help-0

[errant dagger]

1, 2, 1, 2, 1, 2, 1

[barren portal]

do you see it reaches one?

[errant dagger]

ye

[barren portal]

but wasn’t the case earlier

the way you can reason out why (a,m)=1 one is to see it as a diaphantine equation

$2x \equiv 1 \pmod{3}$

[ocean seal]

.doc

[barren portal]

this is really asking is there a number you can find x, such that you multiply and get to 1 modulo 3

[errant dagger]

yeahh

i see that

[barren portal]

which is equivalent to asking, is $2x-3y=1$ solvable?

[ocean seal]

.doc

[barren portal]

Do you see how the equation is the same thing? multiples of 2 and remove multiples of 3 to get the remainder

[errant dagger]

hmm

I see how that equation would degrade to 2x congruent 1 mod 3

by taking mod 3 of both sides

[errant dagger]

how would I know if this is solvable though?

or is this from that bezout identity thing

[barren portal]

yes

see, if you can find two integers such that this happen

the core of this lying in a simple intution

suppose $2x-4y=1$ can you solve?

[ocean seal]

.doc

[errant dagger]

well

it seems impossible no?

LHS has a factor of 2

RHS has no factor of 2

[barren portal]

This is just asking is $2x \equiv 1 \pmod{4}$

[ocean seal]

.doc

[barren portal]

or can you reach one using 2?

[errant dagger]

i see

[barren portal]

There you go the notion of gcd

You can always factor the gcd out

so it will always be multiples of gcd

[errant dagger]

but the RHS is not a multiple of the gcd

so its impossible?

[barren portal]

yes, you can never reach 1

because the equation will always be multiplie of the gcd, here it is 2

[errant dagger]

i see

oki that does make some sense to me thank u 🙂

[barren portal]

The take away is that, gcd is the smallest possible step

and rest are multiples of gcd

[errant dagger]

yes

I appreicate that 🙂

[errant dagger]

i will be back here to ask about these kinds of questions

cus i didnt understand how to do them either

thank u for now 🙂

wait

what would I do if there was a GCD that wasnt equal to one

say

[barren portal]

You cannot simply find it

[errant dagger]

find 6^10 mod 36 or smth

[barren portal]

$2^x \equiv 1 \pmod{4}$

[ocean seal]

.doc

[barren portal]

suppose this is the case

[errant dagger]

sure

[barren portal]

This is really asking. can powers of 2 reach 1 modulo 4

notice, you can always reduce those powers to something modulo 4

right?

[errant dagger]

h,

could u elaborate on that please

[barren portal]

Can you see taking power as some multiplication?

[errant dagger]

yeah

[barren portal]

$2^{10}=2 \cdot 2^9$

[ocean seal]

.doc

[barren portal]

this is really it right?

[barren portal]

compare with this now

can 2^9 be that x?

simply no, there cannot be any integer

[errant dagger]

are u asking if 2^9 can be 1 mod 4?

[barren portal]

$2x \equiv 1 \pmod{4}$

[ocean seal]

.doc

[barren portal]

This is what we have

[errant dagger]

wait what

[errant dagger]

this is different no?

ones multiplication ones power

[barren portal]

still it’s some integer multiplication right?

[barren portal]

Do you see there is no x such that this works?

[errant dagger]

sure

no 😭

sorry im very lost

can we kind of start again from the top

[barren portal]

Alrighty

$2^x \equiv 1 \pmod{4}$

[ocean seal]

.doc

[barren portal]

This is what you have at the beginning

alright?

[errant dagger]

yes

[barren portal]

$2 \cdot (2^{x-1}) \equiv 1 \pmod{4}$

[errant dagger]

sure

[ocean seal]

.doc

[barren portal]

do you see that, now i’m just doing multiplication?

2^{x-1} is just some integer

so it’s really just a multiplication with 2

[errant dagger]

yes

I get that

so you're just calling 2^(x-1) some other variable

[barren portal]

The reason why i’m doing it is, i can use the notion of bezouts and stuff if i have a multiplication equation

[errant dagger]

i see

[barren portal]

$2x \equiv 1 \pmod{4}$

[ocean seal]

.doc

[barren portal]

so can 2^(x-1) be that integer which solves this?

[barren portal]

This is the heart to see, if it reaches 1 modulo 4, and we saw that it’s not the case

There is no multiple of 2 which reaches 1 modulo 4

[errant dagger]

okkkk i see

[barren portal]

2^{x-1} is simply just a multiple of 2

and sure it won’t reach 1

[barren portal]

Do you see 2^{x-1} being a multiple of 2

[errant dagger]

mhmm

[barren portal]

It’s evaluated to some integer right?

and then you multiply 2 with that

[errant dagger]

yee

[barren portal]

but we already know, no integer multiplied to 2 will get us to 1 modulo 4

[errant dagger]

yees

[barren portal]

Well, the idea is to compare solvability of linear congruence of the form $ax \equiv 1 \pmod{m}$

[errant dagger]

yea

[ocean seal]

.doc

[barren portal]

If there is a power that works, then simply that will be our x, or solution

^^ read this again

[errant dagger]

okiiii 🙂

thank u

[barren portal]

Hopefully you get the notion

There is far more beauty in it

Hope you will see it on the go

As a ending note, i’ll ask you this simple story

Suppose there is a store owner who sells milk, and they only have cans of size 4 and 6, ie they can use those cans to give milk,

suppose I need 2 liters, he will first take can 6 and pour it to can 4 so the remaining is 2

now the question is can that store owner give me 13 liters (hint start with 1)?

I gtg, you can dm me the answer

[errant dagger]

i wil think on it ty 🙂

.close

[lone heart]

Channel closed

Closed by @errant dagger

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[next osprey]

how is it 1/6

i thought it'll be 2pi / 6 pi

[fickle sandal]

tanx has a period of just pi

not 2pi

[next osprey]

why?

so its only 2pi for sin,cos,csc,and sec, but not tan and cot?

[fickle sandal]

yes

[next osprey]

hmm

is it just something i should know or is there a way you can show it?

[fickle sandal]

i would say to just know it
but the best way i can explain it is if you plot sinx and cosx together:

what they look like from x=0 to pi is the same as from pi to 2pi but negative

[next osprey]

hmm

bruh

it was wrong

[fickle sandal]

and then when you divide sinx/cosx to get tanx, the negatives cancel out to give the same result

[next osprey]

i belive you

bc other people told me the same thing

[lone heart]

@next osprey Has your question been resolved?

[next osprey]

<@&286206848099549185>

[lone heart]

@next osprey Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rain cliff]

<@&286206848099549185> Help me solve this question

[alpine sable]

!15min

[lone heart]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[alpine sable]

do bruteforce

[rain cliff]

whats that?

[alpine sable]

10!=?
9!=?

like that like that

[rain cliff]

oh ok

so just like test something and if it doesnt work try something bigger or smaller accordingly?

[alpine sable]

exactly

[rain cliff]

ok thanks

that makes sense

sorry for wasting your time

im still new to this factorial stuff

[opal jolt]

well, you would start from the bottom up, but other than that yes, what sen said. Brute force.

[rain cliff]

i also have another question

[opal jolt]

you'd start by 1! = 1
2! = 2
3! = 6
4! = 24
5! = 5*4!
6! = 6*5!...

the other way would be factoring 40320, but that's unnecessary effort. Brute force is a lot faster in this case

[exotic belfry]

which primfactors does 40320 have?

[opal jolt]

which other question?

[rain cliff]

@opal jolt whats the easiest way to answer this question: What is the difference between the sum of all the even numbers and all the odd numbesr up to 50?

[opal jolt]

okay, have you studied arithmetic progressions?

or sequences?

[rain cliff]

no

i wont tell you hat grade im in but its pretty low

what*

so yeah

[opal jolt]

okay. Arithmetic sequences are sequences in which each term is the previous plus a fixed number, d

[rain cliff]

alright

[opal jolt]

in this case, the first term would be either 1 or 2, and the difference would be d=2

you got one sequence for the odds and one for the evens

[rain cliff]

ok

[opal jolt]

actually, if you havent studied this i'm pretty sure they want you to do it the other way.

i'm gonna write the first terms of each list:

1 + 3 + 5 + 7...
2 + 4 + 6 + 8...

first line would be the sum of the odds
Second would be the sum of the evens

[rain cliff]

yes

[opal jolt]

now, how much more are you adding, for each term, on the evens?

[rain cliff]

2?

[opal jolt]

look at each term

look at the first term of each sum. What's the difference between them?

[rain cliff]

1

[opal jolt]

now repeat the same for the second term. What's the difference between them?

[rain cliff]

1

aswell

[opal jolt]

and can you see how it happens for every term?

now, how many terms do you have? In other words, how many odds do you have until 50, and how many evens?

[rain cliff]

25 and 25

so the difference has to be one?

[opal jolt]

no. Look how your difference is one per term

so if you have 25 terms, what will your difference be?

[rain cliff]

25?

because its one more for every term?

.close

[lone heart]

Channel closed

Closed by @rain cliff

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

I need help you have numbers and - and all that u place the numbers on the lines and u put the pluses and all that in the circle. The clear box means deviding

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

Channel closed

Closed by @brittle blade

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[short pumice]

Can somebody help me with exercise 12?

I found the derivative in the area with number 11 and then I equaled it to zero but that yields no solution but in the options it seems like there should be one

[glacial patrol]

Yeah I think thw problem itself is wrong

U could try looking up the errata of the book

[short pumice]

Ok thx

.close

[lone heart]

Channel closed

Closed by @short pumice

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[twilit gull]

How did we get the 2nd last step?

[nimble fern]

cos(C/2)=cos(-C/2)=sin(pi/2-C/2)=sin((pi-C)/2)=sin((A+B)/2)

[twilit gull]

oh yes, got it

thanks for the assist.

.close

[lone heart]

Channel closed

Closed by @twilit gull

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fallow solar]

I guess this problem is wrong

Cuz all i get is a 2 variable equation

[vale wigeon]

you know that T=100 at t=0 and T=80 at t=2

this gets you two equations in two variables A and k

[fallow solar]

Ahhhhhhhh

The water is boiling means that the temperature is 100

[vale wigeon]

yes

[fallow solar]

Aha thx

.close

[lone heart]

Channel closed

Closed by @fallow solar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[long solstice]

https://cdn.discordapp.com/attachments/1081837589780234241/1156479766375968789/image.png?ex=651670b6&is=65151f36&hm=bb59a7032536e48bae85c75fae4ffd56b82da0790280aff8d99e1efdf795cadc&

[long solstice]

I found this on a random note online, but what does this actually mean

my inference: high value is right of the mean (some x standard deviations away where x is an int) and low value is left of the mean (some x std away from mean in the left direction where x is an int)

but is it really that?

[solemn juniper]

It looks like they're making an interval centered on the mean

So yeah your interpretation seems about right

[long solstice]

but okay now that i think about it

x doesn't have to be an int?

[solemn juniper]

Nope, and it very often isn't

But that doesn't matter

[long solstice]

okay sure, the note is kinda stupid which is why i asked

thanks

.close

[lone heart]

Channel closed

Closed by @long solstice

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[strong crow]

how would you show that for any two vectors x, y in R^2, |x + y| <= |x| + |y|, using the law of cosines??

[vale wigeon]

|x+y|^2 = |x|^2 + |y|^2 + 2 |x| |y| cos(theta), presumably

[strong crow]

yeah i got that but not sure how to go from there

[ruby current]

can you bound cos(theta)?

what’s an upper bound?

[strong crow]

-1<=cos(theta) <= 1

[ruby current]

use the latter inequality with the equation Ann gave

[strong crow]

oh i see

got it, thanks

.close

[lone heart]

Channel closed

Closed by @strong crow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[scarlet drum]

find n so \sqrt{(2^n+3^n+4^n)} is a rational number

[scarlet drum]

$\sqrt{(2^n+3^n+4^n)}$

[ocean seal]

xxOctavianxx

[scarlet drum]

n is natural

[minor needle]

1?

[scarlet drum]

so basically find n so that ${(2^n+3^n+4^n)}$ is a perfect square

[ocean seal]

xxOctavianxx

[minor needle]

like the most obvious one, without doing calculations so far

[scarlet drum]

That's right

But it might not be the only one

that's the issue

i gotta calculate to be sure it's the only one or something

[mortal trellis]

maybe mod 4 or mod 9?

[scarlet drum]

What do you mean?

[mortal trellis]

do you know modulo?

[scarlet drum]

yeah like 5%2 is 1 for example

[mortal trellis]

yes so 5=1 mod 2

[scarlet drum]

alright and how would that help?

[mortal trellis]

the point is that if you for example take mod 4, all squares can only be equal to either 0 or 1 mod 4

which gives you a restriction on what n has to be

and maybe you also get a restriction from mod 9

(9 being interesting here cause of the case n=1)

[scarlet drum]

<@&286206848099549185>

[lone heart]

@scarlet drum Has your question been resolved?

[charred summit]

,wolf calc log_2(3)

[ocean seal]

Results provided by WolframAlpha

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

Requested by sherif_player

[charred summit]

So we can do this

$$\sqrt{2^n + (2^{\log_2(3)})^n + (2^2)^n}$$

[ocean seal]

Sherif Player

[charred summit]

Maybe take the 2^n as a common factor

$$\sqrt{2^n(1+2^{(\log_2(3)-1)n}+2^n)}$$

[ocean seal]

Sherif Player

[lone heart]

@scarlet drum Has your question been resolved?

[scarlet drum]

i'll see after i finish clases

thank you anyways

.close

[lone heart]

Channel closed

Closed by @scarlet drum

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lusty socket]

Is the language of valid Python programs, p, such that p accepts all inputs recognizable?

[lusty socket]

It can't be decidable since if it were decidable then it's complement would also be decidable and the complement can not be decidable

[lone heart]

@lusty socket Has your question been resolved?

[lusty socket]

<@&286206848099549185> does anyone know this ;-;

[gusty gorge]

I don't think it's recognizable; given a Python program p, how might you figure out whether it accepts all inputs? won't you have to try all inputs in general?

[lusty socket]

yeah that was my intuition

But universal turing machines are recognizable and they accept all inputs right?

I've become very confused thinking about this for like 2 hours straight over and over >.>

[gusty gorge]

ahh okay it might be recognizable

lemme think

I'm pretty rusty on this, since it's been years, so take everything I say with a grain of salt

[lusty socket]

i appreciate the help regardless, my brain finds this problem undecidable lol

[gusty gorge]

is the set of all univeral turing machines recognizable? that's a little surprising

[lusty socket]

http://www.cs.columbia.edu/~aho/cs3261/Lectures/L16-Universal_Language.html

I'm not sure about the set of all universal turing machines

wait maybe i'm just dumb and read this wrong and got more confused

universal language is recognized by a universal turing machine

but the universal turning machines idk

[gusty gorge]

I think the "universal language" referred to here is the language of all TM-input pairs such that the input is accepted by the TM

in that case, it's recursively enumerable, because you can just run it through the universal TM and see whether it accepts

[lusty socket]

i'm also confused as a proof i've seen for showing that if you have an unrecognizable set and you take the union of it and it's compliment you can prove its decidable by some program that always says yes

but I guess the program that says yes in this case is not decidable, i just got twisted on that

[gusty gorge]

well yeah, if you union a set with its complement, then you get everything

[lusty socket]

yeah that confused me into thinking that the thing that says yes to everything is decidable

but it cant be right

[gusty gorge]

programs by themselves are not "decidable" or 'undecidable"

decidability is a property of sets of strings, i.e. languages

[lusty socket]

for any language or it breaks everything I mean

I think I should have just slept haha, you've cleared this up though this set of languages must not be recognizeable

it would take infinite time to determine whether the language that accepts everything would accept everything so it cant be decidable or recognizeable

[gusty gorge]

yeah that's my intuition for it

[lusty socket]

what if there was a language that accepted everything in 10 steps

it's still undecidable as you would have to check every input which is impossible?

[gusty gorge]

wdym by that? the language of programs that accept everything within 10 steps?

[lusty socket]

wait i confused the problem

that one is the language of strings p->i such that p accepts i after running for 10 steps

not accepts everything

if it accepted everything it would also be unrecognizable as it woud be impossible to determine

but that one is recognizable and not decidable

[gusty gorge]

actually, I'm not sure about that last statement; if you have a limitation on the number of steps, the number of possible configurations of the turing machine is finite

[lusty socket]

hmmm

[gusty gorge]

basically, you can feed all of the inputs in, but they won't matter past a certain length, because the TM can't get to them

[lusty socket]

are you saying it could be decidable. or that it might not be recognizable?

[gusty gorge]

I'm saying that the language of <TMs that accept all inputs within 10 steps> is decidable

[lusty socket]

yeah that makes sense actually, if it loops we can reject it or if it ever passes 10 or halts prior

sorry i'm a bit slow it's 6am and I haven't slept

[gusty gorge]

well, it's not as simple, because it's not whether the TM accepts a particular input within 10 steps

[lusty socket]

oh yeah It's exsactly 10

[gusty gorge]

it's whether the TM accepts all possible inputs (which is an infinite set) within 10 steps

but it turns out to decide this, you only have to try inputs of length 20 or lower or something like that

[lusty socket]

ohhh you're talking about the infinite one

yeah that makes sense I think

i'm going to head to be now, thanks for the help!

[gusty gorge]

have a nice sleep

[lusty socket]

🙂

.close

[lone heart]

Channel closed

Closed by @lusty socket

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cinder sundial]

What is this

Is it “prime” symbol

What is the symbol’s name

[median oar]

Apostrophe

And it’s an English thing

[cinder sundial]

Thank you

[dim oasis]

It’s an apostrophe, comes after s when describing something that belongs to multiple people, or often in place of [‘s] for names that end in s

“The student’s parents” are one student’s parents
“The students’ parents” are all of the parents of students

For a name that ends in s you often just do ‘ instead of ‘s

[median oar]

Stundets

[dim oasis]

Like James’ cat, as opposed to James’s cat

I think both are correct and used interchangeably

But also I’m a math major not an english major so I have no idea what I’m talking about

Achillies’ Heel is a phrase usually meaning a weak point

Reference to this dude Achillies who I can only assume had a debilitating issue related to his heel

[cinder sundial]

My textbook gives in that nouns that follow with -es, -is at its end, should use apostrophe for them possessive

[pliant cedar]

lol this has become an english thing

[gusty gorge]

I think most style guides actually encourage you to write things like James's

[pliant cedar]

in a math server 😅

[dim oasis]

[gusty gorge]

grammar is definitely a concept in math though

[dim oasis]

I wouldn’t know, I haven’t thought about grammar and lit since freshman year of college

[gusty gorge]

is english grammar a context-free grammar?

[dim oasis]

TLDR it’s a stupid thing that the english language does, like every single other thing this stupid language does lol

[cinder sundial]

How do we distinguish whether a word’s possessive should use the apostrophe form. For the word “conscience,” it is hard to tell whether that is a so called “ancient word” used the apostrophe for its possessive

[wheat isle]

Am I tripping or is blud doing english in a math server

[dim oasis]

In general, english follows very rigorous rules that are sometimes also completely ignored for no reason

Also

This is a math server

This was only related to math when you thought it was the derivative of Achillies

[cinder sundial]

I see, thank you so all the information above

[dim oasis]

[cinder sundial]

I will close the channel now, as my question is solved

.close

[lone heart]

Channel closed

Closed by @cinder sundial

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[slow dagger]

i need some help with this -_-

[lone heart]

@slow dagger Has your question been resolved?

[slow dagger]

some <@&286206848099549185> ?

[lone heart]

@slow dagger Has your question been resolved?

[forest cobalt]

!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

[lone heart]

@slow dagger Has your question been resolved?

[slow dagger]

oke idc

[lone heart]

Channel closed

Closed by @slow dagger

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[quartz crow]

I was wondering how I should go about proving this statement: 'There is no positive integer k such that for every positive integer a, a2 +15a+k is prime.'

[lone heart]

@quartz crow Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sleek finch]

hello, i am currently learning matrices, and have just encountered something called a vertical bar/line when solving an equation system, what does that line mean and what are the other uses for it?
here's an example of what i mean:

[worn fox]

its denoting that this is the augmented matrix of a linear system, rather than being interpreted as a matrix in its own right acting on vectors

[sleek finch]

what is an augmented matrix?

[sleek finch]

"being interpreted as a matrix in its own right acting on vectors"
can you explain what did you meant here?

[worn fox]

well a matrix is also something you multiply a vector by to get a new vector

but thats not how you interpret augmented matrices

[sleek finch]

i see, thanks 🙂

matrix row manipulation cannot be done on "normal" matrices, unless i want to change the whole matrix, right?

@worn fox can you anwer that please 🙂

[worn fox]

it depends what you are doing

there are things that row operations preserve and things that they do not

[sleek finch]

when solving a system of equations using gaussian elimination, does it preserve? (my answer would be yes)

[worn fox]

it preserves the solution set yes

[sleek finch]

alright thanks 🙂

.close

[lone heart]

Channel closed

Closed by @sleek finch

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[crude marten]

huys

[crude marten]

I need help with this proof, I can't figure out how it ends up like this

this is my work so far

once we get the 3 components, then what

[worn fox]

Well you want to make it look like the x component of (U' x V) + (U x V')

So probably a good idea to write out what that looks like

[crude marten]

Ok

@worn fox

I looked at a friend's lecture notes

This looks so wrong

(uv)' = (u'v + uv') no? why is there a (negative) + (negative) shouldnt it be the opposite

[worn fox]

it is wrong so do it yourself

[crude marten]

I am

Im here but now what

[worn fox]

.

[worn fox]

.

[lone heart]

@crude marten Has your question been resolved?

[worn fox]

?

[crude marten]

Ok cuh I got it

took a while but I understand now

just had to group them together to see the pattern

[worn fox]

Don't use a dot when you mean an x for cross product

[lone heart]

@crude marten Has your question been resolved?

Channel closed

Closed by @crude marten

Use .reopen if this was a mistake.

[crude marten]

where do u mean this

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[daring dirge]

Eish I last did this in matric gimme a couple min

-2x^2+16x-3y+40

I could be so wrong I last did this kinda math like 3 years ago

Yeah

Ima write it out and send pic

[lone heart]

@peak lodge Has your question been resolved?

[daring dirge]

It’s correct

[daring dirge]

This is wrong

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hardy hedge]

This is a reimann sums question. I believe this is the correct answer but I'm not sure. My work is shown in the image

[hardy hedge]

im assuming there is no way to get the function of the graph. At first glance i thought it was a zoomed in square root function

.close

[lone heart]

Channel closed

Closed by @hardy hedge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[daring dirge]

Np bro

[lone heart]

Please don't occupy multiple help channels.

@daring dirge Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[winter linden]

Im having difficulty solving simultaneous equations including a quadratic in one of the equations.

[winter linden]

x^2 + xy + 2y^2 = 4
2x + 3y = -1

[fickle sandal]

use the second equation to make the first equation purely in terms of x

[winter linden]

should i square the second?

[fickle sandal]

$3y=-1-2x$

[ocean seal]

chlamydia

[fickle sandal]

$y=\frac13(-1-2x)$

[ocean seal]

chlamydia

[winter linden]

a bit confused

this is making it in terms of y no?

[fickle sandal]

yes

[winter linden]

ah u said x

[fickle sandal]

and then you can substitute into first equation to change it all to x

[winter linden]

in my book it says to square the second equation

so 4x^2 + 9y^2 = 1

not sure what to do with the xy from the first tho

[mellow knoll]

that book method will likely work, but imo the substitution method is far simpler & easier to spot

[winter linden]

also can this be written as (-1-2x) over 3? @fickle sandal

the substitution is confusing me

[mellow knoll]

yes

[winter linden]

im only used to the squaring method

[winter linden]

yeah i cant do it this way

[lone heart]

@winter linden Has your question been resolved?

[winter linden]

<@&286206848099549185> Im still stuck on what I should do after i square the second equation

x^2 + xy + 2y^2 = 4
2x + 3y = -1

sq bottom line to give me 4x^2 + 9y^2 = 1

but when i compare the 2 lines

im missing an xy

x^2 + xy + 2y^2 = 4
4x^2 +9y^2 = 1

[mellow knoll]

you squared the second equation wrong

$(2x + 3y)^2 \ne 4x^2 + 9y^2$

[ocean seal]

Frog_Man

[mellow knoll]

$(2x+3y)^2 = 4x^2 + 12xy + 9y^2$

[ocean seal]

Frog_Man

[lone heart]

@winter linden Has your question been resolved?

[winter linden]

oh

Must of taken it down wrong then

thanks

[lone heart]

Channel closed

Closed by @winter linden

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[maiden swift]

how do i write this in an equation

i wrote it as f(x)=x(x+1)(x-3)^2

[winter light]

Yeah, also all multiples of it work as well

[maiden swift]

wdym

[winter light]

So in general the answer is f(x) = ax(x+1)(x-3)²

Where a is a real number

[maiden swift]

so i can write the same thing but with a 4

in front of it

or 5 in front of it

and so on

[winter light]

Yep

[maiden swift]

okok

ty

[winter light]

You're welcome

[maiden swift]

how do i close the channel

.close

[lone heart]

Channel closed

Closed by @maiden swift

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

!show

[lone heart]

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

Channel closed

Closed by @cosmic dew

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

Question: Imagine I flip 100 coins in a sequence, and you need to guess the sequence. You are allowed to ask one yes/no question. What do you ask to maximize the probability of guessing the sequence?

I thought it would be asking if the first toss is heads then based on that answer the number of possible orders goes from 2^100 to 2^99 but not sure how to reduce it further

[alpine sable]

<@&286206848099549185>

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cold socket]

I need help with this problem:

[cold socket]

Let $c$ be a real number, and consider the system of quadratic equations
\begin{align*}
y &=6x^2 - 9x + c, \
y &= 5x^2 - 3x.
\end{align*}For which values of $c$ does this system have:

(a) Exactly one real solution $(x,y)?$

(b) More than one real solution?

(c) No real solutions?

Solutions to the quadratics are $(x,y)$ pairs.

[ocean seal]

AdityaRegmi123

[cold socket]

<@&286206848099549185>

[lone heart]

@cold socket Has your question been resolved?

[cold socket]

<@&286206848099549185>

[lone heart]

@cold socket Has your question been resolved?

[fickle sandal]

solve 2nd equation and put into first equation

[lone heart]

@cold socket Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

Help pls

Idk why I cant solve this😭

I'm stuck at question a and I tried using Pythagoras theorem but I don't know how to simplify it and I think i did it wrong anyways

<@&286206848099549185>

[lone heart]

@alpine sable Has your question been resolved?

[abstract oyster]

(2x-11+2)(x+1)-(1/2)(2x-11)(x+1)=28
=> (x+1)(2x-9-x+5.5)=28<=>(x+1)(x-3.5)=28
x^2-2.5x-3.5-28=0<=>x^2-2.5x-31.5=0
=>2x^2-5x-63=0
No pythagoras needed

[alpine sable]

Thank you

.close

[lone heart]

Channel closed

Closed by @dire glade

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[versed pasture]

I just don't know what (a) is asking

does it just want me to say uniform distribution?

[lone heart]

@versed pasture Has your question been resolved?

Channel closed

Closed by @versed pasture

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[exotic crescent]

hi im not sure if the graph is even correct for this but can someone check what the answer is?

[exotic crescent]

when you graph the system of inequalities it doesnt show that

[fickle sandal]

yeah they're supposed to have the same gradient

maybe a typo

[exotic crescent]

whats the answer supposed to be

[ionic jewel]

its unanswerable because those letters wouldnt exist if it was graphed correctly

[fickle sandal]

y<3x means everything under the dotted line,
y>=3x-5 is everything above the solid line
so C

[exotic crescent]

alright

thanks

.close

[lone heart]

Channel closed

Closed by @exotic crescent

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lone heart]

Please don't occupy multiple help channels.

[misty moat]

need help asap

(x(2x^(2)-3))/(2(x^(4)-3x^(2))^((3)/(4)))
thats what i got

ive got it down to a or d i believe

[fickle sandal]

$\frac{x(2x^2-3)}{(2(x^4-3x^2)^{3/4}}$

[ocean seal]

chlamydia

[misty moat]

yeah that

[fickle sandal]

looks good

the answer hasn't simplified as much as you have

[misty moat]

oh so D

[fickle sandal]

yup

wait no

the power's wrong

it's neither a nor d

[misty moat]

oh b

[fickle sandal]

yeah

[misty moat]

for this i expand right?

and then find the derivative?

[fickle sandal]

product and chain rule would be better

[misty moat]

how would i do that

[fickle sandal]

$y=f(x)g(x), ,f(x)=(x^8+9),, g(x)=(6x-7)^5$

[ocean seal]

chlamydia

[fickle sandal]

and then that's just product rule

[misty moat]

so its either b or d? since its gonna be a positive

[fickle sandal]

true

[misty moat]

alright so d

[fickle sandal]

no lol

[misty moat]

wait wha

[fickle sandal]

g'(x) gives an extra 6

by chain rule

[misty moat]

oh my b

(13x^(7)+10x^(4))/(2\sqrt(x^(3)+1))

i got this

its way off

.close

[lone heart]

Channel closed

Closed by @misty moat

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lone heart]

@viral thorn Has your question been resolved?

[viral thorn]

.close

[lone heart]

Channel closed

Closed by @viral thorn

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tacit dirge]

This question is so confusing

Do we use the two paths test?

We can't apply squeeze therem right

[alpine nacelle]

you should try polar coordinate

doesn't work, mb

you should use two paths test

for example you can take a path where x^3 = y

and another where x^3 = -y

the first one gives 1/3 as a limit while the other gives -1

[lone heart]

@tacit dirge Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[strong river]

yoyo

[fickle sandal]

know implicit differentiation?

[strong river]

yep just have trouble getting a final answer

so i take the deriv then substitue

[fickle sandal]

so $y^2+y^3=4x^3\implies (2y+3y^2)\frac{dy}{dx}=12x^2$ yes?

[ocean seal]

chlamydia

[strong river]

huh

should i move the y values over to one side first?

[fickle sandal]

that'd be more convenient

[strong river]

ok

then take deriv

then substitue

[icy dove]

can someone help me with (b)

[solemn juniper]

!help

[lone heart]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[strong river]

homeslice

[strong river]

anyways what do i do after i substitue in for the point?

[strong river]

thats what i have but is that all i do?

[fickle sandal]

yeah sub x=-1, y=-2 into $\frac{dy}{dx}=\frac{12x^2}{2y+3y^2}$

[ocean seal]

chlamydia

[strong river]

-12=12-4

thats what i got

or

that second 12 should be negative

[fickle sandal]

what about the dy/dx

[strong river]

what do you mean?

the derivof y is dy/dx but im not taking the derivative of y am i?

[fickle sandal]

the question literally asks for the derivative at (-1,-2)

[strong river]

shi

i need to take th derivative after i plug in?

i thought i was supposed to find the deriv then plug in the points and call it a day

[fickle sandal]

yes you do, but that's not what's happened here

presuming you got $12x^2-2yy'=3y^2y'$, something happened to the y'

[ocean seal]

chlamydia

[strong river]

yea forgot them srry

should be -12x=-12y-4y

wait

oh mb

12x^2-2y(dy/dx)=3y^2(dy/dx)

[strong river]

hm

[fickle sandal]

so then you can sub in (-1,-2) and rearrange for dy/dx

[strong river]

ive already substitued for the points but i need to do it again

?

[fickle sandal]

into this?

[strong river]

i got this

.close

[lone heart]

Channel closed

Closed by @strong river

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[somber peak]

any help on how to get started with this

[lone heart]

@somber peak Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[green trail]

Determine the equation of the tangent plane to the unitary sphere in the point $(1/2,1/2,sqrt(2)/2)$

[ocean seal]

Adad R ᵘʷᵘ

[green trail]

Determine the equation of the tangent plane to the unitary sphere in the point $(1/2,1/2,sqrt{2} /2)$

[ocean seal]

Adad R ᵘʷᵘ

[green trail]

Determine the equation of the tangent plane to the unitary sphere in the point $(1/2,1/2,\sqrt{2} /2)$

[ocean seal]

Adad R ᵘʷᵘ

[green trail]

Cool

Now, my question is, i don't understand the tangent plane stuff

I mean, the equation of the unitary sphere is $x^2+y^2+z^2 = 1$

[ocean seal]

Adad R ᵘʷᵘ

[green trail]

Then what, should i replace the point given in that equation, to obtain the limits?

[alpine nacelle]

let's call A the given point on the sphere and O the origin and center of the sphere
then OA is a radius tangent to the plane that they ask of you

it is a normal vector

and therefore the equation of the plane is of the form 1/2 x + 1/2 y + sqrt(2)/2 z + d = 0 where d is some constant

[green trail]

but how did u got that equation of the plane

[alpine nacelle]

if you have a normal vector (a, b, c) of a plane, then the equation of the plane is ax+by+cz+d = 0 for some d

[green trail]

Oh, right
I've been doing many plane parametrizations that i got confused lol

[green trail]

So, that's it?

[alpine nacelle]

you still have to find the d obviously

[green trail]

but how

[alpine nacelle]

by using that A belongs to it so verifies the equation for example

but if you know a bit about scalar product and norm it's even more direct

[green trail]

Gotcha

Could be D=0?

[alpine nacelle]

no

in fact, even if you wouldn't know the exact form of the equation, you would still know d

the equation is ax+by+cz+d = 0
but since OA is a normal vector with A belonging to the plane
it means A which has coordinate (a, b, c) checks the equation
so a²+b²+c²+d = 0
but since A is on the unit sphere, a²+b²+c² = 1, so d = -1

[green trail]

well, it has sense to me

thanks

[lone heart]

@green trail Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lapis stone]

i did my work on paper so its hard to show it on here

[lapis stone]

I am honestly stuck on if I even did the question right because the video the professor gave me I followed on my own work but still got it wrong

ill try it again and then take a picture

this is where im stuck

<@&286206848099549185>

[fickle sandal]

so you have the derivative

now to find gradient at $66?

[lapis stone]

in the video he got rid of the negative exponent

im just not sure how to do that right here when theres the 1/2 on the left side of the equation

[fickle sandal]

oh like this? $\frac{-3}2(325-3p)^{-1/2}=\frac{-3}{2\sqrt{325-3p}}$

[ocean seal]

chlamydia

[fickle sandal]

can you send what he did

[lapis stone]

why would the left side of the equation be -3/2

i can link the video?

or hold up

i can screenshot

[fickle sandal]

yeah that'd be better

[lapis stone]

so like this is just a yt video of a similar problem

[fickle sandal]

left side of the equation means the left side of the equals sign, not the -3/2

[lapis stone]

oh

oopsie

[fickle sandal]

i just multiplied the -3 and the 1/2 together

[lapis stone]

oh

so i missed that step

okay i see

[fickle sandal]

so what's happened is that $x^{-n}=\frac1{x^n}$

[ocean seal]

chlamydia

[fickle sandal]

a property of exponentials

so the (-1/2) power can be turned into a (1/2) power by moving it from the top to the bottom, or vice versa

[lapis stone]

okay

can i stay here until i solve the whole problem?

[fickle sandal]

yeah

[lapis stone]

okay thank you

[fickle sandal]

it's your channel lol

[lapis stone]

lol i just dont want to take up too much time

ahh i got it right

i realized i missed an x at the top

thank you for ur help

[fickle sandal]

np

[lapis stone]

.close

[lone heart]

Channel closed

Closed by @lapis stone

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[agile grove]

Hi there here is a proof for epsilon delta proofs linear functions. What I want to clarify is in the proof section did I do it correctly? I was wondering did I need to add the word "Check" into the proof when turning I x - c I < delta --> I f(x) - L I < E

Also I want to see if I really understand epsilon delta proof so here is an explanation for its significance.
When evaluating lim x --> 5 h(x) = 5 we can observe that the limit is 5. But how do we actually prove that its true? Also we can argue that as x approaches, tends or nears 5 the values of the function shall approach 5, but what does it mean to be near, approach or tends? How great are we talking. This is not a rigorous statement as its confusing. That is where the epsilon-delta proofs comes in handy.

For all Epsilon > 0 (Epsilon is a measurement of how close we can squeeze the distance of h(x) - L), there exists a Delta > 0, such that for every x, 0 < I x - 5 I < delta ( we are observing the neighborhood x-values within delta, which as well is a measurement of how close we can squeeze the distance of our neighborhood x-values to the c its approaching in which our instance is 5. For all epsilon, there is a corresponding delta, where we can find the max-region delta can be for the proof to hold true provided its defined in terms of epsilon. Now as Epsilon > 0 we can do whatever want. We can choose Epsilon to be 100, but the problem is we are observing values far away, thus not giving us info as we approach x --> 5 for h(x) and is hence useless. To avoid this we usually choose an epsilon so small such that the delta will also be very small.

[agile grove]

A question I had thought to myself is why can't we argue the neighbourhood x values for delta being less than or equal to delta.

The problem with a scenario like this is that we would only be considering two specific values where we would be essentially saying the entire proof can hold true if our neighboorhood x-value equals this. That would be wrong as it violates the fact that we must consider all values in the interval as oppose to a specific value.

There may not even exist a proof for this as it would just be considering two specific values.

[lone heart]

@agile grove Has your question been resolved?

[lone heart]

@agile grove Has your question been resolved?

[worn fox]

If you're asking why we don't use <= instead of <, well you pretty much can if you want, it'd be equivalent

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

I would like to verify if this is right:

$rank(kA) = k^{min(m,n)}rank(A)$, where A is a $m×n$ matrix

[ocean seal]

- Miles12345

[alpine sable]

This seems a direct consequence of the method of calculating rank of a matrix (by calculating the determinants of sub- square matrices)

Oh and k is some constant

[worn fox]

The rank of a matrix doesn't change when you scale it by a non zero constant

[alpine sable]

I see

Thank you 👍

.close

[lone heart]

Channel closed

Closed by @shy slate

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[barren portal]

Prove $\lim\frac{3n+1}{2n+5} =\frac{3}{2}$

[ocean seal]

.doc

[barren portal]

I need help with proving this, Let me show what I have tried

$\abs{\frac{-13}{4n+10}}< \epsilon \implies
\frac{13}{\abs{4n+10}}< \epsilon \implies \frac{13}{\epsilon} <\abs{4n+10}$

[ocean seal]

.doc

[barren portal]

$\frac{13}{\epsilon}<4n+10 \implies \frac{13-10\epsilon}{4\epsilon} <n$

[ocean seal]

.doc

[barren portal]

ie choose $N >\frac{13-10\epsilon}{4\epsilon}$

[ocean seal]

.doc

[barren portal]

I reached till here,

[lone heart]

@barren portal Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[stiff seal]

These are all about sequences

Im having trouble writing the rules or pattern for the first term

for example in C: No.2
I can see that it adds by 2 raised to an increas in exponent each term

But i dont know how to write the rule for the first term

[lone heart]

@stiff seal Has your question been resolved?

[stiff seal]

<@&286206848099549185>

[wraith pollen]

a1​ is 5

a2 is 7

[wraith pollen]

which is a1 +2

a3 is 11

[wraith pollen]

which is a2+4

You can see that each term is obtained by adding the next power of 2 to the previous term

[wraith pollen]

an​ = an−1 ​+ 2^(n−2)

[stiff seal]

but wouldn't An-1 mean n=0 for the first term?

I originally had that same rule but the first term was the problem

[wraith pollen]

huh?

ahh okay sorry my bad

well a(n) = 2^n + 3

[stiff seal]

oh

im just dumb

hehe

[wraith pollen]

a(1)=2^1+3=2+3=5

a(2)=2^2+3=4+3=7
a(3)=2^3+3=8+3=11
a(4)=2^4+3=16+3=19

[stiff seal]

🫶🫶🫶

Thank you so much

I got it now

thank you again

.close

[lone heart]

Channel closed

Closed by @stiff seal

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hollow trench]

Hello, can someone help me with making A-B?

I'm not sure of myself

[vale wigeon]

the right endpoint of A is slightly misaligned

[hollow trench]

hm?

[vale wigeon]

actually both intervals' right endpoints are slightly misaligned

they don't hit the points 3 and 5 as they're supposed to

anyway A - B consists of all points that are in A but not in B

[hollow trench]

Yea, I made them "hit" but the drawing was "ugly" and not very understandable so I selected the element and I moved it a bit so it can be readable

I made a diagram on pc so I can share it, I won't use this diagram in my notebook

So, the points from A that aren't in B, this mean {4}

[upbeat gorge]

I suggest using hollow and shaded endpoints and then connecting with a line to visualize the sets

[hollow trench]

I wanted to use colors, unfortunately the website I used to make this doesn't have colors

[vale wigeon]

no, it does not mean just 4 and nothing else

[hollow trench]

{4} * ?

[vale wigeon]

no, A - B is not {4}

you are suffering from EIS

(Everything-is-Integer Syndrome)

[hollow trench]

um

[vale wigeon]

A - B is [3, 5]. idk how else to say it!

[hollow trench]

oh... I got it now, thank you.

have a nice day!

.close

[lone heart]

Channel closed

Closed by @hollow trench

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[barren portal]

Prove $\lim\frac{3n+1}{2n+5} =\frac{3}{2}$

[ocean seal]

.doc

[alpine sable]

limit as n approaches what?

[barren portal]

it’s a sequence

lim n to infy

[alpine sable]

so, infinity?

okay

[barren portal]

This is the intial scratchwork i have tried

$\abs{\frac{-13}{4n+10}}< \epsilon \implies
\frac{13}{\abs{4n+10}}< \epsilon \implies \frac{13}{\epsilon} <\abs{4n+10}$

[ocean seal]

.doc

[barren portal]

ie choose $N >\frac{13-10\epsilon}{4\epsilon}$

[ocean seal]

.doc

[barren portal]

Is that correct?

I don’t know if I’m in right track

[serene onyx]

Cant you just divide everything by n

[barren portal]

which step?

[serene onyx]

Im in hs so im probably wrong but here

[barren portal]

and later plug lim x to infy 1/x =0 ?

[serene onyx]

Youd have (3 + 1/n)/(2 + 5/n)

[barren portal]

i suppose you mean factor all the terms and they and then use limit properties

[serene onyx]

Then fill in infinity

[barren portal]

that’s not a proof

[serene onyx]

Yeah okay then im wrong

Gl

[barren portal]

It’s just evaluating the limits

to evaluate, i can just consider the leading terms

And directly say 3n/2n= 3/2

[serene onyx]

👍

[barren portal]

unfortunately that doesn’t prove it.

@alpine sable

I suppose we need find a stage N in the sequence for an arbitrary epsilon such that the terms after N will be less than epsilion away from 3/2

[alpine sable]

is it you first year at uni @barren portal ?

[muted hornet]

yeah

then you reverse all of the steps

[barren portal]

last year

[barren portal]

How do I reverse a triangular inequality step?

[muted hornet]

oh i didn't realize you used the triangle inequality. where was that?

[barren portal]

After the last step

[muted hornet]

i thought you just said that |4n + 10| = 4n + 10 because n is a positive integer

then rearranged to get n larger than some expression of \epsilon

[barren portal]

I wrote |4n+10|<|4n|+ |10|

I mean idky

[muted hornet]

oh. you dont need to :D

4n + 10 is positive, so |4n + 10| = 4n + 10

[barren portal]

Major

^^

[muted hornet]

[barren portal]

My bad

[barren portal]

Now I have to replace N with n and swin all the way back?

[muted hornet]

sort of. after you choose N > blah blah blah, you rearrange to get 13/\epsilon < |4N + 10|; then you know if n >= N, |4N + 10| <= |4n + 10|

so the inequality is still good (for all n >= N). then you keep going backward

[barren portal]

well, in convergence proofs, the notion is what we emphasise and the intial scratchwork steps are supposed to be hidden?

[muted hornet]

yeah. in the proof you just write your scratchwork backward

[muted hornet]

with this extra step

[barren portal]

Let me see

[muted hornet]

well, sort of backward. i think you can go forward for some part. just gotta make it relatively clear

[lone heart]

@barren portal Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[safe tartan]

could i have help on a vector question?

[alpine sable]

[safe tartan]

is the question asking for the dot product or something or is it as simple as 4 x 12

i dont think i've ever found the dot product of vectors which only their magnitude is know..

[chilly crag]

start by getting a+b+c

which we can nicely rewrite

and then we can use the definition of the scalar product (which is the dot here)
v * w = |v| * |w| * cos(phi) where phi is the angle between v and w

[safe tartan]

oh i see

how do you gey a + b + c again?

[chilly crag]

you start by moving along a, so we arive at Q

then we add b, which moves us where?

[safe tartan]

R

[chilly crag]

yep

then we add c

[safe tartan]

S

a+b+c=2b ?

[chilly crag]

yep

[safe tartan]

right i see

ill try it one sec

16

ah tysm i love when maths makes sense 🙂

[chilly crag]

one sec