help-27

[tough quartz]

Its my first time graphing something that is a variable honestly

[cloud remnant]

tell them you completed the square, found the vertex point and constructed a parabola from there

[light oyster]

Is it just me or is anyone else seeing it pass through the otigin

[cloud remnant]

it is slightly off but you are correct it looks like its passing through the origin but i did not deliberately make it pass through the origin, just by chance it did

[light oyster]

Alr alr

[tough quartz]

Dang

I guess i will just make a parabola

[light oyster]

Watch organic chemistry tutor

[tough quartz]

And pray

Dang my wifi died i cant send messages

Back ig

[tough quartz]

What organic chem has to do with graphing? 🥀

Holy my wifi died

Again

Dang

I will just close it i guess

.closw

.close

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[devout snow]

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[iron peak]

can someone teach me the basic approach whenever you see a question that has trig 2 and asks you something like

$0 \leq x \leq 2\pi$ \
$\cos (4x) \cdot \sin (x) + 2 \sin ^2 (2x) = 1$ \

How many roots of x are there?

[woven radish]

Red.

[fickle slate]

hello

[iron peak]

yeah

i think its more appropriate

i guess i could learn from the question

[fickle slate]

1-2sinx

[iron peak]

itself

okay

[fickle slate]

is what we get right

[iron peak]

$\cos (4x) \cdot \sin (x) = 1 - 2 \sin ^2 (2x)$

[woven radish]

Red.

[iron peak]

here you go

[fickle slate]

yes

[iron peak]

whats 1-2sin

i remember seeing that

[fickle slate]

i mistyped

[iron peak]

Oh wait

wouldnt that go

AHH

it simplifies?

[fickle slate]

yes

[iron peak]

wouldn't we lose a root though

[fickle slate]

cos

[iron peak]

the goal is to find all the roots

for x

i mean

sure

$\cos (4x) \cdot \sin (x) = 1 - 2 \sin ^2 (2x)\
\cos (4x) \cdot \sin (x) = \cos ^2 (2x) - \sin ^2 (2x)$

[woven radish]

Red.

[iron peak]

is this what you're saying

we do

sure

i mean then

id assume

you

open the cos(4x)

cuz you'll have the same term

on both sides

right

that loses roots though.... zz

[fickle slate]

yes or you can take cos4x in rhs

[iron peak]

you get $\sin (x) = 1$

[woven radish]

Red.

[fickle slate]

no need to cancel

[iron peak]

ah?

[iron peak]

rhs?

[fickle slate]

yes since rhs is cos4x

[iron peak]

right hand side

ohh

i mean

that'd

just

sure?

ill do that

[fickle slate]

instaed of canclling we can do this
cos4x(sinx-1)=0

[iron peak]

$\sin (x) = \frac{\cos ^2 (2x) - \sin ^2 (2x)}{\cos (4x)}$

this?

[woven radish]

Red.

[iron peak]

huh

where did sin-1 come from

[fickle slate]

we have sinx cos4x = cos4x

taking cos4x to the other side

[iron peak]

ohh

$\cos (4x) \cdot (\sin (x) - 1) = 0$

[woven radish]

Red.

[iron peak]

right

???

so now

x between 0 and 360 degrees

x = 90

x = 270

no

x = 90 only

for sinxx

and for cos4x

AHH

thats why its 9 roots

i think

cuz 4x is gonna go like that

4x is between 8 pi

i can just multiply the roots i have by 4

cos(x) has 2 roots for 0

2*4 is 8 roots

• 1 root

= 9

imma lose my shit

the thing is

whenever i see this right

how do i say

$\cos (4x) \cdot \sin (x) = \cos (4x)$

[woven radish]

Red.

[iron peak]

i just automatically think

well the easiest way to reach an answer

is to just simplify everything

and remove the hassle

[fickle slate]

that happens

[iron peak]

but the question is unique

something i never cared ab in math before

[fickle slate]

i am going through the same issues

[iron peak]

i self taught myself math and school's math was for me

and since I had to do the "school math exam"

I come across things I've never done

like finding roots

and not losing roots

the concept of "losing a root" is so weird

[fickle slate]

are you learning maths yourself ??

[iron peak]

to me

[iron peak]

yeah

i brute-force a ton of things

but when I must learn a definition

I also go through like a

big enforcement process

for like 60 days after learning trig for the first time

aka hearing of trig

i wrote SOH CAH TOA and drew the whole unit circle

on my desk

5 times

everyday

until I just

[fickle slate]

well clearly schoo; didnt do its job in your case

[iron peak]

didn't need to anymore

[fickle slate]

memorization is not the key here

[iron peak]

it was for learning what sin is at the beginning

or else i wouldnt recognize it

etc.

like derivatives and integras

I might've watched the same visualization videos

over and over

drew them

tried them

played w them

for like weeks

before I even started learning ab them

I also cheated in my physics exams by deriving my own formulas using integrals

[fickle slate]

i am still in school

[iron peak]

something they never taught us

[fickle slate]

wait you are still in school right

[iron peak]

yeah

12th grade

i got uni exam in 20 days

[fickle slate]

oh

i assumed that you were learning maths for fun

[iron peak]

I do both

I did a bunch of

extracurriculum math

for fun

I wanted to major math

until I had a change of heart

[fickle slate]

are you planning to pursue maths in uni

[iron peak]

but I still have a deep interest in math

nope

medicine

neurology

is my dream now

but I wanna perhaps take math if I can

as a hobby

if anywhere in uni I come across some

optional math course

I am 100% taking it

I don't wanna major math as my life

but its like

good hobby

how people doomscroll and play video games

[fickle slate]

probability is common in other majors

[iron peak]

I can take a pen and paper

and scribble math theories

and play with symbols

and write my own equations that i can never solve

for hours

[fickle slate]

same

but i also want to major in maths

[iron peak]

meh

i had many more questions

but

i dont remember

questions I cannot solve are usually because either 1) the guy asking the question doesn't explain it well enough for me to deduce what to do

or 2) I don't know what the fuck I'm looking at

[fickle slate]

there will soon be a 3rd category where questions ar

solvable

you are aware of the theory

but it is almost impossible to figure the path ahead

[iron peak]

yeah

like this question I made

$Opal Psi is a multi-variable or degree-able function where m is the degree of said function P(n,m) = n^m - (n-1)^m, how would you generalize such a function and its behaviours, what are the patterns that emerges from degrees of the Opal Psi and what do they tell?$

[woven radish]

Red.

[iron peak]

woah

rught

i forgot

I know they tell me something I cannot yet comprehend

I can see it

but I cant put it into math

anyway

.close

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[iron peak]

no bro my question is solved

end it

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[bitter herald]

limit n tends to infinity |an+1/an|

[outer eagle]

What did you get?

[bitter herald]

.close

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[clever granite]

Can a one to one bijection exist between all rationals and all irrationals?

[solemn kelp]

consider cardinalities

[clever granite]

Both are infinite and I don't know if either of them is a bigger infinity than the other.

That's why I asked this question here.

[solemn kelp]

have you heard of the famous result that the reals are a “larger” infinity than the integers?

[clever granite]

Yep.

Aleph null and stuff.

[solemn kelp]

the same idea is with rationals

[north roost]

Rational is the same size as natural number

[solemn kelp]

since they are countable too

[clever granite]

So, can rationals and irrationals have a one to one bijection or not?

[solemn kelp]

i don’t want to just give you the answer

that defeats the purpose of helping

[clever granite]

Okay

[solemn kelp]

just think about what it means for rationals to be countable and reals to be uncountable

and irrationals being the complement of the rationals

[north roost]

What did cantor use

[clever granite]

Okay. Thanks.

How do I close this?

[solemn kelp]

.close

[clever granite]

So, a one to one bijection isn't possible?

Okay, I get it.

.close

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[worthy olive]

i hope its not a problem because this is statistics but i dont understand how to get standard deviation in this task using this second formula where is bolded “distribucije frekvencija”

[thin inlet]

https://www.mathspanda.com/ASMa/Lessons/Standard_deviation_from_frequency_tables_LESSON.pdf

[devout snow]

@worthy olive Has your question been resolved?

[worthy olive]

and how do i get quartiles in frequency tables?

[runic grove]

what language is this

[worthy olive]

croatian

[runic grove]

ty

[worthy olive]

i can send a pic of the whole task but it will depend on google translate accuracy

[devout snow]

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[worthy olive]

.reopen

[devout snow]

✅

@worthy olive Has your question been resolved?

[runic grove]

@worthy olive Have you tried looking here?

[worthy olive]

yeah but it didnt help much

[supple knot]

why not

[worthy olive]

cuz im the dumbest person alive when talking about statistics😭

it says to find the mean

like- how

[supple knot]

https://www.mathsisfun.com/mean.html

[worthy olive]

okay

thanks

.close

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[obtuse echo]

I don't even know How to start.

[lunar harbor]

Consider simplifying this first. You may find it helpful to ||take the sine of that expression||

You should get that it’s ||the constant pi/2||

[devout snow]

@obtuse echo Has your question been resolved?

[obtuse echo]

Yeah I have got it

[devout snow]

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[obtuse echo]

what to do next? @lunar harbor

I have got y=1/root 3

Is it 49/3?

[lunar harbor]

For the max? Yeah.

[obtuse echo]

Yes I think that x should only be in the domain since that expression becomes a constant

and I solve for the max of x using the domain of arcsin x

where x=4 is max

and y has only one value which is 1/root 3

Is these correct? @lunar harbor

If yes I may close this channel.

[lunar harbor]

Yes

[obtuse echo]

Thank you , Pigeon!

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[alpine mist]

I don’t know how to start

[lyric timber]

do you know what a point of intersection is

[misty crest]

,av binaryexploitation

[woven radish]

binaryexploitation's Avatar

Click here to view the image.

[misty crest]

word

[lyric timber]

dawg 🥀

ty tho

[misty crest]

solve for either x or y in either of the relations and then substitute that expression into x or y in the other relation and then solve for x or y then go back and find x or y

[alpine mist]

the point where two things cross

[lyric timber]

which are the things in this case

one is the ellipse and the other?

[alpine mist]

the eclipses

[misty crest]

so just an ordered pair (x, y) that satisfies both relations

[lyric timber]

good

so

its basically a system

[misty crest]

🌙

[alpine mist]

so I use system of equations?

[lyric timber]

mhm

basically like knief said, solve for either x or y in 1 and substitute in the other

[valid iron]

yeah you can think it like this
x1,y1 are such points which satisfies both equations
now to find x1 and y1 , we put x1 and y1 in both equations and use simple substiution of x1/y1 from one equation to other

[devout snow]

@alpine mist Has your question been resolved?

[empty coyote]

Is there anyone who can help me in M2. Unit= sequence and series

[alpine mist]

is this correct

how do I graph this

[devout snow]

@alpine mist Has your question been resolved?

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[latent zenith]

I’m not exactly sure how or what methods I need to use to solve these questions

[full cloak]

solving triangles?

alright here is the method:

IF you are given:
3 sides OR
2 sides and the angle BETWEEN them

then you use cosine law

ALL other circumstance uses sine law

a triangle also CANNOT be solved if you are just given 3 angles

[latent zenith]

Is that the only instance when a triangle cannot be solved?

[full cloak]

yes

also for 2 solutions and no solutions... you prob have to solve them

I am very sure that for 2 solutions, it can only happen on sine law ones

remember that sin(x)=sin(180-x)

and I have no idea when it can be no solution, there probably is a few where the numbers just doesnt work out or something

[latent zenith]

Alright thanks 👍

Do you have any references for solving

Or should I just look up people solving it on YouTube or something

[full cloak]

??

you don't know how to solve them?

well you know sine law right?

and you know cosine law right?

[latent zenith]

Yeah

[full cloak]

the last thing you need to know is that all angles add up to 180

then you should be able to solve it

[latent zenith]

Oh wait

Yeah

Ok I got it I think

[full cloak]

nice

[latent zenith]

Thank you 👍

[full cloak]

np

[latent zenith]

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[somber garnet]

im so confused, how do i prove the pythagorean theorem?

[thin fern]

You know that $\vec{OA} \cdot \vec{OB} = 0$

[woven radish]

Ari

[thin fern]

try to write that in terms of a1, a2, b1, and b2

[somber garnet]

y

yea

oohhh

i ghink i see it

ty

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[dull thunder]

I don't get the limit like why does f_x start with y and f_y with x ?

[supple knot]

What exactly do you mean "start with"

[dull thunder]

ummm like ,y and ,x?

[visual torrent]

Do you mean the subscript on f?

[dull thunder]

no

like the limit

WAIT

i was tweaking

it should have that

nvm

i get it

😭

sorry yall

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[tidal crane]

Hello, I'm taking differential equations and I found this exercise in my homework. In class I learned that k can be given any value with the constant to simplify, but in this case I don't know if I can add that squared x. The answer I arrived at is correct but I don't know if the method is valid.

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[rotund mason]

Hello i was wondering if i did this question correct for part A and how do i continue with problem

[frigid jetty]

Well if u draw a circle you'll see 2 answers ig

Solution seems normal

[visual torrent]

I was also going to suggest drawing it out on the unit circle
Itll help to see it visual for sure

[rotund mason]

Ok thanks

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[inland flame]

how do i find the min, q1, med, q3, and max of a sinusioid

[drifting sinew]

Do you know how transformations work?

[inland flame]

yeah but the equations are confusing its y=10+2cos(x-10)

basically i have this project where i make a picture out of 4 sinusoids and then i have to say the centerline, amplitude, period, shift, min, q1, med, q3 and max of all of them

im just confused on the last 5 tho

[restive river]

what's your username language, is it thai

[drifting sinew]

First, understand that cos (and sin) have cycle between [-1, 1]

And i recommend rewriting y = 2cos(x - 10) + 10

This makes it easire to see what transformations are applied first

So, since we changed cos -> 2cos, how do you think the min/max will change?

[drifting sinew]

Tamil

[restive river]

Oo

[inland flame]

is the amplitude bigger

[drifting sinew]

Yes.

[inland flame]

when you say (-1,1) what do you mean

[drifting sinew]

Sorry-

• -1 is the minimum
• 1 is the maximum

[inland flame]

is that for the y axis

because my x-axis is in degrees from -340 to 340 in increments of 10 degrees

[drifting sinew]

Sorry for the late response

[inland flame]

dw

[drifting sinew]

min, q1, med, q3, and max of a sinusioid
these are all y-values

[inland flame]

oh

[drifting sinew]

_ _

[inland flame]

wait can i send my previous math notes bc the way my teacher taught it was that all of those values were x values

[drifting sinew]

I think the file got deleted.

[inland flame]

yeah resending now

[drifting sinew]

Given this, where are you struggling with the current question?

[inland flame]

ok like for example one of my equations is y=-6-sin3x

so the increments should be 30 degrees bc the period is 120 degrees

but my teacher also said you double check the min q1 med q3 max values by doing max-min and it should always be 360

but im not getting 30 when i do max-min

i mean 360

<@&286206848099549185>

https://tenor.com/view/palla-deserto-desert-hot-gif-6014273

anyone here brah

ts due tmrw

https://tenor.com/view/vince-staples-knocking-knock-knock-peep-hole-ramona-park-gif-7308367918900839245

is anyone on their shift

<@&286206848099549185> can i have help

https://tenor.com/view/wall-gif-25740672

me rn

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@inland flame Has your question been resolved?

[inland flame]

no

.close

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[sterile moss]

Is this right? :3

Pls ping

[empty valve]

uh

first two i agree with

HH

uh

[sterile moss]

Thank you! Lmk if u find out the others

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@sterile moss Has your question been resolved?

[empty valve]

ya looks right

oh look at that

uhm although

dont the boundaries change

so from 0 to 8

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[violet fiber]

what am i suppose to put here?

[pseudo basin]

row reduce the augmented matrix, with x, y and z in tow, until you end up with a row of the form [0 0 0 | something]

[graceful cosmos]

Is there a drop-down menu or something? It's unclear what your answer can look like

Or do you just type in absolutely anything?

It's hard to give a hint without answering directly, as this is a "do you know the definitions?" question

So I'll suggest you be very comfortable with linear independence

[violet fiber]

not a dropdown

[violet fiber]

just asking for the linear condition

[devout snow]

@violet fiber Has your question been resolved?

[restive river]

Could you please elaborate ?

[restive river]

Linear -> has only 1 solution

[devout snow]

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[patent compass]

Is this wrong? The 90+Theta is XOA' which can't be what they're possible taking the sin of right? since that is obtuse (>90 deg) so you can't really do sin (90+theta) for XOA'

[patent compass]

And (M'P')/OP' is sinnn (90-theta) not sin (90+theta) as seen in this picture

[devout snow]

@patent compass Has your question been resolved?

[patent compass]

https://tenor.com/view/sad-sad-mario-mario-gif-18405221118743840924

[patent compass]

@dry robin

[leaden crow]

[magic wind]

This looks fine. M'P'/OP' = x/r = cos(theta) = sin(90-theta). But sin(90+theta) = sin(90-theta) for all theta.

[devout snow]

@patent compass Has your question been resolved?

[devout snow]

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[devout snow]

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[ocean hound]

.close

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[primal jolt]

given the ODE,
graph the phase line and classify the equilibrium points
graph, approximately, the solutions on the plane

[fathom verge]

!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

[primal jolt]

so this is the phase line

yeah give me a sec

i'm posting it

[fathom verge]

Oh cool! Sorry

[primal jolt]

no that's okay

and here's the graph

i'm not sure if the graph is correct

i'm 99% sure the phase line is correct

from what I understand:
on every equilibrium point there will be a horizontal solution line

and then i just need to draw a curve converging towards an equilibrium point

can converge upwards or downwards

according to the phase line

[alpine surge]

looks right to me what you did

[alpine surge]

x is like the time or something right?

[primal jolt]

yeah x could be t

[fathom verge]

Yeah this looks quite right to me too

[primal jolt]

probably should be t but its just the independent variable

alright cool, thanks!

this topic is relatively easy then

compared to the rest of ODEs

[fathom verge]

Equilibrium points make physical sense when you think about it

And yeah it's not necessarily hard

[primal jolt]

this course is mostly preparing us for phys 2

from what i know

hence the heavy focus on ODEs

i watched 3b1b's video on odes

i kind of get them

sort of

slope fields i still don't get though

[fathom verge]

You'll do PDEs some day too, this is where the no-fun begins Things are waaaay more complicated

[primal jolt]

yeah some day i'll be doing quantum physics too

but

i prefer not to worry myself with that

(yet)

[fathom verge]

Of course

[primal jolt]

anyways. thanks for the help!

[fathom verge]

Well, you had done all the work

[primal jolt]

right but i had no way of checking if it was correct

other than chatgpt

which

i know

isn't the best

but it's been surprisingly helpful for odes

i've found it works very well with purely math related questions

physics and chem can be a bit more iffy

[fathom verge]

Wolfram doesn't help you?

[primal jolt]

yeah but wolfram doesn't help me solve it when i don't know how to

like, the exam is tomorrow

i've been cramming

and i haven't had much time to learn just practice

chatgpt is useful to learn the basics

then practice my way from there

[fathom verge]

No I meant just to check if your solution is right or not

[primal jolt]

ohhhh

i don't know how to graph odes on wolfram

[fathom verge]

,w solve y'=y^2(y^2-16)

[woven radish]

Results provided by WolframAlpha

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

Requested by matplotlib

[fathom verge]

"Sample solution family"

It's crammed but it looks like yours

[primal jolt]

that doesn't look like my solution

it does?

[fathom verge]

At least above 4

[primal jolt]

well the slope field seems to show i'm right

ok wait a second though

how can i know if the solution curve

uh

i dont know the translation

its... concaveness?

[fathom verge]

Ig? What's the spanish for it?

[primal jolt]

does it matter?

concave vs convex

how it curves

like here i drew the blue line

but could it theoretically be the red line

[fathom verge]

Yes

In fact

I suppose the curve should look like an arctan

,w plot arctan

[woven radish]

Results provided by WolframAlpha

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

Requested by matplotlib

[primal jolt]

for all curves?

[fathom verge]

Because it is also stuck below

[primal jolt]

i'm asked to sketch it approximately though

[fathom verge]

Well, not those above y=4 and below y=-4

[primal jolt]

usually we're not allowed graphing calculators but i read the rules for this exam and there's no mention on graphing calculators

so

maybe i could use it

[fathom verge]

[primal jolt]

.close

[devout snow]

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[dusty valley]

Why did they give the height by way of an invisible line? I don't understand this question.

[scarlet sequoia]

Because the height is always perpendicular to the base and in this case it lies outside the triangle

(what occurs for obtuse triangles)

[devout snow]

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[dusty valley]

What is a "directed" line segment. Why is it using 2 points from separate quadrilaterals?

[pseudo basin]

What is a "directed" line segment.
it's like a segment but you call one of its points its "start" and the other its "end" and give a shit about which is which

[dusty valley]

Let me post image of question, I lost it when I had to copy the text again.

[pseudo basin]

Why is it using 2 points from separate quadrilaterals?
was there an image that you were gonna upload

oh yeah ok let's see then

[dusty valley]

Here it is:

[pseudo basin]

ok and what sequences do they give

[dusty valley]

I should have copied the options, let me do it again.

Here it is with options:

[pseudo basin]

ok right

[dusty valley]

Why would you name a line segment using points from 2 different quadrilaterals, though?

[pseudo basin]

so in the context of translations, a "translation along the directed line segment WA" means a translation that sends W to A

i.e. if you imagined taking like a carbon copy of the blue shape and then shifting it around without rotation

then "translation along the directed segment WA" means aligning the W on the carbon copy to the A on the original page

[dusty valley]

So, they're saying all I need to know is 1 point to 1 point and the rest don't change anything.

[pseudo basin]

dunno what yo umean by 'the rest don't change anything'

[dusty valley]

No changes in rotation, lengths, etc.

[pseudo basin]

a translation is completely specified by one before-after pair, yes

yes thats the whole point of a translation

[dusty valley]

It's just bizarre that they even had to state that. That's what's literally throwing me off, it's like "huh"? Why are you telling me that...it just confuses me.

[pseudo basin]

... you think some of their info is extraneous?

[dusty valley]

It's just a new way of saying something up to this point in the course, I guess, is all I'm saying. So, it's okay but new.

"directed line segment" is new to me.

Normally, it's been "how do we translate triangle ABC to triangle ABC prime". Very simply stated.

Or in the case of a quadrilateral, "How do we translate quadrilateral ABCD to quadrilateral A'B'C'D'."

So, this new speak gave one point and that means move them all in unison, Okay, I can do that.

Thank You

.close

[devout snow]

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[devout snow]

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[sharp moth]

im stumped on this one

[outer eagle]

AP, GP?

[sharp moth]

arithmetic progression and geometric progression

[lavish sigil]

Well I guess you start by subbing a - d, a, and a + d?

[sharp moth]

i tried but it becomes ridiculously long and leads to nowhere

ive tried the formulas aswell b=a+c/2, but that doesnt give anything

[lavish sigil]

I guess you let the first AP be (a, d) and the second one be (A, D)

and work with the two of them

the numbers are annoying

Oh fuck I didn't notice the GP

[sharp moth]

yeah if u plug in that same a-d,a,a+d in the gp thing, it becoems way too long

[lavish sigil]

x + 3, y + 3sqrt(2), z + 11 are in a harmonic progresstion

[restive river]

[lavish sigil]

do you have choices

[sharp moth]

nope

but its an irrational answer, thats the only hint our teacher gave

[lavish sigil]

okay so you get a = 3sqrt(2)

(z + 11 + x + 3)/2 = y + 3sqrt(2)

hmm

this could work

a - d + 7 = a + 3sqrt(2)

[sharp moth]

it doesnt ive tried

[lavish sigil]

are you sure

d = 7 - 3sqrt(2)

Oh wait no

mb

[sharp moth]

ive been on this stupid question for almost 2 hrs ive gave everything i have, its not solved by normal methods

[lavish sigil]

skip lol

[sharp moth]

i want to but now im interested cuz it is a good question

[pure stone]

are these in strict order

[sharp moth]

yes

[lavish sigil]

Something is off

[pure stone]

Think I almost got it

numbers might look very ugly

[deep elbow]

a b c being in AP means c-b=b-a or a+c=2b
a b c being in GP means c/b=b/a or ac=b^2

You will use these

[pure stone]

got answers

[deep elbow]

2y=x+z (first AP)
and x+y+z=9root2
these 2 informations are enough to find y by themselves

[pure stone]

bascially what I used

[deep elbow]

You should be able to find all of them after writing everything out

I recommend trying again before someone explaining a solution to you

[devout snow]

@sharp moth Has your question been resolved?

[devout snow]

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[shy turtle]

Feels bad to be back 3rd time so quickly but

[shy turtle]

In Q3 part 1 I made a series of cosx + cos(3x).... And used the cos AP formula and took derivative

But I am not getting the answer

I kinda have doubt if I correctly applied the formula

.

[lavish sigil]

Maybe just use complex numbers

[ S = \Im \sum_{k=1}^n (2k - 1)e^{i(2k-1)x} ]

[woven radish]

jewels!

[lavish sigil]

Do you know how to solve these mashes of an arithmetic and geometric series

[shy turtle]

I mean I guess I can do it

But it's not how they intend us to solve it

[lavish sigil]

Who is "they" here?

Is there a solution you already have

[shy turtle]

My coaching institute

[shy turtle]

Only the answer key

[storm raptor]

if its jee then just do whatever is fastest

[storm raptor]

this is probably the best

its also how the cos and sin ap formulas are derived

[shy turtle]

Oh

But can't I do it using the formula only

Our teacher said we need to use the AP formula for it

[shy turtle]

But I don't seem to be getting the answer here

[lavish sigil]

¯_(ツ)_/¯

[shy turtle]

Idk what I have done wrong

[lavish sigil]

I don't know any of these formulas

[shy turtle]

Also I don't know how I would solve this I guess

[lavish sigil]

Multiply S with e^(2ix) and subtract

[shy turtle]

The AP formula at the right

[lavish sigil]

I could walk you through using this

[shy turtle]

Hmm

[lavish sigil]

If thats not what you want I'll let someone else come by

[shy turtle]

(I don't get it)

[shy turtle]

I would not mind knowing your method as well

Maybe could be helpful

Sometimes in the future

[lavish sigil]

Well okay

[uneven cape]

which level is this again? looks like precalc, but i don't recall precalc having that many formulas... i am not remembering all that. would definitely be fried if i came upon this

[lavish sigil]

So we'll deal with $S' = \sum_{k=1}^n (2k - 1)e^{i(2k-1)x}$, and your answer is $S = \Im S'$

[woven radish]

jewels!

[shy turtle]

Its in our Limits continuity and differentiability module idk about precalc and all

[shy turtle]

Hmm

[lavish sigil]

$e^{2ix}S' = \sum_{k} (2k - 1)e^{i(2k + 1)x}$

[woven radish]

jewels!

[lavish sigil]

Is that alright

[uneven cape]

oh, calculus. wait, i did caculs, i do not remember all of that 😭

[shy turtle]

Yeah tho why did you multiply S' by e^2ix

(I have forgotten complex numbers sorry)

[woven radish]

jewels!

[lavish sigil]

eh I tried aligning them

Now you subtract the two

[daring yarrow]

Instead of multipling by 2ix what about ix?

[lavish sigil]

@shy turtle do you get why we multuplied by e^2ix

[lavish sigil]

wouldn't work

[shy turtle]

Yeah got it

[lavish sigil]

Okay now subtract

[shy turtle]

Yeah

[woven radish]

jewels!

[lavish sigil]

All fine now?

[shy turtle]

Yeah

[lavish sigil]

Okay

So now the middle term is a geometric sum

do you know how to add a finite geometric series

because I don't remember the formula

[shy turtle]

Yeah

1 sec

This is gonna be <1 right?

[lavish sigil]

Doesn't matter

it's finite

no convergence issues

[shy turtle]

Getting this on adding

[lavish sigil]

Can I trust you

That that's correct

[shy turtle]

Uh

Its

The formula

Wait a sec

https://images.app.goo.gl/Q4Gukex4kk5MnPYcA

This is the formula

r is common ratio

[lavish sigil]

bro why is there even a distinction in the first two cases

[shy turtle]

I used the sum of inf gp but now I think I shouldn't have used it?

[lavish sigil]

yeah its not infinite

[shy turtle]

In infinite series there should be distinction

But yeah at the top it's meaningless in finite

[devout snow]

@shy turtle Has your question been resolved?

[shy turtle]

Back had to go eat

[deep elbow]

I’m sorry but which one is question 3 part 1? the paper is so confusing

[shy turtle]

Oh sorry didn't notice it cut off the Q no.s

It's the sinx + 3sin3x...

We need to find sum

[deep elbow]

Okay

[devout snow]

@shy turtle Has your question been resolved?

[daring yarrow]

👋

[supple knot]

From the right side, you can write S' = dS/dx and use FTC to get S = int(S') and exchange the order of sum and differentiation to integrate term by term.

[devout snow]

@shy turtle Has your question been resolved?

[shy turtle]

The heck I don't understand any of it but I'll close the ticket and thanks everyone anyways

.close

[devout snow]

Channel closed

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[devout snow]

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[willow oxide]

tanθ+sinθ=m tanθ-sinθ=n
Then prove secθ=√mn cosec^2 θ

[devout snow]

Please don't occupy multiple help channels.

[scarlet sequoia]

Have you tried multiplying these expressions and using the a^2 - b^2 formula?

[flint pelican]

@willow oxide you really need to stop multiposting.

[willow oxide]

Sorry

[flint pelican]

Am closing this now since you are being helped in the other channel

[scarlet sequoia]

Since you've already opened the channel and people are helping you there, we can close this one I think

[flint pelican]

.close

[devout snow]

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[long plume]

how do i solve further

[thick ledge]

Convert sin(8pi/5) into 3pi/5

And then use double angle formula for sine

[long plume]

how 3pi/5?

[thick ledge]

Pi + 3pi/5

[long plume]

then ?

expand bracket ?

[thick ledge]

You do know that sin(pi + theta) = -sun theta

Right?

[long plume]

oh yeahh

[long plume]

then like this?

[thick ledge]

How is 8pi/5 = pi +pi/5

??

That would be 6pi/5

[long plume]

sorry

[thick ledge]

Np

[long plume]

i dont get what now

[thick ledge]

Up until now you’re correct

Now how can you write sin(6pi/5) in terms of sin(pi/5)

[long plume]

ok i got the answer 1/16 .. but this is so long 💔

.close

[devout snow]

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[prime narwhal]

For 3 the answer key says it should be B

But when I enter it into my calc they are clearly not the same

[wind mason]

Yeah that’s just a misprint probably

Try to figure out the actual answer

It is one of the options

[prime narwhal]

None of em are correct on my calcuLtor

They all look different

None of them cover the blue line, they are all very close overlapping

[strange nimbus]

That will only show one of them.

[prime narwhal]

Huh wdym

[strange nimbus]

You showed where you typed in what to graph.

You have the function you're supposed to be matching.

Then you have one of the possible answers.

[prime narwhal]

Yea then he told.me it might've been a dif one

So I typed them all in

Just for none of them to overlap the original

[strange nimbus]

OK, type them all in at the same time.

[prime narwhal]

That's what I did there

You can see pink and black.

Behind the green line

And red

None overlap blue

[strange nimbus]

I can't see pink, black, or red in any picture you've posted here.

[prime narwhal]

Dawg

They are behind the green line

Peeking out

[strange nimbus]

Can you show the screen where they're typed in? Like this one ^

[prime narwhal]

Ughh

I can reenter it all ig

I found another issue for after this one but I'll retype it

[prime narwhal]

I must've mistyped

Nvm the solution I got isn't even an option

Oh

3pi/4

[strange nimbus]

Right.

[prime narwhal]

Fuck ok

Ty

.close

[devout snow]

Channel closed

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[strange nimbus]

You're welcome.

[devout snow]

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[restive river]

help

[restive river]

So currently I am doing "Approximating Area" And my two topics are
Find an upper or lower sum given a function

Approximate the area under a curve using rectangles

I just had a question on the uh formua

Ill provide questions rn

How do i Know when to use the two formulas? how could i tell

[devout snow]

@restive river Has your question been resolved?

[wind mason]

Because the question will tell you

Upper sum probably means “overestimate” and you determine that based on the orientation of the curve

[restive river]

i asked ai and it says you take the derivate of whats given and it depends on if its upper and lower and if the derivative is positive or negative is that accurate?

[wind mason]

I would rather say concavity and increasing/decreasing

[restive river]

alr ty

.close

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[zinc veldt]

is 4^3^n always 1 mod 3^(n+1)

[lunar harbor]

yeah

[zinc veldt]

why

[lunar harbor]

lte

[dapper fable]

you can do proof by induction i guess

[lunar harbor]

or that

[zinc veldt]

lifting the exponent?

[lunar harbor]

yes

[zinc veldt]

can I use euler's totient

[lunar harbor]

it wouldn't be my first approach but maybe it would work??

ok yeah you could use it

[zinc veldt]

does euler's totient imply that a^(2*3^n) is congruent to 1 mod 3^(n+1)

[lunar harbor]

if gcd(a,3)=1 then yes

[zinc veldt]

so can you say 2^(2*3^n) = 1 mod 3^(n+1)

which you can rewrite as 4^3^n ?

[lunar harbor]

yeah

[zinc veldt]

then why is it saying i need LTE

because that is going over my head tbh

[lunar harbor]

because there's more than one way to prove it?

[zinc veldt]

oh ok

but I don't need it in this case right

[lunar harbor]

if you don't want to use it

there's other ways

[zinc veldt]

it's saying my reasoning is circular

[lunar harbor]

I'm a human not a bot

[zinc veldt]

so its BS right

[zinc veldt]

ik

[lunar harbor]

so why would you trust a bot that runs off probabilities to pick the next word instead of looking at the big picture

[zinc veldt]

I am pretty sure it's wrong but just making sure

[lunar harbor]

it doesn't have the context of where you're getting the initial statement from

whether that's from rewriting the claim or invoking totient

[zinc veldt]

oh ok that makes sense

thx

[lunar harbor]

but in general it's kinda annoying for ppl to do this to us

[zinc veldt]

sry

[lunar harbor]

becuase it's almost like we're telling you one thing

and then you're replying with a probability dependent bot generated response that lacks the full context and asking if it makes sense given all the context

so some of us take it as a "in one ear, out the other" type of thing

[zinc veldt]

can I use this reasoning to show which p-adic numbers have the square root of -1 defined?

I am thinking euler's totient says the totient of p^n = (p-1)*p^(n-1)

and I use this somehow

[lunar harbor]

eh you're basically trying to prove a special case of hensel's lemma, and the proof I'm familiar with does not use that

[zinc veldt]

oh

can I just test out numbers like this

this is what they used to show that square root of -1 doesn't exist in 2 adics

[lunar harbor]

if you want to gain intuition then go ahead

[zinc veldt]

ok

[lunar harbor]

also the final answer is relatively "nice"

so you can probably guess it if you test enough things

[zinc veldt]

oh cool

I didn't look at the answer yet

[zinc veldt]

oh does work if p is of the form 4n+1

because then p-1 is divisible by 4

and the 4th roots of 1 give you i

and euler's totient gives (a^p^n)^(p-1) congruent to 1 mod p^(n+1)

rip

wait 9 isn't prime though

I meant p being a prime of the form 4n+1

[lunar harbor]

then yes

[zinc veldt]

so that's the "nice" answer?

[lunar harbor]

yeah

[zinc veldt]

wow

yeah it is nice

thanks

idk if my reasoning is correct but I got the right answer ig

ty for the help btw

.close

[devout snow]

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[devout snow]

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[tall summit]

can u explain the steps taken to isolate t to itself? in this problem? i can't wrap my head around it.

[supple knot]

Multiply both sides by -tau

Of the first and last expressions

[tall summit]

lemme try that.

thanks!

.close

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[normal bolt]

IS their any standard proof of the following statement?
If a > 0 and D < 0 <=> f(x) = ax2 + bx + c > 0 (always positive)
or to prove this, putting the solution or value of x into f(x)

[normal bolt]

theres one more if a < 0 and D < 0 <=> f(x) = ax2 + bx + c < 0 (always negative)

[lament kraken]

isnt it just

D > 0 thus the graph does not intersect the x axis (thus graph is either completely positive or completely negative)

a > 0: the graph is concave up

so since minimum value is positive everything is positive

[normal bolt]

oh

similar for the second

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[spice valley]

i need help

[spice valley]

what am i reading

this was a problem set on linear independency

and solving matrixes

i dont even know where to begin

[pseudo basin]

do you know the definitions of cosh(x) and sinh(x)

[spice valley]

yess

[pseudo basin]

ok can you write those out

[spice valley]

cosh(x) = e^x +e^-x/2 and sinh(x) is e^x -e^-x/2

is that right

[pseudo basin]

missing brackets.

[spice valley]

wait ho on

[pseudo basin]

cosh(x) = (e^x + e^(-x))/2 and sinh(x) = (e^x - e^(-x))/2

[spice valley]

cosh(x) = (e^x +e^-x)/2 and sinh(x) is (e^x -e^-x)/2

yes

[pseudo basin]

ok

[spice valley]

soz not used to typing

yes

[pseudo basin]

now can you work out for me what cosh(x) + sinh(x) simplifies to