help-0

[real gazelle]

Oh God lol

Hellish question

So

You can simplify it bit by bit

First of all, can you put the inequality in the form of
[2^{something} \le 1?]

[ocean seal]

eulerEMILYteristic

[wet nest]

I got sin^2(x) -2sinx+5<= 4 sin^4(y)

[real gazelle]

Why sin^4(y)?

[wet nest]

Or sqrt(sin^2x-2sinx+5)<=2sin^2y

[real gazelle]

Oh wait nvm I see sorry

[real gazelle]

Okay start from here and complete the square on the left-hand side

[wet nest]

sqrt((sinx-1)^2+4)

[real gazelle]

Not quite

Not -2

[lone heart]

@wet nest Has your question been resolved?

[real gazelle]

@wet nest did you complete the square yet?

[lone heart]

@wet nest Has your question been resolved?

[wet nest]

.close

[lone heart]

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[torn isle]

Hi, may I know is this correct?

For cosh (x) = 0, x=n*pi?

[vernal basin]

cosh(x) = (e^-x)/2 + (e^x)/2
for that to be 0 x would have to be of the form i*pi*n-(i*pi)/2 with n being any whole number (including negatives).
You can easily see that there is no real solution, since e^x with x in |R is always > 0 and thus adding two such terms can never yield a result <=0

[lone heart]

@torn isle Has your question been resolved?

[lone heart]

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[meager dirge]

Find the equation of the tangent to the graph using first principles.

[meager dirge]

Equation is f(x)=(x^2)-1

Thus; f'(x) = f(x+h)-f(x) / h

Which gives me;
(x+h)^2 -1 - (x^2 -1) / h

[tawny condor]

It's not equal.

You need to take the limit as h goes to 0

[meager dirge]

That's right!
I'll start again.

[tawny condor]

You plugged it in correctly though

[meager dirge]

But expressed it wrong. Good stuff.

[tawny condor]

$\pmap f x = x^2 - 1 \implies \pmap f {x+h} = (x+h)^2 - 1$

[ocean seal]

RedstonePlayz09

[tawny condor]

Now find $\lim_{h \to 0} \frac{\pmap f {x + h} - \pmap f x}{h}$

[ocean seal]

RedstonePlayz09

[tawny condor]

Notice that you just plug in h = 0, because then the expression would not be defined.

You will get division by 0

[meager dirge]

Exactly! That's where I got to

[tawny condor]

Therefore you need to try and simplify the fraction first

[meager dirge]

ok... let me try first.

I'm not sure where I took a wrong turn.

[ocean seal]

dldh06

[meager dirge]

Pfft, sorry.

And thank you. One moment.

I think I just got it. 😮

That's not right still.

2xh+h us 2x(0)+0
which is 0+0

Did I cancel out the wrong h's from earlier?

[wary stream]

You can't cancel the h's like that

Try factoring out an h first, from the numerator

On the line with $\frac{2xh + h^2}{h}$

[ocean seal]

dldh06

[meager dirge]

I could make that;
h(2x)+h^2 all over h.
Which becomes;
2x+(0)^2
= 2x.

[wary stream]

This is not valid still

h(2x)+h^2 all over h.
Which becomes;
2x+(0)^2

Can you factor out h from 2xh + h^2?

[meager dirge]

h(2x+h) all over h?

[wary stream]

Yes

[meager dirge]

OK, I saw those as two distinct parts at first...

Thank you @wary stream

.close

[lone heart]

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[gentle surge]

WARNING: What follows will sound completely stupid

I'll start with a background on myself. I live in new Zealand, currently finishing a degree in business and starting a second on in pure math overseas. I am 16 (saying this as it might affect your advice) and have plenty of time. My parents are crazy rich asians so money is not a problem for me and I do not have a job. This leaves me with plenty of time (12 hrs) to pursue my hobbies.

By the time I'm 30 I want to earn a Fields medal, get a doctorate in math, achieve the rating of Grandmaster in chess, master List's pieces on piano, achieve a net worth of 50 million, and gain 10 kg of muscle.

My chess rating is 2300, i can play one etude from Listz, and have gained 1kg of muscle, achieved a net worth of 70k.

I do not want to seem boastful or prideful but I am saying this so you can give me the best advice possible. My question: Should I focus on mastering mathematics, or be a semi-master of all trades.

I really want to improve my chess, piano, workouts, and business, but its my math that seems to be failing. This has led me to wonder if I should focus all my efforts (10 hours) per day on to math. My analysis is garbage, topology is a pain, and I cant even integrate complex functions. I really love math, but it happens Im bad at the thing I like. If I do focus on math, my other skills will die. But is there a way to master math without losing my other skills?

So again, Math or polymath?

[please do not comment unless you have advice regarding my question, particularly unnecessary comments of my age]

[surreal meadow]

I do not want to seem boastful or prideful but I am saying this so you can give me the best advice possible
this comes off as both. you could have asked just as well for advice on learning about topology without any of the other stuff

there's my advice

[gray isle]

balance

[rose sigil]

what the fuck

[gentle surge]

my question is were to put my 12 hours of free time

[gentle surge]

could you perhaps elaborate?

[gray isle]

dedicate a % of time to your other hobbies / rest

[vale wigeon]

This has led me to wonder if I should focus all my efforts (10 hours) per day on to math.
well there are other options than throwing 100% of your time on math or throwing 100% of your time on not-math

[gentle surge]

how much time would you reccoment I allocate to mathematics

[gray isle]

entirely up to you

[vale wigeon]

nobody can do your time-management for you

[gray isle]

it's up to you to

balance
your time

[gentle surge]

How many hours would be needed to improve my mathematics significantly

[vale wigeon]

improvement in math is not a function of raw time input

[gray isle]

different for everyone

[gentle surge]

from what Ive given you in the question

[gray isle]

different for everyone

[gentle surge]

how many would you recommend for me

[vale wigeon]

nobody can possibly know that except you

[gray isle]

dependent on how well they understand/interpret/recieve/etc info

[vale wigeon]

• it depends on how you spend those hours

[gentle surge]

say 70%

[sour dove]

This is some solicited anecdotal advice but you'll absolutely hit a breaking point and a burnout point trying to do too much. You're young now so it's much easier to do these things now but that won't last forever.

You have a finite amount of time each day in your life and thus you can only do a finite amount of things. you're also a human being and so you'll have days/hours that you can't dedicate time to doing the things you want to do.

So you have you find out what's important to you and prioritize those things. What I do if find whatever free time you have, allocated a partitioned amount of time for each thing I love doing, and then giving myself some wiggle room/forgiveness if it doesn't get all done.

Also, learning/doing things isn't linearly done. All you can do is allocate the time and do your best to retain it. But things like topology or complex analysis might take some slow, patient time to get the concepts down.

[gentle surge]

I read 10 pages and re-read them till I know Ive mastered it

[vale wigeon]

spending 2 hours drilling 5-digit by 5-digit multiplications is gonna have a different impact than spending 2 hours reading an analysis book

This is some unsolicited anecdotal advice
i mean it kind of is solicited no?

[gentle surge]

Ive read up to the 40th page in Abbotts analysis

[sour dove]

fair enough, wrong word

[gentle surge]

and I reread it each time to make sure I've mastered it

[vale wigeon]

also it appears you're pulling some kind of sigma grindset shit

[gentle surge]

?

[vale wigeon]

if you're planning to stuff your days full of studies, studies and studies, when do you rest?

[gentle surge]

When I sleep

and on sundays

[vale wigeon]

that's it?

[gentle surge]

no?

[vale wigeon]

you'll burn yourself out and not even know it

[gentle surge]

when I eat

My health isnt really concerning, I just want to master math

[vale wigeon]

false

your health is a big concern, much bigger than mathematical mastery

you do not want to fuck up your health

[gentle surge]

This is beside the question, do you think I could master math whilst learning these other skills?

[vale wigeon]

i mean there's nothing that prevents you from doing so

[gentle surge]

or is mastery only acheived by focus

[real gazelle]

Getting a Fields medal is also a ridiculously hard endeavor no matter how much time you spend on it

[vale wigeon]

i mean idk you could like, dedicate mondays to math, tuesdays to chess, wednesdays to piano etc.

[real gazelle]

You can spend your whole life on math and never get a Fields medal

[vale wigeon]

also yeah setting a fields medal as your goal is

questionable

[gentle surge]

I thought about that and it wont cut it

[gentle surge]

I'm sure I could do it as I have this much time and money

[vale wigeon]

i will reiterate that YOU DO NOT WANT TO FUCK UP YOUR HEALTH.

if you burn yourself out, it's gonna take YEARS if not decades to recover from, no matter your millions.

[real gazelle]

There is a lot on this world that time and money cannot get you

[upbeat hornet]

The grandmaster goal is very hard if you want to devote any time to the other hobbies

[gentle surge]

ok assume Im a perfectly healthy huan and I cant burn out

[vale wigeon]

self-contradictory statement

also nobody is immune to burnout

[gray isle]

premise is flawed,
ignore

[real gazelle]

Yeah I'm also gonna say, we're not in the business of handing out medically unsound advice in this server

[gentle surge]

Haha I realised that when I spent 10 hours per day just to get to 2300, so I meant rating of Grandmaster e.i. 2800 rating

[real gazelle]

The two goals of getting a doctorate in mathematics and playing Liszt pieces are definitely achievable

[real gazelle]

I have no personal experience on how hard gaining 10 kg of muscle is

The rest of the goals are life-consuming

[gentle surge]

ah, but can I still do the others?

[ruby current]

Can we just stop for a second and ask if we know of any Fields medalists who are also Chess grandmasters, master piano players, multi-millionaires, and bodybuilders?

[gentle surge]

oh the muscle is easy, just keep doing it and ill get there

[tacit arch]

Is this really the right place for this conversation. There's NO MATH being talked about

[upbeat hornet]

You can't become a grandmaster and a fields medalist at the same time

[real gazelle]

Yeah this "et al" guy does that on top of being on the author list of like every paper I read

Insane output fr

[rose sigil]

bourbaki could have done it

[sour dove]

I want to save this thread

[gentle surge]

I look up to Jim Simon and Isaac Newton who could have achieved such a thing

[tacit arch]

Jokes on you, Discord's gonna rebrand as Y and delete it when Elon buys discord

[gentle surge]

but they, seem to have focused on specific things rather than all round things

[ruby current]

It helps to be practical

[real gazelle]

Also this seems to be more of a discussion question than math help

[surreal meadow]

.pin

[real gazelle]

So I'm gonna recommend you move to one of the discussion channels #discussion or #serious-discussion or #chill

[ruby current]

You can achieve a few of these things (John Nunn)

[gentle surge]

before that, could you give me perhaps a specific number?

[real gazelle]

No

No one can give you a specific number

[gentle surge]

a rough number

[real gazelle]

The answer is just no

[gentle surge]

i see

[real gazelle]

This will vastly vary depending on the person

What you're doing

How you're spending your time

etc

[sour dove]

0-100.

give or take

[gentle surge]

there are only 24 hours in a day

[marsh night]

[real gazelle]

Also I don't like how you're diminishing the impact of burnout

[marsh night]

@gentle surge dame really

[gentle surge]

I sleep 7 hours via polyphasic sleeping and drink massive amounts of coffee

I cant feel burnout

[real gazelle]

That is not good for you.

[gentle surge]

?

[real gazelle]

Anyways

[gentle surge]

?? Leo did it all the time

[marsh night]

Not a flex

[gentle surge]

look where he got

[marsh night]

[gray isle]

you'll crash at some point

[tacit arch]

Man if only medicine had studied adverse effects of too much coffee

[real gazelle]

I'm closing this help thread because the help channels are for mathematics

[vale wigeon]

but Y would it do that

[tacit arch]

Those silly scientists thinking stomachs are made of steel

[real gazelle]

If you want to talk more, then one of the discussion channels is probably better

But it's also vastly entitled to think that having a lot of time and money can just win you a Fields medal

[gentle surge]

only 3 cups

[ruby current]

also luck

[gentle surge]

this means I could spend 10 hours a day on math

that is enough no?

[real gazelle]

Again, many people spend their entire lives on mathematics and never win a Fields medal

[gentle surge]

what am I supposed to say to that

I dont think that can be possible

[real gazelle]

Lol

[gentle surge]

how could you spend your life on math

[real gazelle]

You're supposed to learn some humility and respect

[gentle surge]

and never do anything significant in the field

[sour dove]

it literally happens everyday

[real gazelle]

Winning a Fields medal and doing something significant in the field are VERY different things

There are MANY mathematicians doing significant things in the field every day

There are at most four mathematicians every four years who win the Fields medal

[gentle surge]

a Fields medal is easy to recognise

thats why I chose it as my goal

[rose sigil]

[naive valley]

do you expect that every scientist should be able to win a nobel prize? the fields medal is basically equivalent, except for the added challenge that you have to be under 40 to win it

[tacit arch]

Every 4 years

[real gazelle]

My bad

Anyways

This has gone on long enough

And frankly you're being entitled

.close

[lone heart]

Channel closed

Closed by @real gazelle

Use .reopen if this was a mistake.

[real gazelle]

If you want to continue then move to someplace like #chill

[lone heart]

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[flat roost]

how would i evaluate such a limit?

[flat roost]

not sure what to do

[echo socket]

Bring 1/sqrt(x) inside the other roots

[flat roost]

divide everything by sqrt(x)?

[echo socket]

Yes

[flat roost]

after that do i rationalize the sqrt(4x-1)/sqrt(x)

on the top

[vale wigeon]

no need to rationalize

[fossil latch]

Nah you don't have to

[echo socket]

No, combine them into a single sqrt
sqrt(4x - 1)/sqrt(x) = sqrt((4x - 1)/x)

[vale wigeon]

^

[echo socket]

Same thing with the other term

[flat roost]

ohh

how would i evaluate the limit like that

sqrt((4x-1)/x) + 2sqrt((x+3)/x) right?

[echo socket]

Yes, well, first simplify (4x - 1)/x

[flat roost]

expand?

[echo socket]

Yeah, expand would be the better word

[flat roost]

(4x-1)/x to 4-1/x

[echo socket]

Right

[flat roost]

ah i see

[echo socket]

And what does 1/x approach here?

[flat roost]

0

[echo socket]

Yup, same thing with the other square root

[flat roost]

so its just

4

[echo socket]

Correct

[fossil latch]

Except it's inside a root

[flat roost]

Ah i see

thanks so much guys

[fossil latch]

So √4 becomes 2

[flat roost]

ye

and 2sqrt1 = 2

[fossil latch]

That's it, really

[flat roost]

2+2=4

i see

thank you guys\

.close

[lone heart]

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[craggy spire]

Someone help pls

[craggy spire]

im not sure where to go

with this

[lethal belfry]

!status

[lone heart]

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

[craggy spire]

I just said im not sure where to go with this

[lethal belfry]

yeah, sorry

I think pythogoras's theorm should work

that's one way

[craggy spire]

how would i use that in thiscase

a ^ 2 + b^2 = c ^2

but

what does aspect ratio mean

[lethal belfry]

the ratio of the width to height of a screen

[craggy spire]

ohh

so those would be the legs

[lethal belfry]

legs?

[craggy spire]

of the right triangle

[lethal belfry]

oh. Yes

[craggy spire]

Well now what?

oh

wait i k

23.5 ^ 2 + b ^ 2 = 27 ^ 2

[lethal belfry]

I mean if they have given the width, the aspect ratio is irrelevent , I don't know why they have even given it

[craggy spire]

okay so i found that

[craggy spire]

b ^ 2 = sqrt ( 176.75)

i get this but

[lethal belfry]

yeah,looks right

using ratios you'd get anothe answer, but the value is approximately the same

[lone heart]

@craggy spire Has your question been resolved?

[craggy spire]

how would i solve this

@lethal belfry

help!

help!

help!

help!

i get

12.6

after drawing it out

y u delete it my boy

also 12.6 is wrong

[upbeat gorge]

Try visualizing the scenario and drawing a figure for this

[craggy spire]

i did

i got 2 legs

12 and 4

[upbeat gorge]

Show me the figure

[lone heart]

@craggy spire Has your question been resolved?

[craggy spire]

Sad

[lone heart]

@craggy spire Has your question been resolved?

[vale wigeon]

crying out "help!" several times is not gonna make helpers come any faster

[vale wigeon]

12 and 4 aren't the legs though.

[craggy spire]

thats not true

sorry bro

[vale wigeon]

please don't call me bro.

[craggy spire]

okay.l.

sorry dude

[vale wigeon]

...

[craggy spire]

??

[vale wigeon]

my aboutme literally says not to call me either of those words

[craggy spire]

dog ur tripping

[craggy spire]

https://tenor.com/view/kto-kounotoritoken-kounotori-lbow-storkholders-gif-25676349

[vale wigeon]

i am a woman and i do not like being called "bro" or "dude" or anything masculine like that.

[craggy spire]

okay woman 👍🏿

[vale wigeon]

[craggy spire]

dawg it aint that deep

[vale wigeon]

ok you're just being a dick on purpose bye

[craggy spire]

mb broski

[night geyser]

christ is it so hard to not be an asshole

come back in 48 hours

.close

[lone heart]

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[lone heart]

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[neat oracle]

whats wrong in these methods ??

[lone heart]

@neat oracle Has your question been resolved?

[neat oracle]

<@&286206848099549185>

[rose sigil]

what's going on that second part

shouldn't the minus sign in the middle here be a +

[neat oracle]

yes

[rose sigil]

also don't think this is gonna fix whatever you're worried about but just saying

[neat oracle]

sorry

[tepid drum]

check if ln(5-x) is the integral or derivative of a function with known power series

[vale wigeon]

btw your 5 is very easy to confuse with s sometimes, maybe dont do that

also

[vale wigeon]

these two will give you two different power series centered at different points

x=4 vs. x=0

make up your mind as to which one you want

[neat oracle]

in first case i just substituted (4-x) in series of ln(1+x) and calculated R

in second i substituted x/5 in series of ln(1-x)

[neat oracle]

so why is radius of convergence different in each case

just the centered point should be different

[vale wigeon]

well in this case it's because you run into trouble at x=5

so the interval of convergence cannot extend past that

[neat oracle]

in which case ?

[neat oracle]

i dont get it is one of the method wrong ?

[vale wigeon]

for the function ln(5-x)

[vale wigeon]

no,

[neat oracle]

cuz one gives radius of convergence as 1 but another gives 5

[vale wigeon]

the radius of convergence can and does depend on the point around which the power series is centered!

[neat oracle]

if i write series in each case will they be same ?

term by term basis

[vale wigeon]

no, the series won't be the same

one is in powers of x, while the other is in powers of (x-4)

[neat oracle]

but if i expand it ?

will it be same ?

[lone heart]

@neat oracle Has your question been resolved?

[lone heart]

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[uneven isle]

the question seems kinda trivial but im not sure where i went wrorng to end up with an extra answer

[uneven isle]

.close

[lone heart]

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[hasty bone]

Hi

Had a doubt

[barren portal]

@hasty bone post

[hasty bone]

How is the answer 120°

I do know the property that when theres a triangle on complex no. Plane, and it's 3 vertices are cube roots of unity

Then the angle subtended by the inner traingle at origin is 120

But

Here in This question it isn't specified that there's a triangle who's 3rd vertix is 1

So howd we presume the angle to be 120

[neat oracle]

the third vertex is orgin not 1 isnt that specified ?

the angle between w and w^2 is always 120 regardless of any triangle being made or not

he made it just for visualization

[hasty bone]

Oh okk

Didn't know that

[neat oracle]

u can calculate that

[hasty bone]

At origin particularly?

[neat oracle]

if u know the values of w and w^2

then use the tan inverse formula

to find that they are complex conjugate

and argument is 120 and -120

so it makes sense

[lone heart]

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[hasty bone]

@neat oracle righr

But the 120° will be only at origin right?

Another doubt

[neat oracle]

this channel is taken by solo rn

[hasty bone]

As in?

[neat oracle]

choose a channel from #math help available

[hasty bone]

Ok

[alpine sable]

I was thinking using CBS inequality

But i dont get what I want

[neat oracle]

Technically there are infinite points on which it will subtend 120° and those lie on a circle.

[alpine sable]

I was trying using square of sum of integrals

[neat oracle]

Whats fullform of it ?

[alpine sable]

Again nothing

It is in romanian

I translated it

f,g:[0,1]->R continuous functions and that integral in the second image is 0. Show that inequality the first image

[lone heart]

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[lone heart]

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[lone heart]

Please don't occupy multiple help channels.

[hasty bone]

Why did we take this negative sign , when the final result woulda beem cos π/4 regardless

[lone heart]

@hasty bone Has your question been resolved?

[dense acorn]

well the argument is negative, you're just plugging that in

[lone heart]

@hasty bone Has your question been resolved?

[hasty bone]

Howd u assume that

[dense acorn]

I didn't, it would help if you plotted the number (not z but the complex number inside the ( • )^25

and see where it would end up, so what its argument must be

[hasty bone]

Ok

Also

Why is 6π + π/4 = cos π/4

[dense acorn]

if you mean cosine of both, then think about the angle that forms on a circle

[hasty bone]

Ok

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[alpine sable]

I don't understand how the line C = I relates to the C = f(I) function

The intersect at I = 10

But what does that imply

[minor needle]

consumption should not be higher than income

in this case I believe C = f(I) represents a consumption and line C = I represents an income

[alpine sable]

well

[minor needle]

so we should have f(I) < I which is for I >= 10

[alpine sable]

I am just curious how

we related a completely different function for income

with this one?

is it because it's given as a function in the question itself?

or because it's inherently related

[minor needle]

f(I) could differ due to the country, here they say it's given by C = f(I) = sqrt(20 + 8I)

[alpine sable]

alright

so it's just beacuse it's in the question

[minor needle]

yes

[alpine sable]

makes sense then, appreciate the help, ty

.close

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[fervent ferry]

when doing integration with integrting factors, keeping all the constants of integrations where they should be, i get to the general solution.
in here they are separating the particular and the homogeneous.

[fervent ferry]

fox example here i would put a c at the end.

but in my process i would not have divided yet by t.
i would still have
ctx +k = ct^4/4 + c1

i can sub the k, it would merge witht he other c1 and it becomes
ctx = ct^4/4 + c1
then solve for x
x = ct^4/4ct + c1/ct

becomes
x = t^3/4 + c2/t
c2 is by expanding c1/ct into c1/c * 1/t

so in the end i get to the general solution. but the homogeneous is already there.

i don't understand exactly why they are separating the part and homog.

[mortal trellis]

they don't need to do it in full generality

they just need to find one particular solution

because then they know how all solutions look

it is easier if you can just drop some constants because you just want one solution

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[mortal trellis]

= <@&268886789983436800>

[wanton valley]

2

And pls help channels are not the places to joke around

Write .close to close the channel so that people can use it to get help

[vale wigeon]

do not feed the trolls.

don't troll

[real gazelle]

.close

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[tender anchor]

I thought you just swapped t with x but idrk what to do with the numerator dt

[winter light]

Do you know what the fundamental theorem of calculus states?

[tender anchor]

f(x)=F(x)=F(b)-F(a)

[winter light]

Nope

[tender anchor]

o

f(x)dx = F(b)-F(a)?

[winter light]

Since you need some symbols please use LaTeX or write it on a piece of paper

[tender anchor]

okay

[winter light]

Have you got the statement in front of you or you are just try to remember it? If it's the second go and check it and then come back here

[winter light]

That's not the fundamental theorem of calculus actually, I'm referring to the one with the derivative of the integral

[tender anchor]

o ok hold on i see it in my notes

[covert thicket]

That second one ftc 1

[covert thicket]

Yep

[covert thicket]

This one @tender anchor

[tender anchor]

is that it

[winter light]

This is correct, but that's not what you need in the exercise

[tender anchor]

what do i need?

[winter light]

you need this (the first one) @tender anchor

[tender anchor]

okay

[covert thicket]

Now just put the values from the question

[tender anchor]

1/(6+sqrt(x))?

[winter light]

Yes

[covert thicket]

Yeah

That's it

[tender anchor]

thank you

[winter light]

You're welcome

[tender anchor]

.close

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[wicked ginkgo]

How does this work?

[wicked ginkgo]

How do i find a missing length of a bisector?

[tall talon]

Are you familiar with the pythagorean theorem?

@wicked ginkgo ?

[wicked ginkgo]

a squared + b squared = c squared

[tall talon]

Indeed. What does this apply to?

[wicked ginkgo]

right triangles

so that would mean im looking for A?

or b

[tall talon]

What do you mean?

[wicked ginkgo]

For this, if i substitute the numbers

that would leave me with a^2 + 5^2=9^2

right?

[tall talon]

Yes

[wicked ginkgo]

(i'm using 6 as the example)

ahhh ok thank you

I'll try that and come back

[tall talon]

No problem

[wicked ginkgo]

number 6 would be roughly around 7.4

and number 7 is 8

[lone heart]

@wicked ginkgo Has your question been resolved?

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[elder viper]

Hello

[elder viper]

https://cdn.discordapp.com/attachments/328208536029102081/1134996474715963412/image.png

https://cdn.discordapp.com/attachments/328208536029102081/1134996474996985966/image.png

It can probably simply be stated that k+j != k and thus that’s it’s not in L

If I let j = 0, that equality works though

The pumping lemma has two statements that confuse me involving v, one is that |v| > 0 and the other being that uv^iw is in L for i >= 0

[elder viper]

I’d like to get an explanation as to why doing that would not satisfy one of those two statements.

Is it issue that it would only work if i = 0 and that it wouldn’t past that?…

[real gazelle]

Hey! I'll take a look

[real gazelle]

The pumping lemma says you can choose j to be anything > 0

And it should still be in the language L

Because that's not true for this string, that means that L must not be regular

[elder viper]

Ah, thanks for the enlightenment

I was kind of confused, because one of the condition is |v| > 0 as well

and it feels like if j is always zero, then |v| = 0?

Probably not, that’s likely just something for empty strings in general I guess

[real gazelle]

Yeah if j = 0 then you're basically not changing the string at all (you're pumping an empty string)

So it's like, of course that's still in the language L since the original string was in L!

You only get something new if j > 0

[elder viper]

Alright, thank you very much

[real gazelle]

No problem!

[elder viper]

.close

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[real gazelle]

Sorry just to clarify: i + j also has to be ≤ k as you said

Since k is the pumping length

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[meager terrace]

Dealing with a difficult calculus optimization proble, i'm hoping some1 can help me

Here is what I did:

Basically, i checked my answers with someone else and they converted the 5 degrees to radians, and got only 1.6ish m/s while i got 97m/s. They said 97 m/s is too fast for a kite

To me, that doesn't make sense since the problem definition provides radians as a measurement for both

[limpid spade]

faster than trains

[meager terrace]

so is dtheta/dt only calculated in radians?

yeah i know it makes sense, it's too fast, but im struggling to understand why mine is wrong.

[tardy stag]

derivative of sintheta isn't costheta if theta is in degrees

it's like costheta / 180

(this is, i think, the most compelling reason to use radians)

[meager terrace]

hmm not sure i compltely understand

i took the derivative of costheta which is -sintheta

[tardy stag]

that's only true if theta is measured in radians

[meager terrace]

so where did i go wrong in my work? i need to convert 76 to radians?

because the people i check with, they convert -5 degrees to radians

i guess because its a function of time

[tardy stag]

yeah, or use the derivative formula $\dv{\theta}\cos\theta^\circ = -\sin\theta^\circ\cdot\frac{\pi}{180}$

[ocean seal]

Hayley

[tardy stag]

which is basically the same thing as converting it to radians

[tardy stag]

nothing to do with time, it's just because the derivative of cosine is sine, but only if we're using radians, otherwise it's scaled

[meager terrace]

is it because the unit circle

[tardy stag]

uh

i guess?

it's related to the fact that $\lim_{x\to 0}\frac{\sin x}{x} = 0$ but again only in radians

[ocean seal]

Hayley

[lone heart]

@meager terrace Has your question been resolved?

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[ornate palm]

I don't need help, but I have an upcoming exam and would like some challenging algebra 1 problems for about 7 different topics. If this is not the place for this kind of stuff please tell me.

[misty roost]

I'd ask in #prealg-and-algebra

[ornate palm]

thanks

.close

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[alpine sable]

Is it possible to find the x?

[minor needle]

is this line an altitude?

I mean whether it's perpendicular

[alpine sable]

I dont think so

[minor needle]

or is it right triangle

any more info?

[alpine sable]

Ok so with only these info its impossible to find out

[edgy dagger]

Yes

[alpine sable]

So I doubt the problem I had wants me to do a triangle

[minor needle]

Maybe show us the original problem

if possible

[alpine sable]

Its a physics problem

No idea if its appropriate

To show in a math server

[minor needle]

We don't mind, maybe somebody will be able to help

anyway

[alpine sable]

This is what I did to find the angle where the block loses contact with surface

I was then asked to find the distance x that the block traveled

[minor needle]

well

h = 1m, right

[alpine sable]

Yes

Which is why i tried a right triangle

[minor needle]

and BCD is an arc - quarter of the circle

[alpine sable]

Yeah but the distance is to E

[minor needle]

ye ik, but

BE is a stright line? or you didn't assume that

like you made a triangle

and it doesn't seem so

[alpine sable]

I assumed

Thats defently a mistake

Youre suggesting i make it a quarter of cylinder?

Calculate the arc

Find the x till d?

[minor needle]

well, I got

[alpine sable]

Wait cant i do an arc with e?

[minor needle]

x is approx 4.293?

[alpine sable]

No idea

I was asked to find it

[minor needle]

ah I thought you have the answers

[alpine sable]

Ah wait

If i remember it was 2 something

[minor needle]

I've considered

[alpine sable]

Makes sense

[minor needle]

now just trig

and that's it

[alpine sable]

I will in 10 mins

Doing something rn

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

I did 1cos(76.53)

It didnt work

The answer is supposed to be 1.37m

[winter light]

What is, in a right triangle, the cosine of an angle? Do you remember Sohcahtoa

[alpine sable]

Cosine is adj of the angle

Sine is opposite of angle

Thats how we calculate vector forces

Cos is adj/ hyp

If thats what you wanted

[winter light]

Yeah, so in your drawing, you have hypotenuse x, angle 76.53 and adjacent side 1. Which among cos/sin/tan would you choose?

[winter light]

Yes that's it correct 👍

[alpine sable]

Its what the other guy found

Its not correct

The answer is 1.37m

[minor needle]

are sure about theta solution?

[alpine sable]

Yes because thats the answer in the book

13.5

Degrees

There is probably some curvilinear equation I am missing

[winter light]

Well CE is an arch of a parabola, I suppose the block when it detaches it starts free parabolic motion

Hence CE is not a side of a right triangle

[alpine sable]

Yep

[lone heart]

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[ruby elbow]

I know how to mostly do these

but im wondering how the correct second question answer is 2 leq n leq 12

what they mean by this

"both ice roll 1, which is 2"

and "the bound is inclusive, because we know the probability of obtaining that sum 1/36"

where did they get 2 and 1/36 bruh bruh

and where did they get that 12

[median oar]

Domain is just the values of n you can have

Obviously if you roll 2 normal fair 6 sided dice

The sum of the sides won’t be 1

Since that’s not possible we just say 1 is not in the domain

[ruby elbow]

so

she rolled it 2 times

[median oar]

Well what is in the domain then

[ruby elbow]

x is the domain

and

all possible values of x

are in the domain

[median oar]

n is the domain

Your function is P(n)

[ruby elbow]

yea

sorry I was thinking in general terms

is what i thought you meant

x is (n) in this ocasion

[median oar]

Yea

[ruby elbow]

what do they mean by the "lower bound is 2"

[median oar]

Well what values can n take

[ruby elbow]

well

you cant roll 1.10947109749714

so

it would be interger numbers

1

2

3

4

6

[median oar]

Ok that’s good

Is there another limitation

You rolled a pair of fair 6 sided dice

[ruby elbow]

since its talking about a 6 die

then only 6 sides

[median oar]

And you want the sum of the rolls

[ruby elbow]

so it can only be 1, 2, 3, 4, 5, 6

[median oar]

Nope

[ruby elbow]

hm

wait

can she roll mutiple times?

[median oar]

You rolled a pair of dice

[ruby elbow]

ohh

pair

mb

[median oar]

And you’re recording down the sum

[ruby elbow]

im blind

so that's how she got

12

because the the max

you can get

when rolling

and

bro

...

[median oar]

Yep

[ruby elbow]

yep

[ruby elbow]

i didn't see **pair ** of dice

i thought she was only rolling one

maybe I should work on my reading skills

[ruby elbow]

thanks for helping again. I think I'm blind

[median oar]

It is definitely tricky trying to do maths without reading the question

[ruby elbow]

or I should read more carefully

[median oar]

Can’t say I haven’t done that before

[ruby elbow]

cant do maths if you can't read

I'm use to speed reading through books

so

I do the same for everything

not paying attention to deletes

gonna have to start doing that

[ruby elbow]

But thank you anyways

.close

[lone heart]

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[grand hornet]

help

[grand hornet]

how does this happen

its getting simplified

and the 16 just dissapears

wdf

[tardy stag]

if we just look at the numbers themselves

$\frac{16\cdot9}{4} = \frac{\cancelto{4}{16}\cdot9}{\cancelto{1}{4}} = \frac{36}{1}$

[ocean seal]

Hayley

[grand hornet]

oh thanks that clears it up

i was using the negative exponent rule and flipping the fraction before simplifying the numbers

[tardy stag]

you should be able to do it in any order

but some of them are easier to work with than others

[grand hornet]

nah that wouldnt work tho

if you flip the 16 and 4 it doesnt simplify the same

[tardy stag]

well keep in mind that the exponent only applies to those variables

like on the top it's $16(a^{-10/3})$, not $(16a)^{-10/3}$

[ocean seal]

Hayley

[grand hornet]

yes ik

but ur saying i could do it in any ordder

[tardy stag]

yeah

[grand hornet]

if i flipped the 16 and 4 before using the negative exponent rule then it wouldnt simplify the same

i would have 36 over 16

[tardy stag]

you can't flip the 16 and 4 though

[grand hornet]

oh wait

[tardy stag]

those don't have neg exponents

[grand hornet]

i see what you mean

so the coefficient doesnt get flipped when using the negative exponent rule?

just the variable

[tardy stag]

right

since what you have is really like $16\cdot a^{-10/3}$ up top

[ocean seal]

Hayley

[tardy stag]

so they're separate things

[grand hornet]

oh ok thanks

.close

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[grand hornet]

How does that hpn

it dont make sense at all

[median oar]

There’s a typo?

[grand hornet]

no like thats just simplifying

"Leave in radical form"

like what

[grand hornet]

are you sure its a typo

this is the full thing

[median oar]

a just went to the top without getting a - in the exponent

[solemn geyser]

That second line is false it normally should be divided by a^3

[grand hornet]

so what would the correct answer be?

[lone heart]

@grand hornet Has your question been resolved?

[grand hornet]

<@&286206848099549185>

[solemn geyser]

It will be the same but instead of that thingy being multiplied by a^3 it will be divided by it

[grand hornet]

so:

36c^8/a3 times ^3sqrt(b/a)

is that correct

[solemn geyser]

Yes

[grand hornet]

okay thanks

.close

[lone heart]

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[hidden geyser]

How do I write the domain for a removable discontinuity like this again?

[median oar]

I like to use set notation

x ∈ ℝ \ {5}

[hidden geyser]

I’m not a math person and haven’t done this in a while so tbh I don’t know what that means

[median oar]

You could just do all real x ≠ 5

[hidden geyser]

(-infinity,x) is how I write mine

[median oar]

Ah

[hidden geyser]

She gets pissed when I write all reals

Idk why

[median oar]

Oh wait

Sorry I misread the question

The domain is just (-inf, inf)

The function is defined for every x on the reals

[hidden geyser]

Ah ok

So how is it considered a discontinuity

[proven leaf]

because the function isn't continuous at x=5 but is defined

[hidden geyser]

If it’s not continuous at -5 why is the domain (-inf,inf)

[royal socket]

because it's still defined at -5

It doesn't have to be continuous to be defined

[hidden geyser]

Prob asked wrong then

[royal socket]

OH

"On which function is continuous" is different from domain

[hidden geyser]

(-inf,-5) U (-5,inf)?

[royal socket]

Sorry it was cut off here but you said domain 😅

[royal socket]

Yes

[hidden geyser]

Yeah I didn’t know the difference at first

[royal socket]

Dw

Question one should be easy then

[hidden geyser]

I skipped odds

[royal socket]

O

Might as well try them (if u wanna(

[hidden geyser]

But prob same thing except -5 it’s 1?

One with bracket one without

[royal socket]

Not exactly the same

[hidden geyser]

(-inf,1) U [1,inf)?

[royal socket]

Yes

We boogie

[hidden geyser]

Awesome 😎 my professor is going super fast through the calc review but 2/3 of the class doesn’t even remember trig stuff let alone the calc so it’s been a struggle

[royal socket]

Trig is so important for calc

Bless them

[hidden geyser]

Yeah I would always just relearn it before the exam and then forget it right after

Rip

[royal socket]

I guess if you want them to stick you'll just have to do a lot of problems until you're fluent

I forget them a lot of times as well and even I think I'm good at calc lol

[hidden geyser]

The thing is I don’t need math for anything I want to do later on and I only need 1 calc class, I have no love for math (except stats, love stats) so I just want to get it over with 😭

[proven leaf]

aww math is awesome you just need someone to teach you right :)

[hidden geyser]

I came from a pretty poor rural school so yeah the education wasn’t the best, but I always get math related anxiety and idk why

[proven leaf]

or rather in a way that works better for you, esp if you don't like lecture based learning

[hidden geyser]

Like I’m fine doing the homework and studying but once I sit for the exam I get scared before I even start and then it goes downhill from there even though I usually know what I’m doing, doesn’t happen with other subjects tho

[proven leaf]

remember math doesn't change before you take a test just practice and try to find a way that you understand it. I love math because there's usually one solution but many different ways to approach it :)

[royal socket]

at least it's not like english where you're right or wrong or both or neither at the same time and

(laughs in CH)

[proven leaf]

or there's 131 different ways to define "set"

[royal socket]

😬😬😬

[proven leaf]

"What is the definition of set in the given context?"

[royal socket]

one thing that annoys me about maths is the terminology

why does "normal" mean 18361972 different things in different contexts

maybe we shouldn't be having a convo in a help section but oh well

[proven leaf]

nahhh it's fine

[hidden geyser]

Ok but the thing about English is that you’re always right if you explain it well enough

But also it’s so subjective

I’ll get all positive feedback from the professor yet never 100%

How does that even make sense ?

[royal socket]

Ikr what a moment

I've heard it's a blessing to get over 70% in an English uni course lol

[hidden geyser]

Really depends

I have a 95% rn

[royal socket]

Hacker

[hidden geyser]

But I’m not going to take high level English cuz it’s not my major

I’m neuroscience and/or psych rn, still deciding

Prob the higher you go the worse it gets

[royal socket]

Well I mean I don't have to study English next year cuz in the UK it's not mandatory for ur last two years of high school

[royal socket]

Damnnnn

Good luck with whichever you choose

[hidden geyser]

Lmao for us math isn’t required but English is

[royal socket]

😭

[hidden geyser]

I haven’t seen some of the stuff I’m learning in so long lmao

[royal socket]

I'm like full on done with english

It's crazy how i probably won't study it for the rest of my life

But it's therapeutic to think about that

[hidden geyser]

Are you going to study in the UK once you get to college?

[royal socket]

is a college different from high school

[hidden geyser]

College is university

[royal socket]

Ah

Yeah I'm gonna stay in the UK for uni

[hidden geyser]

Good because if you went to a US one they’d make u take writing again lmao

[royal socket]

😭😭

[lone heart]

@hidden geyser Has your question been resolved?

[lone heart]

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[tranquil pivot]

Help

What is this

Lmfao

[magic haven]

what a beautiful name btw

[tranquil pivot]

Thanks

[magic haven]

:D

sorry im preoccupied i cant help you rn i just wanted to tell you

[tranquil pivot]

Lmfaoo ok

[serene junco]

Hey

Have you tried anything yet?

[tranquil pivot]

Nope

Dk how to solve w out ratios

If they gave circumference then maybe

[serene junco]

But they're just asking for the fraction of the circumference taken up by arc AB

like if it was pi, that's 1/2 the circle

if it was pi/2, that's 1/4 the circle

etc

[tranquil pivot]

Ohhhh

Lmao I made it complicated

.125 then

45 degrees outta 360

[serene junco]

well 45 degrees = pi/4

they said it should be less than pi/4

so you want something a bit smaller

there's more than one right answer

anything between pi/6 and pi/4 will work

[tranquil pivot]

Yeah

[heady egret]

we don't know anything about diameter

How do we know the circumference

AB

@tranquil pivot

Are you here Abdullah?

Opposite the 30 degree angle can be 1cm circumference

or 5

or 163622

because we don't know the total circumference of the circle, (hence we dont know its diameter)

value range of x is (0,∞)

you write there like this lol

[lone heart]

@tranquil pivot Has your question been resolved?

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[icy jewel]

i forgor how to use this pls help

[icy jewel]

i forgor summation notation :(

[proven leaf]

https://i0.wp.com/www.columbia.edu/itc/sipa/math/images/01/image008.gif

[icy jewel]

so is i the number u multiply w by each time

oh wait

im dum

its the lower limit

thx

oh

wait what is it then

[proven leaf]

the index of summation :)

[icy jewel]

oooooooh

cool thx

!close

.close

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[lament basalt]

So I don't get why did the angle b turned clockwise as it says in first statement instead of like counterclockwise or anything

It's about proving the sum difference identity

[tardy stag]

clockwise because it's negative

[lament basalt]

Ohh since bcs the radius of circle turns counterclockwise right?

[tardy stag]

so $\beta$ measured clockwise is the same as $-\beta$ measured counterclockwise

[ocean seal]

Hayley

[tardy stag]

yeah CCW is the default