help-17

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[dense fulcrum]

hi guys, the question is: if here there's anybody that can help me with my latex project

[grizzled vault]

[dense fulcrum]

i have to implement this in latex but i really don't understand how to do it

and also how to modify this in latex.

[woeful igloo]

#latex-help is better suited for this

[dense fulcrum]

thank you

[hard atlas]

frankly for these types of things chatgpt can probably help

give it the image and ask it to draw it for you in tikz

[dense fulcrum]

i've already tried but it doesen't really help

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[bleak prawn]

Sooo I did the question and got the right answer but forgot to add +C (as usual)

I meant to type the +C beside the fraction, like this

But I accidentally typed it in the numerator of the fraction and clicked on submit answer

But it still says its correct? Is this a mistake in the system? Or is it the same

[paper depot]

you essentially added -C/81 instead of C

which is fine

the C can absorb a nonzero multiplicative factor

[bleak prawn]

A what? 😅

[paper depot]

like if you write +2C instead of C thats still fine

or +3C or -C or -19.589234C

a constant multiplier on C can be safely absorbed

[bleak prawn]

How come? Theyre different numbers no?

[paper depot]

well sure but you still get the same like

arbitrary additive constant

it is just expressed differently

[bleak prawn]

Ok.... I think I get it but not sure

Like C can just be anything, so it doesnt matter if we add or multiply something to it cause we dont know what C is anyways, right?

[paper depot]

yes ish

[bleak prawn]

What is the 'ish' part 😅

What is slightly wrong about what I said

[paper depot]

i can't really put it into words, sorry

[bleak prawn]

All good, I think I get it

Thanks!

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[languid grotto]

But what "truth" are all these ideas like limits, zenos paradoxes, etf coming down at, like it seems they are all talking about some "idea" which should have a single word for

[vast shale]

what

[languid grotto]

Convergence? I guess

[neat rose]

yes

[languid grotto]

Yes?

[neat rose]

yes

[languid grotto]

So is all calculus just grappling with the idea of convergence

[neat rose]

oui

[languid grotto]

Oui

Ok

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[sweet rain]

The angle bisectors of angles BAD and ADC meet at point O in the trapezoid ABCD. Find the sides AD and DC if you know that OC = sqrt(7) ; OB = 3sqrt(15) ; AB = 5DC and cosBAD=2/3

[sweet rain]

I have proved that AOD is right and that COB is also right

And if I prove that LdBCD is a parallelogram, the problem will be solved

But I have tried almost everything to no avail

here is the problem written out in Bulgarian

I have also proved that OC and OB are angle bisectors as well

[paper depot]

правилно ли съм разбрала, че вече се знае, че трапецът има вписана окръжност? @sweet rain

щом ъглополовящите му се пресичат в 1 точка

[sweet rain]

да, поне аз така си мисля

[paper depot]

ако е така, значи май е равнобедрен

откъдето ще следва, че AD = BC

[sweet rain]

не, това е само когато трапецът е ВПИСАН в окръжност

А този е описан около

[paper depot]

а, да, обърках се

не е задължително да е равнобедрен

[sweet rain]

да

[paper depot]

ама все пак, ако намерим AD, ще ни свърши работата

защото е в сила, че сборовете на противоположните страни са равни

[sweet rain]

ако може би използваме факта, че щом е описан около окръжност, ъгъл A + C = ъгъл B + D?

[paper depot]

откъде така?

[sweet rain]

това пак е ако е вписан в окръжност

[paper depot]

не, ти бъркаш двете работи

[sweet rain]

четириъгълник вписан в окръжност

хмм

[paper depot]

сборът на страните е равен, когато 4-ъгълникът е описан

[sweet rain]

така е!

извинявай

[paper depot]

това мисля, че не е задължително да е успоредник

обаче не съм сигурна

ето ти поне чертежа с абсолютно всички ъгли

$DC = \frac{OC\sin(\alpha+\beta)}{\sin(90-\alpha)} = \frac{OC \sin(\alpha+\beta)}{\cos(\alpha)}$ по синусовата теорема...

[twin meteor]

ann.in.a.teacup

[paper depot]

подобно май може да се получи и за другата основа след известно усилие

защото се знае OB

$AB = \frac{OB \sin(90+90-\alpha-\beta)}{\sin(\alpha)} = \frac{OB \sin(\alpha+\beta)}{\sin(\alpha)}$

[twin meteor]

ann.in.a.teacup

[paper depot]

от AB = 5DC ще получим нещо тригонометрично

cos(2alpha) се знае, но сметките ще са грознички...

само такъв начин виждам @sweet rain

[sweet rain]

да но като не знаме колко е алфа + бета?

[paper depot]

чакай, аз май съм сбъркала нещо...

[sweet rain]

все си мисля, че ни трябва още нещо

[paper depot]

DC/AB ми излиза направо като OC/OB * tan(alpha)

което ми изглежда странно

а бе!!

от триъгълника COB се намира директно tan(beta)!

ама защо тогава ни дават, че AB = 5 DC...

направо само глупости получавам

[sweet rain]

и аз…

[paper depot]

може ли пак да пратиш изходния текст на задачата на български?

[sweet rain]

ами сега не съм вкъщи

но условието което написах на английски

в това на български преведено

[paper depot]

хм

сега не мога да кажа нищо повече със сигурност :(

[sweet rain]

до това стигам аз

и просто не мога да си обясня дали това е нормално

@paper depot

[paper depot]

получаваш противоречие, нали така?

значи или в доказателството ти нещо не е наред, или в самата задача...

[sweet rain]

започвам да си мисля че е задачата…

ако обаче LdDBC е успоредник

двата отговора изкачат веднага

пък чертежа ми по отгоре е почти точен

сметнах ъгъла спрямо косинуса и направих страните с правилното отношение

и изглежда като успоредник

и за мен има логика да е успоредник

защото това е математика 11. клас

не университетска

само, че ме знам как да го кажа

и съм на път да хвърля кърпите

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@sweet rain Has your question been resolved?

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[static mirage]

how do i make a tree diagram out of this?

bc 0.6 and 0.3 is 0.9 and not 1 so im not sure how to do this

or is it supposed to just be 0.6 and 0.3?

[languid grotto]

Send the complete picture

It seems incomplete

[languid grotto]

So 0.1 it wull be early right

Will*

[static mirage]

wait

on time =/ early?

oops

[languid grotto]

Nope

[static mirage]

huh

so theres 3 branches instead right

[languid grotto]

Yep

[static mirage]

ohh

ok ty

that makes more sense

[languid grotto]

[static mirage]

.close

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[static mirage]

.reopen

[vocal sleet]

✅

[static mirage]

nvm idk how to do e..

is it 0.3 x 0.3 x 0.3

i dont rlly get the question

[paper depot]

you want exactly one late arrival out of 3 days

[static mirage]

OH

[paper depot]

so you want 1 late and 2 non-late

[static mirage]

so 0.3 x 0.7 x 0.7?

[paper depot]

which can happen in any of 3 arrangements

that times 3

[static mirage]

o h

oh

ok

oops

ty

i got 441/1000

o its right

ok tyy

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[static mirage]

for this for b i got 5/18 but the ans is 5/9

how do i get to 5/9?

[gilded badger]

P(X|N)

Use this formula

[static mirage]

im not sure how to use that as a formula

[gilded badger]

This

The 5/18 is your P(XnY)

P(Y) would be the probability of picking a left handed glove

[static mirage]

ohh

[gilded badger]

Yez

[static mirage]

so is that 5/18 / 5

o wait no

[gilded badger]

Almost

[static mirage]

5/18 / 5/10 ?

[gilded badger]

Yess

[static mirage]

ok ty

[gilded badger]

👍

[static mirage]

so is it the same with replacement

like 5/18 / 5/10

or wld it be different

[gilded badger]

Idk what you mean by replacement😭

[static mirage]

like

the denominator stays the same

[modest iris]

Yeah so uhhhh,I joined for help with differentiation

[static mirage]

like 5/10 for left handed glove and when u take one and put something back its 4/10

[modest iris]

Find derivative of y=log(x) + e^x + x√x

Please help

[gilded badger]

Hmmm

If u put the same thing back then it should go back to 5/10

[static mirage]

like this

[static mirage]

o ya thaats what i meant it was a typo sorry

[gilded badger]

Ohh

Ya if got replacement it doesn’t change

but like this formula is for conditional events

So wether it’s replacement or not it does not matter

[static mirage]

ok ty

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[static mirage]

sorry im back idk how to do c..

[static mirage]

litteraly hate proobability sm

[gilded badger]

We on the same shit💀

Is it 2/21?

[viral slate]

first part should be 4/33 I think.

[gilded badger]

For c

I think should be right no?

Cuz like it’s either red first or anything but red first

So like 2 possibilities only

[viral slate]

I don't think the order would matter here. Lemme just do the calculations.

[gilded badger]

Okay

[gilded badger]

I mean it’s still a path right🤷‍♂️

[viral slate]

yeah but kinda long. well up to you.

[gilded badger]

Wya gang

[gilded badger]

U got the same answer?

u just x2 right?

[static mirage]

im bnack

sorry

[gilded badger]

All good gang

[static mirage]

is it like

wai

[gilded badger]

Is this correct just to make sure^

[static mirage]

yes

[gilded badger]

Ohh ok ok 👌

[static mirage]

wait

i go it

its js 1/21 + 1/21 right

[viral slate]

I'm getting 40/231 for c.

[gilded badger]

Technically u don’t do it like that I think but that works

2(1/21)(20/20)

Which is just (2/21)

Or u can do (1/21)(20/20) + (20/21)(1/20) =2/21

[static mirage]

o

[static mirage]

i got 1/21 + 1/21

[static mirage]

bit i think 1/21 + 1/21 is easaier so can i do that instead

[gilded badger]

Yeah it works anyways so just do it💀

[static mirage]

omg

why is there a rat

[gilded badger]

Tf is this💀

Yo btw

Are u good in trigo🧍‍♂️

[gilded badger]

^^

[static mirage]

nope

all i know is soh cah toa

[gilded badger]

Ohh🧍‍♂️

Nevermind then😭

[viral slate]

What did I get wrong in this??

[gilded badger]

Oh it’s not 1 pair

It’s 1 red sock

[gilded badger]

^^

HAHAHAHHA

[viral slate]

I see. I'm gonna kill myself. Thnx.

[gilded badger]

Lmfaooo

Ay the process is correct tho😭

Btw u mind helping me with something pls😭

[viral slate]

sure

[gilded badger]

No one helping😔

[viral slate]

I'll try.

[gilded badger]

Look at the channel named bagetto

I can’t do it lmfaoo

Thanks dude🙏

[viral slate]

Out of my expertise bro. Or maybe I'm not getting the question.

[gilded badger]

Ohh all good then

It’s about polar coordinates

I differentiated edy

I just need to simplify it into the specific form they want

But I can’t get it

[viral slate]

You've just sent a part on that channel. I think the question is not complete.

[gilded badger]

Yes I wrote on top the polar equation

The r^2=1/theta^2 +1

Lemme add the other parts if u want

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@static mirage Has your question been resolved?

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[mortal latch]

Hello

[mortal latch]

is this correct

if u need clarification lmk

[reef agate]

Im not sure if this should be shown in a mathematical way, but your reasoning is correct. I'd recommend waiting for someone else to confirm though

[mortal latch]

this is the way it should be shown

Venn diagram

first is deductive

second is inductive

right?

[languid grotto]

Yes

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@mortal latch Has your question been resolved?

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[tropic brook]

could someone please help me with this problem

im going to upload my work in a sec

I think I interpreted the problem wrong

[paper depot]

ok first things first

what letter means what

you should write this down as the beginning of your work

[tropic brook]

oh sorry

so x is nickel

y is dime

and z is quater

quarter

[paper depot]

x is the number of nickels.

x = number of nickels, y = number of dimes, z = number of quarters

it's important to be precise about that sorta stuff

anyway ok

[tropic brook]

oh crap yeah

[paper depot]

your second equation should just be x = y

rather than trying to make anything fancy with it at this juncture

[tropic brook]

oh yeah

[paper depot]

so you then have:

x + y + z = 70
x = y
5x + 10y + 25z = 665

[tropic brook]

so then i should just substitute?

and then eliminate

[paper depot]

well you would substitute one of x and y for the other

so that one of them's gone (but not forgotten) and you are left w/ a system of two equations

aside from that, there's no specific instruction to use a specific method so do whatever you find easiest

[tropic brook]

ok thanks

this helps a lot

[paper depot]

idk how 35z = 370 happened tho.

[tropic brook]

yeah i probably did something weird

thanks though

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[zealous ridge]

can i get help with homework

and this as well pls

[random tusk]

sure man

[zealous ridge]

ok man

can someone help

[warm crane]

Ask question. Maybe someone will help.

[zealous ridge]

my teacher gave me this how do i solve it

[runic shore]

I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

[zealous ridge]

ok for real tho

i need help with this

[runic shore]

HINT

||5x=3x+2x ||

[zealous ridge]

i need a graph

[runic shore]

If you complete the square it will be easier to do

[zealous ridge]

wdym

[runic shore]

$2x^2+5x+3 = 2\left(x+\frac45\right)^2-\frac18$

[twin meteor]

trigonometria

[zealous ridge]

i think i did it right

??

@runic shore

[runic shore]

I don't know. Did you?

[zealous ridge]

ye i did ig

thanks for the help

!

[runic shore]

good job stay curious

[zealous ridge]

💩

[vocal sleet]

@zealous ridge Has your question been resolved?

[flat whale]

<@&268886789983436800>

[gentle sleet]

they trolled on other people's channels too

[autumn trail]

Stop trolling in the help channels

.close

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[lethal heart]

$X = \sum_{i=0}^{n-1} a_i \cdot b^i$

[twin meteor]

Task Bot

[lethal heart]

What is That?

[dark kiln]

that's positional numeration

[lethal heart]

Wdym

[dark kiln]

the value of 6351 is 1×1 + 5×10 + 3×100 + 6×1000

if you read right to left, so 1 is i=0

that's what it does

[lethal heart]

But in which base it gives me

[dark kiln]

base b

[lethal heart]

And how converted it to another base

[dark kiln]

long division

it's kinda slow

[lethal heart]

[AB]_16 How do you convert it in base 10?

Using that formula

[dark kiln]

that formula works yes

B is i=0

a_0

b=16

[lethal heart]

I know I have to convert A, B, b from base 16 to 10

A_16=?_10

How do I do here

[paper depot]

A means ten and B means eleven

[lethal heart]

Yes

[paper depot]

AB_16 = 10 * 16 + 11

[dark kiln]

there are no stps, it's just always true

A is 10 in any base

[lethal heart]

{0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}

[lethal heart]

I don't have to do this

There is first to convert the parts individually

A_16 =? _ 10

How do I do here

[paper depot]

you are overthinking it

you just have to know A means ten

there is no way around it

you have to know what each digit means

there is no process to it

[lethal heart]

I know

[paper depot]

A_16 = 10_10

[lethal heart]

WHY

[paper depot]

as in, "Why is ten represented with A and not some other letter?"

[lethal heart]

Why is the coding that?

[paper depot]

blame the computer scientists

[dark kiln]

because people know the order of letters

[paper depot]

they needed six more symbols to represent the values from ten to fifteen in hex, and they went with the first letters of the alphabet.

and it stuck

and now everybody does it that way

[lethal heart]

So

A_16 = 10_10, B_16 = 11_10

[paper depot]

yes

[lethal heart]

And b?

[paper depot]

??

[lethal heart]

The base

[paper depot]

the base is 16 lol

[lethal heart]

I have to convert it from 16 to 10

[paper depot]

ok then your input base is 16

just as you said

[lethal heart]

Then use that formula above

[lethal heart]

?

Yes

But now I have to convert it

[paper depot]

AB_16 = 10 * 16 + 11

or do you want it written out 100% formal?

[lethal heart]

Where is 16^0?

[paper depot]

16^0 = 1

[lethal heart]

And why did you write 1?

[paper depot]

???

anything raised to the 0th power is 1

i could have written 11*16^0 sure

[lethal heart]

16≠1

[paper depot]

i am not saying 16 = 1

i am saying 16^0 = 1

(anything)^0 = 1

... ok sorry i have to go now

[lethal heart]

Ah also applies now

🙂

Okay, anyway thanks to everyone

.close

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[gaunt pelican]

Can someone help me out with this? I have no idea what to do

[vocal sleet]

@gaunt pelican Has your question been resolved?

[vocal sleet]

@gaunt pelican Has your question been resolved?

[white palm]

some context might help, in what course is this, how are things defined etc.

it’s like multivariate analysis

[neat rose]

more like measure theory

[gaunt pelican]

it's analysis 4, no idea how helpful that is

i believe it's just standard definitions?

it's multidimensional riemann integrals

in terms of context, that is the only context i was given lol, it's a question in my tutorial

[white palm]

like what is your definition of riemann integrability

[gaunt pelican]

darboux sums

[neat rose]

u read bout fubini theorem @gaunt pelican ?

[gaunt pelican]

heard about it, not in my lecture notes tho

¯_(ツ)_/¯

[neat rose]

Idk how this might help

[gaunt pelican]

they were asking my defn of riemann integrals

[white palm]

if I here is a subset of R this is not that helpful i agree because I don’t know how they define the integral over IxJ with the d(x,y).

i mean we gotta start somewhere

[gaunt pelican]

i understand the first part (i think)

[vocal sleet]

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[gaunt pelican]

.reopen

[vocal sleet]

✅

[gaunt pelican]

just the final part showing that hd(x, y) = fdx gdy

think its related to iterated integrals tho

[neat rose]

how did you prove its riemann integrable first?

[gaunt pelican]

f, g are riemann integrable functions, i proved h is bounded on I x J, and then i used riemanns second criterion

[white palm]

yeah I don’t think I can help you much, I mostly had a computational mutivar calc course but not analysis in this context.

[white palm]

if you can say an integral on I x J is an iterated integral yeah i feel this would help, but idk what i’m talking about gl.

[gaunt pelican]

no worries, appreciate it anyways

[vocal sleet]

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[cedar grail]

I'm doing trigonometry homework and I want to know why this is incorrect. To find the answer, I looked at the unit circle and noticed that pi/4 and 7pi/4 have the same coordinates, except they have different signs. How should I approach this problem? Am I misunderstanding the question?

[lone linden]

except they have different signs

This means that they're not the same

You should recall the definition of co-terminal angles

actually is this question in isolation

because all of these angles are in [0,2pi), so there's nothing with coterminal angles of anything like that happening here

so I'm inclined to think that the question is just bad

[atomic pulsar]

7pi/4 is in the 3rd quadrant so its -sqrt2/2, -sqrt2/2 which means that pi/4 and 7pi/4 should be right

idk why its wrong honestly

oh wait nevermind its not

[quiet echo]

This has no correct answer?

[atomic pulsar]

its in the 4th quadrant

so the only correct answers are pi/4 and 5pi/4

[cedar grail]

I see, thank you everyone!! I'll do more studying

[atomic pulsar]

wait

yeah im confused on what the question is actually asking

its just badly worded

[cedar grail]

.close

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[soft lodge]

hi

[soft lodge]

im trying to do

mapping diagrams

relations

Can someone explain this pls

[modern storm]

first of all this is wrong, 2^2 =/= 8, nor 3^2, nor 4^2

it should be 1, 4, 9, 16 at the left side

unless the thing at the top is meant to be x^3

[soft lodge]

wym

[soft lodge]

ohh

thats for something else

[modern storm]

oh, ok then

[modern storm]

Then just simply connect by a line those numbers which are contained in a pair/coordinate

what you are doing is basically connecting the values from the domain of a function to its image

in simpler words: your input to your output

[soft lodge]

what about this

[quiet echo]

That’s good.

[soft lodge]

i honestly

still dont understand

[heady vine]

!occupied

[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).

[hexed shard]

Oh sorry didnt know the rule

Mb

Im new

[heady vine]

Just delete the image and go to another available help room send it there

[hexed shard]

No problem homie

[modern storm]

essentially, when we analyze a function ("transformation"), we assign a value y to every or most values x

f(x) = 2x + 3 -> y = 2x + 3

[vagrant marten]

which grade math is this?

is it college level?

[modern storm]

means that if you choose some "x", by operating with it by replacing it on your function, you will get a value y

[soft lodge]

9th grade

[crimson jetty]

think you need to clarify what doesn't make sense for you

[soft lodge]

how you get the range (y)

[crimson jetty]

the range are the things the function can output

given the possible inputs (domain)

[quiet echo]

About?

[quiet echo]

Think of it this way: a x-input maps to a y-input. The function is like a machine that relates the x-values with the y-values in a unique way.

[soft lodge]

so is this not right

?

i put the x's

1,2,3,4

and the y

1,8,27,64

[crimson jetty]

you cubed everything

but wrote x squared at the top

[soft lodge]

look at this

[crimson jetty]

2^2 is not 8

[modern storm]

Which is just a result of solving y=2x with each value of the domain. Its like an input and output.

The domain and range are just two sets of numbers, which point from the domain to the range

[modern storm]

the part at the top is unrelated

[crimson jetty]

what.

[modern storm]

the thing is, here, you use a transformation x^3 = y

[soft lodge]

the x squared is not related to the diagram

[soft lodge]

i understand that

[crimson jetty]

this by itself can be correct then

you could draw arrows between too

[soft lodge]

shit i should have taken my screenshot properly

everyday i make mistakes that are smiliar to this

[modern storm]

this is the transformation from your homework

still, you can solve just by matching numbers given the values they gave you here

[vocal sleet]

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[soft lodge]

.reopen

[vocal sleet]

✅

[soft lodge]

yeah

i just put the y

i put whatever is the y in the range

so the y's are 1,8,27 and 64

i put those 4 on the right

.close

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[vagrant marten]

can someeone please help me with this?

[vocal sleet]

@vagrant marten Has your question been resolved?

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[vital marten]

can someone help me understand what practical domain is

[flat whale]

Show context

[vital marten]

i guessed on the first blank

and got it right

[silk osprey]

the graph stops where?

[vital marten]

25?

[silk osprey]

yep but does 25 hours after midnight make much sense?

what would 25 hours after midnight really be

[vital marten]

like

in time?

[silk osprey]

isn’t 1 am 25 hours after midnight

[vital marten]

yes

[silk osprey]

so isn’t 1 hour after midnight the same as 25 hours after midnight

[vital marten]

yes

i think so

[crimson jetty]

im confused why it isnt just -5 to 25

is there more to this question

[vital marten]

no there isnt

[heavy yoke]

it's asking for a physically meaningful domain, not just the extent shown on the graph

[silk osprey]

-5 hours makes no sense

[crimson jetty]

it wants you to guess the observations are sinusoidal but its kindof silly since it says these are "observations" which would be scientific, not mathematical

[crimson jetty]

why.

[silk osprey]

time isn’t negative

no one says -5 hours after midnight

[vital marten]

im still confused on what the answer is

[crimson jetty]

you certainly can.

[silk osprey]

sure

[crimson jetty]

-5 after midnight is obvs 5 hours before. observations began then.

[silk osprey]

sure you can think of it that way but no one says that

time is always taken to be nonnegative

[crimson jetty]

no one says the things they would in a math problem either

thats just plain false what

[crimson jetty]

anyways.

the question just wants you to assume the graph is periodic

and so the domain only needs to cover 1 period

presumably.

a lot of assumptions going on here.

"practical domain" doesnt mean anything without a context.

[vital marten]

so wouldnt it be 30?

[silk osprey]

they gave context

[silk osprey]

what

[vital marten]

im so lost

[crimson jetty]

if this were truly scientific, i think -5 to 25 is very practical because thats the time period of where the observations occurred

but given 0 is apparently correct, then I think they want you to give a domain representing 1 period

starting from 0

[heavy yoke]

it seems like you are meant to infer that observations began at midnight, and the graph is extrapolated

[vital marten]

so 1 period is 0-24

[crimson jetty]

yes

[vital marten]

it says its wrong 💀

im so lost

[silk osprey]

bruh there’s no chance they want 25 right

that’s the only other possibility

[crimson jetty]

1 period starting from -5?

is that 0 definitely correct

[vital marten]

ive guessed every number

[crimson jetty]

this question just got dummer

[vital marten]

on the x axis

[crimson jetty]

and nothing?

try infinity?

[silk osprey]

i guess they were taking 0 to be on some fixed day then observing thereafter so 25 hours makes sense?

[silk osprey]

did 25 not work?

[vital marten]

no

[crimson jetty]

infinity makes the next most sense

[silk osprey]

🤔

[vital marten]

thats what i was thinking

[crimson jetty]

time doesnt stop

[vital marten]

but theres no option for it

[crimson jetty]

infinity symbol? no?

[vital marten]

nope

normally theres like a dropdown

when the answer involves infinity

[crimson jetty]

try -5, 25

[silk osprey]

i mean it only says "we do not know that the function works for values before observations began"

it can’t be -5

0 is correct

[crimson jetty]

observations began at -5

that graph is one of observations.

every plotted point is from an observation

[silk osprey]

why would 0 be green

[crimson jetty]

cus the question is fucked

[silk osprey]

no i think it’s some kind of curve fit for the observations

[vital marten]

i tried every number 1-36 😔

[silk osprey]

well this i agree with

[crimson jetty]

go negative then

and 0

[silk osprey]

🤔

[crimson jetty]

it should just be -5, 25 istg

[vital marten]

its okay im asking my school friend but can you help me with a separate problem

[silk osprey]

are you zoomed in on the graph??

[vital marten]

no

[silk osprey]

how is it not 24 or 25

[vital marten]

idk

[crimson jetty]

try 0, 19

sorry no

ubdid

did

-5, 25
-5, 19

thats the only ideas i got otherwise

[silk osprey]

how do you have this many tries though lmao

[flat whale]

Did your teacher give you a definition of practical domain

[vital marten]

no 😊 i searched all of our notes

[crimson jetty]

if u cant get it no one can

[vital marten]

its okay

ill take the -0.25

[flat whale]

[0, inf) is another guess

[silk osprey]

if you type inf it should become an infinity symbol

[vital marten]

it says only integers

[silk osprey]

where?

[vital marten]

when i type in letters

[silk osprey]

show

[crimson jetty]

🤣

[silk osprey]

oh it could be a decimal

[crimson jetty]

but it just cant be

at the same time

wtf would it be

[silk osprey]

bro 23.999

lmao

25.1

[flat whale]

Did you try 12 already

[crimson jetty]

use the zoom tool to find a hidden clue

🤡

[vital marten]

can you help me with this separate problem

[silk osprey]

gave up lmao

[vital marten]

im giving yp

yea

[crimson jetty]

ok so u have the equations

[vital marten]

i dont understyand how to put it in terms of cosine

[crimson jetty]

what is one of the t when C is at a maximum

[vital marten]

im really confused already

[crimson jetty]

use your equation for C

and the graph for C

[vital marten]

okay

[crimson jetty]

how many maximums are there on that graph shown

[vital marten]

3

[crimson jetty]

what is the x axis for one of them

[vital marten]

0

[crimson jetty]

yes

t = 0

has C at a maximum

you can then just compute V for when t = 0

===
To be clear, because of how periodic functions work and these two functions have the same period

Whenever C is at a maximum

V will have the same value

[crimson jetty]

So you can just do this

[vital marten]

V when t=0 is 76.64

[crimson jetty]

exact would be without using your calculator

right i missed u had it already

So you just type out the same thing u typed into your calculator

into that textbox

except you can simplify a bit

[vital marten]

i used a graphing calculator 😔

[crimson jetty]

You take the formula you wrote for V

and plug in t = 0

then simplify it, and thats it.

You cannot simplify the cos part

[vital marten]

so it would be 180cos(120pi(0.003))?

[crimson jetty]

u can simpl that one more step

[vital marten]

it worked!!!!!!!!!!!

so the next part

is to find when the current when the voltage is at a minimum

[crimson jetty]

use the marked point on the graph for V and the symmetry of the graph

symmetry comes from periodicity

half a period changes a maximum to a minimum

[vital marten]

what

[vocal sleet]

@vital marten Has your question been resolved?

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[restive rain]

guys would this just be -11

[cunning plaza]

other way around

[restive rain]

ah i see so just 11?

[cunning plaza]

Area under G = R1+R2 = 30+R2.
Area under F = R3+R2 = 19+R2

[restive rain]

i rlly hate these graph problems man

[cunning plaza]

Then you just subtract Area under G - Area under F

yeah it takes some time getting used to

[restive rain]

can you check if theese are correct ?

[cunning plaza]

first pic lgtm

I think second is wrong

integral of f(x) consists of regions 2 and 3,we know R2 = 27 and the total area (integral of f) is 40.

[restive rain]

for first i did 40-10=30 the next one is 53-10 and then -4

[vocal sleet]

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[obsidian sapphire]

should i leave this angle or find the acute?

[vocal sleet]

@obsidian sapphire Has your question been resolved?

[obsidian sapphire]

<@&286206848099549185>

.close

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[warm rapids]

h

[warm rapids]

how can I solve this limit when x = 0 using l'hopital

[paper depot]

as in you are specifically INSTRUCTED to use l'hôpital?

[warm rapids]

yes.

[paper depot]

blech

well ok your first order of business is to write f(x) as a single fraction

[warm rapids]

yeah I did so

[paper depot]

and then tinker with it somehow until the limit is either 0/0 or ∞/∞

[warm rapids]

but then we get

-infinite/0

which is something you cannot get

[paper depot]

hold up

you got $f(x) = -\frac{x^2 \ln(x) + 1}{x^2}$?

[twin meteor]

ann.in.a.teacup

[warm rapids]

yeah

[paper depot]

uhhh

wait, is l'hop even applicable here wtf

just to be sure we haven't missed anything,

[warm rapids]

teacher said it is

[paper depot]

can you post the FULL instructions?

just in case?

[warm rapids]

in english:

use l'hopital to verify lim equals -infinite

[brittle topaz]

Make them a single fraction

[paper depot]

we've already done that @brittle topaz

[brittle topaz]

ah ic

[paper depot]

the question now becomes, how tf are we supposed to rewrite the function to apply l'hop

cause right now it is a 1/0 form

which is no good for us

[warm rapids]

I think I get it now

[paper depot]

oh? do share

[warm rapids]

you got $f(x) = -\frac{x^2 \ln(x) - 1}{x^2}$?

[twin meteor]

San

[warm rapids]

ah shit

[paper depot]

plus sign inside the fraction

and your incorrect form would not be suitable for l'hop anyway

[brittle topaz]

1/0 is always infinite

[warm rapids]

nvm

[vocal sleet]

@warm rapids Has your question been resolved?

[vocal sleet]

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[novel idol]

(i) given log_27 4=x, express log_6 12 in terms of x
(ii) express z in terms of x and y if 8^x=9^y=12^z

[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

[novel idol]

2

[vocal sleet]

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

[novel idol]

(i) trying to apply log rules to log_27 4, got 2 log_27 2=x, but stuck after
(ii) no clue about this, i assign k = the equation, and got k root x=8, k root y=9, and k root z = 12

[vast shale]

do it step by step

dont jump to ii) if you didnt solve the first

[novel idol]

ii is a separate question tho

wait nvm i solved (ii), just (i) left

[vast shale]

ok so

log_27(4) = ?

[novel idol]

x

[vast shale]

ok

now

write 4 as 2²

take the 2 out using property

what do you get

[novel idol]

2 log_27 2 = x

[vast shale]

ok

now 27 = ?

?²

[novel idol]

27=3^3?

[vast shale]

yes

so

2log_3³(2) = x

take the 3 out

using the property

[novel idol]

wait how

is it 2 log_3 2/3

[vast shale]

log_a²(x) = log_a²(x)¹ = 1/2 log_a(x)

[vast shale]

no

[novel idol]

ohh

so 1/3 log_3(2)

[vast shale]

what about thr 2

[novel idol]

2/3 log_3(2)=x

[vast shale]

are you hungry

okay better

[novel idol]

mb

[vast shale]

now

this is the most u can simplify it

[novel idol]

yah

[vast shale]

now lets get to

log_6(12)

12 = ?

[novel idol]

2^2*3

[vast shale]

take the 2 out

[novel idol]

2 log_6(2)+log_6(3)?

[vast shale]

no

i mean

yeah

but you dont have to do that

[novel idol]

oh

[vast shale]

take the 2 out

[novel idol]

how

[vast shale]

??

we just did this

[novel idol]

2 log_6(2)

[vast shale]

log_a(x²) = 2log_a(x)

no

[novel idol]

but theres 3

[vast shale]

so what

[novel idol]

sqr 3??

[vast shale]

no?

log_a(7⁷2) = 7log_a(72)

no

wtf

discord f it

but

[novel idol]

is it multiply in bracket

[vast shale]

yes lol

12 = 2²*3

[novel idol]

so 2 log_6(2*3)

[vast shale]

yes perfect

[novel idol]

oki

[vast shale]

now do the multiplication back

[novel idol]

to add?

2 log_6(2) + log_6(3)

[vast shale]

no

2*3

[novel idol]

isnt log (a) + log(b)=log(ab)

[vast shale]

im telling you to multiply the numbers out

not to apply log prop

[novel idol]

2 log_6(6)?

[vast shale]

yes perfect

now do you know what thatlog is

[novel idol]

ya

[vast shale]

what is it

[novel idol]

log_6(6)=1

[vast shale]

good

so final value is ?

[novel idol]

2

[vast shale]

okay

soo

we go back to the first log

2/3 log_3(2) = x

[novel idol]

yes

[vast shale]

we have to get 2=x

so that will be how you express it

[novel idol]

x=2? Why

[vast shale]

not x =2

we have to make it in that form

bcz

our second log is 2

[novel idol]

oh

[vast shale]

so this log has to be in terms of x 2

[novel idol]

so uh

[vast shale]

2/3log_3(2) = x

simplify this

[novel idol]

wait i think i found it

[vast shale]

show me

[novel idol]

uhh i cant rlly take pic

ill try to explain

[vast shale]

okay

[novel idol]

3x=2 log_3(2), since this is in base 3 i make log_6(12) into base 3 -> log_3(12)/log_3(6) -> 2 log_3(2)+1/log_3(6)
so 3x=2 log_3(2) , the above becomes 3x+1/log_3(6), numerator is done
denominator: log_3(6) = log_3(3) + log_3(2) = log_3(2) + 1 -> 3x/2+1

so its 3x+1/(3x/2+1) = 6x+2/3x+2 by simplification

i js checked with the ans and its correct, thanks @vast shale !

.solved

[vocal sleet]

Channel closed

Closed by @novel idol

Use .reopen if this was a mistake.

[vast shale]

you welcome

[vocal sleet]

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[rough zenith]

Two people meet at the same point and start walking at the rate of 2m/s at right angls to each other, marking out two sides of a square. At what rate is the area of the square increasing when the two people are each 15m from the origin?

[rough zenith]

Its a related rates problem

heres my working

Let person 1 distance be x and person 2 distance be y

so dx/dt=2 and dy/dt=2

A=xy

dA/dx=y

dA/dx = dx/dt x dA/dx

=2y

When y=15, =2x15=30m^2/s

but the answer is 60

what did i do wrong

[pallid hedge]

why does dA/dx = y and 2y

[vocal sleet]

@rough zenith Has your question been resolved?

[rough zenith]

A=xy so isnt dA/dx=y??

[pallid hedge]

but then according to your work dA/dx = y = 2y

[rough zenith]

dx/dt = 2

so dx/dt x dA/dx = 2y

[pallid hedge]

because dx/dt = 2, dA/dx = 2y
so dA/dt = dA/dx x dx/dt = 2*2y = 4y

[rough zenith]

Oh nah what am I doing

💀

Thanks ig

Sleep deprivation ahh

.close