help-17

[minor carbon]

is it zero?

[sly sierra]

of course

if v does not depend on t then neither does v.v

[minor carbon]

no uhm

v will depend on t

[sly sierra]

what do you mean by constant vector then?

[minor carbon]

like is a constant vector the same as a constant?

is their derivative both zero

or do i do different stuff with it

[sly sierra]

i don't understand what you are asking

[minor carbon]

its v dot v

[sly sierra]

first you said v is constant, then you said it depends on t

which is true?

[minor carbon]

v is a constant vector that depends on t

[sly sierra]

what does that even mean?

[minor carbon]

mb mb

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[visual coral]

So here's something that's been bothering me. I was messing around with tanhx (as one does) and converted it into $\frac {e^{2x} -1}{e^{2x}+1}$, which should obviously have a limit of 1 as x goes to infinity since there's only a constant difference between the numerator and denominator, which means that the limit of tanhx as x goes to infinity is 1.

[twin meteor]

Serphic

[visual coral]

This should mean that the integral of tanhx from 0 to x should also approach y = x as x goes to infinity, and y = -x as goes to negative infinity. while i wasnt really up to actually calculating if this was true, the integral of tanhx (ln(cosh(x) did end up getting approximated very roughly by |x| as x goes to infinity, verified by the limit of $\frac{|x|}{ln(cosh(x))}$ (again, didn't really do more than just a rough check on this one).

[twin meteor]

Serphic

[visual coral]

But when i try to raise e to the power of both of them, the limit instead becomes two. The limit of $\frac{e^{|x|}}{cosh(x)}$ as x goes to infinity is two??

[twin meteor]

Serphic

[visual coral]

what exactly changed?

[brittle cipher]

why would "This should mean that the integral of tanhx from 0 to x should also approach y = x as x goes to infinity"

[visual coral]

my thought process is that since tanhx goes to 1, then its integral should also approach whatever the integral of y=1 is

[brittle cipher]

ignore me I'm too distracted

[hushed pewter]

Oh I see what your question is now

[visual coral]

yeah im sorry i shoulda phrased it better

[hushed pewter]

In general, it seems that, if $\lim_{x\to\infty}\frac{f(x)}{g(x)}=K$, then that does not guarantee that $\lim_{x\to\infty}\frac{h(f(x))}{h(g(x))}=K$

[visual coral]

hrmmmmm

[twin meteor]

SWR

[hushed pewter]

Which is surprising. I don't know what to do with that information.

@visual coral here's a nicer example

$\lim_{x\to\infty}\frac{x}{2x}=\frac{1}{2}$, but $\lim_{x\to\infty}\frac{e^x}{e^{2x}}=0$

[twin meteor]

SWR

[visual coral]

see no i get this one

it makes sense

i think it has something to do with

yeah actually i got nothin

[hushed pewter]

[cobalt crypt]

,, \lim \f {e^a} {e^b} = \lim e^{a - b}

[cobalt crypt]

so you're really looking at the behaviour of |x| - log(cosh(x)) for that limit

,w graph x - log(cosh(x)) for x > 5

[twin meteor]

Results provided by WolframAlpha

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

Requested by tearfox

[cobalt crypt]

that's definitely from 5 to infinity

anyway it approaches a constant which happens to be log(2)

[visual coral]

what the fuck

[cobalt crypt]

you computed $\lim \df ab$ and tried to extrapolate $\lim (a - b)$ from that

[cobalt crypt]

ofc it wouldn't work out

[visual coral]

okay see the thingi s

my thought process was that since they both seem to be roughly equal as x goes to infinity, and e^x increases regardless of x value, they should both approach each other kind of

but

[visual coral]

that does kind of make a bit more sense?

[cobalt crypt]

their ratio approaches a constant

i mean

to make the example more drastic

,, \f {x + \sqrt x} {\log \cosh x} \to 1 \textqq{as} x \to \infty

[cobalt crypt]

but [ \f {e^{x + \sqrt x}} {\cosh x} \to \infty ]

[cobalt crypt]

so like

rip i guess

[visual coral]

it both makes sense and makes no sense

is there like

a specific name for this

welp

.close

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[undone oasis]

I have a doubt about vector fields
(Following up with the actual question, this is to take the channel for myself)

[undone oasis]

I have the following vector field:
F(x,y) = (x^3 * y, x^2 * y^2)
A = x^3 * y
B = x^2 * y^2

The question is:
"Is F exact/conservative in R2? If yes, calculate the potential U"

I checked the first question by stating: it's conservative if:

dB/dx = dA/dy

It turns out that:

dB/dx = 2x * y^2
dA/dy = x^3

They are different.

Can I claim F is not conservative and end the exercise?

[bleak sapphire]

Wait what does F have to do with A and B?

[vocal sleet]

@undone oasis Has your question been resolved?

[undone oasis]

See it as F(x,y) = (A,B)

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[vast shale]

asinx + bcosx can be expressed as ksin(x+p)

so at the midpoint of alpha and beta, the derivative of sqrt3 acosx + 2bsinx would be 0

[silver tusk]

?

we have to solve via quadratic

[vast shale]

?

[silver tusk]

i havent studied derivative yet

[vast shale]

thats unfortunate

[silver tusk]

I want solution by quadratic

[vast shale]

well i dont know how to solve this with quadratics

mb

[silver tusk]

k

<@&286206848099549185>

@vast shale hi

[vast shale]

sup

[versed lagoon]

Hi

[silver tusk]

I have another doubt

[silver tusk]

hi

cot44 + cot46/ cot46- cot44 in terms of tan

@vast shale can u try this

[vast shale]

ye

[silver tusk]

answer is tan46 + tan44/ tan44-tan46 how

[vast shale]

cot is 1/tan

[silver tusk]

ye

wait ye

[vast shale]

ye so use that

[silver tusk]

i didn't think of that

[twin meteor]

coold_boy

LaTeX source sent via direct message.
```Compilation error:```! Missing $ inserted.
<inserted text> 
                $
l.87 \end{document}
                   
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.```

[silver tusk]

what

did u chatgpt it

answer ia incorrect

IsIs*

answer is 1/2

[versed lagoon]

Sorry 😭

[silver tusk]

its ok

[versed lagoon]

I do now so much English soy de México

[vast shale]

open a new one

so others can see better

[silver tusk]

sure

.close

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[hexed orchid]

a vector field F is conservative if it is the gradient of a scalar field G

so you should be integrating not derivig

i dont think its conservative tho

[undone oasis]

Me neither

Because the curl is not null

right?

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[wary mantle]

#linear-algebra message

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@wary mantle Has your question been resolved?

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[severe lynx]

The statement isn’t necessarily true. Here’s a counter example:

Let f(x)=x, a=0, b=3, and P1 & P2 be partitions of [a,b] such that P1={0,1.1,1.2,1.3,1.4,1.5,…,2.9,3} and P2={0,1,2,3}. We have that L(f,P2)=0+1+2=3, and L(f,P1)=0+.11+.12+…+.29=3.8. And yet | |P1| |=1.1>1=| |P2| |.

I think the statement you might be looking for is if P1 is a subset of P2, which we say P2 is a finer partition of [a,b] then P1.

When this is true, then the result should follow for at-least Riemann integrable functions.

Does that make sense?

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@dry pier Has your question been resolved?

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[dry pier]

Yes, and I know how to prove the right statement. Thank you very much.

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[stoic citrus]

#help-4 message

[stoic citrus]

If √11−√7/√11+√7 = 𝑎 − 𝑏√77, find a and b.

pls help me

[tribal hound]

Use the law (A - B)(A + B) = A² - B²

[stoic citrus]

sir but here it is a-b/a+b

[tribal hound]

I know

[stoic citrus]

so how

[tribal hound]

But you may use a trick

For example, using the fact that x/x = 1 if x != 0

[loud walrus]

I already told you to rationalize

Multiply by sqrt(11)-sqrt(7) numerator and denominator

Then show all your working

[stoic citrus]

18/4=a-b√77

came now

[loud walrus]

Idk what part dont u understand from show all your work

Write all steps u do

[stoic citrus]

that will take a lot of time

[loud walrus]

Oh lord

Good luck

[stoic citrus]

wait i am doing

√11-√7/V11-√7=a-b√77

=ratnalising num and denom

=18/4=a-b√77

sir this much

sir pls tell what to do next

noone coming to help??

.close

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[velvet zephyr]

aww

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[lime viper]

Ugh I cant understand how i got this wrong.

[lime viper]

https://tenor.com/view/rage-gif-24341837

https://tenor.com/view/stitch-sad-sad-stitch-gif-14364046974961747120

[shadow raft]

this is the core of this exercise

[lime viper]

?

its soppoes to be 7ms to seconds right

[shadow raft]

7 degrees/ 1 ms

to ? degress / 1 s

[shadow raft]

if you multiply by 1000 ms / 1 s, then the ms will cancel out

[velvet zephyr]

7 deg in 1 milli
in 1000 mili, 7000 deg

[lime viper]

how

[shadow raft]

\begin{align*}\frac{7 \text{ degrees}}{1 \text{ ms}}&=\frac{7 \text{ degrees}}{1 \text{ ms}} \frac{1 \text{ s}}{1 \text{ s}}\&=\frac{7 \text{ degrees}}{1 \text{ ms}} \frac{1000 \text{ ms}}{1 \text{ s}}\&=\frac{7 \text{ degrees}}{1 \text{ s}} \frac{1000 \text{ ms}}{1 \text{ ms}}\&=\frac{7 \text{ degrees}}{1 \text{ s}} 1000\&=\frac{7000 \text{ degrees}}{1 \text{ s}}\end{align*}

[twin meteor]

Flappie

[lime viper]

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[bleak prawn]

long division... what do I do here?

I cant take -4x away from 3x^2

Sorry about my handwriting...

[shadow raft]

yeah you can

3x^2-4x

[bleak prawn]

Ummm

Ok 1 moment

Is it not +4x now?

[shadow raft]

no?

[bleak prawn]

ok...

Yep got the answer

Thanks!

❤️

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[left roost]

This might be a strange one. I have a question regarding vectors/trig.

I have the following:
CameraPosition (Coordinate)
and
CameraDirection (Normalized vector)

Given only these, is it possible to calculate the TargetCoordinate?
Common sense is telling me that it's not possible, since my CameraDirection vector is Normalized, the TargetCoordinate could be anywhere along the vector.

Unless there are some tricks to figure that out by somehow un-normalizing the CameraDirection vector?

[left roost]

I'm working on some camera manipulation code in a shader, I do not have access to source code and I do not have a TargetCoordinate constant available, I need to calculate it if I want to move my camera and keep it tracking to the original target.

[vocal sleet]

@left roost Has your question been resolved?

[vocal sleet]

@left roost Has your question been resolved?

[mellow oyster]

if this is the only information you have, then you're correct that it's not possible since the target could be anywhere on the span of that normal vector

it might be possible with more information

[left roost]

Thanks Neil. Yeah I thought as much, I'm afraid that's all of the information I had. No big deal though, I'll accomplish the goal in some other way. This would have been more convenient is all. Still great to confirm my suspicions.

[left roost]

.close

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[humble linden]

Welp I'm back.

[humble linden]

Anyone open to help?

[slate dagger]

!da2a

[vocal sleet]

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

[humble linden]

Ok so basically

Can you explain quadratics to me?

[lavish river]

assume that u can factor it with integers

(ax+b)(cx+d) for integers a,b,c,d

if u expand it you'll see ac is the coefficient of x^2 and bd of the constant

in the case of the first question, ac=1 and bd=-20

[humble linden]

Why????

Why would you explain something like that I feel like I'm decoding a bomb.

[lavish river]

so for simplicity assume a and c are 1 (or -1)

[humble linden]

Just trying to understand the variable connotations where if I can't even get one of them I am screwed.

[lavish river]

of?

[fallen hawk]

Google Khan Academy

[humble linden]

Tried nearly everything mate.

[shadow raft]

youve asked this same question like 10 times already

[humble linden]

Should I not?

I need the help.

Like alot.

[fallen hawk]

Watch the videos bruh

[shadow raft]

you can, but its been explained to you multiple times but youre just not accepting it

[humble linden]

Because they aren't contextualizing their statements.

And speaking in variables.

[lavish river]

then cd would have to be the factors of 20. in this case +-1,2,4,5,10,20

[shadow raft]

what about this??

[fallen hawk]

Bro just learn the quadratic formula how hard is it

[lavish river]

so u can trial and error and find it from there

[humble linden]

Jac graphing.

I can somewhat factor it now but it's very very annoying.

VERY

[fallen hawk]

Why would you explain rational root theorem for quadratics

[shadow raft]

$f(x)=ax^2+bx+c$ has solutions $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ then $f(x)=(x-x_1)(x-x_2)=\left(x-\frac{-b+\sqrt{b^2-4ac}}{2a}\right)\left(x-\frac{-b-\sqrt{b^2-4ac}}{2a}\right)$

how much more do you need?

[lavish river]

well thats one way to do it

[humble linden]

Facepalm:

[lavish river]

another is the quadratic equation

[humble linden]

I wanted a general synopsis of the entire process.

In words

[lavish river]

i did give it to you

[humble linden]

I don't care.

[lavish river]

and i did explain

ok cool

[humble linden]

I told you I didn't understand AI EOSN QLLA SODOS W + BWISIS

I didn't even care to try

[lavish river]

u didnt say at

which part

[humble linden]

Since people tried far more efficient methods and still failed

Thank you for trying though

[lavish river]

ok.. well bye

[twin meteor]

Flappie

[fallen hawk]

There is this formula. Pretty self explanatory.

Use the formula

Ta fucking da

[humble linden]

Nope

Cuz that's not what I came to learn.

[shadow raft]

what the fuck do you mean nope

[humble linden]

I told you.

[shadow raft]

this is not good enough?

[humble linden]

I want you to teach me quadratics

Not quadratic factoring or formulas

Think!

What do I mean by that

[shadow raft]

wtf you mean by teach quadratics then

what about quadratics doyou want to know?

[humble linden]

Idk what else do quadratics have that might be important?

I'll just tell you

Graphing

[fallen hawk]

https://www.dummies.com/article/academics-the-arts/math/calculus/how-to-solve-and-factor-a-quadratic-equation-with-the-quadratic-formula-192154/

[humble linden]

Parabolas

[fallen hawk]

There you go

[humble linden]

X and Y axis

Etc

[fallen hawk]

Go read

[humble linden]

Nope

[fallen hawk]

Go open a book

[humble linden]

Cuz I'm not solving for it rn.

[fallen hawk]

Why is bro so entitled

Go pay for a tutor dude

[shadow raft]

whats wrong with you?

[fallen hawk]

Fucking 13 year olds

[humble linden]

Cuz I had this conversation 500 times and it's been over 100 hours now and you aren't caring to listen.

[shadow raft]

we arent caring to listen? you dont want to listen

[humble linden]

I want someone who will actually care to follow the question and think about their response.

[fallen hawk]

Because no one will explain an entire subfield of math to you on a whim

I told you, go watch the Khan Academy videos

[humble linden]

No but they can at least contextualize and use interpersonal thought to determine the areas that aren't properly contextualized

I'll tell you

I told you earlier

The roots, graphs, and parabolas.

I want to know about those.

[fallen hawk]

You're using a lot of big words to hide the fact you're lazy

Google, Wikipedia etc

[humble linden]

I already asked AI

And I was going to do that later.

[shadow raft]

!nogpt

[vocal sleet]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[fallen hawk]

God this generation is full of brainrot

[humble linden]

Yawn.

Also I'm not lazy I'm probably more motivated than you actually.

[shadow raft]

how old are oyu even?

[humble linden]

Depends actually

[humble linden]

18

[fallen hawk]

LOOOOOOL

No way

[humble linden]

Anyways

[fallen hawk]

What 18 year old doesnt know parabolas

[shadow raft]

😂

[humble linden]

Explain it then.

[shadow raft]

the super motivated one

[fallen hawk]

Symmetric line goes up or down

[humble linden]

Context?

Fine here

I'll take on my perfect self

Give me a second

[fallen hawk]

Motivated by the function

[humble linden]

Questions:

1: What does a parabola represent, and is it composed of one or multiple values?

2: A y axis typically represents a positive or negative direction but in this case there are only 2 directions and I am uncertain what it is representing. Is there a segmentation or breakpoint where it begins representing a separate value?```

Sorry if I was rude earlier my pain tolerance is strained due to endless hours, more than you'd understand.

I'm also just really really sick of people not carefully thinking their responses out and answering with context in a full-scale manner.

[shadow raft]

at least finally something concrete we can answer

[humble linden]

Since throughout all my experiences every question ended up appearing startlingly simple in such a way that made the teachers look crazy for not answering properly.

[shadow raft]

you do know we're volunteers right? we answer questions because we want to, not because we are forced to. and when you put on such a negative and agressive attitude no one wants to deal with you

[humble linden]

I'm not

I'm actually very nice

[shadow raft]

!volunteers

[vocal sleet]

Helpers are just people volunteering their time to help you. Be polite and patient.

[shadow raft]

well, so far you havent acted like it

[humble linden]

It's just after over 100 hours you start to struggle to handle that pain.

[shadow raft]

and no, its not for you to decide that

[humble linden]

It is.

[humble linden]

You're right and wrong simultaneously you don't realise it but you just said 2 different things.

[humble linden]

Technically I haven't "said" anything rude to anyone here if you take a more multi-faceted look at what I'm actually saying once you understand what I mean by that your perspective on words might change a bit.

[fallen hawk]

You're quite fucking annoying you know that

[humble linden]

Shrug

You too

My pain tolerance is actually higher than yours in terms of communication.

Alot higher.

You already broke from basic stress. Mine and yours.

[fallen hawk]

No, I simply don't need to tolerate you

[humble linden]

Not really.

I don't care how toxic you are I won't really insult you.

You can't make me angry no matter what you do.

I make myself angry through my dedication causing stress due to work.

But do as you wish shrug.

I never really stop working.

It's all I do and it's all I will do.

Ad Astra Per aspera

Though

I should probably pivot if my best efforts fail soon enough.

Since this isn't really working.

[fallen hawk]

If you were so dedicated you'd have read what I explained (before I deleted) or actually opened a book

[humble linden]

?

No because I'm not in my perfect state rn.

That is very hard to maintain.

So I forget.

[fallen hawk]

Also you should stop speaking like an anime mastermind

[humble linden]

I'm just being metaphorical and using various terms you may be unfamiliar with.

You do the same.

You and your friends.

The only reason I got annoyed was the terminology you used without contextualization.

[fallen hawk]

Frankly, its annoying, especially coming from an alleged 18 year old who doesn't know what parabolas are

[humble linden]

It's just when I do it there's nothing important to see anyway.

Yours is more annoying shrug.

Also

Watch this real quick

https://youtu.be/ai7iw0IFefQ

You need a chill pill lol.

Me too but you need it more.

[shadow raft]

in the time you have spent arguing with us, you couldve easily read a chapter on the topic or watched a video about it

[humble linden]

?

Every living moment of my existence is work flappie.

[gaunt sparrow]

If this is going nowhere can we not just close the channel and call it a day?

[humble linden]

I already asked in multiple servers today.

And he decided to stray from the topic.

[lavish river]

you should stop bring that up. its rude

[humble linden]

Don't look at me.

[shadow raft]

we cant close it

[gaunt sparrow]

.close

[vocal sleet]

Channel closed

Closed by @gaunt sparrow

Use .reopen if this was a mistake.

[shadow raft]

damn

[humble linden]

wowa

[shadow raft]

is that a helpful thing?

[humble linden]

?

What is

[vocal sleet]

Available help channel!

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[mild swan]

hi i just need help with this question, i know its very simple but i dont understand where the wires are?? i just need help with question b and onwards thank you :)

[steel snow]

So the fence surrounds the paddock

And the fence is made up of 6 wires

so if I were looking at the paddock from a side view

The fence would be 6 horizontal lines (wires)

[mild swan]

oh

so whats the formula??

[shadow raft]

!statis

!status

[vocal sleet]

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

[mild swan]

2

[vocal sleet]

@mild swan Has your question been resolved?

[glacial osprey]

do the 6 wires have to be equal in length

[mild swan]

i think so

[glacial osprey]

ok you have the perimeter

just divide it by 6

also wdym you think so youre the one posting the problem

[vocal sleet]

@mild swan Has your question been resolved?

[mild swan]

bruh, everything is in the question provided

i’m the one asking for help

[glacial osprey]

ok then the 6 wires have to be equal

just divide the perimeter by 6

to get 6 equal lengths of wire

[mild swan]

thanks

what about C

[odd helm]

can't lie i thought the answer to a was the same as the answer to b

[glacial osprey]

yea it seems the same to me

i dont really get it

for C it seems simple enough

whats 1km in meters

[odd helm]

999.9999... metres

[glacial osprey]

round up

[vocal sleet]

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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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• 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.

[mild rapids]

.rotate

I am using the derivative of theta to get a sign diagram

here is my work:

.rotate

there are turning points in the function of the derivative in +-h root of 3

but idk how to get h

where h is a constant

maybe I could just replace h with a random number

nevermind

i just replaced h=1 in the tan-1 part...

is pi/6...

.close

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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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• 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.

[wraith imp]

i need help with part b) of this question

[wraith imp]

so far, i let x_k be the kth element of the Fibonacci sequence

then r_k = (x_k+1)/x_k

but then im not quite sure what to do to show r_k < φ

[vocal sleet]

@wraith imp Has your question been resolved?

[vocal sleet]

@wraith imp Has your question been resolved?

[vocal sleet]

@wraith imp Has your question been resolved?

[wraith imp]

nvm i solved

.close

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• Be polite and have a nice day!

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[dreamy lily]

I need help with creating and maximizing this table in excel

[dreamy lily]

ive been stuck on it for about a week now

[vocal sleet]

@dreamy lily Has your question been resolved?

[dreamy lily]

.close

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[urban yacht]

An alumni association survey asked each highschool graduate to select the one activity he or she preferred for the association's next event. Some of the people responded by phone, and the others responded by email. The table above shows the distribution of preferred activity, in percent, for each response type used.
For the survey, the number of email responses was as twice the number of phone responses. If a person who preferred a picnic is selected at random, what is the probability that the person responded by email?

            Phone   Email

Dinner 55% 80%
dance

Football 20% 10%
game

Picnic 20% 5%
pool

Party 5% 5%

Total 100% 100%

[shadow raft]

!status

[vocal sleet]

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

[urban yacht]

7

I don't know how to solve it

[shadow raft]

so, 1

[urban yacht]

okay

[shadow raft]

for an intuition, try using integers

[urban yacht]

uh

[shadow raft]

e.g. 1000 email responses

500 phone responses

[urban yacht]

okay

[shadow raft]

then how would the table be filled?

[urban yacht]

uh

wym

[shadow raft]

assume there are 1000 email responses

then you would fill in 800 responses at dinner dance-email

and 100 responses at football game-email

etc

[urban yacht]

okay

1900

[shadow raft]

could you fill in the whole table?

[urban yacht]

but no need

because there is one already

[shadow raft]

alright

sure

[urban yacht]

okay

[shadow raft]

lets do it a different way then

look at the totals at the bottom, how could you scale those, so that email is twice as much as phone responses, and that their totals add to 100%?

[urban yacht]

okay

80 10 5 5

[shadow raft]

look at these totals

now they add up to 200%

[urban yacht]

okay

[shadow raft]

which doesnt make sense

[urban yacht]

okay

[shadow raft]

right?

[urban yacht]

okay

[shadow raft]

okay

so, how do you scale them

so that they are in a 1:2 ratio

and they sum up to 100

[urban yacht]

dunno

thats what im here for

[shadow raft]

im not here to give you solutions

[urban yacht]

wth

[shadow raft]

im here to probe your intuition so you can understand it

[urban yacht]

okay

oh

okay

thank you sm]

🩷

[shadow raft]

So, lets say there are $a$ email responses, and $b$ phone responses. Its given that there are twice as many email responses as phone responses, so $2b=a$. The total responses must add up to 100% $a+b=100$. Solve for $a$ and $b$.

(a and b are in percentages)

[urban yacht]

okay

but what now

[shadow raft]

why is half of it not showing?

[twin meteor]

Flappie

[urban yacht]

oh

[shadow raft]

there we go

so, 2b=a and a+b=100

can you try and solve that?

[urban yacht]

a+b dont have to be 100

it have to be 100%

not 100

no?

flappie

[shadow raft]

yes,

[urban yacht]

a+b dont have to be 100 tho

it have to be 100% only

[shadow raft]

a+b=1

100% = 1

you get my point

[urban yacht]

so is a+b= 1 or 100

[shadow raft]

take a+b=1

[urban yacht]

okay

😰 where are you?

[shadow raft]

im asking you to solve it

[urban yacht]

oh

[shadow raft]

you are the one that has to solve it

ever heard of the idiom, you can lead a horse to water?

[urban yacht]

no

ebglish is my second language

2b=a

so a =

75

b=25

[shadow raft]

not quite

[urban yacht]

a=50

[shadow raft]

2*25=50

not 75

[urban yacht]

mb

[shadow raft]

but then a+b=25+50=75

[urban yacht]

yes

[shadow raft]

which is not 100

[urban yacht]

okay

then what can we do?

[shadow raft]

what grade are you in?

or age

[urban yacht]

12th

[urban yacht]

16

[shadow raft]

12th grade?

[urban yacht]

yes

[shadow raft]

you should really be able to solve simple algebraic equations

[urban yacht]

I did

omg

[shadow raft]

\begin{align*}2b=a\a+b=1\end{align*}

[twin meteor]

Flappie

[urban yacht]

can you stop shaming

anyway

[shadow raft]

your answer is wrong

[urban yacht]

you asked for a+b=100

[shadow raft]

a is not 50

nor is it 75

[urban yacht]

but wtv

omg fine

2b=a

a+b=1

so a=0.25

omg

a=0.5

b=0.25

[shadow raft]

no

your answer is wrong

[urban yacht]

alr just tell me hats's the answer

[shadow raft]

no

[urban yacht]

wth

[shadow raft]

you should be able to do this yourelf

yourself

think about it for more than 3 seconds

[crisp canopy]

do I need to help in here?

[shadow raft]

\begin{align*}a&=2b\a+b&=1\end{align*}

[urban yacht]

it's 2b=a so b is 0.25 and a is 0.5 bro

[twin meteor]

Flappie

[shadow raft]

please do

[urban yacht]

wth

[crisp canopy]

is this the question were trying to answer?

[vast shale]

What's 0.5+0.25

[urban yacht]

its' 2b=a so that makes sense

so 0.25 x 2 is 0.5

[vast shale]

No answer this

[urban yacht]

so 0.5+0.5=1

[urban yacht]

0.75

[vast shale]

It's a+b not a+2b

[urban yacht]

no he said a+2b

[vast shale]

Values of a and b must satisfy both the equations

[urban yacht]

so it doesnt

[vast shale]

What's your original question

[crisp canopy]

nvm

[urban yacht]

here guys

please someone help

[vast shale]

You can either solve 2b=a AND a+b = 100 of you want your answer in percentage

Or solve 2b=a AND a+b = 1 then multiply both a and b by 100 in the end after you find them

Let's take

2b = a
a+b = 1

You say b=0.25 and a=0.5

[urban yacht]

okay

[vast shale]

But a+b = 0.5+0.25=0.75 ≠1

Try to simultaneously solve them.

[urban yacht]

okay

so we will have 2(0.25)=0.5

which is true

a+b=1

[vast shale]

Well guessing values ain't a good option here really

[urban yacht]

so 0.5+0.5=1

[vast shale]

.

[urban yacht]

okay

will you just tell me 😊 I been stuck on this SATs q for 4+ hrs

[vast shale]

Sorry bud

[urban yacht]

dw

?

wait wym

why are you not replying

[vast shale]

We're not gonna spoonfeed you answers lol

[urban yacht]

is that a rule?

[vast shale]

Kinda. Yes.

[urban yacht]

makes sense now

[vocal sleet]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[urban yacht]

huh

[west bone]

sorry

[urban yacht]

np

[west bone]

are you helper,by the way

[urban yacht]

no

are u?

[west bone]

oh ok

$because i am trying to learn how to use $

[urban yacht]

you use it just like that

[vast shale]

#latex-help

[urban yacht]

iceball you can put the steps

!help

[vocal sleet]

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

[urban yacht]

!

!status

[vocal sleet]

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

[urban yacht]

1

[vast shale]

If 2b=a

[urban yacht]

okay

yes

[vast shale]

Ok wait

You have a=2b

What's a+b?

[crisp canopy]

hold on

[urban yacht]

a+b does not work?

[crisp canopy]

lets get basics first

[vast shale]

What's a+b in terms of b, given a=2b

[urban yacht]

a=2b and now a+b

[urban yacht]

Why are you not saying it already

you're not spoonfeeding atp, i seriously want ehlp

and you're not helping me

like i would have came here in the first place

[crisp canopy]

If a person who preferred a picnic is selected at random, what is the probability that the person responded by email?

[urban yacht]

bro's telling me to answer my own doubt

[crisp canopy]

thats what you want answered correct?

[urban yacht]

i didnt answer

[crisp canopy]

this is the question you want answered? yes?

[urban yacht]

yes

please just answer

i am so tired.......

[crisp canopy]

I will try to help in the easiest way possible I promise

[urban yacht]

omg you're so sweet

[crisp canopy]

lets look at the stats of the picnic, how many people responded with phone and how many responded with email

[urban yacht]

okay

[crisp canopy]

so we would have by phone 20% and by email 5% yes?

[urban yacht]

no

how

oh yea

my ah didn't know you were referring to picnic

[crisp canopy]

great, these represent how many people out of a hundred prefer picnics based on their mode of response via email or phone

we also know there were twice as many respondents via email compared to those who responded with phone

[urban yacht]

okay

so what's the solution

[crisp canopy]

assume there were 100 high school graduates surveyed
calculate the number of people who prefer picnics and respond by email:

Total Number Preferring Picnics = (0 .05 * total population) = (0 .05*100) = 5

[urban yacht]

yes

now waht

[crisp canopy]

Calculate The probability that a person who prefers picnic responded via Email is given as :
Probability(Prefers Pinic + Response Type is Email)=Number Responded Via Emails/Total Numbers Prefering Picnic = (percentage picnic email number of people)/(sum all percentages times number of people) =(40/50)=(8)

[urban yacht]

okay

[crisp canopy]

do you understand?

[urban yacht]

i cant read

Calculate The probability that a person who prefers picnic responded via Email is given as :
Probability(Prefers Pinic + Response Type is Email)=

Number Responded Via Emails/Total Numbers Prefering Picnic =

(percentage picnic email number of people)/(sum all percentages times number of people) =

(40/50)=(8)

much better

[crisp canopy]

soooooo do you understand

[urban yacht]

i'll read now

[crisp canopy]

ok

[urban yacht]

you can go btw

ty again

[crisp canopy]

np

[urban yacht]

@vast shale can you confirm this

[urban yacht]

^

[vocal sleet]

@urban yacht Has your question been resolved?

[vocal sleet]

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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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• Be polite and have a nice day!

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[wary mantle]

Just because they have the same angle?

[inner osprey]

ae and yz are perpendicular

hence drop perpendiculars from e, z, and y to the opposite sides of the square

congruence results in ae = yz

[magic wasp]

If ABCD is a square, yes

[wary mantle]

it is

[peak matrix]

proof?

[inner osprey]

circle tangency

[magic wasp]

You have the same alpha angle

Hence congruent triangles

[wary mantle]

Where

Congruent where

[inner osprey]

right triangles with ae and yz as hypotenuses

and with legs on the square

[wary mantle]

How are those right triangles?

[peak matrix]

Drop perpendiculars from E and Z

[wary mantle]

Could someone draw this in please

[peak matrix]

Tp the opposite sides

[magic wasp]

XYZ and AED

[wary mantle]

Yep, those are right triangles

Now what

[magic wasp]

They have the same angles and one side is obviously the same length since ABCD is a square

[wary mantle]

You mean the sides XZ and ED are equal? Why?

[magic wasp]

No, XY = CD = AD

[wary mantle]

Oh

[wary mantle]

Ok, so these triangles are congruent

Ah

We are done

[wary mantle]

How do you come up with this?

Why drop the perpendicular at exactly Y

Why not at Z or something

Or at E

Or at F

[magic wasp]

It's the same

[wary mantle]

What if I drop the perpendicular here

Ah

AED is congruent to QYZ

Right?

[magic wasp]

Yeah

[wary mantle]

When you see

How come you right away think "YZ is the same as AE"?

I mean, that's the idea you need to have

Otherwise you won't pull perpendiculars and stuff

The problem was to find the length YZ

Given R and r

[magic wasp]

If you have two parallel lines and then two more that intersect the first two:

The segment pairs have equal length

That's just a parallelogram

[wary mantle]

Yes

[magic wasp]

Well the angles EAD and BEC (B is to the right of E) are the same

[wary mantle]

Where is B?

Wdym

[magic wasp]

Ok let me redo that

Ok so I have a line AB and a line parallel to it through C

I draw a line through A with an arbitrary angle alpha, it intersects the parallel line at D

Then, if I pick any other point on AB, name it E, and draw a line with the same angle alpha, which will intersect CD at F, the segment EF will have the same length as the segment AD

[wary mantle]

Yeah because that's just a parallelogram

[magic wasp]

If you draw any other pair of parallel line, separated by the same distance as AB and CD are, and do the same thing, you'll get segments of the same length

Well in your original problem, the pairs of parallel lines are AB, CD, and BC, AD

When you draw lines at any point with the same angles, you get segments of the same lengths

That's the intuition anyway

The proof is easier when considering congruent triangles

[wary mantle]

AE is basically the segment EF in your image

[magic wasp]

Yeah

[wary mantle]

But how does ZY have to do anything with your image?

[magic wasp]

The distance between AB and CD is the same as between BC and AD, and the angles BAE and CZY are the same

[wary mantle]

But like, it isn't directly related to your drawing, is it? What we discussed is "the blue diagonal has the same length as the red diagonal"

But this has nothing to do with the blue diagonal

[magic wasp]

How about this: I copied the original twice, but rotated the second one by 90º

[wary mantle]

Oh

Ok it's clear now

[magic wasp]

The fact that I could join the sides of both squares comes from them being squares, so the distances between parallel sides are the same

[wary mantle]

Thanks a lot!

[magic wasp]

[wary mantle]

.close

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Channel closed

Closed by @wary mantle

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• Show your work, and if possible, explain where you are stuck.
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[vital briar]

in a, by all but finite they mean infinite n right? as in every neighborhood of p has infinite elements of the sequence?

[vital briar]

why did they assume N exists when ${ p_n }$ could be something like $\sin (n)$, then there are infinite $p_n$ in every neighborhood of $p = 1$ but ${p_n}$ doesn't converge to it

[dull bear]

They’re saying that outside of that neighbourhood, you can find only finitely many terms of the sequence, which is stronger that saying the neighbourhood has infinitely many elements

[twin meteor]

reg

[vital briar]

aa i don't understand

[vital briar]

like i think i understand what you said but not how it's the same as this

[vital briar]

you mean like for every neighbourhood around p there are only finitely many points outside, so the sin example wouldn't work?

OH

[dull bear]

Yep, like that, similarly something like (-1)^n fails because although there are infinitely many elements of the sequence in any neighbourhood about 1, if you choose a neighbourhood that excludes -1, then you have infinitely many elements outside as well, which isn’t allowed

[vital briar]

it's like
the neighborhood has ALL elements except for some finite number of n?

[dull bear]

Basically yep, only a finite amount (e.g. you could say like p1, p5, p6 aren’t in there, or something like that, just that the ones that aren’t are finite in quantity)

[vital briar]

ahh so true like anything that doesn't converge has infinite elements outside some particular neighborhood of any point?

[dull bear]

Yep, like if you don’t converge to your claimed limit, you can find some neighbourhood such that outside there are infinitely many terms of the sequence (for example, for the (-1)^n example, for both 1 and -1, you just pick a neighbourhood that excludes the other)

[vital briar]

yuss got it, thanks

.close

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• Show your work, and if possible, explain where you are stuck.
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[fallen sand]

pls help

how was it factored?

[near tartan]

That's the whole square

[velvet zephyr]

yeah

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

[vast shale]

What is the y raised to?

[near tartan]

(x/2)² + 2(x/2)(1/2x) + (1/2x)²

[vast shale]

I don't think advertising is allowed

[fallen sand]

what is the topic called so maby i can watch vid on it ?

[velvet zephyr]

factorization?

[vast shale]

@sterile forum

[velvet zephyr]

<@&268886789983436800>

[fallen sand]

.close

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[velvet zephyr]

$(\frac{x}{2})^2+2*\frac{x}{2}*\frac{1}{2x}+(\frac{1}{2x})^2 = (\frac{x}{2}+\frac{1}{2x})^2$

this latex thing is so tedious

[vast shale]

I don't understand a shit lmao

[twin meteor]

Meolve

[velvet zephyr]

#latex-help

It's easy.

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[untold arrow]

a1, a2,a3 is a fundermental set of solution of Ax=0, if b1=2a2-a3,b2=a1-a2+a3,b3=a1+ta2 is also the fundermental set of solution of Ax=0, then what can we know abt t?

[hybrid flicker]

what is A?

[untold arrow]

A matrix

[hybrid flicker]

no further specification?

rank?

dimensions?

[untold arrow]

yes ,that's all we get

[hybrid flicker]

not a square matrix?

[untold arrow]

we don't know

[hybrid flicker]

!original

[vocal sleet]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[untold arrow]

sorry for confusion but that's the original problem with entire originial context

[hybrid flicker]

ok

so

[untold arrow]

ooh wait

[hybrid flicker]

if we write this first set of general solutions in a matrix X = (a1,a2,a3)

[untold arrow]

I used machine translation so it has something off, lemme edited, i'm sorry

fundermental set of solution, or basic set of solution ig

so B= this matrix \times (a1 a2 a3)^T ?

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[untold arrow]

.reopen

[vocal sleet]

✅

[hybrid flicker]

I don't know how you got that matrix

seems wrong

b1 = 2a2 - a3

so 0a1 + 2a2 - a3

so the matrix's first row should be 0 2 -1

[untold arrow]

Ooh yea that matrix is wrong

But if we replace it with correct matrix

Then B= the matrix \times (a1 a2 a3)^T ?

[hybrid flicker]

yes

and if both (b1 b2 b3)^T and (a1 a2 a3)^T are fundamental sets of solutions

(meaning they're a basis of the set of solutions)

[hybrid flicker]

then that matrix, name it M

[untold arrow]

Fundamental set of solution

My bad, translation error

[hybrid flicker]

yes

so

[untold arrow]

Det M=0

[hybrid flicker]

kinda the opposite

you're sending a basis to another basis

so the matrix that does the transformation is invertible

so det M is NOT equal to 0

so now, find the correct matrix M

[untold arrow]

Thanks 🙏💕

[hybrid flicker]

and compute det

[untold arrow]

Totally understand

.close

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[red ravine]

I need help with Set notations

[red ravine]

my solutions are saying this can simplify to A^c union B (from a set X consisting of subsets A,B,C)

We can rewrite the lastbracket as A compliment intersect B

which would just be the objects of B not in A

then union of (A intersect B) and B (not in A) is B

okay because this question provides me with the same info as you

let me assume they do not share objects

so A B and C are not subsets of eachother

that means B^c is A union C

A intersection (A union C) is A

compliment - A^c

ffs

doesnt make sense

A compliment union B is just B

[hybrid flicker]

^c is complement

[red ravine]

yes

[hybrid flicker]

so

you can look at (A n B^c)^c

do you know de morgan laws?

[red ravine]

yes

it would be A^c union B

[hybrid flicker]

yes

[red ravine]

shit

[hybrid flicker]

union yes

[red ravine]

ok

let me see now

after that change

[hybrid flicker]

so (A intersect B) union A^c union B

[red ravine]

okay that was very simple

[hybrid flicker]

so notice that

[red ravine]

yes

[hybrid flicker]

A intersect B is smaller than B

[red ravine]

thank you very much

[hybrid flicker]

so you can get rid of it

and yeah you're left with A^c union B

[red ravine]

.close

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[red ravine]

.reopen

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✅

[red ravine]

omds

im so tired of this

apparently the top cane be simplified to A intersect (B union C^c)

if you have A intersect C compliment, thats just A

because C compliment is A union B

.close

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[mild epoch]

the first screen shot is the answer

where does the -5x4 on the last line come from

shouldnt it be -2x4

[calm light]

looks like a typo

[mild epoch]

in a text book

[calm light]

it should be -2x4

[mild epoch]

whats the point of an answer key if nobody proof checked it

[calm light]

sometimes when ppl are writing, they accidentally write something thinking they’re writing something else

they’re only human

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[royal bridge]

Hi, I’ve done a-c, as well as the computational part of d, but I’m having trouble understanding why the first component of the resulting vector has to be F_n. This is what I have for part d. I just am kind of unsure conceptually.

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[bitter pilot]

Does anyone know how to draw an amplitude and phase spectrum

[bitter pilot]

or explain how this works

.close

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[half jetty]

How do I do the 9th question?

[whole oasis]

use

cos2x identity

$\DoubleCos$

[twin meteor]

Modus

[whole oasis]

3rd one

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