help-27

[indigo zinc]

thx

.close

[devout snow]

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[restive river]

hi

[restive river]

how to solve matrix equasion A²X=B

[queen zephyr]

X=(A^2)^-1 B

[restive river]

ty

[restive river]

does the order change for

XA²=B

?

[queen zephyr]

yes

uhm no wait

it doesnt for x

[jaunty mantle]

depends what X is

XA might not exist

[devout snow]

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[restive river]

.reopen

[devout snow]

✅

[restive river]

when ?

[queen zephyr]

when orders arent posiible

[restive river]

can you give further explanations ?

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[ripe portal]

How can I solve this two sections?

[clever mist]

can you screen shot the whole thing

[ripe portal]

It is in spanish, is there any problem?

[clever mist]

well i can't see the whole thing

[clever mist]

5&6?

[ripe portal]

Only 5 c) and d)

[clever mist]

ok

what work you do you have

[ripe portal]

i can show u the answers i u want

<@&286206848099549185>

[chrome girder]

|z - 1| is not that

you don’t get z^2

[ripe portal]

and what is it, the absolute value?

[chrome girder]

use z = x + yi

so z - 1 = (x - 1) + yi

those are real and imaginary parts

then use formula for absolute value

[ripe portal]

and in the previous one, in section c)

[chrome girder]

im talking about your work for 5c

[ripe portal]

ok sorry

i will try doing it, thanks

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[twin holly]

Hello everyone, my question is the following:

What is the probability of exactly two dices landing on the same side upon throwing 3 dices?

The answer according to my prof should be 30/56 (or simplified 15/28) but I am getting 5/12 which was confirmed by both chatGPT and multiple old discussion threads as the correct answer.
What is the possibility of my professor making a mistake?

[topaz axle]

,w C(6,2) × 2 × 3 / 6^3

[woven radish]

Results provided by WolframAlpha

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

Requested by frownyfrog#3707

[pseudo basin]

@twin holly does your prof provide work or only give you the answer

it's really strange that they'd get 56 in the denominator

56 doesnt divide 6^3 so

very

[topaz axle]

the professor does stars and bars

[twin holly]

I'd say the result should be following:
First dice can be anything 6/6 = 1
Second has to be matching it 1/6
Third has to be different 5/6
There are 3 positions on which this could occur, so:

3*(1/6)*(5/6)=5/12

[topaz axle]

6×5 / 8C3

this is wrong because you can;t throw dice like that

[clever mist]

you can't throw dice like that?

[pseudo basin]

wait so we want our roll to be (a, a, b) in some permutation with a ≠ b right

[pseudo basin]

yeah this checks out

[clever mist]

ya

[topaz axle]

yeah, dice pick a permutation when you throw them

the professor doesn't realize it

[twin holly]

@pseudo basin I only got the answers after prompting the professor. I was refusing to study from a material which doesn’t provide feedback to me in any way. 😄

It’s easy to make mistakes in probability and statistics and when you never get the chance correct them it’s dangerous 🤓

Anyway thank you for your help guys! I guess I'll have to ask him to show me his solution next time I see him.

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[proper osprey]

is simplifying this legit like this?

[topaz axle]

you can make it a bit shorter

if you factor

[proper osprey]

could you tell me how

[topaz axle]

at least i think it's shorter

the numerator is −(something)²

[proper osprey]

oh so i can cancel out?

[topaz axle]

it doesn't cancel out, it's just shorter, and i don;t know what simplify means, maybe it counts

[proper osprey]

you mean setting it in parenthesis?

sorry i'm a little confused

[topaz axle]

i'm not saying this is right

maybe it's unsimplifying it again

[proper osprey]

hm okay i'll check that real quick

[dull otter]

ye

[topaz axle]

originally you just asked if that step is legit, it's definitely ok

the question is what exactly counts as "most simplified", i've no clue

[proper osprey]

it gives me this as a result

[proper osprey]

okay that is more than enough, thank you for your time

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[restive river]

how many solutions are there to the equation [
x_1 +x _2 + x_3 + x_4 + x_5 =21
]
where [
0 \le x_1 \le 3, 1 \le x_2 < 4, \textss{and} x_3 \ge 15
]

[restive river]

okay so there is the painful way of doing it

where u just examine it for each inequality

but what is a less headachy approach

$x_i \in \Z^+$

[restive river]

combinatorics is painful

usually the bruteforce method is the best method

like

what i would do is go like

first you find all nonnegative solutions to [
x_1 + x_2 + x_3 + x_4 + x_5 = 21
]
which is like $\binom{25}{4}$. Then, you have the inequality $0 \le x \le 3$, so u can check for all the $x's > 3$. Meaning $x \ge 4$ to get the solution. So set [
x_1 = y_1 + 4
]
to get[
y_1 + x_2 + x_3 + x_4 + x_5 = 17
]
which has $\binom{21}{4}$ solutions. So your solutions for $0 \le x \le 3$ are [
\binom{25}{4} - \binom{21}{4}]

there is a slight reduction you could do here by making everything ≥0 by setting y_2 = x_2-1, y_3 = x_3-15

oh wait

thats what you were writing

lmao

[restive river]

lmao yes thats it

so that covers like

0 \le x \le 3

but for the other inequalities

would there be like overlap or double counting

yeah, you need to be careful with counting

[topaz axle]

sorry, z+ is no zero?

[restive river]

just

whole numbers

nonnegative integers

0,1,2,3,..

[topaz axle]

okay

[restive river]

so yeah thats nice and all if only we had the 0 \le x \le 3 condition, but we dont

[restive river]

$x_1+y_2+y_3+x_4+x_5=5,$\ for $0\leq x_1,y_2\leq 3,$ and $0\leq y_3,x_4,x_5$

[woven radish]

Toby

[restive river]

oh u did it all at once

ye

cheeto moment

eugh this is so annoying

[restive river]

still a pain to count, but doing it lexicographically, would avoid double counting

lex

lol

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

basically, counting in an orderly fashion

i see

i think my book did the same as you

let me check

i dont get what happened in like

the middle portion at all tho

which part is the middle?

wait nvm this isn't that insane actually, i just need to eyeball it a bit

[restive river]

lmaoo dont worry about it i think i will be able to get it

i hope

aight

alright time to open a second channel because

i have a multinomial theorem question

.close

[devout snow]

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[dull otter]

cannibalization rate

[devout snow]

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[pulsar ermine]

How do you prove inductively f(an)<=y?

[magic thicket]

split cases on the definition

[devout snow]

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[hard night]

to determine if this is a basis, should I find like the determinant? Like if determinant is not equal to 0, then would it be a basis?

[rough tapir]

so ive never dealt with this before but google says you need to prove these three vectors are linearly independent

in other words, a*v1 + b*v2 +c*v3 /= 0

[hard night]

like if they have a pivot in every col?

[rough tapir]

this

it allows you to set up a system of 3 equations by equating coefficients

im not at a place where I can give it a shot but you need to show that the above equation is always true besides when a=b=c=0

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[glacial lynx]

Am struggling with 3 questions that I could not find the answer to

[devout snow]

@glacial lynx Has your question been resolved?

[devout snow]

@glacial lynx Has your question been resolved?

[devout snow]

@glacial lynx Has your question been resolved?

[nova idol]

this is just econ not math

thats not three questions

thats the entire thing

looks like you want someone to do everything for you

[glacial lynx]

i dont care, ive done the rest of the questions that i needed help with only these, i didnt ask for ypu to correct what am asking for 🤣

[nova idol]

you literally listed like 15 questions

that looks like you dont understand anything

or youre just lazy

[nova idol]

and you should care because the amount of people here that know econ and will help you is extremely small

many times nobody answers them

[glacial lynx]

no and i actually managed to answer some of them already

[nova idol]

sorry, 14

[devout snow]

@glacial lynx Has your question been resolved?

[supple knot]

What's your math question

[glacial lynx]

thats it tho

[supple knot]

Kefir already told you it's an econ question

Interpret it as a math question and ask a math question

[glacial lynx]

then youre not the person to help, ill just wait till i find a econ person that can help?

[nova idol]

I know how to solve it

But you asked literally for everything

I’m not going to do that

It doesn’t look like you even tried

If you haven’t learned it then learn it

[nova idol]

Nobody will answer that for you

We are here for specific questions

[glacial lynx]

LOL i already solved the page of the equilibrium the page of the pizza and sausages, still stuck on the MSB and solved B C and D on the last picture

[supple knot]

Go to an econ server

[nova idol]

when you posted originally everything was empty

Idk what you expect me to say

[supple knot]

You're asking in the wrong place

Or ask a math question

[glacial lynx]

how do yk this isnt a 30 question econ quiz, how do yk if i didnt solve all the other questions n neededd help with these🤣

[nova idol]

i didn’t say it was everything ever

But it’s a ton

[glacial lynx]

whats the issue tho, ur job is to help, i never said give the answers did i? wont hurt if you explained wud it?

there vc

theres dms

[supple knot]

!volunteers

[devout snow]

Helpers are just people volunteering their time to help you. Be polite.

[glacial lynx]

if youre willing to help then help, dont questions shit

[nova idol]

it would take forever to explain all that

we are here for specific questions

[glacial lynx]

ok then dont comment?

[supple knot]

Don't be an entitled twat

[nova idol]

nobody wants to do that though

[glacial lynx]

YOU are here for specific questions

[nova idol]

no

[supple knot]

Nope

[nova idol]

Every volunteer is

[supple knot]

.

[nova idol]

That’s what we do

[glacial lynx]

many people wud offer and also wudnt be hurtful to help me with one question either

noone forced you to help with all the questions

[nova idol]

and your proof is what?

Nobody else offered to help

[glacial lynx]

no cus maybe not everyone has the time? am not obv depending on this server all am saying is noone forced you to come and help me

you can help me with one question if you want

[nova idol]

nobody forced me ofc

But nobody will help you if you just post half a worksheet

[glacial lynx]

yeah then stop talkin, you can continue on your life

yes thats fine

thanks for the heads up

[nova idol]

you didn’t even show your work or your conceptual issue

[glacial lynx]

i dont need to post 30 questions of my work

be for real

i posted questions i was struggling with

if someone came to help i woulld offer live stream and if theyre willing to help with ALLL then they will if theyre willing to help with ONE question then so be it?

noone complained

keep ur mouth shut

[supple knot]

<@&268886789983436800>

[glacial lynx]

why come in my channel to complain?

its MY question leave me alone if you dont wanna help dont help me

[hybrid snow]

Man literally waltzed into here and act like he owns the damn place

[glacial lynx]

I came here to post the 3 Questions out of 30 that I could not figure out how to answer, and they start attacking me for it

[hybrid snow]

To be fair, we really don't deal with specialized fields of math other than physics or CS because that's what 99% of people in here are doing

[rose flower]

ngl keifr was the only one you could have depended on u blew it bud. entitlement

[glacial lynx]

Yeah thats fine, whats the issue, ill just wait till one person can help me, am not depending on this server at all its a side quest atp, am working on it myself and asking others for help, but joined this server today to give it a shot, i dont see an issue with posting my questions

[hybrid snow]

Well it's odd that this channel didn't close on its own due to time out. Typically we don't want people hogging channels for more than an hour or two

And for specialized cases of math, they end up being unresolved for the most part

[glacial lynx]

I didnt blew anything, I posted my question, he doesnt need to start questioning stuff, noone forced him to help me with all the questions rather help me with one of them is enough, i never asked for answers i asked for help, if he wanted he wouldve helped me, i didnt force noone. and noone forced him to do all the questions or even give me an answer straight

[hybrid snow]

This channel's been up for nearly 7 hours ...

[glacial lynx]

Yeah i understand

but its worth a try

[rose flower]

!status

[devout snow]

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

[glacial lynx]

And i think it still up becuase the bot kept asking me if its been resolved

[hybrid snow]

In all honesty though, while Kefir's remark was rather crass that doesn't give you the right to tell people to shut their mouths

[glacial lynx]

Yeah I apologise for that but he just pissed me off too much by caring too much

[hybrid snow]

Well we gotta care

[glacial lynx]

No, if you dont want to help, then dont help, ill deal with it myself, and the channel will close by itself

[hybrid snow]

This channel's been up for too long probably due to a bug, and usually we try to redirect specialized cases of math to other servers

Try looking in #old-network

[glacial lynx]

Yeah ill check out, but all im saying, if the channel closes automatically then let it happen. If he can help me he will help me. If he doesnt want to help me then he doesnt want.

[rose flower]

can you copy and paste the question in text form i have some background in econ and can take a look

[glacial lynx]

Suppose that the utility to a consumer can be described as:

U = 10x^0.4, x^0.6

a) Based on the consumer's utility function, what can you say about the utility of the respective good 10x^0.4 and good x^0.6?

Thats the only question I have so far i answered the rest

[digital orbit]

This seems to have calmed down on it's own but in the future please keep in mind helpers are volunteers so be polite to them.

[glacial lynx]

Yeah but teach them to also not come for someone rather explaining and understanding the situation but I understand I will be respectful next time, my apologies

[devout snow]

@glacial lynx Has your question been resolved?

[devout snow]

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[devout snow]

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[summer crater]

Hello,Could anyone help me with this geometry question?I am going to use coordinate geometry to prove since I dont need to consider the relative position of the centres of circle but after drawing the picture(idk if it is true).I found that I cannot use the the relevant information of OI and two radii R,r.I will appreciate your help.Thank you.

[devout snow]

@summer crater Has your question been resolved?

[summer crater]

<@&286206848099549185>

[devout snow]

@summer crater Has your question been resolved?

[devout snow]

@summer crater Has your question been resolved?

[devout snow]

@summer crater Has your question been resolved?

[devout snow]

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[proud perch]

Can we make sense of the area under the curve of a stock chart?

[proud perch]

Haven't really seen this used in technical analysis but I think there might be something to it when comparing return of a stock to the market return

[clever mist]

maybe

[devout snow]

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[obtuse flax]

hey is someone able to help me with number 11

[clever mist]

!status

[devout snow]

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

[obtuse flax]

2 i’m supposed to find the u and du idk if that’s just my schools terms or like actual math words

so u is t^4 + 25

and then du is 4t^3

[clever mist]

so what is the top

[obtuse flax]

i have to do an adjustment right?

[clever mist]

yes

[obtuse flax]

like multiply 1/4t^3?

🥹

[upper schooner]

I wouldn't suggest this as your u tbh

[obtuse flax]

so u is just 25? why not t^4 as well

[clever mist]

no

[upper schooner]

nor that

[obtuse flax]

these are the formulas i was given

[upper schooner]

Take a look at the middle one

[obtuse flax]

so a is t^2 and u is 5?

[clever mist]

yes

[upper schooner]

[other way around - you have $\int \frac{1}{a^{2} + u^{2}} \dd u$]

[clever mist]

wait du is 0

[obtuse flax]

i though du is 2t if u is t^2

[woven radish]

@upper schooner

[obtuse flax]

oh ur right

sorry confusing myself

this is the answer for 11 if it helps

[upper schooner]

Yep, did you end up getting the answer then?

[obtuse flax]

did i write the formula wrong or is it actually a-u and not u-a

bc if it’s a-u then i did not

[upper schooner]

Well you do have that $\int \frac{1}{a^{2} + u^{2}} \dd u = \frac{1}{a} \arctan\pqty{\frac{u}{a}}$ sure

[woven radish]

@upper schooner

[upper schooner]

Taking that to be true, and noting that you're asked for the integral $\int \frac{t}{t^{4} + 25} \dd t$ you already found the substitution you're supposed to make

[woven radish]

@upper schooner

[upper schooner]

Just a matter of doing the steps really

[obtuse flax]

so a is t2 and u is 5

wouldn’t that make the top 0?

[upper schooner]

Remember I said it should have been the other way around! Choose $u = t^{2}$ and $a=5$, and then note that you have a substitution you've made so as you noted $\dv{u}{t} = 2t$

[woven radish]

@upper schooner

[obtuse flax]

oooh i see so you can interchange a and u?

[upper schooner]

Remember that a is a constant and u is the variable

[obtuse flax]

so now i habe to adjust to get 2t on top

so an adjustment of 1/2?

[upper schooner]

yep that's good

[obtuse flax]

so 1/2(1/a?)

[upper schooner]

Hmmm that will appear somewhere at least, but depends on what you mean

[obtuse flax]

1/25(arctan(u/a)?

oh no haha

[upper schooner]

Remember that a=5

[obtuse flax]

oooh 1/10

1/10arctan(t2/5) + C

HAHA!

thank you!!!

[upper schooner]

[devout snow]

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[night bramble]

.

What is the sum of all the possible values of positive integer x such that the remainder of 60/x is 3?

[night bramble]

how do we solve questions like that

[long fog]

Remainder of 60/x is 3

Fins all such x and then their sum

[pastel pasture]

$$\frac{60}{x} = a + 3$$
$$60 = x(a + 3)$$
$$\frac{60}{a + 3} = x$$

[long fog]

A number that divides 57

[long fog]

Wait what?

[night bramble]

only it?

[long fog]

It's xa+3

[pastel pasture]

Now all you need to do is determine integer values for a such that x is an integer

[pastel pasture]

Hmm

[night bramble]

what did we consider x and a

[long fog]

Integers

[pastel pasture]

I think you should help them I can't think right now

[long fog]

Alright np hon

[night bramble]

it's only 57

yes?

[long fog]

Yes

[night bramble]

but how do we solve it for other questions like what are the steps

[woven radish]

fäf

[long fog]

Divisior×Quotient +remainder form

[night bramble]

oh yes so a is 57?

[topaz axle]

xa is 57

[long fog]

So from this we proceed to get $x = \frac{57}a$ and we know that $x$ is integer and hence $\frac{57}{a}$ has to be an integer

[woven radish]

fäf

[long fog]

Other than 1

[night bramble]

so we need to find the factors of 57 right?

[long fog]

Yes

[night bramble]

and we apply that to all questions?

[long fog]

Yep

And we find their sum

[topaz axle]

e.g. we want 60/x remainder 4

[night bramble]

we find the factors of 56 ?

[topaz axle]

divisors of 56 are 1 2 4 7 8 14 28 56

1 2 4 don't work

all the rest do

pretty easy

[night bramble]

oh yeah i got it now

Thank you both for help

[long fog]

Wait a sec

Are you talking about x or a values?

[topaz axle]

x i think

[long fog]

Ah ok

Does 8 work?

[topaz axle]

yes

[long fog]

Yeah it doesn't divide 60

Yeah all others work

[night bramble]

8*8 yes?

[topaz axle]

you jsut drop everything <= a

[long fog]

The numbers you have to remove are the ones that are common factors of 60 and 56

[night bramble]

because they leave no remainders?

[long fog]

Yeah

[night bramble]

I understand

Thank you for help

[topaz axle]

no

92/x remainder 5

no wait

[night bramble]

but 92 is bigger than 60 yes?

[topaz axle]

divisors of 87 are 1 3 29 87
we remove 1 3 because less than 5

not because 1 3 are common divisors of 87 and 92

[night bramble]

i don't understand man

we can choose numbers that are greater than 57?

[topaz axle]

it's a different problem

i'm just objecting to fäf's claim that you remove common divisors

maybe i misunderstood the claim idk

[night bramble]

oh so we just remove the values that doesn't leave the remainder we have?

[topaz axle]

yeah because it doesn't fit

[night bramble]

okay i'll do that, Thanks

[devout snow]

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[prime basin]

Don't even have a single clue

[wooden holly]

Doesn’t seem true

Is there a condition on the numbers except positive integers?

Acc nvm it’s probably true I had a bad counterexample

[devout snow]

@prime basin Has your question been resolved?

[prime basin]

Nevermind I think I got it

.close

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[tulip latch]

Can someone help me with converting from polar to rectangular?

[tulip latch]

How do you convert r=cos(theta) to rectangular?

[hybrid snow]

Multiply both sides by r

@tulip latch

[tulip latch]

Ok

r^2=r*cos(theta)

[hybrid snow]

Well that should be easy to simplify then

If you're familiar with polar identities

r^2 = x^2 + y^2
r cos(θ) = x
r sin(θ) = y

Memorize these

[coral shard]

.reopen

[devout snow]

@tulip latch Has your question been resolved?

[tulip latch]

Oooh

Since we know those 3

We can write it as

Hmm im still confused

[hybrid snow]

Just replace

[tulip latch]

Ok

So i can replace

R with

X/cos(theta)

And then

[hybrid snow]

No

No no no

[hybrid snow]

Look back up here

This is after we multiplied both sides by r

There should be no division anywhere

[tulip latch]

Ooh

Should we replace

r*=cos(theta) with x^2+y^2

?

Since they are both equal to r^2

?

[hybrid snow]

You keep looking at the original

[hybrid snow]

_ _

We first multiply by r

r^2 = r cos(θ)

Knowing:

r^2 = x^2 + y^2
r cos(θ) = x
r sin(θ) = y

You just replace r^2 and r cos(θ)...

[tulip latch]

Oooh

So would it be

x^2+y^2=x?

[hybrid snow]

Yes

But I think your teacher wants it in standard circle form

[devout snow]

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[tulip latch]

.repoen

.reopen

[devout snow]

✅

[tulip latch]

How do i convert to the standard form?

.

[devout snow]

@tulip latch Has your question been resolved?

[tulip latch]

Ooooh

I figured out

You need to add numbers to both sides

x^2 + y^2 - x = 0

(x - 1/2)^2 + y^2 = 1/4

You factor x^2 and x so that you have both of them as a product + a random number

And add that random numbe r to both sides

@hybrid snow thanks for your help!

.close

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[devout snow]

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[sacred oracle]

Hello, could someone help me with this please 🙏

[tacit crow]

the resultant force is going to be the two forces added together

So when u add f1 and f2 what do u get?

[sacred oracle]

(4+p)i+(q-6)j?

[tacit crow]

yes

so now that vector is parallel to -2i-j

Do u remember what vectors need to have in common to be parallel?

[sacred oracle]

Same direction

But how is it going to be parallel? We don't know the exact value of the force to know the direction

[tacit crow]

yes so -2i-j is a multiple of (4+p)i +(q-6)j

[tacit crow]

it says that the resultant force is the same direction as -2i-j so that just meant a they’re multiples of each other. We don’t need to know the exact multiple for this question

We can create this equation

[tacit crow]

do u know why we can do that or should I explain it more

[sacred oracle]

I think I understand why it's a multiple but how do we end up with -16

[tacit crow]

So u compare the i and j components separately

so 4+p=-2k

And we don’t know what k is so we want to eliminate k

[sacred oracle]

Ok hold on let me try it

@tacit crow do we then solve simultaneously?

[tacit crow]

yes

What did u do

Did u get both equations to equal -2k?

[sacred oracle]

I managed to do it till here

[tacit crow]

Yeah that’s good so now u have 2 equations which equal -2k so u can make them equal to each other

so 4+p=-12+2q

because both RHS equal -2k so both LHS must equal each other

[sacred oracle]

It's fine to multiply an equation by a number as long as all the terms in it get multiplied right?

[tacit crow]

Yes

[sacred oracle]

I got it!

Btw do you know why we have to use k?

[sacred oracle]

Like how you did it here

[tacit crow]

So let’s say u have these 2 vectors they’re both parallel, (go in the same direction) only difference is one is 2x bigger than the other

Same for this one

so 2 vectors are parallel if they are multiples of each other

now if the vector (4+p)i +(q-6)j is the vector 2i+4j for example

then -2i-j will be i+2j

however we can’t put 2 in front of the vector because we don’t know if it’s 2x greater or 4x or 5x so instead we put k

because k can be any number

So the bottom equation is similar to the top ones only we have some algebra instead of just numbers

[sacred oracle]

But here it stated that -2i-j is just a direction with no magnitude but we are dealing with force which has both direction and magnitude so is it still fine to do it that way?

[tacit crow]

a force is a vector and all vectors have direction and magnitude

[sacred oracle]

So doesn't matter if it has magnitude as long as they both have a direction?

@tacit crow

[tacit crow]

They both have magnitude even if it doesn’t state that in the question

Because the magnitude of a vector is the length of it and all vectors have a length

[sacred oracle]

I see now

Thanks for your help I got it now 👍 🙏

[devout snow]

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[restive river]

Can the length of a latus rectum be negative?

[low fossil]

can lengths be negative?

what conic are we talking about anyhow?

[restive river]

Parabolas

My teacher put -32 as the length of a latus rectum

Could that be a mistake?

Because as far as I know a distance can't be negative.

[low fossil]

what is the formula for the length of a latus rectum of a parabola?

[restive river]

| 4p |

That's what she told us to use

[low fossil]

what is p here?

[restive river]

Distance between vertex and directrix/focal point

[low fossil]

the mod anyhow tells us that the domain of that function is non negative reals

anyways, in most geometry lengths are taken as positive and thats probably incorrect. probably

[restive river]

You wants us to conceptualize conics, rather than get confused by the formulas that people generally use.

I'll ask her about it.

Since my previous teachers never put - for things like so.

[low fossil]

yea lengths are generally magnitude of the distance between two points and magnitudes are without signs

[restive river]

Yep

Thanks

.close

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[subtle topaz]

can someone check my work?

[subtle topaz]

i need to use implicit diff to find dy/dx

[quaint citrus]

What’s (x+y)’

(Calculate it)

@restive river going from the first line to the second line here is correct?

(x+y)’ = (1 + y’)

Oh wait lol

He alrdy distributed it

Oops mb

Wdym

[subtle topaz]

my bad im supposed to find dy/dx

oh shoot thanks i see now

[quaint citrus]

Shdnt it be this?

[woven radish]

Stephen

[quaint citrus]

R u seeing what I’m saying @subtle topaz ?

[subtle topaz]

Yeah I am

I’m pretty your write I just don’t write it all out

[devout snow]

@subtle topaz Has your question been resolved?

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[forest hound]

i just wanna make sure this is right

[forest hound]

hmm

i think it’s right?

[rough tapir]

where does the 10 come from

[woven radish]

hannibal

[forest hound]

so 10t^3

[unreal eagle]

first you have to apply the power rule

do that and share your answer

[forest hound]

3 log pT

?

[unreal eagle]

yes

now divide both sides by 3

[forest hound]

ummm

[unreal eagle]

i.e. take the 3 to the other side

[forest hound]

so just log p t 3

[unreal eagle]

$\frac {x}{3} = \log_{p}T$

[woven radish]

! saad

[unreal eagle]

can you use this now?

[forest hound]

so just 3?

hella confused

[unreal eagle]

you have $log_{p}T = \frac {x}{3}$

[woven radish]

! saad

[unreal eagle]

remember: $log_{a}N = x$ becomes $a^{x} = N$

[woven radish]

! saad

[unreal eagle]

can you identify your a, x, and N?

[forest hound]

a is p

n is t

x is 3

so p^3=t

[unreal eagle]

x is everything on the rhs

the whole thing

[forest hound]

x/3?

[unreal eagle]

yes

[forest hound]

p^x/3=t

[unreal eagle]

yes

[forest hound]

thank you😭 this is confusing for me

[unreal eagle]

no problem

[forest hound]

.close

[devout snow]

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[mystic musk]

hey I had a question, to find the eigenvalue u solve this part and that implies that the null space of A - lambda I is not empty, which implies that it is not invertible said my teacher and he reffered to the fundemental theorem of inveritble matrices

[vast lava]

How was math made

[mystic musk]

I assume he used this part but this only says for Ax and not for A - lambda I

nvm I think I know he basically says A - lambda I is a matrix called A

[stone stump]

yes

[mystic musk]

and then

he just applies that

[mystic musk]

thank you

[devout snow]

@mystic musk Has your question been resolved?

[devout snow]

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[nimble elm]

What is the derivative of log(x)? I was taught that the derivative of log base a of x is 1/xln(a) so shouldn't the derivative of log(x) be 1/xln(10) ? I look it up and it says the derivative of log(x) is 1/x, so how can these both be true?

[versed jetty]

some people use log(x) to mean log base 10, and others use it to mean log base e, i.e. ln(x).

You ran into someone using the latter

[nimble elm]

whaaaaaaaaaaaaat

[lone ravine]

As said before. In the video they define log as base e and here you are defining log as base 10. So it makes sense that the result is different

[nimble elm]

okay

im trying to find the 2nd derivative of log(x)

and i got this answer but idk if its right

[versed jetty]

is that log as in log base 10 or log base e

[nimble elm]

base 10

?

[lone ravine]

Your second derivative is wrong. Note that 1/(x log 10) = 1/(log 10) * 1/x

And you applied quotient rule incorrectly

[nimble elm]

so h'(x) = 1/xln(10) * 1/x ?

[lone ravine]

No

h'(x) should be right

[nimble elm]

can I write it as (xln(10))^-1 ?

and derivative would be -(xln(10))^-2 * (xln(10))' ?

[devout snow]

@nimble elm Has your question been resolved?

[nimble elm]

No it hasn't.

[devout snow]

@nimble elm Has your question been resolved?

[devout snow]

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[odd elbow]

Hi

[restive river]

tell me its integration please ":D

[odd elbow]

Differentiation

[restive river]

thats cool

[odd elbow]

But it's related to integration

[restive river]

post

[odd elbow]

After "Put arctan(x^3)=t"

How did he got 1/(1+x^6)

[restive river]

ah shit thats some advanced stuff

i dont really know this methode

i believe i saw it once or twice

[odd elbow]

So you can't help??

[restive river]

but i think he done this

arctan (x^3)=t

then tan(t)=x^3

d/dt for it

[odd elbow]

[restive river]

hmmmmmmmmmm

[odd elbow]

I don't think so

Anyways

[restive river]

yeah that shall give sec

[odd elbow]

He applied the chain rule but idk how he got 1+x^6 in the denominator

,w d/dx(arctan(x^3))

[woven radish]

Results provided by WolframAlpha

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

Requested by B.TECH-ChaiWala#5548

[odd elbow]

Machine gets the same

,w d/dx(arctan(x))

[woven radish]

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[odd elbow]

🗿

[restive river]

hmmmmm

[odd elbow]

I'm dumb

I got it

F

.close

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[gentle mantle]

When finding radius of convergence, should I use the direct comparison text

[gentle mantle]

wait

ratio test is easier

how do I find the bounds tho? and if its ( or [

[supple knot]

radius of convergence always uses ratio test

you check endpoints separately on it's own

[gentle mantle]

so this is the problem

I got -x

which would make the radius, what

[supple knot]

doesn't look like you used the radius of convergence process properly

[gentle mantle]

hmmm

ok

ill make notes and show you

[supple knot]

https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/bc-10-13/v/radius-convergence-ratio-test

[gentle mantle]

now I got x

[supple knot]

you're skipping bounding the limit to be less than 1

[gentle mantle]

oh ok

so x,1

x<1

[supple knot]

do you know what the vertical lines mean?

[gentle mantle]

|||

[gentle mantle]

absalute value

[supple knot]

you need that here

[gentle mantle]

ok

|x|<1

now what

[supple knot]

do you know the radius of this?

[gentle mantle]

1

(-1,1)?

[supple knot]

.

[gentle mantle]

ok

how do I do that

[supple knot]

do you knwo what an endpoint is?

[supple knot]

there are 2 endpoints here

[gentle mantle]

yes

[supple knot]

plug them into the series

[gentle mantle]

ok

as n?

-1/x and x

[supple knot]

no

[supple knot]

x is the variable here

not n

[gentle mantle]

oh ok

[supple knot]

the summation of n=1 to infinity is unaffected

[gentle mantle]

ok

so

now i just get an expression with n

@supple knot

[supple knot]

what

[gentle mantle]

I plug in the value in the orignal series with 1 and -1

and it gives me something that idk what to do with

[supple knot]

and ?

do you have a question ?

[gentle mantle]

how do I know if its ( or [

sorry

[supple knot]

if your series converges for one of these values, then it's part of the interval of convergence

hence the name "interval of convergence"

[gentle mantle]

oh ok

ok

ok

ty

.close

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[gentle mantle]

.reopen

[devout snow]

✅

[gentle mantle]

@supple knot I fucked up my limit

I just relized

i didnt get x

I got x/2

making me wrong

[gentle mantle]

that 2 goes to 2n+2 not 2n+1

.close

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[restive river]

How do I find the area?

Break it into 4 bits, 3 right triangles and one trapezoid

And add their area

Ok...

What are the 4 bits?

ok

didn't see that message

I dont get it

Was gonna do a little drawing still, lol

wouldn't it be 2 triangles and 1 trapezoid?

its pretty tricky

It is that, too.

My bad, I like right triangles more. I forgot that was a big triangle

And you've got the base and the height too

oh, ok

either way is fine

Do you know the area of an isosceles triangle?

yep, so for the top triangle, i think its 1400mm

Good! I guess cm works better.

140cm?

im kind of stuck with the trapezoid though

[restive river]

Nope

14 cm²

ok

It's the area.

[restive river]

You don't know the formula for the area of it I assume

yeah not really

It is a right trapezoid, the formula is this: [(a+b)×h]/2

Where a and b are the parallel sides of the trapezoid

And the height is well, the line which creates the 90° angles

ok, give me a second please to calculate and process this

thanks

Of course.

i dont know, but i gave it a go, is it $1312.5mm^2$?

[woven radish]

Kit_Kat

[restive river]

Okay, let's look at the parallel sides. 70+35=105

yep, ok

Height is 5 cm, 50mm.

ok

105×50=5250

And 5250÷2 = 2625

oh, ok, so thats what went wrong

oh

Don't worry

i guess i underestimated it, because i did it twice, and that was one of my answers, hehe

Heh

Now 2625 mm² = ? cm²

262.5cm^2

Try again

26.25cm2

Converting from one unit squared to another is by 100x. Cubic 1000x.

Yes, 26.25cm²

ok, ill remember that

Great. Now we got the last triangle

yup, is it 14cm^2?

How did you come up with it?

cause i dissected into two parts

i dont know

i just quickly did it i guess

so would the answer be...

$40.25cm^2$

[woven radish]

Kit_Kat

[restive river]

Not yet, we've got the last triangle to add. Argh, it's a little harder than I thought

ok

let me try again

For sure, lemme get my pen and stuff too

ok i get it now

im going to calculate it

the last triangle would also be, $14cm^2$?

[woven radish]

Kit_Kat

[restive river]

Nope

But nice try

ok

thanks!

One sec

same

$7cm^2$?

[woven radish]

Kit_Kat

[restive river]

We can draw this perpendicular line

yup, ok

And break down the 70mm line for easier view

ok

Now the middle line is equal to the lower one, 35mm.

yeah

The original triangle on the left and the newly one on the right are identical

Hence, the sides are all the same

ok

would 1 of them be 175 mm2?

Not mm² whem working with lenght

mm

But correct. 17,5 mm

ok, thank you

Now

Do you know the area of a right triangle?

yes

The product of the perpendicular lines divided by 2

yeah

Have you got 4,375 cm²?

$57.75mm^2$

[woven radish]

Kit_Kat

[restive river]

no

Okay, let's break it down

17,5 × 50 mm?

Should be 875 mm

just a sec

yup

Divided by 2?

437.5mm

²

And to cm²?

yeah, forgot it

4.375mm^2

Cm² 🙂

But great

oh

You got all areas now

14 cm² +
26,25 +
4,375

oh, thanks!!

44,625 cm²

Is your final answer👍

ok, yup i see

Thanks for sticking with this

yeah, i appreciate your help

Could've been a careless kid

[restive river]

Thanks a lot.

yup!

Have a nice one.

have a good day!

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[dim perch]

Could someone give a hint as to why $A_n \lhd S_n$?

[woven radish]

blanket

[wicked turtle]

what's the index of A_n ?

[dim perch]

A_n's defined to be the even permutations

[wicked turtle]

yea i know what it is

[dim perch]

o

[wicked turtle]

what is its index as a subgroup of S_n

[dim perch]

n/2?

oh

wait

[wicked turtle]

no..

[dim perch]

no you mean

2

sorry

[wicked turtle]

yes

[dim perch]

not n/2

i was thinkin order LOL

[wicked turtle]

and it's a general fact that any subgroup of index 2 is normal

try proving that if you haven't already

btw, the order is n! / 2, not n/2

[dim perch]

ah you're right you're right

mb

do you have a hint as to why order 2 groups are normal?

[wicked turtle]

it's basically because it forces left cosets and right cosets to coincide

(when there are only two cosets)

let G be the parent group and H a subgroup of index 2

then H has two left cosets and two right cosets

call the two left cosets H and gH

call the two right cosets H and Hk

since left cosets partition G and right cosets partition G, it must be true that gH = Hk

thus the left cosets of H are also right cosets of H

you can show that this implies that H is normal

[dim perch]

ahh

okay im starting to get it now

thank you

[wicked turtle]

sure

[dim perch]

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• Show your work, and if possible, explain where you are stuck.
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[sonic kelp]

I tried:

a = (3 + x)/3

b = (5 + x)/3

c = (7 + x)/3

where x was the middle number, a was the number I had to find, b was the side squares of the middle row and c was the remaining number

x = ( (5 + x)/3 + (5 + x)/3 + (3 + x)/3 + (7 + x)/3) /4

I got x = 2.5, I put it in but the whole thing didn't work. Could anyone help

[light fractal]

why didn't it work?

[devout snow]

@sonic kelp Has your question been resolved?

[sonic kelp]

I put in the numbers after and it wasn't correct

6/6 11/6 12/6
1/6 15/6 13/6
24/6 19/6 18/6

[faint hinge]

Here's what I did (I still haven't solved it):

I tried to find the values. so the top-middle one is (2+1+x)/3, the left-middle one is (4+1+x)/3, the down-middle one is (4+3+x)/3, and the right-middle is (3+2+x)/3

then I tried solving for the middle one which would be (top-middle + left-middle + down-middle + right-middle)/4

[sonic kelp]

Yeah that's what I did

[faint hinge]

where di 5 + x come from

3+2? that side?

[sonic kelp]

Yeah

4+1 = 5 and 3+2 = 5 so they are the same ig?

[faint hinge]

then why is my x value so different from yours

[sonic kelp]

What did u get for x