help-4

[stark wedge]

when you write 3¼ do you mean three plus a quarter? or do you mean 3 raised to the power of 1/4?

[frozen laurel]

3 raised to 1/4

[fossil torrent]

What do you mean by Newton's formula?

[stark wedge]

$x^2 - 3^{1/4} x + 3^{1/2}=0$

[rocky lotus]

Ann

[stark wedge]

like this?

was unclear from your original msg

you can find the roots as complex numbers and then convert them into polar form.

[frozen laurel]

Oh wait

I did something

I think I got the answer

I played around with it

[fossil torrent]

In your original question as you posed it, the sign of the 3^(1/4) was negative

[vale dock]

@frozen laurel Has your question been resolved?

[vale dock]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vale dock]

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.

[sharp cloud]

Hi I need help

[sharp cloud]

I need help from 1. to 3., I have zero knowledge about it but yeah

[wraith heart]

,rotate

pain

[hearty belfry]

😭

[wraith heart]

use pythagorean theorem

[hearty belfry]

do you know pythagoras theorem

[sharp cloud]

a^2 = b^2 + c^2?

[stark wedge]

before we get to pythagoras we need to also find out how to identify the right angle in each triangle

[sharp cloud]

,rcw

pain

[hearty belfry]

it's generally written as a^2 + b^2 = c^2, but yeah

[sharp cloud]

so far thats what Ive done but

I dont get how I'll get EG and BE if there aren't any values for them

[stark wedge]

well the idea for EG is that you focus to just the rightmost face (in which EG lives) and look at triangle EFG or EGH (your pick. if you can't pick, then EFG.)

noting that EG will be the hypotenuse of that triangle, while its legs are the known depth and height of the cuboid

[sharp cloud]

so EG = 4^2 + 3^2

[stark wedge]

EG**^2** = 4^2 + 3^2.

in pythagoras' theorem, all sides are squared.

you shouldn't omit the square on any of them. it's a pretty common stumbling spot.

[sharp cloud]

How about for BE?

[stark wedge]

look at triangle BGE, which is again a right triangle with the right angle sitting at G

[sharp cloud]

oh actually

[stark wedge]

and now its two known sides are EG (which we just found) and BG (which is the length, 12)

[sharp cloud]

its a right angle?

[stark wedge]

yes

imagine tipping the cuboid over so that face EFGH rests on the ground

then edge BG will be upright and thus perpendicular to anything that's level with the ground

incl. edge EG

[sharp cloud]

ohhh so the answer is 13

can you help with no. 3?

[stark wedge]

sure, do you know the SOH-CAH-TOA mnemonic?

[sharp cloud]

yeah?

sin = opp/hyp, cos = adj/hyp, tan = opp/adj?

[stark wedge]

yes.

it's just this mnemonic and figuring out what goes where.

carefully mark all known side lengths and right angles in every triangle involved.

[sharp cloud]

could I ask for help on no. 2, b.?

uh length of BF to be exact

bcs I got 12.64

could I ask help double checking? Cs I think it's wrong

[turbid valve]

[your pen's kinda blocking the diagram]

[turbid valve]

I'm guessin it's this one tho

But I got root(160) too, which is 12 point something yh

[vale dock]

@sharp cloud Has your question been resolved?

Channel closed

Closed by @sharp cloud

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.

[cosmic crest]

need to find error bound on an approximation from simpson's rule.

[cosmic crest]

(delta X ^ 4)/180 all that multiplied by (b-a) times K

,calc ((1/4)^4)/180

[rocky lotus]

Result:

2.1701388888889e-5

[cosmic crest]

,calc 2.1701388888889e-5 * 3

[rocky lotus]

Result:

6.5104166666667e-5

[cosmic crest]

K * 6.5104166666667e-5

need to solve for K

iirc I need to find the max value of K within the given interval which is [1,4]

and choose K to be that

but I don't like graphing. could prob use calc 1 stuff to find max but I forgot, how does finding max point in an interval work again?

[rocky lotus]

Result:

0.0015625

[cosmic crest]

,calc 6.5104166666667e-5 * 24

[rocky lotus]

Result:

0.0015625

[wraith heart]

!original

[vale dock]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[cosmic crest]

integral from 1 to 4 x^4 dx. a. find sympsons rule approximation. b. find error bound on your approximation

I suppose I shouldn't have even included this context

my question is how can I find the max point on the given interval for x^4

[wraith heart]

either plot x^4 or evaluate it for a few values of x in your domain and find a pattern then use calculus to verify your pattern

[cosmic crest]

what were the calculus steps to find a max within an interval?

(I know we need fourth derivative here and the max is 24=K but I wanna know how to solve harder problems without graphing)

[wraith heart]

and https://tutorial.math.lamar.edu/Classes/CalcI/AbsExtrema.aspx

[cosmic crest]

omg yeahhh the 1st deriv test

okay bet that's all I needed, tysm

.close

[vale dock]

Channel closed

Closed by @cosmic crest

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.

[rocky lotus]

brandon

[vale dock]

@tawdry lintel Has your question been resolved?

[vale dock]

@tawdry lintel Has your question been resolved?

[vale dock]

@tawdry lintel Has your question been resolved?

[vale dock]

@tawdry lintel Has your question been resolved?

[charred burrow]

<@&286206848099549185>

[vale dock]

@tawdry lintel Has your question been resolved?

[leaden kraken]

what is the way you use?

[vale dock]

Channel closed

Closed due to timeout

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.

[tight violet]

I need a reminder on how to do these questions cause I forgot

[tight violet]

I forgot how they work I need an explanation on them to jog my memory

[hearty belfry]

do you know what nCr is?

which just means n choose r

[tight violet]

I’m Pretty sure n is the max number of options and r is the amount of options that you can choose between

Like if theres 12 teachers you can choose between 7

So 12c7

Is that right?

[hearty belfry]

yep

[tight violet]

When does it become a fraction though?

Cause in some questions it becomes like

12!/7!

[hearty belfry]

that's because they use this formula

although 12!/7! is the wrong option

[tight violet]

that’s not what I mean in like some questions the answer becomes 12!-7!/9! it’s weird I forgot how that worked

The formula isn’t what I’m concerned about

[tight violet]

Yeah that was just an example

[hearty belfry]

which question?

[tight violet]

Let me find one rq

[hearty belfry]

alright

[hearty belfry]

the wording is a bit confusing but I think it's just another nCr question but you have duplicates for R?

also Darren not knowing how to spell his name is funny to me

[tight violet]

The answer key says the answer is 5! Over 2! Which is 60 cause of the duplicate r but I need to what else can cause fractions like these to occur

[tight violet]

There’s a visual of it

[hearty belfry]

It's dependent on what the question asks if you try to figure out what causes the fraction to occur

like the question says they already had the letter D being in front

so D is excluded

[tight violet]

It would be 1 x 5 x 4 x 3 x 2 x1 I think but the two on the bottom I’m not sure why it’s there could you explain why?

I get it’s cause of the duplicate r but why do we divide and not subtract or smth

[tawny moon]

one hint for some weird counting that may show up: the two Rs are identical, so swapping those two Rs don't change anything and they count as duplicates

we divide instead of subtract to account for the duplicates because for each arrangement of ARREN, you can get an identical arrangement by swapping the two Rs
since they count as duplicates, each arrangement of ARREN actually counts as two arrangements - not what we want here

[tight violet]

Oh

Alright

What about the binomial theorem

How would I solve these questions?

[tawny moon]

have you learnt about the theorem?

[tight violet]

Yeah

It was like 2 months ago so I’m blanking on it a little

[tawny moon]

then this one is just direct application of binomial theorem, then a bit of tedious expansion

use pascal's triangle to help

[tight violet]

I’m not sure how to write something in descending order though

[tawny moon]

descending order of x is just x^5, x^4, x^3, etc.

[tight violet]

The middle term for 211 is 4 right?

[hearty belfry]

you mean 3rd posistion of the terms?

it's to the power of 6 so the middle term would be the 3rd term

[tight violet]

I’m blanking on something cause I remember that one term in the binomial Theorem was the number of terms -1

I thought it was the exponent but I guess not

Like this

[hearty belfry]

that's the defenition of a factorial when you do n(n-1)(n-2).....3x2x1

[tight violet]

Oh it was R that was -1

What’s the trick with these

My bad for the bad lightning I’ll use the flash on my phone

[vale dock]

@tight violet Has your question been resolved?

[tight violet]

The question was determine the number of paths from point a to b

[vale dock]

@tight violet Has your question been resolved?

[vale dock]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vale dock]

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.

[midnight pier]

I was able to reduce the equation to (b-6)(a-3) = 18. and then i basically made cases using the idea of factors of 18.
I was able to get the correct answer (6)
But I keep wondering if there is a neater way to do this that does not involve making so many cases, and i also had a raging fear throughout that i'll miss some cases.

Also I spent a couple of minutes making sure that I didnt have a case wherein both the factors are negative. Is there a cleverer way to know that there arent?

[lament copper]

All the positive factors of 18 are solutions

The negative solutions you do have to check to see if they are positive or not

[midnight pier]

so basically as soon as i know the factors of 18, i can tell the number of positive solutions

[midnight pier]

is this because the coefficient of a and b is 1?

[lament copper]

let (a-3)(b-6)=cd

one solution would be a-3=c and b-6=d

so a=c+3 and b=d+6

if c and d are positive integers then a and b are clearly positive

[vale dock]

@midnight pier Has your question been resolved?

[vale dock]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vale dock]

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.

[stark wedge]

well any multiple of 4 is non-square-free

[ebon glade]

well certainly at most 8 cause two of them are divisible by 4

[stark wedge]

so's any multiple of 9

[ebon glade]

I would probably brute force with a computer and check whether there is a small example with 8

the one divisible by 9 could be one of those divisible by 4

[ruby sleet]

33-42?

[ebon glade]

well that was easy

[ruby sleet]

We just said there can't be more than 8

And here's an example with 8

So...

0

Bc you said you can have 10 non-square free consecutive integers

[ebon glade]

I suppose by crt you can solve a= 0 mod 2^2, a+1=0 mod 3^2, a+2 = 0 mod 5^2, a+3=0 mod 7^2, ...

or is there a nicer solution to that

[ruby sleet]

Yeah that's how I would have done

[vale dock]

Channel closed

Closed by @tawdry lintel

Use .reopen if this was a mistake.

[vale dock]

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.

[prime shore]

can anybody kindly solve this problem?

[magic lynx]

uh

okay

so $f(x,y)=\frac{(x^2-y^{-2})^x(x-y^{-1})^{y-x}}{(y^2-x^{-2})^y(y+x^{-1})^{x-y}}$

[rocky lotus]

Arnavutköy

[magic lynx]

we can rewrite $x^2-y^{-2}$ using the difference of squares formula

[rocky lotus]

Arnavutköy

[magic lynx]

$x^2-y^{-2}=(x+y^{-1})(x-y^{-1})$

[rocky lotus]

Arnavutköy

[magic lynx]

we can do a similar method for $y^2-x^{-2}$

[rocky lotus]

Arnavutköy

[magic lynx]

Thus, $f(x,y)=\frac{(x^2-y^{-2})^x(x-y^{-1})^{y-x}}{(y^2-x^{-2})^y(y+x^{-1})^{x-y}}=\frac{(x+y^{-1})^x(x-y^{-1})^x(x-y^{-1})^{y-x}}{(y-x^{-1})^y(y+x^{-1})^y(y+x^{-1})^{x-y}}$

[rocky lotus]

Arnavutköy

[magic lynx]

combining exponents with the same bases, we get $f(x,y)=\frac{(x+y^{-1})^x(x-y^{-1})^y}{(y-x^{-1})^y(y+x^{-1})^x}$

[rocky lotus]

Arnavutköy

[magic lynx]

let us rewrite this as $\left(\frac{x+y^{-1}}{y+x^{-1}}\right)^x\left(\frac{x-y^{-1}}{y-x^{-1}}\right)^y$

[rocky lotus]

Arnavutköy

[magic lynx]

note that $\frac{x+y^{-1}}{y+x^{-1}}=\frac{\frac{xy+1}{y}}{\frac{xy+1}{x}}=\frac{x}{y}$

[rocky lotus]

Arnavutköy

[magic lynx]

similarly, note that $\frac{x-y^{-1}}{y-x^{-1}}=\frac{x}{y}$

[rocky lotus]

Arnavutköy

[magic lynx]

Therefore, $f(x,y)=\left(\frac{x}{y}\right)^x\left(\frac{x}{y}\right)^y=\left(\frac{x}{y}\right)^{x+y}$

[rocky lotus]

Arnavutköy

[magic lynx]

does that make sense?

@prime shore

[prime shore]

it does!

thanks for helpingg i spent a lot of time pondering over how to solve this

[magic lynx]

np

[fossil pelican]

Why don't people just use Google?

[vale dock]

@prime shore Has your question been resolved?

Channel closed

Closed by @prime shore

Use .reopen if this was a mistake.

[vale dock]

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.

[ivory valley]

Is it correct?

Should have stated R^n -> R

[vale dock]

@ivory valley Has your question been resolved?

[light saddle]

line 2 after "furthermore", what you added in the numerator should cancel out no?

[ivory valley]

I thought I can still write it because it approaches 0

Before that I tried adding and subtracting terms like x(t0)y(t) but it didn't work out

[light saddle]

it should be "that thing" / t-t0 that approaches 0 i think

[ivory valley]

Since continuity is necessary and x,y are comtinuous that would then make xy continuous as well, So I used that

I basically added -y(t)x'(t0) + y(t0)x'(t0) which exists by assumption and goes to 0

lol

realized

[light saddle]

but its $\frac{-y(t)x'(t0) + y(t0)x'(t0)}{t-t_0}$ that you added

[rocky lotus]

bloubbloub

[light saddle]

I mean you realized

[ivory valley]

No

[ivory valley]

That doesnt make sense, I already considered t-t_0

[light saddle]

oh I didn't see the '

[ivory valley]

So basically I added -x'(t0)(y(t)-y(t0)) so an error term that goes to 0

I think

The way I did it, I was looking what I needed to add and subtract precisely

[light saddle]

ok yeah I see

[ivory valley]

I be home in a bit

[light saddle]

I don't see any problems then, since it's very similar to the proof for n=1 anyways

[ivory valley]

I should have added this I guess

[ivory valley]

Thank you very much for your time, patience and help!

.solved

[vale dock]

Channel closed

Closed by @ivory valley

Use .reopen if this was a mistake.

[vale dock]

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.

[grizzled furnace]

someone pls explain

[fickle rose]

the calculator computes arcsin(1/2)

which is actaully 30deg

but arcsin domain is limited to it "cuts" off the other solution at 150deg

[grizzled furnace]

but where'd they get the 150?

[fickle rose]

at 150deg is you draw out the triangle on the unit circle

indeed it has a height of 1/2

as shown on the diagram

[hexed basin]

hey can someone help me w my algebra

[fickle rose]

#❓how-to-get-help

[hexed basin]

idk how to do it been trying for like an hour and a half

[hexed basin]

ty

[grizzled furnace]

bet

[hexed basin]

ty

its js that i dont understand the concept or procces

[grizzled furnace]

send me the thing

[hexed basin]

js one of the problems?

[grizzled furnace]

ye for now

[hexed basin]

3 (2x + 2) - 3x = 6 + 3x

[grizzled furnace]

alr

[hexed basin]

i think im js slow

[grizzled furnace]

do you have to solve for x

[hexed basin]

yea

btw heads up im a little dumb so when u explain it js pls make it simple 🙏

[pliant sonnet]

Its okay once you get it it will be very easy

[grizzled furnace]

or do you isolate x

[hexed basin]

i solve for x

[hexed basin]

ik that because anytime i understand a unit in math i get an a for that unit

[grizzled furnace]

alr

so

yk the distrubitive law?

[hexed basin]

no XD

[grizzled furnace]

oh ok

where'd you get this quesion?

[hexed basin]

school

its a school work packet my teacher gave us all and it ment for class but im using it to study

[pliant sonnet]

You didn’t learn distrubitve law yet?

[lyric sundial]

Yeah it seems weird

[grizzled furnace]

wait do you know how to expand

it's basically the same thing

I have the working out

[hexed basin]

ion jack

havent payed attention in forever in math

[grizzled furnace]

ok.

[pliant sonnet]

Uh

[grizzled furnace]

um ok

well

this is the woking out:

3(2x+2)-3x=6+3x

=6x+6-3x=6+3x

=3x+6=6+3x

=6=6

[vale dock]

@grizzled furnace Has your question been resolved?

Channel closed

Closed by @grizzled furnace

Use .reopen if this was a mistake.

[grizzled furnace]

.close

[vale dock]

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.

[midnight pier]

so i have a cubic polyomial, x^3 + 10x^2 - 11x - 180, i am trying to learn the factor theorem,incase i get to do gcse FM, but im wondering how to factorise/solve a cubic, as the equation is very long, and ive heard about trial and erroring roots of the constant but im not sure if that is the most efficient way

[oak crane]

u need to find possible numbers

so u can use long div or synthetic div

[midnight pier]

so synthetic div is dividing by the root that makes f(x) = 0?

[oak crane]

yep

[midnight pier]

ah kk, ill try that and come back

[oak crane]

$$\polylongdiv{x^4 - 3x^2 - 5x + 2}{x + 2}$$

[rocky lotus]

アキラ (>⩊<)

[oak crane]

u can do something like this in latex btw

just a sample

oh shit i got very active lol

[oak crane]

another sample

$$\polyhornerscheme[x=-2]{x^4 - 3x^2 - 5x + 2}$$

[rocky lotus]

アキラ (>⩊<)

[oak crane]

🙂

i personally like long div bc its easier and faster

[midnight pier]

o

[midnight pier]

w

[midnight pier]

so uh ive forgotten synthetic div..

[oak crane]

thats ok

i can help u

[midnight pier]

cus in my school for the normal igcse its calc only sooo

YES pls

[oak crane]

ok so did u do something?

[midnight pier]

so i have x + 5 root x^3 + 10x^2 - 11x -180

right now

[oak crane]

nice

so u can make it as x=-5 if ur gonna use synthetic div

but are u sure x+5 works?

[midnight pier]

i thought we take the inverse of f(x)

its x - 5 that works

[light saddle]

I just wanted to add that HOLY that is so cool that you can use the bot to do that, thanks for showing

[oak crane]

its x+5

,w (-5)^3 + 10(-5)^2 - 11(-5) - 180 =

[rocky lotus]

Results provided by WolframAlpha

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

Requested by kensukeken

[oak crane]

see

[midnight pier]

OHHHH so if -5 works that means f(x) = f(5)?

and the factor becomes x + 5

[oak crane]

yep

[midnight pier]

ahhhhh

[oak crane]

if it was x+5 that would make it -5 and if x-5 then its 5 🙂

[midnight pier]

so i put x - 5 outside my division?

[oak crane]

for long div?

[midnight pier]

synthetic

or is it same

[oak crane]

for synthetic write it as -5

bc x+5

[midnight pier]

ahhh kk

so it becomes x+5 divide x^3 + 10x^2 - 11x - 180

[oak crane]

thats for long div yes

[midnight pier]

so whats the difference betweeen that and synthetic?

[oak crane]

sorry if my english sucks but in long div u could write the x and makes it easier to solve

as for synthetic u could remove the x

[midnight pier]

oh so synthetic is just -5 divide x^3 + 10x^2 - 11x - 180

also ur english is fine bro

[oak crane]

e.g u have x^3 + 10x^2-11x-180 that would make it 1+10-11+180

[midnight pier]

ohhhh

[oak crane]

we are removing x variables here

[midnight pier]

ohhh so synthetic gets rid of x i seeeee

[oak crane]

yep

[quiet tide]

"sorry if my english sucks" as bro is speaking perfect english

[midnight pier]

so which is more efficient in an exam scenario?

[midnight pier]

lol fr

better english than me gng

(and better maths too)

[oak crane]

sometimes ppl say it sucks and some of them say its good so i cant disagree with this lol

[oak crane]

yea

[midnight pier]

so i use synthetic?

[oak crane]

u can use both

[quiet tide]

if u always speak like this they might just not be smart enough to understand ur english ig 😭

[oak crane]

whatever u think is the best

[midnight pier]

uhh

[oak crane]

its just i speak english bc its the only language they know

[midnight pier]

o its 00:00 lol perfect a brand new day

[oak crane]

lol

[midnight pier]

but anyway

uh

which would you prefer

[oak crane]

i prefer long div

[midnight pier]

kk can you teach me it then pls..

[oak crane]

nice and clean

yea sure

[midnight pier]

thankss

[oak crane]

let me write it down for u

[midnight pier]

kk

[quiet tide]

watchu know about trenbolone vyass

[midnight pier]

OOO

AIGHT

TRENOBOLONE ACETATE AND ENTHATE

[oak crane]

start doing like this

[midnight pier]

acetate better icl

[midnight pier]

yea

[quiet tide]

frfr (i have never touched it im scared)

[oak crane]

u need to divide it just like u are dividing 25/2000

just an example

[midnight pier]

basically binds to androgen receptors in the muscle cells and acts as synthetic hormone(testosterone) to promost MPS(muscle protien synthesis) which enhances rate at which muscle is gronw

[midnight pier]

same lol

[midnight pier]

so uh

wheres the 25 and 2000 come from...

OH ITS AN EXAMPLE

im tapped nvm 😭

so how do i divide x^3 by x for this

[oak crane]

think of a small variable that u could subtract it by x^3

[midnight pier]

so its x^3 - x?

[oak crane]

and for 10x^2 as well

[oak crane]

not quite

[midnight pier]

o

do i divide it?

to give x^2?

[oak crane]

u need to find a variable that makes it x^3 when u multiple so they can go away

[midnight pier]

oh x^2 and x

[oak crane]

x^2 is correct but x isn't 🙂

[midnight pier]

O

uh

x^1...

[oak crane]

so u have x^2 and u need to find something that multiples by 10x^2

[midnight pier]

ohhhhh

[oak crane]

its gonna be a number and variable

[midnight pier]

so x^2 * something = 10x^2

so itll be 10

[oak crane]

leave x^2 as its for now bc thats for x^3

[quiet tide]

i dont even remember the last time i did long division such an ancient skill

[midnight pier]

lol

[oak crane]

we are trying to find 10x^2

[midnight pier]

hmm

10 and x^2

[oak crane]

nope

try again

[midnight pier]

10x and x?

[oak crane]

not quite 😭

think of a small number

[midnight pier]

erm

5x and 2x..

[oak crane]

wait i think im starting making things complicated for u

[midnight pier]

😭

[final adder]

eyy congrats on VA!

[oak crane]

since we have x+5 as divider i want u to find a number that multiples 5 to get lower number

[oak crane]

thanks i got it again after a while

[midnight pier]

so like 5 and a negative?

[oak crane]

5 x [something] = 10

[midnight pier]

OH, 5x(2) = 10x..

or is it not 10x

[oak crane]

nonono

[midnight pier]

shit im tripping lol

[oak crane]

sorry i suck at explaining things 😭

how i can give u a hint

[midnight pier]

nanaa all good my brains fried lol but i aint gonna sleep till i understand this lmao

[oak crane]

ok here's a thing: what are the two number that gives 5x?

[quiet tide]

no 2 numbers give 5x

unless u mean just 5 and x

[midnight pier]

5 and x?

[oak crane]

5x and 1 lol

[midnight pier]

OHHH

SHIT

[quiet tide]

u should watch organic chem tutor video on this

[midnight pier]

yeaaa

[quiet tide]

u will leave with 80% confidence with these problems easily

[midnight pier]

oo

might do tbf

[oak crane]

u can use khan academy as well

[midnight pier]

kk

[quiet tide]

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

[oak crane]

do u get it or still stuck?

[midnight pier]

uh i mean i understand where the numbers come from now

[oak crane]

oh fair

[midnight pier]

and why long division sucks and calculators should take over lol

not the clankers tho..

[oak crane]

now we have x^2+5x

[midnight pier]

kk

[oak crane]

can u continue from this?

[midnight pier]

where do i write x^2 and 5x

[oak crane]

i forgor what do u call this in english

[midnight pier]

long division?

[oak crane]

yes

[midnight pier]

yeaaa

[quiet tide]

thats the dividend

[oak crane]

just solve it like u are dividing

[quiet tide]

if u mean the final answer

[midnight pier]

kk

[oak crane]

i meant this

i forgor what do u call this lol

[midnight pier]

oh my days im so tapped i wrote the cubic above the line.

[quiet tide]

thats part of the dividend

[midnight pier]

Ok i have this

Do i multiply 11x by x?

[oak crane]

nope

multiple it by 5x

[midnight pier]

Why?

[final adder]

the quotient, i think?

dividend's on the inside

dividend/divisor=quotient

[oak crane]

perfect thanks

[oak crane]

bc u'd get 25x

[midnight pier]

huh...

[oak crane]

also i'd suggest making negative so u can get rid of it easily after

[midnight pier]

im kinda lost rn...

[oak crane]

5 times 5x

gives 25x

[oak crane]

i told u i suck at explaining things

[midnight pier]

but why do we do 5 * 5x and not 5 * 11x or something, and isnt it 5x^2

[midnight pier]

fair enough

[oak crane]

bc -11x is negative

[midnight pier]

why does the sign matter?

[oak crane]

it matters bc u need to cancel them at the end

when the next number comes

for 180

does that makes sense?

[midnight pier]

yea kinda

but then why do you multiply the 5 with 5x and not 5x^2

[oak crane]

bc u found a number to get rid of 10x^2 first

[turbid valve]

So, that 5x you get, you're multiplying it by the whole divisor, which here is x+5

[midnight pier]

but its 5x^2?

[midnight pier]

are we talking abt the very bottom line?

[oak crane]

u can continue from here 🙂

[turbid valve]

Do that, write that product below the 5x^2 -11x and subtract

[midnight pier]

o shi ty for the bhelp

[midnight pier]

so i do x^3 + 5x^2 - 0 + 5x^2 - 11x?

[turbid valve]

So, I would have asked a question before jumping straight into (what this is called is) algebraic long division:

Do you know how to do long division (i.e. with numbers)?

[midnight pier]

its been a while but yeahh i think so

[turbid valve]

Make sure you can still do those

[midnight pier]

drop the remainder down, subtract, bring it to the top, drop down and rinse and repeat

[turbid valve]

ye

That's what we're doing here as well (but with shitty letters in the mix )

So here

[midnight pier]

yeaa

[turbid valve]

The first bit's a zero, that can piss off

[midnight pier]

o yea

lol i forgot

[turbid valve]

The rest, 5x^2 - 11x, is the remainder we were doing more rinsing with

[midnight pier]

do i move the 5x^2 to where the 0 was?

[turbid valve]

You wouldn't move digits like that in the number variant would you

So we're not doing that here either

[turbid valve]

So firstly, what product did you get here?

[midnight pier]

true

[midnight pier]

so its 5x^2 - 11 *5?

or just the 5x^2

[turbid valve]

you're getting ahead of yourself

[midnight pier]

o

[midnight pier]

thats what all my teachers say...

[turbid valve]

So remember how you got that yellow term there?

[midnight pier]

yea i divided x^3 by x

[turbid valve]

And then that, once you got that, you'd multiply yellow with pink to get orange?

(and then did the subtraction)

this is the rinsing and repeating we've got to

[midnight pier]

wait wym yello * pink

[turbid valve]

The yellow and pink things I've highlighted

[midnight pier]

ye

OHHHH

i seeee

[turbid valve]

Same thing again at this stage - except here, it's blue times pink, to get purple

[midnight pier]

you do x ^ 2 * x to get the x^3 and the x * x^2 to get 5x^2

[turbid valve]

yeeeee

[midnight pier]

so 5 * x + 5

5x^2 + 25x

[turbid valve]

(essentially we're looking at the big terms to find what to put on the top, and then multiplying this with the whole divisor just to fine-tune and get a new division to check)

[midnight pier]

kk

[turbid valve]

yeee

[midnight pier]

ahhhh

lemme write dis

and subtract to get 14x

[turbid valve]

careful

[midnight pier]

and then bring it up

O

[turbid valve]

You've got a -11 up top

And a +25 below

You want to subtract -11 by +25

[midnight pier]

yea -11 - (+25) = 14

[turbid valve]

...you sure?

expand that bracket out?

[midnight pier]

ah shit

its -14 isnt it.

[turbid valve]

Not quite

[midnight pier]

like -11 - 25 i mea

n

[turbid valve]

Think number-line tactics - minus means left, plus means right

You go left 11, then left 25

Which makes?

[midnight pier]

36...

[turbid valve]

In which direction?

[midnight pier]

negative sir...

[turbid valve]

ye

(no need to call me sir lol)

So -11 - 25 is?

[midnight pier]

lmao its habit i call teachers sir lmao

-36...

[turbid valve]

nah igu lol

[midnight pier]

especially when i forgot my negatives

[midnight pier]

frr

so where do i put -36x? is it next to the 5x?

[turbid valve]

below the
-11x
+25x

---

[HERE]

Same with numbers

[midnight pier]

ahh kk so(lemme get a pic)

[turbid valve]

If you had a
9
4

---

5

[turbid valve]

(one way I avoid this hassle, btw, is thinking "Okay, so I've written down this +25x; what would I need to add to this to get -11x?")

[midnight pier]

uh

[turbid valve]

[this works for me, it may work for you, give it a try and see what works]

[turbid valve]

Back to this tho - now bring down that -180

[midnight pier]

k

so 36 - 180

[turbid valve]

-36x - 180, but yh

[midnight pier]

yeaa

[turbid valve]

wait dafuq how did I not catch that

[midnight pier]

OOPS SHIT

uh

[turbid valve]

we just said this is a minus lmao

[midnight pier]

my signs are

not my strong suit...

yeahh memory of a goldfish im tellling you.. 😭

[turbid valve]

Practise number line stuff as well then

[midnight pier]

if maths had no signs itd be sound

[turbid valve]

dw, it might be basic shit, but that shit's important 🫡

[midnight pier]

yeahhhh thats true af lmao

[turbid valve]

It's never a bad idea to strengthen your arithmetic skills

[midnight pier]

yep thats true

i js keep putting it off lmao

like i always think

[turbid valve]

Onwards then - the "big" term there is that -36x

[midnight pier]

do i revise trig or do the arithmatic on sparx? i always do the trig 😭

[midnight pier]

yea

[turbid valve]

("big", as in it's the one with the higher x-power)

[midnight pier]

so im guessing / by x?

[turbid valve]

ye

Essentially, how many time does the x (from x+5) divide -36x?

[midnight pier]

ahhh so = -36-180

O

nvm

uh

7

wait

no

1

[turbid valve]

x divides -36x how many times?

[midnight pier]

once

[turbid valve]

uhhh not quite?

[midnight pier]

shit. im embarrasing myself here lmao

[turbid valve]

Alternatively phrased, how many multiples of x make -36x?

[midnight pier]

AH

36

[turbid valve]

This might just be a phrasing thing dw

[midnight pier]

😭

[turbid valve]

Not **+**36

[midnight pier]

-36

[turbid valve]

yeee

[midnight pier]

i keep forgetting those damn signs lmao

[turbid valve]

-36 up top

Repeat the process

[midnight pier]

so i divide -180 by 5

so that is

-36

[turbid valve]

So write -36 in the blue bit

[midnight pier]

yea did that

[turbid valve]

Multiply this blue by pink to get the green bit

[midnight pier]

so 36 * x = 36x and 36 * 5 = 180

so that cancels

OH

[turbid valve]

yee

[midnight pier]

ITS JUST X^2 + 5X

WHICH FACTORISES TO

[turbid valve]

WOAH WHAT

[midnight pier]

(X+2.5)(X+2.5)

ah shit

wat have i done..

[turbid valve]

You've written the -36 in there

So the whole quotient (result) is x^2 + 5x -36

that bit's part of the answer too

[turbid valve]

(even if it cancels, if it's the last step, write down the 0 you get under the yellow line - so it's clear there's no remainder)

[midnight pier]

so i write x^2 + 5x - 36 up top

[turbid valve]

ye

[midnight pier]

and then 36x +180 at bottom

[turbid valve]

where the green bit is, yh

[midnight pier]

so that cancels to 0

[turbid valve]

ye

[midnight pier]

then do i factorise

x^2 + 5x - 36

[turbid valve]

YEE

(and this does factorise nicely, thank fok )

[midnight pier]

lmaoo

Uh

So lets see what multiplies to 36 adds to 5

[turbid valve]

btw, this didn't work anyways lol - A^2 + 2B doesn't equal (A + B)(A + B); I think you got confused with difference-of-two-squares

[midnight pier]

Yeaaa

Hmmm

So its x -9 x + 4

X = -9*

X = 4*

[turbid valve]

ye

[midnight pier]

AHHHHH

So thats the anseer

And how to divide cubics

[turbid valve]

So check this again then

We'd begun with a cubic

[midnight pier]

So would it have worked if i do cubic formula

[midnight pier]

Yea

Ah fuck

Its jot over is it..

[turbid valve]

Well the third factor was the thing we were dividing by, wasn't it

[midnight pier]

OH

So 5,-9,4 are the roots

[turbid valve]

If 81 / 3 = 27 (and no remainder), then 3 is a factor of 81

Same logic

[midnight pier]

ahhhhhh

[turbid valve]

Not +5

[midnight pier]

-5

[turbid valve]

the term factor was x +5

So the root is -5 yh

[midnight pier]

Yhhhhh

So is that all there is to it?

[turbid valve]

ye

there was something else you've mentioned, ...

[turbid valve]

This?

[midnight pier]

huh

YE

[turbid valve]

What formula do you have?

[midnight pier]

i heard the top sets doing it and

If i do it next year

Then

[midnight pier]

Uh

Im talking bout the big one

[turbid valve]

fyi there are a few

[midnight pier]

O

Uh

[turbid valve]

(related: read about Nicolo Tartaglia https://en.wikipedia.org/wiki/Nicolo_Tartaglia#Solution_to_cubic_equations - not because of the maths but because it's comical lol)

My guess is you mean this one?

[midnight pier]

Lmao bro saw his work “ by accident”

[midnight pier]

Yhhhh

[turbid valve]

Right, so what you gotta do here is steal the equation's antidepressants manipulate the cubic in such a way that it resembles the first equation here

[midnight pier]

Lmao

Soo

Rearrange

[turbid valve]

Now, the actual method to do that is not really that obvious

Let's see if I can't find a good explanation somewhere...

[midnight pier]

I mean your making it t^3 +pt +q.

[midnight pier]

oki

[midnight pier]

Hiw hard is that

[turbid valve]

(yee - so if there's no squared term, that's easy - but if there is one, it's not as clear-cut)

[midnight pier]

multiply by x…

[turbid valve]

(this is where I look through my uni notes to see if I might find something )

I've stumbled across these notes https://people.math.osu.edu/derdzinski.1/courses/4552/4552-cubic-quartic.pdf btw - not mine

[midnight pier]

lol

[turbid valve]

This being the search term

[midnight pier]

DAMN

This is

Hard

[midnight pier]

lmao yk its tuff when it starts with “math 4552”

[turbid valve]

yh, dw too much about it, it's rather a lot for someone not used to seeing tons of algebra lol

[turbid valve]

4552 is just a module code lol

[midnight pier]

Yeaa i mean i prefer algebra lmao

[midnight pier]

o

Loads of modules then..

[turbid valve]

Like what AQA and Edexcel do with their exams tho

It's semi-random

There's no "this is 0001, this is 0002, etc"

[midnight pier]

Ohhhhh

[turbid valve]

this is a weird way to present Cardano's formula, but it's pretty useful for computation

If it's not clear - find Q and R first; then S and T

[midnight pier]

Where has w come fromv

?

[turbid valve]

Then x_1, x_2 and x_3 are your solutions

[midnight pier]

So why have they put different equations for s

[turbid valve]

for s?

[midnight pier]

Yhh

[turbid valve]

There's just one equation tho?

[turbid valve]

This is the not-at-all-obvious trick to get rid of this substitution

[midnight pier]

Ah fuck im tapped

I meant x

[turbid valve]

ah lol

There're three roots at most for x in a cubic

[midnight pier]

So the replacing thing confused me

[turbid valve]

So we can get them with 3 equations

[midnight pier]

Ahhhh

How do you get those 3?

[turbid valve]

(not unlike taking the plus or minus from the quadratic)

[midnight pier]

o

[turbid valve]

Well I'm reading off of https://proofwiki.org/wiki/Cardano's_Formula for this

[turbid valve]

But this is doing a similar proof

[midnight pier]

K

[turbid valve]

To briefly explain, because I agree this is so not clear lol

It's ridiculously good

Suppose there z were a solution

Further, I'm gonna call a new variable w, so defined up there in that image

[midnight pier]

How do they get the equation for the roots? Do they js make it up or sum

[midnight pier]

Kk

[turbid valve]

If I then rearrange that w-definition to make z the subject, and then plug this into the cubic and simplify, I end up with no w^2 term

[midnight pier]

Ohhhhh

Thats a handy trick tbf

[turbid valve]

I've stolen the cubic's antidepressants turned this into a depressed cubic

[midnight pier]

Hahaha

Js withheld the depressants

[turbid valve]

Now it turns out we've known solutions to these for centuries

[midnight pier]

O

[turbid valve]

[but, as that Tartaglia story explains, because mathy bois were so busy boasting about who had the bigger formula. they didn't want to share it]

https://tenor.com/view/skirk-childe-genshin-impact-yeet-throw-gif-15362850204959438735

[turbid valve]

Given the character being yeeted here is also called Tartaglia, this is an accurate depiction of what these were like

[midnight pier]

Lmaoo

[midnight pier]

😭😭🤣🤣

So its js rearranging in a nutshell

[turbid valve]

ye

[midnight pier]

Ahhhh i see

[turbid valve]

The rest of that PDF involves making some more snarky substitutions to get some nifty formulas

[midnight pier]

yea ill have a proper look in the morning lol

Maths on energy drinks surely breaks laws somewhere

[turbid valve]

This one might be a little easier to digest

The reason these are uni-level explanations at all btw is to do with the context they're in

[midnight pier]

kk

[midnight pier]

wym?

[turbid valve]

Namely - there is a quadratic formula (you learn this in school)

[midnight pier]

yh

Isnt there some quartix one

[turbid valve]

There also happens to be a cubic formula (which is messy to get to, but it exists)

There is a quartic one yh

That PDF covers it right after that cubic one

[midnight pier]

Havent we been talkin bout the cubic one?

Ahhhh

I see

[turbid valve]

after this sorry excuse for a line lol

[midnight pier]

k

[midnight pier]

Yea i cant even understand those letters

Ik the set one

I think

[turbid valve]

yh they explain these along the way, but it's pretty weird to immediately apply this

[midnight pier]

truuu

[turbid valve]

ProofWiki's is easier to use as a tool

Now, the question is - does this generalise?

[midnight pier]

Wym by that

Like generalize

[turbid valve]

Is there a formula for any polynomial?

[midnight pier]

Uh

[turbid valve]

This

[midnight pier]

O thats a question

A good one

If there was

That would be useful

So like if highest power = z: use this and etc

[turbid valve]

Well, it turns out that, in the 1800s, a whole field called Galois Theory was built upon the proof that "lol no there's no quintic one fok you hahahah"

[midnight pier]

Lmao

Is quintic x^5?

[turbid valve]

ye

I'll briefly explain, suffice to say that except for maybe Further Maths AL FP2 students this is certainly beyond the scope lol

We can talk about the collection of polynomials (under certain conditions, e.g. "its coefficients are real") as some object called a ring

[midnight pier]

Ahh

[midnight pier]

Lol

[midnight pier]

k

[turbid valve]

Galois Theory explores whether these rings can be compared to some associated "group" (groups are another maths-y object, and this is the FP2 thing)

[midnight pier]

So a group is a lot of rings?

[turbid valve]

No, rings and groups are different objects

Silly tho it is

You can probably Wiki them if you want for more

The important thing about groups for this discussion is that they may or may not have a property called "soluable"/"solvable"

[midnight pier]

Yhh

Kk

[turbid valve]

[the spelling difference is because the old pricks can't write v properly. but the shit stuck to the fan so here we are with two words]

[midnight pier]

Lmaoo

[turbid valve]

It turns out, from the Theory, that the question "Does a polynomial ring with certain conditions have solutions we can just compute? (i.e. is there a formula?)" is mathematically equivalent to "Is the associated group solvable?"

[midnight pier]

K

[turbid valve]

(we call the associated group the Galois group of that ring)

So: "The ring of quintic polynomials has a formula for their solutions" is equivalent to "The Galois group of this ring is solvable"

[midnight pier]

Kk

[turbid valve]

That last statement - we've proved some-the- -how - is false

So actually there's no quintic formula

[midnight pier]

O

…

[turbid valve]

(thus by extension there's no sextic or septic equations etc. (yes those are actual words wtf is this language even))

[midnight pier]

Is thatcus of the galois group thing

🤣🤣🤣🤣

[turbid valve]

ye

Some Galois groups are solvable

[midnight pier]

So because the ring past quartic doesn’t have the solvable propery?

[turbid valve]

That of the quadratics is, for instance, which is why there's a quadratic formula

[midnight pier]

kk

[turbid valve]

The Galois group of the ring of quintic polynomials isn't solvable (eugh that's a lot to type)

[midnight pier]

so its quartic then quintic

[turbid valve]

ye

cf. "quarter"

[midnight pier]

Ahhhh

[turbid valve]

Anyways there you go, a shitty crash course on a third-year UG maths module

[midnight pier]

Lmao much appreciated

W crash course

Awesome and tnaks for the help with the cubics aswll

.close

[vale dock]

Channel closed

Closed by @ancient whale

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.

[lavish mortar]

Hi, I just have a question about a step taken in a worked solution for an initial value problem

[lavish mortar]

In the last line he does the partial fraction decomposition, but I am lost with what steps he took

From what I can tell, the constant A on the LHS is pi^2/4, and on the RHS B is 1 and C is s

[normal hollow]

s²+pi²/4 -s² in numerator

[lavish mortar]

Here is the problem btw

[lavish mortar]

huh? xD

[lavish mortar]

oh right

why is pi^2/4 used in the numerator pls?

I assume this is to make the decomposition work out nicely but idk how this was decided

In a similar problem, the partial fraction decomposition is for the same denominator, what I am confused on is why the numerator of the fraction that is to be separated is not considered in the partial fraction decomposition

this is dumb question im sry lol

[normal hollow]

It is not a dumb question

And i m not sure how they got thaat either

[lavish mortar]

My approach would be to decompose this

but instead he replaces numerator with the pi^2 term and this is somehow equal to the term being decomposed 😅

[normal hollow]

It's not js that term tho,is it

It's the whole function

, no?

[woeful trench]

(Do you happen to have what comes after the representing part? My guess is that for that second third term, they plan to multiply and divide by pi/4 4 to make things nicer to work with, maybe?)

[woeful trench]

(re this, and...

[woeful trench]

...this )

[lavish mortar]

I will send them now 1 sec

[lavish mortar]

I am doing the partial fraction decomp long hand to see if his result is indeed equal when 2pi^2*exp(5s) is used instead of pi^2/4

[woeful trench]

Ah accidentally read the wrong one, but basically I think they just multiplied/divided the third term by 4 (which is how you get the factor of 8 here, 2 = 8/4)

[lavish mortar]

just done, will send my values for the decomp here

I am mainly hung up on why he did not decompose directly like this

sry if this is very basic stuff, I am pretty lost in this topic

[woeful trench]

Probably to save having to show you the work, also with some of these, you can, with enough experience, see how to decompose them without actually doing all the hard work [of writing out the form and finding the coefficients] (as suggested here )

[woeful trench]

(also, as a side note, that second numerator should be in the form Bs + C, the degree of the numerator being one less than that of the denominator )

[lavish mortar]

what does that mean 😭

[woeful trench]

Hence

[lavish mortar]

did I break a rule?

[lavish mortar]

do you by chance know where I can read up on this? it is not mentioned in lecture notes

[woeful trench]

Yea, try out the work again, but take the decomposition to be $\frac{A}s + \frac{Bs + C}{s^2 + \frac{\pi^2}4}$

[rocky lotus]

@woeful trench

[woeful trench]

And lemme see if I can find something for you

[lavish mortar]

ah so this is the form you need

I would really appreciate it thanks

[woeful trench]

e.g. like this one here (which is more clearly explained by their example than by the screenshot )

Or this one, which is slightly better

[lavish mortar]

omg

thank you man

😭

so what I did was rubbish

this makes sense

Imma do it again

[woeful trench]

Yep you should see it works out if you do it that way

[vale dock]

@lavish mortar Has your question been resolved?

[lavish mortar]

made mistake with first attempt will close in like 10 min

I did it but didnt factor exp(-5s) back in

A and B aren't nonsense now at least

sry to bug you again on this, I just really want to understand what the correct approach is for this specific step of laplace IVP

[vale dock]

Channel closed

Closed due to timeout

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.

[lavish mortar]

got it, I made a stupid

[lavish mortar]

thanks baring with me

.close

[vale dock]

Channel closed

Closed by @lavish mortar

Use .reopen if this was a mistake.

[vale dock]

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.

[orchid thistle]

Hello, Rational Inequalities.
(2x/(x-4))≥1

[orchid thistle]

Hello i have returned from a quiz @toxic ridge

i checked out the wavy curve thing and I still dont understand it

[ivory valley]

What'd your question on that?

[orchid thistle]

how to do the number graph

[ivory valley]

What's a number graph?

[orchid thistle]

the Straight Line

[ivory valley]

Oh

[orchid thistle]

lik ds

[ivory valley]

So you are basically asking for the solution?

[orchid thistle]

he called it the number graph so idk

somewhat

the intervals

[ivory valley]

Okay

[orchid thistle]

how to know the intervals ig

[ivory valley]

Well, in order to attain them you would need to solve this inequality, which would require two cases

[orchid thistle]

(x+4)/(x-4)≥0 i got ts

[ivory valley]

Another approach is the following:
[\f{2x}{x-4}-1 = \f{2x-(x-4)}{x-4} \ge 0 ]
Now you need to see when \textbf{both} the numerator and denominator are positive.

[orchid thistle]

yez i got (x+4)/(x-4)≥0

[ivory valley]

Ok nice