help-27

[restive river]

there you go

congrats

[glacial tinsel]

=60°

Thank you 👍🏻

[restive river]

You're welcome

[devout snow]

@glacial tinsel Has your question been resolved?

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[pulsar tundra]

the question is asking to find the dimensions of a rectangle of the largest area inscribed in a circle with radius 4. I am not getting the right length and I am not able to understand why

[winter patrol]

Your work isn't complete

x alone isn't the dimension of your rectangle

[pulsar tundra]

oh I think I get it. I got the length for only half the Rectangle?

i got to multiply it by 2?

[winter patrol]

yes

[pulsar tundra]

got it!! Thankss

.close

[devout snow]

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[devout snow]

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[green token]

can anybody calculate H here as i got really messed up in calculations

[hollow ice]

yea, h sounds about right

thats how far earths geostationary orbit is from surface

[devout snow]

@green token Has your question been resolved?

[devout snow]

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[devout snow]

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[delicate lichen]

Can someone explain to me the how to get the answer for the the last two questions. This is homework and it's like the 2nd day of school and i understand to some extent but like this stumped me 😓😓 (btw for question 16 it says the end of the 10 years and question 17 it says interest rates for the given period. Srry for the cut off)

[static swallow]

.rotate

[static swallow]

.rotate

caca

[delicate lichen]

Do u want me to rotate for u?? 😭

[ionic geyser]

.rccw

[mystic scarab]

,rotate

[static swallow]

thank you

[ionic geyser]

oh it's a comma not a dot

thanks alberto

[static swallow]

damn ts so economy shi

aint it like (5/100)* 4

and (10,5/100)* 12

[delicate lichen]

What's rhe * for?

[static swallow]

multiply

x

[delicate lichen]

Ah okay ty

Okay wait I tried to do that formula and I got like 0.2 and then I scrolled to the answers

I'm lowk so confused 😭

[restive river]

,rccw

[restive river]

what have you tried

show your work

[delicate lichen]

So basically for the questions 17 a) I did what rhe other dude said and did (5/100) multiply 4 and I got 0.2 on the calc but it doesn't match w the andwe

Answer*

[restive river]

that formula is not correct ig neither is (5/100)^4 =(5/100)*4

this is the one for compound interest

equating that with simple interest should give you the rate

[delicate lichen]

What is the nt for? Also for question 17 I don't think I was given a P

[restive river]

n is the number of periods, here n=1 as the interest is compounded annually

[restive river]

dw P will cancel out as P is same for both compound and simple interest

[delicate lichen]

So is P is just not in the equation anymore?

[restive river]

for CI = $P((1+r_{c})^t - 1)$ \
SI = $P(r_{s}t)$

[woven radish]

Hi

[restive river]

it is, equate SI = CI you will see it cancels out

[delicate lichen]

Whete did the s some from?? And I'm still a bit confused on what t is supposed to be?

[static swallow]

mb mb I dont know a single thing about economy shi

[delicate lichen]

Dw nor do I that's y I'm here in the first place

[restive river]

$r_{c}$ = rate for compound interest \
$r_{s}$ = rate for simple interest \
t = time period which is number of years her

[restive river]

🥀 we all bad at economics here

[woven radish]

Hi

[static swallow]

economy != math

[restive river]

https://tenor.com/view/facts-big-facts-true-so-true-true-story-gif-10768238346551082063

[delicate lichen]

Wait so if there isn't a P in the question how do I substitute the P in the formula or smth

I feel like I'm js making u repeat urself 💔

[restive river]

if you have a(b) = a(c) , you can divide both sides by a so a cancels out because a is common

Similarly CI = SI \
$\implies P((1+r_{c})^t - 1) =P(r_{s}t)$ (P cancels) \
$\implies (1+r_{c})^t - 1 = r_{s}t$

[woven radish]

Hi

[delicate lichen]

Ah okay

[restive river]

sometimes you dont need to substitue you can just work with P as P

[delicate lichen]

Ty bro 🥹🫰

[restive river]

np

[delicate lichen]

Question could u write out the formula but replace the letters w rhe numbers from the question

[restive river]

which formula

[delicate lichen]

This one

[restive river]

what is t for a

and rate of interest

[delicate lichen]

Wait what?? 😓

[restive river]

?

[restive river]

here for 17a

[delicate lichen]

Yes that one

[restive river]

you are given r_c which is rate of compound interest, and t is given as well

just subtitute that

[delicate lichen]

Ahhh okay brb lemme try that rq

So would it be ts?

[restive river]

,rccw

[restive river]

,calc (105/100)^4 -1

[woven radish]

Result:

0.21550625

[restive river]

yh

[delicate lichen]

So then y does the answer say its 5.39 p.a

😭😭

[restive river]

this = r_s * t

0.215 = 4r_s

,calc 0.215/4

[woven radish]

Result:

0.05375

[restive river]

so you have r_s = 0.05375

now r_s is in the form rate/100

so your rate will be r_s *100 = 5.375

,calc 0.21550625/4

[woven radish]

Result:

0.0538765625

[restive river]

hm.. it is closer to 5.39

[delicate lichen]

Okay wrote ts all down ty sm for being so paitent 😌

[restive river]

np

if you have any more doubts you can post else close this channel by typing .close

[delicate lichen]

Okay

.close

[devout snow]

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[devout snow]

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

[elfin canopy]

Im a truck driver, i need to figure out some trip planning stuff. I have to drive 1050 miles, averaging 55 mph, i need to be at my destination by Tuesday at 8am. I need to take a 10 hour break after 600 miles. When should i leave to start the trip?

[vital edge]

,calc 1050/55

[woven radish]

Result:

19.090909090909

[vital edge]

That's your travel time

Add 10 for the break

And round up to be safe

[elfin canopy]

30 hours

[vital edge]

30 hours before

[elfin canopy]

Okay thank you

[vital edge]

Monday 2 am

[twilit field]

anything else you would like to ask?

[elfin canopy]

Yes theres another aspect

[twilit field]

sure. what would it be?

[polar chasm]

Driving time = Distance / Speed (use miles and mph)
Total time = Driving time + Break time

This is the general formula you can use next time

[vital edge]

If anyone nosols me here I swear to god I will murder you

[elfin canopy]

Actually no im good, i just figured it out, thank you guys

[twilit field]

realistically though for the original travel time you'd want to add a couple of hours extra in case of traffic or something.

[twilit field]

oh alright, you may ⁨.close⁩ the channel, and see you around1

[elfin canopy]

Yeah im gonna add 5 hours of buffer so ill leave Sunday at 9 pm

[vital edge]

Safe travels

[elfin canopy]

No traffic all night hopefully

.close

[twilit field]

all the best OP!

[devout snow]

Channel closed

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[devout snow]

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Remember:
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[green delta]

The area of 2 circles are in ratio 16:25. Find the ratio of their corresponding circumference.

Plz help with it. I'm struggling a lot and sorry if it was too easy.

[twilit field]

have you tried anything yet?

[green delta]

I can't solve it

[twilit field]

sure thing, but have you made any progress?

!status?

[devout snow]

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

[green delta]

Nah

[twilit field]

so you don't know where to start.

[green delta]

3

[twilit field]

oh?

can you show your answer and working then?

(that's not the same as no progress!)

[green delta]

My phone's camera is broken

[twilit field]

can you rewrite it in MS Paint or whatever drawing app, or type it here?

[fickle magnet]

try microsoft whiteboard

[green delta]

Wait

[pale schooner]

ש?

[green delta]

Wait a bit longer

Sry for the wait

[pale schooner]

ישראלי?

[green delta]

I know the handwriting is a lil trash

Also it took long since my phone is laggy and I'm not familiar with ms whiteboard

If anyone is not answering I'm closing it by 9:30

[obsidian nebula]

I don't think you can semplify r1 with r2, since those are different varables

C=2πr, therefore 2πr1/2πr2 should be the ratio you need

You can simplify 2π and you Just gotta find r1/r2

Since you have the area πr² you have πr1²/πr2²=16/25

Semplify π you got (r1/r2)²=16/25

[crystal dawn]

might wanna check in with OP to see if he knows why

[obsidian nebula]

Square rooth both sides ratio should end up 4/5

[crystal dawn]

why as in why each step is taken

!nosols <- cuz this is a thing

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

@green delta Has your question been resolved?

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[green delta]

Thx bro

.close

.close

[devout snow]

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[tranquil marlin]

Im doing number 2 and just a quick question, i got that there arent any points of inflexion since concavity doesnt change at x=0 even with y''(0)=0. Now im doing 2b and i dont know whether i should include x=0 within the interval where y is concave up

[thin fern]

Yes

f">=0 is still convex

[tranquil marlin]

Alright, thanks!

So just in general, even if the second derative of a point is 0, if it isnt an inflexion point then it also has a concavity?

[thin fern]

I think it can be an inflection point and still have concavity

I believe f is concave up iff f" >= 0

[drifting sierra]

Convexity/concavity can be strict

[tranquil marlin]

So should my answer be that y is concave up through (-inf;0)U(0;inf) or (-inf;inf)?

[drifting sierra]

All of R should be correct, but you may want to review the definition of "concave up" that you've been given

[tranquil marlin]

Oop, nevermind! Its (-inf;0)U(0;inf)

.close

[devout snow]

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[drifting sierra]

Damn, that definition conflicts with pretty much every definition I can find online

@tranquil marlin if the subject interests you, you could have an argument with your teacher about it

[devout snow]

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[lilac spindle]

How do I go on to solve this?

[fickle magnet]

hmm

[twilit field]

you should probably rearrange the equation so that the sine is left standing alone on the left first.

[fickle magnet]

jus plot the graph

[restive river]

you would need arcsin here

[north hound]

The answers are so ugly.

[restive river]

yh assume they use calculator

[lilac spindle]

yep this does it

[restive river]

,calc 3pi

[woven radish]

Result:

9.4247779607694

[lilac spindle]

Kinda figured it out spending time on it

.close

[devout snow]

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[hazy jasper]

Hi, I am confused with the second part of the question. I did the first half pretty easily but the second half my proof seems very weak, im wondering if I can just make a set with 4-5 elements and show that it has an inverse and identity element but I dont know how that would apply for all.

[uncut crow]

do you know what $\bZ_4^\times$ is?

[woven radish]

generating function shill

[hazy jasper]

i think? its multiplying elements in Z mod 4?

[uncut crow]

i imagine it is the elements in {0,1,2,3} that are relatively prime to 4

[hazy jasper]

oh is it? i thought it was a quick way to write mod 4

[sand quarry]

The identity element isn't 0 btw

Thats for addition

[hazy jasper]

oh right

shi i messed up that q bad

thanks both of yous!!

.close

[devout snow]

Channel closed

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[sand quarry]

I think youre better off drawing a Cayley table btw

The set is so small

[hazy jasper]

you are right thatll help a lot

thnx

[devout snow]

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[blissful hound]

Good afternoon, I am teaching myself python with a text book. I am struggling with the following commands. I am getting a unique graph for each command that only shows the most recent step. For example plt.xlabel('x') displayes a graph with nothing but the xlabel labelled. The show() command is showing nothing.

[vital edge]

<@&268886789983436800>

[modest dagger]

Keep it sfw

That includes code output

[devout snow]

@blissful hound Has your question been resolved?

[blissful hound]

No

sorry, I was having some fun with the plot titles.

[supple knot]

This isn't a math question

Go join a python server

[rare kernel]

dont know if someones gonna say !NOAI but chatgpt is pretty good with coding

[blissful hound]

I think it is more so a system issue.

I like interacting with people when I can.

[rare kernel]

ohk then try it on a different system

or use a different compiler online

like thonny or smth

[supple knot]

Yes python discord server has people

Again this ain't a math question

[devout snow]

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[devout snow]

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[gaunt oyster]

how do i find the maximum area of this cuboid if the 2nd derivative was positive (concave up)?

[winter patrol]

it is possible that there is no max

[gaunt oyster]

ok but how do i prove that then?

[winter patrol]

you only had one solution to d/dx SA = 0
one stationary point,
second derivative indicates that's a local min

(probably also shouldn't mention for maximum surface area that early)

[rain summit]

here's the graph btw

as $x \to 0^+$, $\lim_{x \to 0^+} = \infty$

[woven radish]

1 divided by 0 equals Infinity

[gaunt oyster]

Yeah but then i disproved it by checking with the 2nd derivative

[winter patrol]

better to mention for stationary points

[gaunt oyster]

wait they never taught me this, what does 0^+ mean?

[rain summit]

x approaches 0 from the positive side

[gaunt oyster]

so numbers like 0.01, 0.001, 0.0001 etc?

[rain summit]

?

[scarlet swallow]

Ugh <@&268886789983436800> send him to the shadower realm

[gaunt oyster]

if x was 0.01, 0.001 etc

[scarlet swallow]

Sorry for interrupting anyways 0+ means you go from 0.01 to 0.001 to 0.001 etc. until it approaches/is 0

[gaunt oyster]

oh ok

but how do i prove this

the intuition is not clicking for me now

[scarlet swallow]

Wait a minute your eqn is wrong

Try doing 2nd derivative again, you've made a differentiation mistake there

[gaunt oyster]

ok lemme check again

oh wait the denominator should be a 3x^3

[scarlet swallow]

Also I think the questions wrong, there shouldn't be a maximum surface area

Think about it: you can stretch a cuboid to be infinitely long, so the surface area is infinite, but the volume can still be the same

[devout snow]

@gaunt oyster Has your question been resolved?

[devout snow]

Channel closed

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[devout snow]

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[sly geode]

Hello I need help with this

[sly geode]

How do i find out obtuse ABC?

[viscid dome]

Please solve this!!

[sly geode]

hey this channel is occupied

[devout snow]

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).

[viscid dome]

I m really sry

[twilit field]

use the bearings to aid you.

[sly geode]

ah thank u

[twilit field]

anything else you would like to ask?

[sly geode]

nope, thank you

[twilit field]

alright, then you may close the channel with ⁨.close⁩. welcome to the server and see you around!

[sly geode]

.close

[devout snow]

Channel closed

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[devout snow]

Available help channel!

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Remember:
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[twilit field]

heads-up: your asterisks are missing.

[stone stump]

\* for *

[twilit field]

do you intend to italicize the parts of the messages that are currently italicized or do you mean to put *s there?

if you intend to italicize whatever is italicized right now then my message does not apply and I apologize.

[devout snow]

@outer hatch Has your question been resolved?

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[devout snow]

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[grizzled iris]

How do you guys make math studying enjoyable? I found that normall studying just doesn't work for me and internal brain processes get in the way (I won't discuss that) and I need to engineer the process so that studying becomes more comfortable and stimulating.

[twilit field]

relate it to everyday life, find uses for the math you learnt, and teach/share it to others.

[grizzled iris]

Ok something more specific can I ask?

[twilit field]

sure.

[tribal patio]

I personally love puzzel so I kinda like combinatorics, other than that you can try doing somewhat of mid-easy problems first to boost your mood

[twilit field]

it also kinda depends on what mode of learning you prefer.

[rain summit]

99% of people who tried to learn math memorizes the rules, but instead, you should understand why it works

[grizzled iris]

Yes that's what I am trying to achieve

[twilit field]

different people learn differently, so some people find physical activities more conducive to learning. some people learn better by seeing, some learn better by reading, etc.

[rain summit]

yep, relate to real life like nicole said

[grizzled iris]

Well currently, the only way I study math is I am getting to my worksheet set of problems, and I solve them one by one

[twilit field]

find what works best for you and apply it.

[grizzled iris]

That's what I am trying to d

[rain summit]

so for instance

[twilit field]

mm. this process will be an experiment though, so don't be discouraged if the first few methods you try don't work out too well.

[rain summit]

do you know why $a = a$ for any $a$?

[woven radish]

1 divided by 0 equals Infinity

[grizzled iris]

Because equality sign?

[rain summit]

nuh uh

you gotta understand what equality is here

[twilit field]

do we really want to get into the analysis derivation of equality in this help channel...

[rain summit]

Equality is used when 2 sides have the same value

[grizzled iris]

No please im in 11 grade don't shoot me with calculus yet

[twilit field]

anyway, you said you have something more specific to ask. what is it?

[grizzled iris]

You have to admit that going everyday, to the same worksheet of problems, and just solving them one by one, occasionally asking questions here to learn something more or gooling something isn't super intersting

[rain summit]

that's the process you have to go through

[twilit field]

not only do I admit and agree with you, this is the reason I skip around some problems.

[rain summit]

it's boring ik

you can go a bit higher if you want

[twilit field]

but I only do so if I can fully motivate and oneshot any remaining questions in the same section.

[grizzled iris]

But this is the reason I avoid doing it so much

The discomfort of sitting with this stupid black white question paper and doing it one by one is super boring

[rain summit]

im shooting to calculus as a 9th grader here

[grizzled iris]

This is not how I am going to get good with math

[twilit field]

welp, here comes the calculus despite OP not wanting it. I'll excuse myself before this turns into a shitshow then.

[rain summit]

it's because i wanted to

[grizzled iris]

Yes and I also want

But I am struggling to

[grizzled iris]

No it's fine

[grizzled iris]

So how you do it?

[rain summit]

i just keep on doing it and submit the homework

[grizzled iris]

If you are shooting calculus at 9th grade you possibly didn't find the worksheets as boring as me

[rain summit]

and avoid punishment

[rain summit]

uhh, i shoot up to calculus because i wanted to and i feel confident about my algebra skills

[grizzled iris]

How do you study

What is the process of what you go through

[rain summit]

i do worksheets and textbooks like you do

and i hop into help channels like yours here

to improve my skills

:)

[grizzled iris]

Yes that's what I do also

But there is a slight misalignment here

[rain summit]

?

[grizzled iris]

You do it differently/better than I do

[rain summit]

?

[grizzled iris]

So for you it's "i do worksheets and textbooks like you do"

But psychologically you are going through completely different thing than I

[rain summit]

ngl i also do advanced class

[grizzled iris]

Can you go deeper into "i do worksheets and textbooks like you do"

Add more details

[rain summit]

💀

[crystal dawn]

Infinity, I don't think you can assume everyone has the same motivation you do...

[grizzled iris]

No that's serious question

[rain summit]

you can take over

im not a specialist in this

[grizzled iris]

Yes that's true

[rain summit]

(or is that the right word to say)

[crystal dawn]

I mean as a teacher I've met students who are at different levels in learning, but many of them are outliers in that they do bring their own motivation

still, I have seen some that don't find worksheets particularly interesting, at least not alone

and to be fair, I understand. I used to be subject to boring worksheets all the time too

[grizzled iris]

Yes that's what I want to do

[grizzled iris]

The reason is that they are going through different mental processes compared to the worse students

[crystal dawn]

you're not wrong indeed.

[grizzled iris]

That's the reason they can practice math for 5 hours per day and enjoy it

[grizzled iris]

Because I am not, I know this because I had to research up psychology before coming here

[rain summit]

-# oh lord, didn't expect that coming

[crystal dawn]

ok, I did not expect that answer, but sure

[grizzled iris]

Well, this shit is really threatening me and my future so I had to do something about it

[crystal dawn]

either way, I find myself intrinsically motivated in a way that is extremely difficult to explain

[grizzled iris]

Yes that's what I want to achieve

[crystal dawn]

so in the interests of not speaking on behalf of those who can bring their own motivation in concrete ways, if you want to hear a better answer I'll defer to one of my students

because if you want to see my motivation

#1430149350931173417
#1463931680594329655
I am not hesitant to just rambo into fields like those knowing absolutely nothing and getting cooked by the books and the seniors in this server

as for why, I just love STEM, which is a disingenuous answer. as such I cannot promise you this answer from a student's pov

@twilit field get back here

[twilit field]

I will say my way of motivating myself will not apply to everyone, because I already have a higher field in mind (namely, geometric measure theory and fractal geometry).

but as my bio implies, I love fractals independently of math.

[shell plover]

the reason i think some ppl enjoy doing maths is cuz they have a strong foundations. They dont get stuck in simple things like solving a quadratic, doing some algebraic manipulations etc. And when you get good in these basic things you remove the hard part. Now you can come up with a blueprint of the solution in just your brain without writing anything.

[twilit field]

this has led to me trying to investigate fractals intuitively first, and then when I found out that there are literal fields that do low-level research of fractals, I build a pathway to those fields.

but while working my way there, I try to think of the relationships between any exercise I do and my end goal of understanding fractals.

[grizzled iris]

So Hanako is a teacher

[crystal dawn]

indeed I am

[grizzled iris]

You have paid extra lessons?

[glass canopy]

It would be useful to always ask "What problem was this trying to solve" whenever you are given a definition. This gives motivation to look at examples, and a sense as to why you'd care about this.

[crystal dawn]

no. I teach STEM more or less for free, with asterisks.

[grizzled iris]

I find math interesting as to why and for what purpose it is used

But when it comes to details to solving equations and memorizing stuff that's when it becomes little too costly

[tribal patio]

Damn everyone is having somewhat of pretty cool motivations

[grizzled iris]

I wish I could have one

[twilit field]

I have found little need to memorize most stuff actively.

[glass canopy]

What point is a set of tools if they're unable to be used?

[tribal patio]

I genuinely just do things because I can't bear being worse than my friend in Math

[twilit field]

maybe a few key details here and there, but almost always you can reason things out from the foundational details.

[twilit field]

at first I was like this.

[glass canopy]

Fair enough haha

[twilit field]

then I got to know one particular person from a nearby school (I think she's a Helpful here)..

[tribal patio]

I am still like that lol

[twilit field]

after knowing her the hope of being the best amongst my contacts in math got shattered in a way that I don't mind.

at least now I get friends to talk cool stuff with.

this could be a motivation in itself!

[crystal dawn]

was it the fox

[twilit field]

yes.

[tribal patio]

that's fair

people are are crazy also

[twilit field]

now I'll wait for OP before continuing.

don't want OP to come back to a huge wall of text.

[grizzled iris]

Wait I got lost a little bit

Give me a second to decode the information

[twilit field]

take your time!

[restive river]

what level do you tech

[crystal dawn]

from absolute basics to whatever I know atm.

[restive river]

oh, ic ty

[grizzled iris]

But it's impossible, the fact that I am not able to sit down on my ass and just do it and all of you guys can

There are multiple factors and underlying reasons why is this happening

[twilit field]

I don't sit down all the time.

sometimes I'll be drawing at the whiteboard, sometimes I'd be 3D printing some fractal-related stuff, etc.

math is as much of a science than it is raging lunatics sitting and furiously penning away at proofs and reading papers.

which means you can experiment with some of the more concrete stuff in math.

doesn't apply to all of math, esp. the more abstract fields (infinite-dimensional stuff, anyone?), of course, but for most of early math this method works.

[grizzled iris]

Ok so I knew nothing before joining, and i know more nothing after I am leaving

Counterintuitive interpretation of knowledge

[twilit field]

?

[grizzled iris]

I didn't learn nothing more than I knew

Im sorry for saying this

But reality

[twilit field]

I sympathize with you, but I don't know what else to say, sorry.
do you have any other questions for the channel though?

[grizzled iris]

No

.close

[devout snow]

Channel closed

Closed by @grizzled iris

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
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[quartz bloom]

Whats the difference between

" For any "
"For each"
"For every " .

"There exists some number n"
"There exists a number n"

"There exist at least one n "

[pseudo basin]

none

[quartz bloom]

When we write "there exist some number n" or any other in that part

[pseudo basin]

it means ∃n but in natural language

[quartz bloom]

Do we mean one specific number that exists ,
Or we mean there are some numbers

That satisfy that

[pseudo basin]

"there exists some number n" doesn't mean there's only one such n i.e. there's no uniqueness implied

[sand dove]

Usually we can pick one at random and then do stuff with it, but it doesn't mean the one we pick is special

[quartz bloom]

What about "there exists 'a' number n"

[sand dove]

it's just one of the possibly many who verifies [insert property]

[pseudo basin]

again, uniqueness is not meant

if ever you want to say unique then you have to say "unique" or "exactly one" or something like that

[quartz bloom]

Understood

Thanks

.close

[devout snow]

Channel closed

Closed by @quartz bloom

Use .reopen if this was a mistake.

[grizzled iris]

That is what I am trying to solve, but let's not disrupt another OP's help channel

[glass canopy]

That was posted when this was your help channel

[grizzled iris]

I know,

[glass canopy]

Since that channel is closed/solved;
For the most part, you're building a set of tools with which to solve problems right?

[grizzled iris]

Yes

[crystal dawn]

please refrain from chatting in closed channels, as they may lock or become available without warning.

[glass canopy]

Knowing when/why those tools are used allows you to use them without having to memorise

[glass canopy]

Thanks^

[devout snow]

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

[velvet coral]

why does the textbook need to prove that $$e^{z + w} =e^z \cdot e^w$$? Isn't this true for any numbers? like $$x^{a+b} = x^a \cdot x^b$$?

[woven radish]

LXDL

[pseudo basin]

we dont know that yet at this juncture

e^z is just a formal symbol

it might as well be just a function ⁨exp(z)⁩ that we havent proved shit about yet

[velvet coral]

but here they use ht efact that e^{x+s} = e^x e^s

hence why am kinda confused

because they are assuming what they are trying to prove basically

[pseudo basin]

yeah with x and s real

the goal here is trying to extend it to complex values

[velvet coral]

ohhhwait, you are syaing we only know that the formual $$x^{a+b} = x^a x^b$$ holds only when $a, b \in \mathbb{R}$?

[woven radish]

LXDL

[velvet coral]

but here $a, b \in \mathbb{C}$? Hence need to proce separlety

[woven radish]

LXDL

[pseudo basin]

yes

[velvet coral]

then what about Euler's identity?

like $e^{ix} = \cos(x) + i \sin(x)$?

[woven radish]

LXDL

[velvet coral]

is that something that is proven, or just follows from defn?

because i have seen "proof" that use the taylor sereis of cosx and sinx

[sand dove]

it's the definition of exponential above applied to z = ix

[velvet coral]

i see alr, so not some sort of theroem that can be derived?

[pseudo basin]

it all depends on what arbitrary choice you make for your starting pt

[sand dove]

If your starting point is the definition above, then no, it's just the definition

if your starting point is e^z = 1 + z + z^2/2 + ...

then yes it is a "theorem" that e^(ix) = cos(x) + isin(x)

In the sense that it's not trivial and has to be proven

[velvet coral]

ohh i see okay, because i know there are equivalnet defn/charactiriaiton for e^x when x is real, just wanst sure for when x is not real

[velvet coral]

ah okay, but then we can derive that e^z = 1 + z + z^2/2 .... if we use the starting point as the defn i gave (from the book)

[devout snow]

@velvet coral Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[elder meteor]

What's the derivative of arctan?

aka tan^-1

[kindred mauve]

so they're using the inverse tan function

[elder meteor]

Technically yeah

[kindred mauve]

so is it this

[elder meteor]

pretty much yeah

[woven radish]

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

[elder meteor]

but what you said is correct

[kindred mauve]

and how does this give me 2tanu

[elder meteor]

1/a^2

you factorise with a² in the denominator so it's 1 over a²

[elder meteor]

when you substitute x by 2tan u

the integral simplifies to $\int du$

[woven radish]

Ditril

[elder meteor]

do you see understand why that is?

@kindred mauve

[elder meteor]

what did you do

[kindred mauve]

i subbed in u

[elder meteor]

do you know how you went from the first integral to 1/a arctan(x/a)?

[kindred mauve]

No

[elder meteor]

okay so

what's the derivative of arctan?

[sacred sedge]

do you understand integration by parts first?

[kindred mauve]

1/(x+1^2)

[kindred mauve]

Yes

[elder meteor]

are you sure?

[kindred mauve]

i mean x^2+1

[elder meteor]

yesss

okay so how can you get the derivative of arctan from 1/x²+a²?

as in come back to something similar to it

[kindred mauve]

yes

[elder meteor]

wdym yes 😭😭

[kindred mauve]

oh you mean show you how

[elder meteor]

yess

For the choice as to why they chose x = 2tan(u) it really comes to practice with calculus and noticing the fact the integrand (what's inside the integral) reminds you of arctan so a substitution with tangent could lead you somewhere

[north latch]

wait howd they pull out $-ln(x^2 +4)/x$

[woven radish]

Cowking

[north latch]

thats not the right latex but ok

[elder meteor]

integration by parts

[north latch]

ahh okok

[elder meteor]

you integrate 1/x and differentiate ln

[north latch]

I didnt notice the first step was IBP

[elder meteor]

gulp

[sacred sedge]

it is probably easier to the second step without the trig sub

[elder meteor]

i know

no reason to substitute like that when we know arctan

but it works even if it complicates it

[sacred sedge]

where did the 2sec^2(u) go

[elder meteor]

sec is 1/cos right

sec^2 = 1/cos^2 = 1 + tan^2

[sacred sedge]

oh right

[elder meteor]

yuh

[sacred sedge]

so $$\int 1 du$$

[woven radish]

InterGalactic

[elder meteor]

yes

becomes u + c

x = 2tan(u) so u = arctan(x/2)

hence arctan(x/2) + c

[sacred sedge]

oh welp

[devout snow]

@kindred mauve Has your question been resolved?

Channel closed

Closed by @kindred mauve

Use .reopen if this was a mistake.

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Send your question here to claim the channel.

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

[void heath]

bro

[void heath]

i need help

who gonna help me ):::::

[silver thistle]

U gotta post ur question

[void heath]

uh

i didnt pay attention in class at all

[silver thistle]

factor out (x+3) first and then go from there

I lowkey forgot how to do the division ngl

It’s been a while

[void heath]

synthetic division?

how do i factor

what method

[silver thistle]

Yes

But ngl u don’t really need to do all that

[void heath]

bro js help me

[silver thistle]

Since there’s only one possible answer where it’s (x+3)(factored poly)

[silver thistle]

lol we can’t just give u the answer

[void heath]

ik

can u tell me the steps

[silver thistle]

Do this ^ or long division it doesn’t matter I’m pretty sure

[void heath]

so

how do i do it using synthetic

[steady kettle]

how would you change 27

[void heath]

idk

[steady kettle]

whats 3x3

[void heath]

9

[steady kettle]

how bout 3x3x3

[void heath]

27

[steady kettle]

its 3^3

so change x^3+3^3

and see the formulas

check if each is right

i see only one right

[void heath]

gng

idk

😭

explain better

[steady kettle]

ok

[void heath]

how do i change x^3+3^3

[steady kettle]

wait

[void heath]

how does that corralate to the sanswer

answers

corrolate

[steady kettle]

Can you organize the four equations

[void heath]

wdym

[steady kettle]

for example

(a+b)²(a-b)=
(a²+2ab+b²)(a-b)
=?

can you do like this

[void heath]

bro what

im struggling

[steady kettle]

oof

let x=1

[void heath]

k

[steady kettle]

then its 1³+3³

whats that equal to

[void heath]

30?

28

mb

[steady kettle]

so for the formula,

a=1, b=3 right?

[void heath]

yes

[steady kettle]

put it in the equation

[void heath]

what

[steady kettle]

is 1³+3³=(1+3)²(1-3)

[steady kettle]

this is the first equation

[void heath]

ok

[steady kettle]

is it right?

[void heath]

no

[steady kettle]

then the second
is 1³+3³=(1-3)²(1+3)

is it right

[void heath]

no

[steady kettle]

the third one
1³+3³=(1+3)(1²-1×3+3²)

is it right

[void heath]

u have to use pemdas?

or go in order

[steady kettle]

idk what pemdas is sorry

[void heath]

ok

so like in the (1²-1×3+3²)

[steady kettle]

yeah

[void heath]

what do i do first

1^2?

or 1x3

or 3^2

[steady kettle]

what is 1²

[void heath]

1

[steady kettle]

what is 1×3 then

[void heath]

3

[steady kettle]

what is 3²

[void heath]

9

[steady kettle]

(1-3+9)

[void heath]

7

[steady kettle]

yeap

[void heath]

no

[steady kettle]

?

[void heath]

3rd eqation is wrong

formula

[steady kettle]

(1+3)(1-3+9)=?

[void heath]

so 4th

gott abe right

sike

3rd eqation is right

equation

28

[steady kettle]

got it?

[void heath]

ye

[steady kettle]

!done

[devout snow]

If you are done with this channel, please mark your problem as solved by typing .close

[void heath]

.close

[devout snow]

Channel closed

Closed by @void heath

Use .reopen if this was a mistake.

[void heath]

.reopen

[devout snow]

✅ Original question: #help-27 message

[void heath]

help

[steady kettle]

how many zeros total

[void heath]

4

wait

whats a double zero

2 zeros?

im in 6th grade btw

which is why this hard for me

[alpine python]

wait how can this be answered? there could be irreducible factors

[crystal dawn]

wait.

6th grade?

[void heath]

ye

[crystal dawn]

how old are you, if I may ask?

[void heath]

im in alg 2

[jade pecan]

2 things. how old are u. is this conclusive information

[void heath]

13

bro im just tryna get help

[crystal dawn]

you don't have to send the question twice

[steady kettle]

this is kinda ambiguous

[void heath]

??

[crystal dawn]

if there are no other zeroes and no irrediucibles, then the number of zeroes is the degree of the polynomial

[void heath]

whats a irrecductible

so it would be 4?

[crystal dawn]

quadratic factors with no real roots

[crystal dawn]

as I see it, yes.

again, assuming those two conditions

[steady kettle]

i think so too

[void heath]

ok

[crystal dawn]

what have you learnt about complex conjugates?

[void heath]

so

didnt rly pay attention in class

sike

i was absnet that day

so nothing

[crystal dawn]

then you might wanna revise the material before attempting the quiz...?

[void heath]

thats what im doing now

[crystal dawn]

before, not while...?

but sure, whatever.

[void heath]

ts is not the quiz

its a review

[crystal dawn]

I mean, you can't review what you haven't studied, but I digress

[void heath]

yea im just tryna get help rly

[crystal dawn]

a complex conjugate of a complex number a + bi is the same number with the sign of the imaginary part flipped

so a + bi becomes a - bi

[void heath]

ok

[crystal dawn]

normally it's more productive to learn the material, then come here if you don't understand the material, cuz teaching is a rather tall task for a text help session

[void heath]

u right

thing is

theres no notes online

.close

[devout snow]

Channel closed

Closed by @void heath

Use .reopen if this was a mistake.

[void heath]

!done

[devout snow]

If you are done with this channel, please mark your problem as solved by typing .close

[void heath]

.close

[crystal dawn]

already closed

[void heath]

.close

oh

[crystal dawn]

the prompt was here

[devout snow]

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

[ionic jasper]

Hello, i translated the question and hope it still makes sense and is correct

[ionic jasper]

I think got the solution for the determine how many black balls needs to be added which is 13 i think

but im not quite sure

[devout snow]

@ionic jasper Has your question been resolved?

Channel closed

Closed by @ionic jasper

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Send your question here to claim the channel.

Remember:
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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.

[devout glen]

heyy can someone help me out with this please

[devout glen]

i really dont even know how to read a question like this, so 1 i dont even know how to start

[tall knoll]

1. says something like "give one value of x such that x = g^-1(1)"

[devout glen]

do you mind explaining how to read it like that please?

im so sorry you might need to gently teach this to me

[tall knoll]

"give one value x..." tells you what you're ultimately looking for
"x = g..." is the thing you're solving

[devout glen]

ohhh ok

[tall knoll]

they could've used more words I guess, but what they have is reasonable enough

[devout glen]

then what is that long line with the subscript mean

[tall knoll]

"evaluated at"

[devout glen]

ohh eval at y = 1

alright! then how do i apply this to the graph?

[tall knoll]

smh edits

if x = g^-1(1), what is g(x)?

[devout glen]

i dont understand why its g inverse yknow? like what does that mean and how do i use that for g(x)

[tall knoll]

i'm not sure how to answer "why"

[devout glen]

mm like i dont see g inverse on the graph, or i dont understand how to see it

[tall knoll]

they haven't drawn the inverse, but you don't need its graph

[tall knoll]

what you need is to answer this question

[devout glen]

oh! okay sorry

um 1?

g(1)?

[tall knoll]

no guessing

you have x = g^-1(1), and you apply g to both sides

g(x) = ?

[devout glen]

1

cuz it cancels out

um how do i go forth🌝

[tall knoll]

you can at least solve q2

[devout glen]

im truly sorry and i hope you're not getting frustrated but i genuinely dont know how to tackle this question, like i really need extra supprt

so idk how to solve q2

[tall knoll]

oh we didn't finish q1 yet oops

you know that g(x) = 1, so you should find such an x

look at the graph, it's easier than you think

[devout glen]

0.136

[tall knoll]

indeed

ok now you can do q2

[devout glen]

haha okay thank you

oh its 1

how to do 3?

oh nvm

its just findn slope

wait but of which values

??

[devout snow]

@devout glen Has your question been resolved?

[devout glen]

no

!help

[devout snow]

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

[devout glen]

<@&286206848099549185>

[errant junco]

hi

not helper but Ill try my best

[devout glen]

no worries! im confused on how to read 3?

like i think the first value is the coordinate (1, -7.925)? but idk

[errant junco]

okay so do you know the inverse derivative formula

[devout glen]

no...

[errant junco]

hm okay

so we know that its the inverse of g(x) rightt

[devout glen]

right lol

[errant junco]

if a point (a, b) is on the y = g(x), then (b, a) is on the y = g^ -1 (x)

and if the slope of g at ( a, b) is m,
then the slope of g ^ -1 at (b, a ) is 1/m

so you apply these things

to your graph

you see the red point

(0.136, 1) on g(x) will be (1, 0.136) on g^ -1 (x)

[devout glen]

ohhh my gosh that makes sense

thank you so much

[errant junco]

ok

you think you can get the answers now?

[devout glen]

so we're just finding the derivative of that one coordinate?

or the intant slope

[errant junco]

um no the the slope

[devout glen]

ok

how

its just the tangent right? but how do i find that

[errant junco]

so when you see g prime of 0.136 equals 5.968 its the derivative of g

from the blue curve

so when you look at the blue graph at x= 0.136, you see the point (0.136, 5.968)

[errant junco]

that's what this is saying

[devout glen]

okay yeah, then how do i apply that to question?

like am i finding the slope of the blue line now?

[errant junco]

you are just using that to figure out the slope of red line

you take the reciprocal

you think you got it now?

[devout glen]

no im sorry its still alittle blurry

do you mind providing like the equation and what to plug in? and reciprocal?

[errant junco]

um so you wanna find the slope of y = g^ -1 (x) at point (1, 0.136)

find the matching point on g(x): (0.136, 1), then read the slope of g there, and then take the reciprocal

idk how to explain more 😭

[devout glen]

no but like how do i "read" the slope of g? like is there an equation to do or am i manually going to count on the graph?

like i understand i have to find the slope but the question is how, like i know how to find a slope with two coords, but its only one coord

[errant junco]

this is pretty hard to do without the formula 😭

let me think for a minute and see if there is an equation

I think you can just interpret the graph

[devout glen]

oh thats so weird, i assumed every problem wants you to find a slope with an equation yknow? like i would think manually reading the graph would be innacurate?

[errant junco]

yeah you kinda have to use the inverse derivative formula but without it, we can just do it manually

and I don't think it's inaccurate

think of it like this
the inverse function is just flipped over the line y=x. So the tangent line flips too. when a line is flipped over y=x, its slope becomes the reciprocal

you understand this right

[devout glen]

okay so one coord is the (0.136,5.968) and i look for ones that pass through a corner so like (0.5, 3)

oh okay so i just flip the slope, okay i get it

[errant junco]

from the graph, on g: point is (0.136, 1) slope there is 5.968, so on inverse g, point is (1, 0.136), so flip the slope then it will be 1/ 5.968

[errant junco]

you got it? nice 😊

[devout glen]

okay 5 and 6 are the same so i just need help on 4 then ill be done

whats the diff between this and 3?

[errant junco]

number 3 is the slope and this is asking for the whole line

tangent line

so point on g^-1 you plug them into point slope form, then you got it

[devout glen]

ohh okay

nice thank you!!

!close

[errant junco]

this was pretty hard ngl 😭

[devout glen]

YES THANK YOU

like i thought i was stupid

[errant junco]

do /.close

[devout glen]

.close

[devout snow]

Channel closed

Closed by @devout glen

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[devout snow]

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[green token]

can anybody solve this

[fickle magnet]

Expand using a2-b2

[restive river]

yh

[restive river]

!noans

[devout snow]

The purpose of this server is to help you learn; please don't ask for direct answers. Ask for guidance, explanations, or feedback instead.

[restive river]

we cannot provide solutions

[pseudo basin]

use the symbol ^ for exponents

[fickle magnet]

Mb

[devout snow]

@green token Has your question been resolved?

[devout snow]

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[green token]

wait

[green token]

.reopen

hey somebody help

me

[restive river]

not how it works you were late

[green token]

so i will have to reupload

[green token]

thanks

what to do

[restive river]

what have you tried

[green token]

yeah

[pseudo basin]

"what have you tried" is not a yes/no question

[green token]

but i got the soln which didn,t match the options

[restive river]

can you show your work

[green token]

le me send you my soln

well i can tell you my approach

[restive river]

ig he was about to type regarding that, that's how people tend to type sometimes

[green token]

i basically applies a-b*a2+b2-ab

identity

then used cos2theta identity

hey anybody there listening

[restive river]

use brackets

[green token]

sorry

[pseudo basin]

did you miss brackets and ^ or what

[glossy dew]

yeah proceed then

[green token]

or youna bot

[pseudo basin]

also that is only half of the thing

[restive river]

so a = sin^2(75 ) here and b = cos^2(75)

then

[green token]

yes

then i got [root3]/32

[glossy dew]

the final answer?

[pseudo basin]

can you show the full form of this identity, including the "=" sign

i strongly strongly suspect you misremembered it and so may have applied it incorrectly, or maybe it is even the wrong identity to use at all

[glossy dew]

oh wait yeah

[green token]

wait a min

it,s soln is D

[glossy dew]

what did you do

[green token]

BUT MINE IS NOT MATCHING

[green token]

READ THE PREVIOUS CHATS

[glossy dew]

you never showed what you did

[green token]

WHY

[pseudo basin]

why what.

[glossy dew]

as an expansion of what

[restive river]

ye this is wrong +ab

[green token]

WELL i told you my approach

[pseudo basin]

and where is any cube in the original q

[green token]

wdym

[pseudo basin]

we have shit ^8

^8 is not anything good^3

[restive river]

oh fuck mb i did 2^3

[pseudo basin]

i am questioning execution, not approach

[green token]

well le me try again

[green token]

what

[restive river]

so there were 2 things wrong in your approach

1. it doesnt work here
2. the formula is wrong as well

[green token]

ywah

i got the answer

right this time

[devout snow]

@green token Has your question been resolved?

[devout snow]

Channel closed

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[devout snow]

Please don't occupy multiple help channels.

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[icy stone]

hi i need help in this. i want to find the limit of the given equation without hopital rule, just simplification. can anyone tell how?

[twilit field]

my first instinct is to multiply by the conjugate of the denominator.

[icy stone]

i did, but that results in complexer square roots at the numerator

but i still get 0in denominator

[knotty sage]

Some of the factors here do simplify to x^3-a^3 or x^3+a^3.

But I don’t see how this will help

[icy stone]

btw answer is in terms of a

[tribal patio]

You don't have to expand $(\sqrt{a+x}+\sqrt{a-x})$ in the numerator

[woven radish]

cupcake

[tribal patio]

Try multiply both num and denom by $(\sqrt{a^2+ax+x^2}+\sqrt{a^2-ax+x^2})$

[woven radish]

cupcake

[icy stone]

but ill get 2x in denominator, 2x=0 which is not good

[tribal patio]

Yeah the 2x in denom is indeed annoying

[icy stone]

lemme try the other one

[tribal patio]

But this would get rid of the 2x

[icy stone]

i gott wtver this is

[tribal patio]

Yeah

So

[icy stone]

OH SHIIII

[tribal patio]

Just plug x=0 lol

[icy stone]

i got it

tysm

have a good day mate

[tribal patio]

Ty

[icy stone]

.close

[devout snow]

Channel closed

Closed by @icy stone

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[devout snow]

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Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
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[obtuse lantern]

Please check if my answers are right

Hellooo

[shell plover]

yea this one is solved correctly (if repletion is allowed)

[obtuse lantern]

Next here