help-33

[distant lichen]

question 49

[distant lichen]

i have found horizontal asymptote which is y=2

now im stuck at the vertical one

[fickle slate]

for which number

[distant lichen]

question 49

i have factorised the whole thing to:
((x+1)(2x-1))/(x+2)(x-1)

[wary kite]

set the denominator equal to zero

and make sure the numerator isn’t also zero at that point

[distant lichen]

and what do i do after that

[wary kite]

your vertical asymptotes are equations of the form x = k

that’s all you need

[distant lichen]

i think my vertical asymptotes are -2 and 1

based on my factorisation

[wary kite]

but make sure you write

x =

[distant lichen]

yeah i know

[wary kite]

id cook you in 1s

[distant lichen]

wdym?

[wary kite]

rl

[distant lichen]

how do yk i play rl?

[wary kite]

you’re in the rl server

[distant lichen]

oh

so you just assume i play rl bc im in the server?

[wary kite]

what’s your rank

[wary kite]

yes, why else would you be in the server

[distant lichen]

plat 3

[distant lichen]

idk

[wary kite]

yea you’re cooked

it’s all good man

[distant lichen]

dawg i just play for fun

[wary kite]

💀

it’s alright

i quit like 3 years ago

i played for like 2 weeks in june though

[distant lichen]

oh i havent played in 1 year

[wary kite]

i was gc2

in 2s

gc1 in 1s and 3s though

[distant lichen]

my friend once carried me to diamond he was gc and i just fumbled my ranks back to plat

[wary kite]

sorta how that works

i used to do the same with my friends

[distant lichen]

btw whats ur pfp who is the guy there?

philippines

great

[wary kite]

what

[wary kite]

that’s me bro

💯

[distant lichen]

kaue reacted to my message with philippines flag

[distant lichen]

sure bud

[wary kite]

kaue is from the philippines i guess

[wary kite]

it’s just a random picture

[distant lichen]

oh

[wary kite]

it’s not robin

[distant lichen]

i love it

[distant lichen]

fr?

[wary kite]

they need a robin show fr

[distant lichen]

btw im pretty sure i gotta close this channel bc we just occupying it for no reason

!close

lovely

how do i do it 😭

.close

[marsh citrus]

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[marsh citrus]

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[stiff flint]

is it wrong to differentiate

like this

[marsh citrus]

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.close

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[zenith iris]

hallo

[zenith iris]

it's kinda worked in the book

but we dont know if a_k is pos

non negative*

[zenith iris]

so we use this for a_N > 0

and for a_n < 0, just tweak the inequality above so its < 2L + K and a_{k+N} < a_N (2L-K)^k

am i cooking

[still temple]

surely

[zenith iris]

aight thanks

.close

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[distant lichen]

why do we multiply by numerator except that -5 is +5

[lone heart]

Because it's the conjugate

If you did that, the middle terms will cancel

Like (a + b)(a - b) = a^2 + ab - ab - b^2 and the middle terms cancel, so it's a^2 - b^2

[distant lichen]

but isnt the conjugate over the conjugate just equal to 1?

[glass silo]

Multiplying and dividing by said conjugate means you’re not changing the value of the expression (but hopefully get something that’s easier to work with)

[glass silo]

(Which indeed you should find, if after simplifying you apply this in reverse)

[distant lichen]

so basically you are using the conjugate to just have a easier part even though it equals to 1 if divided

[glass silo]

Yep, often “multiplying by 1” and “adding zero” are tricks to get things that are the same but easier to deal with

[distant lichen]

ok got it

its just that i have to get used to these type of exercises since you kinda have to think for a bit which is the best move to make

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[flat sierra]

Hey guys, so I need help with something regarding the gambling world, so if you dont sympathize with this world, then this was my alert 😄

Basically I won money in a bookmaker, and I went through the KYC, but they are rejecting certain documents, documents that are 101% legal. So I thought, well if they don't verify my account (this means I cannot withdraw my funds), maybe I can bet on things that should loose, in this bookmaker, and bet on the contrary on the other bookmaker, and accept a % loss. You know, I'd at least get 90% of my current funds that nothing. Makes sense?

But I'm not sure, I mean, low odds mean higher probability, but I don't wanna stay there, is there something else I can do in order to "transfer" the money from one bookmaker to the other?

Sorry for talking about this, but I need brilliant minds to help me.

Thanks in advance

[crystal lintel]

i’m not sure this is a math question

[flat sierra]

well maybe there's some math that can help me achieve my goal?

[marsh citrus]

@flat sierra Has your question been resolved?

[marsh citrus]

@flat sierra Has your question been resolved?

[sleek lake]

i didn't get your whole picture yet but if you're just trying to lose as much as possible in a short time, and winning is bad

that's just identical to normal gambling

there's no strategy that would appear from trying the opposite

no okay that's not what you're asking

[flat sierra]

I can re-explain

I probably wasnt clear so I can explain again

[sleek lake]

i get it there's a different site and you bet on the same outcome on 2 different sites in opposite direction

[flat sierra]

right so, I wanna lose money in the book that doesnt let me withdraw, and obviously win in the other one

but the probability of winning in the other one has to be way higher

and we need to take into account that each loss in the book that DOES let me withdraw, will have a high impact, since the payout will be less, meaning I'll need to bet more to compensate the bet of the book that doenst let me withdraw

makes sense?

[sleek lake]

there's no obvious way to make it work at least

[flat sierra]

so rip?

[sleek lake]

like you don't value your old account, so the ability to get old account money every time you lose has no value either, and the bets don't influence the outcome

[flat sierra]

well doing nothing isnt acceptable for me

I do understand what you say though

[marsh citrus]

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[flat sierra]

.reopen

[marsh citrus]

✅

[marsh citrus]

@flat sierra Has your question been resolved?

[copper trench]

Who can solve this

[marsh citrus]

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[boreal tinsel]

how to find the radius of the circle encompassing any given polygon?

[boreal tinsel]

for ex. if i have a concave hexagon (of which all the minimum conditions to uniquely determine it are given like length of all sides, and say a reflex angle and 2 other angle between sides) what will be the radius of the circle which encompasses it? (the circle need not be the smallest such or anything, just something that isnt a lengthy formula, and something i can also utilize to calculate the ratio of areas of the polygon to the circle)

[marsh citrus]

@boreal tinsel Has your question been resolved?

[marsh citrus]

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[boreal tinsel]

.reopen

[marsh citrus]

✅

[boreal tinsel]

<@&286206848099549185>

[marsh citrus]

@boreal tinsel Has your question been resolved?

[woven latch]

What's the question?

[boreal tinsel]

.

wait can i ping helpers every 15mins?

<@&286206848099549185>

[obsidian stratus]

find the length from the center of the polygon to the vertex of the polygon

[woven latch]

Total angle around the center of a circle is 2pi.
If it's inscribed within a polygon the angle around the center divides equally into 2pi/n.

[boreal tinsel]

how do you find the center of the polygon exactly?

[obsidian stratus]

draw it out

it becomes very obvious when you have a diagram

if your polygon is inscribed in a circle, it's center is the same as the circle's center

[boreal tinsel]

that is a very non technical and quite unusable approach for say, 173 sides

[boreal tinsel]

how will i even find that circle?

[obsidian stratus]

...

[obsidian stratus]

what even is your question

[boreal tinsel]

.

[obsidian stratus]

are we looking at smth like this

[obsidian stratus]

define "encompassing"

the term we usually use is "inscribed"

[coral path]

ah yes inscribed

geometry my beloved

[woven latch]

No it's the other way around ig circle is inside triangle or square etc

[boreal tinsel]

no?

[obsidian stratus]

ohhh that

ok that is much harder

[boreal tinsel]

this is accurate bruh what

[obsidian stratus]

so what are we doing

[woven latch]

Okay then my bad

[boreal tinsel]

the circle simply contains the polygon

[obsidian stratus]

do you want a circle inside or outside the polygon

[obsidian stratus]

something like this then

[boreal tinsel]

yes

[obsidian stratus]

alright that makes things a lot easier

[coral path]

if the circle is inside a square, does it touch all 4 sides of the square

[boreal tinsel]

ive pretty much stated a good example here

[obsidian stratus]

sometimes, it is a good idea to consider a simple case, and try to figure out how that would change as you go up

[obsidian stratus]

ok "any given polygon" imma assume you dont want just a regular polygon

[boreal tinsel]

obviously

i think yall should read the example i gave up there

[obsidian stratus]

ok that makes it significantly harder

[obsidian stratus]

okok

[boreal tinsel]

(mb if im comin off as rude)

[obsidian stratus]

ok looking at it again, this question is at a much higher level than me lol

sry i cant help

[boreal tinsel]

nah its basic geometry bruv

and the amount of knowns is huge

[obsidian stratus]

what do we know

you said "any polygon"

[boreal tinsel]

but we have minimum knowns to uniquely determine the polygon

if the polygon is n sides, we'll need 2n-3 elements to uniquely determine it

[obsidian stratus]

ye this is beyond me haha

[boreal tinsel]

<@&286206848099549185>

[marsh citrus]

@boreal tinsel Has your question been resolved?

[boreal tinsel]

<@&286206848099549185>

[marsh citrus]

@boreal tinsel Has your question been resolved?

[marsh citrus]

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[clever spade]

I'm having trouble with this solution notationally

[clever spade]

(1-mean)/0.005 = 3.0902

1-mean=0.015451

mean=1-0.015451 = 0.984549

which is of course incorrect and would be a Z score of -3

I'm just wondering if I'm mistaken with my calculations for the solution based on the provided information?

and alternatively how to calculate the answer for this q

[vital oracle]

they made a mistake, they mistook > for a <
what they shouldve done is
Pr(Z > (1 - µ) / 0.005) = 0.999
Pr(Z < (1 - µ) / 0.005) = 0.001
(1 - µ) / 0.005 = -3.0902
µ ≈ 1.015

[clever spade]

thx

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[vital oracle]

np

[marsh citrus]

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[quaint coyote]

Don't understand the last two questions 🥲

[fathom ridge]

global maximum is the largest maximum and global minimum is the smallest minimum

[quaint coyote]

Why none them hmhm

[fathom ridge]

because the domain isn't closed

notice how as x --> 0 your function approaches its max value but the function itself isn't defined at x = 0 so there isn't a maximum value

the closer you get to 0 the larger the value is

[quaint coyote]

Oh ok thx

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[sudden mauve]

Where is the answer 3 coming from? Ther 1st pic is the question, 2nd is my work, and 3rd is my answer

[glossy flint]

When you compute f o g you first comput g(x) and then f(x). But g(x) has different expressions according to the sign of x, right?

So let's take the first case: x < 0

In this branch g(x) is 1, do you agree?

[sudden mauve]

yes

[marsh citrus]

@sudden mauve Has your question been resolved?

[glossy flint]

Alright
So now we have to put 1 into the "x" of f(x)
But which branch do we consider for f?
We have to look at where the number 1 lives
1 is positive, so we take the third branch of f(x) and so f(1) = 1 + 2 = 3
Therefore whenever x < 0, f(g(x)) = f(1) = 3
Hence (f o g) (x) = 3 if x < 0
Now you can do a similar reasoning for the other case, i.e. x ≥ 0

[marsh citrus]

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[feral island]

i got 251.6 but answer sheet says** 251.716**.. not sure if its just different roundings or if i did it incorrectly. I divided the office into two triangles, one of them is right angled triangle and did theorem pythagoras and used heron's formula for both triangle and add them together to get the area.. not sure if theres any other way

[sinful thistle]

yeah that's the way

[elfin berry]

Result:

26.004807247892

[feral island]

oh so my answer is correct but the answer sheet just somehow rounded those numbers to random decimals that idk

[sinful thistle]

huh, weird

[feral island]

idk i rounded to 4 significant figure

thats what the teacher usually told us to do

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[marsh citrus]

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[marsh citrus]

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[proud basin]

find all triples (x,y,p) such that x^5+x^4+1=p^y with x,y being a posigive integer and p being prime

[proud basin]

easy example is (1,1,3)

then idk what

[sinful thistle]

skill where tf do you get all these questions from

so in essence, x^5 + x^4 + 1 is 0 mod p

[proud basin]

my teacher :(

[sinful thistle]

f

[modern sorrel]

You can factor it to $(x^2+x+1)(x^3-x+1)$, \
so there's some a and b such that $a+b=y$ and $x^2+x+1 = p^a$ and $x^3-x+1=p^b$

[elfin berry]

LooseEthics

[proud basin]

factoring factoring..

hm

[boreal tinsel]

bruh the bot is crazy

[proud basin]

for the first one, sqrt(1-4(1-p^a)) must be odd
sqrt(4p^a-3) odd

idk

[modern sorrel]

Did some quick and dirty number crunching in python, the only x up to 20k for which this is a prime power are 1 and 2. So I guess you need to prove that x >= 3 is always composite.

[proud basin]

i mean p^2 is technichally composite

[modern sorrel]

Well yeah. More than one unique prime factor is what I mean.

Observe that for x > 2 the cube polynomial is greater.

Therefore b > a

Therefore $x^2 + x + 1$ would have to be a factor of $x^3 - x + 1$

[elfin berry]

LooseEthics

[modern sorrel]

But they have different roots

I think that's QED

[proud basin]

so like a comtradiction?

[modern sorrel]

Yeah

If we assume a solution exists for x > 2

[proud basin]

makes sense

thank you!

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[marsh citrus]

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[sleek sonnet]

Have to answer if this statement is true or false. On one hand, there always will exist a y thats bigger than x^2 by letting y = x^2 + 1 but on the other hand, x^2 is infinite

[devout mauve]

you have to pick y first and then x^2<y+1 has to hold for all x

[sleek sonnet]

but is it possible to pick a y such that y = infinity + 1

or am i just tripping

a y that is somehow bigger than all integers squared

actually i think i got it

[devout mauve]

infinity is not an integer

[sleek sonnet]

so if you pick y first, there will always be an integer x such that y = x^2 - 1

so the statement is false

ok that makes sense, you just have to remember that you pick y first

[devout mauve]

well no, for example 10=x^2-1 has no integer solution x

[sleek sonnet]

oh true, i would just use an inequality then

[devout mauve]

yes

[sleek sonnet]

gotcha, thank you

[devout mauve]

for example x=y+1 is a good choice

[sleek sonnet]

oh yes thats very simple

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[sweet pawn]

Let n ∈ Z be an arbitrary element in the ring of integers. Establish the following proposition: the parity of the element n induces an isomorphic parity structure upon its second-power mapping, n^2.

[vernal forge]

!status

[marsh citrus]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[vernal forge]

(n is even/odd <=> n^2 is even/odd)

[marsh citrus]

@sweet pawn Has your question been resolved?

[sweet pawn]

ok but how

like i get what you're saying but i don't get what the question is saying exactly

'isomorphic parity structure'?

[marsh citrus]

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[marsh citrus]

@normal atlas Has your question been resolved?

[amber birch]

https://www.desmos.com/calculator/eusnlpmpja

my first thought is to coordinate bash it

see if you can find an expression for R in terms of m, a, k

since you just want the shape you can let m = 1 for convenience

and say a = 2

https://www.toppr.com/ask/en-au/question/a-variable-rectangle-p-q-r-s-has-its-sides-parallel-to-fixed

knew it the question is online

[normal atlas]

That website doesn't work anymore

[amber birch]

basically it's a parabola somehow

ah you can do it by elimination

from the setup, the y-coordinate of R can go to -infinity

so it can't be a circle

and it doesn't follow a straight line

[normal atlas]

I have solved the question like that but I want a solution that doesn't rely on it being an MCQ question

[normal atlas]

Basically a subjective solution

[amber birch]

jesus then you'd have to do a ton of algebra

basically the algebraic setup in the Desmos equation

[normal atlas]

Ok

Ill try it

[marsh citrus]

@normal atlas Has your question been resolved?

[marsh citrus]

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[bleak quartz]

im stupid nvm

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[marsh citrus]

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[quiet anvil]

These are easy mistakes to make, fwiw. 🙂

Not stupid

[marsh citrus]

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[marsh citrus]

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[tender lily]

13

[marsh citrus]

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[last hound]

True?

[marsh citrus]

@last hound Has your question been resolved?

[last hound]

Help 👀

Ugh

[copper thunder]

please write it again

I don't know about this, I haven't reached this contents yet but it will be easier for others to help you if what you upload is tidy

[last hound]

Please minute

[last hound]

Here please

Or guess imma close and open new channel

!close

/close

.close

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[mint radish]

Hello, any germans here that are good in math, I need a explanation for a problem I have right now

[mint radish]

I don't get how to solve these

[marsh citrus]

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[marsh citrus]

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[tall citrus]

How do I achieve 100% effectiveness? I can add or subtract 5% from any category. The effectiveness will only increase when percentage points are distributed correctly. Disregard the budget spending as it isn't relevant.

[marsh citrus]

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@tall citrus Has your question been resolved?

[marsh citrus]

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[silk cave]

Hi, im struggling to understand the part when the book mentions a_0 and a_n. I understand that for an infinite countable set A, one can extract f’ from f by defining f’ with the codomain as ran f, but I am not sure what ‘the least member of a set’ nor ‘the (n+1)st member of a set’ means, since a set is not ordered

[silk cave]

.close

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[void elm]

f is a map into N

which has an order

we can say that f(a_0) is the least element of ran(f) because ran(f) is a subset of N

[marsh citrus]

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[brittle fog]

What did I do wrong?

[limber hearth]

U have to use quotient rule

If $u$ and $v$ are two differentiable functions, and $v \neq 0$ then, $(\frac{u}{v})' = \frac{u'v - uv'}{v^2}$

[elfin berry]

YakuBros

[marsh citrus]

@brittle fog Has your question been resolved?

[brittle fog]

Okay

But what part of what I did was a miss-step?

.close

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[limber hearth]

Third

[limber hearth]

.close

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[void elm]

[brittle fog]

So I should use quotient on the last one I wrote down?

[limber hearth]

Quotient rule on your function

[marsh citrus]

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[vagrant cloak]

Yo how i solve this someone help😭

Pls

[mossy kettle]

which one?

[vagrant cloak]

Both

I just need to understand what im supposed to do cuz i havent been in class

[mossy kettle]

ah well

what would be the angle of a straight line?

[vagrant cloak]

Uh

180?

I think

[mossy kettle]

that's right

so look at number 7

[vagrant cloak]

Ok

[mossy kettle]

what can we use?

[vagrant cloak]

X and 2x

[mossy kettle]

right but how?

you have parallel lines, so they have some angles equal

[vagrant cloak]

Yeah all the 4 angles the same

[mossy kettle]

no

[vagrant cloak]

No i know

Its like

Nvm idk how to say it

But

[mossy kettle]

well there are 2 angles that are the same

[vagrant cloak]

I forgot what to do with x and 2x

And the other 2 also are

[mossy kettle]

and another 2 that are also the same

[vagrant cloak]

Yea

[mossy kettle]

yes

so using this

what can we do?

[vagrant cloak]

How do i find the degree of the angles

[mossy kettle]

okay so, you said that the the straight line is 180

your x and 2x are on that line

[vagrant cloak]

Yes

I need an equation right??

I think

How i do that

[mossy kettle]

yes

so maybe this might help to better visualize

[vagrant cloak]

Yes yes it did

[mossy kettle]

you have the stright line, its 180 degree

and you have two angles,

what must you do?

[vagrant cloak]

Crap idk

Find the angle

[mossy kettle]

you first find the x

then plug the number into x

[vagrant cloak]

How do i find the x

[mossy kettle]

hint: addition

[vagrant cloak]

Hold on

So by adding both x and 2x i get 180 right??

[mossy kettle]

yes

because they are the angles on the straight line

so you have 2x+x=180

solve for x

[vagrant cloak]

OHHHH

60

Then i plug it in right

But into what??

[mossy kettle]

yes

[vagrant cloak]

2x+x??

[mossy kettle]

x=60

so

one angle is just x

the other one is 2x

what does that mean?

[vagrant cloak]

Omg

2x is 120

X is 60

[mossy kettle]

bingo

[vagrant cloak]

Holy shit

You fucking genius

Thanks bro

[mossy kettle]

you have two angles 60 and 120

[vagrant cloak]

Yes

Is that it

Or is there more

[mossy kettle]

nope for 7

that's all

[vagrant cloak]

Okay good i understand 5 now

Thank you so much😭😭😭

.close

[marsh citrus]

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[marsh citrus]

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[boreal tinsel]

if i can determine a 2d figure uniquely, how can i find the longest possible line that lies inside it?

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[boreal tinsel]

.reopen

[marsh citrus]

✅

[boreal tinsel]

<@&286206848099549185>

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[rare mirage]

hel

[rare mirage]

help

idrk how to solve this

i wasnt here

[valid cape]

if triangle ABC is similar to triangle ADE, what happens?

[rare mirage]

idk

it means there is a ratio

scale factor

[valid cape]

okay...which ratio exactly?

[rare mirage]

1/2x+3

and x/2

and that is the answer

right

[valid cape]

what relation do those ratios have?

[rare mirage]

i think i figured it out now

ty for the help

[marsh citrus]

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[young burrow]

Hi may I know how to do this question?

[cloud field]

connect P and R

[marsh citrus]

@young burrow Has your question been resolved?

[young burrow]

And whag else

[cloud field]

find RQ

[young burrow]

Idk pr though?

[cloud field]

thats why you find RQ

a trapezium is just a rectangle minus a triangle

anything you can do with that information

[young burrow]

Confused

😭

[cloud field]

what if you made OPQR a rectangle

[cloud field]

has left the chat

[tardy hatch]

Hi I’m new to this sub is this where I can ask for help

[cloud field]

#❓how-to-get-help

[marsh citrus]

@young burrow Has your question been resolved?

[young burrow]

Ya

[cloud field]

ok now OR and OP have the same length yeah?

[marsh citrus]

@young burrow Has your question been resolved?

[young burrow]

Yes

[cloud field]

so when you make OPQR a rectangle

its length will be 12

and also, the side PQ will have an extended length

PQ is 5, so the extended length will be?

[marsh citrus]

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[marsh citrus]

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[ember surge]

Hi. I want to self-study math.
I need to learn all middle school and high school math in 1,5-2 years. Could you write a list of books to self-study school math please (I prefer books over videos). I want to learn it because I like it and I need to finish school.
L: English or Russian.

[still temple]

Hi there

You might want to ask this question in #resources as these channels are typically meant for problems

I would recommend

https://www.khanacademy.org/math

For all your math related needs

[ember surge]

Oh, I can't get access to it.

[still temple]

I see

If you just want books, you could also follow the books for the IGCSE and A-Level curricula

I mean this is what I used to learn HS maths

https://www.googleadservices.com/pagead/aclk?sa=L&ai=DChcSEwiNr4PEtceJAxVXomYCHf1FIIcYABALGgJzbQ&ae=2&co=1&gclid=CjwKCAiAxKy5BhBbEiwAYiW--zH9Uxra-ghFDiNyrip5JZvHefZt9gS04miGpPCyH3BQT2QZ5kEe0BoCmo8QAvD_BwE&sph=&ohost=www.google.com&cid=CAESVuD2F0wNmbRRDZ_dJmwSgSFRfrac9prLqjjE5Y7MyOFFHaovgRsyqBYW-ZU537HigorzMDEB8r_HqtKaBtY2oRL4bx6AwJlKvHlzmJpVqLlVQtfpYNtz&sig=AOD64_1u9hKqmznmfBj905_LuCr5-LRaVQ&ctype=5&q=&ved=2ahUKEwjbxPzDtceJAxWSzDgGHfMgAZEQwg8oAHoECAYQDA&adurl=

[ember surge]

Hhmm ok

[ember surge]

Thank you

[still temple]

If you want PDFs of these, I can DM you

[ember surge]

Yeah, that would be good

.close

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[finite tusk]

Is this minimum spanning tree correct?

[devout mauve]

you can take the 41 edge instead of the 42

[finite tusk]

But then KL will be diconnected from the graph

oh wait

Thank youuu

.close

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[loud jolt]

i dont know how to solve for x in the original equation

.close

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[eager plank]

for the turning point.. you can derive the fuction and make it equal to 0

so if y= x - ln(2x) then its derivative will be

y’ = 1 - (1/2x)(2)

so you just equal that to zero

[loud jolt]

thank you!

[eager plank]

Welcome!!

you can dm me any doubts you have today😁

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[loud jolt]

i kinda know how to do this?

i just dont remember what changing the co efficient of x^2 and x does

[wise lance]

it do not have something to do directly to co efficients of x and x^2

[stiff rampart]

i would suggest plotting each step down individually for yourself to visualize whats happening

[loud jolt]

oh right thank you .

.close

[marsh citrus]

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[still temple]

Im trying to learn my algebra are there any websites to give questions for me too do?

[vale kite]

what type of problems

there’s always khan academy

[still temple]

um basic stuff im really new

is that free?

[vale kite]

yes it should be

[still temple]

okay thanks

[marsh citrus]

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[elder grotto]

Would this be correct?

[elder grotto]

I'm mostly talking about how angles CAB and KBM are cooresponding and how ABC and BMK are cooresponding but is one of them consecutive interior angles?

And also, wouldn't the congruence postulate be SSS since there's no given angles?

[marsh citrus]

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[sacred ermine]

hi everyone could someone help me with this question i'm unsure on how to determine which isn't a quadratic equation i just get confused if someone could help me that would be nice

[deft rover]

First what you have to know is what a polynomial is.
examples:
f(x) = 1
f(x) = x + 1
f(x) = x^2 + x + 1
f(x) = x^3 + x^2 + x + 1

Do you see the pattern?

[sacred ermine]

omds we haven't learnt that yet

it's not like that it's

simple

we haven't learnt functions to the power of three yet btw

sorry to sound rude

we only do parabolas to the power of two

i'm just confused how u determine this

[deft rover]

that's fine. the important part is that a quadratic has to have a part that has x^2

and it cannot have things like 1/x, or $\sqrt{x}$

[deft rover]

in this list, can you see the option that doesn't follow the requirement?

[elfin berry]

johnseymour20

[sacred ermine]

why can't it

[deft rover]

because then it wouldn't be a quadratic

the graph isn't a quadratic anymore

[sacred ermine]

but like i thought if the thing was positive it doesn't work

as well

the second term

i thought it had to be negative

[deft rover]

could you elaborate?

[sacred ermine]

i thought it had to be negative so like if u have x to the power of two plus 4x isn't that not possible to plug in

i mean graph so therefore it's not a quadratic

[deft rover]

x^2 + 4x is a valid quadratic

[sacred ermine]

how do you know if it's not a valid quadratic

[deft rover]

I gave you requirements before

the important part is that a quadratic has to have a part that has $x^2$ and it cannot have things like 1/x, or $\sqrt{x}$

[elfin berry]

johnseymour20

[sacred ermine]

where can't it have 1/x

so it can't be

x squared + 1/x

[deft rover]

a quadratic: $ax^2 + bx + c$

[elfin berry]

johnseymour20

[deft rover]

a, b, and c can be any number you want

even 0

you see in that template, there is no 1/x or root x

[sacred ermine]

ok...

so

can c be nothing

right

[deft rover]

yes

[sacred ermine]

okay

thank you

i think i get it

so confusing i don't remember my teacher explaining this

at all

[deft rover]

yeah you can't always rely on teachers

[sacred ermine]

i know it's stupid but she didn't actually teach us this

[deft rover]

well now you know

try doing the exercise again to test your understanding

[sacred ermine]

see now i don't get this

[deft rover]

"general form" requires that all the terms be on either side of the equality symbol

like, one of the sides must be 0

this is general form

[sacred ermine]

okay

so then

do we move all of them to the side

[deft rover]

to put something in general form, yes

but here they simply ask you to judge the options as they are, without manipulation

[sacred ermine]

how do we know which one is ring

right

[deft rover]

look for the option that has "0" on one side

[sacred ermine]

oh

so it's a

so do i just say whichever one had zero is it

[deft rover]

yes, one where all the terms are grouped on one side

[sacred ermine]

thank you

you're the best

[deft rover]

no worries, hope you learned something

[sacred ermine]

wait one question

before i close

for this one here

[deft rover]

sure

[sacred ermine]

isn't this reflected in the x axis bc it's negative

but i don't understand how it's narrower than y=x squared

[deft rover]

that would be true if they said "a reflection of y = 4x^2 in the x-axis"

[deft rover]

so the number in front, 4 in this case, tells you how fast the graph increases

0.5x^2 is slower than x^2, so the graph would be wider

4x^2 is faster than x^2

[sacred ermine]

oh got it so u can js ignore the negative sign rly

i have a question if u get an equation y=x squared isn't your coordinate for x just zero?

[deft rover]

yeah, it has no effect on the width of the graph

[deft rover]

wdym coordinate?

[sacred ermine]

like if it's asking you the turning point

isn't it just zero

[deft rover]

yeah

it's called the x-intercept

[sacred ermine]

why is that

why is it zero though

[deft rover]

because x = 0 is where the graph is reflected

the graph reaches a minimum value at x = 0

[sacred ermine]

huh

[deft rover]

and after that, starts increasing

[sacred ermine]

oh okay so it was 2x squared

it would be two the x coordinate

right

[deft rover]

i don't know what level you're at, which makes it hard to know how to explain it

there are a number of ways of looking at it

[sacred ermine]

oh year nine

sorry i forgot to tell you that

[deft rover]

no. (2x)^2 still has an x-intercept of x = 0

[sacred ermine]

but why

[deft rover]

if you plug in x = 0 into y = 2x^2, you would get y = 0

[sacred ermine]

oh okay

[deft rover]

have you learned the quadratic formula?

[sacred ermine]

but i don't get it

[deft rover]

what part?

https://www.desmos.com/calculator

try graphing a few functions on here to get a feel for it

this is for 2x^2. you see all we did was change the steepness, not the point where it changes direction

[sacred ermine]

okay i think i get it if your finding the turning point and you get x squared it's just having a x intercept of zero

[deft rover]

yeah

all you have is one number multiplied by x^2

so of course, if x = 0, then you get $a * 0$, which is 0

[elfin berry]

johnseymour20

[sacred ermine]

i get it we're good

i think

sorru i'll close this now

.close

[marsh citrus]

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[marsh citrus]

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[marsh cipher]

someone help me out rq

[tired siren]

i cant help but i can say that the image is poor quality

if someone that can help may not even understand

oh nvm i had to click and open in browser

[marsh cipher]

wait i could send you the pdf of it

[tired siren]

i mean sure

[marsh cipher]

i don't understand how they find out P.i

[marsh citrus]

@marsh cipher Has your question been resolved?

[marsh cipher]

@tired siren

someone help me out 😭

[stoic escarp]

page 5

they used the formula

$PI = \frac{1}{f(a)} e^{ax}$

[elfin berry]

moik

[stoic escarp]

you can also see in the notes it says if f(a) = 0 then

$PI = \frac{x}{f'(a)}e^{ax}$

[elfin berry]

moik

[stoic escarp]

they also turned the right hand side from hyperbolic into their e form is so they could find out what e^ax to try

you get e^4x, e^2x, e^-4x, e^-2x

so use the formulas for the PI and sub stuff in

reading from those notes

small f is just the function with the D terms

$in this question its D^2 - 2D - 8$

[elfin berry]

moik

[stoic escarp]

ok

hope this helps ping me if it doesnt but i might reply late

also if anyone knows latex why tf my text so big

[marsh citrus]

@marsh cipher Has your question been resolved?

[marsh cipher]

omg it makes so much more sense now thank you

[stoic escarp]

make sure to read your notes lol

any more questions

[marsh citrus]

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[fringe shore]

Am I missing something?

[fringe shore]

Idk what is incorrect

Pls help

[woven latch]

Expansion of series yields
9[1+0.2+0.2^2+0.2^3+....]

[fringe shore]

So a DOES equal 9?

[woven latch]

No

[fringe shore]

Then what is it

Or at least what am I missing

[woven latch]

Oh you need a
So a would be 9/0.2

[fringe shore]

Lemme see

[woven latch]

Take a close look at both the summations

[fringe shore]

Cool its 45

Aah I missed n-1

I see

Thank you

.close

[marsh citrus]

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[still temple]

$$\sum_{n = 1}^\infty 9(0.2)^{n - 1} = \sum_{n = 1}^\infty ar^n$$
$$\sum_{n = 1}^\infty \frac{9(0.2)^{n}}{0.2} =\sum_{n = 1}^\infty ar^n$$
$$\sum_{n = 1}^\infty 45(0.2)^n =\sum_{n = 1}^\infty ar^n$$
hence $a = 45$

[elfin berry]

Edmund Cloudsley

[still temple]

oh lol the answer already got solved

I was busy typing away latex

[fringe shore]

lol

The visualization of latex helps tho

Thx

[still temple]

happy to help in any way

[fringe shore]

.close

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[dry zodiac]

Given 7 known positive integers
that for any 4 of them, their product is divisible by 10. prove that there is a number out of the given 7 that is divisible by 10

[dry zodiac]

how do i prove that one numver out of the 7 is divisible by 10

i have no idea where to start

[broken zealot]

Assume that there are no numbers divisible by 10

What does the given property tell you

[dry zodiac]

wdym

[broken zealot]

What can you say about the numbers

[dry zodiac]

there are 7 of them

and if you pick any 4 of them its divisible by 10

[broken zealot]

Alright, can there be 4 numbers that are not divisible by 5

[dry zodiac]

no

[broken zealot]

Why not

[dry zodiac]

oh

yes i read it wrong

[broken zealot]

Read what wrong

I wasn’t trying to trick you, I was just asking for your reasoning

[dry zodiac]

i thought hat the product

wouldnt be divisible by 5

[broken zealot]

Right

Ok, same question but for 2

[dry zodiac]

yes?

[broken zealot]

It’s possible to have 4 numbers that are not divisible by 2?

[dry zodiac]

idk

[broken zealot]

It’s the same reasoning

The product won’t be divisible by 2 since 2 is prime

So the product won’t be divisible by 10

[dry zodiac]

.close

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[fleet pelican]

https://discord.com/channels/268882317391429632/1303782308142387221

It's an IB Task 2 Question, I need to create a general rule, the above link goes to a post with images of required diagrams and table

[fleet pelican]

<@&286206848099549185>

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[harsh portal]

I need to reverse/renew the following formula:
outcome.float = ((max.float-min.float) × avg.float) + min.float

What I want to do is make a formula, that can calculate the avg.float, needed to make a specific outcome.float. I therefore already know what my max.float and min.float range is and what the outcome.float needs to be, but I don’t know how to make a formula to calculate what avg.float is needed to make my outcome.float.

This is what i've got so far:
0.100007=((0,4-0,1)*avg.float)+0,1

The avgerage float is calculated on 10 different floats

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<@&286206848099549185>

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[terse vine]

This is like rlly simple but i dont get it

I just learned today in class abou linear ones so ik if its 1 its like rlly positive strong and -1 is like strong negative and 0 means just a horizontal line

but how do i know for these ones bruhh

like i thought a) is i) bc it beocmes like a straight line bu apparently its iii) like how

oh

nvm i just realized

the points matter

[red nimbus]

Is this probability? Have to do with correlation?

Like if the curve just doesn't match at all the points then it's very near 0, implying no correlation

and then you can imagine, the better you find a function that describes that correlation the higher that correlation coefficient becomes or whatever it's called

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[terse vine]

tyy

[marsh citrus]

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[marsh citrus]

Please don't occupy multiple help channels.

[main idol]

!1c

[marsh citrus]

Please stick to your channel.

[main idol]

close one of your channels

[marsh citrus]

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[cunning oak]

i need to prove all these questions using AM -GM

[cunning oak]

in the question 6, cant the cubes cancel out

[eager plank]

no, they dont…

[cunning oak]

oh

why not

[eager plank]

Expand it on paper and youll get clarity!

ill do it hold on

here

[cunning oak]

i still dont really get it😭

cant the cube of ai terms combine with the cube of bi terms

[eager plank]

Oh.. umm, there’s whole cubes too😅

that’s give you a whole power 9’s on every term

[cunning oak]

oh

anyways

can i use normal am - gm on this

[eager plank]

I guess… how would you thoguh

[cunning oak]

oof im stuck😭

[cunning oak]

i was gonna use : (a_n + b_n + c_n )/3 >= cubert(a_nb_nc_n)

[eager plank]

but we need the summation right?

[cunning oak]

yeah

im out of ideas💔

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[woven latch]

What have you done for the first one?

Yeah

Do you know dot product?

Okay
The dot product of two vectors is given by
a⋅b = |a||b|cos(theta)
Where theta is the angle between them.

You know what i and j is in this example right?

Okay
What is the angle between the vectors if they're parallel to each other?

Yeah the value of an angle. Is it 0 30 60 ?

Okay
I I need to find another approach as you haven't learnt dot product yet

I can.
But it's to understand why we do what we do.

So basically you're given two vectors p and q,
And you need to make p+(lambda)q vector parallel to j vector and find lambda.

First, we'll find p+(lambda)q.

We need to find s, such that c-sd is parallel to 2i+j.

c is 3i+4j and d is i-2j
So c-sd is 3i+4j-s(i-2j)
Which yields,
3i+4j-si+2sj

Was writing c

[woven latch]

After this, we take i terms together and j terms together.
So it becomes
3i-si+4j+2sj
(3-s)i+j(4+2s)

Now we equat i term and j term

like
3-s=4+2s
3-4=2s+s
-1=3s
s=-1/3

The vector it is parallel to is 2i+j not i+j

mb

[woven latch]

From here,
We multiply i terms by 2 and j terms by 1 and then equat them

[twilit spear]

What’s the question

Yea I didn’t take a level maths so this is beyond my understanding lol

Sorry

[spark siren]

you have a step-by-step solution, do the same with your values.

and if some step isnt clea ask this exactly.

[marsh citrus]

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[jagged urchin]

I have characters (up to 50), each of whom has two values: power and speed.
I need to assemble them into 3 teams, each of which has 5 characters. A team's power is the sum of the power of its characters, and likewise for speed.
My goal is to find the best way to distribute these characters into teams so that

1. each team has at least S speed
2. the power of the team with the lowest power is as high as it can be

[jagged urchin]

I have observed that it's a bit too many characters to try all possible combinations of teams, even I make sure to not try any repetitions (edit: wrong calculation, but it's more than a trillion).
This is probably also the case if I factor in early stopping from some team not being able to reach S speed.

[crystal lintel]

,w (50 choose 5)(45 choose 5)(40 choose 5)/3!

[elfin berry]

Results provided by WolframAlpha

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

Requested by slayyla

[jagged urchin]

Oh, well, that's even more.

[crystal lintel]

yea once you pick 15 people there are also different ways to assign them to teams

[jagged urchin]

I suppose the order does matter among the 15 units that I select, but only by which team it's put into.

[crystal lintel]

what are the numbers for speed and power like?

like what range of numbers do they take

[jagged urchin]

Power is roughly evenly distributed between 0 and a million.
Speed is from 0 to 30 (but might not be integers), I'm trying to reach 100.

Might be worth mentioning, that perhaps it's not perfectly solvable in a reasonable amount of time. I wouldn't know.

Best I've figured out is some optimizations I can't do. =/
Which is not useless, but also not very useful.

[crystal lintel]

do you have an example set of 50? it would help a lot for me deciding if an algorithm could be feasible

[jagged urchin]

I can generate you a batch, sure.

[crystal lintel]

if it's just going to be generating random integers from 0 to 1000000 and 0 to 30 then it's ok

[jagged urchin]

I really can't predict them ahead of time. Is there any specific property you're curious about?

I suppose it would be more realistic to say that while the power numbers can be between 0 and a million, the lowest and highest ones aren't usually more than 3x apart in value in a given set. But the magnitudes of the sets can vary.

But I don't suppose that helps.

[devout mauve]

feels like you should be able to formulate this as some linear program. let me think a bit

ok an integer linear program should work

set x_i as a boolean variable if character i is in team 1, y_i if they are in team 2 and z_i for team 3

you have the conditions sum x_i = sum y_i = sum z_i = 5

sum s_i x_i >= S, sum s_i y_i >= S, sum s_i z_i >= S

sum p_ix_i >= sum p_i y_i >= sum p_i z_i

and sum p_i z_i -> max

all things considered thats not that many variables and constraints so any solver should be able to solve that

[jagged urchin]

I will need to digest this.
I've done some linear programming before, but I'm not super familiar with it.

[winged forum]

what element can polonium finish its orbital hold of valence electrons if the sixth one can have a maximun of 72?

[devout mauve]

!occupied

[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).

[jagged urchin]

Well, I understand the constraints.
You say there's solvers for these kinds of problems? Is there something simple available as a website that you can recommend, or should I go find one myself?

[devout mauve]

I know that I found a website at some point in the past

but otherwise there are solvers for almost all programming languages easily available

[jagged urchin]

Well, I'll see if I can get one working and if it can give me an answer.

[devout mauve]

gl

[jagged urchin]

Should I close the thread now, or after I get it to work?

[devout mauve]

your choice

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[simple gull]

how do i solve this matrix and what does it mean

[pastel moss]

That's a system of linear equations. You have three columns in that first matrix, right. The first column corresponds to x, the second column corresponds to y, and the third one to z. so basically, if you read from left to right, you have the eqation 0.1*x + 0*y +0*z = 450. then for the next row you have 0.1 * x + 0*y + 0.2 *z = 50, and do the same process for the last one. It's basically a way to solve simultaneous equations

so use your 3 equations to solve for the 3 unknowns

[simple gull]

yes ok but the way it is rn its not solvable no?

basically Eigenvalues but idk how to apply it here

[pastel moss]

it is. the first equation is basically 0.1*x=450, so you can already solve for x.

[simple gull]

4500

no but then it wont require gauss

so its not the same answer

[pastel moss]

then for the next equation, the only remaining unknown is z. and now that you have x and z, you can use the last eq to solve for y

[simple gull]

like look

this is what they did

but i dont get the lower part how did they change the whole values

Ik its Eigenvalues but idk with what

[simple gull]

and then we get this but i dont get the process

[pastel moss]

ok yeah I don't understand that either, sorry