help-33

[stoic saddle]

this original french

[junior owl]

he says the characterics are the : the value "norme de la vitesse" direction and sens

[plain moat]

What

[stoic saddle]

translation from broken franglais: direction and magnitude?

[junior owl]

direction

right

but sense

sens :vertical, horizontal

[plain moat]

x and y components

[junior owl]

thats in the first question

[long osprey]

I found this

[night relic]

sens ca veut dire si c'est vers le NO ou le SE, par exemple

[junior owl]

NW SE?

[long osprey]

nord-ouest, sud-est, mais en anglais

[junior owl]

what did he do in the first step

[serene bramble]

"it"

An integration, since you're going from acceleration to velocity

[junior owl]

shouldnt i do the primitive of vector a to find the velocity?

[serene bramble]

"la primitive d'une fonction" = "the derivative of a function"

But, no

[stoic saddle]

fonction

"fonctionne" is a form of the verb "fonctionner"

[serene bramble]

cocke

Since acceleration itself is a change in velocity over time

i.e. acceleration is the derivative of velocity

oh wait hold on

fuxk me I might be mistranslating

[junior owl]

why did he use M0

[serene bramble]

primitive = antiderivative

Which is what integrating gets you

[junior owl]

so i cant use antideivative in this question?

[serene bramble]

It... didn't, though? it uses OM

[junior owl]

meant OM0

[serene bramble]

An antiderivative is found via integration, which is exactly what was in the GPT-response you just posted

(though, as an aside

!noai is here for a reason):

[marsh citrus]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[junior owl]

mb

found x(t)=-3 nd y(t)=8t+3/8
i dont understand where it went wrong

$x\left(a\right)=c\ ;\ y\left(a\right)=8t+c_{2}$

[elfin berry]

StellarPhoton

[junior owl]

after doing the antiderivative of vector a

vector a =8j

so xa=0 nd ya=8

: /

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[marsh citrus]

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[novel merlin]

what did I do wrong 🥀

[red nimbus]

i noticed you havent changed the bounds after the first sub

[novel merlin]

but I changed it back to x at the end

So I wouldn’t need to no?

[red nimbus]

oh so u r one of those

let me check then further

[red nimbus]

what happened here

[novel merlin]

OH

[red nimbus]

the sqrt just disappeared?

[novel merlin]

BRUH

[red nimbus]

blud

[novel merlin]

😭💔💔💔💔

[red nimbus]

also, if you insist on holding on to the old bounds

write x=0 and x=1 instead of just 0 and 1

[novel merlin]

okok

thank u so much 😭😭😭

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[green gull]

hello, can someone give me a hint on this please

[marsh citrus]

@green gull Has your question been resolved?

[green gull]

has anyone got any ideas?

[fathom sun]

use law of sines

i think that might work

[green gull]

idk, i dont think it would cus we dont know any other ratios except x,2x

.close

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[dusty kite]

How to find what f(x) gives y = 1?

[plain vault]

you start with $f(x) = 1 \Leftrightarrow \frac {2x} {3 - x^2} = 1 \Leftrightarrow \frac {2x} {3-x^2} - 1 = 0 \Leftrightarrow \frac {2x - (3x - x^2)} {3x-x^2} = 0$

[elfin berry]

robins

[plain vault]

then you solve that

you just have to factor by x and eliminate values that make the denominator null

[slim shard]

typo on the last step?

anyways, it would be easier to multiply 3 - x^2 to both sides of the equation directly

[plain vault]

you can also do that

[dusty kite]

Buddy

I get this

Which gives me shit

[plain vault]

how did you go from step 1 to step 2

[dusty kite]

Multiplied everything by 3

[serene bramble]

But you're dividing by (3-x^2) there

Not by (3)

[plain vault]

3 times (3-x^2) isnt equal to -x^2

[serene bramble]

So you can't just multiply that 3 out like that

[dusty kite]

So what now

[serene bramble]

^^^^^

[dusty kite]

No I was trying to get it out of denominator

[serene bramble]

And you do that by multiplying by the whole denominator

Not part of the denominator

Like, it's good intuition to avoid fractions if possible

But you gotta make sure you're doing it correctly

[dusty kite]

Okay so it is 2x * -3+x^2 = 0

[slim shard]

this is !nosols territory

!nosols

[marsh citrus]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[plain vault]

sory

[serene bramble]

What's the * doing there?

'Cause if it weren't there, it'd be correct

[serene bramble]

^ (Directed at this message)

[dusty kite]

How to factor x^2 + 2x -3 now?

Idk how to do that

[serene bramble]

https://byjus.com/maths/factorization-of-quadratic-equations/
I recommend looking at the examples here:

[Though, I feel you should have had some experience with this already]

[dusty kite]

Idk this

[plain vault]

sometimes you can find some values that are evident

you can try with 1, 2, -1, -2 ...

if one of them is a root, you can factor by (x-root)

[serene bramble]

-# I mean, you have mentioned quadratic equations here before

[slim shard]

i dunno why you'd want to test 2 or -2 in this case

[serene bramble]

-# though often misspelling it "quadric"

[plain vault]

i mean i wanted to be general

[slim shard]

anyways, if there are too many factors to list and you don't want to check them all, you can always use the quadratic formula

if you've learnt that

[dusty kite]

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[sturdy python]

what are the components of v if v = 2t + 3p -s t = (20,49), p(21,12) and s(-13,18)

[sturdy python]

i tried finding the norm for t p and s

then i put them in the equation and got 156,18 but none of the answers give that

[marsh citrus]

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[sturdy python]

.close

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[untold spruce]

how can I show that $$\int_0^b t^{p-1}$$ for $$0 < p < 1$$ is integrable? I'm trying to show that $$t^p$$ is absolutely continuous which would imply that, however I get stuck/reverting back to using this integral again making it circular

[elfin berry]

LXDL

[marsh citrus]

@untold spruce Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[undone coyote]

can anyone help me with the sign table

[undone coyote]

i’m lost

[marsh citrus]

@undone coyote Has your question been resolved?

[limber wigeon]

you have to plug in values

so like f(1), f(4), etc

see if the result is positive or negative

[stoic saddle]

i wouldnt say "have to" but it is a way to do that

[limber wigeon]

what easier way is there?

[twilit scarab]

Can't you just draw it

[limber wigeon]

this is a very hard equation to graph

[twilit scarab]

Not really

[limber wigeon]

6 degree polynomial

[twilit scarab]

Just check if a is positive or negative and account for double roots

Just a sketch

[limber wigeon]

thats what i said bro

[twilit scarab]

?

I don't get how it's hard

[limber wigeon]

graph it right now by hand without plugging in values

no calculator

[stoic saddle]

sign chart for each factor individually and then multiply them together

[twilit scarab]

Alright bro

[limber wigeon]

i guess, but that is just as much work

[stoic saddle]

i dont think it is

[limber wigeon]

plug in 5 values to f(x), you are done

[stoic saddle]

you dont need to plug values in at all

(x-3) is positive to the right of 3 and negative to its left

you can conclude this without plugging a single value into f

[stoic saddle]

that is the "calculator in a meat suit" way imo

[marsh citrus]

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[echo scaffold]

I don’t understand how to find the x intercepts. For the old ones we would set it to zero. But the new versions that have a second vertical asymphentote we look at the numerator . But now I don’t know if we look at the numerator before or after simplifying

[marsh citrus]

Please don't occupy multiple help channels.

[odd agate]

you still have an ongoing channel

[gloomy merlin]

You always set y = 0 when finding y intercepts regardless of context

[whole thorn]

x intercepts is just f(x) = 0

a/b = 0 if and only if a=0

so u only need to look at numerator

[gloomy merlin]

Oh whoops

[gloomy merlin]

a and b need to be coprime as well

[whole thorn]

no

just multiply both sides by b

and divide for opposite

https://tenor.com/view/jacob-rees-mogg-boris-johnson-bruh-neutral-face-conservative-party-gif-24805421

mfw when people ask a question in a help channel then go afk

[gloomy merlin]

Im saying that (x-2)(x-3)/(x-2)(x-4) = 0 -> (x-2)(x-3) = 0 is incorrect unless you explicitly restrict the domain of (x-2)(x-3) to exclude x = 2 or remove it entirely by eliminating the common factor between the numerator and denominator

[whole thorn]

ok

[whole thorn]

yes here x needs to be in the domain of f ofc

[echo scaffold]

Also for this one I think k am going insane because I know -10+4 does not equal -3

[whole thorn]

right

but this is 5x - 8x

[echo scaffold]

huh

[whole thorn]

where are you getting -10+4 from

[echo scaffold]

This is the answer key btw I should of said it

[whole thorn]

yeah this is correct

😐

[bright frigate]

what is -10+4

[marsh citrus]

@echo scaffold Has your question been resolved?

[limber wigeon]

.close @echo scaffold

write that

[odd agate]

.close

[marsh citrus]

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[distant stone]

so idk what i did wrong when doing this proof

[distant stone]

because it is wrong

[stoic saddle]

you didn't calculate T(u+v) correctly that's what

[distant stone]

what did i do wrong?

[distant stone]

i don’t see what’s wrong

nvm i’l do it tmr

[devout mauve]

you need to multiply both entries of u+v

to get the first coordinate

[marsh citrus]

@distant stone Has your question been resolved?

[marsh citrus]

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[trim raven]

can someone tell me if b) is right and if it is, is there a simpler way to do it
cus its 2 marks and i feel like my working is messy

[marsh citrus]

@trim raven Has your question been resolved?

[marsh citrus]

@trim raven Has your question been resolved?

[trim raven]

nope 😪

[plush elk]

AE=(|EB|/|DB|)AD+(|DE|/DB|)AB

[trim raven]

thank you

.close

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[oblique field]

based on this video https://www.youtube.com/watch?v=zczGnnM05TQ
someone flips 2 coins and hides them from you. they tell you that one of the coins flipped tails. what's the probability that the other one is also tails?
is it 1/3 or 1/2? the person in the video claims there are 3 cases: T T, T H and H T, so the probability is 1/3, but does that make sense if the order of the coins clearly doesn't matter?

i made this program (python) to test it out (a chooses which of the coins the person was referring to when they told you one was tails, zbroj means sum in my language), and it suggests it's 1/2. did i implement it wrong?

from random import*

coin0 = 0
coin1 = 0
counter = 0
for i in range(1000):
    a = randint(0, 1)
    if a:
        coin0 = 1
        coin1 = randint(0, 1)
    else:
        coin1 = 1
        coin0 = randint(0, 1)
    zbroj = coin0 + coin1
    if (zbroj == 2):
        counter += 1
    zbroj = 0


print(counter)

[marsh citrus]

@oblique field Has your question been resolved?

[quaint elm]

Yes, you implemented it wrong. This is subtle, but yours has the wrong probability distribution. Try implementing it more closely to the scenario:

trials = 0
counter = 0
while trials < 1000:
  a = randint(0, 1)
  b = randint(0, 1)
  if a == b == 0:
    # both heads, discard this one
    continue
  # we have at least one tails
  if a == b == 1:
    counter += 1
  trials += 1

print(counter, trials)

the error you made has to do with the line "a chooses which of the coins the person was referring to when they told you one was tails"

particularly, the person doesn't choose a coin and then decide to tell you whether it was tails; they look at both of them and then tell you whether at least one of them was tails

[oblique field]

huh i see.. this one suggests a 1/3 chance

and i just remembered this formula for calculating probability when something is given

[quaint elm]

yes; what you calculated was P { both are tails | the first one is tails }

[oblique field]

because it's P(both are tails)/P(at least one is tails) = 1/4 / 3/4 = 1/3

alright tysm

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[red phoenix]

q1. why is v_√a bounded? (the 1st -turquoise- highlighted sentence)

[plush elk]

0<a<1 is given prior to that

Thus 0<a^v<1

[red phoenix]

Oh so it's simply
0<a<1
⇔0<v_√a<1 (taking vth root of all the sides)
?

[plush elk]

Yeah

[red phoenix]

q2. how does 2.1.3.3 imply that {1-v_√a} is a positive null sequence?

[plush elk]

1-a^(1/v)=(a^(1/v))(b^(1/v)-1)

[red phoenix]

got it. Thanks!

took me an hour and still could not figure out

.close

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[stable spear]

Hey, I have a couple old exam problems I need checked — I think my solutions are right but not 100%.
I’d like to get fast, precise feedback from someone who really knows the material.

If you’re confident, feel free to DM me and I can send one problem at a time.

[agile kiln]

whats the first problem

[stable spear]

Do you know Algebra & Calculus 1 for Engineering students?

[agile kiln]

I am an engineering student so I could possibly help you

But if you just post the problem in here instead of asking people to dm you, I'm sure you'll get faster replies

[stable spear]

I need that way so best dm me

[main idol]

not how the help system works in the server

see #rules and #❓how-to-get-help

[torpid swallow]

send it i cant wait

https://tenor.com/view/sonic-devil-diabolique-evil-gif-9725651736562738158

[stable spear]

Its different language thats why

sorry

[main idol]

!done

[marsh citrus]

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

[stable spear]

.close

[marsh citrus]

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[torpid swallow]

math has no linguistic barriers broski

[crystal lintel]

[stable spear]

.closed

[marsh citrus]

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[gaunt lynx]

what did i do wrong on the c)?

[gaunt lynx]

,rotate

[gaunt lynx]

,rotate

[gaunt lynx]

what did i do wrong on the c)?

like its wrong but idk what i did wrong

[main idol]

Where are you actually calculating the probability

this is just the range of x values that are within 1 std dev

[gaunt lynx]

yes

but did i do it wrong

-5,6764

sorry my writing is bad

[main idol]

yes a probability is a number in [0, 1], not a range of values

[gaunt lynx]

yes but are the numbers correct

oh omg

it translated wrong

omfg

wait no i didnt

so look

it lies around the standard deviation, which is 5,2764 if i didnt do anything wrong

and do it -5,2764 - 0.4 <= x <= 5.2764 -0,4

But i wasnt sure if i did everythign correct to this pojnt

hello?

[potent scroll]

hello

[marsh citrus]

@gaunt lynx Has your question been resolved?

[gaunt lynx]

can u help

[potent scroll]

yes what do u need help with

[marsh citrus]

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[rose saffron]

$\int_{-1}^{1} 1/x dx =0?$

[elfin berry]

Goofy Joe

[wind hare]

the PV is 0

otherwise it diverges due to the singularity

[wind hare]

https://en.wikipedia.org/wiki/Cauchy_principal_value

[rose saffron]

Odd function symmetric domain why doesn't it equal 0?

[devout mauve]

cause you cant integrate it over the domain

you cant just ignore the singularity

[rose saffron]

So it diverges symmetrically?

[devout mauve]

in a sense, sure

[marsh citrus]

@rose saffron Has your question been resolved?

[marsh citrus]

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[bronze osprey]

The curve models frequency density:

y=k/x^2 where k is a constant. ​

,1≤x≤8

Total frequency = total area under the curve = 112... Find the value for k.

[limber hearth]

What is equal to 112

[bronze osprey]

the area under the freq density curve

[limber hearth]

Which is

[bronze osprey]

the frequency?

[limber hearth]

How do you calc area under curve

[bronze osprey]

OHH integrate

[limber hearth]

So what does it gives

[bronze osprey]

is it -kx^-1?

[limber hearth]

Its a definite integral, you have bounds for x

But the antiderivative is correct yes

[bronze osprey]

whats thatg

antiderivative means same as integratiomn?

[limber hearth]

Yes you integrate, and its correct but here its a definite integral

[bronze osprey]

wait i got the ans i think

i got k=128

[limber hearth]

How did you get this?

[bronze osprey]

i substitured 8 and 1 as x into -k/8-(-k/1)=112 then reaargend to get 7k/8=112 then k=128

[limber hearth]

Yeah seems good

[bronze osprey]

yayy ty!

.close

[marsh citrus]

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[limber hearth]

Antiderivative is the function you get by integrating

An antiderivative of 1/x² is -1/x

[marsh citrus]

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[bronze osprey]

ahh icc

[limber hearth]

(There is infinitely many so its an antiderivative and not the antiderivative)

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[gaunt lynx]

guys this is correct right? why would my teacher give 7/9 points

[gaunt lynx]

wtf man

[main idol]

can't tell without the original question

[gaunt lynx]

alright dont leave tho i gotta translate it rq

[main idol]

maybe

[gaunt lynx]

After the group stage in the Champions League, a knockout round and further knockout rounds follow. There are about 400 football players in action. Only 20% of them, based on experience, get involved in tackles without illegal physical contact (R̄).

45% of the football players receive a yellow card (G). Two thirds of the yellow cards are given to players because of illegal physical contact.

a) Represent the described situation using a tree diagram, an inverse tree diagram, and a contingency table.

did i forget to put anything to it?

[marsh citrus]

@gaunt lynx Has your question been resolved?

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[gaunt lynx]

Stefan is an enthusiastic goalkeeper because he is a member of a football club. He meets his friends there and also likes to drink one or more schnapps.
In the sober state, Stefan hits the goal with a probability of 95%. However, his probability of hitting the goal decreases by one quarter after each schnapps.

a) Calculate the probability that he hits the goal at least once if he shoots three times: once sober and once after each of two schnapps.

[gaunt lynx]

Hello so i dont understand

ik the first one is

0,05*

nvm i got it

[marsh citrus]

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[marsh citrus]

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[granite vault]

Here is the generalized mean value theorem from Abbott. Am I correct that the selected condition can be weakened to the following: $g'(c) \ne 0$ and $g(b) - g(a) \ne 0$ without loss of generality?

[elfin berry]

Dedekind

[cunning fiber]

You can’t place a condition using $c$ because $c$ hasn’t been decided yet

[elfin berry]

Civil Service Pigeon

[cunning fiber]

Ex $f(x)=x^2$, $g(x)=x^3$ on $[-1,1]$

[elfin berry]

Civil Service Pigeon

[granite vault]

Why so? c was defined in the previous part

[cunning fiber]

You don’t know what $c$ actually is

[elfin berry]

Civil Service Pigeon

[cunning fiber]

Just that it exists

Look at the counterexample I sent

[granite vault]

could you please elaborate, this is the counterexample to what? I see that $g'(0) = f'(0) = 0$, so the first part of the theorem holds at $c=0$. The second does not neither in original formulation, nor in my suggestion

[elfin berry]

Dedekind

[cunning fiber]

Sure your statement isn’t false, but it makes the theorem useless. The point is that you’re guaranteed to be able to work with $f’(c)/g’(c)$. With your weakened version, the theorem says “We have a $c$. Whether or not you can divide by $g’(c)$? Who knows.”

[elfin berry]

Civil Service Pigeon

[cunning fiber]

By saying that $g’$ is never zero, there’s the guarantee that no matter what $c$ is, the denominator is “safe”

[elfin berry]

Civil Service Pigeon

[cunning fiber]

Also imma be honest - I meant for this to be a pop in and dip kinda thing

So I gtg

[granite vault]

Yep, makes sence, thank you

.close

[marsh citrus]

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[cunning fiber]

[marsh citrus]

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[still temple]

i got here

@chrome jacinth

did i do something wrong or

[tight furnace]

how did you end up with a degree 5 polynomial

[still temple]

✨ substitution ✨

[tight furnace]

What did you substitute

oh

Ok as far as I can tell none of it is incorrect but I think it's just making the problem worse

[still temple]

that sounds like me when i touch maths yeah

[tight furnace]

probably the answer is to just subtract the n^3-n for 2k+1 from the 2k+3

[still temple]

can you latex this

$\LaTeX$

[elfin berry]

░▒▓█PIE█▓▒░

[tight furnace]

$P(2k+3)-P(2k+1)$ where $P(n)=n^3-n$

[elfin berry]

Dreyuk

[tight furnace]

If you show this is divisible by 24, you're pretty much done

and it's a quadratic, which should make it easier

[still temple]

wow

i got to the start again

can i do LHS = LHS ✅ ✅ ✅ ✅ ✅

[tight furnace]

well it probably won't lead anywhere

[still temple]

wait so you can do this in induction?

[tight furnace]

well your inductive hypothesis is "24 | P(2k+1)"

[still temple]

yuh

[tight furnace]

if you show that 24 | P(2k+3) - P(2k+1)

then you know that 24 | P(2k+3)

[still temple]

[still temple]

i tried that i didnt get very far

like it makes sense

[tight furnace]

stop replacing things with m

just expand the polynomial

[still temple]

okkk

got it thanks

!close

[tight furnace]

no problem

.close

[marsh citrus]

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[final cobalt]

I asked earlier this question and got help but couldn't solved by the method what helper told

I need help with 2nd part where Y is to be found

[maiden haven]

You understand that x = 20 \cdot 19 \cdot 18 right?

hmm this is a bit harder since you can have 2 points that share a neighbour...

You could split it into multiple situations and add up all those possibilities, one where they have no common neighbours, one were only 2 points have a common neighbour, and one where all 3 points have common neighbours

If you understand what i mean

[marsh citrus]

@final cobalt Has your question been resolved?

[final cobalt]

Yes X is simply 20c3 = 20.19.18/3! = 1440

1140*

[maiden haven]

why divide by 3!?

[final cobalt]

20c3 = 20.19.18/3.2.1

Writing 20c3 in short

[maiden haven]

ah right i forgot about the order symmetry stuff

[maiden haven]

I suggest trying this out

[final cobalt]

Let me try once

[maiden haven]

$\frac{20 \cdot 17 \cdot 14}{3!} + \frac{20 \cdot 2 \cdot 15}{3!} + \frac{20 \cdot 2 \cdot 2}{3!}$

if im not mistaken

[final cobalt]

I found your hints to be 1, 10 and 6 respectively

Idont know if it's correct

[final cobalt]

Type out latex it's hard to understand

[maiden haven]

latex doesnt work with spoilers so i didnt latex it, wanted you to try first

[elfin berry]

Quin

[maiden haven]

I think i made a slight mistake somewhere, since you get a rational answer

but this is just proof of concept

[final cobalt]

Didn't understand tbh

🙁

[maiden haven]

In the first part i say, none of the points touch eachother

or share common neighbours

so each time i select a point im basically taking out 3 options at once

second part i say, well 2 points share a neighbouring point, hence why i put the times 2 since it can be of to either side of the first point

in the third part i say, they all share neighbours, so i do times 2 2 times

if that makes sense

but i made a mistake in there somwhere since you dont get integers as an answer, maybe someone else can spot my mistake but oh well

yeah no my method is incorrect , if anyone else knows how feel free

[final cobalt]

oh yes

this is solution they provided

which is again i can't comprehend

[marsh citrus]

@final cobalt Has your question been resolved?

[marsh citrus]

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[thorn sundial]

can someone teach me ambiguious case and grade 11 cartisian planes

[thorn sundial]

i did bad on my test cuzz i didnt know what a ambiugouis case was and im bad at cartiesian planes

[marsh citrus]

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[marsh citrus]

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[novel juniper]

The derivative of the function when x≠0 is

$\frac{1}{2} + 2x \sin\left(\frac{1}{x} \right)-\cos \left( \frac{1}{x} \right)$

am I tripping

[elfin berry]

wai

[devout mauve]

so?

[novel juniper]

oops

right, I have to use the defn of the derivative

.close

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[buoyant vault]

loosely translated from my assignment.

I reached a recurrence relation:

fn = fn-1+ fn-2 + fn-3

how am I suppose to find an explicit formula from this?

[wary lichen]

these things are a pain to solve.

[buoyant vault]

bro... 😭 🙏🏼

[gritty lintel]

[buoyant vault]

this is the warmup

[gritty lintel]

It need not be done manually, though.

It would indeed be a pain to solve if done manually.

[scenic stirrup]

(manually) it involves solving the following cubic:
x^3 - x^2 - x - 1 = 0

This doesn't have rational roots so good luck ig?
Unless it does? yeah no

[wary lichen]

i somewhat recently had a similar problem

Tbh i spent like half a month, plus other things on top obviously

[buoyant vault]

maybe the recurrence relation is wrong? Idk

could u guys check it for me?

[scenic stirrup]

how many binary sequences of length 33 are there
how many do contain this string
therefore how many do not

wouldn't mess around with 3rd order recurrence relations

[buoyant vault]

ok so I can insert the string 11 times

that means I choose an index between 1 and 30 and place the string then create a sequence on top of that

I do that once. then twice. then 3 times up until 11.

so that makes...

sec

[wary lichen]

Just to show why these things are painful

and notice, yours is harder

[scenic stirrup]

Here's the solution set of the derived cubic, just for funs!

[wary lichen]

which, also, the roots are just the easy step

[buoyant vault]

this it?

[buoyant vault]

the entire task is about recurrence relations Idk. they have an answer where they reached a different reccurence relation which is ez to solve but I got this one and it's impossible

[scenic stirrup]

Then you made a mistake in deriving the recurrence relation man
Can you send your working out?

[buoyant vault]

like how I got there?

[buoyant vault]

ah wait that's incorrect

[buoyant vault]

even this is hard af

[wary lichen]

Okay, just to start, assume a smaller string

(for the sake of explanation we will make it 6bits)

[buoyant vault]

ok

[wary lichen]

Lets start from 000000

Place 2 1s together anywhere but at the front

now we have 011000 001100 000110 000011

notice, this splits the string into a "before and after" based on the 011 sub-string

[buoyant vault]

ye but I'd like to interrupt

what about 011011

[wary lichen]

gimme a sec

[buoyant vault]

❤️

[wary lichen]

011000 -> 011 000
001100 -> 0 011 00
000110 -> 00 011 0
000011 -> 000 011

ignoring the 011s

you get a "sub" problem, how many 011 can you fit a 1-string, 2-string or 3-string

for 1 and 2 you obviously cant

For 3-strings you can fit exactly 1

so you double the "weight" of the string 011000 and 000011

[buoyant vault]

ok

[wary lichen]

Thing is, you only have to solve once for each string lenght

[buoyant vault]

yes but is there a pattern

that I can rely on

can't just count all of the ones that I don't want

ok so after testing my recurrence pattern was wrong. fuck me

my bad team. thank u for trying anyways ❤️

.close

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[dry plinth]

Can I get help with a quadratic equation proving thingy

[dry plinth]

the 2nd question, I don't understand it

.close

[marsh citrus]

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[granite valve]

Why'd you close

[marsh citrus]

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[raven zinc]

I was wondering if I got correct answer or not. My answer for this question was 9

[marsh citrus]

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

@raven zinc Has your question been resolved?

[marsh citrus]

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[jolly knot]

hello

[jolly knot]

so we're doing matrices

the first one is X = A^-1 * B?

[tight furnace]

If you're trying to solve for X, then yes

[jolly knot]

yeah

and like the 7th will be

(A+2)X = C+ D

Then

(A+2)^-1 (A+2)(X) = (A+2)^-1 (C+D)?

[jovial blade]

noi its X= B* A^-1

[tight furnace]

What's A+2?

[jolly knot]

7th

[tight furnace]

Bruh

No it's not

A is a matrix

2 is a number

[jolly knot]

yeh, he thought i was doing 2nd exercise

[tight furnace]

how can you add a matrix to a number

[jolly knot]

huh

it was

AX + 2X

[tight furnace]

Right

[jolly knot]

so i take the x out

(A + 2) * X

[tight furnace]

A+2 isn't defined

You can't add a matrix to a number

[jolly knot]

oh so i cant do that?

[tight furnace]

Right

[sharp ivy]

when you factor X, you're left with the matrix-equivalent of "2"

[tight furnace]

you have to find a matrix M such that MX = 2X

[sharp ivy]

which isn't just the number 2

[jolly knot]

so we uhh

[jovial blade]

wow yeah in our school we wrote linear equations in the form AX=B and then solved using X=B*A^-1 so that was my natural instinct

[tight furnace]

you can't do that, it has to be A^-1 * B

ABA^-1 won't equal B

If B is a column vector and A is a square matrix than BA^-1 isn't even defined

[jolly knot]

so do i consider 2X like M?

[tight furnace]

Then you would have 2XX = 2X

which isn't true

[jolly knot]

why

oh yeah

i have no idea what to do

[tight furnace]

What matrix doesn't change something when you multiply by it?

[jolly knot]

I

[tight furnace]

Right

So if I want to multiply by 2

[jolly knot]

2I?

[tight furnace]

Exactly

[jolly knot]

but

isnt

2I

oh yeah its not I^2

right

soooo

instead of writing

(A + 2)

i should do

(A + 2I)?

[tight furnace]

Yeah you got it

Nice

[jolly knot]

okeey

and then as usual

thx

[tight furnace]

np

[jolly knot]

.close

[marsh citrus]

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[jovial blade]

yea ur right i was just misremembering

my bad

[tight furnace]

No worries

[marsh citrus]

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[jolly knot]

ok

[jolly knot]

matrices

wtf do i do here

do i multiply each one for 3^-1

so i get rid of 3

and then factor out the X?

[static quarry]

you could factor it as $X(A + 3I) = C$ if that helps

[elfin berry]

Bungo

[jolly knot]

but on the one number the X is from the right side and another one is from the left

can i do that?

[static quarry]

scalars can go on either side, they commute with matrices

[jolly knot]

or it doesnt matter in I matrices

[static quarry]

(as do diagonal matrices like 3I)

[jolly knot]

whats a scalar

[static quarry]

3 is a scalar

scalar = number

[jolly knot]

but am i required to put 3I?

or can i put 3

[static quarry]

because A + 3 doesn't make sense

[jolly knot]

ok

so it doesnt matter

thx

.close

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[gloomy musk]

May I ask how to prove that A,E,H are in the same line. Im trying to prove triangle BEA is similar to triangle HEO. But im struggling with that way. So I wonder if we could prove BH is the tangent of (O) or is there any hint for the first way? Pls help me😭

[muted nest]

Is AE perpendicular to BO given?

[gloomy musk]

Yupp

The ggle translate isnt that good💔

Srry

[muted nest]

Which part are you at?

[gloomy musk]

The 2nd part of b

A,E,H thingy

[muted nest]

It's alright, I took way too long to realise that E hasn't even been defined properly yet

[gloomy musk]

Oh

Im still learning math in English, i mind not very good at explaining my situation, srry first if it makes u uncomfortable tho

[obtuse umbra]

,rccw

[elfin berry]

Couldn't find an attached image in the last 10 messages.

Jan 13, 2026, 3:19 PM

[obtuse umbra]

yep, vietnamese spotted

[dreamy steppe]

from first part of (b) you can get that A, B, D, E are on the circle, from that you can show that angles marked red are equal (more specifically ABO and AHK)

[obtuse umbra]

toán điều kiện hay toán chuyên

[gloomy musk]

Toán thường t á

[muted nest]

Ok so I used angle chasing to get the result

But ig it's better if you understand in your mother toungue

[gloomy musk]

Oh yea, ive proven it. But im struggling after that part

[dreamy steppe]

then you just need to notice that AHO = OAH and then show that OAE also same

[gloomy musk]

May i know how to solve in ur way too? Cuz i want to know more of how to solve in case there r the others that cant be solve in my way

[muted nest]

One advice by the way, when you are trying to prove 3 points colinear, take 2 separate points, one which satisfy the conditions in the question and one that actually lies on the line

[muted nest]

I'll send my work wait a sec

[gloomy musk]

So the goal is to prove that OAE=OHA?

[dreamy steppe]

actually OAE=OAH this will result in A, E, H on one line

[gloomy musk]

Ohh

[muted nest]

A E' and H are colinear and E' lies on BO
We'll eventually prove E and E' coincides

I forgot to label K but imagine it's there

[gloomy musk]

Wait,since ive alr proven OBA=OAE, is it possible to prove that AHO(=OAH)=ABO so that OAH will equal to OAE

[gloomy musk]

Okayy

[dreamy steppe]

thats correct

[gloomy musk]

Oh that wayyy, im not too familiar w it so i didn't try

[gloomy musk]

Okayyy, ill try

[muted nest]

So we have ADK = AHK
And since AO = HO
AHO = OAE'
And I guess you got OAE = ADE so we got angle EAE' as 0 which means they coincide

[gloomy musk]

Wait wait, im a bit confused. How can OAE=ADE lead EAE' to 0?

Do we subtract the angle or anything else

[muted nest]

You have OAE' = OAE

So the angle in between has to be 0

[gloomy musk]

Oh i understand now

Tyyy

[muted nest]

No problem

[gloomy musk]

I didn't read carefully, srry(⁠•⁠ ⁠▽⁠ ⁠•⁠;⁠)

[muted nest]

Btw BEA is not similar to HEO so you won't get anything

[gloomy musk]

Ohhh

No wonder y i struggle 💔

Ty for telling me

[gloomy musk]

À đr bạn. Bạn bt cái bảng xét dấu là s ko, bữa hôm đó anh trợ giảng kia giảng mà mình ko hỉu lắm💔. Hc có 1 hôm hôm sau ko hc nx nên cx ko cs tiện hỏi thầy

[obtuse umbra]

bảng xét dấu ah

bđt đk?

[gloomy musk]

Đr á

[obtuse umbra]

vc

[gloomy musk]

Đợi mình lấy vở

Đợi tý

[obtuse umbra]

hnhu mik có nghe qua

[gloomy musk]

:0

Hôm đó hc mà chả hỉu j

Hên ko lm bt

À mà bn có hc chuyên ko? Nãy thấy nhắc qua

[marsh citrus]

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[gritty ether]

answer is 158, all i need is just the angles used to get this answer (if u can draw the needed angles it would help

[knotty trellis]

we start knowing this (the red angles are same)

[gritty ether]

thank u but where are the 2 lines to show its an isoscles

isosceles

[knotty trellis]

those are RT and TU, it was said in question that RT = TU

[gritty ether]

ooooo

yea

[knotty trellis]

after that, try expressing the green angle using x, then the orange angles and finally the red angle - it can be expressed in 2 ways

[gritty ether]

so 11 degrees is RT and TU

[knotty trellis]

that'll get u an equation to solve

[knotty trellis]

you're working backwards here, but ye

[knotty trellis]

and its not RT and TU, but rather URT and RUT

[gritty ether]

yeah mb

wait

i used differenet method

[knotty trellis]

are you trying to undestand how they achieved the answer or what are you trying to do?

[knotty schooner]

should i also give it a try or are you guys good

[gritty ether]

i saw a quadraliteral

so i did 360 - RUT - UVS - the last one

[gritty ether]

you answer my question

[knotty trellis]

how did you get the last one?

[gritty ether]

how wouldve u formed it starting with the green angles

[knotty trellis]

or was that used to solve for the last one?

[gritty ether]

the last one i mean like the 2nd pink circle i circled

if that makes sense

[knotty schooner]

what is the answer guys i think i got it

[gritty ether]

158

[knotty trellis]

green = 180 - x
orange = 180 - (180-x) - 23 = x - 23
red = 180 - blue - orange = 180 - 34 - (x-23) = 169 - x

But also, x + red + red = 180 so red = 90 - x/2

so red = red
169 - x = 90 - x/2
169 - 90 = x/2
79 = x/2
x = 158

the key is not to be too afraid of expressing the angles in terms of x

[halcyon elk]

you can also start by finding the green angle. this way, you'll have two angles of the triangel USV so you can find the third!

then another angle chase

[knotty trellis]

oh, thats probably quicker

[halcyon elk]

I like the equation method

[knotty trellis]

green = 180 - 34
red = 180 - (180 - 34) - 23 = 34 - 23 = 11
Now x = 180 - 2*red = 180 - 22 = 158

much better

but no matter where you start, you should be able to get the answer within few minutes

[knotty schooner]

yeah i did that too its pretty simple that way isnt it

[halcyon elk]

equation method is more satisfying tbh

either methods might take a bit depending on ---> how fast OP angle chase's / how fast can they solve an equation

[knotty schooner]

can you check the efficiency of my solution @halcyon elk

[halcyon elk]

what solution?

[halcyon elk]

that works too ig!

[knotty schooner]

so this is isnnt isnt efficient

[halcyon elk]

no no, its good 😭 you did great.
now we shall wait until struc comes back or- let hte channel be closed.

[marsh citrus]

@gritty ether Has your question been resolved?

[marsh citrus]

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[floral charm]

not sure how to do 2a

[floral charm]

how do i take the moment

[gilded wigeon]

shift the normal force to the corner

then calculate torque at that point

[marsh citrus]

@floral charm Has your question been resolved?

[floral charm]

wdym

[high pine]

Have you tried calculating the perpendicular distance from pivot to center of mass?

[gilded wigeon]

so basically this is the case of toppling

what happens here the normal force from the ground is at the edge, aka atpoint P in this case

[floral charm]

yes

[gilded wigeon]

so if u apple a force F horizontally, the fridge will topple right?

so to calculate said force, u have to apply the concept of torque about point P

[floral charm]

yes

[gilded wigeon]

so torque due to weight of object = torque due to force needed to topple

now baland them both

so u do need to calculate perpendicular distance from point P to centre of mass for it

now i hope u can figure it out

[floral charm]

yeah i get it now

.close

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[marsh citrus]

Please don't occupy multiple help channels.

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[marsh citrus]

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[unreal stag]

I’m doing equation x^2-|x| and i put that it is increasing at (-0.5,0) and (0.5, infinity) decreasing at (-infinity, -0.5) and (0, 0.5) Do i use unions between these

[unreal stag]

Also is the little tip at the origin a local maximum?

[sacred river]

Yes I think but take common from these limits put union between them

[unreal stag]

Sorry what does “take common” mean 😭

[granite valve]

f(x)= x^2 -|x|?

[granite valve]

right but what are you supposed to find

[astral bough]

you should not if you are not experienced

just put it as increasing at..intervals and decreasing at...intervals

[granite valve]

yes

[astral bough]

if you say its increasing at (-0.5,0) U (0.5, infinity) then ANY point that satisfy x2>x1 means f(x2)>f(x1), these point can be in 2 different intervals

[marsh citrus]

@unreal stag Has your question been resolved?

[marsh citrus]

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[quartz elbow]

The lengths of the sides of a right triangle are the next terms of an arithmetic sequence and satisfy the given condition. Calculate the lengths of the sides
a) the perimeter of the triangle is 48

[quartz elbow]

i mean i know there's an easier way to solve it

[quartz elbow]

i just want to know what i need to do next to solve it that way

[knotty trellis]

pythagoras

a1^2 + a2^2 = a3^2

substitute for a1, a2 and a3, solve and you're done

[quartz elbow]

yeah but I still get 2 variables
a1^2+16^2=(a1+2r)^2

oh wait substitute this at the bottom

right

[knotty trellis]

i meant sub in 16-v and 16+v

[quartz elbow]

yeaj

[quartz elbow]

oh yeah r=4 thanks

.close

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[floral charm]

F

[floral charm]

how does this not work

let theta = t for ease

CD = rt
BA = r( [pi/2] - [t/2] )

BA = EF

perim = CD + CB + ED + BA + EF + AO + OF
perim = rt + 1.5r + 1.5r + r( [pi/2] - [t/2] ) + r( [pi/2] - [t/2] ) + r + r
perim = pi(r) + 5rt/6 + 5r

markscheme says otherwise

[late geode]

where are your two +1.5r coming from

[floral charm]

cb

and ed

[late geode]

how did you get 1.5r for those segments

[civic ice]

Yea how?

It isn't given that it bisects

[floral charm]

i assumed that ED = 0.5 OD

[late geode]

shouldn't be assuming,
consider (segment) addition/subtraction

also how did you get

BA = r( [pi/2] - [t/2] )

[floral charm]

it should be t / 3

[civic ice]

Yea

[floral charm]

i just miswrote it

[late geode]

no

[civic ice]

?

Oh wait

Ur right

The whole angle is t/3

It won't be pi/2-t/3

It would be pi/2-t/6

[floral charm]

yeah im tripping idk why i wrote that on discord

what i wrote on paper was

2( [pi(r) / 2] - [t / 6] ) + 5r + rt = perim

[civic ice]

Yep

But

The

1.5r part is wrong

[floral charm]

yeah

[late geode]

first part is wrong too

r multiplies to both terms

not just what happens to appear first

[floral charm]

how do i work out CB?

[late geode]

consider (segment) addition/subtraction

OB is also the radius of the smaller sector

[civic ice]

It would be r

[civic ice]

Yea

I saw the given part rn

[floral charm]

ah

[civic ice]

OB=r , CB= 2r

So the total perimeter should be 2r+2[pi/2-t/6]+4r+rt

So basically 6r+2[pi/2-t/6]+rt

Just substitute values then or solve the whole par if u want

[floral charm]

.close

[marsh citrus]

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[zealous sapphire]

18 mice were placed in two experimental groups and one control group, with all groups equally large. In how many ways can the mice be placed into three groups?

[stoic saddle]

!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

[zealous sapphire]

1

[tidal abyss]

have u learnt combination formula?

[stoic saddle]

imagine putting all the mice in one line

the first six go into control, the next six go into exp. group A, the last six go into exp. group B

in how many ways can you arrange the mice in a line ignoring the group breakdown

[zealous sapphire]

18! ?

[stoic saddle]

indeed

now considering that rearrangements within groups don't matter, by what should we divide

[zealous sapphire]

3?

[stoic saddle]

no

what i mean is: if we rearrange the first 6 mice among themselves then we get the same group assignment ultimately

that means we divide by 6!

and again and again for the two experimental groups

and there may or may not be a wrinkle at this point

[zealous sapphire]

oh

but why do we need to divide necessarily

[marsh citrus]

@zealous sapphire Has your question been resolved?

[stoic saddle]

need to
necessarily
you missed the other 17 synonyms of "need" in that sentence that you would need to put if you're a redundant redundancy fan of redundant redundancy

anyway

when you drop the ordering of the first 6 mice, every 6! arrangements which differ just by where those mice are among themselves get collapsed down to 1

[zealous sapphire]

my bad

[zealous sapphire]

alr

[zealous sapphire]

so it will be 18! / 6!6!6!

[oblique kelp]

bros summoning the devil

[zealous sapphire]

😭

.close

[marsh citrus]

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[granite valve]

eh

[marsh citrus]

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[sacred crown]

find the general solution

[sacred crown]

i did find y1=[-2 1]^Te^(5t)

when finding [-2 4, -1 2]u = [-2 1] i seem to get no solution?

[spark otter]

You haven't seen equations X' = AX where A is a matrix before?

[sacred crown]

I have, did a course last year on it, but unfortunately forgot bunch of things

[spark otter]

So you forgot about the general solution ||X = e^(tA)X_0|| ?

[sacred crown]

this was my steps..

[whole sleet]

Where is the vector (-2, 1) coming from?

[spark otter]

It's -2x1 + 4x2 = 0, not -2x1 = 4x2

[whole sleet]

You're looking for the eigenvectors, which is when that matrix gives (0,0), not (-2,1)

OH I see what happened there

[spark otter]

I'm pretty sure that's not what happened

[whole sleet]

That's what they wanted to have happened, I mean

[spark otter]

Yeah, I was saying that's not the case

[sacred crown]

ohhhh

wait😭

yes i see it -2x1+4x2=0

oops😭

i thought I was missing smth, like a special case if no solution can be found, then what to do

[whole sleet]

Well, there is something interesting going on with this question. Feel free to ask if you get stuck again

[sacred crown]

thank you

.close

[marsh citrus]

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[marsh citrus]

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[waxen dust]

[cunning fiber]

[marsh citrus]

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[lethal bridge]

im not sure how to start

[jagged relic]

Start by posting this in a single picture

[lethal bridge]

js click

[jagged relic]

Rule #1 of asking for help: make sure to make it as easy as possible for others to help you

Anyway, at y=0, what is the value of that function? Same at y=1?

[lethal bridge]

at y=1 its just e^-x

at y=0 we have e^0=1

[jagged relic]

Right

Now I don't know how to answer formally but look at an x slice (fix x, find the area under that curve) and show that its area doesn't converge to 0 fast enough for the total volume to converge

(it might help to graph this if you don't have the intuition yet)

(like in Desmos 3D, e^{-xy}\left\{x\ge0\right\}\left\{0\le y\le1\right\})

[lethal bridge]

can i write like this

$\int_{0}^{1}\int_{0}^{R}e^{-xy}dxdy$

[elfin berry]

water beam

[lethal bridge]

as R-> inf

@summer trench what the blud

[summer trench]

hi

[lethal bridge]

jee blud

[jagged relic]

That's fine I guess but I would do dydx instead

[lethal bridge]

$\int_{0}^{R}e^{-xy}dx=\frac{1-e^{-Ry}}{y}$

[elfin berry]

water beam

[lethal bridge]

if i make y constant and integrate in x

and let R go to infinity

i get 1/y

then integrate 0 to 1 from 1/y

and this improper integral diverges

so the whole thing diverges then?