help-0

[dull onyx]

i found the derivative myself

[rigid smelt]

...f'(2)=4 is a given information

[dull onyx]

i found derivative of x and then used 2 instead of x

[rigid smelt]

f'(x)=2ax is the information that you found

[dull onyx]

it literally asks me for the derivative of 2 after that

[rigid smelt]

.

[dull onyx]

and its 4a

wait

i plopped it into google translate i swear this makes no sense

[rigid smelt]

the question IS asking you to find the derivative SUCH THAT its EQUAL to 4

[dull onyx]

b) Determine a so that the derivative of the tangent of the curve of f at point A (2, f (2)) is 4

[rigid smelt]

so f'(2)=4 is a given information, and you will use that to find a

yes

[dull onyx]

a) find f’(2)

[rigid smelt]

sure

anyway, f'(2)=4a is what we got from the first part

but in the second part, the question wants f'(2) to be EQUAL to 4

[dull onyx]

YA

so i did

[rigid smelt]

that means you will use f'(2)=4 as an information to find a

are you clear on what to do?

[dull onyx]

f’(2) = 4 => 4a = 4 so a = 1?

[rigid smelt]

yes

[dull onyx]

Omg thank u sm

i had alrdy done that but i wanted to make sure so thank u<3

wait now rhat it asks for the equation of the tangent do i do y-f(2)= f’(2) (x-2) ?

[rigid smelt]

yes

[still violet]

Hello! I have a question related to exponentiation, e^x. Let's say we have a vector [1, 2, 3]. Then, we apply e^x to each element, like so: [e^1, e^2, e^3]. Furthermore, we divide each element by the sum of each exponentiated element of the vector, like this: [e^1 / (e^1+e^2+e^3), e^2 / (e^1+e^2+e^3), e^3 / (e^1+e^2+e^3)]. This gives the output of [0.09003057317, 0.24472847105, 0.66524095577]. Why, if doing the same process but we apply it to an input of [2, 3, 4] the result is exactly the same? Basically, if we sum the same number to each input element, the result is always the same. Is it because of e?

I would deeply appreciate some help.

[dull onyx]

and will i still assume that a is equal to 1?

[rigid smelt]

wait

[dull onyx]

okayy

[rigid smelt]

does it asks for the tangent for the case a=1

or does it ask for the general case

since you are not providing me sufficient context here

[dull onyx]

the third question is: Find the equation of the tangent

nothing more >0>

[rigid smelt]

just find the equation of the tangent?

[dull onyx]

yep

[rigid smelt]

at any point on the graph?

[dull onyx]

it probably means the one from above then

since it doesn’t mention the point

[rigid smelt]

quite ambiguous,
supposing the tangent is at x=2, and supposing we are talking about the general equation on the tangent, then a is kept as is

or you can suppose that we are talking about the case where a=1

and then continue with your work

[dull onyx]

im so confused

i found the equation y = 4x - 4

assuming that a is 1

[rigid smelt]

since the problem is ambiguously stated, you should add a sentence saying "Suppose...."

this will make your work true

or assume

[dull onyx]

oh okay

but i dont know if ive done it correctly ><

[rigid smelt]

its wrong

[dull onyx]

whaaa why

[rigid smelt]

wait

nvm

forgot to multiply the slope

[dull onyx]

firstly i found the derivative of f(x) then used that to find f’(2) then bc it asks for A(2, f(2)) i said that f’(2) = 4 so a is 1

(this is all of it to make sure i have no mistakes)

ok so wont f(2) be 4 ?

[rigid smelt]

yes it is

like i said i miscalculated

[dull onyx]

oh i think it’s correct

thank u waler!!

ok well another one

Find the angle formed by the x 'x axis that is tangent to point A (-1/2, f (-1/2))
``` i am so lost

[rigid smelt]

so am i

could you show both the translation AND the original text?

[dull onyx]

its in greek

[rigid smelt]

since you alr showed the translation, just show the original text

yeah i know

[dull onyx]

i forgot

[rigid smelt]

oh

[dull onyx]

in the last question it says rhat a=1 too

[rigid smelt]

i thought you had like a paper or something

[dull onyx]

I do

[rigid smelt]

because that question doesnt make sense

[dull onyx]

my teachers hand writing i can barely make it out😭😭

the top one

[rigid smelt]

it really doesnt make sense

x'x axis?

i assume that implies the x axis

and i assume the angle is between the tangent line and the x axis

if so then you just need the slope

[dull onyx]

ive done one with the x ‘ x axis before but it was given

[rigid smelt]

the slope of a line is equal to tan(theta) where theta is the angle formed by the line and the x axis

[dull onyx]

it said that the tangent formed an angle of π/4 x’x axis

[rigid smelt]

again, this is just me rephrasing the questions in my words, so it might be incorrect

[rigid smelt]

i still dont quite get it

[dull onyx]

and then i just did that f’(xo) = 1

me either😭

[rigid smelt]

maybe someone else can help you, i havent encountered this notation before

[dull onyx]

ill try it and letnu know if i get the solution

[crystal tapir]

my man who understands greek

[dull onyx]

they asked me to send the raw untranslated material

[crystal tapir]

i understand greek but literally "that" is so confusing i can barely understand a phrase

[dull onyx]

r u greek?

its some basic greek and a lot of mathematical words that r much more uncommon

[crystal tapir]

nah but my ancestors lived in selanik but during balkan war they left to istanbul

so i know a bit of greek

[dull onyx]

aah okay

[dull onyx]

@rigid smelt i found the solution, not sure if u care but i found the derivative of (-1/2) and it was -1 so the angle is 3π/4

[rigid smelt]

so then my rephrasing was correct

what they meant was:
Find the angle formed by the tangent line at x=-1/2 and the x-axis

[dull onyx]

yup probably

[tawdry shore]

is

anyone here

can i ask a quick question

why does this equal this

[alpine sable]

@tawdry shore because of the index law: x^-n = 1/x^n

anyone able to help with 13?

[glass lichen]

a or b?

[alpine sable]

a first

[glass lichen]

Ok, well you know the displacement vector for the plane going for 5 minutes

and 12:15 is after 15 minutes, so 3 times the displacement will land you at the position after 15 minutes

[alpine sable]

which vector is that

@glass lichen

[glass lichen]

displacement is change in position

so final - initial position is displacement

[alpine sable]

oh so would that be -7i +24j

@glass lichen

[glass lichen]

yes

so every 5 minutes, it will do a displacement of [-7,24] since velocity is constant

[alpine sable]

so the answer should be -21i + 72j but the answer in the book says 19i + 88j

[alpine sable]

did I do it wrong

[glass lichen]

that's the displacement vector, you still need to add it to the initial position

[alpine sable]

I dont understand why?

[glass lichen]

cause you start at [40,16], then go a further [-21,72]

[alpine sable]

Ohhh i get it now! thanks are you able to also help with b?@glass lichen

[glass lichen]

velocity is displacement over time

[alpine sable]

@glass lichen sorry its not working

[glass lichen]

ok well what are you doing?

[alpine sable]

umm im dividing the vector I found by 1/4

[glass lichen]

which vector..?

[alpine sable]

the displacement vector after 15 min

ohh

wait

was i meant to use the one that was multiplied by 3

[glass lichen]

depends on what time you're using, 15 or 5 min

you use the corresponding displacement vector for that time

[alpine sable]

ohh i see

thanks I ended up getting it!

[glass lichen]

$\vec{v}=\frac{1}{t}\vec{d}=\frac{1}{0.25}[-21,72]$

[ocean seal]

Mosh

[plucky crow]

y =f(x+a)

Is there any way to write this in terms of f(x)

[teal epoch]

$y=f\left(x+a\right)$

[ocean seal]

Callaway

[teal epoch]

not trying to help here but if you want your question to be a little bit clear just copy it

[plucky crow]

Its hard to explain but

y = f(x)
consider
y =bf(x)
y/b = f(x)
This is for a y transformation written with f(x) as the subject. How can I do this for an x transformation such as
y =f(x+a) ?

[glass lichen]

No

well depends on what you know about f

[alpine sable]

Holy frek

[plucky crow]

Yh ik but why is it always a shift of -a

No matter what f is

[glass lichen]

cause that's just the definition of horizontal translations

$f(x+a)$ translates f -a units horizontally

[ocean seal]

Mosh

[woven umbra]

Can someone help me with this?

[sleek elbow]

not readable

[woven umbra]

My bad Is that better?

[sleek elbow]

yes, but I cant help rn

[woven umbra]

Oh alright thanks tho

Can anyone else help me out?

please?

[plush ermine]

What is the sum of the probabilities? Please calculate.

A probability model must sum to 1.

[slim elbow]

What is the additive inverse of 2/-9

[vale sapphire]

seeing as though 2/-9 = -2/9, you're asking to find x such that x-2/9=0

that shouldn't be too much trouble

[slim elbow]

Thanks brother

[sleek elbow]

"5. While asking questions, make sure you mention all relevant details, including the context, what you have tried and what you're stuck at. Do not expect others to simply solve your questions for you." @urban pilot

[lyric magnet]

could i get a hint?

i was thinking maybe i can write that since q and p are the midpoints then PB and QC are equal

but then i dont know how to continue

please

[rigid smelt]

Do you want to prove this through just plain geomtry?

Or do you want to prove this using the coords

[woeful pulsar]

main idea: it's isosceles so it's congruent to itself reflected

[lyric magnet]

which ever is simpler i guess

[rigid smelt]

I'd say either is same

But ima use geometry

[lyric magnet]

Ok

my module name is geometry so i guess thats good

[rigid smelt]

So you alr concluded that PB and QC are congruent

[lyric magnet]

yeah

[rigid smelt]

We will be proving congruent triangles

Which we can then ocnclude that PC is congruent to QB

Now choose two triangles that has those pair

[lyric magnet]

how do i name that middle point

do i just call it like Z?

[rigid smelt]

Theres no need for extra points

The points on the diagram are enough to make two congruent triangles

[lyric magnet]

PAC and QAB?

[rigid smelt]

Maybe choose something that also have the pair PB and QC

Ehh no

Not exactly

[lyric magnet]

waitt

[rigid smelt]

You were close

[lyric magnet]

PBQ and QCP

[rigid smelt]

Yeah

[lyric magnet]

ok

[rigid smelt]

Ehh wait sorry, PBC and QBC

[lyric magnet]

ohhh

[rigid smelt]

I misread

This is a better pair

[lyric magnet]

because they share the same base right

and height

[rigid smelt]

Yes

So you alr have two pairs of sides that are congruent

Since we cant do SSS

Theres only one option left

Which is SAS

So lets check if angle PBC=QCB

[lyric magnet]

they have to be

because ABC is isoceles

[rigid smelt]

Yeag

So the triangles are congruent

[lyric magnet]

i see

thanks for help

[glacial kernel]

yes

[plucky crow]

b - can someone decipher the question a bit idk what its asking me to do

is it asking for what arguments of z-4+2i can be made that can not be made from the other locus

nvm i got it now

[pallid sail]

how do i solve this exponential equation

already found a mistake here

[rigid smelt]

The very first mistake is at the second line

When you move -3^(2x-1) to the left side

Shoud be +3^(2x-1) on the left side not -

[pallid sail]

yep

i see it as well now

still no clue how to solve it 🙃

[rigid smelt]

Notice that 2sqrt(2) = 2^(3/2)

And 27 = 9^(3/2)

Or just use log

[median hound]

yo i need some help

i dont understand wether or not its d or e

because on one hand you need to know that the angle of 1 is equal to 4 and 2 is equal to 5 but on another hand you can use common sense to figure it out

[subtle walrus]

if the lines are parallel then what you just said about the angles will follow.

[median hound]

so it would be B?

this is a very foggy area for me so sorry if i look dumb

thx it was b and i wouldnt have figured it out without you

[subtle walrus]

yes that's right

you're welcome

[median hound]

sorry for the second question but sas sss asa is also really foggy

im pretty sure its either c or d because the use both diagonals and intersect using DC together

but im not sure wether or not its angle side angle or side angle side

[sour echo]

i

Anyone can help with this

[subtle walrus]

it's d

[median hound]

can you tell me how you got the answer?

[subtle walrus]

because we will use the fact that AD=BC (S)

and both angles ADC and BCD are right angles (A)

also, both triangles share the side DC (S)

so we used SAS to prove the congruent. And it follows that the diagonals are congruent.

I hope the explanation is clear

[median hound]

thank you

[flat dawn]

I was reading about the Lucas Primality test
https://en.wikipedia.org/wiki/Lucas_primality_test

I don't understand why "If a also survives the second step, then the order of a in the group (Z/nZ)* is equal to n−1"

also apparently there always exists such number a when p>2, question is why

<@&286206848099549185>

[flat dawn]

@glass lichen Can you help me over here maybe?

[glass lichen]

No group theory under my belt

[flat dawn]

welp. I feel like this is basic enough but I don't see it

[sullen karma]

Read it aloud

Work on a another question then come back

[flat dawn]

I don't have another question, I'm reading this out of interest. I don't see why having this for every prime q dividing n-1 implies n is a prime

[marsh shard]

Can anybody help me with this question?

The number of radians in a 540-degree angle can be written as aπ where a is a constant, What is the value of a ?

[glass lichen]

just convert 540deg to radians

[runic hull]

" (because the order of every element of a group divides the order of the group"

I think the argument goes like this

a has some order r, then r has to divide the order of the group (which is at most n-1). But (n-1)/q goes through all divisors of n-1, and thus goes through r. So if you don't see a^(n-1)/q become 1, then a must have order n-1

[flat dawn]

ohhh

[runic hull]

but if you have one element of that order then it generates the whole group

[flat dawn]

right

it doesn't go through all divisors but at least a multiple of them

which is enough here

[runic hull]

oh yes you're right

[flat dawn]

thanks buddy @runic hull

now all I gotta do is realize why such a value a exists

[runic hull]

no problem ^^ not done any group theory in a while, glad I helped

[flat dawn]

it's not showing up in there but it does show up in here
https://en.wikipedia.org/wiki/Primality_certificate#Pratt_certificates

as well as in the original paper which claimed first to show that primes is in NP

(i.e there is a small certificate that can be verified in time bounded by a polynomial of the input length)

[sacred flax]

Can someone explain to me why this is right?

[glass lichen]

$\frac{1}{\sin(x)}\cos(x)\frac{\sin(x)}{\cos(x)}=1$

[ocean seal]

Mosh

[sacred flax]

But what about tanx?

[next spade]

tan x = sin x/cos x

[sacred flax]

ohhhhh thank you

[glass lichen]

tan(x)=sin(x)/cos(x), quotient identity like I had written

[sacred flax]

ok thank you for the help

[alpine sable]

is this correct?

[glass lichen]

yes

[alpine sable]

okie thanks!

can u help me with this?

@glass lichen

[flat dawn]

use the fact that log(a) + log(b) = log(a*b)

and the fact that c*log(a) = log(a^c)

I assume here that all logs have the same base

[alpine sable]

Wait

Why is there no symbol after (x-8)

[flat dawn]

because it's (3 log x) - (8 log x) (with respective log bases)

[alpine sable]

I got confused

hahah

sorry

[flat dawn]

all good

[sacred flax]

huh?

[tawny condor]

@sacred flax Do you need help proving this identity?

[sacred flax]

I need help with simplifying it

[tawny condor]

well that's how u prove it

[sacred flax]

oh ok then

i got Cosx-1

[tawny condor]

what

[alpine sable]

okie thanks!

[sacred flax]

idk this is confusing me

I am showing the answer the actual problem was just the left side

[tawny condor]

Ok

so

try turning the sec to cos

then simplify

Until you get cos^2(theta) - 1

Which equals to -sin^2(theta)

[sacred flax]

wait why does that equal to -sin^2?

I got the cos^2 -1

[tawny condor]

Because

You know that

sin^2(x) + cos^2(x) = 1

this is an identity

which means that

cos^2(x) = 1 - sin^2(x)

right?

@sacred flax

[sacred flax]

oh ok got it

thank you

[tawny condor]

np

here u go in case u need this

[alpine sable]

This free?

[tawny condor]

Yeah

@alpine sable

[vale wigeon]

wrong server?

[dire pilot]

Can I get some help

I'm aware how to do the problem im just curious do I have to divide 3 by 7 or what do I do at the beginning

[noble crypt]

uh you multiply

like (3 * r) / 7

[dire pilot]

oh thanks

[noble crypt]

the same for the latter part

np

[candid torrent]

do a lil subbing

[dire pilot]

42 / 7 = 6 +5 = 5 x 8?

[sleek elbow]

$\frac{3}{7} * 14 + \frac{5}{8} * 8 = \frac{3}{7} * \frac{14}{1} + \frac{5}{8} * \frac{8}{1}$

[ocean seal]

Ladan

[dire pilot]

Did I do it correctly?

[noble crypt]

yep

[dire pilot]

6 + 5

[noble crypt]

if there's a number which does not have a denominator it automatically gets 1 as its denominator

[dire pilot]

opk

thanks so much bro

[noble crypt]

no problem

[sleek elbow]

used this to practice formatting with latex lol

[ocean seal]

Ladan

Ladan

[noble crypt]

noice

[dire pilot]

if something were like this you would turn them into + right?

[tawny condor]

yes

y + 3y

[dire pilot]

so 2 minuses equal plus?

[tawny condor]

yup

u could say that

[dire pilot]

ok

[noble crypt]

yeah

you could get it better on a number line

like by subtracting you go the left side of a number line but subtracting again would make you go right which is the positive side

[tawny condor]

2 things u need to consider @winter salmon

anything inside a square root cannot be negative

and you cannot divide by 0

That should help you find what x CAN'T be

[noble crypt]

just for reference here, does domain mean a set of numbers?

[winter salmon]

[tawny condor]

yeah i guess

[noble crypt]

ah ok

[winter salmon]

@tawny condor so shouldn't it be x is greater than or equal to 3?

[tawny condor]

Yup

[winter salmon]

uh

i put that in

[tawny condor]

there is another square root

so

[winter salmon]

and it said that it was wrong

[tawny condor]

do that one aswel

[winter salmon]

oh yea

im dumb

[tawny condor]

bro there are more stuff XD

[winter salmon]

thanks for the help

[tawny condor]

np

[winter salmon]

so the final answer would be x is greater than or equal to 3 and x is greater than or equal to -1

[tawny condor]

yes but

combine both of these

oh and x doesn't equal 5

[winter salmon]

ok

thanks

[winter salmon]

so what would the final format of the solution be

[tawny condor]

thats how I do it

I marked all 3 of the requirements

filled hole means including that number

unfilled means not including

and because ALL 3 of the requirements need to be met,

look at the picture and see where u got all 3 lines

[noble crypt]

sorry for interrupting but would the solution for this be 3 is less than or equal to x, and x is lesser than 5?

i'm kinda learning this stuff

[tawny condor]

and x greater than 5

3 <= x < 5 or x > 5

[noble crypt]

right it doesn't stop there

kk

[tawny condor]

why or? because it can be either one of them

[noble crypt]

yeah because it x can be either 3 OR greater than it

that's why i said or

[tawny condor]

yup

@winter salmon here u go

[winter salmon]

so x >= 3 and x can't equal to 5 and x>=-1

[noble crypt]

oh and btw which set is this

[winter salmon]

wait

[noble crypt]

natural numbers or real

[tawny condor]

no

it must be BETWEEN 3 and 5, including 3

[noble crypt]

oh i think it's natural numbers cause the portion isn't shaded

[tawny condor]

which is why I am writing 3 <= x < 5

and it could also be greater than 5

so OR x > 5

[noble crypt]

yeah the circle over 3 is darkened meaning 3 is included

[winter salmon]

wait so what would my final answer be im a bit confused

[tawny condor]

this

[noble crypt]

3, 4, 6, 7...

i'm thinking

is that right?

[winter salmon]

ok thanks

[tawny condor]

no u just write this

[tawny condor]

.

thats the whole domain which x can be in

[noble crypt]

i think it should be written as {x : 3 <= x < 5 or x > 5 and x belongs to N}

[tawny condor]

i dont think he's at the lvl where he needs to specify that

N

[noble crypt]

kk

[tawny condor]

@winter salmon are you in middle school?

[noble crypt]

i said it belongs to N cause you haven't shaded

[tawny condor]

u dont have to answer if u dont want tho

[noble crypt]

are you in high school?

i'm in 10th grade

[winter salmon]

uh yea

well

actually

no

im in high school

[tawny condor]

oh ok

[alpine sable]

can i ask

i take that as a yes

how does this happen

[vale wigeon]

x^2 - y^2 = (x-y)(x+y)

[alpine sable]

thanks!

how did i not see that

[fervent gust]

https://media.discordapp.net/attachments/844681108473118750/861322999986257940/276728415518720001.png?width=900&height=402

does this series converge or diverge

with alpha > 0

I tried to use taylor series

like this

https://media.discordapp.net/attachments/844681108473118750/861324320260096000/276728415518720001.png?width=1080&height=239

which means if alpha >= 1/2, the series diverges

but I can't figure out for the case alpha < 1/2

[vague coral]

that taylor expansion looks weird tho

[fervent gust]

idk the real term for this kind of expansion lol

[vague coral]

$\cos (x) = 1 - \frac{x^2}{2}+ ...$ when x approaches 0

[fervent gust]

yea but you have power of n

so you need to use exp

[ocean seal]

Herels

[vague coral]

no

hmm wait

[fervent gust]

but yea for the case alpha >=1/2, you can do a proper taylor series

because $\frac{1}{2n^{2\alpha -1}}$ approaches 0

[ocean seal]

uyitroa

[vague coral]

n is a natural number right ?

[fervent gust]

yea

[vague coral]

🤔

$$(1-\frac{(\frac{1}{n^{\alpha}})^2}{2} + o((\frac{1}{n^{\alpha}})^2))^n$$

[ocean seal]

Herels

[vague coral]

and after this you use exponential form right ?

[fervent gust]

yea

[vague coral]

you will get :
$e^{n log(1-\frac{1}{2n^{2\alpha}} + o((\frac{1}{n^{2\alpha}}))}$

[ocean seal]

Herels

[fervent gust]

yea then I applied taylor series for log(1+x)

[vague coral]

yes

that makes sense

[fervent gust]

which gives us the thing above

[vague coral]

but to know if the series converges or diverges, you have to compare it to a known series that converges

if im not mistaken

[fervent gust]

yea but before that you can check the limit of the general term that's why I used taylor series

you can see that for the case alpha >= 1/2 the general term converges to 1 so the series diverges

[vague coral]

Yes and it goes to 0

oh I forgot about alpha

[fervent gust]

yea

for the case alpha < 1/2, I tried to compare with other known series but no luck

[vague coral]

hmm

you can use D'Alembert criteria 🤔

?

[fervent gust]

the ratio converges to 1

[vague coral]

ripp

[fervent gust]

😔

[vague coral]

but I think you can use taylor expansion again, for the expression with exponential

and after this, thinking about Riemann

[noble sinew]

can also try root test maybe (root is stronger than ratio)

[fervent gust]

also converges to 1

lol

[fervent gust]

how

x goes to -inf for the case alpha < 1/2

[vague coral]

hmmm yea your right

[noble sinew]

not how you do it

find two points on the tangent line to estimate the slope

(besides you should get it was negative)

so for example use the point that is approx (30,150)

that point isn't (60,150)

[sleek elbow]

What is the best/prettiest way of proving the pythagorean theorem in you guys's opinion? (Not sure if open questions like these are ok here so tell me if not)

-shower thought I guess

[fervent gust]

test for one case, since it works for one case it works for all cases. Le best way to prove it

[sleek elbow]

LMAO

[vale sapphire]

the two squares way is one of the most elegant one imo

both squares have area (a+b)^2, remove the extra junk, and done

[cobalt ledge]

This^^

[sleek elbow]

ye thats the one my teacher showed, I quite liked it

[vale sapphire]

mathologer has a video on this

[sleek elbow]

(still like it)

[vale sapphire]

https://www.youtube.com/watch?v=p-0SOWbzUYI

[fervent gust]

btw can I bump my question since it's lost above and still unanswered for 1 hour

[sleek elbow]

what does bump mean?

[vale sapphire]

bring back in the spotlight

[sleek elbow]

$(a+b)^2 = 4 * \frac{1}{2}ab + c^2$
$(a+b)^2 - (4 * \frac{1]{2]ab) = c^2$
$a^2 + 2ab + b^2 - (4 * \frac{1]{2]ab) = c^2$
$a^2 + b^2 = c^2$

(lets hope my formatting is correct 🙏 )

oof

[sleek elbow]

ty

[ocean seal]

Ladan

$(a+b)^2 = 4 * \frac{1}{2}ab + c^2$
$(a+b)^2 - (4 * \frac{1]{2]ab) = c^2$
$a^2 + 2ab + b^2 - (4 * \frac{1]{2]ab) = c^2$
$a^2 + b^2 = c^2$


(lets hope my formatting is correct 🙏 )
```Compilation error:```! File ended while scanning use of \frac .
<inserted text> 
                \par 
<*> 332150399266062347.tex
                          
I suspect you have forgotten a `}', causing me
to read past where you wanted me to stop.
I'll try to recover; but if the error is serious,
you'd better type `E' or `X' now and fix your file.```

[vale sapphire]

you wrote {2] instead of {2}

[sleek elbow]

oh I see

wait

[vale sapphire]

and similar errors elsewhere

[sleek elbow]

$(a+b)^2 = 4 * \frac{1}{2}ab + c^2$
$(a+b)^2 - (4 * \frac{1]{2}ab) = c^2$
$a^2 + 2ab + b^2 - (4 * \frac{1]{2}ab) = c^2$
$a^2 + b^2 = c^2$

[ocean seal]

Ladan

$(a+b)^2 = 4 * \frac{1}{2}ab + c^2$
$(a+b)^2 - (4 * \frac{1]{2}ab) = c^2$
$a^2 + 2ab + b^2 - (4 * \frac{1]{2}ab) = c^2$
$a^2 + b^2 = c^2$
```Compilation error:```! File ended while scanning use of \frac .
<inserted text> 
                \par 
<*> 332150399266062347.tex
                          
I suspect you have forgotten a `}', causing me
to read past where you wanted me to stop.
I'll try to recover; but if the error is serious,
you'd better type `E' or `X' now and fix your file.```

[sleek elbow]

$(a+b)^2 = 4 * \frac{1}{2}ab + c^2$
$(a+b)^2 - (4 * \frac{1}{2}ab) = c^2$
$a^2 + 2ab + b^2 - (4 * \frac{1}{2}ab) = c^2$
$a^2 + b^2 = c^2$

[vale sapphire]

two remaining

[sleek elbow]

am I blind? lol

[vale sapphire]

you can just edit your message yknow

[sleek elbow]

true

sorry

[ocean seal]

Ladan

[sleek elbow]

wait how do you make it write in a new line?

[vale sapphire]

put \\

[sleek elbow]

there we go ty

[dry prawn]

I have a question about even numbers

[sleek elbow]

https://dontasktoask.com

[dry prawn]

Lol

Sorry

Is 0 an even number

[vale sapphire]

yes

[sleek elbow]

yup

[vale sapphire]

relevant video https://www.youtube.com/watch?v=8t1TC-5OLdM

[dry prawn]

Is he right or wrong

[sleek elbow]

leaking chat

[dry prawn]

Illegal?

[sleek elbow]

😄

its fine lol

[vale sapphire]

can't divide anything into base 0

what?

checking if 0 is even isn't about diving by 0 lol

0/2 = 0

or alternatively 0 = 2*0 (amazing, i know)

there, 0 is twice an integer

[ionic jewel]

programmer definition is that a is even if $a \equiv 0 \mod 2$

wrong equality symbol lol

[ocean seal]

bunny

[fervent gust]

anyway for this I tried dividing by $\frac{1}{n^{1-2\alpha}}$

which gives us $n^{1-2\alpha} \cos^n\qty(\frac{1}{n^\alpha}) = n^{1-2\alpha} e^{-\frac{1}{2}n^{1-2\alpha} + o\qty(n^{1-2\alpha})}$

and since $\lim_{x \to+\infty} x \ e^{-x} = 0$

we have $\lim_{x \to +\infty} n^{1-2\alpha} \ \cos^n\qty(\frac{1}{n^\alpha}) = 0$

which means $\cos^n\qty(\frac{1}{n^\alpha}) = o\qty(\frac{1}{n^{1-2\alpha}})$

And since $1-2\alpha < 1$, the series of general term $\frac{1}{n^{1-2\alpha}}$ diverges which means our original series diverges

[ocean seal]

uyitroa

[fervent gust]

but I feel like it's wrong because I wrote a python script to test and for alpha < 0.3, it seems like the series converges

[velvet pelican]

I think it should diverge?

try using the limit at infinity of the summand

[fervent gust]

for alpha < 1/2, the general term converges to 0

and the ratio and root test converges to 1

sooo

[velvet pelican]

huh, it seems to converge for alpha < 0.5

[fervent gust]

oh really for me it seems to diverge when alpha > 0.4

wait are you talking about the series?

or the general term

[velvet pelican]

series

[fervent gust]

yea so there's something wrong in my proof

[velvet pelican]

it definitely converges for alpha <= 0.4 and diverges for alpha >= 0.5

[vale sapphire]

guys

this will never converge

nevermind

[fervent gust]

the case alpha < 0.5 is tough

[hollow grove]

can anyone help me

[atomic tundra]

Please help me with this problem

[fervent gust]

I shouldn't have asked in this channel lol

questions-0 more like questions-for-people-who-dont-read-rules

[velvet pelican]

this sums it up

[fervent gust]

LOL

[atomic tundra]

<@&286206848099549185> Please help

[fervent gust]

im dying

anyway @atomic tundra have you tried writing $\beta = cos^{-1}(\frac{4}{9}) + 2cos^{-1}(\frac{4}{9})$

[ocean seal]

uyitroa

[atomic tundra]

Yes

It didn't help

[fervent gust]

do you know what $\cos(a+b) =$?

[ocean seal]

uyitroa

[atomic tundra]

Yes

CosAcosB-SinASinB

[fervent gust]

so try to calculate cos(beta)

[sullen karma]

0 is even to me 0,2,4,6,8,10,…..

[atomic tundra]

Okay I'll try it

[coral pagoda]

Yes, 0 is even. An even number is a number that is divisible by 2.
0 is divisible by 2, so it is even.

@dry prawn ^

Your colleague's argument has nothing to do with the definition of even/odd

[sullen karma]

^^ ( whole number for the answer )

[dry prawn]

THANK YOU BOB ROSS

[sullen karma]

…

Oh the profile pic

[coral pagoda]

No problem :)

[coral pagoda]

Not necessarily, -2 is considered an even number by definition

[red ledge]

Anyone here?

[coral pagoda]

What's up?

[upper pebble]

"What is the value of A when we rewrite (5/2)^x + (5/2)^(x+3) as A•(5/2)^x?"

the answer is that A equals 133/8, but i don't understand a part of the solution.

(5/2)^x + (5/2)^(x+3)
= (5/2)^x + (5/2)^x • (5/2)^3
= (5/2)^x + (5/2)^x • 125/8
= (5/2)^x • (1 + 125/8)
= 133/8 • (5/2)^x

where does the 1 come from?

[velvet pelican]

the 1 comes from factorising out (5/2)^x.
To make it simpler take (5/2)^x as a, we have
a + a*125/8
= a(1 + 125/8)
...

[upper pebble]

i see, thank you for your help

[honest umbra]

how do I write an equation where the output ratio decreases as the input increases

idk if that makes any sense

Like if I input 10 to the equation it gives back 1, 20 gives back 0.5, 40 gives 0.25, etc and same concept but with different rates

[vale sapphire]

1/x ?

[sullen sigil]

could someone explain the work for (b)?

i don’t understand the whole unit vector thing

my only reasoning is that i’m trying to project v onto u so that means the component of v in the u direction, which is v times e3

[ionic jewel]

wait

what's e_3

[sullen sigil]

the unit vector

[ionic jewel]

in which direction

j?

<0,0,1>?

[thorn kindle]

001

[ionic jewel]

just use the formula for projection

with those two vectors

[thorn kindle]

It is really just asking for the z coordinate of v

[ionic jewel]

well yes but having a consistent way to do it is nice as well

[sullen sigil]

yeah

[ionic jewel]

read: projection formula

[sullen sigil]

uhh so the projection formula is this

[ionic jewel]

yep

that's right

[sullen sigil]

so where did the 3e_3 come from?

[ionic jewel]

what's u dot v?

@sullen sigil

then what's u dot u

then divide

then multiply the rest of that times u

ends up with 3e_3

[sullen sigil]

i ended up with 1e_3 i think i did it wrong

lol

um

oh i see

nvm i just messed up the numbers

[ionic jewel]

alright

glad you got it

[thorn kindle]

Alright.

[icy venture]

[ionic jewel]

is there a "trick" to simplify $\qty(\sum_{n=0}^\infty x^n)^3$

[ocean seal]

bunny

[ionic jewel]

is there a way to push that 3 in there

this is a cubed maclauren series but idk how to simplify

[full wasp]

can u represent it as 1/(1-x)

[glass lichen]

if $\abs{x}<1$ then $\sum_{n=0}^\infty x^n=\frac{1}{1-x}\implies \left(\sum_{n=0}^\infty x^n\right)^3=\frac{1}{(1-x)^3}$

[ocean seal]

Mosh

[full wasp]

this maybe????

[glass lichen]

that's a completely different summation

[full wasp]

well i tried expanding (1 + x + x² + ...)³ and the coefficients seemed to follow the triangular numbers

idrk what im doing though

it also lines up pretty well with 1/(1-x)³ on a graph

[muted raft]

tbh they both aren't wrong....

It looks weird but it isn't wrong

[polar kindle]

I think both are right, I would have to have more information to choose one of the two

[muted raft]

for example, if f is continuous on x=0, then obviously first one is wrong

but

$\vec{v_1}$

[ocean seal]

zslya

I don't recognise the option transparent. Use ,texconfig to see the list of options.

Jul 5, 2021, 1:39 AM

[polar kindle]

how can I put the 1 at the bottom next to the p
$\vec{v{p1}}$

[muted raft]

or like $\vec{v_{p_{1}}}$?

[ocean seal]

zslya

[polar kindle]

how can I put the 1 at the bottom next to the p
$\vec{v_{p1}}$

[glass lichen]

$\vec{v_{p_1}}$?

[ocean seal]

Mosh

[polar kindle]

doesn't have any function that leaves everything inside the braces underneath?

[glass lichen]

Im not sure what you mean

[polar kindle]

sorry for my bad english I'm trying my best

like when I use _ the next letter is down on line right

doesn't have any function that leaves everything inside the braces down on line?

I need to do v_{a_b_c_d_e} ?

[glass lichen]

$v_{a_{b_{c_{d_e}}}}$

[ocean seal]

Mosh

[glass lichen]

just a lot of _'s and {}'s

$v_{a_{b_{c_{d_e}}}}$

_ will only take the 1st char following it and put it in the subscript, if you want more in the subscript you put it in braces

[polar kindle]

wouldn't be what I wanted

like

I want to write v_{test}

I need to writ v_{t_e_s_t}?

[ocean seal]

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

[polar kindle]

like this

[glass lichen]

$v_{\text{test}} \ v_{test}$

[ocean seal]

Mosh

[thorn kindle]

You need an underscore

[velvet forum]

$x{\text{subscript}}_

[thorn kindle]

$x_{\text{subscript}}$

[ocean seal]

AMD

[velvet forum]

oh ok lol

[thorn kindle]

,tex {}^{\text{lmao}}

[ocean seal]

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

[glass lichen]

#bots if you're not gonna ask a question and just spam the bot

[rich basin]

Why can't it be 51 choose 2

It says at least one selected card is an Ace

And so it is conditioned for which it must have an Ace in the set

[full wasp]

it sounds like it matters which ace it is

so u need to multiply by 4 probably

or maybe not idk this is hard

[rich basin]

,w solve 51 choose 2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Travelling Salesman#4998

[rich basin]

,w solve 1275 * 2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Travelling Salesman#4998

[rich basin]

,w solve 2550 * 2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Travelling Salesman#4998

[rich basin]

That is not quite the answer

[full wasp]

dang

[rich basin]

@full wasp Like why wouldn't it be 51 C 2

Wait there are 4 aces

[full wasp]

does card order matter, for starters

[rich basin]

No it doesn't

I don't think it will

[full wasp]

also we should use exclusion principle probably

[rich basin]

Yeah that is what the answer did

[full wasp]

is it 3676

[rich basin]

No

[full wasp]

wait i mean 4804

[rich basin]

Yeah

but how did you get tot hat

So you took out lal the aces

[full wasp]

well i did number of ways to choose 3 cards with no restrictions

that is nCr(52,3)

then i subtracted the number of ways to choose 3 cards with no aces

that happens to be nCr(48,3)

[rich basin]

Okay thanks

[nova shard]

i think i fricked up along the process of solving this. idk where tho

[velvet forum]

is there a permutation version of number choose number in google search?

[full wasp]

do u know how to do synthetic division

[nova shard]

i think so

[full wasp]

try that

[nova shard]

i think i used that to get 5x^2-9x-2

although i'll try again because i might've rushed it

i got the same answer did i make a mistake? (sorry for the doctor handwriting)

[full wasp]

thats long division btw

hold on

[nova shard]

oh

[full wasp]

5x²-9x-2 is correct though

factor it again

like factor the trinomial

[icy venture]

Like using a GCF for ex

[nova shard]

wait a second

i just realized

nvm

[rich basin]

I was wondering if there is a faster way to this rather than brute force

[nova shard]

the question wants to solve like this. in this case i was supposed to take 4 and multiply it by -3, and use that to make a*b=-12. i'd then take 11 and create a + b = 11. i'd then solve for a and b.

same thing here

[rich basin]

Like without dealing this with cases

Sorry, If i am interrupting

[full wasp]

no that is not what it wants

it wants a product of linear factors

you know that p(x) = (x-7)(5x²-9x-2)

[nova shard]

then why did the video say to do it that way?

[nova shard]

yeah

[full wasp]

theres more than one way to do it

but for now just factor 5x²-9x-2

[nova shard]

ok

[icy venture]

I dont think we can use GCFs

[alpine sable]

can anyone help on this

[icy storm]

@alpine sable what do u need help with?

[alpine sable]

^

[icy storm]

@nova shard consider the expression:

[ocean seal]

kyaaa.holo2

[icy venture]

Those kinda look like the slope-intercept forms but instead of B we get alpha and beta and we are multiplying them together

[nova shard]

i gtg

thanks for trying to help me

[viscid lotus]

can someone help me with questions 3-5

[thorn kindle]

H

[full wasp]

H

[alpine sable]

can anyone help me with this

I just need b and c

[full wasp]

well your initial equation is correct

[alpine sable]

It is (:

[full wasp]

,w 50e^(1.86895)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Lollipop#1476

[full wasp]

looks like your answer should be 571788 then

[alpine sable]

oh

Yes but what about the 2nd one

[full wasp]

uhh idk

,w d/dx 50e^(1.8689x) at x = 5

[ocean seal]

Results provided by WolframAlpha

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

Requested by Lollipop#1476

[full wasp]

apparently

[alpine sable]

oh

[full wasp]

d/dx of your function should be like

50 * 1.8689 * e^1.8689t

[alpine sable]

You get like 605

[full wasp]

no you dont

[alpine sable]

Wait

you get

2130

[full wasp]

still no

are u using t = 5

also remember its e^(1.8689t)

sorry if that was unclear

[alpine sable]

ohh

you get 1068614

[full wasp]

well there are your answers

[alpine sable]

Thanks

[full wasp]

np

[alpine sable]

IM so RETARTED I SUBMITTED the wrong answer

[sullen karma]

F

[vagrant kayak]

pls help

[wraith cairn]

what does come alternatively mean

[ember lava]

nene or enen like that

[teal epoch]

is this count: neen?

[wraith cairn]

if that's the definition then I don't think that counts

[vagrant kayak]

no its nene or enen

[ember lava]

i dont think so

[alpine sable]

I've got a question

[teal epoch]

so only enenen or nenene?

[vagrant kayak]

gosh my maths hw is tough

[ember lava]

yes

[teal epoch]

channel busy

[ember lava]

go to a channel that is free

[alpine sable]

oh ok

[vagrant kayak]

@ember lava i have a lot of questions will u help me

[ember lava]

...

[ember lava]

ask away

[vagrant kayak]

u got the answer?

[ember lava]

this one?

[vagrant kayak]

for the previous question

[vagrant kayak]

yes

[ember lava]

i didnt even start

lol

[vagrant kayak]

oof

[ember lava]

i'll do it now

[wraith cairn]

anyone getting 6!/2!?

[vagrant kayak]

ok

[ember lava]

ig

[wraith cairn]

or am I misunderstanding something

why are all the answers so big.

ah.

I think the question means E (stuff) N (stuff) ENEN (stuff)

so the order of ENENEN

doesn't necessarily have to be connected

right?

[teal epoch]

i don;t think so

[vagrant kayak]

i think we have to take enen and then nene

and add the possibility

[wraith cairn]

there are 3 es and 3 ns

[vagrant kayak]

yeah

[wraith cairn]

if you treat ENENEN as one block

[teal epoch]

probably enenen(stuff) only counts

[wraith cairn]

there are 6!/2!/2! combinations

and then try NENENE

also 6!/2!/2!

together gives 6!/2!

I believe the question is just looking for the order

[vagrant kayak]

@wraith cairn r u good at p&c

cuz ihave a lot of questions

[wraith cairn]

what's the point of doing the problems if you aren't doing them.

[vagrant kayak]

dude

[vagrant kayak]

i did most of the problems

[vagrant kayak]

these are tough

[wraith cairn]

ok what other questions do you have

I want to see them.

[vagrant kayak]

ok

[wraith cairn]

are the men and women distinguishable

james, bob, charles etc

[icy storm]

Goddammit i was just in the middle of helping someone out with math and my phone died 😑

[vagrant kayak]

no the same

[vagrant kayak]

i mean they didnt specify

ughh i hate maths

[wraith cairn]

13 looks like 480.

I'm going to assume they are distinguishable

[vagrant kayak]

sure?

[wraith cairn]

do you know how to find the factors of N

[icy storm]

@vagrant kayak regarding the second question, there should be a total of (2+1)×(3+1)×(5+1)×(4+1)×(3+1) divisors, which is 3×4×6×5×4=1440.

[wraith cairn]

if you know that I'll tell you how to get 480.

[icy storm]

I wonder how to find how many factors of the form 2(2k+1) there are.

[wraith cairn]

?? That's not the answer to the question.

[icy storm]

I know

[wraith cairn]

ok.

[vagrant kayak]

so 480 is the answer?

[icy storm]

But I put an upper bound. There is a total of 1440 factors, so the answer must be less than 1440

[wraith cairn]

do you know how to find the factors of N?

[vagrant kayak]

yes

[wraith cairn]

ok

then you want to find how many factors in the form 2(2k+1)

[vagrant kayak]

ok

[wraith cairn]

all primes after 2 are odd.

[vagrant kayak]

ohhhhh i get it now

can u do the committee question also

[wraith cairn]

you have to first explain why it's 480

[vagrant kayak]

no i got the question

pls do this

i am not getting how they come alternatively

[wraith cairn]

you need to do casework for the commitee question

1 woman, 2 women, 3 women, 4 women.

[vagrant kayak]

i am taking 2 cases where one case is 2 women and three men and second case is 3 women and 2 dem

@wraith cairn

is it correct'

[wraith cairn]

why are you not doing 1 woman and 4 women

[vagrant kayak]

ohhh ok

i get it now

[wraith cairn]

for the engineering question

I'm sure it's saying the order now.

so the order has to be ENENEN with letters entwined

or NENENE with letters entwined

I used stars and bars to solve this

you might need to know that

[vagrant kayak]

so whats the answer?

[wraith cairn]

why should I tell you.

I have already told you how to do it.

start off with ENENEN

[vagrant kayak]

cmon

[wraith cairn]

see how many ways you can inject the other letters inbetween

you'll need stars and bars.

I have already told you the answer to your other problem

[vagrant kayak]

i didnt study those

[wraith cairn]

why do you need the answer

it's not going to help solve the problem.

I am going to sleep.

go search up stars and bars.

[vagrant kayak]

ok 😦

[sullen karma]

Nope

Not me

[oak agate]

$(a^(-1) + b^(-1))^(-1) = ab/(a+b)$

[ocean seal]

Mycroft Holmes

[wind lily]

$(a^-^1 + b^-^1)^-^1 = ab/a+b$

[ocean seal]

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

[wind lily]

how do you prove this?

[past sundial]

Is 1 over infinity infinitely large and small? Ping me if u answer it!

[ember lava]

is a+b whole in the denominator?

[wind lily]

yeah

[ember lava]

if it is, then

a^-1 + b^-1 = 1/a + 1/b

if you take lcm and solve,

you should get a+b/ab

[past sundial]

Oops, I posted my question in a current discussion, is it alright if I move my question to another channel?

[ember lava]

(a+b/ab)^-1 =

ab/a+b

proved

[ember lava]

yeah

[wind lily]

alright thanks

[ember lava]

np

[past sundial]

Oki!

[ember lava]

@past sundial you can post it now

[past sundial]

Oh okie

Question: Is 1 over infinity infinitely large and small? Ping me if u answer it!

[fallen sentinel]

So ... now can anyone tell me a good approach

So ... I solved it using cauchy

Any different approach