help-23

[twilit moat]

4x5=5+5+5+5

3x5+5+5+5

2x5=5+5

1x5=5

how about for 1

3x1=1+1+1

2x1=1+1

1x1=1

[hardy rover]

😮😮😮😮😮😮

i get it now

thx you sir for your time 🤗

[safe radish]

@hardy rover Has your question been resolved?

[safe radish]

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.

[sinful wyvern]

The gradient of the curve y=ax^2 + bx at the point (3, -3) is 5. Find the value of a and the value of b.

Guys, why am i wrong?

[frozen marlin]

m isn't 9, it's 5

[sinful wyvern]

Oh wait ure right

[flat frigate]

ren

[sinful wyvern]

I’ll fix it, tysmm

I got it, thankyouu againn

.close

[safe radish]

Channel closed

Closed by @sinful wyvern

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.

[lean otter]

Дана правильная шестиугольная пирамида SABCDEF с вершиной S. Стороны основания пирамиды равны a, а боковые рѐбра равны 2a. Найдите площадь сечения плоскостью, проходящей через:ребро AB и середину ребра SD.

[lean otter]

1 sec

A regular hexagonal pyramid SABCDEF with vertex S is given. The side of the base of the pyramid is equal to a, and the side edges are equal to 2a. Find the cross-sectional area by the plane passing through: the edge AB and the middle of the edge SD.

Please help 😭

i can draw a section but i cant find any value to find an area 😭

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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.

[versed wolf]

$\iint_R x,dx,dy$ where $R$ is the region $1\le x(1-y)\le 2$ and $1\le xy\le 2$

[flat frigate]

harshul

[versed wolf]

I tried using $u = x$ and $v = xy$

[flat frigate]

harshul

[vagrant ice]

good idea honestly

yeah use the Jacobian cause there's no way you can bound it between two functions x = f(y) and x = g(y) or y = f(x) and y = g(x)

[versed wolf]

I get $\iint_S u\left|\frac{1}{u}\right|,du,dv$

[flat frigate]

harshul

[versed wolf]

From these inequalities I get $2\le u\le 4$ and $1\le v\le 2$ which should be $S$

[flat frigate]

harshul

[versed wolf]

Gives me the wrong answer though

I think it's because the substitutions I made are wrong

[vagrant ice]

$1 \le u - v \le 2$ and $1 \le v \le 2$

[flat frigate]

south's secret twin brother

[vagrant ice]

don't sub in the 2nd inequality into the 1st

[versed wolf]

I see

[vagrant ice]

instead just $1 + v \le u \le 2 + v$ as the inner integral bound

[versed wolf]

1 + v you mean

Yeah alright got it, thanks

[flat frigate]

south's secret twin brother

[vagrant ice]

no worries!

[safe radish]

@versed wolf Has your question been resolved?

[vagrant ice]

.close

[safe radish]

Channel closed

Closed by @vagrant ice

Use .reopen if this was a mistake.

[safe radish]

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.

[lean otter]

what have you tried?

GM HM inequality

That's the only thing that came in my mind

It's a multiple correct question

can you express a, b, c in terms of b and r (common ratio)?

Like a,ar,ar^2

sure

then find the harmonic mean of a and ar

2ar/1+r=12

Umm

Are you there??

<@&286206848099549185>

...

.close

[safe radish]

Channel closed

Closed by @dense sapphire

Use .reopen if this was a mistake.

[safe radish]

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.

[vagrant ice]

@mighty haven

[vagrant ice]

you can divide both sides by 6

if 90x = 114 mod 73, that means 90x = 114 + 73k for some integer k

but since the left hand side is divisible by 6

so must the right hand side, and so 73k must be divisible by 6

so 90x = 114 + 73 * 6m or 15x = 19 + 73m

[mighty haven]

but we cant divide with congruence right ?

@vagrant ice

[vagrant ice]

you can't directly

you have to go back of the definition of the modulus

[frozen marlin]

i mean you could've also just noticed

6 has a multiplicative inverse modulo 73

[mighty haven]

so the expression : a = kb +n ?

[vagrant ice]

yes

[frozen marlin]

bc of coprimality

;-;

[mighty haven]

yes we can divide if there is an inverse

[vagrant ice]

yeah so you could just multiply both sides by 6^(-1)

[frozen marlin]

i know lmao

[mighty haven]

what is coprimality ?

[frozen marlin]

coprime-ality

[vagrant ice]

I mean I don't like the word divide

[frozen marlin]

made the word up

[vagrant ice]

you can ofc

[mighty haven]

but what is coprime ?

[vagrant ice]

but then it's not technically accurate

[frozen marlin]

if two numbers don't share any common factors apart from 1, they're coprime

[mighty haven]

and if two numbers are coprime there are inverse ?

[frozen marlin]

if i have "a" and "b" coprime, that means a has a multiplicative inverse modulo b and vice versa

[mighty haven]

so a prime number has a multiplicative inverse for all b ?

[vagrant ice]

no

the highest common factor of 3 and 6 is 3

conversely 4 and 25 are not prime

but they are coprime

[safe radish]

@vagrant ice Has your question been resolved?

[safe radish]

@vagrant ice Has your question been resolved?

[vagrant ice]

.close

[safe radish]

Channel closed

Closed by @vagrant ice

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.

[hollow pendant]

wud the angles be in a shape like this be the same as a normal octogan it’s for my dt

[mellow arch]

is it regular?

well it clearly isn't but like is it supposed to be

[hollow pendant]

i mean it’s not drawn to scale but the lengths between the straight lengths are shorter

[vagrant ice]

if your angles are all 135 degrees then yes

[mellow arch]

how much shorter

[hollow pendant]

like the diagonals r supposed to be shorter

[vagrant ice]

it won't be a regular octagon cause you need to have all 8 sides be the same length

[hollow pendant]

i’m not sure that’s why i’m trying to design it to be equal angles

[mellow arch]

ooo

[vagrant ice]

but it will have roughly the same shape

[hollow pendant]

right alr

[mellow arch]

oh that's interesting

[hollow pendant]

wait i’ve got the full thing

lemme send it

it’s supposed to

wait

[mellow arch]

i think this property only applies to specific shapes like squares and octagons

[hollow pendant]

the principle of it was

so that

when wood was added onto the corner

when they extended the length wud be the same

i’m not sure if it shows in the picture

and idk how the angles wud work to make that the product

[vagrant ice]

how do you extend it exactly?

oh do you mean extend one of the sides so it is parallel to the original side

[hollow pendant]

wdym

[vagrant ice]

and then you want the horizontal and vertical distances moved to be the same?

[hollow pendant]

lemme redraw it with labels

that was what i hoped the product to be

and i’m wondering what the angles wud have to be to get this product

[mellow arch]

yes i believe the angles would be constant

[hollow pendant]

right so they wud be the same?

[mellow arch]

it would be like stretching out a square into a rectangle

yes

[hollow pendant]

right

so wud it js be like a normal octogan then?

[vagrant ice]

yes so those are parallel got you

[mellow arch]

it's not a regular octagon cuz the sides are not equal, but it would have the same angles as a regular octagon

[vagrant ice]

then it has to be an octagon with all angles equal (being 135 degrees)

[hollow pendant]

ohhh ok

[vagrant ice]

cause it's a property of 45-90-45 angled triangles

[hollow pendant]

ok so the angle wud still be 135

then

alr alr thanks guys thats rlly helpful thanks 🙏

[vagrant ice]

that these two marked sides are equal

no worries

so you get 180 - 45 = 135

[hollow pendant]

yhyh alr thanks

how do i do the rep thing

that like gives u guys rep

[vagrant ice]

we don't have that

it's okay just close the channel

[hollow pendant]

alr alr calm thanks anyways guys

[hollow pendant]

alr alr how?

[vagrant ice]

.close

[safe radish]

Channel closed

Closed by @vagrant ice

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.

[dry obsidian]

Hello i wanted to understand something but it's french, anyway here's what i don't understand :
https://cdn.discordapp.com/attachments/908740750085333012/1302648714422386778/image.png?ex=6728e1a7&is=67279027&hm=36be7afb631c84825662f709819b18aaa58893c689c506d910eb8ee26317167e&

[dry obsidian]

The e. part

what i have to do

[fathom adder]

La derivee à droite doit être la même que la derivee en ce point

Et que la derivee a gauche

[dry obsidian]

Tu me sauve jai d'autre question sur ce sujet

[fathom adder]

Normalement c'est ça la dérivabilité en un point

[dry obsidian]

mais dcp genre si le domaine c [-1;1]

je fais f'(-1)

?

[fathom adder]

Pti doute sur l'ensemble la

[dry obsidian]

si c'est ça

[fathom adder]

Ok

[dry obsidian]

alors faut faire quoi

[fathom adder]

Et faut que ça soit finie

[dry obsidian]

Ah ok

et quand par exemple

on me demande demontrer que f n'est derivable ni en 0 ni en 4

faut faire quoi

ou alors si elle est derivable en 0 ou en 4

[fathom adder]

Taux d'accroissement

[dry obsidian]

et genre si jveux faire en 0 je fais f(0+h)-f(0)/h

et le resultat doit etre quoi deja pr que ce soit derivable

[fathom adder]

Plutôt celle la

En haut à droite

[dry obsidian]

what

c'est quoi

[fathom adder]

Un taux d'accroissement

En x= 3

[dry obsidian]

c'est quoi cette formule

jai jamais vu

[fathom adder]

Une alternative à ça

[dry obsidian]

et il marche quand meme ce que jtai dis?

[fathom adder]

Probablement, je privilégie celle que j'ai envoyé mais sûrement que ça marche, c'est la même formule juste de noms different

[dry obsidian]

okk

et le résultat

doit etre quoi pr que ce soit derivable

[fathom adder]

Un reel

[dry obsidian]

et inversement pr que ce le soit pas

[fathom adder]

Un truc pas reel

[dry obsidian]

okk

[fathom adder]

Genre +inf

Ou -inf

(Assez rare en exo, pcq apporte pas grand chose pédagogiquement)

[dry obsidian]

on sais jamais

c un fou mon prof

[fathom adder]

C'est vrai

[dry obsidian]

et

att je cherche j'en profite mdr

tu peux voc ou pas?

[fathom adder]

Non

[dry obsidian]

dacc tant pis et jai trouver jai pas compris la notion de 0- et 0+

[fathom adder]

Ah

[dry obsidian]

mon prof m'a dis que fallais l'utiliser dans des cas

[fathom adder]

C'est ce que je disais ici

[dry obsidian]

mais g pas compris la phrase

[fathom adder]

Enfaîte c'est quand tu arrives vers le point avec ton doigt de la gauche (-) ou de la droite (+)

[dry obsidian]

et quand tu fais une limite de par exemple 1/2^n

c'est 0+ ou -

[fathom adder]

C'est 0

[dry obsidian]

juste 0?

[fathom adder]

Oui

Ça c'est une suite

[dry obsidian]

ah mb

et ta pas un cas ou faut dire 0+ ou -

[fathom adder]

Jv essayer

[dry obsidian]

mrc

[fathom adder]

1/e^x quand x tends vers - infini ?
e^x en -infini c'est 0+
Donc 1/e^x quand x tends vers -infini = + infini

Jai pas souvenir que on marque le résultat d'une limite comme 0+ ou 0- on met juste 0

[dry obsidian]

bah jtai montrer ce que le prof ma envoyer le fais que ce soit 0+ ou 0- sa peut changer le resultat

enfiun de ce que jai compris

[fathom adder]

Oui mais le résultat n'est pas 0+ ou 0-

[dry obsidian]

Ah oui bah jsp

bah mrc pr tout jvais voir dans mes cahiers si j'ai des trucs comme ça

[fathom adder]

Ça marche

[dry obsidian]

.close

[safe radish]

Channel closed

Closed by @dry obsidian

Use .reopen if this was a mistake.

[safe radish]

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.

[wet frost]

how can I find the height here?

[safe radish]

@wet frost Has your question been resolved?

[wet frost]

<@&286206848099549185>

[silver pelican]

we can make two equations

[wet frost]

oh

[silver pelican]

since we know that the rectange is 16,

the side with 17 can be x

and the side with 25 can be 12-x

and plug pythaogrean

[wet frost]

wait why are we

[silver pelican]

and substitute since the height is equal

[wet frost]

why are we making the numbers as variables

[silver pelican]

we don't know the two side

so we have to make a variable

[wet frost]

it's a bit confusing, where do we get the 12 from?

x - 12

[silver pelican]

we know the top base is 16

and you made a rectangle

so the two sides has to be 12

[wet frost]

the two sides of the rectangle?

[silver pelican]

like the base of the triangle with hypotenuse 15 and 17

those bases must add up to 12

[wet frost]

oh i see

[silver pelican]

then we jsut let the height be y

so x^2+y^2=17^2 and (12-x)^2+y^2=25^2

and solve

[wet frost]

is it necessary to write the integers as variables? this is the first time I have seen such thing

[silver pelican]

well we don't know what the bases of the triangles are

so we have to write them as a variable

[wet frost]

I got confused on

writing 25 as

12 - x

and 17 as x

[silver pelican]

no

we can write the base of the triangle with hypotenuse 25 as 12-x

and the base of the triangle with hypotenuse 17 as x

and the heigh as y

[wet frost]

ohh I see

[silver pelican]

(the heights are equal cause a rectangle)

then we use pythaogrean theorem to solve

[wet frost]

alright

[silver pelican]

do you get it now?

[wet frost]

yea

i'll try to solve it on my own given the information

thanks 👍

.close

[safe radish]

Channel closed

Closed by @wet frost

Use .reopen if this was a mistake.

[silver pelican]

yw

[safe radish]

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.

[ruby junco]

When finding the area of a shape like this one (or just weird shapes in general) how do i know whether to slice vertically or horizontally bc ik i have to use whatever gets me out in the least amount of integrals but how do i figure that out

[fathom jewel]

Looks like you have x² on top and below x²-x

[ruby junco]

x^3 mb

[fathom jewel]

I don't know what you mean by the slice thing but you can calculate both integrals from 0 to 1 and take the absolute value

[median vigil]

in this case it looks like it is bounded by a vertical line on the right. that can be a sign that vertical slicing would be easier

[median vigil]

i think it means whether to take integral wrt x or y

[ruby junco]

Mb my prof explains it like that mostly lolol

[fathom jewel]

ahh, is this actually about volume

rotating it around that vertical axis

[ruby junco]

This question is about volume but when i was doing area i couldnt understand how to figure out which way to slice

So i just switched it rq 😭

Ignore the line on the right

[median vigil]

you could use horizontal slicing but it would require two integrals

[fathom jewel]

yup

[ruby junco]

Thats wgat confuses me why does it take 2 why not just 1

[fathom jewel]

because youa are getting the complementary area

[median vigil]

put your pencil on the page, to the left side of the region, then move it right. the first curve you reach when you into the region is your lower curve, the second you reach going out is your upper curve

then repeat for several different vertical levels. are the lower and upper curves you hit different? for every pair of curves you have to do a different integral

[ruby junco]

OHHHHHHHHHHHHHHHHH

TJANK YOU

.close

[safe radish]

Channel closed

Closed by @ruby junco

Use .reopen if this was a mistake.

[dark shoal]

I dont think this is how I'm supposed to write the domain, can someone show me how can i simplify it further

Uhh

.reopen

Wait do i even have to write k

[safe radish]

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.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[fathom jewel]

damn

[chilly warren]

hi

[fathom jewel]

need to open a new channel user.not.found

[chilly warren]

[solar hazel]

[chilly warren]

[safe radish]

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.

[umbral grove]

Both of these questions are really hard for me to do. The second image is me trying to solve Q4, but RS and LS and never even close to looking like each other, no matter what trig identities/algebra I use. For my first attempt, I assumed cos⁶x+sin⁶=(cos²x+sin²x)³=1³=1, but apparently that's wrong. But when I do it any other way, I get really convoluted steps.

[umbral grove]

Sorry if my attempt is really messy! Each X marks an attempt that I think has failed

[thorny pulsar]

i think you are meant to expand cos6(x) out to (1-sin²x)^3 and then it is all sin

cos⁶x+sin⁶ is not (cos²x+sin²x)³

[umbral grove]

i'll try that!

[umbral grove]

I'm not exactly sure why this is the case, but I did hear that it was wrong

[thorny pulsar]

because it is a binomial, it expands into multiple terms

cos6(x) and sin6(x) are terms in it though

[umbral grove]

omg, you're so right!

[thorny pulsar]

you'll just need to some expansion and it will be a polynomial i think

[umbral grove]

By doing that I got 1

[umbral grove]

I had also gotten 1 in my first attempy here, but that was when I assumed cos^2x + sin^2x is eqaul to 1, is that also correct?

[thorny pulsar]

do you know the binomial expansion formula?

[umbral grove]

you mean, (a+b)^2 = a^2 +2ab+b^2

[umbral grove]

oh, was I supposed to do (1-sin^2x)(1-sin^2x)(1-sin^2x)

[thorny pulsar]

yeah

the binomial expansion would be faster here as you dont need to foil it

[safe radish]

@umbral grove Has your question been resolved?

Channel closed

Closed by @umbral grove

Use .reopen if this was a mistake.

[safe radish]

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.

[rain wigeon]

$\lim_{x\to\infty}16x^2(4x^2-\sqrt{16x^4+1})$

[flat frigate]

WaspThe2nd

[rain wigeon]

Not sure how to get rid of the sqrt here in order to get the final answer

[severe pond]

multiply by the conjugate

or you could bring the 16x^2 down and use lhopital i guess

[rain wigeon]

Would you be able to solve this so I can use it as an example?

[severe pond]

!nosols

[safe radish]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[lean otter]

oh woops i've been guilty of that before

[severe pond]

$\lim_{x \to \infty} \frac{16x^2(4x^2-\sqrt{16x^4+1})(4x^2 + \sqrt{16x^4+1})}{4x^2+\sqrt{16x^4+1}}$

[flat frigate]

knief

[severe pond]

i’ll give you that

[severe pond]

you got any stock advice

[lean otter]

um

[severe pond]

never heard of it

[safe radish]

@rain wigeon Has your question been resolved?

[lean otter]

sorry i don't have any, just don't lose all your money ig

[rain wigeon]

Ok, so correct me if I'm wrong. But you multiply the expression by the contents in the brackets in order to get a denominator? In order to multiply by the conjugate?

And the conjugate will be? $\sqrt{16x^4-1}$

[flat frigate]

WaspThe2nd

[lean otter]

4x^2+radical expression from the original problem

[rain wigeon]

Oh wait... nvmd. Just saw the sign changed already

Making that the conjugate right?

[lean otter]

ye, see what knief multiplied by in the numerator and denominator

[rain wigeon]

Yea, missed that he changed the sign outside the sqrt

[lean otter]

great

[safe radish]

@rain wigeon Has your question been resolved?

[lean otter]

how are you doing sir

[rain wigeon]

Just going over the section in my textbook again. Still not making 100% sense to me. I get the conjugate part. Just not sure how to simplify past that

So after multiplying the conjugate the two brackets in the numerator cancel out right, leaving only 16x^2

[flat frigate]

WaspThe2nd

[rain wigeon]

$\frac{16x^2}{4x^2+\sqrt{16x^4+1}}$

[flat frigate]

WaspThe2nd

[rain wigeon]

Can I at this point ignore the 1 since we are dealing with dominant terms only making it irrelevant? And since sqrt{16x^4} simplifies to 4x^2 we can add them together giving a final answer of 2?

[rain wigeon]

@lean otter

Actually revisiting the first steps after multiplying the conjugate you are left with 16x^2(-1) making it a negative. Changing the final answer to -2 I believe

[safe radish]

@rain wigeon Has your question been resolved?

[lean otter]

yes! i think -2 is the correct answer

[safe radish]

Channel closed

Closed by @rain wigeon

Use .reopen if this was a mistake.

[safe radish]

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.

[ashen valley]

In a pigou network (game theory) is the epsilon known to the players of the game, or is it always unknown? I've seen for a traditional pigou network (up c1(x) = 2 + e, down c2(x) = x) has a social optimum and PNE at (up, down) for e = 0, but a unique PNE (down, down) for all other values of e. This would make me think that epsilon is known, as how else would a nash equilibrium differ for different values of e if players don't know they'd gain an advantage by moving?

[safe radish]

@ashen valley Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.

[onyx sphinx]

question 13 part a

[mellow arch]

A double angle identity is involved here

[onyx sphinx]

i got sin^4x +cos^4x = 1-sin^22x 😭

where did the 1/2 for the double angle of sin come from

[mellow arch]

Wait that's correct

Just factor out 1/2

[onyx sphinx]

iOH

BRO

[mellow arch]

Lmaooo

[onyx sphinx]

💀

wait no

i didn’t get that

LOL

[onyx sphinx]

i corrected it

[mellow arch]

Ok so you did + 2sin^2xcos^2x - 2sin^2xcos^2x right

So you get a^2 + 2ab +b^2 form

[onyx sphinx]

what

[mellow arch]

The - 2sin^2xcos^2x can be rewritten as - 1/2 sin^22x

[onyx sphinx]

i don’t think i did that

[mellow arch]

Can you show your working

You do know how to apply a double angle identity right

[mellow arch]

Oh that's why

sin^4x + cos^4x = 1 is not an identity

Wait what

[onyx sphinx]

yeah i’m aware of that but idk what i did

ignore the first line

of the answer

[mellow arch]

Ok

[mellow arch]

In that case the other lines appear correct, except at the end

2sinxcosx = sin2x

So 4sin^2xcos^2x = sin^22x

But what you have is 2sin^2xcos^2x, so you end up with 1/2 sin^22x

[onyx sphinx]

i don’t understand 😭😭

[onyx sphinx]

where did the 4 come from

[mellow arch]

Square this equation

Both sides

[onyx sphinx]

bro i’m gonna kms 😔 how would i come up with this in the exam

[mellow arch]

You actually did pretty well I think

Just the first and last line had some minor mistakes in them

[mellow arch]

Practice more and you'll get better at pattern recognition 👍

[onyx sphinx]

man i did. all the questions in my book 😭

i don’t have anything else that i can practice on atp

[mellow arch]

What exam are you sitting for

[onyx sphinx]

let me just read ur response again cuz i’m still a bit confused

[onyx sphinx]

A level

[mellow arch]

Oh nice I just finished mine

[onyx sphinx]

REALLY??

[mellow arch]

You can find their past year papers online and practice with those

[mellow arch]

Yea

[onyx sphinx]

i leave past papers for the last month bfr my exam

last revision

[mellow arch]

Lol

[onyx sphinx]

what else did u take

[mellow arch]

Just A levels

What else can I take lol

[onyx sphinx]

no like

subjects

😭

[mellow arch]

Oh

[onyx sphinx]

other than math

[mellow arch]

Maths further maths physics and computer science

We might be sitting for different versions of A levels

[onyx sphinx]

damn bro

further math, gotta respect u for that😭

[mellow arch]

Haha

Ok back to the topic

[onyx sphinx]

NO PLS

one question

[mellow arch]

Ok

[onyx sphinx]

how did u study for physics

[mellow arch]

I did past years

[onyx sphinx]

oh ok😭

[mellow arch]

The 4 came from 2*2

[onyx sphinx]

okay i understand now actually

[mellow arch]

Nice

[onyx sphinx]

ok thanks 🙏

[mellow arch]

👍

[onyx sphinx]

wait though

when i expanded the bracket

ok nvm 😭 bro i’m sorry but this quesyion confused the hell out of me

[mellow arch]

So you got it?

[onyx sphinx]

yeah

i have a few other questions under the same topic, can i ask in this channel or do i have to open a new one

😭

[mellow arch]

Idk but I'm available to help you with them rn

[onyx sphinx]

1 c

[mellow arch]

Oh wow

Oh wait I just remembered

Use that to expand and solve

[onyx sphinx]

i did 😭 i thoight i’d get fraction values for the angles but i got decimals 😔

[mellow arch]

Oh yea that's normal

Why can't the angle be in decimals

[onyx sphinx]

idk how to solve it 😭

i tried to factorize it

uh

[mellow arch]

Show me what you've done so far

[onyx sphinx]

here

u can see

on top

[mellow arch]

Oh that was your working

[onyx sphinx]

yeah 😭

tahts all i wrote

[mellow arch]

It's cut off tho

[onyx sphinx]

it’s just sin25=1

for the cut off part

[mellow arch]

Ok

Oh yea cos 65 = sin 25

[onyx sphinx]

😀

oh

[onyx sphinx]

well then i think i can solve it now

[mellow arch]

👍

[onyx sphinx]

how did u find out so quick

[mellow arch]

I know the identity

When I saw 65 and 25 I suspected I could do smth like that

Pay attention to pairs which add up to 90 or it's multiples

[onyx sphinx]

ok i need that mentality 😭 thanks bro

[onyx sphinx]

oh okay

bro can i add u, for help..💀

[mellow arch]

Uhhhh

[onyx sphinx]

no worries

[mellow arch]

I think you can just ask your questions here

[onyx sphinx]

thanks anyway

[mellow arch]

Haha

I did just finish my A levels so I'm free for a bit

Might try to get helper role around here

[onyx sphinx]

gl with that😭

thanks tho, i’ll close this now

.close

[safe radish]

Channel closed

Closed by @onyx sphinx

Use .reopen if this was a mistake.

[safe radish]

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.

[half bane]

I have to find a value that is a division multiplied by a fixed value, don't know how to explain properly, but

( a ) . ( 3600 ) = c

So i have a C value, and need to find A value

[heavy frost]

if you know C then you can divide it by 3600 to get A

by dividing both sides of equation by 3600 to cancel it on the left

[half bane]

how tf i dont think this

Thanks

.close

[safe radish]

Channel closed

Closed by @half bane

Use .reopen if this was a mistake.

[safe radish]

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.

[devout walrus]

can anyone help with this? i have no idea where to start

[shy hill]

I think you can ignore anthony and heidi for now, do you know how to solve the equation

[devout walrus]

Yeah i am ignoring them.

the thing is i have no clue on how to solve the equation

[shy hill]

the x^n is making it complicated

what if you replace it

[devout walrus]

there

thats not the point but

[shy hill]

yeah

now do you know how to solve it

it's kinda cool but not super easy to see

[devout walrus]

sadly no

[shy hill]

that won't help you :(

[devout walrus]

;(

[shy hill]

can you write the left side in terms of u+3 only

it's kinda tricky actually

also you added 3^4 twice when you expanded

otherwise you could try brute forcing as well with rational root theorem

[shy hill]

would recommend this still

[devout walrus]

i came up with this one actully

im not sure if its correct tho

[shy hill]

one of your signs is incorrect

but otherwise that's the idea

I did it with u's though

so (u+3)^4 - (u+3)^2 = 12

and then (u+3)^2 = v, so v^2-v = 12

[devout walrus]

oh damn

[shy hill]

but your way works as well I think

should be +

[safe radish]

@devout walrus Has your question been resolved?

[safe radish]

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.

[brazen parrot]

Excuse me idk what i did wrong

[brazen parrot]

The answer is -3/4

[austere cypress]

$a^n \cdot a^m = a^{n + m} \neq a^{n \times m}$

[flat frigate]

kaue

[brazen parrot]

Thank u'

.close

[safe radish]

Channel closed

Closed by @brazen parrot

Use .reopen if this was a mistake.

[split fulcrum]

bum chicken

[brazen parrot]

.close

[safe radish]

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.

[candid ocean]

Convert to radian measure:

-135*

[candid ocean]

Why is this the answer???

i get -3pi/4

oh

[severe pond]

well because they didn’t use a negative angle

[candid ocean]

i see yeah

but do i have to do that tho

do i always have to find the positive

[severe pond]

depends on the grader

[candid ocean]

what does that reaction mean

😭

[severe pond]

QED

that which was to be shown

[candid ocean]

ah

okok tyy

[severe pond]

you’re welcome

in general get the positive angle though

no one’s going to mark you wrong for that

[candid ocean]

kk

[junior smelt]

Is this the full question btw?

[safe radish]

@candid ocean Has your question been resolved?

[candid ocean]

yes ahaha but there abcdefg

i was just confusing abt the negative part bc the answer key kept showing the posiitve ones

but i get it

:))

[junior smelt]

Hmmm, strange then I guess

[safe radish]

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.

[versed pendant]

Not math related, but how to do 3d rotation in desmos

[safe radish]

@versed pendant Has your question been resolved?

[versed pendant]

<@&286206848099549185>

[safe radish]

@versed pendant Has your question been resolved?

[undone burrow]

not sure if there's a native way of doing it
but if you need it around x, y, or z, you can do a rotation matrix,
multiply it out and make it a function

[safe radish]

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.

[tardy sundial]

What are the rules for function composition?

[tardy sundial]

I see that f has a nonnegative domain, where g can have any real domain.

[lunar roost]

Yo

What’s the problem

[tardy sundial]

I have to prove whether or not the compositions are the same

[hasty wagon]

very good, it's indeed having tricks on the domain

[tardy sundial]

The specific part I don't understand is why f(g(x)) is defined for all reals, whereas g(f(x)) is not defined for all reals.

[severe pond]

$\sqrt{x^2} = |x|$

[flat frigate]

knief

[severe pond]

x^2 is always positive for reals

or 0

even if x is negative

[hasty wagon]

this is because when you evaluate g(f(x)) you'll first need to consider the domain of f(x)

[tardy sundial]

I don't really understand why the order matters.

[tardy sundial]

doesn't this limit the domain?

[severe pond]

no

because the input of the square root must be >= 0

x^2 >= 0 for all x

hence sqrt(x^2) >= 0 for all x

[severe pond]

in fact, this is true

[hasty wagon]

well, domain of f(x) needed to be non-negative reals, so when for the range of f(x), it will be non-negative reals only, now from this range, we can see the domain of g in g(f(x)) can only have inputs in the range of f.

[severe pond]

if you graphed it you’d see that f(g(x)) is |x| whereas g(f(x)) is just the branch of y = x where x >= 0

[tardy sundial]

I'll try and take a minute to process what you wrote

[tardy sundial]

I wrote this to make it clearer to me, but I'm still not sure I understand.

[hasty wagon]

pretty good.
For the first one, we need to first evaluate g(x), that is x².
it is valid for all real numbers.
For the second one, we need to first evaluate f(x), that is x^½.
it is valid only for non-negative real numbers.

that is why the domain (starting step) of f(g(x)) is R,
and the domain (starting step) of g(f(x)) is non-negative reals

[tardy sundial]

Okay, I am following this.

Ah, I know what m y question is

Then, why is f(g(x)) = |x| and g(f(x)) not

?

[hasty wagon]

they both are |x|.
but just one with a restricted domain, and one doesn't

[tardy sundial]

Like, if I just look at the expressions, it seems to be the same.

[tardy sundial]

Okay, I think I understand

[hasty wagon]

and infact x and x^(1/2) is non-negative, so for g(f(x)) we can just write g(f(x))=x

[river karma]

g

yo

[tardy sundial]

I see. Thanks.

[river karma]

guys play minecraft why you ?

[tardy sundial]

.close

[safe radish]

Channel closed

Closed by @tardy sundial

Use .reopen if this was a mistake.

[river karma]

g

guys let's paly minecraft

[safe radish]

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.

[proper moth]

what would be h'(x)?

[sand anvil]

ok so the answer i got was 20 but i checked it using photomath and it gave me 2 so i was just confused

wouldnt h'(x) be -2f'(x)

and then f'(3)=-10

so -2*-10= 20

wait so is it -10 or am i right?

sorry just wanna make sure

[proper moth]

You're correct

[sand anvil]

ok thank you

.close

[safe radish]

Channel closed

Closed by @sand anvil

Use .reopen if this was a mistake.

[safe radish]

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.

[sinful glen]

You want to setup the hessian matrix and implement the values of the stationary points and find the determinant. If the determinant is 0 then the point could be a max, min or inflection but we can’t tell

[modern bloom]

yes so I wonder how can we tell it by other way, cuz we can't tell by hessain but there's def other ways out

[sinful glen]

I’m not aware of another solution

I can search it up but I don’t think I will find anything useful ;/

[modern bloom]

I'm sure that there must be smth but we just don't know

[sinful glen]

From what I found there’s either you can figure it out by yourself, basically could it be a max or a min, or you are screwed

if you implement 0,0 in your function you get 0. Now ask yourself if there are any values x,y so that f(x,y) < 0 if there are you know that 0,0 is a minimum. Same for the maximum ask yourself if there is f(x,y) > 0

You get what I mean?

[safe radish]

@modern bloom Has your question been resolved?

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.

[mental star]

How do i differentiate 5^x

[mental star]

with steps please

[frozen marlin]

just use the chain rule then i guess, not much more

is tex broken

[flat frigate]

ren

[frozen marlin]

FINALLY

[mental star]

haha thank you

so

[frozen marlin]

nw

[mental star]

wait

do i set x to u?

[frozen marlin]

no

[mental star]

and then

[frozen marlin]

x ln 5 = u

[mental star]

oh right

i got it now thank you :]

you’ve been a great help

[frozen marlin]

np

[mental star]

.close

[safe radish]

Channel closed

Closed by @mental star

Use .reopen if this was a mistake.

[mental star]

.reopen

[safe radish]

✅

[mental star]

uhh

how do you prove that?

im confused on where ln 5 comes from

and why is it not

x5^x-1

,help

[flat frigate]

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!

[unkempt venture]

that works if the exponent is independent of the variable you're differentiating with respect to

[mental star]

oh right okay

and about ln5?

[mental star]

or rather this?

[frozen marlin]

??

what?

[mental star]

sorry sorry!

[frozen marlin]

no no

i just dont get ur question

[mental star]

didnt mean to ping you

[frozen marlin]

all g

[mental star]

im just confused on how you get the natural log in this

[frozen marlin]

$$5^x = e^{\ln 5^x} = e^{x\ln 5}$$

[flat frigate]

ren

[mental star]

oh right okay

[frozen marlin]

is that a thing

[unkempt venture]

this works because e^x and lnx are inverses

[flat frigate]

ren

[frozen marlin]

OH they are

well you get that from the power rule

[glacial meadow]

The natural log is the inverse function of e^x

[mental star]

OH RIGHT?

[flat frigate]

ren

[glacial meadow]

So, by definition, e^ln(x)=x, or, in this case, e^(ln 5)=5

[mental star]

okay i think i got it

thank you

thanks everyone!

.close

[safe radish]

Channel closed

Closed by @mental star

Use .reopen if this was a mistake.

[safe radish]

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.

[fathom plume]

lf someone to explain ^

[fathom plume]

ik how to use to formulas to prove events are independent alr but idk why they work

[green fern]

Do you know that $P(A|B)= \frac{P(A \cap B)}{P(B)}$?

[flat frigate]

cristorenzo99

[fathom plume]

ye

[green fern]

So, if they are indipendent, $P(A) = P(A|B) = \frac{P(A \cap B)}{P(B)} \implies P(A) = \frac{P(A \cap B)}{P(B)}$

[flat frigate]

cristorenzo99

[green fern]

So $P(A)P(B) = P(A \cap B)$ if A and B are indipendent events

[flat frigate]

cristorenzo99

[green fern]

And the converse is also true because if $P(A)P(B) = P(A \cap B)$, then, dividing by $P(B)$: $P(A) = \frac{P(A \cap B)}{P(B)} = P(A|B)$, so $P(A) = P(A|B)$, which means A and B are indipendent

[flat frigate]

cristorenzo99

[fathom plume]

gimme a min bro ima get my brain to process allat 😭

[safe radish]

@fathom plume Has your question been resolved?

[safe radish]

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.

[lean otter]

Can I send something that is math but the actual topic is Chemistry?

[flat jolt]

yea?

[lean otter]

Okay I'mma start sending it

It's all about Organic Chemistry

Like Akane, Alkene, Alkyne?

[solar hazel]

[covert yoke]

@lean otter I don't understand the question, but I'm not an organic chemist person. Is your question something along the lines "consider the carbon hydrogen molecules represented by these graphs, how best to name them?"

[lean otter]

I guess I can uhm show my notebook

This is how :3

[desert belfry]

first is 2,3-dimethyl-6-ethyldecane

[lean otter]

Wait! I thought your not suppose to answer the question!

[desert belfry]

Then what kind of help do you need? Explain how the naming process works?

[lean otter]

It's like unexpected since Kiomi told me that if I ever need help with the process this server never says the answer and only helper the helpees solve it!! I feel very worried and I thought this is a good opportunity to learn about the process but since I believe you already said the answer, Kiomi told me that I should report anyone who does revealed the answer because helpers help helpees and not show answers..

But I don't want to do that I want to be kind so I'll give you a chance since I know you didn't mean to! So All I need is the help on how the naming process works! Hehe!

[desert belfry]

Sure. Take the longest carbon chain, that's your base name - first four are irregular, the rest are just numbered in greek, for example 8 is octane, 10 is decane, etc.

[lean otter]

Okay got it!

[desert belfry]

What you care about are multiple bonds and appended groups.

[lean otter]

Okay!

[desert belfry]

So you number the carbon atoms from one end of the base chain to the other.

[lean otter]

Left to Right?

[desert belfry]

iirc the convention is whichever way has the closest group or multiple bond.

[lean otter]

If I go left to right it will be 9 if I go right to left it's 2

and teacher said to go to the lowest possible number

[desert belfry]

Yes, so in this case you go from the right.

[lean otter]

and then the thing on the upper right is called an isopropyl

It means it has 3 bonds

or groups...

or branches...

or stems..

or...

eheh..

[desert belfry]

There's no isopropyl in the first molecule.

[lean otter]

The one at the bottom?

[desert belfry]

The bottom one does.

[lean otter]

That's a methyl!

Teacher says that if it has one bond for carbon it's a methyl!

[desert belfry]

Correct. The top one has methyl at 2nd and 3rd carbon.

Then there's the last group at 6 with 2 carbons.

[lean otter]

Can you tell me the diffierence of Methyl and Isopropyl?

[desert belfry]

Methyl is one carbon atom away from the base chain. Isopropyl is 3 atoms, connected at the middle one. It's in the bottom molecule at 7.

Just propyl is also 3 carbons, but connected at one of the edges.

[lean otter]

I don't get it.. is it okay if you draw the difference?

[desert belfry]

sure thing

[lean otter]

I mean in line structure

[desert belfry]

Like this? Black is the base, blue is the group.

[lean otter]

YESS Thank youu

[desert belfry]

The full name then is (position)-(group 1 number prefix)(group 1 name)-(position)-(group 2 number prefix)(group 2 name)(base name)

At least for what you have here, multiple bonds add a bit more.

With that being said, can you now put together the name for the second molecule?

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

3 - Isopropyl, 6 - propyl, decane?

[desert belfry]

The base is decane. There's one isopropyl group, that much is correct. Not sure where you see the propyl.

Also there's 4 methyl groups.

[lean otter]

Nuh uh

Look closely

[desert belfry]

?

This thing, not my examples.

[lean otter]

No no

[desert belfry]

3-isopropyl-6-propyldecane would be this.

[desert belfry]

Yes, this is the second one redrawn.

[lean otter]

Left to right 5, 8
Right to left 2, 5

Correct?

[desert belfry]

That's not the longest chain. That starts in what you labeled as the isopropyl.

[lean otter]

That doesn't look correct?

There are 3

and we start at the bottom?

So... This is really how we count?

Okay I have no choice since I couldn't understand it and it will take us a lot of time

Let's move on.

[desert belfry]

It needs to be the longest chain.

The one you labeled has 9 carbons, this one has 10.

[lean otter]

2, 3 - methyl, 6 - propyl, deecane

[desert belfry]

Almost, the 6 group has 2 carbons, not 3.

[lean otter]

How can you be so sure that it doesn't have isopropyl?

What system are we following?

[desert belfry]

The base molecule needs to be the longest chain of carbons there is. That's the convention.

[proper moth]

Study the rules here:
http://www.chem.uiuc.edu/GenChemReferences/nomenclature_rules.html

[desert belfry]

Technically 2-isopropyl-3-ethylnonane describes the same structure, but if you wanted to buy that chemical you won't find it because no-one calls it that.

[lean otter]

uhm..

I still don't get it

[lean otter]

Isnt it suppose to look like this for isopropyl?

[desert belfry]

The first thing you need to do is select the base chain. Identifying the appended groups comes later.

[lean otter]

Left going right okay

no wait right going left

[desert belfry]

right to left, yes

[lean otter]

so 10

[desert belfry]

correct

[lean otter]

2 is one bond up...

Methyl..

[desert belfry]

ya

[lean otter]

3 is one bond down

another methyl?

[desert belfry]

yes

[lean otter]

propyl?

6 is 2 bond down propyl

so.. 4?

[desert belfry]

The group at 6 has 2 carbons. Propyl is 3.

[lean otter]

2 - methyl
3 - methyl
6 - propyl

[lean otter]

HUH? BUT ITS ONE???

[desert belfry]

No, I mean propyl has 3 carbon atoms.

[lean otter]

That's isopropyl?

[desert belfry]

No, isopropyl is three atoms connected at the middle. Two atoms is ethyl.

[lean otter]

Ohhh

2 - methyl
3 - methyl
6 -ethyl
decane?

[desert belfry]

Right, now put it all together.

[lean otter]

2, 3 - methyl 6 - ethyl decane?

[desert belfry]

Almost there, just two more things.

The groups are supposed to be in alphabetical order.

And we have two methyl groups, so we need a number prefix.

[lean otter]

6 - ethyl 2, 3 - methyl decane?

[desert belfry]

yes

[lean otter]

Is that the answer?

[desert belfry]

the prefix

[lean otter]

I thought I had it

[desert belfry]

two methyls, so it's dimethyl

[lean otter]

2, 3 - dimethyl 6 ethyl decane

[desert belfry]

similarly three would be trimethyl, four tetramethyl and so on

When ordering the groups you only use the group name, not the prefixes.

Confusing, I know.

[lean otter]

ehhh not really

I kinda got it why

Specifc I guess

Anyways

[lean otter]

Correct?

[desert belfry]

No, 6-ethyl-2,3-dimethyl decane

[lean otter]

I thought it's alphabetic order

[desert belfry]

It is, but only the group name, not the number prefixes.

[lean otter]

6-ethyl-2,3-dimethyl decane is the final answer?

[desert belfry]

Yes

[lean otter]

okay next

[desert belfry]

First you find the length of the base chain.

[lean otter]

Left to right
2, 5, 6, 7, 8
Right to left
2. 3. 4. 5. 8??

So right to left?

[desert belfry]

On the right the first branching is on the third carbon. On the left it's the second.

[lean otter]

Left to Right
2, 5, 6, 7, 8
Right to left
3, 4, 5, 6, 9

So it's left t right

[desert belfry]

yea

You need to keep in mind that the base chain isn't always in a neat row, it can go up or down.

[lean otter]

2 - methyl
5 - methyl
6 - methyl
7 - isopropyl
8 - methyl
decane

[desert belfry]

great, now put it together

[lean otter]

2, 5, 6, 8 - butyl 7 -isopropyl decane

correct?

[desert belfry]

No, butyl is a single group of four carbons. You have four groups of one carbon.

[lean otter]

pentyl?

[desert belfry]

So again it's methyl with a prefix.

[lean otter]

penmethyl?

tentramethyl

[desert belfry]

tetramethyl, yes

[lean otter]

2, 5, 6, 8 - tentramethyl 7 -isopropyl decane

[desert belfry]

There you go.

[lean otter]

My Mom just walking by calling me crazy

because I keep saying giberrish while guessing at the middle of the night

[desert belfry]

Organic chemistry does that, yeah

[lean otter]

Thank you Im going to sleep now

[desert belfry]

anyway great job, though you might wanna practice to get it down fully

[lean otter]

Thank you

[desert belfry]

np

[lean otter]

.close

[safe radish]

Channel closed

Closed by @toxic orchid

Use .reopen if this was a mistake.

[safe radish]

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.

[flat crystal]

Context behind the question is that we're using wuadratic equations
My problem is that i don't know how to set this up

[flat crystal]

Area = l * w, and therefore, Area = l * (x)
And 900ft is more akin to peremiter vs area, yeah?

[potent jolt]

Yeah, 900ft is telling you the total amount of fence

its not exactly perimeter since its missing one side

+______Forest
|      Forest
|      Forest
|      Forest
+______Forest

might get messed up on mobile but

you know those 2 parallel sides measure x

let's say the other one measures y

since you got 900ft total for those sides, you have $900 = x + x + y = 2x + y$

[flat frigate]

Sires

[potent jolt]

subtracting 2x from both sides gives you that the side y = 900 - 2x

now, the area of a rectangle is just the product of its sides

so $A(x) = x \cdot y = x \cdot (900 - 2x) = 900x - 2x^2$

[flat frigate]

Sires

[potent jolt]

Now, notice the sign of the x² is negative, so that means its gonna be a parabola that goes up up, reaches a peak, then goes down forever

so for b) you gotta find where that peak(also known as vertex) is and how high is it

you think you can do this part? (you said you needed help setting it up, so I assume you know the rest)

[safe radish]

@flat crystal Has your question been resolved?

[flat crystal]

Yeah, i can find the vertex with this. thank you!

[safe radish]

Channel closed

Closed by @flat crystal

Use .reopen if this was a mistake.

[safe radish]

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.

[sly lintel]

i need to determine the polynome of the graph here. but i don't know how. :(

[sly lintel]

and there cant be any variables in the equation (except x obviously)

[lone arch]

Clearly the function is of odd degree with leading coefficient being negative

You agree, right?

[sly lintel]

yes!

[lone arch]

So the first function we'd think of is of degree 3

[sly lintel]

makes sense, yes

[lone arch]

In the case that it's splitting over R, we can represent it as f(x) = (x-a)(x-b)(x-c) where a, b, c are zeros

If it's not splitting, we can only say f(x) = ax^3 + bx^2 + cx + d

From the diagram, you can read off two zeros

[sly lintel]

-1 and 0,5 right?

[lone arch]

Yes, what are their multiplicities?

[sly lintel]

ohh sorry i dont understand the word (english is not my first language :,(

[lone arch]

The multiplicity of the zero x = 2 in for example (x - 2)^2 would be 2

In (x - 2)^3, the multiplicity of the zero x = 2 would be 3

A zero of even multiplicity looks like this: