[sharp arrow]

whatever

[astral mortar]

You never know

[sharp arrow]

[amber python]

am-gm and CS are the same thing

[twin swan]

nah there’s no way in hell

they ask usamo qs

[sharp arrow]

[twin swan]

usamo is so far removed

[edgy cedar]

Im literally at christ's

[sharp arrow]

[twin swan]

lol pulled the “i work here” card

[amber python]

[sharp arrow]

i’m low

[edgy cedar]

lol what

[sharp arrow]

[amber python]

wtf chris just unloading

[twin swan]

linty make ur own help

bro these aren’t related

ur just posting notes

[edgy cedar]

no one can read it

[amber python]

[astral mortar]

What should I do for interviews

[amber python]

https://cdn.discordapp.com/attachments/903463352582434866/1034053933791985735/118663865264242688.png

[sharp arrow]

even im having difficulty reading it

[twin swan]

LOL

wtf

it’s pretty smart

break it up into sums where you know the min and max will be

[astral mortar]

This is so chaotic

[astral mortar]

Whatever tbh Cambridge interview is calm

[amber python]

lmao chris brought everyone here

[sharp arrow]

it’s actually u

[twin swan]

so who sent you those problems @astral mortar

[amber python]

[astral mortar]

A friend

[twin swan]

this friend is trollin

[edgy cedar]

Whens your interview

[astral mortar]

6th dec

[sharp arrow]

good lick

[amber python]

[twin swan]

if you want practice try 1988 imo 6

[edgy cedar]

Calm

[sharp arrow]

luck

[astral mortar]

Too easy

[twin swan]

LMAO

what a guy

[sharp arrow]

[astral mortar]

@edgy cedar how long do you prepare for Cambridge interview

[edgy cedar]

a night before

[amber python]

you have your own solution

[edgy cedar]

just search my name

somewher

[astral mortar]

Calm

[twin swan]

british people man

[edgy cedar]

search faq

[astral mortar]

Wait how do you do thos 2^x + 25^y = z^2 integers

[sharp arrow]

frequently asked questions

[amber python]

[sharp arrow]

[twin swan]

mmmmmooddddddullaaarrr

[edgy cedar]

difference of 2

[amber python]

z^2 - 25^y = (z - 5^y)(z + 5^y)

etc etc

[astral mortar]

Okay here

Now what

[twin swan]

realize they must be power of 2

[edgy cedar]

you won't get into cambridge like this icl

[amber python]

2^x =

[twin swan]

imperial college london?

[astral mortar]

Bruv

I got an offer from Warwick

[twin swan]

[amber python]

[astral mortar]

It’s better for maths

[sharp arrow]

[astral mortar]

Wait so call them 2^m and 2^n

[amber python]

just search

[edgy cedar]

sqrt(x-1)+sqrt(y-1) <= sqrt(xy)

by c-s

[sharp arrow]

am-gm my beloved

[astral mortar]

The only solutions are 3,0,+-3

Hey look

[twin swan]

lol wtf

[amber python]

hölder

[twin swan]

lmfao

he goes to cambridge ofc he’s elitist what do you espect

[edgy cedar]

[amber python]

[sharp arrow]

pure in cambridge

[twin swan]

indeed

[sharp arrow]

bri’ish ppl here

[edgy cedar]

@astral mortar where did you apply

[astral mortar]

Trinity

[edgy cedar]

lol

i got rejected by trinity

pooled by Christ's

even if you get an offer from trinity

its gonna be S S

[twin swan]

no senior wrangler

https://tenor.com/view/byuntear-bob-sponge-spongebob-cry-sad-gif-25905087

[sharp arrow]

this all is gibberish to me

imma leave

[twin swan]

uk sucks that’s all

[edgy cedar]

[sharp arrow]

wait till u come india

[amber python]

[sharp arrow]

,w wake up

[amber python]

,w wuhan university

[sharp arrow]

[amber python]

wuhan univeristy has one amazing campus

[twin swan]

isn’t it tsinghua

wuhan

[astral mortar]

Lmao u suck

[amber python]

qinghua bruh

[twin swan]

sorry bruh

[amber python]

wtf is tsing

[twin swan]

Mao Tze-tsing

[edgy cedar]

trinity sucks

[twin swan]

china is weird bro

lot of memorization tho

[astral mortar]

How does the pool work

[amber python]

imagine being chinese

[sharp arrow]

imagine being human

[edgy cedar]

wdym

oh

[sharp arrow]

[amber python]

[edgy cedar]

its in the message request

thing

[wicked kelp]

no one help here🤧🤧

[sharp arrow]

i ignore all message request who straight up ask questions

[amber python]

i ignore all message requests

[sharp arrow]

how did u accept mine

oh we r friends

[amber python]

[astral mortar]

How do u do this

[sharp arrow]

faq man good luck for ur uni

[wicked kelp]

All of you just talking ... I send the question too many times here but no reply

[sharp arrow]

[astral mortar]

Thanks

[sharp arrow]

im out

[edgy cedar]

u will get in bro dw

[amber python]

should wish deep gl for jee

[edgy cedar]

i did

[astral mortar]

That’s why u got rejected from trinity

[sharp arrow]

by ignoring

[wicked kelp]

Can any one here help in me question related to real Analysis?????

[wicked kelp]

??

[twin swan]

so its not like ur royally fucked

[sharp arrow]

#❓how-to-get-help

[twin swan]

i hear they give offers to everyone tho

and that fulfilling the offer is the hard part

[astral mortar]

It’s calm

[sharp arrow]

[astral mortar]

AA AA

[amber python]

[twin swan]

u doing pure math?

[astral mortar]

2 A stars

[wicked kelp]

too many times I send the question here

[astral mortar]

Yes

[twin swan]

nice

[sharp arrow]

#real-complex-analysis

smart ppl hang out there

[edgy cedar]

how do you get very active role

[twin swan]

you

be very active

[sharp arrow]

get no life

[amber python]

be me

[edgy cedar]

[sharp arrow]

be circle

[twin swan]

man what happened to circle

pizza boy

stfu linty

[amber python]

shes studying

abstract algebra

[twin swan]

GROUP

groop

[sharp arrow]

shes still actively helping

[amber python]

gruup

[sharp arrow]

grout

[twin swan]

abstract algebra extracts a heavy toll

[amber python]

the toll goes to me

[twin swan]

billionaire

[amber python]

[sharp arrow]

[twin swan]

dude

[edgy cedar]

this is not gonna come up in interview

[twin swan]

stop doing MO problems

i swear that was on some indian math oly

[astral mortar]

Interviews are calm if I can this

[long basin]

What the fortnite

[twin swan]

yea well the thing is

[sharp arrow]

[twin swan]

to do that you need a shitton of practice

reliably*

that takes time

you dont have time

and its not necessary in any case

[astral mortar]

It’s calm bro dw

[amber python]

[sharp arrow]

do ppl still play fortnite in 2022

[twin swan]

battle royale

[amber python]

is calm british slang

[twin swan]

i haven o idea

[astral mortar]

I do interview questions in my head

[twin swan]

i've never heard calm ever

i usually hear "to be fair"

or "chav"

or sometimes "nonce"

[amber python]

to be fair

[twin swan]

linty

ur a nonce

[edgy cedar]

i say calm on daily basis

[twin swan]

imperial just different then

calm cambridge

[sharp arrow]

bri’ish

[amber python]

calmbridge

[sharp arrow]

do u hav tea everyday

[twin swan]

[amber python]

[twin swan]

had more tea in the states

[amber python]

have bubble tea every day

boba

[twin swan]

boba

[sharp arrow]

[twin swan]

doraemon

[edgy cedar]

[sharp arrow]

doraemon

[amber python]

dory

[twin swan]

https://tenor.com/view/dory-thinking-gif-26052646

[amber python]

that isnt dorymon

[sharp arrow]

not that fish

[twin swan]

shhh

[astral mortar]

What has my help channel turned into

[amber python]

[twin swan]

if u keep doing MO problems

[sharp arrow]

[twin swan]

that fish will haunt you

[sharp arrow]

lol

[twin swan]

bro do graph sketching or something

that comes up quite a bit doesnt it

[astral mortar]

This is not mo

[twin swan]

[astral mortar]

That’s calm

[twin swan]

ok sure can i give u one?

[amber python]

👀

[astral mortar]

I can sketch graphs with two eyes closed

[sharp arrow]

@ mod

[twin swan]

sketch y(y-1) = x(x-1)

go @astral mortar

[amber python]

chris delete

[twin swan]

^

chris stop advertising

[sharp arrow]

chris delete

[twin swan]

how the hell did he even get an invite link

[astral mortar]

Difference of two squares

[twin swan]

k

[astral mortar]

Then it’s calm

[twin swan]

BRo

SKETCH IT

[sharp arrow]

what is this interview thing

[twin swan]

weird stuff uk unis do

[astral mortar]

It’s just

2 straight lines

[twin swan]

describe it more bro

[astral mortar]

Passing through 1/2,1/2

[sharp arrow]

[twin swan]

show ur work

LMAO

[astral mortar]

I cba

Too easy

[twin swan]

LMFAO

BRO

DID U DESMOS IT

[sharp arrow]

cba

[amber python]

[sharp arrow]

[astral mortar]

Bro it’s literally just difference of two squares

I apply to trinity for a reason

[twin swan]

LOL

[astral mortar]

[twin swan]

ok faq

[sharp arrow]

ok uh if we shooting quest lemme shoot

sketch e^x sin x

[twin swan]

does an interval of 1000 consecutive integers where none of them are prime exist

[sharp arrow]

[astral mortar]

It’s just enclosed by e^x and -e^x

Calm

[amber python]

[twin swan]

CALM

[sharp arrow]

no uh

[twin swan]

https://tenor.com/view/fableforge-ttrpg-dnd-calm-zen-gif-25204344

[astral mortar]

Yes I literally asked pure the other day

[sharp arrow]

tell about its behaviour

[amber python]

calm

[astral mortar]

He said ❗

[twin swan]

but isnt it calm

[sharp arrow]

wtf is calm

[twin swan]

LMAO

[amber python]

lax

[twin swan]

lax

[sharp arrow]

[twin swan]

laxative

[amber python]

chill

[sharp arrow]

LaTeX

[twin swan]

$\LaTeX$

is it still dead

[astral mortar]

Tbh idk how to do this

[twin swan]

RIP

[sharp arrow]

[amber python]

🪦

[astral mortar]

❗

What does this mean

[sharp arrow]

[twin swan]

think factorial

[amber python]

not calm ❗

[twin swan]

thats all it means

i like how pure gave the hint lol

[edgy cedar]

you wont get in bro

[twin swan]

toxic

wait this is just british banter

[sharp arrow]

[twin swan]

BB

[amber python]

[twin swan]

🅱️🅱️

[astral mortar]

Don’t talk to me you got rejected from trinity

[twin swan]

[amber python]

🅱️

[sharp arrow]

ur so rude

[amber python]

🅱️🅱️

[twin swan]

🤣

[sharp arrow]

wtf is BB now

[twin swan]

british nuance flying over chris' head

[astral mortar]

It’s just a joke chill

[twin swan]

british bantah

[amber python]

brit bant

[sharp arrow]

[twin swan]

bantbrit

[sharp arrow]

oh wait i forgot

its due tmr

my assignment

[twin swan]

gl deep

[sharp arrow]

not again

[amber python]

[astral mortar]

Calm do it tar morning

[sharp arrow]

[amber python]

like last time

gl deep

[sharp arrow]

[edgy cedar]

A grid of size 2xn is covered with 2x1 dominoes. How many ways are there to do this? What about a grid of size 3xn and 3x1 dominoes?

@astral mortar

my trinity interview q

[sharp arrow]

[astral mortar]

Calm

I do this in my head

[edgy cedar]

maths econ blah blah

I hate economics

[amber python]

[astral mortar]

Lmao

[sharp arrow]

[astral mortar]

Imaginemajoring in econ

[amber python]

who are the ones with nitro here

[sharp arrow]

[astral mortar]

How do you this

[amber python]

chris admitting to a main 👀

[sharp arrow]

loopholes

[amber python]

recurrence relation bs

[astral mortar]

Okay calm

I do this in my head

[amber python]

[sharp arrow]

can u stop using calm

[amber python]

deep is sick of the calm

[astral mortar]

I don’t use roadmap English

[edgy cedar]

bye

[astral mortar]

K lol

[amber python]

[sharp arrow]

constipators

[zinc ginkgo]

@astral mortar change your name to faq-interview-help-channel

[trim jolt]

@astral mortar Has your question been resolved?

[sharp arrow]

lmao

[astral mortar]

.close

[trim jolt]

Channel closed

Closed by @astral mortar

Use .reopen if this was a mistake.

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.

[brisk nova]

What do I do in first one

[broken cave]

Then a is equal to?

Means what's the value of a?

@brisk nova

[brisk nova]

I know but I don't really know how to solve it

Can I make it 4a ln(1+x)/x

[broken cave]

I am just asking about your question

[brisk nova]

Oh

A is a constant

I need to know it

[obsidian sage]

maybe l'hopital's rule..?

[broken cave]

Yes ln(1+x)^4a = 4a ln(1+x)
You can imagine saying (x+1)=u then
ln u^4a = 4a ln(u)

[brisk nova]

What js that

I can't use U substitution rule

[obsidian sage]

can I post yt links?

[broken cave]

See formula 3

a is a constant

[brisk nova]

Yes

[brisk nova]

I think so

[obsidian sage]

https://www.youtube.com/watch?v=Gh48aOvWcxw

[brisk nova]

Lemme check

[obsidian sage]

this explains it pretty well

[broken cave]

Ok

[broken cave]

,rotate

Oh tex is offline

[brisk nova]

I found it

[broken cave]

Good

What it is?

a²-4a+4=0 ?

[obsidian sage]

I got that too

[broken cave]

Yupp same

[broken cave]

And apply the quadratic formula then

[brisk nova]

So basically

Is it gonna be

4a+1

[broken cave]

Yes lim_{x approaching to 0}ln(1+x)/x = 1

[broken cave]

Why plus one

4a×1

[brisk nova]

Multiply?

Oh

[broken cave]

Yes

[brisk nova]

Okay

Then

I will make it

Minus 4

Or

[broken cave]

a²-4a+4=0

[brisk nova]

Uh

Factorization it

?

[broken cave]

Well you could use the quadratic equation

[obsidian sage]

I think factorising it is simpler

[broken cave]

Yes you could do it

By factoring it

Or the quadratic formula

Anything you like

[brisk nova]

Ok um

My question is

[broken cave]

a²-2a-2a+4=a(a-2)-2(a-2)=(a-2)²

So a=±2

[broken cave]

Yes

?

[brisk nova]

Wait

[obsidian sage]

did you mean root 2?

[broken cave]

Yeah it is

[obsidian sage]

I think it's just 2

[brisk nova]

X=2

[broken cave]

Oh sorry 2

[obsidian sage]

ye

[brisk nova]

Can you guys help me write it down using sreps

Steps

I will try writing it now

[broken cave]

Wait

[obsidian sage]

Smth like this?

sorry it's a bit blurry

[obsidian sage]

I think it's a bit of a jump from line 2 to 3, but if you understand it that's all good

[brisk nova]

I have a rule that ln(1+x)/x =1

But im supposed to get the 4a out of the thing?

Before doing the rule?

[obsidian sage]

it's a constant so you can take it out of the limit so to speak

[broken cave]

Got it?@brisk nova

[brisk nova]

Thanks alot

I got number 4

Problem with it

[broken cave]

Yeah I can do it

[brisk nova]

Is it gonna be 3ln2

[broken cave]

No 4 right

1/3 ln(2)

[brisk nova]

How

[broken cave]

2 min

I m showing u

[brisk nova]

Okay

[broken cave]

Got it?

[brisk nova]

My questjon js

If I multiply 1/3 inside don't I need to multiply 3 outside

[broken cave]

You don't need to

[brisk nova]

Why

[broken cave]

You don't have to multiply

[brisk nova]

We multiply 1/3

[broken cave]

You could just take 1/3 as a constant

[brisk nova]

I can just take it out

?

[broken cave]

Let's just say 2^x+1= c ok ( c is a random variable)

[brisk nova]

Ln2

[broken cave]

Then
lim c/3x right ?

and we can write that as

Lim 1/3 × c/x

Cause 1/3× c/x = c/3x right

[broken cave]

For not making my hands ded

[brisk nova]

Wait

So like

I could have directly took the 3 out

[broken cave]

Yes you could directly put the 1/3 out

[brisk nova]

As 1/3 x 2^x-1/x

[broken cave]

Yes

And by using the formula

Formula no 4

You will get 1/3× ln (2)

[brisk nova]

I got it

Thanks alot

[broken cave]

Welcome what's your age btw?

[broken cave]

🫂

[brisk nova]

Im 16

[broken cave]

Oh I am 14

[brisk nova]

Wow

Im surprised mister rabbit?

[broken cave]

Arnab *

[brisk nova]

Arnab

Is rabbit

[broken cave]

Yech

[brisk nova]

Right

[broken cave]

Nope Arnab means sea in my language

[brisk nova]

Oh

It means rabbit here

[broken cave]

Yes

[broken cave]

Oh 😂😂

Wow

[brisk nova]

Last one in this page

How do I do it

[broken cave]

The derivative ?

[brisk nova]

I think so

[broken cave]

Ok wait

[brisk nova]

How do I get dy over dx

[broken cave]

@solid kiln

Now online wait

Let's say
$f(x)=sec(x/4) + sec (π/4)$

Wow offline

This bot is .......

[brisk nova]

Yea

Sec pi/4 is a constant

If we make it derivative we can get rid of it

[broken cave]

Yes

[brisk nova]

I need to know how to get dy/dx if i don't know the derivative of x

[broken cave]

Just find the derivative of
sec(x/4)

That's it

And sec(π/4) is a constant so it is = 0

[brisk nova]

I think

Isk

Idk

[broken cave]

What's the derivative of sec?

[brisk nova]

Sec.tan

[broken cave]

sec(x/4).Tan(x/4) I think so but I am having doubt bec of 1/4 here

[brisk nova]

My issue is we need to like

Put the derivative of x/4 outside

[broken cave]

I don't know how did it came

,w d/dx(sec(x/4))

[brisk nova]

Dx over dy

Not dy over dx

@broken cave

Probs u switched it

[broken cave]

Oh

Extra 1/4

[broken cave]

Oh yeah

[brisk nova]

Is it cuz of 1/4

X whole term

OVER 4

[broken cave]

I didn't knew this one

But the used chain rule

I totally forgot about that

d/dx(f(g(x))= f'(g(x)) × g'(x)

[brisk nova]

I was speaking about chain rule

That we need to get derivative of the x/4

And multiply it

[brisk nova]

But idk names in enflush

[broken cave]

Yess

[brisk nova]

Ok imma write it down

[broken cave]

Yes

What would you expect from me it's 3 am in my area

[brisk nova]

I dunno

Almost 12 here

[broken cave]

Pm or am?

[brisk nova]

11:46pm

[broken cave]

Oh it's 3 am in my area an I m tired

[brisk nova]

Can I simplify this more?

[broken cave]

You can but you don't have to

[brisk nova]

Okay

[broken cave]

👍

[brisk nova]

Do u know what to do in number 2

3

[broken cave]

If x= Tan(1+y) find dx/dy?

Or dy/dx

[brisk nova]

Yea

[broken cave]

What is it?

[brisk nova]

I need to find dx/dy then flip it

Dy/dx

[broken cave]

Implicit derivative?

[brisk nova]

What

[broken cave]

Where you flip the other constant terms

[brisk nova]

I think so

[broken cave]

You could Google it

But if you are taking the derivative of d/dx(Tan(1+y) then it would be = 0 cause y is a constant with respect to x

But if you take d/dy then you could use the chain rule

[broken cave]

It will be
Sec²(1+y) then

[brisk nova]

Flip it

1/sec

[broken cave]

1/sec²(1+y)?

I used my full brain

[brisk nova]

= cos²(1+y)

[broken cave]

How?

Oh 1/sec = cos

Got it

Oh I am sleepy

I have to sleep

3:30 am now

Byee

[brisk nova]

Goodnight

Now time to integrate these things

.close

[trim jolt]

Channel closed

Closed by @brisk nova

Use .reopen if this was a mistake.

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.

[limber pelican]

I am not sure how to solve for the x values that y^2-2x^3-12x^2=0

[limber pelican]

The values of x that have horizontal tangent lines actually

[trim jolt]

@limber pelican Has your question been resolved?

[trim jolt]

@limber pelican Has your question been resolved?

Channel closed

Closed by @limber pelican

Use .reopen if this was a mistake.

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.

[zinc ginkgo]

read this

[trim jolt]

@old quarry Has your question been resolved?

[zinc ginkgo]

you don't even have a question why are you pinging helpers

why are you talking to me

.

begs for help. cusses at helper

lol

☮️

[trim jolt]

Channel closed

Closed by @old quarry

Use .reopen if this was a mistake.

[zinc ginkgo]

<@&268886789983436800>

[trim jolt]

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.

[quaint gazelle]

sqrt(x²)=|x|

well its true

for real numbers

by definition

sqrt(x)

is the POSITIVE number

such that

sqrt(x)² =x

you cant take the root of a negative number

yes but its squared so its positive

because its false

unless specific values of theta are taken

where 1-cos is positive

oh nvm

1-cos is always positive

what am i thinking

cos <=1

-cos >= -1

1-cos>=0

no