help-13

[smoky whale]

Where exactly?

Will my whole answer change?

[stuck walrus]

yes because your original answer is wrong

[stuck walrus]

wherever h is lol

[smoky whale]

I’m dead confused

[stuck walrus]

What are you confused about

[flint heron]

this a tets

[smoky whale]

?

I only have 30minutes left 😭

Been stuck for 2 hours

[stuck walrus]

Bruh is that a test?

[smoky whale]

No it’s a revision sheet

How can I have a test 😭

[sick gazelle]

i got it, u gotta write h in terms of r from the total surface area equation

[smoky whale]

H= A- 2pi r^2/ 2pi r???

[sick gazelle]

then before differentiation, u shd put the h in terms of r while writing the vol, it will avoid the dh/dt thing

[smoky whale]

H= A- 2pi r^2/ 2pi r??? Correct?

[sick gazelle]

wut is A?

[smoky whale]

Surface area

[sick gazelle]

then put the value to A and get it only in terms of r

[smoky whale]

A= 100pi

[sick gazelle]

there shd h= 100 - 3r²/ 2r

check it

[smoky whale]

What about pi

Cancel

[sick gazelle]

cancelled from denominator

[smoky whale]

Out

[sick gazelle]

yea

[smoky whale]

Sorry yes

[sick gazelle]

so u got h in terms of r

now wut do write the vol?

[smoky whale]

So r= 2 sqrt5

[sick gazelle]

check again

[smoky whale]

Sub it in the

[sick gazelle]

v = πr²h - 2/3πr³

right?

so sub here

before differentiating

[smoky whale]

Yea

[sick gazelle]

do u understand y we are substituting it before deifferentiating?

thats the main part

[smoky whale]

Wait what are we substituting in V?

[smoky whale]

This

[sick gazelle]

in this eqn we sub h in terms of r

[sick gazelle]

yea

[sick gazelle]

we did it bcuz we dont have any data regarding dh/dt which we get after differentiating with product rule without sub h as r

so we sub it

[smoky whale]

Ohhh 😯

[sick gazelle]

u got it?

after subbing it u might equate to zero n stuff, then you'll get linear eqn in r, solve for r, then when u get r

[sick gazelle]

sub r in this eqn

u got h, u got r wut else do u want? a million dollars?

[smoky whale]

I got them as 2sqrt5

[sick gazelle]

wut u got r?

i got different

[smoky whale]

What did you get

[sick gazelle]

r = √100/√13

wuts the linear eqn u got after differentiating n equating to zero?

[smoky whale]

I got different because maybe I did it wrong

[sick gazelle]

calci mistake check it

my eqn is 50π - 9πr²/2 - 2πr² = 0

a freak i didnt diff it sry my bad

really sry for wasting ur time

[smoky whale]

That’s alright, can you fix it?

[sick gazelle]

its 50π - 9πr - 4πr = 0

yea

was just curious, wuts the value of k u got? sry for wasting so much time

[smoky whale]

That’s okay, my mind is crazy right now, so I can barely understand at this moment. Is it okay if you show me your working that way I can feel a relief

I’ve done so much questions for this revision in a really busy house

Hence I requested

[sick gazelle]

sry i did it in mind... i dont have paper pen, im in a bed rest rn

[smoky whale]

Then can you type it?

[sick gazelle]

this is kinda rough.. hope u understand it

[smoky whale]

This is much better

I thank you so much for this

[sick gazelle]

wlc

[smoky whale]

Ok so now, do I restart all of my working out and consider yours?

[sick gazelle]

yea u can get the idea from my work and try to do it on ur own, thats much better

[smoky whale]

Ok

So what you did was get h interms of r and got the volume

Now, after that, do I differentiate?

[sick gazelle]

yes, after sub h interms of r

[smoky whale]

After differentiate?

[sick gazelle]

no no, i mean u sub, then u diff

[smoky whale]

Ok

[sick gazelle]

always remember, dont sub any value after diff, do it b4 diff

[smoky whale]

Ok

[smoky whale]

What exactly do I need to do?

[smoky whale]

What exactly do I need to do

[sick gazelle]

sry?

[smoky whale]

Like after you wrote it on paper

What do I do

Like did you answer the whole question?

[sick gazelle]

yes? u had to find the value of k basically

and we got it k=5 thats it

[smoky whale]

So the whole question is answered?

[sick gazelle]

yes h = 5r

expressed

[smoky whale]

What is r

Oh I saw

[sick gazelle]

numerical value?

[smoky whale]

Nvm nvm

[sick gazelle]

ok

[smoky whale]

I saw

[sick gazelle]

also u might think

[smoky whale]

This here all of it answered the whole question?

[sick gazelle]

we had h = 100 - 3r² / 2r already but it was not like h = kr form (this prob is common with most of us)

[sick gazelle]

yes but dont just copy it, it was just a doubt u had that was cleared i hope, so that now u can solve it by urself

[smoky whale]

Yes

[sick gazelle]

and btw is this ur channel? like everyone gets their own channel?

[smoky whale]

Yes

[sick gazelle]

how?

[smoky whale]

It was available so I got in

[sick gazelle]

i see

anyways have a gud day

[smoky whale]

May I ask how you got 3r^2? It was 2

[sick gazelle]

ok so look up the total surface area i wrote

[smoky whale]

Ok

Oh yes I saw

I missed that

Sorry

Yes, have a great day, it was so lovely working with you

Thank you very much

Just one more question. Did we get a maximum volume?

[sick gazelle]

u can put the r and h values if u want the max vol

[smoky whale]

Yes

I have a different question

I have done many questions about z scores but this one is complicated

[cedar kiln]

@smoky whale Has your question been resolved?

[cedar kiln]

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[cedar kiln]

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[worldly arrow]

i want to learn how to do mental math, to start i would like to learn how to do addition super quick.

[worldly arrow]

what should i do

[crimson delta]

practice

[livid hound]

start with pen/paper

[crimson sedge]

you can try using the abacus mentally

[worldly arrow]

whats the abacus

?

[royal loom]

https://tenor.com/view/math-raccoon-abacus-computing-gif-17631243

this thing

[worldly arrow]

oh

what i would do before was this

34
+63

in my head

but is this not the best way

?

[royal loom]

I'd add the ones place

first

anything that carries over, you can add to the tens place

so here you'd get 4+3=7 easily in your head

nothing caries over

and then do 3+6=9

but remember this was the tens place

so it is really 90

so then 90+7=97

[cedar kiln]

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[crimson sedge]

The question is to make an expression for these (roots of polynomials).

[crimson sedge]

this is my work so far

but I am unsure as to if I have come to the right conclusions

[dire geode]

[crimson sedge]

also, if it is right is there a pattern depending on the degree of polynomial and the power to which you are raising the sum of pairs, triplets ect. of roots?

also, I may have used non standard notation: the z is just the number of terms.

[gleaming cloud]

nahh this has to be a prank

[crimson sedge]

how so?

[gleaming cloud]

a lot of notation to be explained imo

[crimson sedge]

How? apart from the z, the rest is standard. The rest is just what I have been taught + websites, textbooks ect. The concepts used are multinomial expansion and roots of polynomials

redpenbluepen has a good vid on this

I presume if you have the advanced role you should now what multinomial expansion and roots of polynomials are

The general definition looks the same to what I have done

i'll try to rewrite it better then

[dire geode]

you say polynomials here, but later define cubics. can you define the variables you use

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

I checked with some numbers, to which I had the answer to. I got the right answer using the results I got, so I am probably alright with this one. Sorry for torturing you with what my brain decides to come up with lol.

[cedar kiln]

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[toxic crag]

How do i do question 1 in exercise 2?

[honest coral]

both terms must be 0 for the expression to be zero

both terms also have a factor in common, so set that factor to 0 and solve for x

[lunar lynx]

Why ?

[honest coral]

wait true, they could be additive inverses

[lunar lynx]

Yes

[honest coral]

my bad

[toxic crag]

what does setting the factor to 0 mean?

because i think the common factor is (2x-1) right?

[honest coral]

yas

[toxic crag]

so how do i set it to 0?

[honest coral]

2x - 1 = 0

because the main equation is true when the common factor = 0

[cedar kiln]

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[dire geode]

$\frac{1}{\frac{a}{b}} = \frac{b}{a}$

[wraith dagger]

riemann

[distant pecan]

oh

so

tanx?

idk

what now @dire geode

[dire geode]

what is your question

[distant pecan]

idk

i just dont understnad

[dire geode]

which part

[dire geode]

this fractioN?

[distant pecan]

well i dont understnad how that correlates to that

[distant pecan]

well yeah but how does that correlate in any way to the problem

[dire geode]

,tex .sohcahtoa

[wraith dagger]

riemann

[distant pecan]

i know this

[dire geode]

write tangent in terms of sine and cosine

[dire geode]

then use this

[distant pecan]

uh

oh

so

its cos/sin>?

is that the only solution

[dire geode]

do you know how to write cotangent in terms of sine and cosine?

[distant pecan]

its

cosx/sinx

i have it written down

@dire geode

[distant pecan]

what abt it

[dire geode]

you really don't need to ping me so often

[distant pecan]

yeah

[dire geode]

this is correct

[distant pecan]

but what now

whats the answer

[dire geode]

compare it to this

[distant pecan]

wdym

[dire geode]

compare means to look at them and find similarities or differences

[distant pecan]

means?

i dont understand

[dire geode]

i was explaining the word "compare" for you

[dire geode]

wasn't that your question

[distant pecan]

im confused on what im supposed to do

what are the answers

[dire geode]

the answers are the ones that equal to 1/tan

[distant pecan]

yeah and how do we find ghat

[dire geode]

which one of these four equal what you found

[dire geode]

this is your answer when i asked you to simplify 1/tan

[distant pecan]

first

is that the only answer

[dire geode]

compare that to cotangent

[distant pecan]

i did

[dire geode]

cotangent is the last choice here

cot x = cotangent of x

[distant pecan]

so the answers are 1 and 4

.close

[cedar kiln]

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[hushed spoke]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[hushed spoke]

yes can you simplify it further

yes

there are other ways to solve this

but this one works too

you know this identity sin(x) = cos(90-x)?

sin(x ) = cos(90 - x) = cos(y)

that makes sense

you have it write there

no no no no

sin(x)= 6/10

x is not equal to 6/10

[cedar kiln]

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[crimson sedge]

so i know the solution for this

[crimson sedge]

i just need to know what exactly is the process going on here exactly

i.e. what am i actually picking as my stars and bars

like, i guess the 3 warehouses are the bars?

but that doesnt make much sense since they are all indistinguishable...

[brittle lynx]

The warehouses or the books?

[crimson sedge]

the books

[brittle lynx]

So why would the warehouses as bars not be correct

[crimson sedge]

okay so you will have 3 groups

separated with two bars

oh so ig it would be 3002 choose 2

hm

fair enough okay

[brittle lynx]

Yes that seems right

[crimson sedge]

understandable. Thank you

.close

[cedar kiln]

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[fair geyser]

@crimson sedgeit means warehouses are distinguishable

oh ok i misread

[cedar kiln]

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[wispy forum]

Hey, been stuck on this question for a while (multivariable calc) and while I've tried reading the solution I don't really understand it - it suggests using a parametric transformation that looks like this, but why are you not able to just convert it to spherical coordinates and then move on? Shouldn't the values for y be enough to decide an angle 0 and the angle for rcos(phi) be decided by the z > 0?

[wispy forum]

I don't really understand what you accomplish with the parametrics either, is it needed to calculate the jacobi-matrix? 🤔

ah wait I guess it's because going to spheric would mean you'd be calculating the volume rather than the surface area, is there no way to calculate the volume as a integral of 3 variables and then get the surface area from that? Considering the derivative of the equation for volume is literally the area equation

[cedar kiln]

@wispy forum Has your question been resolved?

[cedar kiln]

@wispy forum Has your question been resolved?

[cedar kiln]

@wispy forum Has your question been resolved?

[cedar kiln]

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[crisp brook]

This is a computing question, but it is related to Fermat's Little Theorem. The task is to calculate a^b^c (mod 10^9 + 7) efficiently, but I am having trouble understanding their solution. The solution states "Fermat's Little Theorem tells us that a^(p - 1) ≡ 1 (mod p), so we can calculate a^(b^c (mod 10^9 + 7 - 1)) (mod 10^9 + 7)."

For example: a = 3, b = 4, c =5,
Let x = b^c (mod 10^9 + 7 - 1), then the answer is a^x (mod 10^9 + 7).

I don't understand how they can do it this way.

[silent finch]

wdym

thats the definiton of the theorem

[crisp brook]

Could you help me try to understand it better? I don't get how the answer can come out like that

[silent finch]

the way they presented the theorem is kind of misleading ig

what the theorem says is $a^n \equiv a^{n \pmod{p-1}} \pmod{p}$

[wraith dagger]

kappa

[crisp brook]

wait... I've never seen it in that form

[silent finch]

when n=0 you get a^{p-1}==1 (mod p)

[crisp brook]

wait how does it become a^{p-1}==1 (mod p) when n = 0?

[silent finch]

$0 \equiv p-1 \pmod{p-1}$

[wraith dagger]

kappa

[silent finch]

and a^0=1

[crisp brook]

right

[crystal raptor]

thats really not what the theorem says

[silent finch]

oh thats the way it was presented to me

[crystal raptor]

i would imagine that follows from the theorem

[crisp brook]

Let me see if this works:
Fermat's Little Theorem
tells us that
$a^{p - 1} \equiv 1 \pmod{p}$
, so we can calculate
$a^{b^c \pmod{1e9 + 7 - 1}} \pmod{1e9+7}$
with modular exponentiation.

[wraith dagger]

Qang

[crimson sedge]

bro

nvm

[crisp brook]

Right, so how does that transition into $a^{b^c \pmod{1e9 + 7 - 1}} \pmod{1e9+7}$?

[wraith dagger]

Qang

[silent finch]

Use it on n=b^c

[crimson sedge]

reduce the exponent b^c modulo (10^9 + 7 - 1) instead of modulo 10^9 + 7

[crisp brook]

wdym reduce it

[crisp brook]

what did ΣΑC mean that the theorem doesn't say that

[crimson sedge]

find the remainder b^c is divided by (10^9 + 7 - 1)

[crystal raptor]

what kappa said just wasnt the standard statement of FLT

[silent finch]

the way i wrote it isnt FLT,

[crimson sedge]

bc of euler's thm

[crystal raptor]

now whats going on is that if you want to reduce the exponent you have to reduce mod phi(p) = p-1

[silent finch]

yeah

or multiplying by a^{p-1} which is 1

[crisp brook]

Sorry I don't really understand that

[silent finch]

youll learn it later, just use the thing i wrote for now

[crisp brook]

Alright, I'll look into it after

Thanks, I understand it now

[crimson sedge]

what pokemon is that

[silent finch]

if yorue curious search eulers totient theorem

axew

[crimson sedge]

ok thx

[crisp brook]

.close

[cedar kiln]

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[crimson sedge]

i meant the platapus but ok

[cedar kiln]

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[crimson sedge]

So first find the ratio of the sides

is 3/4

wait

for the first one

RS = 18 and UT = 36

so wouldn't it be 1/2?

since 18/36

when you compare similar figures, you are comparing the left to the right

so its 18/14

thats equal to 36/DC

ohhhh

ye

i have one more question

for this one i have a possible answer and im not sure if im right

but thats just for the ratio of the sides

i know

one sec

oh hell no bro

this is a five minute convo

aint no need for a break

WHAT

tiem is money

whats

the

...

im lowkey lost

:)

ok to figure out why

we must look at how area is calculated in relation to how sides are calculated

how would i find the area if i don't have the height?

no height needed

disregard that figure

imagine a line

lines are 1 dimension

adding on a plane, like a trapezoid takes 2 dimensions, length and width

okay

when you scale a figure, you're multiplying both dimensions by the same factor. For example, if you double the size of a rectangle, you're doubling both the length and the width. So the new area is the old length (doubled) times the old width (doubled), which is four times the old area.

so, the area ratio is what????

you got this

24/48

DC is 48

NONONONO NO TRAPEZOID

DISREGARD THE PROBLEM

OH

OH

MB

I AM TEACHING GEOMETRY MORE IMPORTANT

this is why im confused

i was literally just learning geometry

and then suddenly it switched to trig

and now its whatever tf this is

So, when you scale a figure, you multiply both dimensions by the same factor

yes

so double a rectangle, you double both length and width

so the new area is the old length doubled times the old width, so four times the old area

so the area ratio is the square of the side ratio

thats why sides are denoted as for example 3 inches

while area is 3 in^2

and volume (3 dimensional) would be 3 in^3

👯‍♂️ 🎉 👯 🥳 👯‍♂️ 🎉 👯 🥳 👯‍♂️ 🎉 👯 🥳 👯‍♂️ 🎉 👯 🥳 👯‍♂️ 🎉 👯 🥳 👯‍♂️ 🎉 👯 🥳

if ur doing geometry, the best book is geometry by ray c jurgensen

i have

5 days left.

to finish.

everything.

bruh what did u do

now i am interested

add me, i need to see the journey unfold

there is no journey.

if i dont finish

youll never hear

actually nevermind, i probably wont commit bc im lazy

from me

ever again :D

wait how much have u completed

uh

i dont want to tell u

youll make fun o fme

i need to scoop sis

40%..

BUT.

ok u still have 5 days tho

NO

5 DAYS ISN'T ENOUGH FOR SOMEONE LIKE ME

my schedule is packed

like rn

i gtg

can’t finish that question

are u like the child of those asian moms on yt

because i have practice

[crimson sedge]

yes

gl

thats insane

you know what u should tell her

wgat

its like people at the movie

like involution u know

one person gets up in the movies

THEN EVERYONE GETS UP SO THEY CAN SEE

and in the end people are climbing skyscrapers and renting apartments to see the screen

in the end you and your mom suffer

ok goodluck

LOL

i need to find

one of those people

that enjoy doing math

and treat it like an activity

and ask them for answers

that would double my speed

[obsidian coral]

No because we aren't here to give you answers

[crimson sedge]

yeah i had an asian mom but she never breathed down my neck bc i was naturally good at math and able to skip grades and stuff

ur lucky

if u had my mom

she would still breath down ur neck

even if u are good at math

[crimson sedge]

yeah

i know that

i know like my cousins

its like really scary

bc they go to high schools or places like that where there is high suicide rates

its super scary seeing those stories

goodluck tho

bounce back

ultimate mood killer srry

i didnt even realize it lol

goodluck tho

[cedar kiln]

@crimson sedge Has your question been resolved?

[wanton sail]

please let them work it out themselves if possible

!nosols

[cedar kiln]

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.

[wanton sail]

The more the helpee works out on their own, the better! :)

[cedar kiln]

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[crimson sedge]

can someone explain what do they mean by what yhe result implies

i got 0 for the definite integral

[sand meadow]

i think it means area above x axis is = area below x axis

maybe

[crimson sedge]

thanks so much!!!

.close

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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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

Show your work, and if possible, explain where you are stuck.

[crimson sedge]

I think the question can be rephrased as what is the probability that a male person will watch the world series

[crimson sedge]

Which indicates you would have to find the number that will watch among males

The total of males

Which is 121

Maybe

Hmm interesting

So go with it

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[crimson sedge]

I guess might be a bit of a weird question; but for pigeonhole principle questions, what's a good way to recognise what are your 'boxes' and 'pigeons'?

[crimson sedge]

i kind of struggle with recognising which one is which sometimes

oh hm i think i got an idea

.close

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[crimson sedge]

dude i cant understand

[crimson sedge]

i do everything right

ane the variables arent orthogonal

ive done like 10 of these

and cant get it right

I project 5,0,-7 onto 0,4,2

so dot them together over dot 0,4,2

-14/20

to (5,0,-7) - (-14/20) (0,4,2)

and the result is not orthogonal to 5,0,-7

[bold hinge]

here's a secret

you can row reduce before you do gram schmidt

this makes things a lot easier

,w row reduce ((0,4,2),(5,0,-7))

[wraith dagger]

Results provided by WolframAlpha

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

Requested by .endtimes

[crimson sedge]

🙏 🙏 🙏

[cedar kiln]

@crimson sedge Has your question been resolved?

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[onyx grail]

I got a question..

If 1000 elves compete for a place at the Christmas meeting, the selection process goes like this.

There is a Elder elf which stands at the start of the row of the 1000 elves. The counting begins at the elder elf. There are 1001 elves in the row (including elder elf).

So every 2nd elf (including elder elf) is disqualified. Then with the left overs, this process repeats until elder elf is disqualified. The left over elves are the ones that get to attend the meeting.

Thus, how many elves attend the meeting?

[onyx grail]

I said 200…

[tropic oxide]

wait so the elves stand in a circle right

[onyx grail]

Yes

[gritty galleon]

why does this seem like LR?

eh nvm

its not

[tropic oxide]

so we start counting with the elder elf (who let's say is #1), then elf #2 is out, elf #3 is in, #4 is out and so on

then elf #1000 is out, #1001 is in, and ...

[onyx grail]

Yes

[tropic oxide]

we get right back to the elder elf who is out

[onyx grail]

1001# would be elder elf again.. right?

[tropic oxide]

no, elder is #1

there are 1000 elves NOT counting him

[onyx grail]

oh yeah 💀

[mystic abyss]

just curious where did you get this question from?

i just did one that's almost identical to this 2 days ago

[onyx grail]

Ty for your help Ann

/end

[tropic oxide]

it's .close

[onyx grail]

.close

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[primal lodge]

https://cdn.discordapp.com/attachments/808386688308477962/1136935848202469427/Screenshot_192.png

[primal lodge]

how is answer 0?

[tropic oxide]

who's saying the answer is 0?

[primal lodge]

the site lol

[tropic oxide]

i'd like to disagree with them

[primal lodge]

i have 1 right?

[quick coral]

111 = 3*37 in prime
so this one works and all others are multiples of 111 so they have at least one factor more
so answer is 1

[tropic oxide]

111 is 3*37

[quick coral]

yeah

[primal lodge]

so 1 is the correct answer right?

[tropic oxide]

yes

[crimson sedge]

Y'all remeber that??

Or just pure magic

Oh nah you divided by factors okay

[primal lodge]

lol i used primality test

[tropic oxide]

111 is divisible by 3

[crimson sedge]

Yes yes yes

I thought they used the table of 37 ☠️

[primal lodge]

and found out it's divisible by 3 which is pretty dumb

😭

[royal loom]

well it is clear that the rest are divisible by 111 and either 1,2,3,...,9. So it is really the only like important one to check

[primal lodge]

since i could've just added 1+1+1

[tropic oxide]

btw can you show where on the site it says the answer is 0

[crimson sedge]

Sue them

[cedar kiln]

@primal lodge Has your question been resolved?

[primal lodge]

i'm guessing they just had a typo

and wanted a prime instead of 111

https://cdn.discordapp.com/attachments/808386688308477962/1136942740437995600/Screenshot_194.png

here

[tropic oxide]

hm

[primal lodge]

anyway it's okay not a big problem

you guys confirmed it

i was not sure myself since i had 37*3 as well

thanks

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[eternal patrol]

What is cos30/cos33?

[eternal patrol]

Used cos(A+B)

Cos(30+3)

[cinder shard]

but we dont know cos 3

is that defs the right value? (33)

[eternal patrol]

I mean
Using binomial approximation, since theta is very small, cos3 is 1

Sin 3 is uh π/60

[cinder shard]

if you are doing that then sure

then what is the problem?

where are you stuck

[eternal patrol]

Got (210√3)/(210√3-11)

I wanna check my answer

😅

[cinder shard]

i mean if you just want to do that why not plug it into a calculator

lol

and see how close you are

you are using an approx.

[eternal patrol]

Oh no right😅

Thanks
I will try using calculator

.close

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[cinder shard]

i dont have pen/paper right now, but if you dm me ur working out as screenshot i can glance over

GL

[eternal patrol]

Oo

I will copy it in neat first

[cedar kiln]

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[rancid cloud]

Solution please

[quick coral]

what have you tried ?

[vagrant elbow]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[vagrant elbow]

damn

right uh so

What values can a square root output

[static fern]

i see an error in your work, $x(x+3)-2(x-3) \neq (x+3)(x-3)(x-2)$

[wraith dagger]

FireBlazer

[rancid cloud]

Send me solution please

[static fern]

solution to the problem or the proof of my last message?

[rancid cloud]

Solution to the problem

[vagrant elbow]

!nosols

[cedar kiln]

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.

[static fern]

also, the solutions are very ugly, just saying

most likely there's a typo in the problem statement

if the 6 was -6 in the third radical, the equation would be nicer i think

[cedar kiln]

@rancid cloud Has your question been resolved?

[cedar kiln]

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[zealous summit]

Can someone explain to me what the arrows mean?

I'm having trouble trying to figure out the significance of the arrows

[zealous summit]

I know $f$ means function, but what does $GL_{2}$ mean as well?

[wraith dagger]

Nanners

[zealous summit]

Does it mean $GL_{2}\mathbb{R}$ implies all the real numbers except 0?

[wraith dagger]

Nanners

[zealous summit]

That being said, why is the bottom arrow different from th e top...

[crimson sedge]

$GL_{2}(\mathbb{R})$

[wraith dagger]

rbit

[zealous summit]

oh is the 2 significant of a 2x2 matrix?

[crimson sedge]

this is the set of all invertible 2x2 matrices over the field R

which forms a group under matrix multiplication

[zealous summit]

okay i kind of get it...

Wait okay so...

i know it has something to do with how

if the det is not equal to 0

then the matrix is invertible

[crimson sedge]

yeah

and as for the arrows

$f: A \to B$

[wraith dagger]

rbit

[crimson sedge]

this declares that f is a function that maps elements from set A to set B

[zealous summit]

OH and i GET IT (i think) the fact that $(ad - bc) \in \mathbb{R}$ means that it IS a homomorphism because the matrix on the left can be both mapped to the same thing

[wraith dagger]

Nanners

[crimson sedge]

$x \mapsto y$

[wraith dagger]

rbit

[crimson sedge]

also this actually defines the function, how elements are mapped exactly, you may also often see this as just f(x) = y

[crimson sedge]

wait first of all, do you know what a group homomorphism is?

[zealous summit]

Not conceptually but I kind of know the definition

[crimson sedge]

but you know groups right?

[zealous summit]

yes

[crimson sedge]

in general homomorphism can be seen as structure preserving maps/functions. So we can actually define homomorphisms for all kinds of structures like groups, rings, fields, vector spaces, ...
As for groups, a group homomorphism f: G1 -> G2 needs to satisfy the condition that f(g*h) = f(g) * f(h) for all elements g and h in G1

[cedar kiln]

@zealous summit Has your question been resolved?

[cedar kiln]

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[autumn bane]

I'm stuck on making it a perfect squared trinomial, i tried using complete the square but I'm confused on how to get the third term

[spice kraken]

use the formula

[obsidian coral]

using complete the square
Do you know what to do?

[autumn bane]

i tried taking the half of 16 then square it with 2

but im kinda confused after that

[obsidian coral]

What do you mean square it with 2?

[autumn bane]

uh (b/2)^2

[obsidian coral]

And what value did you get?

[autumn bane]

is it not right?

64

[obsidian coral]

This is right

[obsidian coral]

This is it

[autumn bane]

Ah so the third term is 64?

[jaunty mural]

well show the steps up to this point perhaps

on paper

[obsidian coral]

square it with 2
Is a redundant statement, "square it" already means raise to the second power, so you didn't need to say "with 2"

[autumn bane]

oh

[autumn bane]

mb but this is the third term or no?

[obsidian coral]

You applied the formula, and that's what you get, so what are you confused about?

[autumn bane]

I thought it was wrong but thanks

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[unkempt scarab]

Let $f(x)$ be a real polynomial, and assume that $a$ is a real root with multiplicity $\geq 2$. Show that $a$ is a root of $f'(x)$.

[wraith dagger]

Michael

[unkempt scarab]

Dunno how I can show this. Any ideas?

I understand it of course when I look at some specific graphs, but it's just to show it mathematically which is difficult

[south tundra]

Say the multiplicity of $a$ is $m \ge 2$, then [f(x) = (x - a)^mg(x), ] right?

[wraith dagger]

A Lonely Bean

[unkempt scarab]

Aha, yes

[south tundra]

What's f'(x) then?

[unkempt scarab]

Then you can just differentiate with productrule?

Hmm

[south tundra]

Yeah, what would that yield?

[unkempt scarab]

$m(x-a)^{m-1} \cdot g(x) + (x-a)^m \cdot g'(x)$

right?

[south tundra]

Correct, except that x should be m in the very beginning

[unkempt scarab]

oh yes, oops. That was a typo

[wraith dagger]

Michael

[south tundra]

And when we plug in x = a, what does f' become equal to?

[unkempt scarab]

0

[south tundra]

Yup

[unkempt scarab]

since both terms become 0

[south tundra]

As a sidenote here, it may look like the fact that m >= 2 was not used

[slate lintel]

here's a question: at what point in that proof did we rely on that? ^

was already typing that when you said it lol

[south tundra]

Hint: ||When would 0^(m-1) be undefined?||

[unkempt scarab]

Uhm

[unkempt scarab]

Ah yes, then if m is less than 2, it becomes 0^0 or 0^negative which is undefined

Alright so it fixes itself basically?

[south tundra]

Yup, so the case m = 1 has to be considered separately

[unkempt scarab]

Yeah

[south tundra]

And you will see that the term (x - a)^(m - 1) just becomes 1

Hence the conclusion there is different

[unkempt scarab]

Yes, right

Well thank you! I understand it now :)

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[placid flower]

Okay I give up. I tried solving this one complex analysis excercise for 30 mins now. I think I'm making a mistake with the singularities I think! I basically have to integrate funciton along the curve. I first trie to use residuetheorem but didn't manage to fufill al the conidtions to use it. The correct solution is a btw. second picture is residue theorem!

[placid flower]

My problem is that no matter how I integrate I always get 0

[slate lintel]

[placid flower]

I tried applying resiude theorem by splitting the integral with partial expansion to (i/2)/(z+i) and (-i/2)/(z-i) but I can't use residue theorem since the curve isnt around i

[slate lintel]

why do you think an answer of 0 is a problem?

[placid flower]

1. it's not an option the mulitple choice so wrong

and that would be only true for sets without a singularity

and I have singularity +i/-i

[slate lintel]

there's no singularity within the curve though

[placid flower]

you are right

huh

the thing is the solution says a)

and I don't think that they would make such a mistake

hmmm

[slate lintel]

doesn't seem right, there's a language issue I guess but I think that should be 0...

[placid flower]

it only says let curve be..

what is value of integral

[slate lintel]

that's a simple closed curve right?

[placid flower]

I think

it should be the circle around 1

with radius 1

[slate lintel]

I think they messed up

and meant to have you integrate around i

[placid flower]

that would be crazy

but then the excercise would make more sense

[opaque onyx]

the curve doesn't encircle -i

doesn't encircle i either

[slate lintel]

yeah the function is holomorphic in the region they gave you

but I think they meant for it not to be

[placid flower]

or wait

is that supposed the be an i

because in the multiple choice

there is also that weird thing

and why would the say pi*1

[slate lintel]

that did seem strange to me

[opaque onyx]

oh yeah they write it like that in the answers

[placid flower]

WOW

that is super cringe

[opaque onyx]

that is

also

you don't need to do partial fraction expansion for stuff like this

here you could calculate the limit of (z - i)/(z^2 + 1) as z -> i or for simple poles you can just differentiate the denominator (idk if you've seen that yet)

[placid flower]

I'm not sure

don't think so

thank you guys for your help 🙂

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[placid flower]

.reopen

[cedar kiln]

✅

[placid flower]

I have seen that actually you are right

just in another context

we looked at finding the order of poles

yeah it's smart to also do that here

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[placid flower]

How do I find Laurent-Series around 3i of this function?

[placid flower]

Should I start by doing +3i -3i

or getting out the 4

out

I think I got it nvm

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[junior wasp]

Ab//cd

Ab=bd

How to proove

<@&286206848099549185>

Prove that abd is equilateral

Yes

Can u help me

Thxx

[tawdry bison]

hmm were there no other givens?

[elfin compass]

Is that parallel or some other notation

[junior wasp]

Parallel

[junior wasp]

No

U guys think there's something wrong with the question?

[tawdry bison]

you can prove the two triangles congruent but i’m not sure if you can prove them to be equilateral triangles..

[elfin compass]

Ad bd are equal so isosceles triangle so angle dab=abd

[tawdry bison]

as far as i know to prove a triangle to be equilateral you need to prove the 3 angles to be congruent or the 3 sides to be congruent

you can’t do either of them here

[junior wasp]

How do I prove the 2 triangles are congruent?

[tawdry bison]

so can you find 2 angles that are congruent here?

[slate lintel]

it's not fully constrained i think, can't you do this?

[elfin compass]

Abd =bdc alternate interior angle

[tawdry bison]

my wifi is really bad so i can’t load the image LMAO

wait it loaded

i’m not sure what you mean by that though?

[elfin compass]

Continue parallel lines to left

And draw

Can u show the diagram

And name points on the drawn parallel

E and f

[tawdry bison]

wait how does that help prove them to be equilateral

[elfin compass]

Then adf=bad and adf+bdc+adb=180 but adf and bdc are equal

And equal to the the 2 angles of the needed triangle

After substitution all 3 angles will come as equal and triangle is equilateral

[tawdry bison]

wait why does adf=bad?

now i’m confused

[elfin compass]

Adf=bad as alternate interior angles

I am very bad at explaining tho

[tawdry bison]

what.. i’m getting confused by the diagram now

where even is c and e and f

wait ignore c

just e and f

[elfin compass]

This

[tawdry bison]

is e on top and f on the bottom?

[elfin compass]

Yes well I guess e had no use tho

I will end up confusing you more so I guess wait for someone else to answer sorry

[tawdry bison]

isn’t adf an obtuse angle while bad is acute

[elfin compass]

Can you post a diagram with construction

Wait I took wrong sides as equal bruh I solved another question I solved for ad and db equal

[cedar kiln]

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[untold shadow]

can someone explain how second option is correct

[violet flume]

hmm what makes you think its not convergent?

[untold shadow]

hmm i am clueless actually

i just saw solution f ta

[violet flume]

I just ask because to me this looks like an unweighted average

and it doesnt appear that any of the terms are gonna be greater than 1

[untold shadow]

means ?

[violet flume]

so assuming it doesnt bounce around

[violet flume]

yea, its a mean

the subsequent term in the sequence is the average of the previous two

[untold shadow]

right

[violet flume]

and it looks like the terms are gonna be capped out at one

[untold shadow]

just hold on one thing in this sol is not getting into my head

[untold shadow]

ohh

[violet flume]

so just to me, id be skeptical if i was told this did not converge

[untold shadow]

capped out ? what does that mean ?

[untold shadow]

here the second last line

i am unable to understand why that is so

[violet flume]

no term of the sequence will be bigger than one

[crystal raptor]

are there more than the two options you're showing?

[violet flume]

[untold shadow]

yeah

[violet flume]

yea i was curious too

[untold shadow]

i will post that

it is mutiple correct question

i understood why the 4th option is correct

[untold shadow]

but unable to understand the second last line here

[dire geode]

lmao how did you know this

[violet flume]

he referenced the fourth option earlier

[untold shadow]

in the solution ta says 4th option

[untold shadow]

yeah

[crystal raptor]

im not really sure why they carried on writing after showing that (4) was true

[crystal raptor]

oh i see

[untold shadow]

idk but does this thing like hold true for any sequence ?

or does it just apply in this particular question

[crystal raptor]

uh that should just be true for any sequence

if you loosen what "equals" should mean for limits tending to infinity or not existing

[violet flume]

you youre adding all the terms together, and then you get the telescoping right

then assuming youre adding up to some $m$, you have $a_{m-1} + 2a_m = a_0 + 2a_1$

[untold shadow]

ohh

[wraith dagger]

jan Niku

[violet flume]

this is where youre wanting to apply the property

to get the 2/3 answer

right?

[untold shadow]

idts

ig

wait

[untold shadow]

he uses this property to get the limit

[untold shadow]

ohh then ig i understood why it converges to 2/3

[crystal raptor]

i mean they havent really shown its convergent

just that if it is convergent, it must converge to 2/3

from what I can see, its hard to follow bc you're sending fragments of the solution

[untold shadow]

ohh, that sounds confusing

[untold shadow]

my bad just hold on i will send all at once

@crystal raptor @violet flume this is the whole solution

from start to end

[crystal raptor]

yeah so they've really only proved this

for example if i had the recurrence $a_n = -a_{n-1}$

[wraith dagger]

ΣΑC

[violet flume]

show that its ||bounded and increasing|| ?

[crystal raptor]

its not monotone it bounces around

[violet flume]

i mean the original

unfortunate timing

[crystal raptor]

yeah that original

[untold shadow]

yeah checked first 4 values, the valuses like oscilated

[crystal raptor]

isnt monotone

[untold shadow]

up and down

[violet flume]

oh

[untold shadow]

yeah

[untold shadow]

so is the fucntion converging ? or are we assuming it converging and then finding what it might converge to ?

[crystal raptor]

in what they've written they've assumed it converges and found what it would converge to

[untold shadow]

ohh

[crystal raptor]

it is atleast not clear to me that they have actually shown it converges in the first place

[untold shadow]

ohh

where can i find questions like these with recursion

[crystal raptor]

idk just google like recursive sequence limits

[untold shadow]

btw how does this converge ?

wouldnt it be inf/inf ? in the right most side

[dire geode]

where is there even a division happening

[violet flume]

consider what the limit of that second piece is

[untold shadow]

wait

[untold shadow]

2 + 86^n/100^n ?

so 2 + inf/inf ?

[red cove]

focus on the angles

[dire geode]

oh

r^n goes to 0 for all |r| < 1

[untold shadow]

idk i feel i am dumb or something, lately i am not even applying basic simplifications

[untold shadow]

ohh

is it same for series of r^n for r < 1

[dire geode]

is what the same

[untold shadow]

limit as n tends to inf

[dire geode]

you're asking if something goes to zero

what is that something

[untold shadow]

limit as n tends to inf of series r^n for r < 1

[crystal raptor]

$\sum_{n=1}^{\infty}r^n\ , r < 1$?

[wraith dagger]

ΣΑC

[untold shadow]

would this be converging ?

[untold shadow]

yeah

[crystal raptor]

you actually need |r| < 1, but then yes

[untold shadow]

thanks all

.close

[cedar kiln]

Channel closed

Closed by @untold shadow

Use .reopen if this was a mistake.

[crystal raptor]

it does not converge to zero, it converges to something else

[cedar kiln]

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>.
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• 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.

[subtle yew]

Hello. Is it possible to create a function for the following wave pattern?

[subtle yew]

If so, how? I don't know where to begin

[sand meadow]

it is possible

[subtle yew]

May I know how?

Because I have no idea about how to make functions out of a drawn wave form

[sand meadow]

no one does

it is complex to form a function from a graph

[subtle yew]

So it's impossiible them?

Oh

Right, but what would the general approach be?

[sand meadow]

i don't know..

[subtle yew]

Well, from this,, it appears that after the first two oscillations, the frequency doubles

but in alternating oscillations themselves

[sand meadow]

lagrange interpolation formula

it could give close approximate of function but not exact

[subtle yew]

right

I mean

I guess I gotta google all that then, I presume

[sand meadow]

yeah..

[subtle yew]

alright *sigh*

How do I close this?

Thank you :>

.close

[cedar kiln]

Channel closed

Closed by @subtle yew

Use .reopen if this was a mistake.