help-23

[sharp cedar]

hold up

Calculus 6E ( 2007 ISBN 9780495011606 ) James Stewart

[proud belfry]

what page

[sharp cedar]

wait

[proud belfry]

found it

the textbook has it nice and tidy

[sharp cedar]

the hell

[proud belfry]

what the fuck did your school do to this amazing textbook

[sharp cedar]

why is my textbook

what the fuck

hold up

[sharp cedar]

university 😂

[proud belfry]

i was right

s isnt a variable

it means fucking square root

[sharp cedar]

nahh they fucked up our textbooks too so we dont cheat

LMAO WHAT?

wait

[sharp cedar]

what edition are u on

[sharp cedar]

bc this is on the 6th

[proud belfry]

says it in the screenshot, 6e

[proud belfry]

holy shit

funniest shit ever

id be crying if i wasnt laughing

[sharp cedar]

where the fuck is the s

[proud belfry]

it means square root

there isnt an s

[sharp cedar]

huh

wtf

how

[proud belfry]

s means square root

bc ur university has a

[sharp cedar]

OH

OH

[proud belfry]

questionable anti cheat policy

[sharp cedar]

FOR FUCK SAKE

FUCKING HELL

FUCK ME

[proud belfry]

they fucking defaced your textbook

[sharp cedar]

YK HOW MANY DAYS

HOURS

I WASTED

TRYNA FIGURE

WHY THIS ISNT SOLVABLE

MY GOD

[proud belfry]

reminds of those demorgan fuckeries we did in logic class

[sharp cedar]

finally

i got

1/5

oh my lord

thanks for the help @proud belfry

[proud belfry]

sue your university for emotional damages

hey what university do you go to

so i can avoid it

[sharp cedar]

ikr i should

[sharp cedar]

😂 😂 😂 😂 😂 😂 😂 😂

dk if u know it

ain shams university

in cairo

[proud belfry]

alright im safe i dont live in egypt

[sharp cedar]

yh

ur safe

dont ever

eer

ever

come there

its

bad

where u from

if u dont mind me asking

[proud belfry]

casnda

canada

[sharp cedar]

ah

thats nice

my uncle is there

[safe radish]

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[raw glen]

Can someone please confirm if the method I used for Q. 24 is correct or not

[safe radish]

@raw glen Has your question been resolved?

[raw glen]

<@&286206848099549185>

[ripe epoch]

whats the Question

i cant understand the Question

[ripe epoch]

.

[ripe epoch]

oh ididn even saw that

which one

[spice furnace]

Why don't you just evaluate the expression using a calculator

[raw glen]

Calculators are not allowed

[ripe epoch]

can anyone see me?

hear me?

[raw glen]

@ripe epoch Q. 24

[ripe epoch]

that is a very unnecessary Q so i refuse to provide assistance🥲 , nobody will ever ask Qs related to values that are already known.

[raw glen]

.close

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[upbeat spruce]

what is the Jacobian of (x^2*y)/(x^4+y^2) at point a = (1,-1) ?

[lean otter]

u mean jacobian determinant

or matrix?

[upbeat spruce]

matrix

[lean otter]

oh

so here f is the function you have

and the rest should be pretty straightforward?

at the end just plug in 1,-1

you should get it

algebra is a rigorous thing mostly

[upbeat spruce]

I guess I just wanted to check my work (kind've), I ended up getting <0,0> and that could be it but not 100% sure

[lean otter]

so if you try to find reason its tough bro

so how about showing your work?

[upbeat spruce]

so

[lean otter]

pic or smth

[prisma wren]

Jacobian should be a matrix, not a vector. A 0 matrix jacobian is possible tho

[upbeat spruce]

Jf (x,y) = < 2xy/(x^4 + y^2) - 4x^5y/(x^4 + y^2)^2, x^2/(x^4 + y^2) - 2x^2y^2/(x^4 + y^2)^2>

Jf(1,-1) = <0,0>

[lean otter]

bro i hand it over to you coz i dont know much about jacobian

[upbeat spruce]

yeah mb, I meant <<0>|<0>>

[lean otter]

in you do help my friend here

so he flew off?

huh

[upbeat spruce]

guess so haha

cheers though

[lean otter]

ok let me try

so he meant the final matrix is a zero matrix?

is that it

?

and did you end up with a zero matrix?

[upbeat spruce]

well

it sometimes can be I suppose

[lean otter]

why cant it it should be possible

[upbeat spruce]

and yes I ended up with 0 matrix

[lean otter]

so you followed the partial differentiation?

bro i gotta go as well

i will think a bit more

and come back

if i get time

[upbeat spruce]

it's just that with this particular function, when I try to find the tangent approx at that point, I end up getting T(x,y) = 0, which just seems kinda dumb. That's as far as my intuition goes at the moment.

[lean otter]

sorry ok?

[upbeat spruce]

all good, cheers

[safe radish]

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@upbeat spruce Has your question been resolved?

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[soft parrot]

.help

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[soft parrot]

help

[soft parrot]

how does the maths work

i know ln is log e

is it both side divide ln

[potent seal]

First they divided by 20 on both sides

And then they took ln

[soft parrot]

how ln works

[lime dust]

Like any other logarithm but base e

Ln(e)=1

[soft parrot]

i dont know law indices

idk how -lambda and 21 get down

[lime dust]

log(a^b)=blog(a)

Maybe “b” wasnt the best letter to use xD

[soft parrot]

i sitll dont understand how the ln and log

get in the equation

is it to get rid of e by making it = 1

[lime dust]

You can use any log u want in any base

They used ln because there is an e^whatever involved

[soft parrot]

okay

this is more confusing

[lime dust]

Which part is confusing u

[soft parrot]

first 2

lines

[safe radish]

@soft parrot Has your question been resolved?

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@soft parrot Has your question been resolved?

[hot thistle]

the first line is presumably from some context we don't have

the second is presumably trying to find a t value that gives you half of the starting quantity N_0 = 20

so you want (N(t_{1/2}) = \frac{1}{2}N_0 = \frac{1}{2}\cdot 20)

[flat frigate]

maximo¹

[hot thistle]

i am using N_0 to mean N(0), like the picture did

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@soft parrot Has your question been resolved?

[safe radish]

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[nimble phoenix]

can someone help me rq with trig

[hoary wind]

Which bit are you stuck on?

The interpretation of the angle of depression or the calculation itself?

[nimble phoenix]

i just dont know how its 21.725

[hoary wind]

Because it's degrees minutes seconds

a minute is 1/60th of a degree

And a second is 1/60th of a minute

You can calculate it manually as 21 + 43/60 + 30/(60^2)

Or on your calculator

[nimble phoenix]

ohhh yea

ok

so like converting dms to degrees

[hoary wind]

There's a DMS key it looks like a degree sign with ' and ''

Yeah

[nimble phoenix]

ok

thanks

[hoary wind]

Np

[nimble phoenix]

.close

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[ruby notch]

Find all 4-tuples (p,q,r,s) of primes such that p^2 + q^2 + 4r^2 + 6s^2 = 2024.

[safe radish]

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

[ruby notch]

2

[safe radish]

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

[ruby notch]

I tried seeing which numbers can be even or odd, but I'm stuck after that. I noticed that p and q both have to be odd and that they add up to an even number and that 4r^2 + 6s^2 is going to be even.

[tardy mango]

take both sides mod 6

[ruby notch]

Just did. What should I do after?

[tardy mango]

that should be it

do yk what you can say about a prime mod 6 (assuming we're dealing w/ an odd prime)

[ruby notch]

Well it can either be 2, 3, of 5

[cold aurora]

Alternatively, Hint: ||There is such a number n that for most primes p, p^2(mod n) is a constant. Make use of that.||

[ruby notch]

Wait it can be 1 or 5 mod 6

[tardy mango]

See what you can do with this, particularly ||considering p^2 mod 6||

[ruby notch]

Therefore, p^2 must also be 1 or 5 mod 6

Maybe 1 and 5 add up to 6. So if I have two primes that are 1 and 5 mod 6 I can get 0. Same thing goes for 4r^2 + 6s^2

[tardy mango]

Therefore, p^2 must also be 1 or 5 mod 6

How did you get this?

[ruby notch]

I mean if you square 1 mod 6 you get m1 mod 6 so it stays the same. If you square 5 you get 25 which is also 1 mod 6. So it's always 1 mod 6, sorry.

[tardy mango]

I'll let you work on it for a bit from here

[ruby notch]

I noticed that at least one of the primes needs to be 2 or 3. What do I do from there?

[tardy mango]

plug them in and repeat

[ruby notch]

I got that p or q must be 3.

So now the problem is q^2 + 4r^2 + 6s^2 = 5 mod 6?

What should I do after?

[tardy mango]

q^2 + 4r^2 = 5 mod 6

Now play around with your residues

[ruby notch]

Does r have to be 2?

Wdym, 2 doesn't work for p nor q but it can work for r right?

[tardy mango]

Did you not deal with the case where the primes are 2?

Take ||the equation mod 4||

[ruby notch]

So q^2 must equal 1 mod 4 and 1 mod 6.

[tardy mango]

??

[ruby notch]

Wait are you talking about the original equation or the simplified one?

[tardy mango]

Original

[ruby notch]

Oh so then q^2 + 2s^2 = 3 mod 4 since we know that p^2 = 9

[tardy mango]

p^2 + q^2 + 2s^2 = 0 mod 4

All of them are odd

Then return to the thing mod 6 and test residues of 3 and 1

I gtg but this is basically it

[ruby notch]

thanks I got it now

.close

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[zenith sigil]

Last question which one is the right answer

I’m confused on which one would be right

[safe radish]

@zenith sigil Has your question been resolved?

[zenith sigil]

<@&286206848099549185>

[tight perch]

Sup homie if nobody gets to your question in a few minutes I can try to take a look at it (currently occupied atm)

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[stray whale]

How do you find a slant asymptote

[stray whale]

And also how do you find holes in a rational function

[zenith sigil]

can you send an example

@stray whale

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[glossy cedar]

Hey help

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[safe radish]

Please don't occupy multiple help channels.

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[river briar]

( f(x) = x^3 - 3x^2 + 2x + 1 ). Find the absolute maximum and minimum values of ( f(x) ) on the interval ( [-1, 2] ).

[flat frigate]

Nuclear

[safe radish]

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[cloud rock]

How do i simplify and get the restrictions for 6x(9x -3x^2 -10)

[icy lance]

what do you mean 'the restrictions'

[cloud rock]

like

what x cant be

i think i have to simplify it first but i have been stuck on how to

for so long

[icy lance]

you mean if you had f(x)=6x(9x -3x^2 -10), find the domain of f

do you think theres anything x cant be, just looking at it

[cloud rock]

i mean x cant be 0

the question i got was
Simplify. State Restrictions, if any

[umbral swan]

why?

[cloud rock]

if 6 is multiplied by 0 then anything with x would be 0

this is confusing

[icy lance]

and?

whats wrong with it being 0

[umbral swan]

what is your actual question/task :D

[cloud rock]

.

this

thats it

thats all it says

i think it would be easier if i just simplify it first right?

[umbral swan]

well uh simplify: -18x³+54x²-60x

state restrictions: ???

[cloud rock]

D:

[icy lance]

it wouldnt be a simplification, nor would it really be necessary to expand it

[umbral swan]

why do you want it to not be 0?

[safe radish]

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

[cloud rock]

idk my teacher told me most of the times i wouldnt want to be 0 during class

and then he just like left

to help another student

[umbral swan]

what's the context then?

[cloud rock]

simplify and then state restrictions if there are any

[umbral swan]

no what's the context

[cloud rock]

of?

[umbral swan]

of the task

[cloud rock]

yeah

thats about it

[umbral swan]

which subject

which field

[cloud rock]

functions

[umbral swan]

and within functions, what aspects did you look at?

roots? derivatives? ...

[cloud rock]

multiplying, dividing, adding, subtracting functions rn

[umbral swan]

yh but if you're uncertain what your initial task is then we can't help

e.g. if it were: Find all x such that 6x(9x -3x^2 -10) = 0 then it'd be something solvable

[cloud rock]

wait i might have it

i mean it doesnt say i have to state restrictions if there isnt

i think i just simplify it

what my teacher just taught us was different ways to simplify functions

[icy lance]

what are you considering as simplified

expanded or factorised

[cloud rock]

factorised

[umbral swan]

ok, for a specific purpose?

or just arbitrarily simplified

[cloud rock]

this

he gave us another sheet and it says "make sure to check if you cannot factor any further"

[icy lance]

alright, what are your thoughts then

[cloud rock]

idk if im over thinking it but i just multiplied everything inside the bracket like lunatic did and got -18x^3 +54x^2 -60x

and im just stuck on that

i just moved on to the next question

[icy lance]

thats the opposite of factorising

[cloud rock]

yeah

idk what to do, i tried getting 2 numbers that multiplied -3 and - 10 and added to +9 but i couldnt

so thats really all i got rn

[icy lance]

you cant think of any factors of 30 that sum to 9?

then try something else

you can check with the quadratic formula to see if you actually can factorise it cleanly

its possible you just cant

[cloud rock]

with -3x^2 + 9x - 10?

i did that but it came out to a negative number

[cloud rock]

i have one more question

how do i factor the bracket part, so
-3x^2 + 9x - 10

[icy lance]

(you cant)

[cloud rock]

D:

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[dense wadi]

how do we evaluate this integral

[versed wave]

u sub

[dense wadi]

fk ty

im stupid for not realizing

.close

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[stark violet]

velocity is just the derivative of a function S(t), where S would be the position at t time right? So, for the first part of this question

[stark violet]

velocity would be

?

[lean otter]

yeah

velocity is the derivative of displacement

accelerations the derivative of velocity

derivative looks correct too

basic chain rule

-1/2, -3/2 yep

ur good

[stark violet]

tysm. was confused for ages thinking too hard on it

.close

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[nimble phoenix]

help

[nimble phoenix]

idk if im doing this right

[lean otter]

Do u want to find x or what?

[nimble phoenix]

its asking for the area

[lean otter]

Idk if iam getting this right i am not a pro but that's by using cos alpha=Adjacent side/The string then calculate the are by (Base x height)/2

[nimble phoenix]

i have no idea

[lean otter]

I believe it's right triangle right?

[nimble phoenix]

no

the angle is 85

actually i got it

igotta use law of sines

not cosine

.close

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[mellow mountain]

using (y-k)^2 = 4p(x-h) where p=distance from focus to vertex

so its (y-2)^2 = 4* 1/4 * (x+1)

which is (y-2)^2 = x+1

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

x= y^2 -4y +3

.close

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[scenic wind]

is my fbd correct? and how do I get the reaction A and B

[safe radish]

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[safe radish]

@scenic wind Has your question been resolved?

[safe radish]

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[soft reef]

hi can i get some help on if something makes sense

[safe radish]

Please don't occupy multiple help channels.

[soft reef]

does it make sense to double this number in this scenario

[atomic geode]

close your already opened help channel first

[soft reef]

i did

[safe radish]

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[torpid tendon]

i'm assuming integration by parts but idk if i'm doing it right

[torpid tendon]

unless it's u sub

i'm going to try u sub first

it appears to not be u sub

[mellow gulch]

use integration by parts

18 is a constant so you can move that to the side

[torpid tendon]

it makes the expression even more complicated (aka i get another integral that i have to use ibp again), is this supposed to happen and i just keep doing it?

[mellow gulch]

are you sure? it shouldnt be getting more complicated. maybe you are using the wrong u and v

[torpid tendon]

i set u to cos (3x)

maybe i should try u =x

i'll see how that goes

figured it out, thanks for the pointer!

.close

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[split fulcrum]

Trigonometric functions are periodic so they repeat. You can use that knowledge to set up an equation when you integrate until you get to the same problem you had started with, then make an equation

[safe radish]

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[devout harbor]

any ideas why my x is greater than 1?

I feel like I'm making a super simple error but can't quite seem to spot it

[vagrant ice]

The numerator is just (4 choose 1) * (48 choose 2)

Take the 4 kings in the deck: now choose 1 of them

Now there are 48 other cards in the deck: now choose 2 of them

[devout harbor]

why is it not necessary to select the suit like in the other problems?

[vagrant ice]

There's no mention of the suit here

The cards are either kings or not kings

[devout harbor]

sorry, the rank I meant

[vagrant ice]

Do you have an example where you used the rank in your calculation?

[devout harbor]

consider the probability of choosing 2 kings in a deck,

from 3 draws without replacement

solution: first select the rank (kings), then select two kings from the rank (4 choose 2), then choose the remaining card (48 choose 1)\

[vagrant ice]

You don't need to select the kings in that problem as well

Hold on

[devout harbor]

hmm

interestingly enough my expected value is 3, which is certainly wrong

[vagrant ice]

I honestly don't think you should multiply by 13 in any of those

Yeah

[devout harbor]

bro you might be cooking

lemme change

[vagrant ice]

I'm basing my reasoning off of the hypergeometric distribution

That distribution tells you there should only be 2 nCrs in the numerator

And 1 in the denominator

[devout harbor]

holy shit

https://tenor.com/view/cooking-cook-chef-masterchef-lilb-gif-13910066

[vagrant ice]

(The hypergeometric distribution is the distribution when you take objects out without replacement)

[devout harbor]

this is you my bro

[vagrant ice]

No worries

[devout harbor]

it worked

[vagrant ice]

Yeah don't worry I studied this at uni

[devout harbor]

me as well

clearly not as good

[vagrant ice]

Interesting

Yeah haha

[devout harbor]

I think I was getting confused because I did pairs a little while ago

but now it doesn't matter, I'm just doing kings

[vagrant ice]

Counting is indeed confusing

[vagrant ice]

Yep that's why

[devout harbor]

appreciate it bro!

.close

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[copper hawk]

help me w iv plsss

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[silent ocean]

how do i solve this

[silent ocean]

its part of a physics qs

[hard crest]

what are you trying to solve?

[desert pasture]

!original , please

[safe radish]

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

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[wintry flower]

Find m,if vector a(m;4) is co-directed by vector b(-1;3)

[wintry flower]

answer is 12

[safe radish]

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@wintry flower Has your question been resolved?

[silent ocean]

.reopen

[hard crest]

this isn't your channel

[silent ocean]

mb

[safe radish]

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[wintry flower]

.close

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[modest holly]

is it B?

[hardy lion]

check all answers that apply

yes, B is one of them

[modest holly]

C

[hardy lion]

ok

[modest holly]

thats it?

[hardy lion]

is that all?

[modest holly]

yea i would assume

[hardy lion]

why are the other two not even?

[modest holly]

not symmetric with y axis?

[hardy lion]

look closer at D

[modest holly]

what about it?

[hardy lion]

is it even

[modest holly]

yea

actually it is

its just reflected over x

axis

[hardy lion]

is the graph cut off in the screenshot

[modest holly]

is it possible for a function to be neither even nor odd?

because d might be that

[hardy lion]

can you send a picture of d

[hardy lion]

so do you think its even or odd

[modest holly]

even

[hardy lion]

yes

[modest holly]

thank you

im going to close

[hardy lion]

youre welcome

[modest holly]

.close

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[crystal badger]

where am i going wrong?

[crystal badger]

wouldn't it be the same answer for b) and c)?

[light shoal]

arctan(b/a) doesn't give you the correct angle in general

because (-b)/(-a) = b/a

so it can't distinguish between quadrants 1 and 3, or between quadrants 2 and 4

[crystal badger]

but its not **-**a
its -3/3

[light shoal]

you can see that for (b), -3 + 3i is in quadrant 3, so its angle is between pi/2 and pi

[light shoal]

a and b are general variables, i'm not claiming that they're both positive

[crystal badger]

isn't it in quadrant 2?

[light shoal]

oops, i can't count haha

quadrant 2

angle is between pi/2 and pi

[crystal badger]

so how would i proceed in terms of showing my work?

[light shoal]

arctan returns a number between -pi/2 and pi/2

so if you're in one of the quadrants in the left half plane, you need to add pi or subtract pi as appropriate

[crystal badger]

how would i know whether to add or subtract?

[light shoal]

to get into the range you want

for quadrant 2, you know the answer has to be between pi/2 and pi

you got -pi/4 from arctan

so add pi

[crystal badger]

thank you

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[sonic geyser]

FInd the volume of the solid
bounded by x^2 + y^2 = 9 and 2y + z = 6

[weary stream]

z?

or x?

[sonic geyser]

z

[weary stream]

what is z in this case

[sonic geyser]

It's part of the equation of the plane

[weary stream]

so its a 3 d one?

[sonic geyser]

Yes

I used $\int \int_{D} z \ dxdy$ but I'm not sure if I made the limits right

[flat frigate]

Rub05

[weary stream]

lemmy see

[sonic geyser]

Did you get it? @weary stream

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[random spindle]

d is γ is the edge of the bounded area i
the plane bounded by the curve y = 1 − x2, 0 ≤ x ≤ 1, and the coordinate axes,
one turn counterclockwise.

[random spindle]

I used greens formula but i get wrong answer

so with applyin greens formula i got 1

now i Should Integrate 1 dxdy with the bounds 0 to 1?

but solution does this only why?

I need help with understanding solution

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@random spindle Has your question been resolved?

[random spindle]

@raven vessel

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.close

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[coral shoal]

I got 10/10 on this paper even though wolfram says this is wrong

[coral shoal]

how tf is this correct

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[coral shoal]

.clos

.close

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[split swan]

hello, i need help with a solving trig equations over interval problem

[split swan]

cotx(secx+2)=0 range: -90*<x<=270*

I got x=180*, 210*, 330*, 360*

dk if that's correct

[tardy mango]

,w solve (cot x)(sec x+2)=0, -pi/2 < x \leq 3pi/2

[flat frigate]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[safe radish]

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

[rose plume]

prob I don't think so because you got some x's outside -90 < x <= 270

[split swan]

wait what i'm so confused

isn't -90 * the same as 270 * or am i trippig

so like full circle

[rose plume]

.

[split swan]

wait what

i'm still really confused sorry

[rose plume]

!status

[safe radish]

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

[rose plume]

ok, separate $\cot x (\sec x + 2)=0$ as $\cot x = 0$ or $\sec x + 2 = 0$. You get this part?

[flat frigate]

sssssssssssvvvvvvvvvvccccccccccc

[split swan]

yup

and uhh i know how to graph the line things

i think

im js stuck on intervals

[rose plume]

ok let's do this by cases. First consider cotx = 0. How can you rewrite cotx in terms of sinx and cosx?

[split swan]

cosx/sinx

[rose plume]

Ok, you have cosx/sinx = 0. Can you get rid of something (assuming that something is not 0)?

[split swan]

i mean i think cosx

would be zero?

[rose plume]

yes

you just need to make sure you're not dividing by 0. Luckily here there is no problem ignoring that

[split swan]

okay

[rose plume]

ok, from -90° < x <= 270°. when does cos(x) = 0?

[split swan]

um

it's on the range i think

like exactly on the range

[split swan]

okay

like an x=0 thing?

[rose plume]

do you know how to use the unit circle (x,y) = (cos,sin)?

[split swan]

kinda

like i know unit circle is r=1 and stuff

special ratios

[rose plume]

ok you get what we doing here?

[split swan]

yup

i understand this part

[safe radish]

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[violet cloud]

Hello, im not sure what the question is asking when it says defined, does it mean how many different matrices there are?

[compact nebula]

Basically if you can add them or not

[violet cloud]

oh okay, so if it has the same dimensions then?

[compact nebula]

p much

[violet cloud]

fanks

.close

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[mossy quartz]

Here's what I tried

• I assumed b = Ka where K is a constant (so let's say a point P(a, Ka) lies inside the triangle
• then I assumed a random point Q(1,2) to lie inside of the triangle
• I put the x and y coordinates of both P and Q in the equation 3x + 4y = 60
• Here, i used the concept of the position of a point w.r.t. a line which is L1 multiplied by L2 > 0 (since both the points lie on the same side of the line)
  (L1 = when coordinates of P are put in the eq, similarly L2 = when coordinates of Q are put in the eq.)

[mossy quartz]

i have an inequality with K and a so idk how to proceed

another way to solve this would be to consider cases, for ex: when x = 1, how many y coordinates exist such that they satisfy the conditions and then you'd have to keep going until x = 20

[hard crest]

this is probably how i'd do it :/

[compact nebula]

Are you allowed to write code for this or do they want you to do this by hand

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[mossy quartz]

Ah well fair, that would be quite time taking

[mossy quartz]

by hand

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[mossy nova]

Need help with discrete math

[mossy nova]

I need help with c,d,e,g,h

[umbral swan]

for c) you know that m=21 n=20

and n=2 * 2 * 5

so f(21/20) = 21² * 20² / (2*5)

likewise for d)

you know m=60 n=121

n=11*11

@mossy nova

[safe radish]

@mossy nova Has your question been resolved?

[mossy nova]

i got 17,640

and for d I got 4,791,600

how would I do e?

with a factorial

and g and h

where I get the inverese

[umbral swan]

Well what are n & m

[umbral swan]

didn't calc them as I'm not on my setup, but sounds about right

[umbral swan]

for e) you know that m=1

n=10!

so what is S_n?

= {2, 3, 5, 7}

Meaning f(1/10!)

= 1² * (10!)² / (2 * 3 * 5 * 7)

[mossy nova]

m is 1

[umbral swan]

@mossy nova

[mossy nova]

and n is 10 factorial

[umbral swan]

yop

[mossy nova]

but how did u get 2 3 5 7

for the prime factorization

[umbral swan]

because 10! Contains these factors

it contains all primes up to 7

because the next one is 11

and 11 isn't a factor in 10!

[mossy nova]

oh ok

i got 62705664000

[umbral swan]

kk

[mossy nova]

and whats the apporach for the last one

these numbers look extremely huge though

[umbral swan]

did you get g)?

[mossy nova]

oh wait i didnt lol

i got 23 for f

[umbral swan]

but f(23) = 23² ≠ 23

[mossy nova]

1^2 * 23^2 / 23

[umbral swan]

well that's 1/23 what you meant

f^-1(23) = 1/23

then yes

then for g)

you want to find natural n, m such that
24 = m² * n² / S_n

notice that if for instance we start our finding process at n=1 m=1

then the product on the right is just equal to 1

And if we increase m, the product strictly increases

and if we increase n, the product doesn't necessarily increase, it may also decrease

[mossy nova]

yea

[umbral swan]

and since:
1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25

we know that m is between 1 and 4

[mossy nova]

ok

[umbral swan]

because with m=5, 5² would already overshoot

[mossy nova]

yep

[umbral swan]

and m can also not be 4, because then we'd need
4² * n² / S_n = 24

or could it, wait a sec

yeah no it can't, because then n² / S_n would have to be equal to 3/2

since 4² * 3/2 = 24

but that would mean all factors from n² and S_n cancel out

except the 3 from n²

and 2 from S_n

which can't be, since n² would have to contain 2 twice

ok so now we know that m is either 1, 2 or 3

now you can either rule out more cases of m or try out these three and look for values of n

@mossy nova

would help if thee were present

if m=3 then:

3² * n² / S_n = 24

meaning n² / S_n = 24/9 = 8/3

but again, that can't be, because the 3 would also have to still be contained in n²

you can't maximally reduce n² / S_n such that you get 8/3

meaning m=1 or m=2

if m=2 then:

2² * n² / S_n = 24

meaning n² / S_n = 6 = 2*3/1

= 2*3*2*3/(2*3)

however note that 2 would be contained as a common factor

regardless of how we expand n

it must contain the factors 2 & 3

so m=2 is ruled out

meaning m=1

therefore n² / S_n = 24

note that 24 = 2 * 2 * 2 * 3

= (2 * 2 * 3)² / (2 * 3)

meaning n = 12 works

f^-1(24) = 1/12

Now you may wonder how the hell would we do h)

if this iterative process takes so long

Well let's look at the number:

831600 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 7 x 11

= 2⁴ x 3³ x 5² x 7 x 11

remember that n & m can't share any factors

and since 831600 must contain m²

m² can at max contain 2⁴ and 5²

Can n² / S_n contain 2⁴?

no, because the 2 would get filtered by S_n

n² can only produce an even exponent for 2^x

but S_n will reduce that exponent by 1

likewise for 5²

what I mean to show by that is

if you want to determine f^-1(831600) or any number

you first get its prime factors like above

and ALL factors with even exponents belong to m²

ALL factors with odd exponents belong to n²

meaning m² = 2⁴ * 5²

meaning m = 2² * 5 = 20

and n² / S_n = 3³ * 7 * 11

= 3⁴ * 7² * 11² / (3 * 7 * 11)

meaning n = 3² * 7 * 11 = 693

m/n = 20/693

and I hope that the above may enlighten you a little as to why this process is so genius

as you split a number into its prime factors, which are unique

and distribute the odd/even factors on the numerator & denominator

But because you squared them

they actually cover all combinations of prime factorizations of a rational

which makes it a bijection!

🦇

@mossy nova you'll probably just skim through, but in case you don't, hope I could spark your interest a little :]

[safe radish]

@mossy nova Has your question been resolved?

[mossy nova]

holy shit

@umbral swan ty bro

[umbral swan]

np

[safe radish]

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[soft chasm]

Does anyone here know how to use Rguroo?

[safe radish]

@soft chasm Has your question been resolved?

[soft chasm]

no

[soft chasm]

<@&286206848099549185>

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[misty fractal]

This problem is for determining whether the series (for natural (n))
[\sum_{n=1}^\infty \frac{\sqrt{n + \sin n}}{n^2 + n \cos n}]
converges or diverges.

I have been unsuccessful in conducting either the Limit Comparison Test or the Comparison Test, would anyone have a hint?

[flat frigate]

ricey

[misty fractal]

I have had the chain of inequalities
[ \frac{\sqrt{n + \sin n}}{n^2 + n \cos n} \leq \frac{\sqrt{n + 1}}{n^2 - n} \leq \frac{\sqrt{2n}}{n (n-1)} = \frac{\sqrt{2}}{\sqrt{n}(n-1)} ]
which isn't very useful? Due to the minus sign in the denominator, which is very frustrating.

[flat frigate]

ricey

[misty fractal]

I have a hunch that I can compare this guy to a (p)-series
[\sum_{n=1}^\infty \frac{\sqrt{2}}{n^\frac{3}{2}}]
which should allow me to conclude that the original series converges. But because of that (-1) I am having a lot of trouble

[rose plume]

look im just dumb

[misty fractal]

hey no worries, thanks for trying
that doesn't seem to work though because I still have a negative sign on the bottom

[light shoal]

try showing that $\sqrt{n}(n-1) > 2n^{3/2}$ for sufficiently large $n$

[flat frigate]

Bungo

[misty fractal]

hmm

[light shoal]

the factor of 2 should help

if it was a 1 then you can't make it work due to the -1

oh wait

sorry

make it 1/2, not 2

i was thinking upside down haha

[misty fractal]

then i can bound that above by sqrt(2)/(1/2)n^3/2?

[light shoal]

the idea is that sqrt(n)(n-1) is too small to make the bound n^(3/2) work, even though it behaves that way for large n
so scale n^(3/2) by 1/2 to give yourself some room

[misty fractal]

which gives me the desired p-series?

ah

[light shoal]

yep you'll still compare with 1/n^(3/2)

[misty fractal]

so i throw a fraction in below

[light shoal]

yep

[misty fractal]

ok, brb

[light shoal]

standard trick

[misty fractal]

ok, so i now have
[\frac{\sqrt{2}}{\sqrt{n}(n-1)} \leq \frac{\sqrt{2}}{\frac{1}{2} \sqrt{n} (n-1)} = \frac{\sqrt{2}}{\frac{1}{2} n^{3/2} - \frac{1}{2} n^{1/2}}]

[flat frigate]

ricey

[misty fractal]

maybe i induct on n

wait that's not useful

uhhh

[light shoal]

no the idea is:
$$\frac{\sqrt{2}}{\sqrt{n}(n-1)} \leq \frac{\sqrt{2}}{\frac{1}{2}n^{3/2}}$$
for sufficiently large $n$ (you have to show that part)

[misty fractal]

$$\frac{\sqrt{2}}{\sqrt{n}(n-1)} \leq \frac{\sqrt{2}}{\frac{1}{2}n^{3/2}}$$

[flat frigate]

ricey

[misty fractal]

oh

[flat frigate]

Bungo

[misty fractal]

okay

i'll induct

maybe

brb

i'll give this a try

seems reasonable

[light shoal]

you can actually do it without induction

just try solving this inequality for n:

[misty fractal]

ah

[light shoal]

$$\sqrt{n}(n-1) \geq \frac{1}{2}n^{3/2}$$

[flat frigate]

Bungo

[light shoal]

if i didn't make a mistake somewhere, i think it's true for all $n \geq 2$

[flat frigate]

Bungo

[misty fractal]

alright i got it, thanks! @light shoal

now i'll proceed to finish off the proof, and update here

[light shoal]

nice

[misty fractal]

Maybe I should check n=1

[light shoal]

do you care about n=1?

only the tail of a series determines whether it converges or not

the first few terms (or any finite number of terms) make no difference to whether it converges (although they can change what value it converges to, if it converges)

[misty fractal]

oh right

[misty fractal]

ok that makes sense

i don't care about the limit, i only care if it converges

[light shoal]

yep

[misty fractal]

hm i guess i'd have an issue with n=1 for the part where i use sqrt(2)/sqrt(n)(n-1), since the denomniator would collapse to 0

i'll just include it anyway, no harm i suppose

[light shoal]

yea, already for the second expression in your inequality chain you need to assume that n >= 2

[misty fractal]

ah right

ok i'll add that there then

alright, i'm satisfied with this. Thanks @light shoal !

.close

[safe radish]

Channel closed

Closed by @misty fractal

Use .reopen if this was a mistake.

[light shoal]

cheers

[safe radish]

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[lavish blade]

hey idk how to solv this differential equation

[lavish blade]

so first i solv the homogenouse equation

but idk the particular solution form

i try ax^2+bx+c

but it didn't work

so I guess that's not it

[radiant phoenix]

no no

this is IF

[lavish blade]

what is IF

[radiant phoenix]

integrating factor

[lavish blade]

oo ok

[radiant phoenix]

dy/dx+P(x)y=Q(x)

[lavish blade]

ooo okey

so when ther is dy/dx+P(x)y=Q(x) always IF ?

[radiant phoenix]

ye

[lavish blade]

or variation of the constant to ?

[radiant phoenix]

dym variation of parameters?

[lavish blade]

maybe I don't know the terms in English

[radiant phoenix]

thats overkill

[radiant phoenix]

use IF

[lavish blade]

ok

but it would work

?

[exotic cypress]

definitly overkill im dying over and over

[radiant phoenix]

yeah why not

[lavish blade]

ok ok ty

thanks for the help <33

.close

[safe radish]

Channel closed

Closed by @lavish blade

Use .reopen if this was a mistake.

[radiant phoenix]

im also doin undetermined coeff lmao

[sonic dove]

YEAH @lavish blade WE HAVE TO APPROACH THROUGH if

[safe radish]

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

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[brittle raptor]

This is the given, and I need to know HOW to do it and if I'm correct.
So, mean = 500,000
SD = 50,000
and we're looking for 20%

I DO NOT KNOW WHAT TO DO WITH THE 20% SO I CHATGPT'ED
And they said to turn it into the 80th percentile (how?)
I looked at 1.0 and 0.1 decimals and it's saying 0.7910
But GPT and other AI's are saying it is 0.8413 or roughly 0.842
I do not know how, and i want to know.

Moving on, wsince we have now z = 0.842, I calculated x by:
x = mean + (z * SD)
x = 500,000 + (0.842 * 50,000)
x = 500,000 + 42,100
x = 542,100

Am I correct, is my method correct? And please help me to understand the 20% and 80th percentile stuff too. Thank you.

[vagrant ice]

You need to convert the area of 0.20 from the right = 0.80 from the left into a z-score

Figure out how many standard deviations away it is from the mean

[brittle raptor]

How do I do that?

I actually don't know, I've been researching but I'm not sure what to research for

[vagrant ice]

Using a GDC or Wolfram Alpha etc

[brittle raptor]

Do you mind uh giving me the formula?

[vagrant ice]

The formula requires integration so don't do it that way

[brittle raptor]

Oh, then how do I get the calculator to check it then?

[vagrant ice]

https://www.wolframalpha.com/input?i=normal+distribution+80th+percentile

[vagrant ice]

Which calculator do you have

[brittle raptor]

Wolfram is open rn

[vagrant ice]

+0.842 standard deviations btw

https://www.wolframalpha.com/input?i=normal+distribution+calculator&assumption={"F"%2C+"NormalProbabilities"%2C+"pr"}+->"0.8"

How you get there is to type in normal distribution calculator

Then choose probability

[brittle raptor]

OHHH OKAY

But how did

20% transform into 80th percentile?

So if its 80% it is 20th percentile?

[vagrant ice]

So the percentile means from the left

[brittle raptor]

oh so its decreasing?

[vagrant ice]

0th percentile means the area such that 0% of values are to the left

[vagrant ice]

No

The cumulative distribution function is always increasing

[brittle raptor]

O H

[vagrant ice]

Like we normally convert it to the left cause that's the one most calculators use

[brittle raptor]

Oh alright okay so

If it says 40%

60th percentile?

Just to clarify

[vagrant ice]

40% to the right is 60th percentile

40% to the left is the 40th percentile

[brittle raptor]

Oh my greatness now I'm getting confused..

Okay so you said that

[brittle raptor]

From the left

[vagrant ice]

Here let me show you a picture

[brittle raptor]

20% from the left and now it turned into 80%

Oh SURE

[vagrant ice]

So if the white area is 80%

The blue area must be 20%

So that the total area is 100%

[brittle raptor]

OHHHHH

OH OKAY THAT MAKES BETTER SENSE

But how do we determine whether we're looking for the left or the right side?

[vagrant ice]

Usually we're looking for the left side

[brittle raptor]

OH ALRUGHT THEN

Okay so just to clarify and stuff

We use 1 - x under what circumstances?

When we're looking for the left right?

And when we're going right we just use x

[vagrant ice]

When you have the right and you want the left

[vagrant ice]

When you have the left already you just use x

[brittle raptor]

OH OKAY THEN GOT IT

Alright, goinf back to my orignal solution though

Is it uh... Correct?

Did I do it properly?

[vagrant ice]

This is surprisingly correct

On the other hand AI might get a lot of other problems wrong

[brittle raptor]

Thank god

[vagrant ice]

But you understand x = mean + z * SD at least

[brittle raptor]

Yeah im aware of that, so I primarily use AI for formulas

[brittle raptor]

Yes I do, I also know how to calculate for z

[vagrant ice]

Yeah sure thing then

[vagrant ice]

Nice

[brittle raptor]

I was just flabbergasted by how 0.8 turned into 0.842

Since I wss looking at 0.8 and 0.1 on the table