help-27

[dusky belfry]

we know

[young spade]

For any given polynomial of degree "n"

[dusky belfry]

c(x - 2)(x - b)(x -a)

[young spade]

You can always factorize it to n factors of the form (x-a1)

Which are your original roots.

up to some scalar multiplication for all terms.

[dusky belfry]

gotcha, let me try doing it myslef

myself

[young spade]

Id swear you already got the roots yourself.

If you recall what are the roots of a polynomial / function, it should be pretty clear why we can express it like that.

[dusky belfry]

yea

so

2(x-2)(x-b)(x-a)

for b and a

let me see

[young spade]

Are you sure that its x-2?

[dusky belfry]

hold it

[young spade]

Remember they are of the form, (x-A) where A is your root.

[dusky belfry]

right, the root is -2 not 2

sorry

so

[pseudo basin]

btw

why do you have literally every single pronoun role

[dusky belfry]

it's a very long story

Anyways

I tried to solve it

This might be dumb but I'm using a system of equations, $2x^2 + bx^2 + cx^2 = -\frac{1}{2} x^2$ and $2 + b + c = -3$

[woven radish]

ℕ∈ℝD ALERT: Gonçalo Gonçalves

[dusky belfry]

this didn't help

they cancel themselves out when I tried to substitute it

oh

[pseudo basin]

idk about anybody else but i am very confused as to what your goal is and what exercise/problem you're doing rn

[dusky belfry]

oh wait

sorry

my

bad

it's multiplication

damn it

[dusky belfry]

hold it

I'll copy

the whole thing

[pseudo basin]

i don't think it's a long story btw, i think the truth is that you went and clicked every single role in there just for fun and/or to deliberately make it hard for ppl to know how to refer to you

[dusky belfry]

kkkkkkkkk

"little menace"

the name they give me in my neighbourhood

Consider the polinomial P(x) = 2x^3 - x^2 - 13x - 6. Part I: Show that -2 is a root of the polinomial (done). Part 2: Represent P(x) in the form of P(x) = a(x-b)(x-c)(x-d)

[dusky belfry]

That's the problem question

[pseudo basin]

ok

you know how to do polynomial division yes?

or in your case the ruffini thing or whatever

[dusky belfry]

yeah

I know how to do that

[pseudo basin]

then you should divide 2x^3-x^2-13x-6 by x+2

[dusky belfry]

alright, let me try

[devout snow]

@dusky belfry Has your question been resolved?

[dusky belfry]

alright sorry for the long

I tried to find the roots myself

after doing the

division

wasn't successful

anyways, Q(x) = 2x^2 - 5x -3

so

$2(x^2 - (\frac{5}{2})x - \frac{3}{2})$

[woven radish]

ℕ∈ℝD ALERT: Gonçalo Gonçalves

[dusky belfry]

one of the 2 other roots is negative

one is positive

being x^2 + ax + xb + ba = (x - a)(x- b)

I need to find b and a

what came to my mind was a system of equations, but I think I messed up the algebra

reviewing rn

[dusky belfry]

the result of the division is Q(x) btw

maybe I just don't know the theory behind it or something

[dusky belfry]

it isn't ofensive to do this is it?

[pseudo basin]

i would say it is mildly offensive actually. if you truly dont care if ppl call you "he" or "she" or "they" or anything else, that's called any pronouns and we have a role for that.

if you have a preference, then there are roles for every combination.

if nothing covers it, "ask pronouns" and put your pronouns in your bio.

[dusky belfry]

not my goal, give me a sec

[pseudo basin]

and resist the impulse to use the pronoun field for funny/business or whatever else some people (usually guys) get up to

[dusky belfry]

is it better

?

[dusky belfry]

fine

I'll take it seriously

there

[dusky belfry]

done

[pseudo basin]

ok

good

[dusky belfry]

anywho, back to it

how do I find the zeros after dividing it?

I know this is not the place to give answsers

but I don't really know how to do

it

the system of equations didn't work so...

[dusky belfry]

so the solution is P(x) = 2(x + 2)(x + \frac{1}{2})(x - 3)

So my division is wrong

,w \frac{(2x^3 - x^2 - 13x - 6)}{(x+2)}

oppd

opps

[woven radish]

Results provided by WolframAlpha

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

Requested by goncalo_goncalves123

[dusky belfry]

ok no, the roots are correct, yeah, algebra

it's an algebra mistake

I can fix that

first let me see what the right result is supposed to be:

,w 2(x+\frac{1}{2})(x-3)

[woven radish]

Results provided by WolframAlpha

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

Requested by goncalo_goncalves123

[dusky belfry]

hmm

not really useful but ok

I'll do it

good news

[dusky belfry]

the division, after all, was made correctly, I just didn't know how to move to the roots

[devout snow]

@dusky belfry Has your question been resolved?

[hollow bolt]

i'd just use rational root theorem and then use synthetic division like ann said earlier (didn't see til now lol)

that's how most people solve higher order polynomials with rational roots

[dusky belfry]

how does it work

one of the roots is a fraction

the other an integer

[dusky belfry]

no offense intended, but it seams like it works, but also like it is not the right way to solve this, my manual didn't really

every teach this

but if it's the only one that works

I'll note it down either way

I just thought there was a better way to get there

[hollow bolt]

it's pretty straightforward tho, no?

[dusky belfry]

yea

[hollow bolt]

after you find each of the possible roots you perform synthetic division on the original polynomial

[dusky belfry]

for sure

It never teached it tho, so you know how it is, you raise an eyebrow

[hollow bolt]

and then there's stuff like upper/lower bound theorem and descartes' rule of signs that speed up the process

[dusky belfry]

https://tenor.com/view/rock-one-eyebrow-raised-rock-staring-the-rock-gif-22113367

like this

[hollow bolt]

you probably will learn it soon enough

[dusky belfry]

yea

you're right

[hollow bolt]

once you do, look into these

[dusky belfry]

hey, I've heard of descartes rule somewhere

[hollow bolt]

https://www.youtube.com/watch?v=Iaq7z7reznM
https://www.youtube.com/watch?v=ytI2jXM2WtQ
https://www.youtube.com/watch?v=YaU5JTe3cPU

[hollow bolt]

*note roots, zeros, x-intercepts, and solutions are used interchangeably

[dusky belfry]

they are the same thing?

[hollow bolt]

all of the stuff i just said?

pretty much yea

[dusky belfry]

O no I mean this

not all you just said

I will watch all videos

don't worry

[hollow bolt]

oh yeah but there are some slight nuances

zeros/roots can be complex, x^2 + 1 = 0 has roots ±i

x-intercepts must be real points on a graph, x^2 + 1 has no x-intercepts

[dusky belfry]

ok... thankfully for me, there is no imaginary numbers to learn on the textbook

[hollow bolt]

multiplicity matters too

for f(x) = (x - 1)^2, there's one zero/root at x = 1 (with multiplicity 2), but only one x-intercept at (1, 0)

and "solutions" are a bit broader

solutions to f(x) = g(x) find where two functions intersect, not necessarily where one equals zero

you'd rewrite as f(x) - g(x) = 0 to find zeros

[dusky belfry]

yea

makes sense

welp,

that clears it

[hollow bolt]

other related terms include:
- horizontal intercepts (less common synonym for x-intercepts)
- solution set (the complete set of all solutions)
- critical points (the zeros of a derivative for stationary points, but can be undefined for singular points)
- eigenvalues ("zeros" of the characteristic polynomial)
- roots of unity (complex numbers where z^n = 1, a bit of a stretch for this context tbh)

[dusky belfry]

sorry

thought you had finishe

[hollow bolt]

nw

[dusky belfry]

I was aobut to close this

[dusky belfry]

"no way"? is that what it means

[hollow bolt]

no worries

[dusky belfry]

oh

sorry

^^^not gen z^^

.close

[devout snow]

Channel closed

Closed by @dusky belfry

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[potent compass]

can someone help me

[upbeat forge]

which one(s), and what have you tried?

[potent compass]

question 1

i got only one thing correct

I don’t understand why ii? is 1/5

why 5

[upbeat forge]

okay, so what are your answers to q1?

[upbeat forge]

what would be your answer?

[potent compass]

1/10

[upbeat forge]

how many Es are in the word?

[potent compass]

wait not can we start w the v

[upbeat forge]

sure. you mentioned ii) first, so I thought you wanna start with that.

so what about i) is confusing you? what was your answer to that?

[potent compass]

1/5

bc there’s one v out of 10 letters

[upbeat forge]

so for 1 V out of 10 letters, why is it that your fraction is 1 out of 5?

[potent compass]

idk

[upbeat forge]

notice how your reasoning doesn't add up. your fraction doesn't describe the situation!

based on what I've told you now, what do you think is the correct answer?

[potent compass]

i still don’t know

[upbeat forge]

again, you have 1 V out of 10 letters.

[potent compass]

yeah

[upbeat forge]

if you have one slice of a ten-slice pizza, what is the fraction of the pizza you have?

[potent compass]

1/6?

[upbeat forge]

why?

[potent compass]

bc one is gone

huh

[upbeat forge]

and the 6 comes from...?

you have a 10-slice pizza.

[potent compass]

9

[upbeat forge]

the total number of slices don't change.

even if you took a slice, there were 10 slices to begin with.

[potent compass]

but you took one out of the 10

[upbeat forge]

sure. but the pizza still started with 10 slices. you can't compare your slice to the number of remaining slices, it makes no sense!

[potent compass]

i still don’t get it

we have 10 slices of pizza

we took one out

[upbeat forge]

9 slices remain, correct. but the fact is that the total number of slices is still 10.

[potent compass]

why is it still 10

one is gone

[upbeat forge]

ok, by your logic, let's see what happens if we take this to the extreme.

say I take all ten slices.

what's the fraction of pizza that I have? you're gonna tell me 10/0. but this fraction is clearly absurd!

[potent compass]

don’t you have all ten now

[upbeat forge]

yes! and so the fraction should be 10/10!

oops.

[potent compass]

ok

[upbeat forge]

I have 10 slices out of 10 slices.

similarly, if I took just one, I have 1 slice out of the 10 slices originally present.

[potent compass]

yes

[upbeat forge]

so the fraction should be?

[potent compass]

1/10/

?

[upbeat forge]

excellent!

and so we now have 1 V out of 10 letters total. the fraction is?

[potent compass]

1/10

[upbeat forge]

correct.

and that's the final answer to i).

[potent compass]

oh ok

would 1ii) be 2/10

[upbeat forge]

correct.

you would then ideally simplify it.

[potent compass]

ohh

[upbeat forge]

anything else you would like to ask?

[potent compass]

Not rn

But Ty

[upbeat forge]

alright, then you may .close the channel, and see you around and good luck with the rest!

[potent compass]

I can’t solve them

[upbeat forge]

that is why I asked this, my friend.

[potent compass]

I just got the questions

And started solving

[upbeat forge]

I see. I presume then you mean to leave the channel open for future questions. alright.

[potent compass]

Yeah Ig so

[potent compass]

Could u explain mutually exclusive

[upbeat forge]

if two events are mutually exclusive, they cannot happen simultaneously.

for instance, you can't flip a heads and a tails on a single coin at once.

so flipping a heads and flipping a tails on the same coin are mutually exclusive events.

[potent compass]

So they happen one after the other

[upbeat forge]

they need not happen exactly one after another. you could flip five heads in a row, for example.

[potent compass]

Dies mutually exludive gave something to do w replacenrnt

[potent compass]

Just not st the same time?

[upbeat forge]

but if one happens, the other is not happening at the same time. whether it will happen next is not known.

yes.

[manic vigil]

is saying that they are not dependent on each other wrong btw?

or is using it as a definition wrong

[craggy dagger]

the problem is that "independent" has a specific definition

[upbeat forge]

independent events can be not mutually exclusive.

[craggy dagger]

in particular independent events are mutually exclusive if and only if at least one of them have probability 0

[potent compass]

If I’m a beginner and learning it for the first time

Where would you say I should start

Ik it but it’s all jumbled

[craggy dagger]

probably have examples you can fall back on

like standard examples with flipping multiple coins or rolling multiple dice

[upbeat forge]

most useful being coins or dice.

[potent compass]

Oh ok

I need help tho

[noble acorn]

With what?

[upbeat forge]

I'm still waiting for your next question.

[potent compass]

Number c1)

Would you count all the numbers

For total

[noble acorn]

C1?

[potent compass]

Or add them to find the total

[upbeat forge]

which c1)?

q2? q3?

[potent compass]

Number 3, c1)

[noble acorn]

So 3c?

[potent compass]

Yes

[upbeat forge]

you are told that the universe (or our "pizza") is the first ten integers, aka 1-10.

but you are not told to do anything with their values.

so you would use the count and not the total here.

[potent compass]

Could to explain more

[noble acorn]

We pick one number from the first ten positive integers

[upbeat forge]

think of each number from 1-10 as a slice of pizza.

you're now picking one random slice.

so in total, you have 10 slices of pizza. you don't have 55 (which is what you get if you add the numbers from 1 to 10 together).

[potent compass]

oh ok

[noble acorn]

So what is the size of s then? If we are just looking at the number of elements inside s?

[potent compass]

The thing is there are a lot of questions with different ways to do probability

[potent compass]

Size over 10

[upbeat forge]

most of them are just some variant on counting, to be honest.

[noble acorn]

Yeah, so p(a)=6/10. p(b)=4/10.

[potent compass]

Oh ok

Tysm

[upbeat forge]

for example, rolling a random number on a fair D6 die is 1/6, flipping a fair coin is 1/2, etc.

[noble acorn]

Then we how do you think we find the probability of a and b?

[potent compass]

Ic ic

[upbeat forge]

I'll leave this to the other helper then.

[potent compass]

Count the numbers in the intertwined part of the circle

[noble acorn]

Yes, thats right :—) what is the new subset?

[potent compass]

Wdym subset

Is it the one it’s over?

[noble acorn]

Well our sets are A and B right?

[potent compass]

𝓨𝓮𝓼

[noble acorn]

We get those given to us

So we create a new one, with only numbers that appear in both A and B

[potent compass]

So a or vc

[noble acorn]

That is a subset

[potent compass]

Oh ok

That’s 1 and 3

[noble acorn]

And the value of that is?

Since theyre equally likely.

[potent compass]

For questions 3d, can I say that they a rent mutually exclusive bc they share two numbers

[potent compass]

2/10

[noble acorn]

Yep

[potent compass]

Thank you so so much

[noble acorn]

Its mutuslly exclusive when A intersect B is zero

[potent compass]

Huh

[noble acorn]

Fancy way of saying when their intersection is zero theyre mutuslly exclusive and vice versa

[upbeat forge]

you mean A intersect B?

[noble acorn]

Mb, yup

[upbeat forge]

if A union B is zero then those events might as well not exist.

[noble acorn]

Yeah, had union on my mind since i was gonna try to explain the difference between OR and XOR

[potent compass]

I need help with 4c)

[noble acorn]

How many total students are there?

[potent compass]

30

[noble acorn]

How many enjoy netball, only netball, and both netball and cricket respectively?

[potent compass]

14 enjoy netball

8 enjoy only netball

20 enjoy them both

[noble acorn]

Are you sure?

[potent compass]

For which

[noble acorn]

For the both

Think of it this way

[potent compass]

Is both all together

[noble acorn]

14 people in total like the sport, 8 of those only enjoy that particular sport, then how many of those 14 enjoy other sports?

[potent compass]

6

[noble acorn]

Sounds about right

Then how many students dont enjoy sports at all?

[potent compass]

10

[noble acorn]

Right.

The probabilities are A/total students

Where A is the number of people it applies to

[potent compass]

What about number 5a

[noble acorn]

Just transfer the information to the two way table?

[potent compass]

Idk wht a two way table is

Or how to plot it

[noble acorn]

Just a normal two column table where you plot event and probability

So A, B, A union B, a intersect B, not A union B

[potent compass]

Like this?

[noble acorn]

Well more things can happen than just A and B

What it both? What if neither? What is the probability something happens at all?

[potent compass]

Then how do I do the

[noble acorn]

Ok, draw a 4x4 grid

[noble acorn]

That is a 1x4 grid

4 rows 4 columns

Oh wait

You count the lines nvm

[potent compass]

What does nor mean

Neither a nor b

[noble acorn]

The lines above mean not btw

Wanna fill it out?

[potent compass]

Idk how to

[noble acorn]

Ok how many events in a and b and the intersection are there in total?

[potent compass]

Three

[noble acorn]

?

[potent compass]

Wait wdym

[noble acorn]

How many in B

[potent compass]

Wdym events

The number?

[noble acorn]

A and B are «events»

They can either happen or not happen

Or both can happen at the same time

[potent compass]

So 6

I used the 5b) questions

[noble acorn]

6 in B, 2 in A, 1 in A and B right?

From the graph

[potent compass]

I used the bi,I,iii,iv,vi and bio

[noble acorn]

Huh?

[noble acorn]

Yeah that makes sense

Ok, how many events have a in them

[potent compass]

6?

[noble acorn]

?

[potent compass]

5

[noble acorn]

??????

[potent compass]

Then how

[noble acorn]

How many are inside the circle called A

[potent compass]

1

[noble acorn]

This is the one right?

A is the left circle, b is the right circle

[potent compass]

Yes

[noble acorn]

What is the sum of numbers inside A

[potent compass]

3

[noble acorn]

Ok, what about only inside a, not B

[potent compass]

5

[noble acorn]

The 3 is irrelevant rn

Just inside the circle

[potent compass]

Oh ok

[potent compass]

2

[noble acorn]

Right, so the numbers of events in Only A is 2 right?

So this is our table so far

What about, only B?

Damn i must suck at explaining.

Uhh. We have two events right? Either A can happen, B can happen, Both can happen, or neither can happen

[potent compass]

Does the line on b mean b complement

So everything not b

[noble acorn]

Yes

[potent compass]

Ok thanks

Could you give me a few minutes

I need to prepare for school

[noble acorn]

And the sum of b complement and b is on the right hand column

[potent compass]

Wait so the a column

Is everything the is a

And a with dash

Is b

[noble acorn]

Total events in bottom right

So the total numbers of B are 7, B and A at the same time is 1, B complement so, not B is 5

Thats how you read those

This is the SOP (sum of products) way of representing it iirc

[devout snow]

@potent compass Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[potent compass]

.opem

.reopen

[devout snow]

✅ Original question: #help-27 message

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[potent compass]

Oh ok

[potent compass]

.close

[devout snow]

Channel closed

Closed by @potent compass

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[weak herald]

can anyone help me with the two highlighted questions?
sorry if it's kind of basic, I just forgot some of the principles 😅

[weak herald]

first num is -3/5 second is -2/7

[upbeat forge]

what are the instructions for this question?

[weak herald]

find the other coordinate.

[upbeat forge]

is there supposed to be a specific answer?

[weak herald]

in a circle

oops

[hazy viper]

shall i watch yt video or try to solve myself ..

[weak herald]

so the function is a circle

with the radius of 1

yeah.

[upbeat forge]

so a unit circle.

[untold ravine]

,ok so if a coordinate, say (x,y) lies on the unit circle, what equation does it satisfy

[weak herald]

a^2+b^2=1?

[untold ravine]

yes

nice, now what is our a here

[weak herald]

x

b is y

just plug the numbers in ?

[untold ravine]

and in problem 9, what is the value

[weak herald]

so...

[untold ravine]

well, there's one more step after you plug it in

[weak herald]

9/25+y^2=1?

[untold ravine]

correct

[weak herald]

I think I can solve that.

[untold ravine]

but be careful

sine (x,y) lies on the third quadrant

will y be positive or negative

[weak herald]

will be negative.

[untold ravine]

correct

can you do the second question similarly

[weak herald]

it's like
2 1
3 4
right?

last question.

[untold ravine]

yes

[weak herald]

^?

[untold ravine]

what?

[weak herald]

it's like
2 1
3 4

?

[untold ravine]

yeah the quadrants are like that

[weak herald]

thank you!

have a nice day

.close

[devout snow]

Channel closed

Closed by @weak herald

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[random belfry]

hey, can someone help me please

[random belfry]

\int_{0}^{1} \frac{\arctan^{2}(x)}{1+x^{2}},

@woven radish

[upbeat forge]

put $ signs around your LaTeX.

[random belfry]

$\int_{0}^{1} \frac{\arctan^{2}(x)}{1+x^{2}},

$\int_{0}^{1} \frac{\arctan^{2}(x)}{1+x^{2}},$

[woven radish]

peste

[random belfry]

THANKS

i need help with this one

using t = arctanx

[untold ravine]

what did you get

[random belfry]

i dont know what should i do tbh

[untold ravine]

ok firt what is dt/dx

[random belfry]

dt= 1/1+x²
dx = 1/cos²

so cos²/1+x²

[untold ravine]

how did you get dx = 1/cos2

[random belfry]

x = tan(t) so dx = 1/cos²

[untold ravine]

try again, you should get dt = 1/(1+x^2) dx

[random belfry]

yeah i already have dt = 1/(1+x²)

[untold ravine]

then put it in

[random belfry]

into what? o.O

[untold ravine]

into the integral

[random belfry]

i dont know how :((

[eager cobalt]

@random belfry where are u not understanding whats going on

[random belfry]

i dont know what is dt, dx and what should i do

[eager cobalt]

see we are assigning a new variable t which is equal to arc tan^2 (x)

[random belfry]

yes

[eager cobalt]

now we are differentating on both sides

do it tell me what is obtained

[random belfry]

differentate arctan^2 = arctanx/x²+1

[eager cobalt]

mutiply a 2 at the top arctanx in rhs too

[random belfry]

Oh yeah

2arctanx/x²+1

[devout snow]

@random belfry Has your question been resolved?

[devout snow]

Channel closed

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[devout snow]

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[charred turret]

Pls help me understand why my method is wrong

[charred turret]

<@&286206848099549185>

[ocean gale]

Uhm can you explain what u did? 😭

Oh I get it

[charred turret]

Do you not understand my writing 😭 ?

[ocean gale]

Now I do lol

[charred turret]

I choose 3 mangos from 5

[ocean gale]

Yea

[charred turret]

Thank god, this is the best of writing capabilities

[ocean gale]

but u have three factorial for the ways you can distribute the three mangoes

then the other two mangoes is just given to the other children

[charred turret]

But aren't they randomly being distributed by 3²×3⁷ where 2 are the number of left mangos ?

[ocean gale]

I think this over counts some cases

[lucid crow]

each child should receive at least one mango

[charred turret]

I accounted that in (5C3)3!

[ocean gale]

What I would do is distribute all the magoes first

so just break it down to casework

[charred turret]

But why is this method wrong 😭

[ocean gale]

I think that gives all the possible ways to distribute mangoes w/o overcounting

[ocean gale]

your overcounting something

I dont know how to explain it but you are overcounting some ways

[charred turret]

Can you like give a example if possible on how im overcounting pls

[ocean gale]

Ok I think i understand why there is overcounting

so

lets say we have the 5 mangoes right and they are distributed like 2,2,1

[charred turret]

Yep

[ocean gale]

Since the mangoes are unique we can say the mangoes are m1, m2, ...

so if the first kid has m1 and m2

you counted having m1 and m2 seperatly

although they are the same case

do you understand?

[lucid crow]

The error lies fundamentally in how you interpret the distribution constraint

[charred turret]

But isnt it like this for all the fruits then , say first kid gets all the apples , but isnt that correct ?

[ocean gale]

no because the magoes have a requirement

this means they special ✨

[lucid crow]

the correct method must consider the possible partitions of the number 5 into 3 parts, where each part is at least 1, and then assign those partitions to the children (since the mangoes and the children are distinct)

[charred turret]

But i accounted that that by (5C3)(3!)

[ocean gale]

you overcounted it such that if a child has two mangoes you counted m1 and m2 as one way and m2 and m1 as one way although they are the same

this is because if you have the 5C3 you can get m1, m3, m4 for first child secong and third

and then the other two are distributed randomly

so we can have something like m1 + m2, m3+m5, and m4

doing this you can also get this case

[charred turret]

Ohh I get it now where i went wrong

[ocean gale]

where you get m2, m3, m4 as you initial

[charred turret]

Thank you very much

[ocean gale]

u get it now?

[lucid crow]

https://tenor.com/view/yay-yeah-happy-dance-gif-18266119187889292563

[ocean gale]

lol

[charred turret]

😭 that was pretty dumb tbh

[ocean gale]

nah its fine

when I started counting i be doing stuff like this too dw

[charred turret]

.close

[devout snow]

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[devout snow]

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[junior anchor]

Can anyone help me in solving this without using this method? (cause its lengthy)

?

Iv asked chatgpt and all that but Iv yet to find a proper solutions pls help <@&286206848099549185>

[harsh sierra]

its not that lengthy

and the problem very much intends for you to use AM GM

[junior anchor]

Yup

but we have to subsitute value of a,b,c in terms of x,y,z. and solve. Isnt that lengthy

[harsh sierra]

no

its 4 lines

[lucid crow]

simplify and use the cauchy-schwarz inequality?

[junior anchor]

Oh

but how?

[lucid crow]

substitution, using given solutions

or what part do you find difficult?

[junior anchor]

The simplifying

Simplify what?

[devout snow]

@junior anchor Has your question been resolved?

[devout snow]

Channel closed

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[devout snow]

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[uneven cape]

uhhhhhh, how do i solve logarithmic equation f(x) = g(x) for:

f(x) = log{2}((32-4x-x^2)/(x+1))
g(x) = -3(2^(x-2))+1

[cold haven]

im assuming {2} is the base of the logarithm?

not a square or anything?

[uneven cape]

yes, assuming it's the base of the logarithm

i got to this step:

[cold haven]

$\log_2\left(\frac{32-4x-x^2}{x+1}\right)=-3\left(2^{x-2}\right)+1$

[woven radish]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[cold haven]

that is what you’re looking at?

[uneven cape]

[log{2}(4) - log{2}(3) - Xlog{2}(2) + log{2}((log{2}(-2) + log{2}(4) + log{2}(x + 8) + log{2}(x - 4) - log{2}(x + 1))]/X = 0

that's where i got to

you can obviously see a lot of consensible logrithms, but i feel like that wouldn't help at all

[cold haven]

[uneven cape]

i know i'm supposed to change it into a single logrithm, but like, how do you change the log inside a log into a logrythm? like, wtf

unless... wait

hold on

i feel stupid

shit, mb

i wrote it worng

[cold haven]

i honestly don’t think this is an elementary equation.

[uneven cape]

does this mean i can't get someone here to solve it 😭 ?

[cold haven]

Maybe..? Just know i don’t think anyone is going to want to touch it.

[uneven cape]

oh... you actually have to put in effort to solve it? bruh...

alright, i'll be awaiting a ping 🦗

[cold haven]

Plotting the two functions in desmos, you’ll get an answer around -9.243866. I don’t see a closed form for this though.

[uneven cape]

bruh, i'm supposed to get an exact value, am i just cooked then?

[cold haven]

[uneven cape]

bruh

[devout snow]

@uneven cape Has your question been resolved?

[cold haven]

Through some more desmos fuckery there’s also a solution at 3.9997963153

[devout snow]

@uneven cape Has your question been resolved?

Channel closed

Closed by @uneven cape

Use .reopen if this was a mistake.

[uneven cape]

.reopen

[devout snow]

✅ Original question: #help-27 message

[pure kelp]

did you check your domians?

sometimes these questions are easily solved if you have an idea of the domain and ranges of the functions

[uneven cape]

first one had a domain of X E (-infinity , -8)U(-1 , 4)
the second one X E (- infinity, infinity)

[devout snow]

@uneven cape Has your question been resolved?

[devout snow]

@uneven cape Has your question been resolved?

[tender cobalt]

are you sure you wrote the equation correctly?

[uneven cape]

yes bro

[tender cobalt]

can you screenshot where you originally got this problem from?

and include as much around the problem as possible, like instructions

[mighty thicket]

If this isn’t solved when I’m at my pc I’ll solve it

[tender cobalt]

keep in mind theyre looking for exact solutions, there are two that exist

[mighty thicket]

Yeah I haven’t had much look into it

Oh yeah it looks of

Odd

[tender cobalt]

let us know if you find anything useful, try not to clog up the channel

[mighty thicket]

Maybe the question asks for an interval where the values are ?

[tender cobalt]

still no response from VV0IF on whether thats true or not

theres also problems like "find the solutions to this many decimal places" which just means to use a calculator

[tender cobalt]

@uneven cape you still here?

unless you have a screenshot to prove otherwise, it seems impossible to find an exact solution to this problem

the best you can do is approximate the solution with a calculator

you can also use an approximations on -3 * 2^(x-2) + 1 to get the approximations x ≈ 4 and x ≈ -3 - √39

[mighty thicket]

yeah he definitely copied it wrong

[devout snow]

@uneven cape Has your question been resolved?

[heady crag]

please help me

[uneven cape]

uhhh, okay, yeah, i copied it wrong, but still though, now that have solved everything else, techincally, is there a way to solve it, or does it have to be in decimals?

[mighty thicket]

idk if theres a way to solve it

if i dont know the real question

1 negative can change a questions outcome from n to r

[uneven cape]

no, i copied it wrong, there were 3 equations and i used the second one and the first one instead of the third one and the first one

but is there anyway to solve it?

[mighty thicket]

theres no way for me to know if the equations are wrong m8

[uneven cape]

uhhhh, so, would you rate this as unsolveable?

[mighty thicket]

idk send me the full question

[uneven cape]

find f(x) = g(x) for:

f(x) = log{2}((32-4x-x^2)/(x+1))
g(x) = -3(2^(x-2))+1

[devout snow]

@uneven cape Has your question been resolved?

[devout snow]

Channel closed

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[lean shale]

hey, biology server slow, need help (please dont ban me)

[lean shale]

hold on lemme get image

i only know xylem is vascular, the teacher didnt explain the other 2 tho and google isnt giving me straight definitions so im unsure

[carmine veldt]

what the

[lean shale]

im sorry its not math

but i need help

[soft citrus]

[carmine veldt]

no I'm lowk js scared of biology

1213 tho

guard is clearly dermal, cuz its specialized epidermal cells that form stomata

[soft citrus]

I think xylem is a vascular tissue

[carmine veldt]

the other two are parenchyma units

both mesophyll

[lean shale]

is mesophyll dermal?

[carmine veldt]

no

ground

[lean shale]

oh yea

[carmine veldt]

why are you on roblox for 8 hrs

[lean shale]

uhhh

its always open, and im afk in a game rn

[carmine veldt]

🙏

you can type .close or .solved if doubt's done

[gloomy aurora]

palisade is upper epidermis

[gloomy aurora]

of leaf

[carmine veldt]

ain't no way

[gloomy aurora]

guard cells surround stomata

[gloomy aurora]

mesophyll, is parenchyma

[carmine veldt]

palisade is under the upper epidermis tho

[gloomy aurora]

idk i dont remember school bio

[gloomy aurora]

hint: spongy is given so its parenchyma

[carmine veldt]

yeah its upper epidermise --> palisade --> spongy mesophyll --> lower epidermis

[drifting mauve]

wrap this up quickly please because its not maths related, idk if the mods will like it or not

[lean shale]

okk ig its 1213 unless otherwise stated

we will see

.close

[devout snow]

Channel closed

Closed by @lean shale

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[devout snow]

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[wraith ember]

How can i find the limts to +∞ to
2x^3 + 4x^2 -2(x^2 + 1 ) * ln(1+x^2)

[eager cobalt]

replace x by new variable h which is xh=1 now replace all x with 1/h solve ull get the answer

[wraith ember]

So it becomes
2*(1/h^3) + 4*(1/h^2) - 2*(1/h^2 +1 ) *ln(1+ 1/h^2 ) ?

Which goes with
0 + 0 -2*ln(1)

[wraith ember]

For what reason xh=1

?

[eager cobalt]

thats a way for solving any qn where the value of the function tends to infinity

so for further simplification we use xh=1

[wraith ember]

Am i wrong at this point?

[eager cobalt]

simplify the terms by getting h in numerator

[wraith ember]

So we just creat a new value which is 1/h = x
Doesn't that means 1/h is approaching+∞ instead which is 0 ?

[eager cobalt]

do the same for the expression inside log

[wraith ember]

I haven't studied log yet ._."

[eager cobalt]

no

we create a function h which tends to 0 for x tending to 0 in 1/x

[eager cobalt]

ill help

now solve and send yr working

[wraith ember]

Ok

[wraith ember]

I still dont get it how this well help

[eager cobalt]

TRY MAN

why so confused ill explain

[wraith ember]

Nvm , im dumb 🥲
I got it

[wraith ember]

I did

[eager cobalt]

tell me what did u understand

[wraith ember]

But i still dont understand ur way to solve it

[wraith ember]

I tried another way which is getting x^2 + 1 as a common factor

[eager cobalt]

then?

[wraith ember]

The " - " ruined it

Its going to be +∞ -∞

[eager cobalt]

try by my way pls man

[wraith ember]

Aight , if xh = 1
So x = 1/h
Then should i work with it In this function as 1/h approaches ∞ and replace everything with 1/h

. close

.close

[devout snow]

Channel closed

Closed by @wraith ember

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[devout snow]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[quick cypress]

!occupied

[devout snow]

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

[quick cypress]

Can anyone explain me what it this

<@&286206848099549185>

[turbid bane]

This is a youtube video

[quick cypress]

Yeah so what's the thing going in that video

[turbid bane]

I'll watch it in 5 mins busy

[quick cypress]

Okay dude

As you say

[errant harbor]

!15m

[devout snow]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[cold haven]

!15min

[devout snow]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[dapper parcel]

wtf is this question

[quick cypress]

It's not question but what going in there explain me?

[errant harbor]

what do you not understand from it

which specific part maybe

[quick cypress]

What is going on there like how a circle kr any other shape become a straight line visualization

[vital edge]

<@&268886789983436800> very thinly veiled attempt at self promotion (the linked youtube channel is their own video)

[dapper parcel]

oh lmfao

[cold haven]

TM it just looks like a cringy phonk edit that really doesn’t have a meaning but.

Ig it’s just “sine” waves of different shapes?

[cold haven]

OH REALLY!?

[errant harbor]

omg lol

[vital edge]

Yes they have a link to it in their profile too

LMAO THEY REMOVED IT

[errant harbor]

xD

[cold haven]

I’m dying

[errant harbor]

this is funny asf

[copper harbor]

@quick cypress do not use this server, and certainly do not use the help channels to advertise your youtube channel

[errant harbor]

i was just abt to try and watch the video

[dapper parcel]

lmaooo

[errant harbor]

(vine boom sound effect)

[vital edge]

I got sus cuz the name of the channel "Aviral Mishra" was a helpee here recently

[cold haven]

like i said — cringy phonk edit with no apparent value/meaning

[dapper parcel]

no clue if that really helps in advertising

[vital edge]

Turns out guy just changed his username and hoped no one would notice

[errant harbor]

is it thhe type with the einstien music

[copper harbor]

anyway

[cold haven]

[copper harbor]

.close

[devout snow]

Channel closed

Closed by @copper harbor

Use .reopen if this was a mistake.

[harsh stream]

No way lmfaooo

[dapper parcel]

einstein type shit

[harsh stream]

He almost had it

[errant harbor]

is it srsly just an edit bro

[cold haven]

“MaTH iS bEauTiFuL”

[errant harbor]

like no math content at all 🥀

[cold haven]

not really. Ig it’s just sin waves on different shapes but it’s not explained at all

[vital edge]

The maths equivalent of forking a repo and calling it your own

[errant harbor]

it the typa thing someone would get by searching "math" on tiktok i suppose

[dapper parcel]

it doesn't even have any mathematical meaning 😭

[errant harbor]

i thought it would be forier transform related or smth

[cold haven]

nope. Just a cringy attempt at advertizing.

[harsh stream]

I subscribed

😊<3

[cold haven]

[devout snow]

Available help channel!

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[alpine salmon]

guys guys

[alpine salmon]

I made a few problems on maths , wanna try them out?

[ebon coyote]

No

[uneven coral]

If you've got one you have to ask, then go ahead, otherwise you can go to #math-discussion

If you've got one to ASK, then please do, otherwise kindly close the channel

[devout snow]

@alpine salmon Has your question been resolved?

[ebon coyote]

.close

[devout snow]

Channel closed

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Remember:
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vital edge]

I don't understand the question

[uneven coral]

Strange question

I guess it's about impulse

[pseudo basin]

we kick the first ball and it hits the second, and that one hits the third and so on

[normal bolt]

What i understood is 1st ball is given velocity then it hits 2nd ball then 2nd ball third and so on till 10th

[pseudo basin]

and then ball X should have enough KE to reach the top and complete the cycle?

[uneven coral]

And they're elastic so nothing is lost

[normal bolt]

yes

[vital edge]

Oh okay I thought that was a ball

[normal bolt]

yes it says complete a circle

[vital edge]

Didn't realize that was a circular loop on the path

[uneven coral]

lol me too

I was like shouldn't the 10th ball rotate back, then I realised it's a loop

So assuming there weren't 10 balls and there was just one, with what velocity should it be thrown in the loop so that it completes the circle?

[pseudo basin]

wait but hold on

how is it even relevant that there are 10 balls and not 100

if the balls are identical and collide elastically shouldnt the momentum be transferred perfectly so the previous ball becomes stationary

[uneven coral]

Exactly

Just know it for one ball

The rest doesn't even matter

It's like a pendulum

[pseudo basin]

so why are they given at all

[uneven coral]

To confuse ig, or to check concept clarity, or we're both wrong

[normal bolt]

at the last the 9th ball will collide 10th ball and that should make it complete a circle? am i correct?

[uneven coral]

Yes

[pseudo basin]

sure

[uneven coral]

Imagine a pendulum

[pseudo basin]

but we can also pretend we are just kicking ball #10 directly

[uneven coral]

It doesn't matter how many balls there are, you'd still need the same force to lift the last ball to a certain height, it's as if the other balls aren't there at all

That's basically an example of perfect elasticity in real life

[normal bolt]

i can't think why the author of this question would add those balls and not given directly velocity to 10th

[uneven coral]

Maybe to check concept clarity, or it's also possible that me and Ann are wrong, can you tally answers?

If you can, then solve it as if there's only one ball, and see if it's correct

[ebon coyote]

-# I'm still struggling on what the author is doing introducing an r=1 circle here without explanation

[normal bolt]

if you compute with formula for vertical circular motion it gives correct answer

[uneven coral]

For just one ball right?

[normal bolt]

yes the 10th ball

[ebon coyote]

Is ball X connected to the circle, and the aim is to get it to swing around?

[uneven coral]

It's a loop, the 10th ball revolves around it

[normal bolt]

sqrt(5rg)

[uneven coral]

Yeah it's correct then, IG the author just chose an arbitrary number of balls to check concept clarity

Because in perfectly elastic collision, e = 1, so no velocity is lost

[ebon coyote]

Then my guess would be, since the table is smooth, and the contacts are all elastic, the question is analoguous to "With what speed should ball X travel at the bottom of the loop so that it completes a revolution?"

[normal bolt]

sqrt(50)

[ebon coyote]

-# not that I have any idea though lol, but that'd be my rationale behind it

[uneven coral]

Yeah we have a formula for it

[ebon coyote]

Why're you using g = 10

The question tells you what to take for g

[uneven coral]

With what velocity a ball must travel to perfectly revolve around a circle

[uneven coral]

Yeah he'd have a perfect answer otherwise too

[normal bolt]

thats the solution they attacthed to it

its not good

[uneven coral]

But they've given the value of g

[ebon coyote]

Yh, the answer's wrong, since g = 9.8 is explicit here

[uneven coral]

You're supposed to use that value

[normal bolt]

they are not even using that 9.8 in their solution

they're drunk

[uneven coral]

Yeah god knows why

[pseudo basin]

sqrt(5Rg)?

how did magic number 5 come

[halcyon rivet]

Wait we can ask physics questions in this server?

W

[normal bolt]

as i can recall there were different cases is vertical circular motion but they provided this formula in the solution

i can explain the working of the formula but i didn't recall during the exam

[uneven coral]

It's a formula ig

For vertical circular motion

There must be a way to derive it, but I can't think of it right now

[normal bolt]

I have that derived in my notes

[uneven coral]

wasn't there also a sqrt(2rg)?

[glossy dew]

yeah it isnt relevant

[normal bolt]

yes that is there

there is different condition for that formula

[glossy dew]

at highest point\
$T = 0$\
$mg = \frac{mv_H^2}{R}$ ($v_H$ = velocity at highest point)\\
using MEC between lowest and highest point of motion:\
$2mgR = \frac{1}{2}mv^2 - \frac{1}{2}mv_H^2$\
$4mgR = mv^2 - mgR \implies v = \sqrt{5gR}$

[fickle slate]

it is equivalent to solving it for just one ball

dont know why they gave 10 identical balls

[uneven coral]

Just to check concept clarity ig

[fickle slate]

that was the condition for incomplete circle/projectile motion if i remember correctly

i might be really wrong here

[uneven coral]

Ahhhh I see, thanks mate

[uneven coral]

Dude derivations fire up some good part in the brain, like bro just Conserved Energy but it looks so satisfying

[devout snow]

@normal bolt Has your question been resolved?

[junior anchor]

Yup the sqrt(5rg) is minimum velocity required to complete a full circle

Its derived using work energy theorem

[uneven coral]

Yes, blurple_galaxy did

[junior anchor]

Yea this

[devout snow]

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[earnest rivet]

bit stuck on part (ii), i tried to use the same idea as before, integrating, but i dont seem to be able to get a 4b involved. although i feel like this may be because a>0 and b^2<4ac in part (ii) may not be sufficient for the graph to always be >0?

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@earnest rivet Has your question been resolved?

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[timid scroll]

can someone help me tell where i went wrong in my proof?

[timid scroll]

line 11 is supposed to be a universal introduction, not a disjunction. But despite that fix, it seems that I have miscalculated somewhere

[timid scroll]

oh is it supposed to be

9. ∃xR(x,a)
10. ∃y∃xR(x,y)
11. ∀y∃xR(x,y)

right?

@dry robin

[devout grotto]

i'm not 100 on this since my predicate logic is rusty

but it looks like you might need to bring in line 2 to justify line 11

or that your reasoning is off

[timid scroll]

i got it

.close

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[terse helm]

Where do i start

[autumn girder]

Do you know the SAS theorem for proving congruency?

[terse helm]

two sides and the angle between them are congruent?

is the answer UVW = EGF

like i get the theorem but not how to type it out

[autumn girder]

If two triangles, have two pairs of sides such that the length of the sides and the angles between them when paired together are equal, the SAS theorem states that the triangles are congruent to each other

[terse helm]

ok yes

understood

im just not sure the way i type the answer out

[autumn girder]

The name of first triangle and then the second triangle, so in your case since you think $\triangle UVW \cong \triangle EFG$, you would type exactly that, UVW in the first box and EFG in the second

[woven radish]

@autumn girder

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@terse helm Has your question been resolved?

[terse helm]

YES TYSMM

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[dusk moat]

hey, this is uni stuff, discrete maths, Hilbert-style Calculus, cant use deduction theory

[dusk moat]

these are the axioms i can use and modus ponens

what i have rn

[autumn girder]

What is the question?

[devout snow]

@dusk moat Has your question been resolved?

[devout snow]

@dusk moat Has your question been resolved?

[dusk moat]

any ideas cuz im at the point i might just give up haha

<@&286206848099549185>

[devout snow]

@dusk moat Has your question been resolved?

[vital edge]

I'm sorry what exactly does the question mean

Why is there a regular &

What does the comma mean

Could you share the question heading please

Also what the heck is the ⊢ doing here

[devout snow]

@dusk moat Has your question been resolved?

[devout grotto]

predicate logic, yes?

[vital edge]

Is it asking what conclusions you can draw based off what's given

Or is it asking to draw a specific conclusion from the first half

The use of the ⊢ confuses me

[devout grotto]

⊢ usually means, "given the left side, the right side follows"

[vital edge]

I know that lol

That wasn't my question

Also given that OP hasn't responded in 1.5 hours I doubt I'm getting my question answered

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[sand pumice]

how would i go about solving this? (i implies ii and i implies iii were already proved, the exercise is asking to show ii implies iii)
i constructed nested intervals with each behing half the length of the previous, but i cannot figure anything else out

[jagged harbor]

selfish-ish question, what's your definition for compactness in R? I'm used to (iii) being the definition for compactness

[sand pumice]

if every sequence for a set K has a subsequence converging to a limit in K
another one im allowed to use is if it is closed and bounded

[jagged harbor]

sure. have you already shown (ii) => (i)?

[sand pumice]

yep

[jagged harbor]

ok, that's my two useless questions, thank you lol

back to thinking

[sand pumice]

👍

[jagged harbor]

what I'm wondering is, you have a closed interval I_0 containing K, presumably because K is bounded, but how do you define the next interval I_1?

[sand pumice]

i thought of bisecting it into two halves

and pick the one that cannot be finitely covered but im not sure if i can just do that

[jagged harbor]

if A and B are two sets satisfying (iii), does A u B also satisfy (iii)?

[jagged harbor]

yeah it took me apparently 4-5 minutes to ask that question, crazy lol

if this is true, then the contrapositive is true too: if A u B does not satisfy (iii), then at least one of A, B also does not satisfy (iii)

so yeah, you should be able to split it in half safely, I think

you can use the ordering to safely address left vs. right halves

[sand pumice]

not sure, but i think yes

[jagged harbor]

yeah it's like, if C and D are coverings for A and B, they both admit finite subcovers, whose union is finite and covers A u B

[sand pumice]

okay thank you

[sand pumice]

👍

[jagged harbor]

or you can phrase it as a contradiction for yourself here right, because the open cover {O_lambda} is fixed

[sand pumice]

i dont think i understand what you mean

[jagged harbor]

idk if I understand what I mean either so I have to go through the motions myself lol

[sand pumice]

oh 😭

[jagged harbor]

ok, O = {O_lambda} is a covering of K, so it also covers every subset of K, yes? Then for each subset M of K, you can show that if M is not finitely covered by O, and if M contains a subset T that is finitely covered by O, then M-T is not finitely covered by O.

[jagged harbor]

you can be fancy and try to phrase this as a contrapositive, but contradiction feels more natural I think. Plus it carries this idea

[sand pumice]

ohh

[sand pumice]

wait how do i use that here?

[jagged harbor]

you want to construct a nested sequence of closed intervals (I_n) that does what you want, so my thinking was you can use your idea of splitting I_0 in half recursively

say you're at an interval I_n = [a, b], with I_n cap K being not finitely coverable by O, and you say A = [a, c] with c = (a+b)/2

if A cap K is also not finitely coverable by O, then you want to define I_{n+1} := A

but if $A\cap K=[a,c]\cap K$ happened to be finitely coverable by $\mathcal{O}$, then since [I_n\cap K=\left([a,c]\cup(c,b]\right)\cap K=\left([a,c]\cap K\right)\cup\left((c,b]\cap K\right),] it must be the case that $(c,b]\cap K$ is not finitely coverable, so we want that half

[woven radish]

Flip

[jagged harbor]

you do have to briefly mention that if (c,b] cap K is not finitely coverable by O, then [c,b] cap K isn't either, so there's no funny business with including or excluding the midpoint

you need to include the midpoint only because these intervals are supposed to be closed, right

[sand pumice]

right

[jagged harbor]

it is also specifically not finitely coverable by our collection O