help-27

[frozen aurora]

i think she doesn't understand what the shading represents really

[undone egret]

Yeah

That

[restive river]

blud latexting evry shit

[rain summit]

-# yes

[restive river]

https://tenor.com/view/pepe-why-pepe-pepehands-crying-gif-12683546

[undone egret]

ngl that was confusing me a lot 😭

[rain summit]

-# needed to practice my latex skills

[restive river]

you'll get used to it

[frozen aurora]

if you take any point from the shaded region, it will satisfy the inequality you were given. that's all that means
all of the points i wrote satisfy y >= 3x-3, so they are inside the shaded region

[rain summit]

so a graph here, is just a collection of points that satisfy the condition

[frozen aurora]

the shaded region is a collection of all such points

[noble solstice]

idk if someone said this but you can use the concept of power of a point to get the side correct

[undone egret]

concept of power of a point ??

[noble solstice]

yea

[rain summit]

the graph $y \geq 3x - 3$ are just points that satisfies the condition, which when filled will get a shaded region

[undone egret]

no idea what that is

[woven radish]

1 divided by 0 equals Infinity

[frozen aurora]

wdym power?

[noble solstice]

ok so

basically

[mystic scarab]

Me neither lol, probably it's something for the olympionic math, too advanced
Is it? @noble solstice

[noble solstice]

it's a method our teacher uses idk if it has a formal name

[noble solstice]

no i learnt bout it for JEE

😭 😭

[rain summit]

.

[undone egret]

yeah im only year 10 lvl (started year 11 but havent been introduced to anything) and im behind so i don't understand a lot of what'sin here 💀

[noble solstice]

ok so we input 0,0 in the function of a line

and check the sign

[restive river]

tf noone teaches that in jee

[mystic scarab]

JEE is one of the math Olympics!! And one of the toughest 😅

[noble solstice]

[rain summit]

getting off topic now

[noble solstice]

fair-

[rain summit]

let's focus on helping the OP

[teal stirrup]

jee is easy

[noble solstice]

but off topic

yeah

[rain summit]

-# dm modmail for a new nickname

[frozen aurora]

ok i gtg now but let's keep it to 1-2 helpers please

[rain summit]

who's helping

[restive river]

i back out

[undone egret]

okay so I don't really understand with the two separate things

-3 > -6

that's the satisfied inequality ?

[noble solstice]

just input 0,0 for x,y and if it is positive that side will be shaded for greater than 0
and if the function is negative the opposite side is shaded for graduated than zero

[teal stirrup]

greater than not greater than or equal to

[undone egret]

what? Isn't it greater than or equal to?

isn't -3 bigger than -6

or am i just slow

[rain summit]

$\geq$ means $>$ or $=$

[teal stirrup]

yes

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

so $-3 \geq -6$ is true

[undone egret]

so it's... true..???

[woven radish]

1 divided by 0 equals Infinity

[undone egret]

what do you mean "why would"

[teal stirrup]

the statement is true

but it's not something you would write

what's the question?

[rain summit]

check the pinned message

[undone egret]

no that's old

[rain summit]

also get a new nickname

[undone egret]

hold on let me find it

[teal stirrup]

no?

[undone egret]

this was what it started from I guess, the confusion

I know this is the answer, but I don't understand why that's the answer

I don't understand what the inequality represents -- the shading -- in relation to the equation

like

[noble solstice]

write the inequality as ax + by + c >= 0
then just input 0,0 for x,y and if it is positive that side will be shaded for greater than 0
and if the function is negative the opposite side is shaded for graduated than zero

[undone egret]

how do you determine where the shading should be, just based on greater than/lesser than/ETC

[undone egret]

what's ax + by + c > 0 ?? I don't think I've seen that before

Are you american perchance? I'm australian so maybe it's different ?

[noble solstice]

here a, b and c and constants

[restive river]

the inequality is the condition and the graph shows all the points that satisfies the condition

shade*

[undone egret]

but that's reliant on a graph / visualisation, no? I'd rather just be able to figure out without visualisations because I've had exams in the past where I relied on visuals and couldn't do it at all without them

[teal stirrup]

Show all points ( 𝑥 , 𝑦 ) that satisfy the condition “ 𝑦 is at least as big as "3𝑥 − 3"

[noble solstice]

noo

[teal stirrup]

what I would do here

[noble solstice]

any function that represents a line

[undone egret]

the condition ? I think I get that

[noble solstice]

yea it requires some visualisation

[restive river]

What do you don't understand

[undone egret]

how to tell what needs to be shaded entirely based on the greater than, lesser than variant sign

[restive river]

generally you take O(0,0) as the test point

if the condition is True the side which has origin is the shaded part

[undone egret]

the side which has origin ??

So uh

We have coordinates though

so the -1, -3 needs to be shaded..??

[restive river]

like take this yours for example.

y >= 3x-3
0 >= 3x0 -3
0 >= -3

Which is True

[undone egret]

how do you tell whether it does, or does not, need to be shaded ?

based on the sign?

[restive river]

Therefore the inequality contains origin

therefore the shade should be done on the left

since that contains origin

[undone egret]

so if it satisfies or does not satisfy the given coordinates ??

[mystic scarab]

It must be shaded if the given inequality is satisfied, no more no less
Otherwise not

[restive river]

Yeah

If it satisfies the given inequality

the shade should contain the point

[undone egret]

but what does the sign do then ??

I'm really hung up on the sign still

[restive river]

which sign?

[undone egret]

it's confusing me

like with different equations too

[restive river]

thats greater than or equal to?

[undone egret]

Yeah

But like

Ok nevermind I think I get it but I'll just keep doing questions to see if I get it

I think I know how to do this one

[restive river]

Do you mean how to find out if it has equals to or no?

[undone egret]

Uhh no I know that one

(uhh is just me thinking when im typing btw it's not sarcasm)

[undone egret]

basic linear graphing right

[restive river]

yes

[undone egret]

So test the origin now ?

to see if the inequality is satisfied ?

[restive river]

pretty much

[undone egret]

Because the origin holds true, and it's shaded, does that mean this is correct?

[restive river]

that means the inequality contains origin, correct

[undone egret]

I think I just got the uhh thing wrong

oh wait nvm i see my error

i was thinking of it as -(2/1) but it's (-2)/1 ?

[restive river]

keep learning!

[undone egret]

https://tenor.com/view/meme-mahoraga-jjk-brainrot-i-understand-it-now-gif-1125266490897382197

I think I FINALLY got this dang topic 😭😭😭 after like 30 mihnutes

[restive river]

Good job

[undone egret]

Should I close this now ?

[restive river]

If you have no more questions

[undone egret]

Alr!!

.close

[devout snow]

Channel closed

Closed by @undone egret

Use .reopen if this was a mistake.

[restive river]

-# do open for new query help me get helpful

[undone egret]

in that case lol

.reopen

[devout snow]

✅ Original question: #help-27 message

[undone egret]

I forgot how to do the gradient equation lol

how do you tell what's x2 and y2

[mystic scarab]

Wdym?

[mystic scarab]

Ohhh

[undone egret]

fairly simple question it's just slipping my mind rn

[mystic scarab]

You can pick whichever you like to be the first point, having coordinates (x1, y1)

[undone egret]

Ohh

So just whatever coordinate set ?

Is it easier to just put the second set as the bigger one ? (bigger values)

[mystic scarab]

It really depends on the numbers given (especially when they are negative), so there isn't a general answer

[undone egret]

What's easier to work with?

[mystic scarab]

Again, there's no answer 😅 It depends on the exercise itself

[restive river]

there will be cases where both take same effort

[mystic scarab]

Yeah indeed

[undone egret]

Would (3, -21) be easier to work with ? I'm just basing it on the fact (0, -9) has 0 as x

[mystic scarab]

Mmmh I don't think you have the right idea

[restive river]

I don't think you have to put much forethought into this

It will just come to you through practice

[undone egret]

do you keep it as a fraction? Iforgot

[restive river]

it can be both

[restive river]

Integers are integers and fractions are fractions

you can chose to convert it too

[mystic scarab]

Don't forget the minus sign 😉

[undone egret]

it was minus a negative so I just changed it to +

-21 - -9

[restive river]

-21

[undone egret]

oh

oops

[restive river]

mhm

[mystic scarab]

Try to never write the 1 in the denominator, it's so awkward

[restive river]

if it is simpliable to integer then simplify, else keep in fraction imo, depends if you are comfortable with fraction

[undone egret]

Ahh so just keep it as unsimplified?

[mystic scarab]

Just keep it as -4

[undone egret]

simplify else keep? What does that mean ?

oh wait I forgot it was -12 OOPS

[restive river]

like for example you can write 12/4 as 3

just write 3

its more simple

[restive river]

punctuation

if you can't, leave it

[undone egret]

yeah my brain is kind of fried okay after an hour of straight maths (plus roughly 2 hours in school today) it's kinda been melted

[restive river]

Do take breaks

[undone egret]

I completely forgot it was. a whole number.

4/1... 4....

[restive river]

Jamais vu, don't worry about it

Happens to the best of us

[undone egret]

I thought this was english not french 😭

[mystic scarab]

If this happens, it's a HUGE sign you need a (big) break

[undone egret]

hhhfahfHDHSFH true 😭

[restive river]

do 1 hour - 10 minute splits

Or you'll be fried

[undone egret]

Ok I'm gonna go play w/ my cats and eat something, tysm for all the help!!

[undone egret]

Lol good idea

.close

[devout snow]

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[devout snow]

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[ionic jasper]

Hello, i translated it from german and i dont got the original task.

[ionic jasper]

I just canz really figure out the,right way

[neon folio]

Right

So we can determine the probability of a red ball

And of a yellow ball

[restive river]

not enough information

would be good if you have original question

[neon folio]

We can set up an equation

This is the original

[restive river]

no this is translated

Could you show the original question in German?

[restive river]

how would you find number of red balls without any relation

I mean it does the say the game is fair

oh missed that

[neon folio]

We use Laplace

[restive river]

mb

[ionic jasper]

I dont got it

[neon folio]

So

[ionic jasper]

What equation

[neon folio]

How many balls are there in total

[ionic jasper]

X+2

[neon folio]

And how many red balls

[ionic jasper]

X

[neon folio]

Yeah

So

Whats the probabilit of drawing res

Red

[ionic jasper]

x/x +2

[neon folio]

Yeah

And you do this 2 times in a row

2 red

Whats the probability

Oh sorry

2 yellow

[ionic jasper]

(2/x+2)²

[neon folio]

Genau

Weißt du was ein Erwartunfswert ist

[ionic jasper]

Ja

Der muss 0 sei

[neon folio]

Ja

Entweder wir ziehen 0 gelb

Oder 1 gelb

Oder 2 gelb

Nur bei 2 gelb gibt's ne auszahlung

Sonst verliert man den Einsatz einfach

Also

Wie bestimmen wir den Erwartungswert

[ionic jasper]

Ich schreibs auf papier 1sec

.

So?

Und das jetzt lösen?

[neon folio]

Genau

Warte nein

Also E(x) heisst

Wir addieren alle (Gewinn * Wahrscheinlichkeit)

Was ist der Gewinn

Wenn wir 2 gleb ziehen

[ionic jasper]

Ja wir hatten 2 formeln für e(x)

[neon folio]

Ok

[ionic jasper]

5

Oh

Also nur den hinteren teil meiner gleichung?

Das vor dem plus weg.

[neon folio]

Wenn du E(x) =0 benutzt

Dann ist E(x) der erwartungswert des gewinns

Und dann brauchst du natürlich die jeweiligen gewinne

[ionic jasper]

Hö

[neon folio]

Zeig mal deine formel

Für E(x)

[ionic jasper]

1sec

Ganz oben in blau

Das ist die neuere

Die wir heute hatten

Die andere war dieses eine u= p×n

Mü

[neon folio]

Ja das ist bei den binomialen

Ok

Also

Wir können entweder

Den erwartungswert des gewinns bilden

Oder der auszahlung

Welchen willst du

Aus meiner sicht ist der erste besser

Aber wie du willst

[ionic jasper]

Ok

Dann das

[neon folio]

Also

Was bedeutet gewinn

[ionic jasper]

Gelb und gelb

[neon folio]

Ok

Gewinn = Auszahlung -Einsatz

Korrekt?

[ionic jasper]

Nicht andersrum?

Nvm

[neon folio]

Ok

[ionic jasper]

Oh

[neon folio]

Jetzt

[ionic jasper]

Gewinn ist 4,2?

[neon folio]

Ja

Bei 2 gelb

Und bei 0 oder 1 gelb?

[ionic jasper]

-0,8

[neon folio]

Ja

Jetzt

Gewinn * Wahrscheinlichkeit

xi * P(xi)

Oder wie bei dir

k1 * P(x=k1)

k2 * P(x=k2)

[ionic jasper]

Oh

Check

[neon folio]

Nehmen wir den fall 2 gelb

Wir brauchen

Gewinn (2 gelb) * P(2 gelb)

[ionic jasper]

Hä

[ionic jasper]

Also nicht die gleichung dann lösen

[neon folio]

Wir addieren ja die produkte

E(x) = k1 * P(k1) + k2 * P(k2) +...

[ionic jasper]

Ja

[neon folio]

Die k's sind die heweiligen gewinne

J

[ionic jasper]

Ja

[neon folio]

Welche möglichen gewinne haben wir

Bei diesem spiel

[ionic jasper]

-0,8 und 4,2

[neon folio]

Ja

Also

K1 wird -0.8 sein

Und k2=4.2

Wir haben also 2 produkte

Die wir addieren

E(x) = k1 * P(k1) + k2 * P(k2)

[ionic jasper]

Also wie die eine sache die ich schon hatte nur halt statt 0 -0,8 und statt 5 4,2?

[neon folio]

Ja

[neon folio]

Dieser war der erwartunfswert der auszahlung

Machen wir später

[neon folio]

Nun stell diese gleichung auf

[ionic jasper]

Hab

[neon folio]

Ok

Und E(x) = 0

Faires spiel heisst, 0 Gewinne

0 Verlusste

Also E=0

Da hier E der erwartungswert des gewinns ist

[ionic jasper]

Und jetzt die gleichung lösen

[neon folio]

Ja

[ionic jasper]

Ivh versuchs

Komm net weiter

Das 1- check ich nicht

[neon folio]

Ok

Um's einfacher zu machen

Schreib einfach p

Anstatt von 4/(x+2)^2

[ionic jasper]

1-p also

[neon folio]

Ja

0= -0.8(1-p) + 4.2(p)

Und jetzt nach p lösen

[ionic jasper]

Oh

P = 1/6,25

[neon folio]

Ja

Und p steht für was

[ionic jasper]

Das jetzt in die ursprüngliche 1-...?

[neon folio]

Wir haben ja

P

Anstatt

Etwas

Was ist dieses etwas

[ionic jasper]

.

[neon folio]

Ja

P= 4/(x+2)^2

[ionic jasper]

Oh

[neon folio]

Jetzt einfach nach x lösen

[ionic jasper]

Ich habs

[neon folio]

Und fertig

(Denn x ist ja die anzahl roter bälle)

Die wir suchen

[ionic jasper]

Pq formel?

Oder bin ich ganz falsch

[neon folio]

Oder

Einfach

$(\frac{2}{x+2})^2 = 0.16$

[woven radish]

Googoo Gaga

[neon folio]

Und 0.16 = 0.4^2

Btw

Hoffentlich kannst du's sehen

$(\frac{2}{x+2})^2 = 0.4^2$

[woven radish]

Googoo Gaga

[ionic jasper]

Oh

Wow

Hast dus einfach gesehen

[ionic jasper]

Das

[neon folio]

🤣

Ist doch offensichtlich

[ionic jasper]

Holy shit

Vielen dank malwieder

Hab den test wiederbekommen gehabf

9np nur, da ich eine aufgaben richtig reingeschissen hatte mit vierfeldertafeö

[neon folio]

😪

[ionic jasper]

Aber wiedermal retter in der not

Danke

[neon folio]

🙏

[ionic jasper]

.close

[neon folio]

Gerne

[devout snow]

Channel closed

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[devout snow]

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[mild verge]

I need a crash course in polynomials, fractions, algebra and perimeter (I have an entrance exam coming up and I forgot everything Abt these topics)

[winter patrol]

you could try speedrun through khan academy

[neon folio]

Huh

Ramonov mod

Crazy

[winter patrol]

and/or do past/mock/trial papers to pinpoint specific issues
#study-discussion would be more appropriate
if you don't have a specific math question you're stuck on atm

[mild verge]

Okey dokey!! Thx! .close

.close

[devout snow]

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[sand pumice]

<@&268886789983436800>

[devout snow]

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as this action is irreversible, and this channel may abruptly lock.

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[tranquil steeple]

how to solve these type of sum i can solve these type of sum when it's a definite intergal but how to solve when its indefinite

[glossy dew]

multiply by sec^2(x) on both sides

[tranquil steeple]

someone ban him

[glossy dew]

<@&268886789983436800> um uhh

[tranquil steeple]

ohhh okii

[meager phoenix]

Massive bot scam attack here

[glossy dew]

p common

[tranquil steeple]

then i have to put t=tanx right

[glossy dew]

mhm

[tranquil steeple]

okii

.close

[devout snow]

Channel closed

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[short hare]

<@&268886789983436800> what?

[glossy dew]

level 1 crook

[tranquil steeple]

.reopen

[devout snow]

✅ Original question: #help-27 message

[tranquil steeple]

so is r intercept is x intercept??

[restive river]

pretty much

[tranquil steeple]

OHHH OKK AND SINCE THE PERPENDICULAR M BECOME ITS NEGATIVE RECIPROCAL RIGHT?

[restive river]

yea m1.m2=-1

[tranquil steeple]

OKII

THX

.CLOSE

.close

[devout snow]

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[swift frigate]

ok so if b/c is equal to 3/4

but c = 1

so would b equal 0.75

[restive river]

yeah

[swift frigate]

ok

[restive river]

but why do you need that?

[swift frigate]

what would be the quicker way to find cosine i forget

[restive river]

why don't you just find the base

[rain summit]

use the identity that $\sin^2 \theta + \cos^2 \theta = 1$

[winter patrol]

you don't necessarily need to have the radius of your circle to be 1

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

solves the problem real fast

[winter patrol]

you could use 3 and 4 directly

[swift frigate]

so is that the square of the result or an altered operation entirely

[rain summit]

i mean, they gave you $\sin \theta$

[woven radish]

1 divided by 0 equals Infinity

[winter patrol]

its pretty much the same,
pythag

[rain summit]

so you can use this identity to find $\cos \theta$, especially when $\frac{\pi}{2} < \theta < \pi$

[swift frigate]

and im saying is sin^2(theta) just the square of the result

[woven radish]

1 divided by 0 equals Infinity

[restive river]

why dont you just do b=sqrt(h^2-p^2)

[restive river]

this and that is probably the fastest

[swift frigate]

can someone answer this

i care more about this

[rain summit]

wdym square of the result?

this is the square of what the question gave you

[restive river]

9/16

[rain summit]

cool

[restive river]

yea

[rain summit]

so $\cos^2 \theta = \text{?}$

[woven radish]

1 divided by 0 equals Infinity

[restive river]

yh you can change the sign for costheta later

[swift frigate]

is sin^2(theta) = to sin(theta) = ans^2

or no

[rain summit]

$\sin^2 \theta \neq \sin \theta$

[restive river]

sin^2(theta) is just the value of sin(theta) squared

[woven radish]

1 divided by 0 equals Infinity

[restive river]

since sin^2theta=sintheta*sintheta

you just square the value

[swift frigate]

there we go

so yes

[restive river]

no way lol

[rain summit]

goodness

anyways

[swift frigate]

thats not what i was asking

[restive river]

you got the answer you wanted

[rain summit]

now you got your confusion resolved, can you solve the problem now?

[swift frigate]

alright so sin^2(theta) would equal (3/4)^2

[rain summit]

yes

[pseudo basin]

brackets

[rain summit]

-# ||goodness gracious... i'd rather latex if i were him||

[rain summit]

use the identity...

no need to delete lol

and i'd rather work with fractions than decimals

[swift frigate]

is what i wrote above correct

[restive river]

it is

[swift frigate]

so cos^2(theta) is 0.4375

7/16

[restive river]

yeah

[swift frigate]

sqrt of (7/16)

[ancient valley]

Bracket
Sqrt(7/16)

[restive river]

,calc sqrt(7/16)

[woven radish]

Result:

0.66143782776615

[restive river]

yh

[swift frigate]

oh its approximate

yeesh

ok so the final answer would be sqrt(7/16)

but no its not

[restive river]

dont forget the sign

[swift frigate]

negative right

[restive river]

yh

[swift frigate]

ok it still says its wrong

wait no

there we go

forgot the sqrt notation

ok welp done

[restive river]

[swift frigate]

thank you

.close

[devout snow]

Channel closed

Closed by @swift frigate

Use .reopen if this was a mistake.

[restive river]

do come with doubts in future and help me get helpful 🥀

[swift frigate]

.reopen

[devout snow]

✅ Original question: #help-27 message

[swift frigate]

so i tried sqrt(15/16) first and it didnt work

wait no

well ya you cant simplify it down

and the signage is correct

[jaunty bane]

this is a new question?

[swift frigate]

am i not ok to reopen my old one for a new question

[jaunty bane]

no, I'm asking so I can pin the new one for you

[swift frigate]

so im not taking up two channels

[jaunty bane]

if it's the old one then I won't pin the screenshot

[swift frigate]

its new

[rain summit]

quadrant 1?

[swift frigate]

ya both should be positive

[rain summit]

what do you mean it didn't work?

you inputted your answer as $\frac{15}{16}$

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

maybe they wanted exact forms, not decimal approximations

[restive river]

well the problem is thats sin^2theta

not sintheta

sintheta = sqrt(15)/4

[swift frigate]

i first put it in as sqrt(15/16)

and it said it was wrong

[rain summit]

show us the result

show us your sqrt(15/16) attempt

[restive river]

I think its his doodle

[mystic scarab]

What about this? Is it marked wrong? Let's hope not 😅

[swift frigate]

i dont have it screenshotted and i only have one attempt left

[rain summit]

try that then

but before you submit

send the screenshot

[restive river]

I think they marked sqrt(15/16) wrong and that as right

[mystic scarab]

Yeah me too

[rain summit]

before you submit

send us the screenshot

[restive river]

maybe the math teacher accepts only the most simplified answer, who knows

[restive river]

what was the answer

[swift frigate]

i guess i'll find out later

when im done with the assignment

[restive river]

watch it be sqrt(15)/4

[rain summit]

-# i told to send the screenshot before submitting...

[restive river]

well whatever

[swift frigate]

ya i didnt have a screenshot

[restive river]

doesn't count towards grades

[swift frigate]

of when i did that

[mystic scarab]

You said you had a further attempt

[rain summit]

i meant before you hit send and lose your last attempt

[swift frigate]

here i can actually just reset the assignment

[mystic scarab]

...

[rain summit]

...

[restive river]

do they ask decimal compulsory?

[rain summit]

damn

[scenic tulip]

[square root (4^2-1)]/4?

[rain summit]

$\frac{\sqrt{15}}{4}$

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

wut?

or uhm

,w calc sqrt(15)/4

[mystic scarab]

@swift frigate so you didn't try this?

[woven radish]

Results provided by WolframAlpha

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

Requested by iaminfinityiq

[rain summit]

0.968

[swift frigate]

trying it

[mystic scarab]

Alright

[restive river]

wierd they accepted this earlier

[swift frigate]

ok ya it was right

[swift frigate]

thats what im saying lol

[rain summit]

hold on

[swift frigate]

well as long as im right in my math

i dont really care

but its annoying

[rain summit]

they accepted $-\sqrt{\frac{7}{16}}$

[woven radish]

1 divided by 0 equals Infinity

[swift frigate]

sure did

[restive river]

not how my professor thinks but yh

[swift frigate]

literally the question before this

[rain summit]

but not this

[swift frigate]

i mean bc its a practice assignment

[restive river]

oh ok

[swift frigate]

im thinking maybe because its calculating the decimal and the previous one didnt reach its rounding limit

[rain summit]

hm

[swift frigate]

maybe

[rain summit]

anyways

anymore questions?

[swift frigate]

ya i can close now

.close

[devout snow]

Channel closed

Closed by @swift frigate

Use .reopen if this was a mistake.

[swift frigate]

thank you

[ancient valley]

It might be sqrt(7)/4
As the root can be simplified

[swift frigate]

sqrt(15)/4

how can it be simplified /gen

[swift frigate]

?

[ancient valley]

Sorry read it as sqrt(7/16)

[swift frigate]

oh ok lol

[devout snow]

Available help channel!

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[wispy warren]

hello I'm not arriving at the correct answer

[wispy warren]

and here's my work

[rain summit]

why matrices and stuffs?

[wispy warren]

that's how I was taught to approach these problems

[rain summit]

i'd just do some substitution

for instance, $z = 1 - x - y$ and substitute into the remaining 2 equations

[woven radish]

1 divided by 0 equals Infinity

[stone stump]

no, row reduction is better

[wispy warren]

we're forced to solve these with gaussian elimination

[stone stump]

anyway this looks correct

but you are not doing all cases

you are dividing by 1-a for example

[wispy warren]

yes true

but I didn't know it was gonna involve a division with 1-a

[stone stump]

wdym you didnt know

[rain summit]

if $a = 1$ for instance

[woven radish]

1 divided by 0 equals Infinity

[stone stump]

you saw it during the calculation at some point

[wispy warren]

i saw it after setting the condition

a != 3

[stone stump]

yes

so you saw it

Case 1: a != 3

Case 1.1: a=1

Case 1.2: a != 1

or however you wanna do it

[wispy warren]

alrighty

thanks for the help

.close

[devout snow]

Channel closed

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[devout snow]

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Remember:
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[sage mirage]

So ... I'm pretty bad at mathing and I want to know where I'm missing the problem

A tool costs c ingots to craft.
It takes r to repair
Each time the item is repaired it loses 10% max durability => efficiently reducing r value by 10% * q (q being the actual repair quantity)

To find the q quantity when the repair efficiency drops to the equivalent cost of recrafting an item I'm writing this :
repair cost fall off = repair to craft value ratio
r * q * 0.1 = r / c

But I'm unable to find a correct simplification for q = ??? where q = 8, r = 5, c = 1 ... at least that's the kind of result I'm expecting. But I could also be wrong on that. (My thinking is that for a 1/5 ratio, when the repair efficiency falls to 1/5 it is equivalent to craft back the item, 1/5 = 0.2 = 20%, the repair efficiency falls at 20% at the 8th repair ... but it seems I'm unable to write and resolve that with maths )

So I need help to learn back how to simplify this and if the equation I posed is even relevant 😅
I'll be glad to improve a bit more at math with whoever has a little time for this

[pseudo basin]

efficiently
i think you meant effectively there btw...

so... repairing an item restores its durability to full, but at the cost of 10% of its current max durability?

im actually not sure how it works from your description here

[sage mirage]

Most probable, English is not my native language and I lack some sleep it seems 😅

[pseudo basin]

what's your native language

[sage mirage]

French

[pseudo basin]

i speak french

[sage mirage]

As you'd like then

you're fluent in french ?

to know how I should express myself

[pseudo basin]

jsp s'il est une bonne description mais je vais te comprendre

[sage mirage]

ok allons y alors 😉

Donc :

1. L'objet commence à 100%
2. A chaque réparation l'objet perd d'abord 10% de sa durabilité maximale PUIS est réparé à 100%
3. c est le coût abstrait de création de l'objet
4. r est le coût abstrait de réparation de l'objet
5. q est le nombre de réparation effective
6. Je veux poser une équation qui me permet de toujours trouver q, quand q rend aussi efficace la réparation ET la réparation pour toujours trouver le moment où rempalcer l'objet

(et c'est surtout un entraînement pour me remettre doucement à ré-employer les mathématiques et devenir meilleur)

[pseudo basin]

alors attends, on mesure la durabilité en quelle unité ?

[sage mirage]

Je pense que ça a peu d'importance : ce sont des pourcentages non ? 🤔 (je me trompe surement)

[pseudo basin]

si l'on crée une pioche en diamant dans minecraft elle commence avec 1562 points de durabilité, dans ton analogie serait-elle à 1406/1406 après une réparation ?

[pseudo basin]

pourcentages avec un dénominateur changeant ...

[sage mirage]

Ah ! Je pense que j'ai fait une erreure d'énoncé : c'est 10% de la valeur maximale, et pas 10% de la durabilité max actuelle

[pseudo basin]

euhhhhh

[sage mirage]

Pas sûr de comprendre le "dénominateur changeant"

[sage mirage]

en gros : pour la pioche de Minecraft : elle perdra 156.2 à chaque fois

et pas 156.2, puis 141, ...

[pseudo basin]

alors la pioche commence à durabilité 1562 / 1562
puis on l'utilise et sa durabilité tombe à (...) / 1562

on la répare

elle revient à 1405.8 / 1405.8

alors ok le nombre 1562 est inconvenant

disons que la durabilité maximale est 1000 "points" au début

on utilise l'objet et durabilité tombe à (...) / 1000

on le répare et il revient à 900 / 900

[sage mirage]

puis 800/800

etc ...

[pseudo basin]

ok alors

on ne peut réparer l'objet que 9 fois en total

la création d'un nouvel objet coûte c et chaque réparation coûte r ... et c'est quoi q exactement ?

[sage mirage]

L'idée c'est que je veux une équation pour pouvoir facilement intervetir r et c et que ce soit utilisable dans plusieurs contexte.
Dans le cas présent : c = 5, r = 1

c = Pondération abstraite des ressources nécessaires à la crétion de l'objet

[pseudo basin]

intervetir ?

[sage mirage]

r = Pondération abstraite des ressources nécessaires à la réparation de l'objet

[sand dove]

intervertir I think

switch

[pseudo basin]

ce que je comprends pas en ce moment est la signification de q et pas sa valeur

[sage mirage]

q = Quantité de réparation

[sage mirage]

remplacer

[pseudo basin]

quantite ... le nombre de fois qu'on peut le faire ?

[sage mirage]

replace*

[sage mirage]

Plutôt le nombre de fois où on a réparé

the number of time you are repairing the item

[pseudo basin]

alors ... qu'est ce que tu veux calculer

[sage mirage]

quand q fait tomber l'efficacité de réparation au même niveau qu'à la recréation de l'objet

[pseudo basin]

ah ok

[sage mirage]

d'où en premier instinct : r * q * 0.1 = r / c

Mais je ne suis pas sûr 😅

et je n'arrive pas à le simplifier parce que je suis mauvais. Ahaha !

[pseudo basin]

alors on se demande "après combien de réparations est-il plus efficace de recréer un nouvel objet que de faire encore une réparation ?"

[sage mirage]

Exactly!

[pseudo basin]

r * q * 0.1 = r / c
this sounds like bullshit to me

[sage mirage]

Ok must be 🤣

I'm trying

How would you pose the equation then?

En français on dit "poser une equation" ... I don't know how to say it in english

[twilit field]

"how would one derive the equation/relationship" would be the standard way to ask that question, but yours is perfectly understandable!

[pseudo basin]

ok alright

so i think it's most convenient to take the durability of a "fresh" tool as 1

then repairs restore it to 0.9, 0.8, 0.7 etc. in general, the q'th repair restores the tool to 1 - 0.1q durability

obviously we want to delay repairs as much as possible so we can assume we use the tool up completely (or like until it's just before breaking)

so the q'th repair will, in the moment, restore 1 - 0.1q durability for a cost of r

while a fresh recraft will give us a tool with 1 durability for a cost of c

the "bang for buck" in each case is (1-0.1q)/r and 1/c resp.

r and c obviously are positive

$\frac{1-0.1q}{r} < \frac{1}{c}$

[woven radish]

Ann

[sage mirage]

I didn't even knew '<' was valide within this sort of equation 😛 (I must be around college level if it's not lower rn)

[sage mirage]

This sounds faire. Let me try to simplify this

[twilit field]

this is an inequality, not an equation, just for your information.

[sage mirage]

thanks 👌

[pseudo basin]

it's an inequality

[sage mirage]

$1-0.1q<\frac{1}{c}r$

[woven radish]

Moltenhead

[pseudo basin]

you can also write $\frac{r}{c}$

[woven radish]

Ann

[twilit field]

so I believe OP's objective here is to solve the inequality for q?

[sage mirage]

$0.1q<\frac{r}{c}-1$

[woven radish]

Moltenhead

[pseudo basin]

nop

[sage mirage]

$q<\frac{\frac{r}{c}-1}{0.1}$

[pseudo basin]

nop

[woven radish]

Moltenhead

[sage mirage]

yeah ... was pretty sure to mess things up right there

[pseudo basin]

if anything $-0.1q < \frac{r}{c} - 1$ from which $0.1q > \frac{r}{c} - 1$

[woven radish]

Ann

[twilit field]

missing negative sign!

[pseudo basin]

thus $q > 10\left( \frac{r}{c} - 1 \right)$

[woven radish]

Ann

[sage mirage]

Ok it's a bit of a gymnastic to implement this right back into my brain but I think I'm eventualy connecting the dots

how do you simplify this with an equation again? since you can't invert the sign

you multiply both sides by -1 isn't it ?

(I'm feeling very dumb and rusted rn. Ahaha!)

[twilit field]

I don't understand French, but I think you may benefit from expressing this in French? because as written, I'm not exactly sure I get you properly.

[pseudo basin]

you don't "invert the sign" ever

with inequalities as well as equations the fundamental thing you do is "apply the same OPERATION to both sides"

[twilit field]

Ann, he might also be referring to the inequality sign.

[pseudo basin]

this is the condition under which a repair is more costly than a recraft

[sage mirage]

$-0.1q < \frac{r}{c} - 1$ resolves to $0.1q > \frac{r}{c} - 1$

[woven radish]

Moltenhead

[pseudo basin]

yeah. multiplying by -1 (or any other negative) flips the inequality symbol.

$a < b$ means $-a > -b$.

[woven radish]

Ann

[sage mirage]

Hmmm ... I think I'm missing something then

[pseudo basin]

would you like me to try and explain this in extremely simple terms

[sage mirage]

shouldn' t $\frac{r}{c} - 1$ turn into $(\frac{r}{c} - 1) -1$ then?

[woven radish]

Moltenhead

[pseudo basin]

... ok i made a typo but your correction of it is wrong

it would be $\left( \frac{r}{c} - 1 \right) \times (-1)$, which simplifies to $1 - \frac{r}{c}$

[woven radish]

Ann

[sage mirage]

Ok so let me think through it again

(sorry if I'm slow)

$\frac{1-0.1q}{r}<\frac{1}{c}$ = $\1-0.1q<\frac{r}{c}$ = $-0.1q<\frac{r}{c}-1$ = $0.1q>(\frac{r}{c}-1)*(-1)$ = $0.1q>1-\frac{r}{c}$ = $q>\frac{1-\frac{r}{c}}{0.1}$ = $q>10(1-\frac{r}{c})$

[woven radish]

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

[twilit field]

don't use equal signs in an inequality.

prefer using something like $\Rightarrow$ to indicate your next step.

[woven radish]

Nicole

[sage mirage]

$\frac{1-0.1q}{r}<\frac{1}{c}$ $\Rightarrow$ $\1-0.1q<\frac{r}{c}$ $\Rightarrow$ $-0.1q<\frac{r}{c}-1$ $\Rightarrow$ $0.1q>(\frac{r}{c}-1)*(-1)$ $\Rightarrow$ $0.1q>1-\frac{r}{c}$ $\Rightarrow$ $q>\frac{1-\frac{r}{c}}{0.1}$ $\Rightarrow$ $q>10(1-\frac{r}{c})$

[woven radish]

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

[twilit field]

also, you can space each new step out by putting a \\ before each right arrow to make them appear on new lines, if you want it to be easier to look at.

[sage mirage]

$\frac{1-0.1q}{r}<\frac{1}{c}$ \$\Rightarrow$ $\1-0.1q<\frac{r}{c}$ \$\Rightarrow$ $-0.1q<\frac{r}{c}-1$ \$\Rightarrow$ $0.1q>(\frac{r}{c}-1)(-1)$ \$\Rightarrow$ $0.1q>1-\frac{r}{c}$ \$\Rightarrow$ $q>\frac{1-\frac{r}{c}}{0.1}$ \$\Rightarrow$ $q>10(1-\frac{r}{c})$

[woven radish]

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

[sage mirage]

missing the 1 in the second inequality but I think that's how I'd simplify with what I just learned ... did I missed something? 🤔

[twilit field]

I don't see anything wrong other than the second line's left side.

which should be 1 - 0.1q, as you noted.

[sage mirage]

Pfiouu ... thanks for the help! I'll try to do that more often. Was fun though ❤️

And I'll try to apply that for my current need ! Thank you very much @pseudo basin & @twilit field

[twilit field]

good luck!

anything else you want to ask?

[sage mirage]

Nope. that was my little math puzzle for the day

[twilit field]

alright, then you may .close the channel. welcome to the server!

[sage mirage]

I'll do! Thanks again and have a great day!

.close

[devout snow]

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[devout snow]

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[spare hawk]

So I was thinking abit about if I know the chord length(c) and segment length (s) if it was possible to deduce how big the disc would be.

After some fooling around i got the following expression
c/2s = sin(a/2)/a

Where a is the angle of the circlesector that would contain the segment.

My thoughts are that since c and s are know there is only one unknown variable a so i should be able to solve it but the fact that one angle is in a trigonometric expression and one is not is confusing alot.

Is it possible to solve it algebraic or is it only possible numerically?

[polar chasm]

Wdym by segment length?

[alpine python]

yeah i don't think that can be solved

unless maybe it has a solution at a special value

[spare hawk]

Sorry means arc length

[spare hawk]

Ahh great then I can give up on this endevear without regrets ^^'

Thank you

.close

[devout snow]

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[restive river]

,, c = 2R \sin(\frac{\theta}{2})

[woven radish]

Hi

[restive river]

s = R\theta

,,\frac{c}{s} = \frac{2}{\theta}\sin(\frac{\theta}{2})

[woven radish]

Hi

[restive river]

hm..

would you be able to solve for theta

in [0,2pi]

.reopen

eh

[devout snow]

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[warm lion]

Can someone help me with this problem? ||So far I have thought about using extremal principle, but I don’t know where to begin||

[devout snow]

@warm lion Has your question been resolved?

[faint zinc]

Let's assign each cell a value based on the number of cells that it is less than or equal to. Consider each pair of cells, either one cell is less than the other, or the pair is equal. In the case where one is less than the other, for the pair of cells, we add 1 to at least one of the cells.

So this means, on average, each cell has at least 1/2 added to it for each neighbor.

This corresponds to the average cell (in the best case scenario with no ties) having a score of 4

How can you use this lower bound on the average to show that at least one cell must attain the average?

@warm lion

[warm lion]

I see now, thank you so much!

.close

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[shy hill]

I need help with vectors and trigonometry theory

[woven vale]

those are two very broad topics, do you have a specific homework question we could start with?

[young spade]

The general idea about a vector, (and which i suppose your case is for robotics), is that its an arrow pointing somewhere

and for certain measures, the size of that arrow matters

[shy hill]

Exactly

first i have define a workspace

[young spade]

for your case $\bold i, \bold j, \bold k$ are the orthonormal vectors, which are usually meant to form a "space" $(x,y,z)$

[young spade]

if you assume x to be left-right, y to be back-forth and z down-up

[graceful cosmos]

Did you have a specific question about this stuff?

[shy hill]

yes first question theory

i have a point, in this case is the origin [0,0,0]

another point is the arm of the robot for example [300,200,50] in mm for example

what is the direction vector of this points

[graceful cosmos]

The length of v is given by √[x² + y² + z²], where x in your case would be (300 - 0)

Divide your vector by that length

That gives the direction vector. That is, a vector in the same direction, but with length 1

[shy hill]

okay

are there diferent kind of vectors right?

https://medium.com/@sepideh.92sh/part-i-how-robots-understand-space-kinematics-and-the-power-of-rotation-matrices-6b2ba5bc07be

[graceful cosmos]

Can you reword the question?

Like, define "kind".

[shy hill]

ok

nevermind forget the question

focus this position vector

P = Px · i + Py · j + Pz · k

i,j ,k is a unit vector

what mean this ? the valor of the i,j,k only can be 1 or-1 right?

sorry 1

[graceful cosmos]

Valor? That word might not be translating correctly

[shy hill]

ok

what is i,j,k?

[graceful cosmos]

The magnitude of i,j,k are each 1

However, i, j, k are each pointing in different directions

[graceful cosmos]

Note that your picture has all of i,j,k in it

You need some sort of vectors to start with, so you can build more vectors out of them. We typically use i j k as the "starter vectors"

[shy hill]

ok

i need practice

[graceful cosmos]

Oh, actually this might help:
i = (1,0,0)
j = (0,1,0)
k = (0,0,1)

[shy hill]

right

a vector is always between 2 points right?

in coordenate system

[graceful cosmos]

Say a robot is moving (1,1,0) m/s.

There's no starting point or ending point, just a robot's speed, expressed as a vector

[shy hill]

i will check the theory but thanks for the answers 🙂

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[ornate dragon]

hi, what does the “u” stand for?

[winter torrent]

that letter is read as "mu", pronounced like "mew"

and it's the mean / average

[ornate dragon]

ohh, so is it just the same for the ungrouped data formula?

[winter torrent]

it's a very common symbol for mean yes

that and $\bar x$

[woven radish]

hayliänus austrǎlis

[ornate dragon]

ohh okay

thank u so much

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[lofty verge]

Man this question pisses me off

I ended up guessing 3/4

[uncut crow]

ts pmo

[lofty verge]

correct answer is 1/2

yeah

I have no clue what a unique plane means exactly?

I mean a plane is like an piece of paper that is infinitely wide and long (I think)

And BTW while there is an answer key, it only says 1/2, it doesn't specify which two conditions are in that 1/2

[uncut crow]

wtf is the point of asking for a probability here. why don't they just ask how many of them uniquely determine a plane

[lofty verge]

no clue

[uncut crow]

a collection of points uniquely determines a plane if there is only one possible plane that passes through all of them

[lofty verge]

ah i see

so like Condition D is obviosly not

because the plane could be any rotation along that line

[uncut crow]

correct

[lofty verge]

well i feel like A & B are good so, let me try graphing C real quick

[young spade]

try to simplify 8y-64=24x

You dont really need to graph it

[lofty verge]

well i didnt actually do it
guessing it simplifies to y=3x+8

which makes those two lines identical

which makes condition C not form a unique plane

right?

yep i just confirmed that myself

OK this actually makes plenty sense now, i guess it wasnt that hard

but still, real annoying question lol

thanks all!

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[obsidian plank]

what is this asking me

[obsidian plank]

here is some work I did

but I don't know what it wants

ik sin theta is y but idk how that applies here

[thin fern]

what's the definition of sin

[obsidian plank]

opp / hyp

[thin fern]

right

It's not asking you to actually compute anything it just asks for the side ratios

so which side is opposite to theta, and which side is the hypotenuse?

[obsidian plank]

hyp is c or 15 and opp is a or 9

[thin fern]

well yes but what are the names of the sides

like try to match the format of the answer choices you're given

[obsidian plank]

I'm not sure I understand what do you mean the names of the sides other than the variable thats there ?

[thin fern]

yes

like instead of a, say BC

since that's what it asks for

[obsidian plank]

wait but why would a be bc ?

oh i see

I'm fucking cooked bro

I didn't look at the graph

[fierce forum]

pythagoeren therom

[obsidian plank]

wait how am I supposed to lets say represent y when its a fraction like for example sin theta would be the 9 or bc but thats all I need

do you understand what I'm saying

like since sin theta is y all I would need is BC

[thin fern]

sin theta is BC divided by the hypotenuse

sin theta is only y on the unit circle, when the hypotenuse = 1

I think you're confusing that

[obsidian plank]

yeah but the hyp is 15 I thought ?

dude this is confusing as fuck

[thin fern]

It is

I'm saying that generally, sin theta is not equal to y

it's equal to opposite over hypotenuse

[obsidian plank]

OHHHHHHH

I see now

that shit just clicked

thanks gang @thin fern

[thin fern]

[obsidian plank]

.close

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[hidden star]

what are you troubled on this?

[glacial tinsel]

To find OAB

[hidden star]

what have you done so far?

[glacial tinsel]

Found CAB = 105

[restive river]

what is the property of two radii in a circle

[glacial tinsel]

They are equal?..

[restive river]

correct

and how does this help us in this question

OA and OB are the radii of the same circle

Therefore.. ?

[glacial tinsel]

OBA and OAB are equal?..

[restive river]

good

I think you can do it from here now

you already know what angle CAB is

[glacial tinsel]

Oohh ok

OAB=45°

[restive river]

Yes!

So what is CAO?

[glacial tinsel]

105-45