help-33

[small ravine]

oo i c

yeh

[waxen dust]

The way you solve this is you split this into 4 cases

$x+2+x-2 \leq 6; x+2 \geq 0, x-2 \geq 0 \ -(x+2) +x - 2 \leq 6; x+2 < 0, x-2 \geq 0 \ x+2 - (x-2) \leq 6; x+2 \geq 0, x-2 < 0 \ -(x+2) - (x-2) \leq 6; x+2 < 0, x-2 < 0$

[small ravine]

okhh

[elfin berry]

USS-Enterprise

[waxen dust]

You solve each of the 12 inequalities, find the intersections on each row then the union of everything at the end

I see I used x, meant to use z

Anyway you get $x \in [-3, 3]$

[elfin berry]

USS-Enterprise

[waxen dust]

This is not something you can do

[violet relic]

Why not?

This is inequality

|a+b| <=|a|+|b|

[waxen dust]

Oh

I thought you said equals

Sorry

Didn't see the less than

[violet relic]

.close

[marsh citrus]

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[orchid oracle]

How do I find the range of y = log(sin(x))
I've already found the domain; x \in U ] 0+2kΠ, Π+2kΠ [

[orchid oracle]

I dont really get how to start with this problem

[marsh citrus]

@orchid oracle Has your question been resolved?

[stark trail]

Well

if it was just log(x)

do you know what the range would be

[orchid oracle]

All of R

[stark trail]

okay

but what if I said

you can only put a limited range of x's into log(x)

like says

from x=-1 to x=1 is all that you can put in

what would it then be?

[orchid oracle]

Hm

🧐

[stark trail]

well you atleast should know immediately you can't input negatives

so really this is just 0 to 1 right?

[orchid oracle]

Well log neg is undefined

yes 0 to 1 can be put into this log(x)

0 not included

btw

[stark trail]

and then what would be the possible outputs? the range?

[orchid oracle]

i dont know

should I know the log function for this?

[stark trail]

yes

[orchid oracle]

or graph it?

[stark trail]

,w plot y=log(x)

[elfin berry]

Results provided by WolframAlpha

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Requested by austinu

[stark trail]

as x->0 (from the right) log(x) approaches negative infinity

but at x=1, log(x)=0

so do you now know the range?

[orchid oracle]

range is projection on y axis

so

all negative

R^-

[stark trail]

and if that is including 0

then yes golden

Okay but anyways that was just an example right? a digression from the real question

I asked you, what is the range of log(x) if you can only input x from -1 to 1

and you told me it is (-inf, 0]

correctly

But here's the real question

What is the range of log(x) if you can only input y where y=sin(x) ?

Well this is a bit different right

how do we know what y is?

Well we don't exactly, but we do know that y is at most 1, and at least -1

right? because -1<=sin(x)<=1

[orchid oracle]

coming from the definition of sin?

[stark trail]

yes

,w plot y=sinx

[elfin berry]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by austinu

[orchid oracle]

yh

[stark trail]

So was our example really an example? Or did I trick you into solving it

[orchid oracle]

Okay yes, but I just read that from the graph

What if

there is no graph

[stark trail]

you should be familiar with basic functions like sine, cosine, log(x), e^(x)

and their graphs

[orchid oracle]

Ah

[stark trail]

it isn't as complicated as you might think

[orchid oracle]

Think i get it now

Thanks

.close

[marsh citrus]

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[stark trail]

no problem

[marsh citrus]

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[dusky viper]

how do i determine where the hozirontal asymptote is, if it even has one

[unborn ibex]

A

no sorry

D

[dusky viper]

brother the answer doesnt help me

[unborn ibex]

do the lim

[dusky viper]

never touched limits

[unborn ibex]

divide the function by x^2

you will get:
2 divided by (1/x^2) - 1

then when x --> infinity
then 2 / (1/x^2) - 1 --> -2

since 1/(x^2) --> 0

when x --> infinity

[dusky viper]

aight

thx

.close

[marsh citrus]

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[marsh citrus]

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[violet relic]

Finding rank of matrix by determinant works for all type of matrix?

[violet relic]

Augmented matrix rank and rank of matrix doesn't equal for option A but i want to know about Determinant method

<@&286206848099549185>

[reef ginkgo]

1

because D=0

hey

hum ....

[marsh citrus]

@violet relic Has your question been resolved?

[marsh citrus]

@violet relic Has your question been resolved?

[violet relic]

<@&286206848099549185>

[reef ginkgo]

didn't you understand?

[violet relic]

No

[reef ginkgo]

why?

[mighty tide]

yeah that's true

replace all the thetas by 1

and it would work

x+y+z=1

[marsh citrus]

@violet relic Has your question been resolved?

[marsh citrus]

@violet relic Has your question been resolved?

[violet relic]

.close

[marsh citrus]

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[whole sparrow]

Why

.reopen

[violet relic]

What?

.reopen

[marsh citrus]

✅

[whole sparrow]

My doubt isnt cleared

Idk why the image isnt sending

[whole sparrow]

Can you tell how to do this

[violet relic]

.close

[marsh citrus]

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[long cape]

why are you not allowed to divide matrices? isn't it just the inverse of multiplication?

[long cape]

like if you write it correctly so that it's clear, not using fractions

A ÷ B

for addition, subtraction is just the inverse of addition
isn't it the same idea here?

[devout mauve]

for starters, is $\frac A B$ supposed to mean $AB^{-1}$ or $B^{-1}A$ ?

[elfin berry]

Denascite

[devout mauve]

no one actually writes ÷ anywhere

[long cape]

that's why I said, not using fractions

[thick junco]

ok

[long cape]

why tho? it's a math operator

[thick junco]

does A ÷ B mean $AB^{-1}$ or $B^{-1}A$ ?

[elfin berry]

Out Of Nosh

[devout mauve]

that no one except kids uses

[long cape]

oh right

AB is different from BA

and since addition is commutative for matrices, we can use subtraction

but since multiplication is not commutative for matrices, we cannot use the inverse of multiplication on matrices (division)

interesting insights... how those things (inverse and commutative property) are directly correlated to one another for matrices in very important ways...

[long cape]

but wouldn't it be AB^-1? that's the only way to read it

so the real issue here, is with division we can only divide with respect to the right side

[devout mauve]

the real issue is that no one uses the symbol ÷

[hushed egret]

A/B, B\A

[devout mauve]

so why introduce it again for matrices

[long cape]

it's still used

[stoic saddle]

i was about to bring that up, snow

[still temple]

o

[stoic saddle]

not for matrices it's not lol

[devout mauve]

there is absolutely no advantage to introducing it

[still temple]

[stoic saddle]

ok but no like. MATLAB, a language specifically designed for manipulations with matrices of all kinds, has two operation symbols

[long cape]

I mean, it's not a made up symbol.. i guess it's for kindergarten/elementary tho
we use fractions now

and negative exponents

[stoic saddle]

A / B is the same as A * B^-1 while B \ A is B^-1 * A so you can distinguish left vs right division.

[devout mauve]

yes thats my point. you stop using it and start using fractions

[stoic saddle]

that way it is unambiguous and nobody has any doubt as to what you are writing

[long cape]

it's like partial fractions, I hear there is an issue with them in the math community

[devout mauve]

what?

[long cape]

uhm..

wrong term maybe

where you have 2 1/4

[devout mauve]

mixed fractions?

[long cape]

big 2

yeah

[devout mauve]

eww

yeah

[main idol]

don't use those either

[devout mauve]

also just for kids

[stoic saddle]

if you must: $2 + \frac{1}{4}$

[elfin berry]

Ann

[long cape]

https://tenor.com/view/orange-symbol-kyocera-divide-gif-17757102

[long cape]

2 1/4 does not mean 2(1/4)?

I forget lol

2/4 = 1/2

[devout mauve]

well thats the point of why it is awful notation

[long cape]

lol

it really means this??
2 + 1/4

[devout mauve]

for kids it means 2+1/4

[long cape]

wtf

[stoic saddle]

"two and a quarter"

is how you read that

the notation causes confusion the moment you try to do anything remotely complicated with it

[long cape]

i guess the lesson learned
2 1/4 = 2 and 1 quarter
2(1/4) = 1/2

brackets are important?

[devout mauve]

the lesson is to not use one of them

[dry prawn]

Useful in speech more than in writing

[long cape]

but really, brackets or × or ⋅ should be used to begin with, if it's gonna be multiplication

2 1/4 doesn't show any of that, so red flag already

[main idol]

.

[devout mauve]

× shouldnt be used for multiplication either

[long cape]

I don't know if I would necessarily assume these to be multiplication, as much as we "want them to be"...

[long cape]

for the reasons above

but I can also understand why people hate them

maybe because we are so used to bringing the term next to a fraction up to the numerator?

like what if it was a variable instead of a number on the left side

are we always gonna need to use brackets to indicate multiplication?

i guess that is the biggest issue with them.. absolutely horrible for math with variables

.close

[marsh citrus]

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[long cape]

.reopen

[marsh citrus]

✅

[long cape]

.close

[marsh citrus]

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[summer trench]

according to my red and white labellings we can say that x=R=r

but i dont think x is equal to R is equal to r

R is the top radius of this paraboloid while r is something radius inside the paraboloid

like first he wrote R in place of x and then r in place of x

[still temple]

Arey sir namaste

[summer trench]

oh bade din bhai

[still temple]

😂😂

x= r ≠ R

[summer trench]

chal sawal bata abhi

[still temple]

Arey rukk

Dekhnede

[summer trench]

ya x=R neq r

[still temple]

Yahi sahi hai

[summer trench]

toh tum keh rhe ho ki ye iit madras mechanical ke sir ne isme hag diya?

[still temple]

Halaki x = R bhi possible hai, par yaha jo diya hai
Usme unhone r assume kiya hai
x = r rakha unhone y = kx² => y = kr² jisko unhone H height maanli

[still temple]

Han

UNLESS

[summer trench]

mere ko toh y=kR^2 dhik rha hai

[still temple]

H is the total height of paraboloid

[summer trench]

y=H

[still temple]

Abey sunn

Diagram mai chotta h hai

Likha BADA H HAI

Bada H is height of paraboloid

Chotta h is height of particle instable orbit

Par phri tan(90-x) mai sir ne hagg diya

Hatt bc

x = r hi hoga

Diagram dekhle

bada R rakhne pe to Height of paraboloid milega

Apne ko to height of particlechahiye na

@high niche haramkhor

left side mai H nhi dikh rha diagram ke????

[summer trench]

are sun rha hu smghne de bhai

[summer trench]

dhik rha hai but smgh me nhi aa rha kuch

ruk zara dhekne de

[still temple]

R -> H
r -> h

Aisa

[summer trench]

12 gahnte se mu*h nhi mari toh dikkat ho rhi hai

[still temple]

NNN bhai

[summer trench]

kya?

[still temple]

Best of luck

Mera to screentime shuru ho rha

[still temple]

Abey y = kx² mai
R rakhega to H - Total height of praboloid
r rakhega to h - height of particle

Samjha?

Tere liye limit badhake aata hu rukk

[summer trench]

?

[summer trench]

ho thoda thoda smgha ruk

[still temple]

Abey 6 second mai tab band hone wala tha

[still temple]

Samjh aur bata

[summer trench]

?

[still temple]

Tu question pe dhyan de

Han aur wo white mai jo x likha hai , wo r hi hai

Chotta r hi samjh

[summer trench]

no

#discrete-math

[still temple]

#❓how-to-get-help

Then wait for someone to answer idk

[summer trench]

#help-11 post your question atleast

ha ruk dhek rha mai

[still temple]

#discussion

Ping krna mujhe

No, 11th

[summer trench]

ok

@still temple ha toh bidu dhek

jo mai smgha ki

[still temple]

Han

[summer trench]

y=kx parabola ki normal equation hai like general equation

[still temple]

y =kx²

Sahi hai

[summer trench]

toh isme k ki jgay H R ke terms use krliye kuki uske sath relation lana tha

[summer trench]

are ha feeling smgh

[still temple]

Han bhai

Feeling

[summer trench]

haina fir uske baad

[still temple]

Na sunn

[summer trench]

nhi

phle tu meri sun

shant baitha reh abhi

pura hone de phle

[still temple]

jaise tune x ki jagah pe r dala na
to tujhe y milega, usko h mana

[still temple]

Han han bol

Ro mat

[summer trench]

ha whi bolne ja rha tha pura sunegga bkl

[still temple]

Han sir bolo, sorry sir

[summer trench]

are yrrrr tum bade tharki ho ksm se mere pas hai bhi nhi uske

[still temple]

Question oe dhyan dena bkl

😂😂

[summer trench]

toh iss equation ka slope nikalne ke baad hamse x=r and y=h leke substitue kardia usi me kuki ab hame usme relation chahhyiye

toh hamlgoo ko sari cheej ka sath me relation mil gya

right baby?

@still temple idhar aao zara

[still temple]

Padhne de

[summer trench]

ok babe

[still temple]

Oh yeah

Sahi hai

r daalne pe h milega
R daalne pe H milega

[summer trench]

ha dalne pe milega

ha

ye sahi hai

ha ok smgh aa rha hao

hai

@summer trench

!done

[marsh citrus]

If you are done with this channel, please mark your problem as solved by typing .close

[summer trench]

.close

[marsh citrus]

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[marsh citrus]

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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>.
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[narrow gate]

could somebody walk me through I would simplify this? Is this just FOILing then dividing as much as possible?

[bleak ibex]

You can notice that $\frac{3}{4} \cdot (8x^2 - 20) = 6x^2 - 15$

[elfin berry]

Jelle

[bleak ibex]

so the left numerator and right denominator will cancel and just leave 4/3

and the right denominator can be factored with difference of squares

[narrow gate]

Holy what

I'm trying to do it the long way

[narrow gate]

That is a really cool trick I didn't see that

If I were doing this the long way would I do it like this?

wait no the 32 is in the wrong place ugh

[narrow gate]

could i even divide these?

im seeing how google did it, but how the hell do you remember how to do this? like is there not some long method that will always get you the answer?

Not to mention the answer it gives isnt a possible answer for my work sheet what the heck is going on here?

Like how would I solve a huge polynomial being divided by another polynomial like this and be able to get a definitive answer

[marsh citrus]

@narrow gate Has your question been resolved?

[marsh citrus]

@narrow gate Has your question been resolved?

[dusk otter]

I will help

If it asks just to simplify then this might help.

only need to factor out some numbers and see that difference of squares.

@narrow gate

[narrow gate]

okay im stupid give me a refrehser on difference of squares

[dusk otter]

no worries so

i wrote the formula

with red

you want me to demonstrate it?

[narrow gate]

could you write in discord? Im having trouble reading your handwriting

[dusk otter]

a2-b2 = (a+b)(a-b)

a2 means squared

i don't know how to use that bot yet sorry

[narrow gate]

okay that makes sense

``aa-bb

(a+b)(a-b)``

[dusk otter]

yes!

[narrow gate]

so using this you are factoring out numbers and you can just keep doing that to simplify it?

[narrow gate]

instead of doing it the super long way I was doing it

[narrow gate]

quesiton would this even work or is it jusut so big and unweildy theres no way

i really like having a "this method will always work even if it takes forever" card

[dusk otter]

only use it when you see difference of two numbers that can be written to the power of two

[dusk otter]

I see, it is okay to try diffrent methods

long division?

[narrow gate]

yes like i was doing here

[narrow gate]

i actually multiplied them here then wanted to see if i could just straight up divide it to simplify

[dusk otter]

seem it didn't work out.

[narrow gate]

yeah i gave up it was way to big

[dusk otter]

the best way to aproach these is to use identities like (a+b) squared (a-b) all squared

that difference of squares is helpfull too

sorry for bad spelling

there are more but it depends on your grade

[narrow gate]

11th

algebra 2

[narrow gate]

im not sure if we've actually learned this yet or if theyre just testing me

[dusk otter]

It is great that you tried at least

[narrow gate]

so basically you use a mix of things to try and simplify it (and ill probably learn more methods to be able to actually do it)?

[narrow gate]

yeah thats true

[dusk otter]

yes

you know the basic rules of these algebraic expressions right?

like x+x is 2x etc

[narrow gate]

yes yes

theyve taught me that its just a lot to try and do it all at such a big scale

[dusk otter]

these identities help you spread out these expressions and simplify all of it

[narrow gate]

like~~ 2x^2/y^2 = ((x+x)(x+x))/(y*y) ~~ this is wrong im stupid

2x^2/y^2 = (x(x+x))/(y*y)

[narrow gate]

why are you calling them "identities"? what does that mean?

[dusk otter]

as they are general formulas to help you solve

like some rules

not rules but you get it

like a short way

want me to write the basic ones for you?

[narrow gate]

sure

i think ive only reeally seen the difference of squares atleast that i can name

[dusk otter]

done

let me send it to you

hope it is lisible

[narrow gate]

What are the names for these?

also ive seen these ! things are they factorials 🤨

or does that have nothing to do with what your showing me

[dusk otter]

These are called algebraic identities

there are more formulas but for the moment i think it is great to practice more on problems that are using these

[dusk otter]

nono factorials is that n!

the product of all positive integers less than or equal to a given positive integer

those formulas help you "FACTORISE"

as a really simple exercise

try factoring x squared - 4

[narrow gate]

a what now

I would just be able to turn x^(-4) into 1/(x*x*x*x)

atleast thats how i think im supposed to do it

i know nothing about factorials i just know that ! at the end of the number means its a factorial and that means something important i think i get into it next math subject

[dusk otter]

but it is correct!

[dusk otter]

yeap, pay attention

oh nono

there is a missunderstanding

factorise this expression 4x^2 - 8

[narrow gate]

x(x+x+x+x)-8 ?

[dusk otter]

if i knew how to use the bot

[narrow gate]

that bot uses LaTeX if you want to use it youd have to learn how to write in latex which i think is pretty easy i havent used it in a while though

[dusk otter]

$\4x^2 - 8$

[elfin berry]

Wolfgang Composer

$\4x^2 - 8$
```Compilation error:```! Undefined control sequence.
<recently read> \4
                  
l.57 $\4
        x^2 - 8$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.```

[narrow gate]

,help

[elfin berry]

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!

[dusk otter]

okay so i should not edit it if i made a spelling mistake

$\4x^2 - 8$

[elfin berry]

Wolfgang Composer

$\4x^2 - 8$
```Compilation error:```! Undefined control sequence.
<recently read> \4
                  
l.57 $\4
        x^2 - 8$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.```

[dusk otter]

bruh

[narrow gate]

yikers

[dusk otter]

$(4x^2 - 8)

[elfin berry]

Wolfgang Composer
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[dusk otter]

big bruh

[narrow gate]

🙀

[dusk otter]

you see the formula we use here?

[narrow gate]

is that in here

err i dont see anything in here that looks similar to this maybe im stupid

[dusk otter]

don t say that

[narrow gate]

no im just staying im stupid not dumb theres a difference

[dusk otter]

((2x)^2 - (2\sqrt{2})^2)

[elfin berry]

Wolfgang Composer

[dusk otter]

now seeing something?

[narrow gate]

wait what the heck

what is going on in the 2nd part

[dusk otter]

writing it as a square

[narrow gate]

$(2sqrt(2))(2sqrt(2))$

damn it hold on

[dusk otter]

okay!

[elfin berry]

tateorrtot
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[narrow gate]

hmmm

lemme just draw it

this

whats the point of doing this espically the sqrt of 2 thing

[dusk otter]

to write it as a perfect square

so

we have this

(4x^2 - 8)

[elfin berry]

Wolfgang Composer

[dusk otter]

okay?

we use the formula:

(a^2 - b^2 = (a + b)(a - b))

[elfin berry]

Wolfgang Composer

[dusk otter]

that one

for this we need to form two perfect squares

[narrow gate]

wouldnt that be the sqrt of 8

$\sqrt(8)$

[elfin berry]

tateorrtot

[dusk otter]

yee!!!!

[narrow gate]

wait is the sqrt of 8 just

2*sqrt(2)

[dusk otter]

YESSS

[narrow gate]

huh 🤨

how the hell does that work

[dusk otter]

we initially have 8 right?

[narrow gate]

yes

[dusk otter]

to use that formula i wrote

you need to write 8 as a x² number

is that clear?

[narrow gate]

yes

that is i see that

its just
2*sqrt(2)

this black magic

[dusk otter]

(8 = (\sqrt{8})^2 = (2\sqrt{2})^2)

without "in"

[elfin berry]

Wolfgang Composer

[dusk otter]

does that make sense?

[narrow gate]

🤨

i see how you go from this to this

but this to this is a stretch for me

[dusk otter]

ouuuu

you don't know how to break down the square roots?

[narrow gate]

nope ive never seen that before

is it like 8/4=2 so then they both become two or something im trying to figure out how that happened

[dusk otter]

well then you are getting a too advanced leasson 🥲

[narrow gate]

😔

thats okay ill get to it eventually

[dusk otter]

(2\sqrt{2} = \sqrt{2^2 \times 2} = \sqrt{4} \times 2 = \sqrt{8})

no

i ll write again

(2\sqrt{2} = \sqrt{2^2 \times 2} = \sqrt{4 \times 2} = \sqrt{8})

[elfin berry]

Wolfgang Composer

[dusk otter]

yes like this

[narrow gate]

😵‍💫

i understand steps 2->3->4 but 1->2 is a stretch

[dusk otter]

ou

sorry for that

i though you learned this before

at school

[narrow gate]

i think i mightve but skimmed over it and forgotten it since i havent done this in forever

[dusk otter]

well hope i helped you a little

[narrow gate]

yes sir 🫡

is this farewell

[dusk otter]

bye!

[narrow gate]

👋thanks!

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[rain dove]

Hey guys, can I get some help on a standard to vertex form?

[rain dove]

I was wondering how my teacher got that answer.

the reason that I am confused is that I got everything right. I thought I had to multiple -38 by -16 before putting it behind the parenthesis

it might take awhile before I get some help so im going to shower

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[frozen python]

people of mathamatics

[frozen python]

i need helpo

how do i make the fins stop

or the shading i mean

how do i make the shading stop at the rocket sides

[paper raptor]

it appears your best bet for desmos here is use the polygon() function

cause desmos doesn't like inequalities with two variables

the polygon() functions takes points as inputs

[frozen python]

oh

[frozen python]

wha tis the polygon function

[paper raptor]

polygon((3,1),(4,2),(5,8)) makes a triangle :)

https://www.desmos.com/calculator/lffpbvjtx7

[frozen python]

oh

so u just insert cords

[paper raptor]

albeit those curves could be kind of annoying, but desmos just really doesn't like inequalities of two varables

idk why

[frozen python]

ok ty

so like

theres no way i can do a curve though

i can't just limit that

?

@paper raptor

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[paper raptor]

.reopen

[marsh citrus]

✅

[paper raptor]

woah wait desmos does 2 variable inequalities now

ok that makes this easier

@frozen python what's the equation of the outer body of ur rocket?

[marsh citrus]

@frozen python Has your question been resolved?

[frozen python]

uhm

y<-\left(x\right)^{2}+50\left{y>20\right}

for the uper half

@paper raptor

i think i got it now though

so its alr

a friend helped me do that part

and i think i can use the polygon equation you rpovided

thank you

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[quaint kayak]

is there any way of finding the derivitave of this without applying ln to both sides

[long osprey]

using the chain rule, yeah

nicest thing would probably be to rewrite $x^{\cos x} = e^{\cos x\ln x}$

[elfin berry]

Edward II

[long osprey]

(or if you know the rule for exponentials with other bases which I always forget and rederive using that, just use it directly)

[quaint kayak]

ight

thanks

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[scarlet salmon]

Is it impossible for something of the same dimension as it’s parent space to have an orthogonal counterpart? E.g. is it impossible for a plane to have an orthogonal counterpart when it is a sub space of R^2? And so on upwards?

[marsh citrus]

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[marsh citrus]

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[marsh citrus]

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[umbral eagle]

2h

question h

[unborn ibex]

there is a forumal for this

[umbral eagle]

Hmm I'm not too aware of the formula

[jade edge]

i will personally using heron

but if you have a pretty good at visualizing i think you dont need a formula (if I not mistaken

[umbral eagle]

What's the formula for the triangle area with the cross product thing

[marsh citrus]

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[sterile scroll]

okay the sum of a1 + a2 . . . + an-1 + an = (2a1 * d(n-1)) * n/2. What if i want to find a1 + a3 + a5 . . . an?

[desert socket]

well, sum of a1+a2+a3...an is equal to (n/2)*(2a+(n-1)d)) IF AND ONLY IF they are in AP

common difference is d

so, a3-a2=a2-a1=d

now, a1,a3,a5 would again be in AP.
Now the common difference would be 2d instead of d

[sterile scroll]

yes its an AP

[desert socket]

also, number of terms would be (n+1)/2 if n is odd and (n/2) if n is even

so, the sum a1+a3+a5...an=(n/4)(2a+((n/2)-1)2d) for even n

[sterile scroll]

okay let me think of it

i understand why it is n/4

[desert socket]

$n=2k,\ \ a_{1}+a_{3}+a_{5}...+a_{n}=\frac{\left(\frac{n}{2}\right)}{2}\left(2a+\left(\frac{n}{2}-1\right)2d\right)$\$n=2k+1,\ a_{1}+a_{3}+a_{5}...+a_{n}=\frac{\left(\frac{n+1}{2}\right)}{2}\left(2a+\left(\frac{n+1}{2}-1\right)2d\right)$

[elfin berry]

B-eard

[sterile scroll]

okay thanks👍

[marsh citrus]

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[marsh citrus]

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[summer trench]

!status

[marsh citrus]

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

[formal raft]

if i find the area of sector XYW and subtract area of triangle XYZ from it will I be left with part D only?

[formal raft]

5. I have a question about someone else's work/solution.

anyone?

<@&286206848099549185>

<@&286206848099549185>

@summer trench

won't u be able to help me?

[spark siren]

IMHO no.

[formal raft]

ok

[formal raft]

then umm is this equal to 5?

if so then why?

@spark siren sire, u there?

[formal raft]

if I do this my answer matches

with the book

but doesn't make sense

on that D thingy

[spark siren]

i think you should be more detailed in what is given and what is asked. posting a sketch with nearly no information and asking if something is 5 doesnt make it easy to help

[formal raft]

sorry sir,

each side of the square is 10cm as it is the radius of the circle

[spark siren]

all the lines i added have length oft the radius (and there are some more). therefore you should be able to determine the angles i marked (an much more). so you should be able to solve your example.

so you should be able to calc the small square, and the 4 parts outside the small square.

[marsh citrus]

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[marsh citrus]

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[glad yoke]

Why if PxD=Hf(D) i can obtain P doing this

[glad yoke]

(D|I)~(Hf(D)|P)

<@&286206848099549185> pls help

[spark siren]

some context available?

[glad yoke]

I need to get a invertible matrix P that PxD is equal to the hermite form of D

i know how to do it but i cant understand why

I would use an amplied matrix (D|I) and then transform D into Hf(D) and the thing that is on I place is P

But I dont understand why

<@&286206848099549185>

[marsh citrus]

@glad yoke Has your question been resolved?

[glad yoke]

<@&286206848099549185>

[marsh citrus]

@glad yoke Has your question been resolved?

[marsh citrus]

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[flint reef]

What is the LCM of

[flint reef]

I'm trying to find x

[sullen flare]

For compact two-dimensional surfaces without boundaries, if each loop can be continuously compressed to a point, then the surface is topologically homeomorphic to a 2-sphere (usually just called a sphere). The Poincaré Conjecture, proven by Grigori Perelmán, states that the same is true for three-dimensional spaces.

Someone to solve it

[wooden citrus]

You want x or what is that lcm?

[flint reef]

I'm trying to find x

If I want to find x I need the LCM

[wooden citrus]

Not really

You can just multiply by x, x+1, and 10

[flint reef]

Isn't that the LCM?

[wet holly]

in other words multiply by the lcm

[flint reef]

You litearlly just described the LCM to mebruh

[wooden citrus]

Isnt that depends on x

[wet holly]

polynomials have lcms too

[waxen dust]

It's the lowest multiple of all 3 denominators

[wooden citrus]

Anyway just multiply by the lcm then

[flint reef]

K thanks

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[amber sequoia]

I can't seem to find the mark scheme for this past paper

[amber sequoia]

<@&286206848099549185>

[marsh citrus]

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[marsh citrus]

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[amber sequoia]

I don't understand transformation and enlarging

[safe badger]

I think you can just multiple all the perimeter values by -2 (?)

[amber sequoia]

Idk

[deep oar]

no, you have to take the coordinates of the vertices, and multiply them by -2

eg, (3,1) becomes (-6,-2)

[amber sequoia]

Ah ok that make more sense

[amber sequoia]

What about the 'around a centre' bit?

[deep oar]

you just imagine that point as (0,0)

since its already (0,0) you dont have to worry in this one

basically move the axes over to that point? if that makes sense

[amber sequoia]

I don't understand

[deep oar]

so if it said to scale by a factor of 3 around center (2,2)

you would pretend that that point is (0,0), and you would count the coordinates from that point

or, actually you can think about it like this

if you need to scale the point (3,4), you would subtract (2,2) from it to get (1,2), then multiply by 3 to get (3,6), then re-add (2,2) to get (5,8).

that part is hard to explain properly, sorry

[amber sequoia]

I think I understand

Thanks

!close

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[still temple]

what algebraic manipulatio is done herE?

first you have (2+11 i) ^1/3

[nova totem]

Hm, try demoivre's theorem

Turn 2+11i into re^(iθ)

[still temple]

well

i am on page 1 in complex numbers

havent heard of that

[nova totem]

So you're not familiar with $re^{i\theta} = r\cis(\theta)$?

Hmm

[still temple]

no

[nova totem]

Lemme see then

Heh I broke it

Yeah I see no other way than DeMoivre's

[still temple]

not to doubt you

but DeMoivre was born in 1667

[nova totem]

He is dead

[still temple]

this equation was postualed in the 1500's

[deep oar]

just cube both sides, i think?

[nova totem]

I mean if you wanna establish the equality sure

[deep oar]

yeah thats it

[nova totem]

I'm pretty sure he's asking how to get from the left to right

Not prove the equality

[still temple]

this is a simplificaton

I give you this:
(sqrt(-121) + 2)^(1/3)

[devout mauve]

you can always assume that (2+11i)^1/3 has the form a+bi and then cube both sides and compare stuff. that should probably work

[deep oar]

yeah that too

[still temple]

what is that called

this is mentioned on page 1

[devout mauve]

what is what called

(educated) guessing?

[still temple]

a+bi

or will DeMoivre's

work

[devout mauve]

well complex number

[still temple]

some guy said that

[marsh citrus]

@still temple Has your question been resolved?

[still temple]

im watcing a video about it now

ill be back later for some questions

[marsh citrus]

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[small canyon]

I need help

[lean flame]

!status

[marsh citrus]

What step are you on?
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2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
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7. None of the above

[small canyon]

1

[vagrant gull]

This belongs in #old-network message

[small canyon]

Oh ty

[marsh citrus]

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[spark vale]

hi can someone explain why part b is 0 and not 1

i thought it was one because if you do f(-x) the first part will be -5x^5 and the rest would be positive i think? so wouldn't there only be one sign change ?

[hollow crescent]

well if u graph the function it has a negative root so might be error

[spark vale]

so you think it should be one neg real rool as well?

[marsh citrus]

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[spark vale]

.close

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[sweet rune]

yo

[sweet rune]

i need help

[next raft]

send the question directly

[sweet rune]

okay

give me a second

[marsh citrus]

@sweet rune Has your question been resolved?

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[desert dirge]

accurate name

[marsh citrus]

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[marsh citrus]

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[sinful vortex]

where did i go wrong on this question? not sure what to do

[spark atlas]

The x(x+6) part seems wrong

I believe it should be (x-3)(x+2)

[sinful vortex]

i messed up the on the factoring there yea

i just didn't factor it at all

[spark atlas]

Ya but that happened some times so don’t worry about it too much

You got all the harder factoring correct so

[sinful vortex]

is there any reason why the 3 should be negative? i haven't written it out so im just assuming the multiplication works out so that the 3 should be negative

[spark atlas]

Well I can’t think of anything besides it works

But I guess you can take out the negative if you want

[spark atlas]

But ya it just works

[sinful vortex]

gotcha

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[sharp mauve]

is the function of the negative side -5(t-2) because it starts at 2?

[sharp mauve]

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[lost stratus]

Other description material

This 3a is super difficult'

[random palm]

so basically from one vertex to the complete opposite vertex?

first we need to find the total resistance of the cube

[lost stratus]

resistance is 2 ohm per edge

[random palm]

use a lot of logic and symmetry exploit to find the equivalent resistance across the total system

[lost stratus]

it can be set up as a bunch of equations

But we fucked it up somehow and dont get the correct result

[random palm]

or simpler

the equivalent resistance of cube containing R resistors on each edge is 5R/6

where R is the resistance

so , as you said R is 2

so $R_{eq} = \frac{5}{3} \Omega$

[lost stratus]

Its actually not for a physics class

Thats why we are putting it into a list of equations

[elfin berry]

Bettim

[random palm]

then im sorry im of no use

[lost stratus]

but

if you can calculate it with omega

then its fine too

@random palm

I just have to calculate with python hehe

[random palm]

yea but this way you can check your final answer

[lost stratus]

alright

basically I need to get all the values for I_1, 2, 3..

how would I go about that? @random palm

[random palm]

i dont think it could be solved that way tho

you can use Kirchoff's

[lost stratus]

yeah

we are using kirchoffs

[random palm]

hold on i had a reference

[lost stratus]

so for example:

I_1 - I_4 - I_6 = 0

I_2 - I_5 - I_7 = 0

I_3 - I_8 - I_9 = 0

[random palm]

yes

[lost stratus]

but what I don't understand is how to get the values of u

[random palm]

kirchoff alone wont do it

[lost stratus]

U = 12.6

[random palm]

we have to loop law and symmetry

[lost stratus]

but

U-u_1 = R * I_1

U-u_2 = R * I_2

U-u_3 = R * I_3

but I don't know how to find the rest of the equations

[lost stratus]

yeah, but the problem is that this doesnt show me how to get equations

[random palm]

well yea thats what, idk either how to form equations for loops

simpler systems add up

but those which require kirchoff is hard

[lost stratus]

yeah idk what to do either

<@&286206848099549185>

[marsh citrus]

@lost stratus Has your question been resolved?

[lost stratus]

<@&286206848099549185>

[marsh citrus]

@lost stratus Has your question been resolved?

[marsh citrus]

@lost stratus Has your question been resolved?

[marsh citrus]

@lost stratus Has your question been resolved?

[marsh citrus]

@lost stratus Has your question been resolved?

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@lost stratus Has your question been resolved?

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[marsh citrus]

@toxic adder Has your question been resolved?

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[sonic stag]

hi

[sonic stag]

can u help me with this

especially number 4

do not steal my channel plz

[marsh citrus]

@sonic stag Has your question been resolved?

[sonic stag]

not yet

[jagged relic]

!status

[marsh citrus]

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

[marsh citrus]

@sonic stag Has your question been resolved?

[sonic stag]

not yet

[marsh citrus]

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[paper cedar]

how does the system
α + iβ = 3 + 2i
αi - β = -2+3i

gives 0=0 ??

[cunning basin]

same as normal simultaneous equations

[copper raven]

row2 <- row2 - i*row1, that's the operation that was done on the system

[paper cedar]

understood thanks

.close

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[fossil grail]

how do I turn into a characteristic equation this:

[fossil grail]

ik it becomes x^2-x-6=0 but how

[still temple]

make like the substitution r^n = a_n

[fossil grail]

becomes x^n and so forth

[still temple]

yes then just factor the smallest exponent

[stoic saddle]

идеята е да намериш такива стойности на $x$, че редицата $a_n = x^n$ отговаря на уравнението

[elfin berry]

Ann

[fossil grail]

x^n-2 ?

[stoic saddle]

слагаш $a_n = x^n$ в рекурентната релация (не знам как точно се казва на български, но говоря за това $a_n - a_{n-1} - 6a_{n-2} = 0$) и делиш с $x^{n-2}$

[fossil grail]

да, така се казва

[elfin berry]

Ann

[stoic saddle]

добре

[fossil grail]

как се получава след това

x^2(x^n+2...

?

чакай

[stoic saddle]

$x^n - x^{n-1} - 6x^{n-2} = 0$

[elfin berry]

Ann

[stoic saddle]

$\frac{x^n}{x^{n-2}} = x^2$, $\frac{x^{n-1}}{x^{n-2}} = x^1 = x$

[fossil grail]

аа деля просто двете страни на x^n-2

[stoic saddle]

точно така

[fossil grail]

x^n/x^n-2 = x^(n-n+2)

x^(n-1)/x^(n-2)=x^(n-1)-x+2

[elfin berry]

Ann

[fossil grail]

aaa qsno

да

да да

[fossil grail]

ъм, аз имам още по една задача за решаване

но да затворя ли това?

[stoic saddle]

можеш да затвориш и да отвориш нов канал или да стоиш тук, както си искаш. препоръчваме обаче да има само по една задача в един канал

[fossil grail]

благодаря

.close

[marsh citrus]

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[cerulean oxide]

how do i times this

[marsh citrus]

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[analog meadow]

Is there a larger number than (Fish Number)^(Fish Number)?

[hazy lion]

fish number?

[analog meadow]

ye

[hazy lion]

whats a fish number

oh, nvm

[abstract knot]

what is a fish number

[hazy lion]

its a googology thing

[analog meadow]

I have been scrolling in the googology wiki for 30 minutes

oh nvm

https://googology.fandom.com/wiki/Ultimate_Oblivion

[marsh citrus]

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@still temple Has your question been resolved?

[marsh citrus]

@still temple Has your question been resolved?

[tiny crater]

@still temple what do you need to solve

Did you used the sinus theorem?

For and triangle that does not have and 90° angle

Yes

Sorry I am not from england

I cant say every Word right

What do you need

Is it unit circle

Okay

Are There any proportions

Or only a And b are 1 cm

But radius of the circle is 1cm

Or no

Bro

I am lost

Side a And side b

Is 1cm

It is unit circle

Sides a And b are practicaly radii

Am I right?

I know sin

A And b are sides of trianhle

It is a circle with radius 1cm

Then sides a And b have 1cm

If you need side c you can't use pythagorean theorem Bc the triangle is not right angled

You can see that the angle B has 45°

[marsh citrus]

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[bronze niche]

Why did Zeller's Congruence formula fail here?

[bronze niche]

nvmd I found my mistake, since m = 13, then the date would be 13th month of 1981, thus D = 81