help-33

[north otter]

wait why

[plush sorrel]

it helps with the simplification cuz ur tryna take out factors

you're tryna make something u and something du

also n = 2k is the math way of saying this is even (where k >= 1)

[north otter]

oh really

[plush sorrel]

yeah

[north otter]

bruh

[plush sorrel]

substitue anything for k and it will be even

[north otter]

wait

so you do n = 2k to make sure that it's even?

so that k is odd?

[plush sorrel]

i don't follow i mean if n = 2k that's basically saying no matter what k you have, even or odd, it will be multiplied by 2 making it even

[north otter]

oh

ok

[plush sorrel]

like if k = 3 then 2k = 6 which is even satisfying that n is even

bruh lmk if im even helping btw i don't think im explaining this well

[north otter]

okay

that makes sense

[north otter]

you are

😭

it makes sense

i just dont get how ppl know to do 2k but now it makes sense cuz you're saying n is even

[plush sorrel]

so what would m equal what u think

[north otter]

so thanks :D

wait

i have a q

so if

2k is even

does that mean that k HAVE to be odd?

no right

so we cant let m = k

[plush sorrel]

naw

naw \

[north otter]

ok

2k-1

?

make m odd?

[plush sorrel]

yeahh nice

but + 1 is safer

[north otter]

ah

ok

[plush sorrel]

u don't want a negative

so tell me bro

[north otter]

true

[plush sorrel]

what's n equal to and what's m equal to

if n is even and m is odd

[north otter]

n = 2k m = 2k+1

are we just considering 1 case

or

[plush sorrel]

naw u got those mixed up

[north otter]

ih

mb

mbmb

the other way around

[plush sorrel]

bruh ill be honest i don't like memorizing the cases

[north otter]

oh

😭

[plush sorrel]

i just look at the problem, think of what to do, then I do it

[north otter]

how is bro built like that

😭

[plush sorrel]

i remember tho i messed up in the exam by going in a loop so i switched it up

[north otter]

i just cannot logic my way through math

[plush sorrel]

then ur cooked in physics lmao

feel free to memorize the cases though it's probably better if ur just tryna pass

ok anyways u substusive n = 2k

[north otter]

am i

we have formula sheets tho

anyway

[north otter]

okay

so case 1 is n = 2k m = 2k+1

right

[plush sorrel]

i guess

[north otter]

😭

continue pls

[plush sorrel]

naw im telling u i don't memorize this stuff

like bro step back from the cases right

i'll post the question again hol on

[north otter]

lamoooo

okay

[plush sorrel]

like what would you think u should be

[north otter]

u?

u sub?

[plush sorrel]

ye

[north otter]

ine sec

[plush sorrel]

like let me tell u what i see

[north otter]

we're uysing

IBP right

[plush sorrel]

what's IBP

[north otter]

integration by artd

parts

[plush sorrel]

o naw just u-sub

[north otter]

uhhh

[plush sorrel]

just so u know, if u don't understand, just try watching some youtube videos on this concept. that's how i self studied calculus

[north otter]

ok

i think

u should be

cscx

nvm

[north otter]

i tried..

[plush sorrel]

big bro

let me tell u how i would approach this maybe you can take away some methods

[north otter]

yes

[plush sorrel]

yo can we just call

is that fine?

[north otter]

uhh

u wanna screenshare and write?

or smth

[plush sorrel]

naw im tired of typing and copying and pasting ur question all the time

[north otter]

alr

sure

[marsh citrus]

@north otter Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[unique timber]

Hello, I would like some hints for this question. Initially I tried finding midpoint between the 2 points but I don't think thats correct

[stoic saddle]

finding the midpt is a fine first step

[ionic ferry]

Well you know that distance between two points is 10

[stoic saddle]

the center will lie on the perpendicular bisector of segment AB

[ionic ferry]

The centre and these two points

[stoic saddle]

correct-ish (after correction) but not relevant to part (a) here unfortunately.

[ionic ferry]

Ahhh maybe you have a shorter method, I was going for Centre as (x,y) and then applying distance formula to both the points

Then finding x and y and showing that it lies on the line just by substituting those values

[stoic saddle]

@unique timber still here?

[unique timber]

Something like this?

[stoic saddle]

ish

but my idea's to show that the perp bisector of AB is the line y = x/2 - 4.

[unique timber]

ohh

[ionic ferry]

Ahhh yeah, the dotted line

[unique timber]

but how did you know AB and y=x/2-4 are perpendicular to eachother ?

[stoic saddle]

the center will lie on the perpendicular bisector of segment AB
this is bc the perp bisector of AB consists of precisely those points which are the same distance from A as from B.

[unique timber]

i see thank you for the explanation

ah so I should find the midpoint and also gradient of AB? then find the perpendicular gradient

got the answer thank you

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[torpid pulsar]

When u differentiate I'm getting like this but idk how did he get 1😭

[marsh citrus]

@torpid pulsar Has your question been resolved?

[marsh citrus]

@torpid pulsar Has your question been resolved?

[wild orchid]

It looks to me like an error

the video multiplies x^(y-1) times yx^-1 and gets x^(y-2) instead ofd x^(y-2)*y

[torpid pulsar]

ohhhh thnk godd

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[tall pond]

did i go wrong somewhere

because idk what to do now

[copper raven]

it might be better if you add C+iS from the get go

instead of getting C and S seperately

[tall pond]

oh

so 1 + (e^itheta)/2 + (e^2itheta)/4 + ...

?

[copper raven]

yes

[tall pond]

bruh that looks way better yeah

i shouldve done that

idk why i didnt just do this

thanks

.solved

[marsh citrus]

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[hearty dust]

i asked gpt a math question and got this

[hearty dust]

can someone explain with a visual what this means?

for reference I asked it why -56.3 and 123.7 is equivalent in terms of the seperation between two vectors

i still dont get why even with the explanation

[sick walrus]

I recommend showing the original question for context too.

[hearty dust]

okay

[ionic ferry]

Okay so you have done ABcos(theta) and ABsin(theta) yeah?

[hearty dust]

yep

[ionic ferry]

Then you'd have tan(theta) = -1.5

[hearty dust]

did the tan theta and got arc tan

i alr did all tht yea

[ionic ferry]

Then arctan(-1.5), and that lead us to those angles you mentioned

[hearty dust]

but how are they equivalent

i cant visualize the meaning of this

how can the difference between two vectors be negative

[ionic ferry]

Well, how can angles be negative?

[hearty dust]

by going clockwise

??

[ionic ferry]

Alright, now imagine, y axis

oh mb, I meant the x-axis

Now, draw a line that is at an angle 123.7 degrees from it

So it kinda goes to the left-ish side

[hearty dust]

okay im following so far

[ionic ferry]

Now extend that line past the x-axis, below it, now what angle does that part of the line make with the x-axis?

[hearty dust]

oh is that how that works

[ionic ferry]

Yup

It's negative only because it's clockwise

[hearty dust]

okay so lets say we have a negative angle

what do we subtract or add to get the positive ver

[ionic ferry]

Alright

[hearty dust]

just 180-it?

[ionic ferry]

Well, take the magnitude of it (positive) and subtract it from 180

[hearty dust]

okay so I get the visualization that u have provided above

but im still not satisfied

how can the vectors have negative angle diff

[ionic ferry]

Well the same way our lines did

However, considering it is tan

IG we take it from 0 to pi yeah?

[hearty dust]

whatt do u mean

[ionic ferry]

Like one sec

Let me check

[sick walrus]

,rccw

[hearty dust]

btw this is the part im still unsatisfied with

[ionic ferry]

Okay that probably wouldn't work

[hearty dust]

these seem to be completely different angle differences

which is why im still struggling to see why they are equal

[ionic ferry]

Well, draw the vector 2 to equal lengths on both sides

[hearty dust]

?

ohhh

i get it

[ionic ferry]

Why can't the vector 2 exist both above and below vector 1

[hearty dust]

oooh

wait so the angle that we get from that one cos formula

is always taking the smaller angle

??

[ionic ferry]

Sorry, which cos formula?

[hearty dust]

AxB = mag a b cos theta

smth like this

the cross product one

[ionic ferry]

That takes sin(theta) though

[hearty dust]

sorry i meant dot product

A.B = mag a b cos theta

[ionic ferry]

Yeah this one

What about it?

[hearty dust]

.

[ionic ferry]

Well basically you see

Ahhh one sec

The principal domain of sinx is -pi/2 to pi/2 yeah?

[hearty dust]

principal domain?

[ionic ferry]

Uhhh how do I describe it

Well basically the domain inside which we input values into sinx

Similarily, prinicipal domain of cosx is 0 to pi

[hearty dust]

wut cant we put anything into sin x?

or am i tripping

[ionic ferry]

I mean we can

That's why IDK how to explain it

Well basically the basic domain

[hearty dust]

uhh

[ionic ferry]

Okay see

y = arcsin(x) gives a graph only from -pi/2 to pi/2

[hearty dust]

okay

[ionic ferry]

Similarily, y = arccos(x) gives a graph only from 0 to pi

So like, they are the principal domains

IDK how else to explain it, but it is something

[hearty dust]

mhm icic

😭

[ionic ferry]

Like you try to bring value into these domains before solving sin and cos

[hearty dust]

ah

[ionic ferry]

So 123.7 is outside principal domain of sin but is in the principal domain of cos

So we'll use that for dot product

And -56.3 is inside principal domain of sin but is out of the principal domain of cos

So we'll use that for cross product

[hearty dust]

oh ok

[ionic ferry]

Also you can wait here for a helper who could explain better

[hearty dust]

nah i understood the important thing earlier so its all good

thanks bro

.close

[marsh citrus]

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[still temple]

hi all i have this problem here

[still temple]

i know thew angle theta is 75 deg

and im looking for the distance between H and G

im really stuck tho i just cant seem to make any progress

each floor is at 3.048m from each other

and it has to be floor 5, 6 or 7

[glad hornet]

Could you give the full question

[still temple]

its several documents but this is all the information im given

the image is the question

sorry

[glad hornet]

is g on ground

[still temple]

yea

its a shape sort of like this

[glad hornet]

y and w also on ground right

[still temple]

yea

this is image from online not the course

it took me like 45 mins of staring at it to realize it was all on the same level just 3D

[maiden edge]

4.645?

[still temple]

for?

GH?

[maiden edge]

yes?

idk not sure

[still temple]

not possible :(

[maiden edge]

:(

[still temple]

thanks tho

i think i also stumbled on that number earler

[maiden edge]

lmaooo

[still temple]

5 * sqr(2)?

[glad hornet]

wheres h at

[maiden edge]

whats theta tho

[still temple]

dont know

[maiden edge]

HYG?

[still temple]

theta is 75

HYG = 75

[maiden edge]

no like angle between

[still temple]

yea 75

pic not scaled

[maiden edge]

oh wait

[still temple]

or 5pi/12 is what im given

[maiden edge]

its 3d tf

[still temple]

yea

exactly

[maiden edge]

where did the 4 come from?

is it given

[still temple]

from this? no this is just an example sorry

like same "shape"

cause i also could not see the 3D at first

i keep getting 26.4m but this not possible either :/

[maiden edge]

ygw is 90 right

[still temple]

not necessarily

i tried for that and thats how i get final height of 26.4

which is stil not possible

ygw could be anything less than 180

literally any value is possible right

theres an infinite n of solutions here

well

3 solutions

5 * 3.048, 6 * 3.048 or 7 * 3.048

[maiden edge]

the answer is 33 right

[still temple]

no

[maiden edge]

?

[still temple]

needs to be one of these

+-3.048

[maiden edge]

im getting 7 * 3.7

[still temple]

hmm yea might be it

how did u get that?

[maiden edge]

simple pyth

[still temple]

a

[maiden edge]

trigno*

chose ygw as 90

got yg from that

then applied tan 45 = p/b

[still temple]

i get 7.07 for yg

[maiden edge]

same

[still temple]

so height of 26.4 right

out of range :/

but also cant assume YGW is 90

[maiden edge]

the theta isnt making sense to me tbh\

[still temple]

y not?

[maiden edge]

cant visualize it :(

[still temple]

:(

ive written out a proof of all the solutions being possible without having the value of ygw

so i will talk with my prof about it

thank u for ur efforts @maiden edge

.close

[marsh citrus]

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[finite forum]

for b

why is it C(6, 2) · C(4, 2) = 90

I did P(6, 3) * 2

[stoic saddle]

what is your reasoning for P(6,3) * 2

[finite forum]

6 slots, 3 different commericals, the order doesn't matter, each is shown twice so * 2 the permutations?

[stoic saddle]

uhh ok so it's just a leap of logic huh

[finite forum]

idk i guess

[stoic saddle]

C(6,2) C(4,2) is reasoned as follows:
C(6,2) ways to pick which two of six slots commercial A goes in
C(4,2) ways to pick which two of the remaining four slots commercial B goes in
the remaining two are filled with commercial C

each is shown twice so * 2 the permutations?
this is uhhhhhhh nonsense.

[finite forum]

so you just multiply those together

[finite forum]

yeah i agree

[finite forum]

and you don't calculate C because it would be division by 0

[stoic saddle]

??

what.

where is the division by 0

do you mean C(2,2)?

C(2,2) is 1.

[finite forum]

yes

[stoic saddle]

and also there isn't any division by 0 anyway,

because 0! is 1

[finite forum]

yeah okay i tripped up for a second

that makes sense

i was wondering why C(2,2) wasn't calculated but it's just 1

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[rare owl]

how did we determine the range of alpha? and i seriously dont get how we did the second half of this question, basically everything after the cosine law. can someone explain?

[hexed junco]

Sum of a triangle =180, all angles are positive
=> angle C and angle A must add to less than 180
=>60 +2a <180

[rare owl]

ohh right ty

i thought of that too but didnt think of setting up an inequality like that for some reason so i js kept going in circles lmao

[hexed junco]

Whats the next part youre stuck at

[rare owl]

i think i got it actually

it was this part

but ig i can see how it works now

[hexed junco]

Ight cool👍

[rare owl]

.close

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[toxic terrace]

Is this a valid proof?

[cunning fiber]

I'd argue this is moreso because multiplication of numbers is commutative

[toxic terrace]

that's true

[cunning fiber]

oh unless you're transposing A^T to get A and A to get A^T

eh should be fine then

[toxic terrace]

yeah I am, but your statement is also true

[cunning fiber]

maybe make $(A^T)^T=A$ more explicit if you're going that route though

[elfin berry]

Civil Service Pigeon

[cunning fiber]

since you're so detailed with everything else

might as well be consistent

[cunning fiber]

[toxic terrace]

thanks pigeon!

[cunning fiber]

[cunning fiber]

!done

[marsh citrus]

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[cunning fiber]

.solved

[marsh citrus]

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[celest plaza]

I am studying ODEs and I have to specifically use methods to solve first order but higher degree differential equations to solve the equation

p^3 - 4xyp + 8y^2 = 0

where p = dy/dx

(I apologise for not writing in latex)

I am facing problems in being able to factorise the cubic polynomial and then solving it further, I tried solving for x but that did not work out

[marsh citrus]

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

@celest plaza Has your question been resolved?

[celest plaza]

<@&286206848099549185>

[hoary sapphire]

@celest plaza still open?

[celest plaza]

yes

[hoary sapphire]

since you know it's cubic try $y = x^3 t (x)$

[elfin berry]

ben

[celest plaza]

can you please explain it once? I am not familiar with this method or technique, but even if I write it like this, then what?

[marsh citrus]

@celest plaza Has your question been resolved?

[marsh citrus]

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[loud coral]

I do not understand how to solve this at all. Would appreciate hel

[tardy meteor]

which one do u need help with

[loud coral]

i mean, is it just the areas added up?

each fill in on the right

[peak gate]

for example $A(0) = \int_{0}^{0} f(t) dt$

[elfin berry]

nilo

[peak gate]

use the graph given and the shaded areas to find each one

[loud coral]

Also this

No clue

so for the first one, the accumulation to 0 is 0, to a is 9, to b is 19, and to c is 34. or are 0-a and b-c negative?

[peak gate]

0 to a and b to c would be negative because the area is under the x-axis

u got it tho

[loud coral]

okay, thank you

[peak gate]

like from 0 to b

[loud coral]

hold on, i think i can do the second one, i am doubting myself

[peak gate]

it would be -9+10

[loud coral]

0-b

yes

1

Here are my answers. For the bottom section, the A confuses me

I understand it’s a function, but does it mean area? If so, would that mean that the c prompt is increasing, and the d prompt is flat? What would that mean for the last two?

does A(x) mean area?\

[marsh citrus]

@loud coral Has your question been resolved?

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[unique timber]

Hello I'm confused on what to do next for b) and would like some pointers please

[marsh citrus]

@unique timber Has your question been resolved?

[cedar plover]

Have you tried $r=3$?

[elfin berry]

Gol D Roger

[unique timber]

no, how did you get r=3?

[cedar plover]

You distribute the $1-x^3$ and use the same idea you used in the earlier exercise

[elfin berry]

Gol D Roger

[unique timber]

Got it! Thank you so much

.close

[marsh citrus]

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[nova idol]

P is a randomly chosen dot that can be inside or outside of the rectangle ABCD

How can I prove the equation

[marsh citrus]

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[limber hearth]

!msgdel

[marsh citrus]

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[marsh citrus]

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[nova idol]

why ?

[marsh citrus]

The original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.) Please claim a new channel, and don't delete the first message of any future channel you claim.

[nova idol]

alr

.close

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[chilly flicker]

I need to find the value of magnitude t1 and t2 but I have no idea what to do now

[marsh citrus]

@chilly flicker Has your question been resolved?

[marsh citrus]

@chilly flicker Has your question been resolved?

[chilly flicker]

here’s some preview with the q but idk if it’s very relevant

[cunning fiber]

This is a system of linear equations

you can either do the standard substitution/elimination (ex. multiply the second equation by sqrt 3 and add the two equations)

or nuke it with cramer's rule

[chilly flicker]

ooh okay i’ll attempt solving it rn

i do wanna make sure i got the right answer tho cus im not confident in my arithmetic skills 😭

[cunning fiber]

you can always substitute your solution back into both equations to see if it works

[chilly flicker]

i just checked and it does omd

thank you!!

[cunning fiber]

[marsh citrus]

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[tiny bear]

Let $X$ be a set. Define $$\tau_c = { A \subseteq X : X \smallsetminus A \text{ is finite} }$$ $(X, \tau_c)$ is a topological space here. If $X$ is infinite, then $(X, \tau_c)$ is not a $T_2$ topological space

[elfin berry]

Halex

[tiny bear]

Any example?

I know X is finite then it is T2 space

[elfin cairn]

remind what is T2

haussdorf?

[tiny bear]

Yes

House Door

[elfin cairn]

the intersection of any two non-empty open sets is non-empty

thats it no?

[indigo nest]

What no

Given any two disjoint open sets there is an open set disjoint from both of them

[elfin cairn]

thats not haussdorf

[indigo nest]

Nvm no

Given any two points

There are disjoint open neighbourhoods containing each of rhem

That's hausdorff

[elfin cairn]

yeah

[elfin cairn]

it can't be hausdorff for this reason

[indigo nest]

Ah I thought you were defining hausdorff lmao

[elfin cairn]

oh xD

[marsh citrus]

@tiny bear Has your question been resolved?

[tiny bear]

What

Could you elaborate

[elfin cairn]

what Xavier said is the definition of hausdorff

so if they were two open neighborhoods of two different points, these neighborhoods will always have non-empty intersection so they cannot be disjoint

[marsh citrus]

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[granite dove]

Yo why when we proof a implication we must assume that P is true
What if it was false

[fervent rampart]

the implication just says "if P is true, then Q is true". if P is actually false then it says nothing about whether Q is true, so you can think of it as saying "if P is true, then Q is true, and if P is false, then Q may or may not be true idk"

[ripe carbon]

if i say "if I become president I will cut tax" but I lose the election, you have no reason to expect me to cut tax because I am not president

so because P was false we have no expetation of Q, therefore the whole statement is true

[marsh citrus]

@granite dove Has your question been resolved?

[devout mauve]

in other words, we don't care what happens if P is false so we dont have to talk about that case

[marsh citrus]

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[granite dove]

My second question

Why the proposition of direct proof method should be like that

[marsh citrus]

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[granite dove]

.

[granite dove]

That’s wonderful explain thank you

[ripe carbon]

$P \to Q \equiv T$

[elfin berry]

Player_X_YT

[ripe carbon]

so either P is false or P and Q are true

what can we do with this?

[granite dove]

What

[ripe carbon]

it says "given the implication that P -> Q is true"

[granite dove]

I mean why the proposition like that
P and (P implies Q) Implies Q

Why not directly P implies Q

[ripe carbon]

to see if you can tell they are equivalent, which you can I see

[marsh citrus]

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[boreal rock]

How many four letter words can be formed with or without meaning from the letters of the word
'EXAMINATION'

[marsh citrus]

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[old wind]

i'm not sure how to go about starting this. can someone help me?

[spark otter]

I'm guessing you just need to show the definition of inclusion

[old wind]

i think so but i feel like i'm getting tripped up bc of gamma and delta here

[spark otter]

Start writing the usual proof

You'll see that it's easier than you think

[old wind]

so $x \in A_\alpha$ for all $\alpha \in \Delta$. i'm assuming we can do something with $\alpha$ then since $\Gamma \subseteq \Delta$?

[elfin berry]

ushygushytoes

[spark otter]

Well yeah... you want to prove $x \in A_\alpha$ for all $\alpha \in \Gamma$

[elfin berry]

Raphaelisius Maximus MMIII

[spark otter]

And so using your inclusion...

[old wind]

i'm feeling a little hesitant, but could we choose an $\alpha$ such that $\alpha \in \Gamma$ as well?

[elfin berry]

ushygushytoes

[compact crag]

Determine
Where f(x)is increasing and/or decreasing

[old wind]

sir i'm still using the channel for help 😭

[still temple]

i can help u

if u make a new channel and tag me

[marsh citrus]

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[old wind]

.close

[marsh citrus]

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[sturdy python]

im confused how am i supposed to graph f(x) = 2 squareroot x + 9 - 8

[sturdy python]

the summit is -9,-8

but how do i continue

its a square root function

[quick kindle]

2sqrt(x+9) - 8?

[sturdy python]

yes

[quick kindle]

do u know how the graph of sqrt(x) looks like?

u just need to transform it

[sturdy python]

yeah but i dont have any x or y

i just have h,k

[marsh citrus]

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[north otter]

i dont get this, can someone explain

[main idol]

do you know what a linear transformation is

it needs to satisfy two or three properties depending on how it was taught to you

[static quarry]

one way to approach this is to recognize that $L$ contains the origin, so you could equally well write it as just $$\left{t\begin{bmatrix}2 \ 1\end{bmatrix} : t \in \mathbb R\right}$$

[elfin berry]

Bungo

[north otter]

yes

[north otter]

uhh

i dont understand

[main idol]

set s = t + 4 and find L in terms of s

[north otter]

whu/..

why...

[main idol]

to understand this

[main idol]

you just need to verify this for the proposed T

[still temple]

hey

where do i go to ask for hel

p

[north otter]

im still so confused..

[main idol]

you're gonna need to put in more effort then.

form a question or show some calculation

[marsh citrus]

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[full rampart]

This is the original question:

I'm well-aware that this could be solved with trigonometry, but I would prefer to have a more constructive proof.

Like "langley's adventitious angles" problems.

Well, I would like some tips on how I should continue, but for now my main plan to prove the collinearity of F, D, and B.

If you have any better idea, please ping me.

[marsh citrus]

@full rampart Has your question been resolved?

[full rampart]

<@&286206848099549185> You guys taking 3 business days to read my crappy hand writing. 😞

[marsh citrus]

@full rampart Has your question been resolved?

[woeful whale]

CF=CB radius
→ ang F = ang FBC (let =x)
ang F + ang FBC + ang CBE + ang BEC = 180°
x+x+80°+80° = 180
x=10°

ang ABD = ang ABC-ang FBC
= 80°-10° = 70°

ang ADB = 180° - ang DAB - ang ABD = 30°

but this only works if you have proven that CF = CB

[full rampart]

I'd thought of the same way but ang FBC = ang DBC is not given.

[hexed junco]

F,D and B arent colinear in this construction

[full rampart]

They are.

[full rampart]

And it is what I'm trying to gain insights on.

[hexed junco]

Well what i mean is its not given nor proven yet

[full rampart]

They are supposed to be collinear, but I'm trying to prove it.

Ohh, I get what you mean.

Yeah the earlier proof was missing that.

But thanks tho. @woeful whale

[marsh citrus]

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[fickle shell]

I think I know how to do the question, but I am still learning how to 'write' the proof if that makes sense

Is this correct? Any mistakes? Anything you would add or take away to improve it slightly?

[stoic saddle]

the statement is not symmetric
the relation is not symmetric, rather.

also your curly braces look a bit odd

aside from this your proof is... mostly fine, i don't really have anything to add besides that it has a general air of "someone new to proof-writing wrote this"

[fickle shell]

Alright thanks!! These were exactly the things I wanted to know haha

❤️

.close

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[agile moat]

I thought I understood how to solve this, but apparently I do not.

My Process was:

(-(b)/(2a)) for X (I got 3)

Then I solved for Y

2(3)^2-(12)(3)+14
18-36+14
-14

Original Answer: (3,-14)

[tidal raven]

Its correct

[rancid geode]

y coor

,calc 2(3)^2 - 12(3) + 14

[elfin berry]

Result:

-4

[paper raptor]

check the math on 18-36+14 again

that does not equal -14

[agile moat]

good lord xD thank you

.close

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[craggy pelican]

guys

[craggy pelican]

do u think it's posible to calculate (1/2)!

[devout mauve]

sure, its sqrt(pi)/2

if we use the gamma function to extend the factorial

[craggy pelican]

what is gamma function?

[devout mauve]

a way to extend the factorial to other numbers

[craggy pelican]

you mean make a graph of function x! and then find (1/2)!

or what?

[devout mauve]

make a graph of x! for positive integers x and then connect those points "nicely"

[craggy pelican]

ok

i had this idea before

but how to connect them in nice way??

hello?

[devout mauve]

well if I write down the formula for Gamma thats probably not very helpful to you

[charred egret]

Gamma extension doesn't work at non positive integers

tho

[devout mauve]

there are several ways to extend the factorial

the Gamma function is in a certain way the most natural one

[devout mauve]

well no extension of the factorial can work for negative integers

if you want to keep n!=n*(n-1)!

[marsh citrus]

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[vague raven]

how do i prove this is divergent or convergent

[vague raven]

what method do i use

[noble ember]

hi

[knotty trellis]

compare it with a different (larger) sequence, which has the same limit

do you know what sequence it looks similar to?

[obtuse umbra]

of course you graph

[silent ledge]

I believe this converges.

I think you can compare this to the Basel sum.

[knotty trellis]

That's an overcomplication honestly

this is not even a sum

[silent ledge]

wdym

Isn't it 1/1^2 + 1/2^2 + 1/3^2 + .......?

[knotty trellis]

thats basel sum

[knotty trellis]

this is just a sequence

4 / 10, 16 / 82, ...

[silent ledge]

oh, it's a sequence

[knotty trellis]

and even if it was a sum, i'd probably use geometric instead of basel

[marsh citrus]

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[simple briar]

x√9-4√5 < (this but with a line under) 3√5-6
x is lart of N with a star on top

[simple briar]

Part

Whats geogebra

[cunning fiber]

!occupied

[simple briar]

Really?

[marsh citrus]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[calm harbor]

$x\sqrt{9 - 4\sqrt5} \le 3\sqrt5 -6$

I've pinged yoy at help-19

[pine star]

thx

[simple briar]

Everything after x is under the square root

[elfin berry]

🌙 ЅκψΑиdΝιɡħτ

[calm harbor]

like this?

[simple briar]

Yes

[tawdry rampart]

What does lart with star on top mean?

[simple briar]

Part of N, i dont know how it is said in english but if x is part of N it means it is positive and whole

And with star it means it doesnt contain 0

[tawdry rampart]

Ah just N works

[simple briar]

okay

[tawdry rampart]

N means natural do 1, 2, 3 ...

[simple briar]

Yeah

I dont really understand the square root part with the 9 and 4√5

[tawdry rampart]

Do you need help singing for x?

[simple briar]

Wait i dont know what it is called in english first

How do you call something like this (-3;4]

( meaning it doesnt contain the number and [ meaning it contains the number

[tawdry rampart]

Intervals

What language do you speak?

[simple briar]

I think thats what they re called

[simple briar]

Romanian

They re called intervale

[tawdry rampart]

Oh

[simple briar]

And i need to find the interval x is part of

[tawdry rampart]

Can you use a calculator?

[simple briar]

I tried photo math but it doesnt really explain the square root part

[viscid violet]

√(9-4√5) =√5-2

[tawdry rampart]

Are you supposed to calculate the the thing in the intervals

Like with decimal places?

[viscid violet]

Now x(√5-2)<=3√5-6

x<= (3√5-6)/(√5-2)
x<=3(√5-2)/(√5-2)
x<= 3
x belongs to (-inf,3]

[viscid violet]

@simple briar

[tawdry rampart]

That is correct

But don't hand out answers

[marsh citrus]

@simple briar Has your question been resolved?

[marsh citrus]

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[finite forum]

dont get this

[marsh citrus]

@finite forum Has your question been resolved?

[finite forum]

<@&286206848099549185>

[slim shard]

,tex
\begin{align*}
\cos x -2x-\frac 12&=0\
\cos x&=2x + \frac12
\end{align*}

[slim shard]

you can draw the line $y=2x + \frac{1}{2}$ on the graph

each intersection between this line and the curve in Diagram 1 will show a real root of x

[finite forum]

ah

i get it

.close

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[tawdry rampart]

. @earnest canopy do you need help in opening a new channel?

[earnest canopy]

Nah bro, I figured that question

[earnest canopy]

It was actually easy

[tawdry rampart]

Nice

Well you opened this one

[earnest canopy]

?

Do you play chess @tawdry rampart

[main idol]

!done

[marsh citrus]

If you are done with this channel, please mark your problem as solved by typing .close

[tawdry rampart]

I do

[earnest canopy]

Whats your rating?

Mine is 2200

[tawdry rampart]

Li chess or chess.com?

[earnest canopy]

Chess.com

[tawdry rampart]

WHAT

[earnest canopy]

Its lower on lichess 😂

I play bullet tho

Sometimes blitz

[tawdry rampart]

Still bro

2200 is crazy

Mine is around 1000-1110

[earnest canopy]

How much time have you played?

Since how long*

[tawdry rampart]

I have been playing for a long time

But not professionally

[earnest canopy]

Years or months?

[novel juniper]

Okay, please don't use a channel for casual talk too much

[tawdry rampart]

My father taught me

[novel juniper]

#discussion exists

[earnest canopy]

Same lol

Alright sir

[tawdry rampart]

Like 6-7 years ago

Kk

Maybe more

Lemme count

.close

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[craggy pelican]

guys

[craggy pelican]

can you give me a question on sets of numbers please?

[novel juniper]

What kind of questions

I can give you something like : Show $\abs{\N} = \abs{\Q}$

[elfin berry]

wai

[novel juniper]

Or simpler?

[craggy pelican]

simpler please because this topic is new to me

[novel juniper]

okay, what have you done so far

[craggy pelican]

i'd like a question on operations on sets of numbers with index

[novel juniper]

Index can be over N ?

or finite

( I ask as I'll change my question based on that)

Like can you find $\bigcap_{i=1}^{\infty} [0,\frac{1}{i}]$

[elfin berry]

wai

[craggy pelican]

i'll try it

ty

[novel juniper]

cool

If this is too hard , lmk

just ping me, as I'll be solving stuff for my course

[craggy pelican]

ok

[craggy pelican]

=∅

[novel juniper]

try again

[craggy pelican]

=0

[novel juniper]

It is 0, can you prove it

[craggy pelican]

in all of sets of this set u can find 0 and no other numbers intersects cuz in 1/i we can always find a bigger number for i which at the result will give us smaller number so there is only 0 intersects in all sets

and 0 intersects cuz the numbers of every set in this set is 0 =< x =< 1/i so we can find 0 in every set

[marsh citrus]

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[marsh citrus]

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[void iron]

hopefully this is legible, i think this ks right solution?

[cunning fiber]

,w (x^3+y) dx - x dy = 0

[elfin berry]

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[void iron]

so where did i go wrong then 😭

[lone pecan]

?? this is the solution??

[void iron]

yeah that's how ive been taugt to solve it

[lone pecan]

wa

sorry , can you if possible rewrite your process

and share it over

or if you want another method to tackle the question first

we can do both
finding the mistake in your method first , then looking at easier alternatives

[void iron]

dan

dang

[cunning fiber]

making it exact was fine

[void iron]

isn't the same equation, but it's pretty much the same process i did to that question

[cunning fiber]

I don't know what happened after that

$f_x=x+\frac{y}{x^2}$, $f_y=-\frac{1}{x}$

[elfin berry]

Civil Service Pigeon

[void iron]

can you crop what you're confused about

[cunning fiber]

The idea is that you can integrate $f_x$ with respect to $x$ to get $f$, then differentiate that to get $f_y$.

[elfin berry]

Civil Service Pigeon

[cunning fiber]

It looks like you're trying to do some kind of "N without y" business

actually hold on

you didn't even integrate the entirety of M with respect to x

[void iron]

yeah that's pretty much what's going on here

[lone pecan]

cant we just divide it with x^2 directly

[cunning fiber]

I think the idea is to practice the actual algorithm

I mean they got there anyway

with the algorithm

[lone pecan]

ohhh they wanna make them practice with this first

[cunning fiber]

in hindsight

actually

nevermind I have no clue what you did

[void iron]

idk what i'm doing wrong either man 😭

threw it into chat gpt as a last ditch effort and idfk what it gave me

[cunning fiber]

$\left(x+\frac{y}{x^2} \right) \dd{x}-\frac{1}{x} \dd{y}=0$

[elfin berry]

Civil Service Pigeon

[cunning fiber]

what did you identify as M and N here anyway

[void iron]

WAIT

oh mh god

i think i know what i did wrong

[cunning fiber]

oh wait did you use M_y instead of M

[void iron]

....yep

[cunning fiber]

rip

[void iron]

AAAAAAAAA

[cunning fiber]

[void iron]

thank you everyone!!

[novel juniper]

Yes

[marsh citrus]

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[marsh citrus]

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[celest herald]

What is tukey method

[marsh citrus]

@celest herald Has your question been resolved?

[marsh citrus]

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[austere scroll]

So it gives the equation f=ma

To get the mass I thought you would just do f/a = m and input any values in from the graph into the equation and I got the answer right because it was similar to 3.

The book says that you can get acceleration by itself by doing a=f/m which is somehow the inverse of the slope but that’s what I don’t understand. What I’m trying to ask is the way to get the specific answer

[quick kindle]

do u mean to say the mass is the inverse of the slope?

[austere scroll]

Sorry I wasn’t reading directly from the book— it says to find a by itself a=1/m*f and says the slope of the stream line is inverse of the mass of the object

I don’t get how that helps us find the answer however

[quick kindle]

u dont need to find a. ur goal is to find m which is precisely 1/slope

can u find the slope of the line?

[austere scroll]

Okay so I have m=f/a and slope=a/f but I’m struggling to find a connection. how would I use reciprocal rule?

[quick kindle]

slope = a/f but guess what! 1/slope = f/a

[austere scroll]

So if you put the constant in the denominator you can just flip the other side?

[quick kindle]

the way fractions work is if u have
a/b = c
and you do 1/c then you get b/a.
to see this, you can try doing 1/(a/b)
and see that this amounts to b*(1/a)

[modern solar]

i can see you’re trying to understand the relationship for those 3 but just incase i’m throwing this triangle here

[marsh citrus]

@austere scroll Has your question been resolved?

[austere scroll]

Ok so I’ve spent forever on this and I got that u take the reciprocal of slope=a/f which is 1/slope and we know slope is a/f so it’s just 1/a/f and then we can flip it using the divide to multiply rule to get 1/slope = f/a which is just mass and then slope is 3-2/10-6 which is just .25 so it’s 1/slope or 1/.25=4 so mass is 4

[austere scroll]

Thank you!!

[austere scroll]

My final question is how I would spend only like a minute on this question rather than like 15. Is that even possible? It’s an SAT question which is like a minute per question

[quick kindle]

just have a solid understanding of the fundamental equation and what the slope represents

[austere scroll]

Okay well thank you so much for your help

I appreciate it

[marsh citrus]

@austere scroll Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[rare owl]

can someone tell me if this is correcttt im missing a solution

[proud basin]

!xy please

[marsh citrus]

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.

[proud basin]

theres infinitely many solutions to this

[rare owl]

oh sorry i meant another solution is x=-a+b+c

a, b, c are js any constants im assuming

[oak oxide]

Yes it's , what's the problem

[rare owl]

i do get the solution when i use the quadratic formula but

from liek my first attempt

the method i shared above

im missing that solution

so i wanted to know where i messed up :p

[oak oxide]

Here you didn't use quadratic formula

You use the fact that f(x)=f(a) => x=a

Which is true but not cover all the cases

[rare owl]

why is thatt

i thought u only missed solutions if u divided the roots or smth 😭

[oak oxide]

,w graph x^2

Aw

[elfin berry]

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[oak oxide]

Quadratic looks like this, it's symmetric with respect to x=-b/2a ( in form ax^2+bx+c=0)

[sick walrus]

or rather, these two pairs?

[oak oxide]

x-c-b=a ? um... And x=a-c-b...

[sick walrus]

that is for the OP to think about.

[oak oxide]

But then x=a+b+c and x=a-b-c...

[rare owl]

are you saying there’s 4 pairs?

im so heartbroken rn this was supposed to be an easy question 😭

[sick walrus]

there will be extraneous solutions, of course.

[rare owl]

how do i identify them

i still didnt get the other root yk

maybe the way i solved it is not correct?

[sick walrus]

substitute them back into the original equation.

I also would not have done it this way.

[rare owl]

yeah fairs i was experimenting with this question a lil

i did solve it using a more

[sick walrus]

in fact, you seem to implicitly assume that just from pq = rs, p = r or q = s.

[rare owl]

conventional way

and i got the answer

[sick walrus]

this is very false for fairly straightforward reasons, and is thus not allowed.

[rare owl]

THERES FOUR OF THEM ☹️

[oak oxide]

That's no right, pq=rs then p=r and q=s

[rare owl]

ig theres a repeated root but

whos doing all that

[sick walrus]

2(3) = 6(1).

[oak oxide]

2=1?

[rare owl]

YES thats what i was thinking

where i messed up

[oak oxide]

Or 2=6?

[sick walrus]

???

[sick walrus]

why did you think I mentioned this?

[oak oxide]

You said p•q=r•s then p=r or q=s right?

[sick walrus]

I said OP assumed that.

[oak oxide]

Ohhh

[rare owl]

should i js avoid this way of solving altogether?

[oak oxide]

[sick walrus]

the better way is to pull everything to the left.

[rare owl]

alrightt ty for the help tho

.close

[marsh citrus]

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[oak oxide]

We can just uhh, use symmetrical...

[halcyon elk]

so..? what are they? all of the possibilites i tried to consider give me x=a.

[oak oxide]

x=a is roots then x-(b+c)/2=(b+c)/2 - a