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[alpine sable]

how does the exponent minus thing work? for example (-6)^2 = 36? why? bcz we have 2 and not 3? if we had an odd number would it be -? i forgot the rule

[wind cloak]

If you multiply -6 * -6 you get 36

if you multiply -6 * -6 * -6 you get -216

in general an odd exponent means you keep the negative

for an even one you can do away with it

[alpine sable]

if the exponent is even, the number is positive

ok, i've got 1 more question

with which number will i abbreviate the number 2?

6, right?

[vale wigeon]

??

what do you mean by "abbreviate the number 2"

might this be something lost in translation

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

so basically, $x_1 = \frac{6+\sqrt{12}}{-2}$ and $x_2 = \frac{6-\sqrt{12}}{-2}$

[ocean seal]

TheGeneralisedPerson

[alpine sable]

or the other way around

whatever you prefer i guess

[lone heart]

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[keen orbit]

original problem

[waxen flame]

It does say to give your answer to one decimal place.

[keen orbit]

ah sheit

ty

[waxen flame]

👍

[keen orbit]

.close

[lone heart]

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[lone heart]

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[true sandal]

What does Marginal Cost mean in derivatives? Is it the cost of an individual item?

[naive valley]

do you have an example of the usage of that term?

offhand i think it could mean the cost of buying one additional item if you've already bought N, but I could be wrong

[true sandal]

not really

let's say a problem gives me

P(x), the profit function and
p(x), the price demand function

and it wants me to compute the cost of producing the 69th product

is it basically asking me for the Marginal Cost?

[true sandal]

Or is it asking something else?

[lone heart]

@true sandal Has your question been resolved?

[true sandal]

can someone confirm?

[lone heart]

@true sandal Has your question been resolved?

[lone heart]

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[alpine sable]

the school offers a high school student 18 different subjects, 5 of which are compulsory for each student for the student. in how many different ways can he choose subjects if he has to study 12th altogether subjects?

[alpine sable]

how

help someone

[icy crane]

ideas?

[alpine sable]

idk

[icy crane]

what if the problem said that you have 18 compulsory courses. how many different ways to study would we have then

[green folio]

Isn't this permutations and combinations?

[alpine sable]

yeah

but calculators doesnt work

so thats why i am here

[green folio]

Sad i forgot how to do these

[alpine sable]

you have 18, 5 of them are obligatory, but you need 12 at the end

[alpine sable]

man i skip math

boring subject

i like history

[green folio]

Not at all

[green folio]

Me in a parallel universe

[alpine sable]

then you prob introvert

[green folio]

Not at all

[icy crane]

I know that because you wrote it before. I am asking a question to a different, simpler problem

[alpine sable]

1 ig

[icy crane]

yes, correct

[alpine sable]

dude idk math

so

wait

18:12?

5+7 = 12

[icy crane]

no no

[alpine sable]

what then

[icy crane]

you have a student choosing subects, so there has to be a choose in there, right?

[green folio]

Combination?

[alpine sable]

yes

[icy crane]

you know the choose operation

[green folio]

Man I don't remember ig its 5 permutation 13-7 comb? Me correct? @icy crane

[alpine sable]

basically i need to choose 7 out of 13

so how many different ways

[icy crane]

that's it

you know math

[alpine sable]

aaand

how many then

13:7

or what

lmao

[icy crane]

doesn't your book have instructions how to calculate 13 choose 7?

[alpine sable]

i dont have book

[icy crane]

notes?

[green folio]

7C13

[alpine sable]

nope

[green folio]

That one?

[icy crane]

the other way around anand

[alpine sable]

i said i skip math

[green folio]

💀

7 at the top ryt?

[icy crane]

nope 😄 13 is at the top

alright teoo

[alpine sable]

13/7

?

[icy crane]

google "13 choose 7"

[alpine sable]

1716?

i got that answer ages ago

[icy crane]

13/7 is 1.85714285714. you can't have 1.85714285714 ways of doing something

[alpine sable]

i thought its just stupid

[icy crane]

big numbers can be stupefying but aren't stupid

indeed, you have 1716 different ways

[alpine sable]

wtf man

😭

i had it 30 mins ago

im stupid

[icy crane]

you have to go back and study what "choose" means to understand it tho

[alpine sable]

aight thanks

[alpine sable]

im not learning in english

so not my fault

[icy crane]

just say that you're bored to learn math right now 😄 it's not a problem

what language are you learning it in

[alpine sable]

latvian i live in latvia

i skip math

on exams i got everything 9/10 except math

silly me

[icy crane]

https://lv.wikipedia.org/wiki/Binomiālkoeficients

[lone heart]

@alpine sable Has your question been resolved?

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[random kiln]

Question 5 can you find the domain

[tiny vigil]

do you know how to solve inequalities with absolute values?

[random kiln]

Yes

[tiny vigil]

alright, can you show your progress? where did you get stuck?

or did you get the wrong answer

[random kiln]

1 sec

I don’t even know how to start my problem isn’t the absolute it’s the fraction

[tiny vigil]

you started it correctly

now you solve these two separately

try to get 0 on the right side, in both of them

[random kiln]

Like this ?

[tiny vigil]

yes

you can subtract 3 if you find the common denominator

likewise on the right side

[random kiln]

What is a common denominator

[tiny vigil]

you can turn 3 into a fraction

that has the same "bottom"

[random kiln]

Wouldn’t it be 3/1

[tiny vigil]

no, because 1 is not the same as x-3

[random kiln]

If i flip 3 to 1/3 then don’t i have to flip the other term too

[tiny vigil]

but we can call 3/1 an intermediate step to what you want to achieve

you can't just flip a 3

it has to be equal when you rewrite stuff like this

[random kiln]

So how is it done ?

[tiny vigil]

ok let me show you this

how would you solve this, assuming you can only do magic to number 2? and leave the left side alone

[random kiln]

That’s what i am trying to figure out I don’t know what to do ?

[tiny vigil]

see what I did there?

[random kiln]

It’s the same ratio

I get it

So 3 can become 18/6 maybe

[tiny vigil]

we want the same denominator, the thing at the bottom

let me show you even more then, to not drag this

[random kiln]

Well the denominator is x-3 how do we do that ?

[tiny vigil]

damn, wrong again

there

[random kiln]

Hmm how about x-6/x-3

[tiny vigil]

almost right

just make sure you multiply (x-3) times 3 correctly

[random kiln]

That’s 3x-9

[tiny vigil]

yup

and since the bottom is the same, you can have one fraction, and "connect" them

[tardy cobalt]

sup me new

how old should i be to get into this server

[tiny vigil]

13+

please check out #info and #❓how-to-get-help

[tardy cobalt]

i beter leave 😦

me 11

bye

[tiny vigil]

cu]

[random kiln]

Ok so what do we do with 3x-9

[tiny vigil]

well you end up with x+2-(3x-9) right?

and you have one denominator already

[random kiln]

Like this ?

[tiny vigil]

yepp

now you can simplify the numerator

[random kiln]

What now

[tiny vigil]

you didn't do it right

when you see something like this it's good to imagine a -1 there

-1 * 3x is -3x, do you see your mistake?

[random kiln]

But there is a negative outside the bracket so - - =+

[tiny vigil]

but 3x inside the parenthesis is positive

positive * negative = negative

[random kiln]

Ok

[tiny vigil]

if you look at the pic I sent, you can literally multiply the parenthesis by -1, and you will get it

-3x, but PLUS 9, because 9 is negative

this is a common pitfall, be super careful with it

when you subtract a parenthesis, you need to flip the signs inside

subtracting is just adding a something with a flipped sign

so when you have 9 - 8, it's also 9 + (-8)

5 - (5-9) is also, 5+(-5+9)

[random kiln]

i got that So what do i do after that

[tiny vigil]

solve both for x

when you have the simplest form, and you get like x+smth/x-smth, you can split them

like top>0, bottom>0

then you solve for x

[lone heart]

@random kiln Has your question been resolved?

[tiny vigil]

@random kiln you need more?

when you consider one of the cases you prepared at first step

you already have a simplified fraction, like (x-1)/(x+2)>0

you can solve it like any equation, you check where are the zero points, you write it out on the numberline

check which interval satisfies >0

you do the same thing on the other side, and you do union of the intervals you find

[random kiln]

Oh ok thanks i got it now

[lone heart]

@random kiln Has your question been resolved?

[lone heart]

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[cerulean helm]

Nvm

I got it

.close

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[bleak shoal]

VERY QUICK QUESTION, no actual math involved:
For part (b), why do we take the integral of f(x) from -1 to x, instead of the integral from -1 to 1? I can tell by doing them both which one produces the correct answer, it's just been a while since I've done integration and I can't really tell why we don't take the integral from -1 to 1. Is this just "how it's done" for cumulative distribution functions?

[burnt ravine]

By definition of Fx

[bleak shoal]

so no matter what it's always done this way? integral from a to x when trying to find the cumulative distribution function?

[burnt ravine]

yes but u can see there's an issue if x≤ -1 : it's gonna be 0

[bleak shoal]

you mean if i take the integral from x to -1?

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[subtle delta]

Do you know how to find angle AEC?

[normal bridge]

nvm

complementary

[subtle delta]

Yeah, and CED is complementary right

Using the given info that the triangle is isosceles u should be able to see how to find it now

[normal bridge]

@subtle delta idk why but I'm still stuck

nvm I was confused about finding cde but I understood, ty :)

.close

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[pallid laurel]

Hi, I need help with part (b) of this question

I've been trying different sequences to compare with $a_k = \frac{1}{k^{\frac{1}{k}}k }$

[ocean seal]

QT

[pallid laurel]

but none of them seem to work

[vale wigeon]

why not just 1/k

then the ratio will be k^(-1/k) which i'm pretty sure goes to 1

[pallid laurel]

oh? i didnt know that haha

nice, thank you!

.close

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[pallid laurel]

oh wait

.reopen

[lone heart]

✅

[pallid laurel]

acc nah, its good, thank you

.close

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[upbeat timber]

how would i find the ACB angle? we’re doing trigo and thats all the info i have

[hard patio]

cube?

yea?

[upbeat timber]

yea

triangle through cube kinda

ik it has something to do with sin cos tan obviously but i have no measures

[haughty yoke]

maybe u need to express it with some letters?

[upbeat timber]

the answer is in numbers though

like degrees *

<@&286206848099549185>

[cerulean helm]

It's probably 45 °

Since you are splitting a right angle in half

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@upbeat timber Has your question been resolved?

[lone heart]

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[idle stone]

Hello

[idle stone]

Im having some trouble with this question

[spare crane]

hi

can someone help me out

how do i do this

[lone heart]

@idle stone Has your question been resolved?

[idle stone]

.close

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[lone heart]

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[vague coral]

the classic way of proving an equality of sets is to take an element from the first set and prove that this element is also in the second

other method, use the properties you know about intersection, union etc..

[alpine sable]

im supposed to use induction to prove it

sry shouldve mentioned that

[vague coral]

well try it

[alpine sable]

would those be the base cases for induction

[vague coral]

should be fine

[vague coral]

I wasnt even thinking about induction

[alpine sable]

o

well im kinda confused because for induction we have a base case we need to prove and then we need to prove p(k) -> p(k + 1) but the first thing i dont get here is, how would i determine the base case

well i know it would be when n = 1 cuz its the least

[vague coral]

yes, now do it

[alpine sable]

the base case is just the same as the inductive hypothesis tho

[vague coral]

?

[alpine sable]

like if i do n = 1 i end up with the same equation except its just B

and apparently there are 2 base cases here which i dont really get

[vague coral]

For $n=1$, we have :
$$A \cup \left( \bigcap_{i=1}^1 B_i \right) = A \cup (B_1 \cap B_1) = A \cup B_1$$
so the statement is true for $n=1$

I forgot that the bot is still dead

[lone heart]

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[grave frost]

ok so this is in a game it may not be as relevant to others but I put a buy order for 14,000 spider essence for 38,819,200 coins each being like 2,773 coins, and then however sell offer is 3,015 coins

[grave frost]

how much profit would I make?

[last ether]

Skyblock?

[grave frost]

yup

[last ether]

Don't invest in spider essence I lost 17 m

[grave frost]

oh dam

[last ether]

Or I just suck

Probably that, bazaar flipping doesn't go well

For me

[grave frost]

I mean marketing is good right now

and according to my calculations which are probably incorrect im making 7.6 billion if it fills

[last ether]

The profit is (sell price)(amount sold) - (buy price)(amount bought)

[grave frost]

ou

that would make more sense

[last ether]

Maybe if I was better at investing I can actually max out my Divan's armor 💀

[grave frost]

aha

I personally dont even do mining

so I dont feel the pain you do

[last ether]

I mean it's good money for now

[grave frost]

mining is a chunky money making method

how much senither weight do you have?

[last ether]

8k I forgot

I don't take it too seriously and I spent too much time fucking around so

I'm garbage at the game but like

[grave frost]

so you hvae 8k senither weight??

[last ether]

https://sky.shiiyu.moe/stats/Umbraleviathan/Pear

6k

Apparently 6k

I thought I had 8k

[grave frost]

thats over 2x better than me

[last ether]

Well the bazaar takes a tax

So the profit isn't gonna be exactly what I showed you

[grave frost]

mine is the most reduced

[last ether]

I believe it takes a 0.1% tax for anything bigger than 25m?

[grave frost]

I think the total would be like 1% tax

[last ether]

But like you lose 10k coins so like that's nothing

[grave frost]

or something like that

yeah so it doesnt count in that way

[last ether]

You can disregard it

Yeah rn I'm just focusing on getting combat and mining 60

[grave frost]

ou dam

im planning on getting a terminator

but thats a way to go

so aiming for skill avg 40 before hand

I should probably close this ticket right?

[last ether]

Yeah

Also I hate slayers but I need a term 💀

I'll close it

.close

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[alpine sable]

I found this and I'm naturally dumb

[alpine sable]

Jake is 4 feet 3 inches tall and casts a shadow 6 feet 3 inches. The tree next to Jake casts a shadow 10 feet 3 inches long. How tall is the tree?

51 inches

75 inches

123 inches

[last ether]

Relatable

[last ether]

Similar triangles

[alpine sable]

ok

thanks

.close

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[alpine sable]

No just answer the yes/no question bro

[lone heart]

@alpine sable Has your question been resolved?

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@alpine sable Has your question been resolved?

[alpine sable]

the UK left the EU the answer is YES

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@alpine sable Has your question been resolved?

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[alpine sable]

i am so fuckin overwhelmed

[outer lark]

ok so

what do you know about roots

or x-intercepts

[alpine sable]

i know how to find them from vertex form

[outer lark]

vertex form does not hint towards the location of the roots

the x- intercepts (roots) of the function are when y , h(x) , f(x) = 0

[alpine sable]

the x interepts

yeah

the roots are when the function is turned into ax^2 + bx + c

[outer lark]

I mean

the roots exist in every form
the function always exists in a form you can collect information from tho

you can find the roots from the vertex form yes, but you can't just read numbers and see them

here we can see

that the x intercepts are when y , h(x) = 0

so we can equate the function h(x) to 0

which do you think is easier to find values of x for when h(x) is 0?

ax^2 + bx + c or

the form in the question?

[alpine sable]

the form?

[outer lark]

yes

so what you mentioned earlier

ax^2 + bx + c

this is a form

and so is this

$a(x-\alpha)(x-\beta)$

[ocean seal]

Clarkie

[outer lark]

where alpha and beta are roots of the function

[alpine sable]

so -3, and -2 are the roots?

[outer lark]

close

[alpine sable]

3 and 2?

[outer lark]

yes

think of it like, you want to know when this expression will equal 0

and 0 multiplied by anything is just 0 right

so if either of those brackets equals 0

then you have a root

hence you can set the inside of these brackets to 0

3-x = 0 and 2-x = 0

hence x =3,2 when y=0 so they are our roots

[alpine sable]

and so for x intercepts i make x = 0?

[outer lark]

for y - intercepts yes

[alpine sable]

oh wait

so then what do i do for x intercepts?

[outer lark]

make the function = 0

$0 = \frac{1}{2}(3-x)(2-x)$

[ocean seal]

Clarkie

[outer lark]

and for what values of x does that statement hold true?

[alpine sable]

uhhhhhh, 3 and 2?

[outer lark]

exactly

so they are your roots

[alpine sable]

ohhhhh

[outer lark]

roots = x intercepts

which is why this form is useful for finding them, you normally factorize functions to find them easily

[alpine sable]

then whats the mid point?

[outer lark]

well that comes from knowledge of quadratics

in this case

quadratics are an even function

so f(x) = f(-x)

[alpine sable]

how is tan(u)-tan(v)= sin(u-v)

[outer lark]

meaning you can easily find the midpoint as being half way between the roots

or the x coord from the vertex

they are equivalent

[last ether]

#❓how-to-get-help

I mean isn't the mid point just the x value of the vertex

[outer lark]

yes

but you can also find it between the midpoint of the roots

sometimes quicker ig

as for knowing if its a maxima or minima just pay attention to the leading coefficient on the x^2 term and if its positive then you have a minima and if its negative you have a maxima

<@&268886789983436800>

[covert shuttle]

No

Also please don't interrupt help channels

[alpine sable]

so (3 + 2)/2

?

[outer lark]

yeah that would be your x coord

of the vertex

[alpine sable]

how is tan(u)-tan(v)= sin(u-v)

[alpine sable]

ok, and then how do i figure out the final two boxes?

[last ether]

Bruh wtf happened

Ain't no way

[last ether]

Dude stop interrupting this guy's channel

[last ether]

The extremum is the vertex

So h(midpoint)

Do you know what extrema are

[alpine sable]

its -0.125

so its a minimum?

[alpine sable]

sorry it says help0

isnt that the channels im supposed to ask in

[last ether]

No

You didn't read what it says

#❓how-to-get-help

The help-0 in the image is, believe it or not, in a category called "help (available)"

Go to that category

[outer lark]

yes

[outer lark]

yes

also use fractions

[last ether]

-1/8 if I can use a brain

[outer lark]

yes

as my early school teacher said

fractions are your friends

[last ether]

I'm surprised you don't have the Helpful role

[outer lark]

I dont feel like I know enough maths

[last ether]

I mean im currently taking Multivariable calc and I have the rule

You Def know more than me lol

[outer lark]

im a little first year university noob and have only self studied topics that are for further years, maybe once I get a little more proficent with some of the harder stuff and expand my understanding I would feel comfortable getting it

multivariable calc is very cool

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[twilit cypress]

hello

[twilit cypress]

Anyone available to look at some linear algebra for me?

I can't see what I am doing wrong. The solution says that for an eigenvalue of 5, I should be getting the vector [1, 3], but I am getting [1/3, 1]

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@twilit cypress Has your question been resolved?

[twilit cypress]

<@&286206848099549185> Anyone able to take a quick look? I am thinking the solution must be incorrect since all the other examples have been going well for me, and I just got to another one that just seems that the given answer is incorrect

[twilit cypress]

Thanks anyways peeps. Ill open this channel back up for other people here

.close

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[cunning trout]

How do i do this?

[outer lark]

that is a geometric series

and you can setup an inequality with the relationship of a sum of a geometric series

[cunning trout]

Oh i see

Got it, thanks

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[ocean terrace]

Hey y'all quick question I'm doing some studying on vector operations, What does this symbol mean?

[native edge]

Damn

[ocean terrace]

Indeed

[stable tusk]

alpha it’s just a constant

$\alpha$

[ocean seal]

Larry the Cucumber

[ocean terrace]

Thank you, Where can I learn more about constant?

[stable tusk]

it’s just another greek letter

I don’t think it has any special meaning

[ocean terrace]

So in this context it represents just an arbitrary value?

[stable tusk]

yeah

[last ether]

No way Larry knows mathematics?

Larry you're so cool you can have my firstborn son

[ocean terrace]

Thank you sir Larry the Cucumber 🙏

[last ether]

Also in this case, α is a scalar multiple of vector u

[ocean terrace]

Interesting I haven't read about scalars yet almost there

Thank you!

[last ether]

Well scalars are numbers

Just numbers

No direction with them. They're a directionless magnitude

Or what my teacher calls them, "jobless numbers"

[ocean terrace]

I see

[peak bough]

I wanna be a jobless number when I grow up

[last ether]

On god

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@ocean terrace Has your question been resolved?

[lone heart]

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[eternal kestrel]

Please help me solve this through implicit differentiation

[gilded vessel]

what are you stuck on

@eternal kestrel

[eternal kestrel]

solving for dy/dx once i differentiate both sides

[gilded vessel]

alright show what you get after you differntiate both sides

[eternal kestrel]

2(dy/dx) = [(y-3)-(x+3)(dy/dx)]/(y-3)^2

[gilded vessel]

okay good

so first you can start by removing the fraction

how would you do that

[eternal kestrel]

2(dy/dx)(y-3)^2 = (y-3)-(x+3)(dy/dx)

[gilded vessel]

good

now you can move the other term with dy/dx to the left hand side

so you have all the the terms that have dy/dx on one side and the other terms on right side

[eternal kestrel]

2(dy/dx)(y-3)^2 +(x+3)(dy/dx)= (y-3)

[gilded vessel]

perfect

now you can factorise out dy/dx

on the left side

[eternal kestrel]

dy/dx(2(y-3)^2+(x+3)) = (y-3)

[gilded vessel]

great

now you can divide both sides by whats in the brackets on the left side

and you will have dy/dx by itself

[eternal kestrel]

the application tells me its wrong for some reason

[gilded vessel]

show what you input as the answer

screenshot of the application

[eternal kestrel]

oh it wanted me to turn the numerator into a 1

thanks for the help

[gilded vessel]

alright

no problem

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[muted sluice]

Hi again, I posted this question (calc 3) a little bit ago but I didn’t get a reply, I’ve reworked it a few times but I’m still stuck

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[gritty verge]

hello!

[gritty verge]

so i have a question which is i need to evaluate the following series to find out wether it diverges or converges

lemme add a pic

can i use ratio test?

or wld limit comparison be better?

nvm solved it with ratio test

.close

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[white sable]

letter b

I know it is with polar coordinates, because it is a sphere, but the changes for the integral are not made

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@white sable Has your question been resolved?

[tacit arch]

find the limits of the square in polar coordinates

express x=2 in polar coordinates

similarly for y=2

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[lethal frigate]

can someone help me solve this problem (lhopital rule)?

[echo socket]

Rewrite cot as cos/sin

[lethal frigate]

isnt this a indeterminate case of 0*infinity

[echo socket]

Yeah

[lethal frigate]

so how can rewriting cot would help me solve this

[echo socket]

?

Cuz you'll have 2x/sinx * cos(pi - x)

Which is -2 cuz cos(pi - x) approaches -1 and x/sinx approaches 1

If you wanna do it the hard way then just rewrite 2xcot(pi - x) as -2x/tanx

[lethal frigate]

when i rewrite cot isnt it cos(pi-x)/sin(pi-x)?

how did it become just sinx

[echo socket]

sin(pi - x) = sinx

[lethal frigate]

oh i forgot about that trig identity 🥲

@echo socket thank you very much, i finally understand now

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[kind schooner]

not sure how to start or what to compare with

[echo socket]

a0 is f(1)
a1 is the slope of f(x) at x = 1 (same as f'(1))
a2 is the second derivative at x = 1 (f''(1)), which is positive when the graph is concave up and negative when the graph is concave down

You should be able to tell the signs of these by looking at the graph

[kind schooner]

ohhhhh ok got it thanks

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[green folio]

That pfp-

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[cyan grove]

Hi, in this triangle, the point P is (0;1), and R is (2;1/3). I need to calculate the area of triangle PRT, but I'm struggling to find the perpendicular height - I believe that it is PR which my calculations state is 2.108 units long, whereas the memo says its 2 units long on the dot. How did they get 2?

[void solar]

PR is a linear line right. You can find gradient of that.
Then RT is a linear line perpendicular to that. So you can find it with one point R and gradient

Then find y int of that linear line

That’s one way to do it

[cyan grove]

y intercept of PR?

[void solar]

RT

Which will give you T

Oh wait

It’s already given to you

[cyan grove]

yeah

[void solar]

Sorry let me read the question again

Distance formula

T to R

Is that what you wanted

[cyan grove]

which one would be classified as the perpendicular height in the triangle PRT?

is that PR?

[steel olive]

@cyan grove 2 is the perpendicular height from R to PT

i calculated it

its exact 2

[cyan grove]

ah okay, i must have typed it in wrong on the calculator then

did you use the distance formula?

[steel olive]

i first calculated area using PR,RT(found rt using distance formula)

then found out height on PT

[cyan grove]

alright, thank you so much!

.close

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[mighty fulcrum]

how can I get rid of the f?

[void solar]

In this case couldn’t you just root both sides by f

Since they equal

[gray isle]

the rhs is the simplification of the lhs (assuming b>0)

[void solar]

Oh

[gray isle]

there's not much that can be done about the f

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[mighty fulcrum]

thanks

[lone heart]

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[final minnow]

Maybe this out of topic but someone can help me , who's good in english

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[minor needle]

Vieta's formulas

x^2 - 5x + 8 = 0
α + β = 5
αβ = 8
let u = cbrt(α) + cbrt(β)

calculate u^3 and try to use formulas

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[mortal trellis]

I mean if you are working over C then it depends on which cube roots you take

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@boreal kernel Has your question been resolved?

[ocean seal]

ayushch80

ayushch80

ayushch80

ayushch80

ayushch80

ayushch80

[stuck cape]

@boreal kernel

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[alpine sable]

I need help

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[primal lintel]

need help with b

[primal lintel]

i would assumed you could just do $7! / 2$

[ocean seal]

splooze

[primal lintel]

but the odd numbers appear more

so not too sure

the last digit needs to be either 1, 3, 5, 7

[echo socket]

Is it stated that the digits must not repeat?

[primal lintel]

no it's not, but they shouldn't

the answers too low for them to include repeating

oh

it's just

$6! * 4$

[alpine sable]

I needd help

[ocean seal]

splooze

[primal lintel]

#❓how-to-get-help

[alpine sable]

24

[primal lintel]

no

[alpine sable]

what

[primal lintel]

6! = 6 * 5 * 4 * 3 * 2 * 1

[echo socket]

Looks like the 4 is there because there are 4 possibilities for the last digit

[primal lintel]

yeah

[echo socket]

And 6! for the others

[primal lintel]

yeah

funky stuff

[alpine sable]

i dont understand your english

[primal lintel]

@alpine sable

search up factorials

this '!' symbol

means factorial

so 3! = 3 * 2 * 1

5! = 5 * 4 * 3 * 2 * 1

[alpine sable]

wich grade problem is that?

[primal lintel]

i started learning it in 11th

when i was 16

[alpine sable]

im in 7

[primal lintel]

but i've known about it a little before

ah okay

[alpine sable]

[primal lintel]

you'll learn it one day

anyway

cheers for the help all

.close

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[paper sage]

I should calculate the length of the curve

I know which formula I should use

.close

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[tender jay]

I'm looking for how to do this, as much as the answer

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[steady basin]

Could someone explain to me how the section I’ve pointed to has been derived and how that’s equal to P(F)

cuz i derive P(F given CG) x P(CG) to be equal to P(F intersect CG)

<@&286206848099549185>

is it due to the law of total conditional probability?

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[paper sage]

Does someone know how to solve this?

[echo socket]

Length of the curve y = f(x) is the definite integral of sqrt(1 + f'(x)^2)

[paper sage]

Yeah I tried and I got this

But don’t know how to move on really

[echo socket]

Make the denominators common

So that you may factor (1 - x^2) out

[paper sage]

I got this

[echo socket]

sqrt?

[paper sage]

Sry

Sqrt over the whole ofc

[echo socket]

You can factor the denominator out of the sqrt

[paper sage]

Yes

[echo socket]

Now expand the nominator

You'll see it turn out to be square of a nice enough expression

[paper sage]

I still have the sqr in nominater

[echo socket]

No, just expand and you'll see

[paper sage]

I got this

[echo socket]

Collect the x^2 terms

You get 1 + 2x^2 + x^4

Which is the same as (1 + x^2)^2

[paper sage]

Wait what

[paper sage]

You mean 1-2x^2

[echo socket]

1 - 2x^2 + x^4 + 4x^2 = 1 + 2x^2 + 4x^4

[paper sage]

Sorry I miss the square on my 4

Missed*

[echo socket]

Yeah

So you should get (1 + x^2)/(1 - x^2) as the integrand

Do you have trouble with integrating this?

[paper sage]

No I can manage that

Thank you so much @echo socket

[paper sage]

I think I should do +x^2 and minus x^2 right

[echo socket]

I'd rewrite the expression as (2 - (1 - x^2))/(1 - x^2)

So that I have 2/(1 - x^2) - 1

And I'll just decompose the fraction

[paper sage]

Hmm do u think my method work?

[echo socket]

Rewriting it as 2x^2/(1 - x^2) + 1?

[paper sage]

No just add and subtract

X^2

[echo socket]

That's what you get doing that

[paper sage]

Oh okay it’s the same thing yeah

[echo socket]

Well, if integrating 2x^2(1 - x^2) is simpler for you than integrating 2/(1 - x^2), sure

[paper sage]

I will try and apply PFD

[paper sage]

On 2x^2(1 - x^2)

It should work right?

[echo socket]

What's PFD?

[paper sage]

partial fraction decomposition

[echo socket]

Ah

You'll have x^2/(1 - x) and x^2/(1 + x) though

[paper sage]

Yeah

[echo socket]

I guess you can get away from that with u-sub, sure

u = 1 - x and u = 1 + x

[paper sage]

Okay let’s try

Did u find something faster than that?

I mean do u think I can avoid PFD

[echo socket]

2/(1 - x^2) is decomposed into 1/(1 - x) + 1/(1 + x)

Ah

Not sure if decomposing is avoidable

[paper sage]

Mm

Okay no problem

[echo socket]

Integrating this yields ln(1 + x) - ln(1 - x)

[paper sage]

Yes

[echo socket]

Actually absolute values of the arguments but they're positive anyways

[paper sage]

Ofc

But do I need to write them out

I’m not sure

[echo socket]

If you wanna be formal

[paper sage]

Ofc

[echo socket]

Just mention that 1 + x, 1 - x > 0

So just ln((1 + x)/(1 - x)) evaluated at 1/2 and 0 - integral of 1 from 1/2 to 1

Lucky for us that ln is 0 at x = 1

So it's just ln((1 + 1/2)(1 - 1/2)) - 1/2

ln3 - 1/2

[paper sage]

And that is the right answer!!

Thank you so much @echo socket

@echo socket just one question

[echo socket]

What is it?

[paper sage]

I can’t complete my PFD

[echo socket]

You shouldn't have constant coefficients there

Should be quadratic forms

[paper sage]

So I should use Ax+b

?

[echo socket]

No

Ah

Wait

I think it should be Ax^2 + Bx + C

Or you can just use the fact that I mentioned above

2/(1 - x^2) = 1/(1 - x) + 1/(1 + x)
So
2x^2/(1 - x^2) = x^2/(1 - x) + 1/(1 + x)

[paper sage]

Alright I think I get it now

[lone heart]

@paper sage Has your question been resolved?

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[prime badge]

like what

give any example

[lone heart]

@alpine sable Has your question been resolved?

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[novel bay]

Hi need help

[alpine sable]

hi

[novel bay]

Hi

[alpine sable]

send problem

[novel bay]

I have a few questions about constraints

particulary linear algebra

Here

[alpine sable]

5 x1 + 5 x2 < 40
5 x1 + 3 x2 > 36

2 x2 < 4 , x2 < 2

understand it?

[novel bay]

A bit yeah

[alpine sable]

im just multi 5

then reduce it

countinue??

[novel bay]

Yep

Go ahead

[alpine sable]

4 x1 + 4 x2 < 32
7 x1 + 4 x2 > 14

3 x1 > -18 , x1 < 6

=====>>>>> 0 < x1 < 6 , 0 < x2 < 2

are you here?

[novel bay]

Yep

[novel bay]

I think i get what you got the answer here

[novel bay]

How about this one?

This is for a quesion later

[alpine sable]

i cant understant what it was say can you type it

[novel bay]

Oh sorry. I understand how you got the answer for the first question

[alpine sable]

no i mean 6

[novel bay]

Oh wait

I cant type it

Determine which of the following statements is true about the given tableau:

[alpine sable]

ok

[novel bay]

a.)It requires additional pivoting.
b.) It indicates no solution to the problem.
c.) It is the final tableau.

[alpine sable]

sorry but i can't understant what it need

[novel bay]

Its okay we can skip it

Can you solve 8?

[alpine sable]

.

[novel bay]

Yep this one

[alpine sable]

-x1 + x2+x3 >-10

• x3 > - 3
  -x1 + x2 > -13,,,

3x1 - 8x2 >-15

• x1 + x2 > -13 === -3x1 +3x2 >-36
  -5x2 >-51

x2 < 10.2

understand??

[novel bay]

Yep

Continue

[alpine sable]

now you can find x1???

can you??

[novel bay]

I cant yet

sorry

[alpine sable]

ok

-x1 +x2 > -13
-x2 > -10.2
-x1 >-23.1

x1< 23.1

it's finished but check again the number

[novel bay]

Which letter is the correct answer?

[alpine sable]

when you have x1 and x2 you should delete x1 or x2 then it's solved

[alpine sable]

just recheck

are you know what i do , do you know metode

[novel bay]

No i do not

[alpine sable]

do you want learn it or not

[novel bay]

Sure

[alpine sable]

ok for example
x1 + x2 < 0
x1 - x2 <8
just reduce it

2 * x1 < 8 , x1 < 8/2 , x1 < 4

are you understand?

what is your grade?

@novel bay

[novel bay]

Im grade 1

11

Sorry

[alpine sable]

i think you have to know it

[alpine sable]

can understand it

[novel bay]

I think I get it now

Thankoyu

[alpine sable]

👍

[novel bay]

Have a nice day Mojtaba

Btw can I add u

[alpine sable]

if need help send me in direct

[novel bay]

WIll do

Sent you a friend request

[alpine sable]

.close

[lone heart]

@novel bay Has your question been resolved?

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[drowsy hornet]

this was on an answer key to a problem. I keep getting sqrt(5) instead of sqrt(3) like the answer key. Who is correct?

[vale wigeon]

you

[drowsy hornet]

.close

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[icy wedge]

|x + 5| + |-2x +1| = 0

[icy wedge]

solve for x

no idea how to start

[tall topaz]

sketch the graphs and see where they intersect

[icy wedge]

like how?

[reef grove]

you know that if you take the amount of a number, that it will always give you a positive result right?

or 0

[icy wedge]

yeah

[alpine sable]

Why such a strenuous approach

[reef grove]

so |x + 5| and |-2x +1| are always postive

or 0

[icy wedge]

yeah they are

[reef grove]

so when is the sum of these 2 equal to 0?

[icy wedge]

When they're the opposite of one another

[tall topaz]

OOps

thought it said 8 for some reason

[icy wedge]

wait no

now im confused

[late mango]

just in case you haven't figured it out, you forgot to square 2 in the denominator

[reef grove]

what is the opposite of 3

[icy wedge]

-3

[late mango]

this is going to give you a situation where |a| = -|b|

in this case, we know absolute values can never be negative

so

the only possible way is to

[icy wedge]

english is not my first language so i cant tell if its -3 or 1/3

[late mango]

have a = 0 AND b = 0

if a = 0 and b = 0 don't have common solutions, it's empty set

[icy wedge]

I see

Alright thank you very much

.close

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[raven rover]

Inverse functions pass both the vertical and horizontal line test, if that is sufficient for your purposes

[lone heart]

@slate kayak Has your question been resolved?

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[lone skiff]

guys today I learnt how to get the mid point between any 2 numbers
for example the mid point between mid(1,3) = 2 --> (1+3)/2 = 2
but with even numbers mid(1,4) = 2 --> (1+4)/2 = 2 (int)
I noticed : if difference is even it gets me the mid point in first half, not second half

then I tried it with negative numbers and it worked fine

but when I tried it with positive/negative at the same time something strange happen

mid(-2,1) --> (1 + (-2)) / 2 = 0

which is mid in second half not first half, I don't understand why does this happen

[lone skiff]

does anyone know why?