help-0

[jade birch]

@neat kayak try an unoccupied channel and read #❓how-to-get-help

[neat kayak]

oh sorry

[alpine sable]

alright no worries. so when encountering a rational inequality like this one, you can try looking to solve whenever the num=0 and den=0 (undefined), so that those values of x won't yet be our solution but we'll be our x values where our (x²(x-1)³)/(sqrt(x+7)) will touch the x-axis and hence between those x-values, we'll want to test out some values in those intervals to check whether the (x²(x-1)³)/(sqrt(x+7)) is non-negative (so ≥0) or non-positive (so ≤0), which would be our solution, since it's asking whenever ≤0.

as this might be a whole new methodology to you, i will recommend watching a video for you to get kind of used to the method for later to get here and try your problems.

https://youtu.be/gfnVHwhEe6U

[merry plank]

oh okay, i'll watch it

if i still need help w any of them after the fact should i ask?

[alpine sable]

of course. feel free to do so

[merry plank]

ok thanks

[tawdry saffron]

question says:
a bowling ball with radius 10cm rolls in a horizontal V-shaped slot with an opening angle of 60°. The speed of the center of the bowling ball is 18km/h

What is the distance between the centre of the ball and the bottom of the slit

why do they mention the speed

of the bownling ball

or am I just interpreting it wrong

do you need the speed?

I think I know a way to solve it but the speed makes me doubt it

[vapid oak]

i think the speed is irrelevant

[sage jacinth]

use 30-60-90 triangles to solve it

lines tangent to a circle are perpendicular to the radius

[tawdry saffron]

okay yea

I'm on a good path to solve it now, the speed made me overthink

[lucid nova]

can someone help me with this?

the question is what is the last digit of 2^2017

[alpine sable]

I'll give you the hint that you only need to look at the last digit

[lucid nova]

i know the answer is 4

but idk how they got that

[alpine sable]

You can see a pattern if you write out the first few terms

You can probably try the powers of 2

And see when they repeat

Basically a pattern

And divide 2017 by the number of times after which they repeat

And get the last digit by comparing the index

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32

unit digit repeat after every 4 powers you can notice

[lucid nova]

oh thank you very much

[hoary fiber]

people help

[glass lichen]

matrices are equal iff all their entries are

[hoary fiber]

k

thanks

got it

[brisk tree]

I'm confused between α>=2 and α>2 :/

[median gorge]

Think about what it means for a function to be strictly increasing

[brisk tree]

For all x>y f(x)> f(y).

[glass lichen]

Im assuming this is a calc class?

[brisk tree]

Yes

We always set f'>0 for strictly

[glass lichen]

so answer Lachlan's prompt in terms of calc

[median gorge]

Alright, cool, however is there another way..

Yep

Cool

[glass lichen]

yeah, so you'll have strict inequality

[median gorge]

So now just solve that inequality for alpha

[brisk tree]

so isn't x^2 strictly increasing for all x>=0?

I'm confused because of the domain of x...

[brisk tree]

Because this definition is true even if alpha is greater than equal to 2

[median gorge]

Yes, x^2 is strictly increasing for all x >= 0 however in this case was have x(alpha-x)

For instance, this is what the function looks like when alpha = 1

[brisk tree]

Alpha=2 seems fine tho

Don't you think?

Besides it's (0,1)

[brisk tree]

If you apply the f'>0 condition for strictly increasing then you'd have got x>0 but x=0 holds too :/

[median gorge]

Yeah

I think I see what you're saying

Here is what I would do

I would say that we want f'>0 for all x in the domain

We know the derivative is alpha-2x

So alpha-2x>0

Right

[brisk tree]

Yes

[median gorge]

This gives us alpha>2x

Now we want alpha to be greater than 2x for all x in (0, 1)

Notice that it doesn't exist at 1

So if alpha = 2

That is greater than 2x

And so I would say that alpha >= 2 is all good

[brisk tree]

Yeah cause 2>2×0.999999

Okay thanks a lot!!

[sage summit]

I don't think completing the cube counts as witchcraft

and typically completing the cube is used to reduce from x³+bx²+cx=d to x³+cx=d

what chapter is this in

[warped phoenix]

WHA

WITCHCRAFT

WHAT MATH IS THIS, WHAT LEVEL I MEAN 😭

is this like calculus 3 million

[sage summit]

does it talk about uuh

covering spaces

groups

deck transformations

if the book is about riemann surfaces what's the chapter about

ah xD

lol

not sure if they intend it to be solvable

[pseudo summit]

How to deal with periodic tithes in the quadratic formula?

Should I round it?

[alpine sable]

Deoends

Depends*

[austere bridge]

might be worth asking in one of the advanced channels. Check #get-advanced-access first

[cinder beacon]

is any1 here smart at math

[tranquil parcel]

Or maybe physics server

[ionic jewel]

no sorry, none of us actually know math

[paper oar]

no I just took an L on AP Calc

Jk just ask your question

[cinder beacon]

ill pay someone 25 tom if they can help me in mathe today

[paper oar]

...

I don't think that is how it works in here...

[cinder beacon]

it might not but i will

[ionic jewel]

have you considered posting your question

[alpine sable]

A square of side 1 contains several circles in its interior. The sum of the circumferences of the circles is equal to 10. If you draw a straight line parallel to a side of the square, how many minimum circles will it always intersect?

Please help

Options are: 2,3,4, can't be determined

[alpine sable]

I've thought about it a lot but to no avail

[red phoenix]

You drawn it out?

[gleaming snow]

-25x0 do you right it as -0 or +0 if put in an equation

[ionic jewel]

definitely can't be determined with that much information, trivially you could make a circle of circumference 1 and stack 10 of them on top of each other, then depending on where you line is you either go through 0 or go through 10

[ionic jewel]

you write it as 0, -0 is not a thing

or rather, -0 = 0 and is always written like so

[gleaming snow]

100-25x0+1

= 100+0+1?

[ionic jewel]

yep

100-0+1 is fine too in this case

it's the same answer either way

[gleaming snow]

Ok

[alpine sable]

I did

But wasn't getting anywhere

Since symmetrical orientations didn't work

Also found out the sum of radii of all the interior circles

But that isn't getting me anywhere

I think I found the total number of circles to be in between 9 and 16 but I'm not sure

<@&286206848099549185>

[alpine sable]

↑

[ionic jewel]

is there something wrong with my answer?

[alpine sable]

Wait I didn't see

I'm sorry :(

[alpine sable]

Oh I see

[ionic jewel]

mine seems quite a bit too trivially disprove it, but i don't see a problrm with it

[alpine sable]

Yep

[ionic jewel]

perhaps they mean non-overlapping circles, but i still suspect you can't determine it

[red phoenix]

I believe it requires that it always intersects circles

But the wording of it all is a bit dodgy

[alpine sable]

Yeah

It's more on the puzzle side ig

[warped phoenix]

is this channel free

gonna assume it is

how did they get that as the condition probability

I got $\frac{\frac{79}{98}\cdot \frac{79}{91}}{\frac{79}{91}} = 0.806$

[ocean seal]

TheMane3

[warped phoenix]

The probability of A, that they have AC, is 79/98, and the probability of C, that they have a companion animal, is 79/91

[noble sinew]

Just read in the C yes coloumn

79 yes and 12 no

[red phoenix]

Would love to look at it but can’t right now 😥

[alpine sable]

Awh it's okay

Tysm for taking the time :)

[warped phoenix]

why would you only look there

[noble sinew]

Because it is conditional?

Given C=yes

So look there

[warped phoenix]

but 79/91 is the probability they have a companion animal @noble sinew

since the amount of people with an animal is the same as the amount of people with ac, i get why they use 79 again, but we're not looking for how many people have an animal right

we're looking for people with ac

so 79/98 is the probability they'll have an ac right

[noble sinew]

Im saying all you have to do is look here

Clearly the prob is 79/91

[warped phoenix]

79/91 is the probability they have an animal

right

[noble sinew]

It is the conditional prob that the question asks for

[warped phoenix]

but its also that right

79 people have one, 12 people dont, so theres a 79/91 probability that they have one

[noble sinew]

No?

[warped phoenix]

what

[noble sinew]

Both the 79 and 12 are under yes

[warped phoenix]

oh 🤦‍♂️

[noble sinew]

But just do what I said

No reason to do what you are doing

[warped phoenix]

what would i do in a future question like this

[viscid oriole]

Hello guys, i am re-learning math because i want to get better at it, and there is one thing i don't understand even now about fraction word problems, why for example here must i multiply the fractions to get the right result? Please help me to understand.

[glass lichen]

of means multiplication

[noble sinew]

Look in the coloumn I marked

All you have to do

[warped phoenix]

ok

how do i know if a question is conditional

like what here tells me its a conditional probability

[warped phoenix]

the fact that its in the table?

[viscid oriole]

i mean i remembered the structure but i still would want to understand more in depth if possible, because at first i thought that i have to divide to get the answer

[glass lichen]

*1/4 is the same as dividing by 4, so yes

[warped phoenix]

<@&286206848099549185>

?

[glass lichen]

nowhere

you just determine the independence of the events

[warped phoenix]

well thats what i did originall i think, the probability of someone having air conditioning is 120/180, and the probability of someone enjoying opera is 120/720, 120/720 * 120/180 = .1111...

since 120/720 * 120/180 does equal .1111, it would be independent

did i do that the right way?

[glass lichen]

$P(A\cap B)=\frac{120}{1080}=\frac{1}{9} \ P(A)P(B)=(\frac{720}{1080})(\frac{180}{1080})=\frac{1}{9}$

[ocean seal]

Mosh

[glass lichen]

so yes they're independent

[gaunt magnet]

anyone good with calc

that can check my work

[warped phoenix]

interesting

why do you do the full thing

like umm

why the totals

720/1080 and 180/1080

howd u know to use those

[glass lichen]

cause that's how many people there are

Probability is desired/total...

[gaunt magnet]

no

[warped phoenix]

what

[gaunt magnet]

#help-1

go to ques 1

i took this channel

[warped phoenix]

dude what

[glass lichen]

they were using it before you

end of story

[gaunt magnet]

no yall didnt talk for 15 mins

this is mine

end of the story

[glass lichen]

besides, you only want work checked. Use wolfram and show some respect

anyways

[gaunt magnet]

nah

i need help

[glass lichen]

there are 1080 people total, so I divided by the total

[warped phoenix]

ohhhh

[gaunt magnet]

😼

[warped phoenix]

hold on, if its okay with you im going to write out my steps for one of these questions

and see if i get it right

[glass lichen]

yeah

[warped phoenix]

ok 1 sec

[gaunt magnet]

Guys?

check my answer

[glass lichen]

No

[gaunt magnet]

who asked u

[glass lichen]

You did

[warped phoenix]

(actually what would i search to find questions like these? 😅)

[gaunt magnet]

i never pinged u

[warped phoenix]

dude quit it

[glass lichen]

well same source you're getting your other questions?

[gaunt magnet]

u just took my channel

[glass lichen]

they did not

they were still using it

[gaunt magnet]

they didnt talk for 15 mins

[warped phoenix]

that was the last question in my book about it lol

[glass lichen]

you did every single question in a book?

[gaunt magnet]

this guy is cheating on his exam

[warped phoenix]

its a chapter of the book

and there were like 10 questions on it

its ok

[gaunt magnet]

proof

[warped phoenix]

i tjink i found one

[glass lichen]

dude shut up

stop being an ass

[gaunt magnet]

yall are very immature

[gaunt magnet]

bozo

[warped phoenix]

ok so ill make the questionnnnnn...."is the probability of liking snowboards and the probability of liking snowmobiles independent?"

would that work

[robust flax]

bruh

[glass lichen]

sure

[warped phoenix]

ok

[gaunt magnet]

im gonna leave but u stole my channel

@glass lichen F you btw

[warped phoenix]

cool

[gaunt magnet]

bye now

[warped phoenix]

bye bye

[gaunt magnet]

mosh has no life

for stealing my channel

[warped phoenix]

didnt you say bye just a message ago

[glass lichen]

Just ignore them, they're just a troll

[gaunt magnet]

ye il leaving

[gaunt magnet]

cap

this guy is a capper i came for help

i come here for daily help

[glass lichen]

anyway, yeah just determine if those events are indep. like you chose

[warped phoenix]

@glass lichen so the probability of liking snowmobiles is 80/125, and the prob. of liking skateboards is 80/105, 80/125 * 80/105 = 0.488, so now we look at the totals like we just did in the last question i think, so 125/160 * 105/160 = 0.512, since 0.488 is not equal to 0.512, they're not independent?

😓

[gaunt magnet]

lol he just ghosted you.

[glass lichen]

You didnt use the total sample space

[warped phoenix]

wdym?

[glass lichen]

you divided by 105 and 125 for some steps

[warped phoenix]

oh

should they all have been out of 160

[glass lichen]

yes

[warped phoenix]

ahhh ok

[glass lichen]

$P(A\cap B)=\frac{80}{160}=0.5$

[ocean seal]

Mosh

[gaunt magnet]

ok are u done

ok

i take channel now

[glass lichen]

you're using channel 1...

[gaunt magnet]

no

[glass lichen]

Like is this a really hard concept to understand or are you just being needlessly petty

[gaunt magnet]

Stop being such a karen

[glass lichen]

stop being such a dick

[gaunt magnet]

LOL

🔥

[glass lichen]

Like all you've said is "is this right" when any calculator/CAS can answer that for you.

[alpine sable]

why do even need this channel anymore, your question has been answered?

[shell heron]

how old are u, like 10?

[gaunt magnet]

no u need to stop the cap cause it dosent answer every ques

[glass lichen]

And then you opt to constantly break rules and present yourself as a superior

[warped phoenix]

hmmm what about here

bruh

[gaunt magnet]

says the one playing roblox 😂

lol

[shell heron]

so what

[warped phoenix]

@gaunt magnet we're still doing this?

[gaunt magnet]

okk

[shell heron]

thing is

im programming in roblox

and actually testing out games

but go off

[gaunt magnet]

sure

[warped phoenix]

dude

51/160 chance that they're a senior and working part time

[glass lichen]

yes

[warped phoenix]

how would i determine if that bit of info is independent 😅

[glass lichen]

then find probability of each and multiply them

[warped phoenix]

each what

[willow wadi]

we pop at ur party

[glass lichen]

P(senior) and P(working part time)

[willow wadi]

Hello kind people, anyone of u help me in Math

[glass lichen]

#❓how-to-get-help #rules

[warped phoenix]

channel in use

[willow wadi]

👍

[gaunt magnet]

you wont get any help from that karen mosh

[willow wadi]

Ok

Ill wait

[glass lichen]

Or just.. use any of the other channels

[warped phoenix]

channel in use

[alpine sable]

Oh sorry

[warped phoenix]

so P(senior) = 80/160, and P(part time work) = 51/59, multiplying both, I got 0.432, 51/160 = 0.319, so that means its not independent?

or was i supposed to do 51/160

[glass lichen]

not 51/59

yes, 51/160

[warped phoenix]

80/160 * 51/160 = 0.159

now what 😅

51/160 = 0.318

[glass lichen]

compare

[warped phoenix]

0.318 isnt 0.159.....soooooo not independent

[glass lichen]

yes

[warped phoenix]

ohhhh

wait whaaa

[glass lichen]

oh they want you to use conditional

[warped phoenix]

the first one is saying 59/160 isnt equal to 51/160, and the second one is saying 80/160 isnt equal to 51/160

they're both true

[glass lichen]

yeah not sure, but they shouldnt be independent

[noble sinew]

independent if P(A|B)=P(A) so the one you picked is wrong

so not independent if P(A|B) != P(A)

[warped phoenix]

but they're both true arent they

the first one says 59/160 doesnt equal 51/160

and the second one says 80/160 doesnt equal to 59/160

[noble sinew]

yes but first one has nothing to do with independence

[warped phoenix]

ah because it doesnt follow the formula for independence?

i see

[strong carbon]

How does the second one do?

[warped phoenix]

because it shows P(A) doesnt equal P(B given A)

which is the formula for independence with a conditional probability

the first one shows P(B) doesnt equal P(B given A) which doesnt follow the formula

so while theyre both true, one has something to do with independence and the other is random i believe

[strong carbon]

Ah I see

[native cloud]

Can anyone help me solve this problem?

[chilly bobcat]

help me in the problem pls

[gloomy lintel]

Yeah so just add up the probabilities when D is 1 and when D is 2 unless I’m oversimplifying it

[native cloud]

So you mean only add D1 (0.301) and D2 (0.176)?

[gloomy lintel]

Yep bc it’s 2 or below

But the only thing that’s lower than a 2, as an outcome is 1

[native cloud]

Circumference: [2πr] 2 x (3.14) x (radius)
Area: [r^2π] (radius squared) x (3.14)

[native cloud]

oh okay thanks

[chilly bobcat]

I do not understand;c

[wary stream]

Do you know the equation for circumference and area of a circle?

[chilly bobcat]

yes

[wary stream]

Apply that concept to that problem

[chilly bobcat]

but I don't know how to find it

[crude moss]

https://cdn.discordapp.com/attachments/238956921581862913/870417893127487508/unknown.png

please\

i really need help

[native cloud]

그니까

반지름 곱하기 파이 2제곱이

원의 넓이고

[wary stream]

What's the equation for circumference and area?

[native cloud]

반지름 곱하기 2에 곱하기 파이가 원주입니다

@chilly bobcat

[ionic jewel]

i wonder how well google translate works for translating math words to other languages

Google 번역이 수학 단어를 다른 언어로 번역하는 데 얼마나 잘 작동하는지 궁금합니다.

[native cloud]

I'm Korean

[ionic jewel]

circumference is twice the radius times pi

둘레는 반지름 곱하기 파이의 두 배입니다.

yeah but im not korean

im just curious how well it works

[native cloud]

xD

Pretty okay

[winter bay]

I would guess since math words are niche that translate would do fine with it

[ionic jewel]

i feel like it might start having trouble if i got too technical though

not sure

[winter bay]

I think the issue usually occurs when the sentences become complicated

[chilly bobcat]

the radius is half the line the circumference the bottom line of the circle

[winter bay]

Or colloquial stuff is used

[native cloud]

몰라서 물어본거 아니였어요?

[torn raven]

how do i solve this ? i dk how they got 62%

[stray parrot]

Ah for the area just do πr² for the area

For the perimeter do 2πr

[stray parrot]

Didnt know people still play roblox lol

[stray parrot]

Sometimes it works sometimes it's terrible lmao

[stray parrot]

Ywah it's prwtty accurate

[ebon oar]

anoyne help?

pls

'='

[glacial hedge]

Does anyone know how to "solve" this>

it seems wrong... but maybe im missing someting

[placid zinc]

I don't see any reason to think so

[alpine sable]

I FORGOT ABOUT ALL OF THIS HELP

[placid zinc]

This is basically saying "all 2×2 matricies have non-real eigenvalues"

[stray parrot]

Of?

[arctic delta]

can someone explain why the inequality is important for the limit not existing, if it was = 0 there, an asymptote wouldnt be there?

[solar cradle]

If x approach 3 from the right, the limit goes to positive infinity and if it goes to left it goes to negative infinity

x - 3 > 0, if and only if, x > 3, so the limit from the right goes to positive infinity. If the limit was approaching 3 from the left it would be negative, because x-3<0

[arctic delta]

what does the 16 > 0 signify?

[ebon oar]

nevermind no one responede on time

i figured it out anways

[solar cradle]

That 16 > 0? If the limit of the numerator was negative, then the whole limit would approach negative infinity

[arctic delta]

cuz it's done the same way for approaching from the left

[solar cradle]

The limit of just the numerator exists

so it would be the same

[noble sinew]

If num approached 0 then you had 0/0 expression which you can’t say what value it is just like that

Hence the important part is num doesn’t approach 0

[arctic delta]

ah, so its saying part of the reason that the func is approaching inf is that the numerator is more than 0?

[noble sinew]

That it isn’t 0

Because then you can just apply product rule and find limit which is what they did (without saying)

[arctic delta]

in this are they just making the 5 have the same denominator by multiplying the denominator of the left side

[slender forge]

Yes

[wicked plover]

wow

[slender forge]

If u look at the part with the five u can see that the numerator and denominator would cancel out leaving u with 5 meaning same as multiplying by 1

[slender forge]

His question was a quick answer

[arctic delta]

got it, i overthink this sorta stuff too much

[slender forge]

It’s all good I did too

Just make sure u get this stuff down ull use it later down the math line

[arctic delta]

for sure

[slender forge]

What math class/grade is this?

[arctic delta]

its an online intro into calc

[slender forge]

Precalc?

[arctic delta]

yea

[slender forge]

Ya these algebra skills will start to become more important def work on it

[arctic delta]

i'll try

[slender forge]

U can also hmu if u need help with that kinda stuff btw

I’m kinda studying math in college rn just a more specialized degree than standard math degree

[arctic delta]

if you're cool with that, thanks, thats a bit reassuring

[slender forge]

Yah np might be a little busier come the end of august when classes come up but for now 🤷‍♂️

[arctic delta]

yea im just trying to get through my course before august ends, gotta get through a mid term, two units, one assignment and a final before then

[slender forge]

College or high school?

[arctic delta]

college ye, its a online one

[slender forge]

Completely online college or just this course?

[arctic delta]

its a completely online one, im planning on transferring the credits from this into my actual uni

[slender forge]

What year/what are you going for?

[arctic delta]

finished my second semester, going for business but i need this credit to try and transfer from law

[slender forge]

That’s cool which business degree or just general business?

[arctic delta]

haven't really put much thought into that so im not too sure

maybe accounting or finance

[slender forge]

Both not bad choices tbh

I found accounting kind of boring and liked finance but I have friends who thought opposite

[arctic delta]

hope i dont find whatever i get into too boring

[slender forge]

If u do switch 🤷‍♂️

Better to waste some money than rest of ur life

I just finished my freshman year back in April my sophomore year starts end of august btw

[arctic delta]

nice, just stressful to think about but true

[glass flare]

how do i create a right left arrow in latex

[austere bridge]

$\rightarrow$?

[ocean seal]

cgodfrey

[austere bridge]

oh

$\leftrightarrow$

[glass flare]

??

[ocean seal]

cgodfrey

[austere bridge]

there we go

[glass flare]

oh lol

[austere bridge]

or $\longleftrightarrow$

[ocean seal]

cgodfrey

[glass lichen]

$\iff$

[ocean seal]

Mosh

[glass flare]

$\longlongleftrightarrow$

[austere bridge]

$\Longleftrightarrow$

[ocean seal]

cgodfrey

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

[glass flare]

$69x^4+420x^3+69x^2+420x=69$

[ocean seal]

JeffTheRef

[glass flare]

$e^{\pi i}+1=0$

[ocean seal]

JeffTheRef

[glass flare]

$ x{\leftrightarrow}x$ and $\iff$ and $ x{\longleftrightarrow}$

[ocean seal]

JeffTheRef

[solar cradle]

There's a latex help channel and testing channels

[glass flare]

ohh sorry

i though this is #latex-testing

[clever mountain]

So i'm not very good at math but i was wondering how to use this function to squish a number between 0 and 1, i'm trying to figure out what to set x and e to.

[glass lichen]

e is e...

[clever mountain]

and that would be what XD

[glass lichen]

like 2.71828... irrational garbage

$e=\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^n$

[ocean seal]

Mosh

[gaunt magnet]

o

https://tenor.com/view/cat-leaving-leave-oops-bye-gif-17519616

[clever mountain]

thanks. the first time i searched it i thought it was exponent, not eulers num

[glass lichen]

I mean you could've guessed from the function notation it was the number e

since S was only a function of x

But yes, $S:\mathbb{R}\to (0,1)$

[ocean seal]

Mosh

[willow wadi]

<@&286206848099549185>

[sage jacinth]

is l4 the left riemann sum with 4 rectangles

[sterile crescent]

If z= a-ib, then mod z will still be, root(a^2+b^2)?

[remote lodge]

going to sound stupid here but..

how is the 4/6 simplified?

[vapid oak]

$\frac{4}{6}=\frac{22}{23}=\frac{2}{3}$

[ocean seal]

Omfish

[remote lodge]

Ok thanks Omfish 😅

[carmine lion]

how to do part (a) and (b)

for part a

i solved $P'(x)=0$ and got $x=0, -\frac{2B}{3A}$

[ocean seal]

abe

[carmine lion]

but how do i rule out x=0 as a solution

what reason should i state

also for part b, should the 2nd term on the LHS be -4B^3?

because i get 8B^3=0 when i simplify part B

and the quesiton stated B cannot be 0

[wild marten]

if x = 0 then A(0) + B(0) + D = 0 or D = 0 but according to the question A, B, D are non-zero so 0 isn't a solution

[carmine lion]

yea

ok

now part b

[carmine lion]

ty for part a

[flint willow]

Hey, um idk if you have already solved it yet. But if not, just substitute the value of X you got from the part a (That is -2B/3A) in the original equation.

That is it

[carmine lion]

yes

and i get 8B^3=0

which means B=0

but B cannot be 0

as the question had imposed ccertain restrictions earlier

soooo

idk whats going on

[wild marten]

see, if you substitute $\frac{-2B}{3A}$ in the original equation, you get:
$$A\cdot \frac{-8B^3}{27A^3} + B\cdot \frac{4B^2}{9A^2} + D$$
$$= \frac{-8B^3}{27A^2} + \frac{4B^3}{9A^2} + D$$
$$= \frac{-8B^3+12B^3}{27A^2} + D$$
$$= \frac{4B^3}{27A^2} + D$$
$$= \frac{4B^3+27A^2 D}{27A^2}$$
But since our equation equals $0$, we get that:
$$4B^3 + 27A^2 D = 0$$
Hence, proved

[ocean seal]

Schrödinger's Smile

[wild marten]

does my solution help?

[carmine lion]

oh wait nvm

sorry

[wild marten]

for what?

[carmine lion]

nothing

i made a silly mistake

[wild marten]

ohk np

[carmine lion]

yehh

[covert agate]

hi

[alpine sable]

bruh

this isnt a grammar server

[covert agate]

does the logical statement “either a or b” mean “a xor b”

[alpine sable]

but yeah youd be wrong. because its either, not both

meaning only one is true

[covert agate]

so yes

[alpine sable]

yes

[covert agate]

lol brilliant is wrong

[placid zinc]

@covert agate
XOR is a precise mathematical function
"either a or b" is imprecise.

Sometimes they're the same, sometimes not.

[covert agate]

huh

[vale wigeon]

"either a or b" does not unambiguously mean "but not both"

[covert agate]

statement: “either you or me is math major”
reality: both math majors
conclusion: statement false?

[dry berry]

can someone help?

[willow wadi]

<@&286206848099549185>

[vale wigeon]

why are you pinging helpers on gansta's behalf

[willow wadi]

it say u can ping helper after 15 mins

so i help him

and ping for him

[dry berry]

well im back

i got the solution but i don't really understand it

[willow wadi]

@vale wigeon helper he no understand

[dry berry]

so here it is

[vale wigeon]

ah yes

do the words 'asymptotic equivalence' ring any bells to you?

[dry berry]

never heard 😛

[vale wigeon]

that's what the tilde means that you circled

essentially, we say $f(x) \sim g(x)$ if $\lim \frac{f(x)}{g(x)} = 1$ (as $x$ approaches whatever we need it to approach)

[ocean seal]

Ann

[vale wigeon]

asymptotic equivalence means, roughly, that one function can be replaced with another in a product

this can be accomplished without explicitly mentioning it by multiplying your fraction by x^2/x^2 and grouping the x^2/tan^2(x) together (and acknowledging it approaches 1)

[dry berry]

ok...

but if so can we substitute tanx = x on the numerator so that the limit equals 0?

[vale wigeon]

no

one function can be replaced with another in a product

this means that if f ~ g then we have lim h*f = lim h*g

asymptotic equivalence is also preserved if raising both functions to a constant power, which covers doing this in the denom of a fraction

[willow wadi]

https://tenor.com/view/cat-computer-working-busy-genius-cat-gif-15705968

[dry berry]

so it is product only...

thanks @vale wigeon

i think i get it

although i just read the definition 😛

[golden falcon]

technically you can use equivalences in sums, but you'd have to prove that you don't miss anything behind that o(x), or whatever you'd be left with, when you do that. With multiplication it's guaranteed(can be proven in general) that you'd be fine.

[golden falcon]

that's not how it works. You first post a question, then ask for help.

Use subtraction

[woeful pulsar]

just apply the subtraction algortithm

you can do it with small numbers, you can do it to large numbers

can you do it if the numbers are smaller?

then can you follow the same steps to subtract?

[golden falcon]

You will get banned or muted if you act uncivilised

[woeful pulsar]

if you want you can show your rough work as you go along

[golden falcon]

here you go

cool

[woeful pulsar]

sounds quite inappropriate

[golden falcon]

now try doing that, but instead of milk use numbers you were given and instead of pouring it out, subtract them

[woeful pulsar]

it says don't click it

trivially we don't click it

[alpine sable]

#❓how-to-get-help

[woeful pulsar]

also aren't you asking for help on subtraction

[vale wigeon]

kaden, what are you doing?

[golden falcon]

He's struggling with subtracting

[vale wigeon]

what is all this about?

[woeful pulsar]

or just trolling

[vale wigeon]

asters?

[woeful pulsar]

asters?

[vale wigeon]

what's an asater?

[woeful pulsar]

sounds like troll

[ionic jewel]

^

[woeful pulsar]

okay probably troll

[vale wigeon]

okay you are definitely a troll

<@&268886789983436800>

that is an obscene gif that you definitely did not need to post either

[tall wing]

gross

[golden falcon]

what first grade subtraction exercise does to mf

[tall wing]

banned

[lament rock]

can anyone explain how they got 1/k(k+1) = a/k - b/k+1

[indigo jetty]

partial fractions

[manic glade]

can i get some help understanding what this means

[vale wigeon]

f is a function from A to B

g is a function from the powerset of B to the powerset of A which sends each D ⊆ B to its preimage by f

[analog fable]

Hello I was doing a worksheet and this question popped up, can anyone help me?

[jagged imp]

do you know about eulers formula for polyhedrons

v-e+f=2 for any polyhedron

v being the number of vertices, e the number of edges and f the number of faces

[ionic jewel]

another Euler's formula? didn't even know about that one

[wind bane]

that one is pretty neat and generalizes to any finite dimension

[quaint python]

? <@&286206848099549185>

[lusty plaza]

I don’t know the answer but I will say that the helpers in this discord tend to help people more when there’s a demonstration at an attempt at solving a problem when posting

[mild tartan]

help, ping me when u get solution, thanks

[jagged imp]

,rotate

[jagged imp]

I simply will not

[mild tartan]

im quite stupid

@jagged imp help me!

[jagged imp]

the question is missing information

[mild tartan]

oh

nvm im retarded

its c)

i thought it was a question itself

was tryna help my friend find ans

[short spear]

𝑎 is directly proportional to the square of 𝑏 and inversely proportional to 𝑐. Find the effect of 𝑎 when 𝑏 is increased by 10% and 𝑐 is increased by 20%

imma need some help

with this question

[wind bane]

have you tried anything at all?

[alpine sable]

𝑎

[alpine sable]

how did u type these special characters

a𝑎

[short spear]

i copy pasted

[alpine sable]

interesting

wat

[wind bane]

please ask in another channel

[short spear]

yeah but i got stuck at one point, there's an explanation for it but i don't know how they went from one step to another

[alpine sable]

channel is occupied

[wind bane]

all of them are open but this one atm lol

we dont help with exams here

you will straight up be banned from the server if you ask for help on an exam

[alpine sable]

mods offline rn tho

[wind bane]

okay...

[wind bane]

whered you get stuck

[short spear]

this is the explanation

and i don't know how they did this

from the first one to the second

[mild tartan]

wdym by effect

[short spear]

so like how much it changes from the original value

[wind bane]

what happens to a when you increase b by ten percent

[mild tartan]

oh

[wind bane]

so multiplying b by 1.1 has the effect of increasing b by ten percent. same with multiplying c by 1.2; it has the effect of increasing c by 20 percent

[mild tartan]

i think i got it

[wind bane]

k is just some proportionality constant

[short spear]

yeah

[mild tartan]

the increased/decrease of a will be in %?

[short spear]

yeah

[wind bane]

and after carrying out some computations, the effect of increasing b by 10 percent and c by 20 percent has the effect of scaling a by a ratio of 1.21/1.44

there are some typos in the solution, mainly just that they forgot to write b^2 in a couple places

[short spear]

i still don't how they inputted kb/c

[wind bane]

a_new is given by k(1.1 b)^2/(1.2 c) which is in turn equal to (1.21/1.2) kb^2/c

is that what you were asking

[short spear]

yeah

ohhhh

right i figured it out

[wind bane]

cool

[short spear]

wait quick question

how did they square 1.2

[wind bane]

they shouldnt have because thats wrong. good catch

this "solution" is riddled with errors

[short spear]

yeah the marker must've been in a rush

ah well thanks anyways

[forest garden]

Guys is there a formula to finding a general sequence from a recursive sequence? Like for example how do we get from a[1] = 1; a[n] = a[n-1] + n to a[n] = (n(n+1))/2 ?

[vale wigeon]

no

there is no formula in general

it can be very hard if the recurrence relation is nasty enough

[forest garden]

Ah I see. So the only way is just to like... get something by the slope of the sequence or something?

[ionic jewel]

there are a lot of techniques for solving recurrence equations

i took a class that almost exclusively focused on solving them

[forest garden]

I see. So there are actual ways other than just trial and error?

[ionic jewel]

the real moral of the story is that you can just plug it into wolfram and not learn how it works

[forest garden]

Hm right

[ionic jewel]

absolutely, but I'm not going to go into detail here

[forest garden]

Yea it's okay

[ionic jewel]

it's kinda like differential equations, different types need different solutions

not all of them are easy

[vale wigeon]

if your recurrence relation has a certain form there are techniques which let you solve it

[ionic jewel]

^

[forest garden]

Right

But

[ionic jewel]

master theorem go brrr

[forest garden]

I appreciate it, the info I mean

Thanks

[ionic jewel]

https://en.m.wikipedia.org/wiki/Master_theorem_(analysis_of_algorithms)

[forest garden]

Oooo

[ionic jewel]

this is a way to solve some subset of them

[forest garden]

Using Big O?

I never thought something like that can help lol

[ionic jewel]

this isn't quite what i was thinking it was, but there's something in here that gives you the exact forms

[forest garden]

I see

Thanks!

[graceful river]

y=x makes 45 dgree angle with the positive direction of x-axis

right?

[rigid smelt]

yes

[graceful river]

so how do i do b

[rigid smelt]

,rotate

[rigid smelt]

can you post the other pic again?

[rigid smelt]

im wearing a neck brace rn from all of the other vertical pics

,rotate

[graceful river]

that img is just for thq context of the question

ignore a

[rigid smelt]

if a line makes a 45 degree with the positive x-axis then the slope of the line is tan(45) or 1

[graceful river]

yeah

which is y=x

oh

it sais coordinateS

so all i have to do is x=x^3-x^2

and get all x coordinates

[rigid smelt]

no y=x is just one of the line that has slope 1

[graceful river]

oh

nvm then

[rigid smelt]

there are infinitely many lines with slope 1

all of those make a 45 degree angle with the positive x-axis

[graceful river]

so what do i di

do

[rigid smelt]

you have the general equation of the tangent

and you also have the slope

which is also?

(not talking about 1)

[graceful river]

huh?

[rigid smelt]

the slope of the tangent is what?

how do you find the slope of the tangent line to a curve at some point (a,b)

[graceful river]

rise over run

[rigid smelt]

ehh no

[graceful river]

or y2-y1/x2-x1

[rigid smelt]

thats the slope of the secant line

lemme ask you, how did you find the coordinates in question a?

[graceful river]

well

if u differentiate it

u get f'(x)

[rigid smelt]

yep

[graceful river]

u put f'(x)=0

[rigid smelt]

why?

[graceful river]

which then is parallel to x-axis

[rigid smelt]

why do you know f'(x)=0 gives you the coords where the tangent line is parallel to the x-axis?

[graceful river]

bc that tangent line has to be a horizontal line

when dy/dx=0

[rigid smelt]

not the answer im looking for, but yes

the derivative at that point is the slope of that tangent line

[graceful river]

yes

[rigid smelt]

what is the slope of the tangent line in part b?

[graceful river]

OH I GOT IT

since m=tanx

1=tank45

the gradient of the tagent line must be 1

so therefore

1=dy/dx

[rigid smelt]

yes

[graceful river]

since the domain is bigger than 0

x=1

y=0

[rigid smelt]

yes

[graceful river]

ughhhh it was this ez all along

how was i this stupid

thx bro

[clear apex]

BRUHHH

IM CRYING INSIDE

IDK HOW TO DO THIS QUESTION

somebody help me on how to do this

[vale wigeon]

have you made any progress or are you stuck not knowing how to begin?

[clear apex]

i kinda did

gimme a sec

i send ss

[vale wigeon]

please do

[clear apex]

i went up to this

but like where do i go next

[vale wigeon]

aha

alright, this is in line with what i was going to suggest

so you see that the two segments in the lower left are equal to each other, yes?

[clear apex]

can u highlight

or can i call u and stream it?

[vale wigeon]

one moment

i will highlight it

[clear apex]

kl

[vale wigeon]

here

[clear apex]

yh those

[vale wigeon]

these are what i'm talking about

they are equal

[clear apex]

ik

[vale wigeon]

let's call them both z, as i did on the pic

[clear apex]

ok

[vale wigeon]

then we have that (x+z)^2 + (y+z)^2 = (x+y)^2, don't we?

[clear apex]

yh

i did that originally and got nowhere

[vale wigeon]

what do you get when expanding this?

[clear apex]

ok

u get

x^2 + 2zx + z^2 + y^2 + 2zy + z^2 = x^2 + 2xy + y^2

[vale wigeon]

2z^2 + 2(x+y)z + x^2 + y^2 = x^2 + y^2 + 2xy

indeed

we can simplify this to z^2 + (x+y)z - xy = 0

[clear apex]

wait what

[vale wigeon]

subtract x^2+y^2 off both sides

then divide by two

[clear apex]

oh

[vale wigeon]

or are you asking how to get from your thing to mine?

[clear apex]

yh

acc nvm

can u continue pls

[vale wigeon]

the area is equal to (x+z)(y+z)/2

which should be clear if you look at the diagram

[clear apex]

ok

[vale wigeon]

(x+z)(y+z) = z^2 + (x+y)z + xy

= (z^2 + (x+y)z - xy) + 2xy

does this make sense to you?

[clear apex]

yh kinda

[vale wigeon]

well from this we see directly that (x+z)(y+z) = 2xy

[clear apex]

OH

ok

pls continue

[vale wigeon]

we're one step away

[clear apex]

bruh

i get it

2xy / 2 = xy

[vale wigeon]

exactly!

[clear apex]

THX SO MUCH

[vale wigeon]

a little clever algebra goes a long way

[clear apex]

lol

[vale wigeon]

i'm serious

[sleek elbow]

sounded funny I guess

[vale wigeon]

it's true though. a lot of problems crack open when all you do is algebraic cleanup without being afraid of what the end result may be

[sleek elbow]

yeah true

[clear apex]

are u guys from uk?

[alpine sable]

A cubic equation $x^3 -5x^2 + 17x - k = 0$ has a root $\alpha$ at $x = 2 - 3i$ \\
a) Find the other complex root and the real root \
b) Hence find the value of k

[ocean seal]

ZED_118

[vale wigeon]

not me

@alpine sable have you made any progress thus far?

[sleek elbow]

me neither

[clear apex]

us?

[sleek elbow]

germany here

[vale wigeon]

russia

[clear apex]

bruh u guys are smart

[sleek elbow]

Ann is, im not lol

[clear apex]

u guys do alevel?

[alpine sable]

I did b) first and found k = 13. But I'm not sure how I should find the other roots

[vale wigeon]

how did you find k to be 13?

[sleek elbow]

in 3 years (we should stop this smalltalk)

[vale wigeon]

ah wait, i think i know how you did it

[alpine sable]

plugging 2-3i into the x

[vale wigeon]

you plugged in alpha

okay yeah

well

the conjugate of 2-3i will be a root as well, bc the coefficients are all real

for the third root you can either get the sum of the roots from the x^2 coefficient, or the product from the constant term

[alpine sable]

2 + 3i?

[vale wigeon]

yup

[alpine sable]

could you explain why?

[vale wigeon]

vieta's formulas

[fair crater]

If that's not within reach maybe comparison of coefficients would work, but I didn't try this out yet

[vale wigeon]

alternatively, just expand $(x-a)(x-b)(x-c)$ and observe that you get $x^3 - (a+b+c)x^2 + (ab+bc+ca)x - abc$

[ocean seal]

Ann

[fair crater]

^

[alpine sable]

ah

but where did you get (x-a)(x-b(x-c) from?

[vale wigeon]

i was trying to explain why the "read sum & product off coefficients" trick works

[alpine sable]

yeah i understood that

[vale wigeon]

so i told you to expand a generic cubic in factored form with a, b, c as its roots

[alpine sable]

how do you know that (x-a)(x-b)(x-c) is a generic cubic?

[vale wigeon]

...

are you asking me why i named the roots a, b and c instead of something else? or what

[alpine sable]

no

[vale wigeon]

the roots are what i wanted to give names to here

[alpine sable]

im asking how is (x-a)(x-b)(x-c) a generic cubic

how did you generalise that

[vale wigeon]

every cubic can be factored completely over the complex numbers

i mean, ok, i'm also setting the leading coefficient to 1, simply to get it out of the way

[alpine sable]

what do you mean by that?

[fair crater]

Before you go further, what would you understand 'the alternative' would be?

[alpine sable]

you mean what i understand by this?

[fair crater]

No, I assume from your question that

You potentially see a cubic polynomial not of the form (x-a)(x-b)(x-c)?

[alpine sable]

No, I just want to understand how you get to that form

[fair crater]

Right so basically an assumption is that a cubic polynomial can have up to 3 roots

These polynomials are factored into the form (x-a)(x-b)(x-c) where a,b,c are the roots

[Anyway I wrote here assumption, but it can be proven]

[alpine sable]

how would you prove it?

[fair crater]

I wouldn't prove it, but someone smarter than me did prove it

But anyway if you can accept it has 3 roots

Then you should be able to accept the 'decomposition' of ax^3+bx^2+cx+dx^0=(x-q)(x-w)(x-r)

For any (a,b,c,d) to corresponding (q,w,r)

[alpine sable]

So basically, you're assuming that $ax^3 + bx^2 + cx + d = 0$ with roots $\alpha$, $\beta$ and $\gamma$ can be factored into $(x - \alpha)(x - \beta)(x - \gamma)$ which in turn gives you $x^3 - (\alpha+\beta+\gamma)x^2 + (\alpha\beta+\beta\gamma+\alpha\gamma)x -\alpha\beta\gamma$ \\
however, wouldnt you have to first divide the first equation by a? \
$\frac{ax^3}{a} + \frac{bx^2}{a} + \frac{cx}{a} + \frac{d}{a} = 0$ Meaning that in the last equation, $\alpha+\beta+\gamma$ is actually divided by a??

[fair crater]

Oh, right, that's definitely a miss on me

[ocean seal]

ZED_118

[fair crater]

Right, since I messed up, it's x^3+bx^2+cx+d=(x-q)(x-w)(x-r)

a can't fit into the previous cubic polynomial form since it would need to be multiplied with the x-es

The previous form would require a=1 basically

[alpine sable]

Alright, I think i get it anyways. But Im still curious as to how you prove (x-a)(x-b)(x-c)

@vale wigeon

[vale wigeon]

"prove (x-a)(x-b)(x-c)"?

[fair crater]

There are 2 parts to that statement: the existence of 3 roots, and that you can factor polynomials out that way

[alpine sable]

why is the background white here?

[vapid oak]

that user must be in light mode ig

[vale wigeon]

how dare you slander me so

[alpine sable]

yes. prove that a cubic of the form $ax^3 + bx^2 + cx + d = 0$ can be factored into that form

[ocean seal]

ZED_118

[vale wigeon]

you're essentially asking me to prove FTA for cubic polynomials

dont feel like doing that rn

[vapid oak]

maybe research Vieta's Formula

[vale wigeon]

@vapid oak no, it's a config option. ,tex --color light

[alpine sable]

FTA?

[vale wigeon]

fundamental theorem of algebra

[alpine sable]

ah

you would have to prove that

?

[fair crater]

Yes

The factor theorem needs to be separately proved too

It's the 2 parts I mentioned

[alpine sable]

So I should either try understanding how the fundamental theorem of agebra is proven, or I can simply go on with life just assuming that I can do (x-a)(x-b)(x-c)

[fair crater]

From what I see, you could probably do it in university math year 1/2?

But before that I don't know how you would get the requisite knowledge (assuming standard curricula)

[alpine sable]

so

going back to the initial question

I use (sum of the roots) = 5?

2+3i + 2 - 3i + c = 5

this?

hence the real root is 1?

[warped phoenix]

for dependence of a conditional Probability, P(A|B) should not equal P(A), in the example my teacher is doing, she says it's dependent because P(N|B) isnt equal to P(B), how does this make sense? In order for it to be dependent, shouldn't P(N|B) not equal P(N)?? Why does she compare it to P(B)

[fair crater]

You can check polynomials quite easily, no?

[warped phoenix]

anyone?

<@&286206848099549185>

[glass lichen]

nowhere in that is that claimed

[halcyon geode]

Hard to read whatever is there tbh

[warped phoenix]

thats what she says

[glass lichen]

if you mean why she wrote about P(B) and P(N|B)... that's cause those are the givens...

[warped phoenix]

@glass lichen No she wrote it weird but when she talks she said "Because P(B) and P(N|B) are not equal, it is dependent"

thats what im confused about

[glass lichen]

so ask her...

probably just a misspeak

[warped phoenix]

she wont respond until monday

[glass lichen]

so wait

[warped phoenix]

i need to get this done today, regardless, how are we supposed to know if it dependent or not, we'd find P(N), right?

[glass lichen]

idk why 1 thing is gonna nullify everything else you've been taught in class / this discord, so dont make a big deal out of it

yes you need P(N)

[warped phoenix]

ok

ill be home in a couple hours and try again

[velvet condor]

easy question

let x^6-3x^2y^4=69
and y^6-3x^4y^2=6969
calculate x^4+y^4

[vapid oak]

can i rewrite in latex to see if i understand right cuz its a bit confusing

[velvet condor]

sure,

btw how do i use align thingy:)))

[vapid oak]

$x^6-3x^2\cdot{y^4}=69 \ y^6-3x^4\cdot{y^2}=6969. \ Calculate {x^4+y^4}$

[velvet condor]

i think u may need ~

[glass lichen]

$x^6-3x^3y^4=69 \ y^6-3x^4y^2=6969$ Calculate $x^4+y^4$

[ocean seal]

Mosh

[drifting basin]

That was hurting my head trying to read that haha

[ocean seal]

Omfish

[vapid oak]

whatever sorry im wasting time

hey i just graphed the two equations, it looks like there arent any solutions for x and y

[velvet condor]

doesnt matter:))

[drifting basin]

Did you graph the first one as x^6 - 3x^2 * y^4

[vapid oak]

yep