help-0

[novel urchin]

*last

[frigid geyser]

can you write it in like $F_{n-1}$, $F_n$, $F_{n+1}$, $F_{n+2}$

[ocean seal]

xdk1235

[novel urchin]

Wow

[novel urchin]

Ye

[frigid geyser]

what is fibonacci squared in terms of $F_{\text{thingy}}$

[ocean seal]

xdk1235

[frigid geyser]

and before x after in terms of F_thingy

[novel urchin]

Oh

the second one

[solemn grove]

Fn-1 x Fn+1 ~ (Fn)^2

approx

[novel urchin]

what does dollar sign represent

oh

[solemn grove]

apologies

[novel urchin]

np

[solemn grove]

i was just tryna see if that’s what you were tryna say

[novel urchin]

which sequence is this for

[solemn grove]

i just made your observation an equation

[novel urchin]

oh

[solemn grove]

it’s meant to be approx instead of ~

[novel urchin]

so the bofore and after

[solemn grove]

yeah

basically,

[novel urchin]

ok

i understand now

i wasnt doing it in terms of fibonnaci

i was just using it's own sequence

ok ty

[solemn grove]

their difference is literally one, then Fn-1 x Fn+1 = ((Fn)+1) (Fn)-1))

[solemn grove]

ohh

makes sense

[novel urchin]

ok tysm

how u close

[solemn grove]

wdym

[novel urchin]

how do u close the session

[solemn grove]

.close

[novel urchin]

.close

[lone heart]

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[left oak]

how does $\frac{x^2}{x^2-1}$ simplify to $1+\frac{1}{x^2-1}$?

[ocean seal]

Serky

[frigid geyser]

$x^2 = x^2 - 1 + 1$ for the numerator

[ocean seal]

xdk1235

[left oak]

nvm I know how

[rapid nova]

[
\frac{x^2}{x^2-1} = \frac{(x^2 - 1) + 1}{x^2-1} = \frac{x^2-1}{x^2-1} + \frac{1}{x^2-1} = 1 + \frac{1}{x^2-1}
]

[ocean seal]

rept1d

[left oak]

thanks for the help

.close

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[edgy cape]

idk how to integrate this

I tried splitting it

but idk what happens to the u/√u

like how to simplify that

[frigid geyser]

$\frac{u}{\sqrt{u}} = \sqrt{u}$

[ocean seal]

xdk1235

[edgy cape]

thanks

.close

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[edgy cape]

I have no idea what I am doing for this

I can't get a simple enough integral after the u-sub

[alpine sable]

how do i get help

oops

sorry

[fiery adder]

#❓how-to-get-help

[frigid geyser]

$\frac{x+1}{x} = 1 + \frac{1}{x}$

[ocean seal]

xdk1235

[frigid geyser]

and $u-1 = \ln x + x$

[ocean seal]

xdk1235

[edgy cape]

but where would I use u-1

[frigid geyser]

or $1 - \ln x - x = 2 - (1 + \ln x + x)$ whichever you like

[ocean seal]

xdk1235

[edgy cape]

this is what I got after using du

[placid zinc]

u = 1 + ln(x) + x
du = (1/x + 1) dx = (x+1)/x dx

Huh. What a coincidence, there's a (x+1)/x dx right there

[edgy cape]

ohh so then I get ∫(2-u)/u *3du

because (x+1)/x dx = du, and there is a 3

and also because 1-lnx-x is the same as 2-u

but then my final answer has an lnx inside ln

how does that make sense

[placid zinc]

Why not?

[edgy cape]

I have never seen an ln inside an ln ever

[placid zinc]

Yeah can happen. There's ln in a denominator in your integral, so ye

[edgy cape]

alright, thank you so much for your help

.close

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[alpine sable]

.close

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[alpine sable]

Solving question g

I don’t understand how to find 4th degree equations from finite differences

[remote heron]

can you use LIP?

its a lot of work

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

@remote heron what is LIP?

[remote heron]

lagrange interpolation polynomial

i used an online calculator and it gave your answer

im not sure if there is a better way

it usually just involves a lot of algebra

https://en.wikipedia.org/wiki/Lagrange_polynomial this article is pretty good but wordy

what have you been using? @alpine sable

[alpine sable]

Just algebra

standard form and substitution

[remote heron]

oh wow

the LIP looks complicated but its really just making sure all the other terms go to 0

then scaling a 1-factor by the output you expect

[alpine sable]

I wouldnt mind using that lol

just that I need to use algebra for class

[remote heron]

try it for a linear one first

well idk how you do it with a 5th order

thats insane

[alpine sable]

4th but yeah

[remote heron]

its 5th order

[alpine sable]

3rd and under makes sense

[remote heron]

wait

[alpine sable]

its 4th degree

[remote heron]

nah its 5th

just the leading coefficient goes away

n+1 points for a n degree polynomial

i think

[alpine sable]

honestly ive got no idea

[remote heron]

like 2 for a line

[alpine sable]

thought it was 4

[remote heron]

3 make a parabola

anyways

you wanna work through example together?

[alpine sable]

since ^4 is the highest degree in the answer

[remote heron]

or try it on your own

[alpine sable]

ive been stuck on it for a while now

[remote heron]

i think a linear example is good

personally

like uhh

[alpine sable]

I have to use algebra though

thats the only issue

[remote heron]

oh

then i got no idea

[remote heron]

i know how to do with LIP and calculus

[alpine sable]

this is basically where im at

[remote heron]

oh

[alpine sable]

i have three variables

[remote heron]

i guess you could use a system

thats a nightmare though

[alpine sable]

and can get c=3

but after that how am i supposed to get b and d

any ideas?

[remote heron]

heres e

Ax^5 + Bx^4 + Cx^3 + D x^2 + Ex + F

sorry, f

f(0) = your constant

[alpine sable]

How do you know its Ax^5

not Ax^4?

[remote heron]

6 data points

idk lets just say

[alpine sable]

wdym by data points

[remote heron]

i might be wrong

like

interpolation points

there is a unique polynomial of degree at most n

you dont know that its only degree 4

it could be 5

[alpine sable]

do you think we could hop in a call?

[remote heron]

sure

[alpine sable]

Kinda hard over text

alright appreciate it

[remote heron]

go to 384

<-

[lone heart]

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[gaunt moat]

hi

[gaunt moat]

okay so im doing

find the values of k that make the function continouys over the given interval

f(x) =

8x + 1, x < k
7x − 2, k ≤ x ≤ 8

k= _______

what should i do to try and solve this

[glass lichen]

what's the definition of continuity?

[gaunt moat]

from what i remeber is if you can draw the point of the line without picking up your pencil and lim f(x) =f(1)

[glass lichen]

the latter

the former is the intuition for the definition

f is continuous at a iff $\lim_{x\to a}f(x)=f(a)$

[ocean seal]

Mosh

[glass lichen]

so you require that the sided limits around k exist and agree on the same value.

[gaunt moat]

so

i have to find a number to be for x

that can work for the top and bottom equations

[glass lichen]

maybe, but no

$\lim_{x\to k^-}f(x)=\lim_{x\to k^+}f(x)$ is what you're solving.

[ocean seal]

Mosh

[gaunt moat]

okay so how would i go about this ?

im trying to find k as it approches from the left and right ? should i draw it maybe ?

[glass lichen]

find each of the limits.

[gaunt moat]

how do i do that without a limit number like x -->1-?

[glass lichen]

you have a limit number

it's k

[gaunt moat]

so i plug in k and negative k?

[glass lichen]

no

ok, what branch corresponds to x values to the left of k?

ie x<k

[gaunt moat]

so negatives ? sorry im confused

[glass lichen]

look at your function

what branch of the function (8x+1 or 7x-2) corresponds to values of x<k?

[gaunt moat]

im not sure how to know since i dont know the value of k

[glass lichen]

use your eyes

do you understand how f(x) is defined Yes or No?

[gaunt moat]

not really

[glass lichen]

ok for now, suppose k=1

what does x<1 mean?

[gaunt moat]

x is smaller than 1

less than *

[glass lichen]

yes, so for example if I want to find f(0), I'd note that 0<1, then look at the part of the function that corresponds to those values

namely, 8x+1

f(2), I'd look and see 1<2<8 and plug 2 into 7x-2

[gaunt moat]

so 14-2 =12 ?

but why would you plug 2 in

[glass lichen]

...

it was an example.

[gaunt moat]

im so confused lmao

[glass lichen]

cause you said you didn't understand how f was defined.

anyway do you understand how a piecewise function is defined now? Yes or No
If no, be specific in what you don't understand

[gaunt moat]

okay so i dont understand how im suppose to oknow what to plug into the equation to start working on it ive never had x<k or k ≤ x ≤ 8

ive always had something like x^3-kx+8, x ≤ 1

and x^2+2kx+2, x>1

things like that

[glass lichen]

$\lim_{x\to k^-}f(x)=\lim_{x\to k^-}8x+1=8k+1$ since $x<k$

[ocean seal]

Mosh

[gaunt moat]

so would i do 7k-2=8k+1 and solve for k based of that ?

[glass lichen]

yes.

[gaunt moat]

okay lemme write this down so i dont forget

okay so k=-3

[glass lichen]

yes.

[gaunt moat]

is that the final answer or what do i do next ?

okay nvm that was the final answer

thanks for the help sorry for being difficult my brain is mush rn wasnt able to pay attention in class today too well

[glass lichen]

not even going to attempt to decipher that

[gaunt moat]

yea it didnt copy over well lol

f(x)= (x^2+10x+24)/x+6 but the top branch is x cannot equal -6 and the bottom x=-6

but for x+6 there is like a k two spaces below that ?

[glass lichen]

$f(x)=\begin{cases}\frac{x^2+10x+24}{x+6}&\text{if }x\neq -6 \ k&\text{if } x=-6\end{cases}$

[ocean seal]

Mosh

[glass lichen]

Just take a picture next time.

but anyway, apply similar logic.

[gaunt moat]

okay i will

[glass lichen]

$\lim_{x\to -6}f(x)=f(-6)$ for it to be continuous at $x=-6$

[ocean seal]

Mosh

[gaunt moat]

would i factor ?

or should i not do that

[glass lichen]

only one way to find out

[gaunt moat]

haha

ill do that

okay so i factored it and i now have (x+4)

now i have no idea what to do from here

so

is it -2 ?

how would i go about this ?

[lone heart]

@gaunt moat Has your question been resolved?

[gaunt moat]

close

.close

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[tawdry spindle]

had a brainfart

how would this graph's transformation look like?

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[proud bobcat]

i think i did this one right

[proud bobcat]

but im not entirely sure, It didnt show x was even with t = 1 and then didnt show that if itd be a multiple of 4 then t would have to be 2/4

[lone heart]

@proud bobcat Has your question been resolved?

[lone heart]

@proud bobcat Has your question been resolved?

[slender gull]

Well you could simply do it this way, every 2t number is an even number for all integer T.
For 2t to be a multiple of 4, t must be even.

For all even t, 2t is a multiple of 4.
While for all odd values of t, 2t is not a multiple of t.
That's because odd numbers don't have a factor of 2, so 2 times an odd number won't get you a four.

So yeah, frame like this maybe.

@proud bobcat

[proud bobcat]

oh thank you i realize now that point of being a factor of two is essential to it

i wasnt sure if she meant just her specific statement there had something wrong with it or the entire thing but i realized the entirety

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[severe sluice]

you can just multiply the 2 lengths?\

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[restive palm]

Hello!

[restive palm]

If $\ket{\psi} = \int \Phi(x) A\ket{0}dx$

[ocean seal]

Bryan

[restive palm]

Where A is an operator

How do I get $\bra{\psi}\ket{\psi}$

[ocean seal]

Bryan

[restive palm]

Not sure how to deal with the integral here

[lone heart]

@restive palm Has your question been resolved?

[tacit arch]

You're not given an inner product ?

Lot of unknowns as well

A, Phi, integral domain

[restive palm]

What do you mean?

[tacit arch]

What's the context of the question

You've given little details

Is it just this?
https://quantummechanics.ucsd.edu/ph130a/130_notes/node108.html

[restive palm]

My ket actually contains an integral over x

[tacit arch]

I can see that

What's the definition of your dot product

Aka inner product

[restive palm]

I'm not really sure of different definitions for the inner product other than $\int g^*(x)f(x)dx$

[ocean seal]

Bryan

[tacit arch]

What's your other variables

Idk, seems like you should go back to your notes and look up definitions before you calculate anything

[restive palm]

I'm asking a question for generality, not trying to solve something specifically. I do not have notes on the subject

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[alpine sable]

.open

[keen ruin]

It's 2.a) that i have issues with

I've Tried to equal the base with 0 but i don't know how to proceed

@tough tangle

Sorry to bother but i want some help regarding this problem

[restive palm]

It's continuous whenever the denominator is non-zero: It's zero only when x^2-y^2 = 1

[keen ruin]

that s all?

IT s zero when x^2+ y^2=1

not minus

Right?

[restive palm]

No

You have to subtract 1 from both sides

[keen ruin]

ok and after that ?

[little drum]

Put $x^2 + y^2 = t \geq 0$

[ocean seal]

Ansh

[keen ruin]

that s it?

[little drum]

No

of course no

Then you'll have f(x,y) = $\frac{1+t}{1-t}$

[ocean seal]

Ansh

[little drum]

find point of discontinuity for g(t) and plug in "t" in terms of x, y to get where your f(x,y) is discontinuous

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[eager ravine]

if i have |a| = |b|, solving for a would give me a = ±|b|. how can i solve for a while removing the absolute value sign on b?

[covert agate]

do you know what |x| is

[eager ravine]

the absolute value of x

x will always be positive

i guess, what i mean is, is this ±|b| = ±b true?

[alpine sable]

yes

because the sign is not even inside the vertical lines

[eager ravine]

so how do i go from ±|b| to ±b?

[alpine sable]

again, how do you define absolute value?

[noble sinew]

no, writing it like that you are also saying +|b|=-b is true

[eager ravine]

how so?

shouldn't it be +|b| = +b?

and -|b| = -b

[noble sinew]

that is what it should be

not what you wrote

+-|b|=+-b means you are saying all 4 combinations of + and - are equal

[alpine sable]

what does |-b| equal to?

[eager ravine]

i don’t really get this

[eager ravine]

i believe if b is positive then |-b| = b, but if b is negative then |-b| = -(-b)

[alpine sable]

okay..

[noble sinew]

+-|b|=+-b means |b|=b, |b|=-b, -|b|=b and -|b|=-b

[noble sinew]

it doesn't just mean these 2

[eager ravine]

oh right

[eager ravine]

so i can't do this then?

[noble sinew]

sure you can

[eager ravine]

cause i have a^2 = 4(t^2), so i thought of taking the square roots of both sides
sqrt(a^2) = sqrt(4(t^2))
|a| = |4(t^2)|
a = ±|4(t^2)|

so i was hoping maybe i can do
a = ±2t

but i'm not really sure how to go from a = ±|4(t^2)|

[noble sinew]

yes its just a=+- 2t

[eager ravine]

so how can i go from a = ±|4(t^2)| to that?

[ocean seal]

BritS

[noble sinew]

I mean what is your 3rd line?

how did sqrt just disappear?

[eager ravine]

my bad i made a mistake

gimme a sec

this is what i end up with

[alpine sable]

hold on

[noble sinew]

like I already said

[eager ravine]

yeah i made a mistake there

[eager ravine]

so how do i get to a = ±2t from here

[alpine sable]

being meticulous is hard to be fair

you did great anyway

[noble sinew]

you get the same solution set for both

a=|2t| gives a=2t or a=-2t

same for a=-|2t|

[eager ravine]

that gives
|2t| = -a
2t = ±(-a)

so ±(-a) = ±a?

[noble sinew]

again wrong use of +-

[eager ravine]

yeah i think so

[noble sinew]

but yes +-(-a) is equivalent to +-a

yes?

[eager ravine]

wait, i'm kinda confused

i thought ±(-a) won't equal ±a

[alpine sable]

hold on...

[eager ravine]

cause then
-a = a or -(-a) = -a

[noble sinew]

yes I'm saying the equal sign is false

but they are equivalent

+-(-a) means -a or a

clearly the same we get from +-a

[eager ravine]

but the minus comes first?

[noble sinew]

If I say x=-1 or x=1 that is the same as saying x=1 or x=-1

or saying x=+-1 is the same as x=+-(-1)

[alpine sable]

no difference

[noble sinew]

so clearly they are equivalent

[alpine sable]

yes

[eager ravine]

so equivalent and not equal?

can i do that in an equation?

[noble sinew]

?

the problem with writing +- x = +-y is it gives 4 pairs like I have told you

but clearly the solution set to +- x is the same as the solution set to +-(-x)

[noble sinew]

like I said here

[alpine sable]

x here is the solution

[eager ravine]

i mean first i got
a = ±|2t|

then from |2t|, i can get
a = |2t|
2t = ±a

or
a = -|2t|
|2t| = -a
2t = ±(-a)

[noble sinew]

and the two equations give the same solution set?

like I have said a few times

[eager ravine]

yeah i believe so. but i've just never heard an equivalent equations but not equal

like you said ±(-a) and ±a are equivalent but not equal

[noble sinew]

Thats like saying: x=1 or x=2 is clearly the same as x=2 or x=1, agree?

but we can't conclude 1=2 from that

honestly just use "or" instead of +- if confused

clearly 2t=a or 2t=-a and 2t=-a or 2t=a are the same

[alpine sable]

ss taken from google, or is a conjunction that connects two or more possibilities or alternatives

[eager ravine]

aah i see

so if i do it by case, i should get a = ±2t right?

[alpine sable]

yes

[eager ravine]

a = 2t or a = -2t

[alpine sable]

yes

[eager ravine]

i see

i'll give it a try

[alpine sable]

all good?

[eager ravine]

hopefully

thanks

[alpine sable]

sure, but when you're done, please use .close

[eager ravine]

got it

.close

[lone heart]

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[alpine sable]

thank you for the responsibility

[lone heart]

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[knotty pike]

hey

[knotty pike]

if someone could help me find the value of c that would be helpful because i’m kind of lost

3x-4y+c=0

and it passed through the point (-4,6)

i kept getting confused during this

[tawny relic]

write in the form y=mx+b

[knotty pike]

yes but how do i do that if i don’t have the c value?

don’t i need that to write in the form y=mx+b

[tawny relic]

what is the ans

[knotty pike]

not sure that’s why i’m trying to solve it lol

[cunning trout]

Okay look

Plug in values of x and y in the standard equation

And solve for c

I edited

@knotty pike

[knotty pike]

um alr

[cunning trout]

-12-24+c=0

Solve this equation

[tawny relic]

that means c=36

so that is all you had t o do

[cunning trout]

Now we can cross-check that

[tawny relic]

by substitution

[cunning trout]

Which should be c=36=36 which is correct

[knotty pike]

oh

so for 3x-4y+c=0 i would just do 3-4?

[tawny relic]

no

i don't know what you understood

[cunning trout]

We’re PLUGGING IN the values in the equation

[knotty pike]

sorry i’m a bit confused

[cunning trout]

It’s okay

Understand the word plugging

You’re putting the values of x and y in the equation

[tawny relic]

okay do you know how to substitute values in an equation?

[knotty pike]

i’m pretty sure

[tawny relic]

that is it

[knotty pike]

oh

[cunning trout]

3(-4)-4(6)+c=0

[knotty pike]

ohhh

[tawny relic]

the coordinates (-4,6) are in the form (x,y)

[knotty pike]

yeah yeah

[tawny relic]

you just substitute the values

[knotty pike]

that just hit em

me

[cunning trout]

Yh

[tawny relic]

so who explained better

[cunning trout]

Bruh

[knotty pike]

you both helped me good lol

[cunning trout]

Lol

[tawny relic]

choose one

[cunning trout]

Are you alright?

[tawny relic]

yes you know feedack

[cunning trout]

Stop wasting his time please.

[tawny relic]

alright stop acting like that plz

i only asked a question

u jealous

[cunning trout]

@knotty pike just shut the channel

What?

[tawny relic]

write .close

[knotty pike]

it’s positive 36 not negative right

[tawny relic]

yh

[knotty pike]

alright

thanks for the help

.close

[lone heart]

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[hearty orbit]

is the complexity for $2^{(2n^2 + 4n)} * 2^7$ = $2^{(2n^2 + 4n)} $

[ocean seal]

goldenturtle

[lone heart]

@hearty orbit Has your question been resolved?

[lone heart]

@hearty orbit Has your question been resolved?

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[hearty orbit]

<@&286206848099549185>

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[jaunty crane]

a wire with a length of 2 m is cut into 25 parts with the condition that the lengths of the wire cut form an arithmetic progression. given that the total length of wire for the three shortest sections is 4.2 cm. What is the length, in cm, of the longest wire?

[lone heart]

Please don't occupy multiple help channels.

[placid zinc]

Thoughts on the question so far?

[jaunty crane]

no sorry

pls help me

[placid zinc]

The lengths form an arithmetic progression. What equation could be used to represent the length of wire n (given the first wire has length a)?

[jaunty crane]

im not sure

f this

.close

[lone heart]

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[stable plume]

hello

[stable plume]

Can someone show me example of separate differential equation

$dy/dx=x^6$

[ocean seal]

cakeee

[stable plume]

Have to transform that to $y=$

[ocean seal]

cakeee

[stable plume]

$dy=x^6dx$

[ocean seal]

cakeee

[stable plume]

What i can do next

[solid cargo]

U mean u have to find y so that d/dx(y) = x^6?

[stable plume]

Have to find y from dy/dx=x^6

[solid cargo]

Kk

[glass lichen]

just integrate both sides.

[stable plume]

y=x^7/7?

[glass lichen]

missing something.

[stable plume]

oh yeah

😄

+C

thanks

.close

[lone heart]

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[formal bison]

.reopen

[tidal fog]

help plzzzz

.close

[lone heart]

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[vale wigeon]

When are two elements equivalent in this case?
when they're homotopic

yes, a trivial fundamental group is a fundamental group that is iso to the trivial group

[pale kestrel]

I would think of the elements as 'kinds' of paths.

You can prove it is a group

by composition of paths

[lone heart]

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[wicked wing]

I am trying to generalise a summation
$$\sum_{j=1}^{n} j^{\alpha} x^j \binom{n}{j}$$
So I figured out a way to do this using derivatives and a sequence of functions \
Let $f_0(x)=(1+x)^n$\

$f_1(x)=x*f'_0(x)$\
$\cdots$\

$f_{\alpha}(x)=x*(f_{\alpha-1}(x))'$

[ocean seal]

whitedwarf

[wicked wing]

Now is there a way to write a closed form for these functions other than their recursive definition

[alpine sable]

whats alpha?

[wicked wing]

Natural number

[little drum]

Is alpha fixed?

[wicked wing]

Yes

[little drum]

okay :o

[placid zinc]

Is fα(x) the final answer?

[wicked wing]

Yea

[little drum]

I think you can do uhh

[placid zinc]

Neat, like a chain of derivatives

[little drum]

T_T okay won't help probs

[wicked wing]

I was trying to do this iteratively it got real messy real fast

[little drum]

why you trying to do this though?

[wicked wing]

For fun obvsly I am curious 😅

The original question was where alpha =2 and x=1/2 n=2005

[placid zinc]

It's so close to binomial theorem haha

But not quite

[wicked wing]

Yea tru..

[little drum]

with alpha = 2 is easy actually but ... uh not sure for higher alphas

[wicked wing]

Lol I think you are kinda right but u know I thought we will get like Bernoulli number or sth

As of with sum from 1 to n k^n

[wicked wing]

In the formulas

But I guess not lol 😅

[little drum]

No.. it might be, I'm just not well informed.. tag @ helpers in 5 mins and maybe someone who can help better might show up

[wicked wing]

Aight

[wicked wing]

<@&286206848099549185>

[wicked wing]

Thanks for the efforts so far

Both of u guys 👍😅

[placid zinc]

I see exactly how you got that recursive sequence, haha. Tried the same thing, but ended up in the same pit. Maybe that can be adjusted to the answer? I'll think on it.

[little drum]

@hasty elk ? Have any clue about something that looks like this?

or how to arrive at this

$$\sum^n_{j=1} j^{\alpha} x^j \binom{n}{j}$$

[ocean seal]

Ansh

[lone heart]

@wicked wing Has your question been resolved?

[wicked wing]

I will close this channel in an hour or so

😅

[lone heart]

@wicked wing Has your question been resolved?

[wicked wing]

Aight thanks for the help everyone I guess it really doesn't have anything nice to it

I will close this channel now

.close

[lone heart]

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[lone heart]

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[lone heart]

@tender pebble Has your question been resolved?

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[bitter burrow]

https://docs.google.com/forms/d/e/1FAIpQLSdUJQ7ly88Z0mRqKUJp88YV8gQi61roG0o76V15mFWnRmcrxg/viewform?usp=sf_link

[bitter burrow]

pls help

[wary stream]

That's a survey based on yourself

[bitter burrow]

does it matter

??

[wary stream]

Did you even read what that link was?

[gray isle]

seems they want to harvest our data for something

[bitter burrow]

yes

for my IA

[lone heart]

@bitter burrow Has your question been resolved?

[lone heart]

@bitter burrow Has your question been resolved?

[lone heart]

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[alpine sable]

I am kind of just guessing what to do

so basically we know a vector equation is something with s and t elements of the real and directions with (-2 , 1 , 1) and (4 , 2 , 2)

so would question a be

[lone heart]

@alpine sable Has your question been resolved?

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[alpine sable]

how do I find the antiderivative of this

reverse product rule?

[tacit arch]

multiply out the terms

[alpine sable]

oh wait I can just expand it

[tacit arch]

you got it

feel free to .close

[alpine sable]

how

.close

[lone heart]

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[tacit arch]

.close

[lone heart]

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[median mauve]

I don't understand this things:

[median mauve]

how do you find b.

for example: for this data:

[noble sinew]

Find correlation and sample sd of x and y

$\hat{b}=r_{xy}\frac{s_y}{s_x}$

[ocean seal]

ScapeProf

[median mauve]

[median mauve]

what is $\hat{b}$, $r_{xy}$?

[ocean seal]

LittleMouse

[noble sinew]

The best (least squared) estimate for b and correlation

[median mauve]

is this the same thing?

[noble sinew]

Probably

[median mauve]

[noble sinew]

In general you just use any software if you are asking how to compute

Doing by hand is very annoying

[median mauve]

ty

.close

[lone heart]

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[median mauve]

$$f(\frac{\pi}{2})+2f(-\frac{\pi}{2}) = 1$$

[ocean seal]

LittleMouse

[median mauve]

$$f(\pi)+2f(-\pi) = 0$$

[ocean seal]

LittleMouse

[pale kestrel]

$$f(x)+2f(-x)=\sin x$$

[ocean seal]

Shuri2060

[pale kestrel]

there's a trick to doing this

Specific value substitution probably doesn't help here

[median mauve]

😮

[median mauve]

what trick

[knotty spire]

f(x) might be an odd function

[pale kestrel]

hmmm how to give a clue

[knotty spire]

Not sure yet

[pale kestrel]

Substitution is good approach.

Specific values might not be.

[median mauve]

😮

[knotty spire]

Well I am happy to report that your clue helped me at least.

[wanton junco]

not sure you can prove that here tho

or if it's even true actually

but I don't think you need it
do you .. ?

[knotty spire]

Nope, you don't

It was just my brain on sleep deprivation overanalyzing

[wanton junco]

lmao

ngl my first instinct was also odd functions cus x -x

[median mauve]

-1?

[median mauve]

[knotty spire]

yup

[median mauve]

yey

[pale kestrel]

what's going on

[median mauve]

I got -1

[pale kestrel]

uh

what?

f(x) = -1 ???

[knotty spire]

no, he means

[median mauve]

f(\pi/2)

[pale kestrel]

I didn't actually do it

[knotty spire]

f(pi/2) = -1

[pale kestrel]

uh sure

but like i said

substituting actual values doesn't help

[median mauve]

hmm

[wanton junco]

same
can vouch

[pale kestrel]

Alright, that's a good approach to find f(pi/2)

Now can you generalise?

[median mauve]

[knotty spire]

Hm wait, your second equation

Did you multiply both sides by -1 and then assume f is odd?

[median mauve]

I put x = -pi/2

[knotty spire]

oh, right

Ignore me

[pale kestrel]

@little drum some fun

[little drum]

f(-x) + 2f(x) = -sinx

f(x) was not the impostor

[pale kestrel]

The approach is right, (i was not paying attention to the math)

[median mauve]

o

😮

[pale kestrel]

Anyone check?

[knotty spire]

oh god, imagine dealing with an uncountable infinity of potential suspects

I mean the answer I got was -sinx

[little drum]

oh god not amogus here

[knotty spire]

which is sin(-x)

[pale kestrel]

gud

$$f(x)+2f(-x)=\sin x$$
$$2f(-x)+4f(x)=-2\sin x$$

[ocean seal]

Shuri2060

[pale kestrel]

yh i agree

[median mauve]

[pale kestrel]

The trick is to substitute expressions into the parameter

[little drum]

substitute $A = f(x), B=f(-x)$

[pale kestrel]

Get simultaneous equations

[ocean seal]

Ansh

[pale kestrel]

and eliminate

[little drum]

eliminte

[pale kestrel]

For these function questions usually

I saw a pretty good one the other day 🤔

[little drum]

gdni8 zzzz

[median mauve]

this is easier than yersterday

[pale kestrel]

$$f(x) + f\left(\frac{x-1}{x}\right) = 1+x$$

[ocean seal]

Shuri2060

[pale kestrel]

@median mauve have a go at this one 🤔

The way to solve is similar idea

heh heh

[knotty spire]

Let there be a b, where b is a solution to the given equation. Answer: b.

[median mauve]

🪄

[knotty spire]

I shall save this one for personal purposes.

[little drum]

Say f(x) = 2 for some x = a in the domain

Put x = a in the equation

[pale kestrel]

this is interesting, ima try 🤔

q

[little drum]

No

x = a

where a is an element in the domain of f(x) whose image is 2

or in simpler terms, f(a) = 2

[wanton junco]

what is goal?

find func?

[knotty spire]

yes

[wanton junco]

it doesn't look very nice ... :(

[median mauve]

[little drum]

Hey what's up?

[little drum]

Put a instead of 2, and f(a) = 2

so you have $f(f(a))\cdot(1+f(a)) = -f(a)$

[ocean seal]

Ansh

[little drum]

and f(a) is just 2

[median mauve]

why f(a) = 2

[knotty spire]

Because the task tells you that 2 is in the range of the function

so f(a) must equal to 2 for some a in its domain

And you can use that fact to get a neat equation

[median mauve]

😮

I am dumb

-2/3

[knotty spire]

should be

[median mauve]

is 2 the only ans?

[little drum]

x/(x-1) = x

1/(x-1) = 1

x-1=1

x=2?

[knotty spire]

You lost 0

[little drum]

be confident with Algebra

[little drum]

[median mauve]

[knotty spire]

always be careful when dividing by x 😉

[little drum]

here, you can't divide with x

[median mauve]

😮

[little drum]

x can be 0 and 2

[median mauve]

nicew

[pale kestrel]

$$g(x)=\frac{2x}{x+k}$$

[ocean seal]

Shuri2060

[median mauve]

so am i correct?

[pale kestrel]

idk

$$g^2(x)=\frac{2\left(\frac{2x}{x+k}\right)}{\left(\frac{2x}{x+k}\right)+k}$$

[ocean seal]

Shuri2060

[pale kestrel]

$$g^2(x)=\frac{4x}{2x+k(x+k)}$$

[ocean seal]

Shuri2060

[pale kestrel]

$$g^2(x)=\frac{4x}{2x+kx + k^2}=x$$

[ocean seal]

Shuri2060

[pale kestrel]

g(x), x not k

isn't this just a quadratic in x?

looks right to me

[median mauve]

so I am right?

seems like

[pale kestrel]

🤷‍♂️

be more sure in yourself

[median mauve]

[pale kestrel]

You should substitute back in to check

To make sure the conditions are satisfied

[median mauve]

k, ty

M11 is easier than M12 LOL

I use 3 days to complate M12

1 hours for M11

LOLOL

.close

[lone heart]

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[alpine sable]

i got a question about triangles. how can you show that this is true (or not)?

[wanton jasper]

i would use similar triangles

[alpine sable]

but all other angles are different. the only thing you have is equal base, height and therefore area

[wanton jasper]

eqaul bases, angles, and one of sides

[alpine sable]

oh yeah, ig if you have two sides in common, they're similar

[languid ingot]

I'm pretty sure this statement is true if and only if the original triangle was isosceles to begin with

[alpine sable]

wait, for real??

[languid ingot]

Ah wait, my bad

It can never happen) @alpine sable, prove by contradiction

Assume all the angles are equal

What do you see?

[alpine sable]

well, 1 equal angle and 2 equal sides

[languid ingot]

What happens when a segment is both a median and a bisector in a triangle?

[alpine sable]

it's isosceles?

[languid ingot]

Yes

It also gives that it's an altitude, but let's work with yours, this means those red lines equal to the triangle's sides which is a contradiction by triangle inequality

[alpine sable]

but i thought if two triangles share two sides, then the angles are all equal?

[languid ingot]

?

[alpine sable]

like

if two sides are equal, then the triangles are similar, no?

or was it two angles

[languid ingot]

No

2 angles

There are many other ways as well

[alpine sable]

damn.. this question is a lot harder than i thought then

[languid ingot]

Not that hard if you put your mind to it, alright, let's work through this

Why is it a contradiction if all 3 angles are equal?

Since a=b we have that BD is the altitude of the triangle ABE since it's a bisector and median

[alpine sable]

yeah that'd mean that the two red lines are the same line at the same position

[languid ingot]

Yes since they'll both be altitudes

Which is impossible in a triangle

[alpine sable]

mhm

how am i supposed to show that two line segments split an angle in 3 equal parts though

[lone heart]

@alpine sable Has your question been resolved?

Channel closed

Closed by @pale socket

Use .reopen if this was a mistake.

[lone heart]

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[hollow flare]

@wary stream

[wary stream]

Yes?

[hollow flare]

so lets continue

[wary stream]

So your attempt?

[hollow flare]

, rotate

[wary stream]

You didn't try anything?

[hollow flare]

no i was trying to understand the video i just didnt wanna be confused

in video a and b is given whats a and b in my question

[wary stream]

Any two points you want

[hollow flare]

ok fine lets go with p and q

[wary stream]

So then, do that

[hollow flare]

a = 2i and b = 3j

[wary stream]

You can use that form, not it's not needed

The form <2, 0>

Is good

[hollow flare]

how am i supposed to plug in the points ...

oh nvm wait

so P(ax,bx) and q(ay,by)

a dot b is axbx + bxby

0 + 0 = 0

[wary stream]

Written wrong but yes

[hollow flare]

...

so i got 0 for a * b

[wary stream]

Yes

[hollow flare]

now whattt

[wary stream]

|A||B|

[hollow flare]

so the formula for it is sqrt((ax)^2 + (ay)^2)

[wary stream]

Yes

[hollow flare]

which point do we pick?

any?

P?

[wary stream]

If you're using P and Q, then |P| and |Q|

[hollow flare]

ohh plug in x and y for a from p and x and y for b from q?

sqrt((2)^2 + (0)^2) sqrt((0)^2 + (3)^2)

sqrt(4) sqrt(9)

[wary stream]

Yes

[hollow flare]

now whattt

so thats theta = cos^-1 (0)/(|sqrt(4)| |sqrt(9)|)

[wary stream]

You don't need the | | anymore

Because $|A| = \sqrt{(A_x)^2 + (A_y)^2}$

[ocean seal]

dldh06

[wary stream]

So |A| = sqrt{4}

Which could be simplified

[hollow flare]

2

[wary stream]

Also sqrt(9)

[hollow flare]

3

2 and 3 gets what tho multiplied?

[wary stream]

So you have $$\theta = \cos^{-1}{\frac{0}{6}}$$

[ocean seal]

dldh06

[wary stream]

Yes

Because it's |A||B|

[hollow flare]

does this even give any angle bro

omg it gave me 90 degreees

so im assuming it is right?

[wary stream]

Yes

[hollow flare]

ok so now

[wary stream]

So you did P and Q

You need P and R

And Q and R

Same exact process as above

[hollow flare]

all the sum should add up to 180 correct

[wary stream]

Yes

[hollow flare]

ok im gonna write it and keep checking it occasionally

P(ax,bx) and R(ay,by)
a dot b = axbx + bxby
6 + 0
= 6

[wary stream]

Yes

[hollow flare]

sqrt((2)^2 + (0)^2) sqrt((3)^2 + (4)^2)

sqrt(4) sqrt(25)

[wary stream]

P(ax,bx) and R(ay,by)
FYI, not properly written. It's (ax, ay)

And (bx, by)

[hollow flare]

well yeah u get my point

[wary stream]

They're coordinates

[hollow flare]

ohh

ok 2 * 5 is 10

[wary stream]

Yes

[hollow flare]

theta = cos^-1 6/10

[wary stream]

Yes

[hollow flare]

thats 53.13

[wary stream]

Yes

[hollow flare]

now why do we do PR not RP or thats same thing?

[wary stream]

It's the same thing, multiplication is commutative

[hollow flare]

okkk

Q(ax,bx) and R(ay,by)
a dot b = axbx + bxby
0+12
= 12

also im writing letters so i can reference it what numbers i used

[wary stream]

Yes

[hollow flare]

sqrt((0)^2 + (3)^2) sqrt((3)^2 + (4)^2)

sqrt(9) sqrt(25)

3*5 is 15

[wary stream]

You mathed it wrong

Recheck sqrt((3)^2 + (4)^2)

[hollow flare]

so theta = cos^-1 12/15

[wary stream]

Yes

[hollow flare]

36.87 so 37

lets add all

omg its 180 finalllly

[wary stream]

Is that it?

[hollow flare]

i mean there is more but i wanna work on that after dinner lol

so in like 2 hours

[wary stream]

Apply the same process for the other question

[hollow flare]

oh no its different problems

[hollow flare]

for the one we did thats it

also PQ is what? vector? segment?

vector right

[wary stream]

Depends on the context, I believe

[lone heart]

@hollow flare Has your question been resolved?

[hollow flare]

@wary stream u wanna know another problem

[wary stream]

Sure