help-33

[past atlas]

ah

in an alternative universe

we could have called the output x

and input y

[amber birch]

have you seen this btw? this shows the 1-to-1 relationship more clearly

[past atlas]

then you could say the opposite

but other than that it is just a definition

[amber birch]

oh yeah it's a historical accident that we use the letters x and y for variables

[past atlas]

several inputs lead to one output?

one output can have several inputs?

[amber birch]

cause x doesn't appear in many European words

and that x is the x-axis and y is the y-axis, it's just history

[amber birch]

we don''t use the word 'function' for those

we use the word relation

[past atlas]

yeah i am cool with xa nd y being where they are

[past atlas]

okay to be clear if output and input is used in somewhere i dont know where

[past atlas]

i dont know what to call it

[amber birch]

wdym?

[past atlas]

you called it the definition of a function

y can only have one value

i just tried to but it is laymans terms i guess

with saying input and output

[amber birch]

y is the output and x is the input

yeah so one input gives one output

[past atlas]

two inputs still gives one output

or is that a new topic

like is that unrelated

[amber birch]

oh that's related

[past atlas]

to what you were explaining with a definition of a function

[amber birch]

it's the example I gave you, f(x) = x^2

f(-2) = 4
f(2) = 4

that's still a function

[past atlas]

yeah okay

[amber birch]

basically what I mean is that one input can't give more than one output

two different inputs can give the same output

[past atlas]

yeah that's what i tried to say with this

[past atlas]

and this

[amber birch]

then we can't call that a function

[past atlas]

wait really

[amber birch]

yeah

[past atlas]

crap

wait

[amber birch]

it's a relation then

[past atlas]

mmm

okay so f=ma is not a function

but f=2a is a function

[amber birch]

well it is actually, it gets trippy when there are two independent variables

if you plug in a value of m and a value of a

[past atlas]

but arent there two inputs then?

[amber birch]

you get one number, F

[past atlas]

yes

one output F has several inputs m and a

[amber birch]

yeah that's also a function actually

[past atlas]

or am I using the word input wrong

[amber birch]

you just don't study functions with more than one input in high school

or you always have to rearrange them into y = f(x) first

so the correct way to think about a function is actually with sets

[past atlas]

i remember that confusing me big time before, y = f(x), all of a sudden they introduced f(x) instead of just y and i never understood why

i still dont quite understand why

[amber birch]

a function maps one set to another set

[past atlas]

why couldnt you write y(x) instead

[amber birch]

a set is just a collection of numbers

[past atlas]

yeah i am vaguely familiar with sets

[amber birch]

oh you absolutely can, it shows up in differential equations for example

[past atlas]

i have never done any problems related to them

[amber birch]

it's just a convention that we don't usually write y(x)

[past atlas]

it was just weird because one day in school we were doing y=kx+m

and it was related to graphs

"makes sense" i thought

then all of a sudden f(x)

speaking of the Law of Universial Linearity

I thought initially that meant f * x

[amber birch]

well f(x) is like your function machine then, it takes in an input and spits out an output

[past atlas]

obviously that is a long time ago

but that was my first impression

then they say y=f(x)

like what are you talking about i thought

anyway now i get they are the same but i still dont understand why they couldnt have introduced it as y(x)

it confused the hell out of me

they could have just said "we just call it f insted of y", the (x) just shows what variable the functions output depends on

then i would have understood

[amber birch]

sounds like bad maths education lol

[past atlas]

i lived on an island

so probably was

not many teachers

especially not math or science

[amber birch]

oh that sucks

[past atlas]

but that is not an excuse i didnt apply myself at all

but at the same time i had no reason to like math more than what i was good at which was multiplication tables

anyway thank you for answering my questions, clearing up confusion and chatting with me

i gotta go back to my book now

you have been very helpful thank you

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[jovial mulch]

Im probably jumping too high of a level, question wise

[jovial mulch]

nvm

im not doing this

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[exotic wolf]

hi

[exotic wolf]

could anyone please try to explain what this means*?

its the last part i dont get

[zealous osprey]

Chatgpt

[exotic wolf]

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[silent marten]

Hiii

[red phoenix]

Guys for this I got 1/169 for the probability but they key says the answer is a about 0.6 percent. 1/169 is 0.005... so I don't get it.

[red phoenix]

Hi

[spice bay]

0.6% is 0.006

not very far from 0.005

[hollow glen]

problem is, you didnt account for the fact that the first card doesnt get put back

[silent marten]

I got 0.0045 for the first question 😭😭😭

[red phoenix]

so?

how?

[silent marten]

4/52 ( probability of getting a Jack ) * 4/51 ( probability of getting a king knowing a jack was drown )

[red phoenix]

https://tenor.com/view/facepalm-gif-4576513125411549651

[red phoenix]

o

k?

so

ohh

so its

[silent marten]

But that doesent give me 0.6%

😭😭😭

Actually it does

Mb

[red phoenix]

,,4/52 x 4/51

[elfin berry]

Pl@nnΣd∀φd⋔MDCXXI

[red phoenix]

https://tenor.com/view/laugh-laughing-ha-happy-lol-gif-5151447877773057567

[red phoenix]

1/13 * 4/51

4/663

= 0.006033182... !

oh i get i

and got it

thx guys!

Ty: @silent marten , @spice bay , and @hollow glen !

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[marsh citrus]

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[red phoenix]

.reopen

[marsh citrus]

✅

[red phoenix]

guys

@silent marten @hollow glen @spice bay

[spice bay]

yes?

[red phoenix]

this is not = 0.6

[spice bay]

it’s 0.6%

as you wanted

[red phoenix]

how?

4/663?

[spice bay]

0.6% = 0.6/100

= 0.006

[red phoenix]

oh i forgot it was a percet

thx

[red phoenix]

ty

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[obtuse plume]

Really quick question

a+2b-(-a+b) becomes 2a+b

but when solving parentheses

-(-a+b) i thought it would be -(a-b)

[obtuse plume]

do we remove the - between the 2 terms?

[urban shard]

-(-a + b) = a - b

[obtuse plume]

so we remove the - between the 2 terms when solving it?

[urban shard]

well what specifically is your question? to simplify -(-a + b)?

[obtuse plume]

well my question is here

a+2b - (-a+b)

what happens with the - sign in between those 2 terms?

since if we solve the parentheses it would be a-b

but it wouldnt become a+2b-a-b, but instead a+2b+a-b

[urban shard]

okay well - (-a + b) is otherwise written as a - b

because you distribute the negative to each term inside the parenthesis

so you have -(-a + b) = a - b

and so going back to your initial question, a + 2b + (a - b)

[elfin berry]

nyxie9151

[urban shard]

which is why you're left with a + 2b + (a - b)

[obtuse plume]

ah so in other words, we can basically see it like this

-1(-a+b) = -1x-a = a
-1*b = -b

[urban shard]

not sure your formatting worked there lol

[obtuse plume]

no it did not heh

[elfin berry]

nyxie9151

[obtuse plume]

-1 * -a = a
-1 * b = -b```

[urban shard]

if this is what u meant then sure

[urban shard]

yes but you add the two ofc

since it's -1 * -a + -1 * (-b)

[obtuse plume]

yes so a-b

[urban shard]

yes like so^

[obtuse plume]

that makes sense now, my book didnt really make it clear that we distribute the - sign into the other terms

[urban shard]

[obtuse plume]

thank you!

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[rocky lark]

$\frac{x-\sqrt{2x^2+3x+1}}{2-4^x}\geq0$

[elfin berry]

card

[rocky lark]

Pls help

[whole quiver]

is that the original ques

[rocky lark]

Yes

[whole quiver]

get critical points

and then use wavy curve

[rocky lark]

I Need to factor the polynomials

[whole quiver]

uhm?

what you have to find?

[rocky lark]

https://brilliant.org/wiki/wavy-curve-method/

I am following these steps

But I'm already stuck at the first step

[whole quiver]

it's for that particular example

when will be 4-2^x = 0? 2-4^x=0

[rocky lark]

x=2

No

[whole quiver]

check edited msg

[rocky lark]

2-4^x=0 2=4^x x=1/2

x=1/2

[whole quiver]

yes

now when will that root term be 0?

[rocky lark]

Mmm

[whole quiver]

factorize
2x^2 + 3x + 1

[rocky lark]

(x+2)(x+1)

[whole quiver]

yes

[rocky lark]

x=-2 , x=-1

[whole quiver]

now plot all critical points

don't forget x=0

[rocky lark]

Thanks

So the solution are x=0,-1,-2,1/2

[whole quiver]

no

plot it in number line

and apply wavy curve there

[rocky lark]

I dont know

[whole quiver]

how do you generally solve inequalities then?

[rocky lark]

But then why did we only consider the root in the numerator?

[rocky lark]

I want to use this method

[whole quiver]

they are the critical points

[whole quiver]

I suggest you to watch some yt video

[rocky lark]

But shouldn't I solve x-√..... =0?

[whole quiver]

I messed up

damn it

sorry

[rocky lark]

In this case for =0 there are no solutions

The numerator

Now I have to go and watch some videos, thank you very much

[whole quiver]

back

sup

[whole quiver]

ohk

(I messed up as I was actually thinking something else)

if you still need help, lmk

[marsh citrus]

@rocky lark Has your question been resolved?

[marsh citrus]

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[celest folio]

so i first worked on the numerator and made sure they had the same common denom

i did (4) * (1/(4+x) - (4+x) * 1/4

(4/16+4x)-(4+x)/16+4x

canceled the 4s

x/16+4x * 1/x

left with 1/16+4x

1/16+(4*0) = 1/16

where did i go wrong

[runic temple]

sign error

check your subtraction step

[celest folio]

is it when i did 4 - (4+x)

shoulda done 4- 4 -x?

so im left with -1/16

[runic temple]

also please use parentheses for numerator and denominator

yeah thata correct

[celest folio]

yea trying to understand this has to be a nightmare

id take a picture but my handwriting isnt any better

[runic temple]

itd be fine if you used more parentheses

[celest folio]

thanks

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[dusty panther]

💀 wat dis

[obsidian wren]

wait i am thinking

[dusty panther]

o wait

nvmnvjm

[dusty panther]

apparently there's no solution

bru

itds aight

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[obsidian wren]

i got a solution

i need a paper to write it

[proud ice]

There are no real solutions

[dusty panther]

yea

wat

.reopen

[marsh citrus]

✅

[dusty panther]

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[dusty panther]

wat

[proud ice]

[marsh citrus]

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[minor nebula]

help

[minor nebula]

i have a lot of theories in my mind but im not sure

basically angle dab = angle dcb

idk if this is right

and then DE = DE

[versed pagoda]

this is correct

[minor nebula]

but then im really stuck after

[versed pagoda]

wait sorry

no

[minor nebula]

i put the reason for that is property of kite

[versed pagoda]

angle DAB = angle BCD right

since it's a kite

[minor nebula]

yes

[versed pagoda]

and length of AB = length of BC

[minor nebula]

yes

[versed pagoda]

yeah ok you wrote cdb so wanted to make sure we're clear on t hat

[minor nebula]

yes yes

its clear

oops sorry my mistaje

[versed pagoda]

ok

[minor nebula]

thenim stuck

[versed pagoda]

and ofc since it's a kite length of AD = lenght of CD

[minor nebula]

umm yess

okay now what do i do

like i think i need to prove anfle dae is = dce

but idk how to do that

[versed pagoda]

Have you learned that the one diagonal of the kite is an angle bisector already?

[minor nebula]

yes

ohh ok

[versed pagoda]

mhmm

Haven't done this in a while haha

I believe you can also show this using SSS

because the hypotenuse and the base are obviously same

and that the short diagonal which is the height here is cut midway by the long diagonal

[minor nebula]

wait so

ill just prove that the bisector there also serves as a midpoint

but how do i do that again

[versed pagoda]

I think that's a bit long to prove but its a standard proof. I'd just google it tbh

[minor nebula]

um

[cobalt dagger]

@minor nebula what did your teacher / professor give you for the precise definition of “kite”?

[marsh citrus]

@minor nebula Has your question been resolved?

[marsh citrus]

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[stiff merlin]

so when multiplying the 2nd equation by 3, why does 6y become -18y instead of just 18y

[proud basin]

its a mistake on their part i think

cause it should be +18y

[stiff merlin]

ok yeah i was super confused and wanted to make sure i wasnt missing something, ty!

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[wary bluff]

for b part i basically need x, y s.t f_x = 0 and f_y = 0 right?

f_x = 3y-3x^2
f_y = 3x - 3y^2

so (1, 1) would be the answer?

[cunning fiber]

you’re in R^3, not R^2

[wary bluff]

how would I do this then

oh

I plug in x=1, y=1 ?

[cunning fiber]

Yeah

You also forgot x=0, y=0

[wary bluff]

oh ye true lol

alr bet ty

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[gilded pivot]

can someone give me any advice on how i can deal with that pls

[cunning fiber]

Hint: what happens when you square both sides?

[stoic slate]

I would not call that a hint

[gilded pivot]

ahahahah

well thx

[cunning fiber]

fixed

[gilded pivot]

i got it quickly with that

@cunning fiber lets go for something harder i guess

any hint?

[cunning fiber]

square both sides

[gilded pivot]

but how do i deal with absolute values @cunning fiber

[cunning fiber]

Elaborate

[gilded pivot]

it looks like i will need to use triangular nequality

somehow

how do i develop when i square it with absolute values @cunning fiber

[cunning fiber]

$|x|^2=x^2$

[elfin berry]

Civil Service Pigeon

[gilded pivot]

@cunning fiber

what can i do

[cunning fiber]

Eh you’re basically done

Think of what assumptions you can make without loss of generality

Alternatively, you could’ve not expanded out the square and instead factored the right hand side

[gilded pivot]

i dont really see

maybe i dont get ur point in english

cause im french

[cunning fiber]

https://math.stackexchange.com/questions/129137/use-of-without-loss-of-generality

[gilded pivot]

if x >= y

[cunning fiber]

Try it

See what happens

[cunning fiber]

???

Just assume $x \geq y \geq 0$ and you get $$x-2\sqrt{xy}+y<x-y$$

[elfin berry]

Civil Service Pigeon

[cunning fiber]

Alternatively, working off this gives you $$(\sqrt{|x|}-\sqrt{|y|})^2 \leq |\sqrt{|x|}-\sqrt{|y|}| \cdot | \sqrt{|x|}+\sqrt{|y|}|$$

[elfin berry]

Civil Service Pigeon

[cunning fiber]

Anyway, I gotta dip, but just pick one and run with it

[gilded pivot]

alright thx

[marsh citrus]

@gilded pivot Has your question been resolved?

[marsh citrus]

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[blazing fossil]

I'm struggling with a proof problem that is probably related to pigeonhole principle. Can anyone help me with this?

Prove that if 19 points are chosen from the interior of a 6x4 rectangle such that no three points form a straight line, then 4 of those points will form a quadrilateral of area at most 4

[full fulcrum]

hello, im studying approximations of binomial random variables with normal standard variables. so if $Y$ approximates $X$, and I need $P( X \geq 25)$, why does my professor then write $P(Y \geq 24.5)$ ?

[elfin berry]

atif

[full fulcrum]

he always adds/subtracts 0.5

I understand why this is neccessary if we want $P(X=25)$ then $P(24.5 \leq Y \leq 25.5)$ is the correct approximation if i understand correctly

[elfin berry]

atif

[full fulcrum]

GOT IT

.close

.close

ah it;s closed

[marsh citrus]

@blazing fossil Has your question been resolved?

[blazing fossil]

No 😦

[marsh citrus]

@blazing fossil Has your question been resolved?

[blazing fossil]

<@&286206848099549185> pls help me

[marsh citrus]

@blazing fossil Has your question been resolved?

[still temple]

How to do this

[still temple]

No bro not that complicated

This is the working out pls explain it

[marsh citrus]

@blazing fossil Has your question been resolved?

[humble pasture]

i dunno how your teacher did it that quickly but an easier solution is using a subtitue

$sprt{9-x^2}$

[elfin berry]

bip

[humble pasture]

anyway ill show by writing it out if you are still struggling

[still temple]

Yess plss bro

[humble pasture]

so you have to replace $\sqrt(9-x^2)$ with t

[elfin berry]

bip

[humble pasture]

and then to find what dx is to that t variable you have to take derivatives for the both sides

which when you take the derivate of $\sqrt(9-x^2)$ it turns out the negative of the function you had at first so you just replace it with that

[elfin berry]

bip

[still temple]

Ooh thank u

[humble pasture]

np

[marsh citrus]

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[unkempt herald]

help

[marsh citrus]

@unkempt herald Has your question been resolved?

[marsh citrus]

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[wispy ledge]

Am I going wrong with a?

[wispy ledge]

,rccw

[marsh citrus]

@wispy ledge Has your question been resolved?

[wispy ledge]

<@&286206848099549185>

[marsh citrus]

@wispy ledge Has your question been resolved?

[marsh citrus]

@wispy ledge Has your question been resolved?

[wispy ledge]

<@&286206848099549185>

[slate yarrow]

your last step is wrong it is ${k}{\cdot \left( \frac{6k^2-3k-1}{2}\right)+(3k+1)^2$

[elfin berry]

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

[marsh citrus]

@wispy ledge Has your question been resolved?

[marsh citrus]

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[hexed pilot]

expecting a telescoping series. tried sophie-germain identity but got too messy. doesn't convert into trigonometric forms either. cant think of much else, so help

[hollow glen]

you tried partial fractions? (you can factor 4r⁴+1)

oh right thats the sophie germain identity,

[knotty trellis]

I think it works though

[hollow glen]

yeah it does

[knotty trellis]

nvm, maybe not

[knotty trellis]

it does?

[hollow glen]

yeah it telescopes nicely

[lucid turret]

https://tenor.com/view/what-deam-telescope-gif-15248295

[knotty trellis]

Oh, right

i see

I think i got it

[knotty trellis]

Yeah, try partial fractions as @hollow glen suggested

[marsh citrus]

@hexed pilot Has your question been resolved?

[hexed pilot]

what do you break the numerator into?

@hollow glen @knotty trellis

[candid wedge]

(4r^2 - 1) - 1

[knotty trellis]

you can find it through that method with A, B

i'll write it out

wait a moment

it should look like this I believe?

[elfin berry]

MæthIsAlwaysRight

[marsh citrus]

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[velvet cairn]

What's wrong in the syntax

[void elm]

write 0.02

instead of .02

[nova solstice]

Are the 2 and the 0.02 inside the square roots?

[velvet cairn]

It's √(2) divided by 10

The first term I mean

Something is wrong with my calculator it seems

[velvet cairn]

Yep
Got ot

.close

[marsh citrus]

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[past atlas]

Hello, I am trying to simplify an expression:

[past atlas]

This is how far I have gotten:

[ruby junco]

Okay

[past atlas]

I could simplify the numerator

but idk how that helps me

[ruby junco]

In lost in your first step?

[past atlas]

I didn't send my first step sorry

I will try to find it

[ruby junco]

👍

[past atlas]

(I'm on my laptop)

[ruby junco]

First thing I would do

is write 2/1 as a fraction

and cross multiply everything

to get everything as a fraction

then expand and collect terms

[past atlas]

Someone was helping me

and they told me I could do that as the first step

[ruby junco]

Hang on let me do it for you on paper

i’ll try and make it as clear as possible

[past atlas]

Thank you

I'm pretty dense so that would help a lot

Not stupid but dense

[ruby junco]

Don’t worry about it

just grabbing paper

[past atlas]

You could use a different example than the one I have given to explain something if you'd like

[ruby junco]

does this make sense

[past atlas]

Okay so honestly I am not following along with that but

I didn't send all my notes and actually arrived to the end part as well

let me send a pic

[ruby junco]

Cool

let’s see

[past atlas]

after this i did:

[ruby junco]

actually you can do this without finding common denominator if u don’t get that

[past atlas]

the common denominator seemed really messy

at least for me

[ruby junco]

You can do it

like

[past atlas]

like i understand the concept but that seemed really hard

[ruby junco]

if you do it in two steps

you can combined the two fractions

then turn two into a fraction

and cross multiply that

want me to show u that way?

it’s just a bit long

[past atlas]

was your way faster/more efficient?

i want to learn the more efficient way

or was it more about

you didnt have to do the steps

[ruby junco]

Most effective way is with finding a common denominator

[past atlas]

because you are more confident

okay

[ruby junco]

But if you don’t understand

it might help you to do it like one fraction at a time

because you’ll understand it like that i think

[past atlas]

it was kind of hard to see your notes due to lack of light

[ruby junco]

okay let me re write

and do it the long way

[past atlas]

i will try to do do the common denominator on my own in the meantime

[ruby junco]

sound good

[past atlas]

im very confused on how to simplify the last step as well

[stoic slate]

Simplify the last step?

Is already simplified

That is why it is called last step

[past atlas]

i just called it the last step as in that is the last step i was on

but if it is already simplified that is good

[ruby junco]

Actuakky

i’m not going to show you this way

because it’s too long

and it won’t help you

[stoic slate]

It is

[ruby junco]

it’s better you learn it the proper way

[ruby junco]

yeah

[past atlas]

the proper way is the common denominator thing right?

[ruby junco]

yeah

[stoic slate]

You should learn to multiply by 1

[past atlas]

i am still working on that so i will send a pic soon

[ruby junco]

👍

[past atlas]

bro

[ruby junco]

I mean this way is so stupidly long for n o reason

[past atlas]

i just figured it out

i get why this is faster now

[ruby junco]

hahaha good stuff

[past atlas]

they cancel

wait

actually

hold on i think i might have done something wrong let me continue XD

[stoic slate]

For example a/b + c/d
You multiply by one both fractions

1 * a/b + 1 * c/d

And rewrite 1 in a convenient way.

d/d * a/b + b/b * c/d
(da/db) + (bc/(db) = (da+bc)/(db)

[ruby junco]

let me know if you want that written on paper

cause i always struggle reading it when typed out

[stoic slate]

You can use latex

$2x$

[elfin berry]

Samuel

[ruby junco]

That’s so cool

[stoic slate]

For example, the original exercise

$\frac{x}{x-2} + \frac{x}{x+3} - 2$

[elfin berry]

Samuel

[past atlas]

Yes

Also sorry to disappoint but I am having trouble with the common denominator

[stoic slate]

There is no common denominator here

[past atlas]

No no I mean

so

so I extend $x/(x-2) by (x+3)$

[elfin berry]

Neo

[past atlas]

that didnt work XD

[ruby junco]

Do you understand

the working i sent

[past atlas]

sorry le tme check that

[ruby junco]

because that’ll help i think

[ruby junco]

you need to make a common denominator in order to add them together

that’s the point

[past atlas]

yes

i did understand that

i guess i am having trouble on my own due to a lack of practice

it also took me a long time to read through that and follow each step

but I did understand

did i add them together too early?

[ruby junco]

it doesn’t matter

[past atlas]

or should i have just expanded the numerator

[ruby junco]

it might be helpful for you

to expand then add tho

so you can visually see how to collect terms

[past atlas]

i think collecting terms is easy but for some reason it wasnt intuitive for me to expand the terms in the numerator

[past atlas]

i did this when i said

[ruby junco]

Do you have another problem we could work through similar to this one?

[past atlas]

yes the next problem looks similar but I haven't tried it yet so I don't know how it would be plus I'd like to try it on my own first

[ruby junco]

@ me if u need me

[past atlas]

I will try it then show my work

[ruby junco]

give it a go and let me know if u need any help

[past atlas]

oops

i havent checked the solutions yet

@ruby junco

[ruby junco]

send the problem

please

[past atlas]

sry is it my handwriting?

[ruby junco]

It just makes it easier for me to follow nothing to do with your handwriting haha

[ruby junco]

I see what you’ve done

but i’m not sure why you’ve done it

[past atlas]

uh oh

[ruby junco]

why have you factorised the bottom?

It’s not wrong

technically

does it make it easier for you

[past atlas]

i dont know a lot of the problems here have required me to solve things by facotrizing

like i am having troubles with these but about 70% i can solve on my own without asking for help

70% is really bad success rate though

i factorized the bottom in hopes of finding a way to simplify it

[ruby junco]

actually no here

factorised

makes it sinpler

i take it back

because otherwise you get a disgusting bottom part

[past atlas]

i dont normally do this

this chapter im in has taught me to do it often

a lot of the problems are like this

i imagine if i ran into a problem where i dont need to do this i might try it anyway for no good reason

im very bad at understanding the logic behind why i should do something

there is no way to teach yourself that except practice/being born with it i think

but im not born with it so i practice

most people are probably not born with it/develop it early in the life

[ruby junco]

Practice

[past atlas]

at least i hope not because then im cooked

[ruby junco]

I think you did it wrong btw i’m just working through it

[past atlas]

yeah i am practicing like a madman

[ruby junco]

for you

[past atlas]

yeah thanks let me know what is wrong

[ruby junco]

yeah two seconds

i’ll reply when i’m done

[past atlas]

i still havent checked the solutions

[ruby junco]

nope your all good

well done

I like how you spotted the nice little shortcut

where you can just multiply the right side by a

to get a common denominator

[past atlas]

the book is really good tbh

i have never thought about math this way before and it is really cool

unfortuantely there arent that many practice problems

but the explanations have been straight to the point and fairly intuitive to follow along

[ruby junco]

just make them up for yourself

What topics do you struggle with ?

[past atlas]

algebra

fundamental algebra

and as a result

everything else

but i have passed grades despite that

but i didnt learn much so it sticks

complex numbers

is also something i never really understood

argument of z

all that stuff never clicked

i could emulate it but never understood it

[ruby junco]

Hang on

[past atlas]

nor do i remember now

[ruby junco]

your learning complex numbers

and algebra

at the same time

[past atlas]

im an old man unfortunately

[ruby junco]

I mean those are like

complicate opposite sides of the spectrum LMAO

[past atlas]

i just brute forced my way through school im going into uni the 26th

im cooked

[ruby junco]

Never say that

do you know all of the algebra rules like off my hesrt

[past atlas]

this stuff is in the "preparation" chapters

for my uni program

[ruby junco]

really?

[past atlas]

yes

i think it is meant to be a refreshener

[ruby junco]

yeah orobsbly

[past atlas]

it isnt a long chapter

im just not getting through it very fast

[ruby junco]

We’ll have you learnt the fundementsl rules

[past atlas]

i think will struggle less with the new topics

[ruby junco]

like literally how numbers work

etc

it sounds stupid

but it helps

[past atlas]

that depends, and honestly my guess would be no

no it doesnt sound stupid

my honest answer is no

[ruby junco]

let me find a screenshot

[past atlas]

i cant explain how numbers work

[ruby junco]

i used to struggle with the exact same thing

[past atlas]

there is a number line

there are real, imaginary, complex etc

rational irrational

i think i vaguely know the differences now but not confidently and

i could never do any problems associated with them

[ruby junco]

are u confident with this sort of stuff

[past atlas]

oh

yeah yeah i am

[ruby junco]

ok ok good

[past atlas]

confident is the wrong word but i know of this and use it

and usually get it right

some slip ups

[ruby junco]

this stuff you need to know

[past atlas]

but otherwise that is nothing new to me

[ruby junco]

like it needs to be like raising a leg

[past atlas]

for me it is like raising a leg but i am very fat

[ruby junco]

HAHAHA

[past atlas]

it takes me a little longer

[ruby junco]

love that

that’s fine

[past atlas]

and a little more effort

[ruby junco]

you got anything else you need help with?

[past atlas]

but in the end im jsut raising a leg

[past atlas]

no not right now, should i check the answer for this now?

[ruby junco]

it’s correct

[past atlas]

oh neat yeah i checked it you are right

cool i will keep practicing now but i need to leave campus first they are closing in 40 minutes

[ruby junco]

Good luck with your studies

[past atlas]

thanks

.close

[marsh citrus]

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[still temple]

why is θ on B too?? I understand a*senθ but I don't get why θ on B

[cobalt sedge]

coz ABD + DBC = 90

and DBC + DCB = 90

[still temple]

what

How?

[cobalt sedge]

Coz its given in the figure?

[still temple]

I know they are right triangles but how do they sum 90?

[cobalt sedge]

90 degrees is right angle?

[still temple]

yeah?

[cobalt sedge]

And sum of angles in triangle is 180

[still temple]

mhm?

[cobalt sedge]

so for tria BDC, you have sum of angles at B + C + D = 180

and D is 90

so DBC + DCB = 90

[still temple]

AH, I thought you were talking about the whole triangle, thank you so much

1 sec I'm gonna see if that's right, I still don't get something

Yep, ty

[cobalt sedge]

npnp

[still temple]

.close

[marsh citrus]

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[marsh citrus]

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[still temple]

C

[still temple]

I got w = xi/(1 - y) from conjugates

But idk what to do next

[marsh citrus]

@still temple Has your question been resolved?

[desert dirge]

i sense something is missing here

[still temple]

What

[desert dirge]

you havent actually shown a question

theres no context

[still temple]

Tf

[cunning fiber]

,w \frac{i+z}{i-z}, z=(sqrt 3)/4 + (sqrt 13)/4 * i

[elfin berry]

Results provided by WolframAlpha

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[cunning fiber]

,w x*i/(1-y), x=(sqrt 3)/4, y=(sqrt 13)/4

[elfin berry]

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[cunning fiber]

,w -(4i+sqrt 3+isqrt 13)/(-4i+sqrt 3+isqrt 13)=(i*sqrt 3)/(-4+sqrt 13)

[still temple]

How did you know z

[cunning fiber]

Idt this is right

Can you show how you got that

[cunning fiber]

My intuition told me that it’s wrong, so I took advantage of the fact that something can’t always be true if there’s a case where it’s not true

[still temple]

Maybe it’s the negative

Of that

[elfin berry]

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[cunning fiber]

Yeah it (probably) is

[still temple]

So uh what to do

[cunning fiber]

$w=\frac{xi}{y-1}=\frac{x}{y-1}i$

[elfin berry]

Civil Service Pigeon

[cunning fiber]

Note that w is purely imaginary

[still temple]

Yea

[cunning fiber]

So if you find the range of $\frac{x}{y-1}$ for $x^2+y^2=1$, then you’re done

[elfin berry]

Civil Service Pigeon

[cunning fiber]

Personally, I would consider the square of the quantity since $$\frac{x^2}{(y-1)^2}=\frac{1-y^2}{y^2-2y+1}$$

[elfin berry]

Civil Service Pigeon

[cunning fiber]

allowing you to avoid the square roots

——————

However, it’s far more efficient to use the exponential form and let $z=e^{i\theta}$

[elfin berry]

Civil Service Pigeon

[cunning fiber]

Followed by sum to product on the numerator and denominator

[still temple]

How

[still temple]

How

[cunning fiber]

#help-33 message

Differentiation bash

[cunning fiber]

Recall that $$e^{i \theta}=\cos \theta+i \sin \theta$$

[elfin berry]

Civil Service Pigeon

[cunning fiber]

Actually, you could substitute $x=\cos \theta$ and $y=\sin \theta$ here tbf

[elfin berry]

Civil Service Pigeon

[cunning fiber]

And then $w=\frac{\cos \theta}{\sin \theta-1}i$

[elfin berry]

Civil Service Pigeon

[still temple]

And then what

[cunning fiber]

Find the range of it

[still temple]

Numerator is between -1 and 1 while the denominator is between -2 and 0

I’m not sure

[cunning fiber]

The endpoints of the range aren’t achieved at the same values

[still temple]

What’s next

[cunning fiber]

Well how do you typically find the min/max of a function?

[still temple]

Differentiate?

[cunning fiber]

There you go

Do that

[still temple]

I take i as a constant right

[cunning fiber]

I wouldn’t even worry about i

I’d just find the range of $\frac{\cos \theta}{\sin \theta-1}$

[elfin berry]

Civil Service Pigeon

[cunning fiber]

Plus, the ideas of “max” and “min” are a bit blurry when you venture into the word of non-real numbers (since “greater” and “less than” aren’t very well defined)

[cunning fiber]

Yeah that’s fine so far

[still temple]

You can’t get 0 tho

[cunning fiber]

So what does this let you say about the range?

Hint: ||asymptotes||

[still temple]

Uh all real numbers?

[cunning fiber]

So returning back to this, what’s our locus?

[still temple]

x = 0?

[cunning fiber]

Yeah, you could say the set of all complex numbers with a real part of zero or the set of all purely imaginary numbers

Either suffices

[hushed egret]

,, \f {i + z} {i - z} = \f {i + z} {i - z} \f {-i - \conj z} {-i - \conj z} = \f {1 - \abs z^2 - iz + \conj {iz}} {\abs {i - z}^2} = \f {-2i \Re(z)} {\abs {i - z}^2}

you can do the calculation directly

[cunning fiber]

^ this is why it’s not always a good idea to convert to rectangular before doing conjugates

[still temple]

That isn’t xi/(y - 1)

I think

[hushed egret]

oop

[still temple]

I was gonna do something like that but I got confused on the conjugate of i - z

Do I just conjugate the imaginary and keep the sign of z same

[hushed egret]

,, w \conj w = \abs w^2

[hushed egret]

so you just take the conjugate

,, \conj {i - z} = \conj i - \conj z = -i - \conj z

[still temple]

Oh I see

Tysm

.close

[marsh citrus]

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[coral shoal]

I've been debating whether this is true or false. The answer key says that it is false; however, I do see merit in it being true because aren't limits that approach infinity technically undefined since they don't approach a real number (at least that's what I've been taught)?

[iron marlin]

i think it is poorly-defined

[coral shoal]

the question?

[iron marlin]

yeah

"for the same reason" is poorly defined

[cunning fiber]

(Also, the two one-sided limits for the limit of 1/x aren’t the same)

[coral shoal]

yeah that's what I've been talking about with my friends

[coral shoal]

yeah ik

but my thought process was that the fact that limits to infinity don't exist overrides that

[iron marlin]

if a teacher/professor gave you the question, demonstrate (perhaps using epsilon delta) that both don't exist, and since you used the definition, they both do not exist "for the same reason"

[coral shoal]

haven't learned epsilon delta proofs yet, that's like next week

but I agree, I'll talk to my teacher about it

scammed me out of a precious 2% :(

anyway ty

.close

[marsh citrus]

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[eternal sequoia]

I have some math that seems to require loop from a program or simulation. Is there a way that I can avoid this mathematically without having to use a simulation or program for loops?

[eternal sequoia]

For example, I want to find the minimum distance between two particles, where Particle One has some initial velocity. But, the two particles repel one another the closer they are. But, I want to find the time at which the minmum distance is achieved

But to do this, it seems as though I run into a circular dependency

Is there a way to avoid this and still get the answer I want?

[timid merlin]

To avoid using simulations or loops to find the minimum distance between two repelling particles, you can model their motion with differential equations that account for the initial velocity and the repulsive force. By differentiating the distance function between the particles and setting it to zero, you can find the critical points where the minimum distance occurs. Solving these equations analytically, or using approximation methods if needed, allows you to determine the time of minimum distance without relying on iterative simulations

[marsh citrus]

@eternal sequoia Has your question been resolved?

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[primal drift]

I got an answer but I dont think I did it properly

my answer was root 52 or 2 root 13

[sand fable]

not that

[calm harbor]

Explain how you did it

[primal drift]

I think I misread it

because I just did root 8 times root 26 times 1/2 which resulted in that answer

but I think its wrong cause everyone else seems to be using angles

[calm harbor]

No it’s not how you do it

[primal drift]

Yeah I figured

cause everyone else was talking about angles in order to do this

[calm harbor]

Area = 1/2 * a * b * sintheta

[primal drift]

where would thetha be?

[calm harbor]

CBD

[primal drift]

wait CBD or GBD

[calm harbor]

CBD

C-cat

[primal drift]

like here

[calm harbor]

yes it is

[primal drift]

oh do we just need that angle

[calm harbor]

Ofc, do you think we need anything else?

[primal drift]

cause cos sin law angles formula solves for it

[calm harbor]

✌️

[primal drift]

we would need a and b?

[calm harbor]

You have a and b already

Look carefully

[runic temple]

if you want a clever solution, rotate ABC 90 degrees counterclokwise about B

[primal drift]

The only non calcluated values are Ac and DG

[runic temple]

remind me later, yall continue with the other solution for now

[calm harbor]

Sure

[calm harbor]

Honestly, have you seen the formula before?

You look unfamiliar to it

[primal drift]

in true honesty I have never

[calm harbor]

Bruh

[primal drift]

were we supposed to learn it somewhere?

[calm harbor]

It’s necessary for this question

[primal drift]

ok I can learn the formula than

[calm harbor]

Ig I’ll let @runic temple introduce their method first

[primal drift]

ok thanks for trying to help me

[sand fable]

both r fine ways of doing the problem

[tired ore]

you should try to finish most of it today since the later questions are a bit harder

[runic temple]

are yall friends?

[primal drift]

no just solving problems through this course

[runic temple]

oh ok

[primal drift]

anyways how did you do this?

[runic temple]

can you draw the rotated triangle for me

[primal drift]

ABC right

[runic temple]

yes

rotate it so BC becomes BG

[primal drift]

like this

[runic temple]

like this

[primal drift]

or that

[runic temple]

its useful to make the copy in the diagram

[primal drift]

ok I will do

[runic temple]

we know what do we know about the heights of the two triangles?

the two being BDG and BGA'

[primal drift]

wait that is true

Since its two triangles just halfed

do we just solve for the formula and then half it again

[runic temple]

what

[primal drift]

oh nvm from your question earlier the heights are the same

[runic temple]

what ahout their bases?

[primal drift]

same base

[runic temple]

righr, because AB=A'B and ABDE is a square

[primal drift]

so if we solve for ABC its the same as solving for BDG

[runic temple]

so all we need to do find the the area of ABC yes!

[primal drift]

since base and height are alike

WOw

honestly your a smart guy for thinking outside the box

who knew something so intimitading could be simplifed using just one trick

[runic temple]

geometry can have some reallyclever solutions sometimes

[primal drift]

I see anyways thanks so much for help it was much appreicated

cause this trick I was mesmorised by how it is even possible but it works

so thankyou so much for the help

[runic temple]

yourw welcome

also you get the special benefit of no trig or nagles required

[primal drift]

I was fine with trig I just never used that formula before

[runic temple]

its useful to know that formula too

but in this scenario, its not necessary

[primal drift]

Anyways thanks for the help man Im just gonna try to finsih up till question 4 cause I know 5 and 6 are a nightmare