help-42

[native dragon]

like

all of them got 20 cases too

but idk how theyre getting 26

i can think that

theyre putting it in the formula

[proper echo]

but there are no other cases than these which could allow for condition to be satisfied-

[native dragon]

m!/ 6! ( m-6)!

and

26-6 is 20

so like

does that have any relation

idts

[proper echo]

i didn't quite catch u there

i wudnt approach this with the formula tbh

[native dragon]

just one second

let me see if i can find the proper question

[proper echo]

cuz many times, directly applying the formula results in over or under counting of the number of cases

plus when u split it up into all possible cases u can be confident that u didn't miss anything , so

[native dragon]

no no like

we are given to find m choose 6

im splitting that formula

and i know m is 26

for now

cuz im trying to find some relation between 20 and 26

let me look for the question

got it

thats it

and the answer is 26

100%

[proper echo]

oh and what does |R| represent here?

[native dragon]

the number of elements in R

[proper echo]

ah alright

so does something like (1,1,1,1,1,1) count in R?

[native dragon]

uuhhh

im not sure about that

probably that should count

[proper echo]

the reason why we're not getting the required answer probably has to do with the fact that we didn't really make any use of condition one

[native dragon]

right

how are we gonna use that

[proper echo]

becaus the answer would be A∩B, where A and B are our conditions, and they are being simultaneously verified

so in order to satisfy A, we need to have a subset of S that has a total of six elements, such that any of those 2 must satisfy a-b>=2

[native dragon]

like any of the 2 numbers(elements) should satisfy condition B?

the numbers in R

right?

[proper echo]

yeah

that should be it

[native dragon]

right

[proper echo]

however the 'any two' is quite troubling

u cud imagine A∩B being something like (6,3;4,2;5,1)

while there are pairs that are satisfying the second condition, the set does not comply with 'any' two elements following |a-b|>=2

[native dragon]

so how do we proceed then

[proper echo]

hmmm am wondering the same

i hope we're understanding the question correctly

[native dragon]

yeah so basically

were taking set R

from S

S x S

so that R has 6 elements

and from that R

we take ordered pairs

which satisfy B

[proper echo]

cuz i dont think we're gonna end up with m being 26, idts there are gonna be that many sets which'll satisfy both the conditions

[proper echo]

is it just ordered pairs, or is it that any two must satisfy

[native dragon]

wdym any two

[proper echo]

cuz these ordered pairs are still fine

[native dragon]

oh right so if R is like 1,1 1,3 2,2

somin like that?

[proper echo]

see, what am trying to say is,
suppose ur set of A∩B is
(x1,x2,x3,x4,x5,x6)
now for ANY two to satisfy the second condition, any two distinct elements must give you a |difference| >=2

however, if we're fine with x1-x2>=2, but x1-x3=1, then its a completely different story

[native dragon]

oohhh right

no all of them should satisfy

[proper echo]

the number of ways of selecting any two elements from that set would be 6C2, and every single pair produced by 6C2 should satisfy |a-b|>=2
that's what it means for ANY two to satisfy

[native dragon]

like the final set that we get

thats what youre talking about right

[proper echo]

yaaa

[native dragon]

yeah

all of them should satisfy

[proper echo]

all as in any two right, just to confirm we;re on the same page

[native dragon]

no like
x1-x3 also has to be >=2

[proper echo]

yaya

we're one the same page

[native dragon]

i think so

wait no

[proper echo]

okay well let's try with a trial and error approach first

[native dragon]

one sec

well get a set like this

{ (x1,x2) , (x3,x4) , (x5,x6) }

where the bracketed guys satisfy it

i think i misunderstood your statement my bad

[proper echo]

yeaa that's simpler to solve tbh

[native dragon]

yeah so x1 - x3 doesnt come into the equation at all here

its just x1 - x2 and the rest

[proper echo]

that's a relief

[native dragon]

okay so

[proper echo]

alrighty

[native dragon]

we got 20 cases

then?

[proper echo]

ya, now we have to arrange them in 3 pairs

since every case has two numbers

we have to pick only 3 numbers from the 20 cases

and that will be one unique set, the order does not matter

[native dragon]

wait im not getting you

so we have 3 pairs in the final set

thats okay

[proper echo]

yes

[native dragon]

every case has 2 numbers

okay

[proper echo]

and those three pairs, are any 3 cases from our 20 cases

[native dragon]

uh huh

oh right

so we pick 3 cases from 20 cases

[proper echo]

every case has 2 numbers
we need 6 numbers in our set
so we pick 3 cases from 20 cases
and the order does not matter

[native dragon]

uh huh

[proper echo]

so it should be 20C3 as the total number of ways of building the desired set

let me see real quick if this somehow undercounts

idts it undercounts

now if you equate 20C3 to MC6, what do we get

[native dragon]

26

right

[proper echo]

wait wait

are we getting 26?

[native dragon]

no

were not

[proper echo]

arent we getting a 5 degree expression💀

[native dragon]

uuhhh

[proper echo]

6 rather💀

[native dragon]

wait up

[proper echo]

wait see if there is a way to write them all in the form of m(m-1)...(m-5)

[native dragon]

no no

i checked in a calculator

the values are different

wayyyy different

[proper echo]

yea we can't write it like that

if we cud get something as neat as 20.19.18.17.16.15

ah wtf

[native dragon]

our teacher gave this problem for 5 mins for everyone to get settled
and by the time i got 20 cases
a couple of guys got 26
and he moved on to another topic quickly
and i forgot to ask either

all i know is that

other people were getting 20 cases as well

and then somehow they got 26

[proper echo]

damn i see

the only thing i can think of rn

is to group the cases instead of choosing them

[native dragon]

i asked my friends but no one replied yet 😭

[native dragon]

like what

[proper echo]

there is this formula by which you can group the numbers in sets of group sizes

[native dragon]

idk that i think

[proper echo]

i dont think that's the right way to go about it either, but i honestly don't know how did we go wrong with this one

[native dragon]

yeah exactly

theyre choosing

6

and thats the numbers

and

do we have 26 numbers somewhere

lmfao

💀

should i ping the helpers 😭

[proper echo]

yeah actually, i dont seem to be making any meaningful progress here🥲

[native dragon]

<@&286206848099549185>

[tame tulip]

Could you repost the problem?

[native dragon]

one sec

[verbal finch]

16 possibilities is correct

[native dragon]

16 cases wont be in the set

[verbal finch]

?

Y

[native dragon]

cuz a-b > = 2

and theres 16 cases which are less than 2

1,1 2,2, 3,3 4,4 5,5 6,6
6 here
1,2 2,3 3,4 so on

5 cases

then the opposite of them cuz ordered pairs

another 5

so 10 + 6 = 16

so 20 cases which fit the condition (ii)

from S x S

[tame tulip]

?? then why did you need us?

[native dragon]

the answer

is 26

m = 26

i cant figure that part

and im 100% sure its 26

[tame tulip]

🤔

gimme a sec

i'll try to see it from your view

[native dragon]

mhm okay okay

[tame tulip]

That looks right...

[native dragon]

exactly

😭

[tame tulip]

should get someone over to check as well...

@verbal finch come here. This looks correct already from what he's telling me

[verbal finch]

Just type in all the 20 possibilities

[proper echo]

we didn't consider repetition a possibility

can our set have repeated elements?

[native dragon]

do we get the answer from there 💀

i dont know either, thats all the question states

[proper echo]

i mean all we can do is try

[native dragon]

1,3 1,4 1,5 1,6
2,4 2,5 2,6
3,5 3,6
4,6

3,1 4,1 5,1 6,1
4,2 5,2 6,2
5,3 6,3
6,4

[tame tulip]

Is this your notes? Can you give us the issued question?

[native dragon]

our teacher wrote it on the board

i copied it

[tame tulip]

👍

[verbal finch]

Alr

So what now

[tame tulip]

Yeah, this looks correct. The set S has 6 elements and these are all probable repetitions of repeated elements

[verbal finch]

U need relation with 6 things in it

[native dragon]

yes

[tame tulip]

yeah

[native dragon]

ordered pair

is one element

[verbal finch]

So 20C6 it is

[native dragon]

so 6 numbers in total

[verbal finch]

Mhm

[native dragon]

wait

but arent 20 the cases

[verbal finch]

?

[native dragon]

like

we need 3 ordered pairs

and we have 20 ordered pairs

why is it 20C6

shouldnt it be 20C3

oh wait

WAIT

my bad

6 elements

[tame tulip]

there we go

[native dragon]

so

6 ordered pairs

right

20C6

and i prolly must have heard 20C6 as 26C6

so

maybe thats the case

💀 🙏

[tame tulip]

I think that's right 👍

[native dragon]

my bad yall

hope this is correct lmfao

THANK YOU

[tame tulip]

👍

[native dragon]

.close

[calm coral]

Channel closed

Closed by @native dragon

Use .reopen if this was a mistake.

[verbal finch]

Ping when u reply

[tame tulip]

@native dragon You gotta ping when you reply

[verbal finch]

Oops my net mb

[native dragon]

ah okay okay ill keep in mind

[calm coral]

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[limber plume]

How to solve?

[wintry echo]

try adding and subtracting 1 in the parenthesis

you should be brought back to the limit of e

[limber plume]

Do you mean in the fraction or outside the fraction?

[wintry echo]

in

[limber plume]

Ok lemme try

[wintry echo]

If you can, send photos too

[lyric ravine]

Also:
$\left(\frac{3x-4}{3x+2}\right)^{\frac{x-1}{2}} = e^{\left(\frac{x-1}{2}\cdot ln\left(\frac{3x-4}{3x+2}\right)\right)}$

[potent lotus]

quickdoom

[limber plume]

I can't simplify it by adding and subtracting 1.

[limber plume]

How can I get the form of (1+1/x)^x = e

[wintry echo]

rewrite the exponent

[limber plume]

Rewrite as what? I don't get it?

[wintry echo]

wait

that's for now

in the red part you have to write something which, multiplied by that exponent, takes you back to the initial exponent

But perhaps it becomes too complicated

[wintry echo]

I think it's better to do it this way

[limber plume]

Pardon! I Don get that method

[wintry echo]

ok

so

you agree that

$2=e^{ln{2}}$?

[potent lotus]

Fluffy McGiggles

[wintry echo]

?

example

$x^{log_{x}(y)}=y?$

[potent lotus]

Fluffy McGiggles

[limber plume]

yeha i know that

lemme try again

[calm coral]

@limber plume Has your question been resolved?

[limber plume]

im not getting how to calculate the limit of that @wintry echo

[glad parrot]

the limit of (x-1)/2 as x goes +inf is +inf

and to get rid of the indeterminate form for the quotient you have to factor by x in the numerator and denominator

and you will get a limit of 1

[wintry echo]

Where Is the problem

[glad parrot]

pinged message

[wintry echo]

could you send a photo of where you arrived @limber plume

[native dragon]

hey guys im with @limber plume over here

we cant understand how to simplify it further

like from the first step

[native dragon]

from here

@wintry echo

[native dragon]

also wdym the quotient
like which part
and how do i factor

im dumb 😭

[glad parrot]

3x-2 = x(3 - 2/x )

[glad parrot]

top and bot of fraction

[wintry echo]

send photo

[native dragon]

uh huh

[native dragon]

i havent done anything 💀

cant figure out

wait lemme try once

[wintry echo]

.

[native dragon]

yeah after this

[wintry echo]

add and subtract 1 in the logarithm

[native dragon]

ooohhh

apply the same method you used before right?

[wintry echo]

Yes

[native dragon]

except we're doing it in the power of e

[wintry echo]

Yes

[limber plume]

ik 💀

[native dragon]

right right

yep got it

answer is 1 right

[wintry echo]

No

🤦

[native dragon]

😭

wait up

1/e?

[limber plume]

💀 . making mess

[wintry echo]

👍

[native dragon]

cool cool

thank you

[limber plume]

.close

[calm coral]

Channel closed

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[calm coral]

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[sleek yacht]

32+?+3 =8+27+a+b

?=a+b

Should I be seeing another relation

I’m trying to find ? Btw

[cerulean cradle]

?

Are the areas given?

[sleek yacht]

Yes it’s area

[cerulean cradle]

is any angle mentioned ?

[sleek yacht]

no

[cerulean cradle]

Or the side lengths ?

[sleek yacht]

No

[cerulean cradle]

Okk

Lemme try

@sleek yacht hey

I got something on the web

https://images.app.goo.gl/jHagUrwAfyPzh1te7

This is the exact question

[sleek yacht]

Yo what the

[calm coral]

@sleek yacht Has your question been resolved?

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[remote mural]

I do not understand. Desmos shows wrong answer

[dull wagon]

what's desmos showing

[dull wagon]

seems fine

[remote mural]

Yes

But what is the solution trying to say?

[dull wagon]

the first part was identifying the natural domain to heavily reduce the amount of values to investigate

and of those values only x=9 works

[remote mural]

mhmm

[dull wagon]

which is also the only integer in the interval desmos gives

[remote mural]

but the question doesnt say integral solutions, no?

OH

my bad

So sorry

.close

[calm coral]

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[lost arch]

why is this wrong

[lost arch]

<@&286206848099549185>

[ancient helm]

You forgot to include andrews x candies

[lost arch]

wdm

@ancient helm

[ancient helm]

in part c

there's three people

you only added two people up

[lost arch]

yh

got

it

ty

silly mistake

.close

[calm coral]

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[lucid wedge]

the top is the stage I am at now, the bottom is the final answer

how do I rearrange it into that

[near crag]

I have the same request as before

doesn't even have to be latex

just something I can read

(e+g)/(ef-d)

[lucid wedge]

yeah my writing is not great lol I’m doing it now

my stage: $w^{2}=\frac{e+g}{ef-d}$
final answer: $e=\frac{g+dw^{2}}{fw^{2}-1}$

[near crag]

lol I did interpret it correctly

[potent lotus]

EtherealGalaxy

[near crag]

well you want to solve for e, so maybe you could multiply both sides by ef-d and move everything that contains e to the left hand side

[lucid wedge]

ok that sounds good I’ll try that now rq

now I have $w^{2}-e=g(ef-d)$

[potent lotus]

EtherealGalaxy

[lucid wedge]

im not sure how I can expand those brackets

[lucid wedge]

you did say everything that contains e here though thats not everything

[near crag]

If you have g amount of ef - d then how much do you have of ef and how much do you have of -d

[lucid wedge]

hold up I followed your instructions incorrectly too this is more correct

e(fw^2-1)=g+dw^2

[lucid wedge]

idk this ima be honest but I think I’m getting closer

[near crag]

oh yeah

that's looking pretty good

I actually managed to read your handwriting this time

[lucid wedge]

yooo 😂

[near crag]

poggers

[lucid wedge]

I think I’m close

[near crag]

you definitely are

[lucid wedge]

just no clue how to slap those brackets away

cause that’s all I need

[near crag]

if it was e*2=g+dw^2 then what would you do

[lucid wedge]

divide by 2

[near crag]

mhm

[lucid wedge]

but surely I can’t just make the other side (g+dw^2)(fw^2-1)

that just looks wrong lol

[near crag]

What does e*2=g+dw^2 look like if you divide by 2

[lucid wedge]

wait I’m so stupid lmao it’s dividing

[near crag]

yeah exactly

[lucid wedge]

g+dw^2/fw^2-1

[near crag]

yupp

pretty sweet right

[lucid wedge]

and that’s the answer?!

[lucid wedge]

yes

[near crag]

yes, although it might be good to note that fw^2 cannot equal 1

because then we'd be dividing by zero

[lucid wedge]

yeah ok

well thank you for your help!

I will keep this all in mind for future similar questions

[calm coral]

@lucid wedge Has your question been resolved?

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[rugged steeple]

for the 6.12.18....(6n) why did he write it as for the 6.12.18....(6n)(6n+6) instead of just pluggin in n so it becomes 6.12.18....(6n+6), i thought all we do is plug in n+1 for all the n's and do the ratio test

[calm coral]

@rugged steeple Has your question been resolved?

[hollow lion]

6(n+1) = 6n+6

[rugged steeple]

but why do they include the 6n still

why is it still (6n)(6n+6) in the denominator

[hollow lion]

The denominator is the product of all terms of 6n for n = 1, 2, … , inf
So for n+1 you have one more term

In a similar way, which may be more familiar to you, if it were (n+1)! Then this is also just one more term —> n! (n+1)

Well I guess it is actually (6n)!…

@rugged steeple

[rugged steeple]

ohhh that makes more sense

cus what i was thinking was that you just plug in n+1 to any n you see but i guess its different for this case

thank you!

.close

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[languid bone]

this answer is incorrect, right? it should be x - 1/8sin(8x) + C

[formal pulsar]

yup, it should be sin(8x)

[languid bone]

alright, just wanted to make sure, thank you

.close

[calm coral]

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[potent lotus]

kisnar

kisnar

[fleet verge]

What is your question?

[dull wagon]

go through standard process of sub

considering ||x^3 = x^2 * x|| will be useful

have you ever done integration by substituion before

next step is usually get a relation between dx and du

[potent lotus]

kisnar

[fleet verge]

So what du u have?

[dull wagon]

do you know how to differentiate

you pretty NEED to know before doing integration

you've must've had to work with dx before

before this

u'

no

u = 1 - x^2
du/dx = u' = ?

[eternal shard]

haha i am crying

[dull wagon]

you usually have functions of x, ' is used commonly used to indicate derivative with respect to x

yes

[fleet verge]

You have it there

Continue with the sub then

U have u, du, dx

U have everything

[potent lotus]

kisnar

kisnar

[fleet verge]

Expand

Distribute

[potent lotus]

kisnar

[fleet verge]

Now it’s trivial

[potent lotus]

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

[fleet verge]

[eternal shard]

[potent lotus]

faiyrose

$-\frac{1}{2} \left{ \frac{u^{\frac{3}{2}}{\frac{3}{2}} - \int u^{\frac{2}{3}} \right}$
```Compilation error:```! Missing delimiter (. inserted).
<to be read again> 
                   {
l.49 $-\frac{1}{2} \left{
                          \frac{u^{\frac{3}{2}}{\frac{3}{2}} - \int u^{\frac...
I was expecting to see something like `(' or `\{' or
`\}' here. If you typed, e.g., `{' instead of `\{', you
should probably delete the `{' by typing `1' now, so that
braces don't get unbalanced. Otherwise just proceed.
Acceptable delimiters are characters whose \delcode is
nonnegative, or you can use `\delimiter <delimiter code>'.```

[eternal shard]

#help-0 message

[fleet verge]

[fleet verge]

We got rickrolled

[calm coral]

Channel closed

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[distant remnant]

find the t for which eqn h = ut + 1/2gt^2 where g is constant , t is time , h is height , u is velocity is at maxima by using differentiation

[pine patrol]

we know that dh/dt=velocity
so put v = u +at by first eqn of motion
do basic differentiation and get the ans

integration*

[distant remnant]

i am not getitng it

the answer is t = u/g

how is differentiation of d(ut)/dt = u

@pine patrol

[pine patrol]

bro it is given u is the velocity at maxima

[distant remnant]

but u is not constant

it is a variable too

[pine patrol]

if it is not constant then differentiate the eqn and put it equal to 0 and get u

[distant remnant]

thats what i am asking it is not constant how will you differentiate

u is not related to h or t

it will become du/dt

which has no solution

[pine patrol]

bro i am not getting your ques can you please tell the question again

[distant remnant]

if h = ut + 1/2 gt^2

where only g is constant

then at what t will h be maxima

[pine patrol]

is the ans u by g

[distant remnant]

yes

but how

[pine patrol]

see ...differentiate the eqn

[distant remnant]

wait see

[pine patrol]

you will get dh/dt= u +gt

but at maxima dh/dt=0

[distant remnant]

dh/dt = d(ut)/dt +1/2g d(t^2)/dt

right

[pine patrol]

so 0=u+gt

t=u/g

[distant remnant]

my question is how d(ut)/dt = u

if u is not constant

[pine patrol]

see we are differentiating it with respect to time

so its like u(t^1-1()differentiation formula)

so t^0=only u will remain

[distant remnant]

oh ok i understood u is not dependent on t so we will not differentiate it right ?

[pine patrol]

no its not like that

[distant remnant]

than like why u yook u out of differentiation

[pine patrol]

see can you tell me the differentiation of x=6t with respect to t

[distant remnant]

is will be 6

[prime yacht]

|| Is the question asking for the time where velocity is at maxm? ||

[pine patrol]

exactly ... thats why its u

[distant remnant]

no distance / height

[pine patrol]

h is at max

[distant remnant]

oh ok got it thnx

ok

[prime yacht]

|| Shouldn't g be -ve for there to be a maxima rn there's only a minima ||

[pine patrol]

see thats upto you i have let it +ve

[distant remnant]

i got the right answer thnx

[pine patrol]

and in the ques its constant

[distant remnant]

g is always constant

[prime yacht]

But we found the minima by solving for derivative = 0

[pine patrol]

well thats not always true in some ques we were asked about varied g with depth

[distant remnant]

actually in a graphical system there is no such maxmia and minima we are jsut finding the turning point of graoh

by this method

as graph can be extended to positive as well as negative infinity

[distant remnant]

thnx btw

[pine patrol]

no problem

[calm coral]

@distant remnant Has your question been resolved?

[calm coral]

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[royal raft]

is b also true for even numbers?

[cerulean cradle]

yes

[royal raft]

can you give me an example

[cerulean cradle]

X = -2

[royal raft]

ohhh

[cerulean cradle]

Yeas its true

[royal raft]

I forgot n could be negative

[cerulean cradle]

Always

[cerulean cradle]

n is odd i didnt see

So -ve will stay -ve

Hence always true

[brittle isle]

b does not have to be true for even numbers

consider x = -3, y = 1, n = 2

[royal raft]

ok I see i'll try writting up the proof

[ancient helm]

so does +ve mean what I hope it means

[cerulean cradle]

It simply means positive

[ancient helm]

excellent, much appreciated

[calm coral]

@royal raft Has your question been resolved?

[calm coral]

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[topaz raft]

im confused how do i find avg speed lol

[winter loom]

it's distance/time

[calm coral]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[topaz raft]

💀

[graceful dust]

blud...

[winter loom]

Where is the answer?

[topaz raft]

but dist/time alone doesnt work i tried it

i have to do somethign else

[winter loom]

Nah that should, show work.

[surreal shore]

i am really sorry , sent it to this channel by mistake

[topaz raft]

i dont have distance anyways

[cerulean cradle]

Consider it

[winter loom]

Assume the 100km/h takes time t

Or consider the distance

Consider one of the two things and rewrite everything in its terms.

It'll get cancelled out eventually.

[topaz raft]

wat

[winter loom]

If the distance were say, d

What time did it take to travel from A to B

[topaz raft]

d/100

[winter loom]

Hiw about B to A

[topaz raft]

d/200

[winter loom]

And what total distance did you travel all this time

[topaz raft]

3d?

[winter loom]

How so?

[topaz raft]

oops

i meant 2d

[winter loom]

Yeah.

[topaz raft]

what comes next

[winter loom]

.

You have it all in terms of d.

[topaz raft]

i do?

[winter loom]

yeah?

[topaz raft]

what do i do with d/100 and d/200 and 2d?

[winter loom]

What's 2d?

[topaz raft]

the total distance

[winter loom]

Yeah and d/100 and d/200 wound be the time it took to travel from A to B and B to A.

So the total time, would be their sum.

[topaz raft]

ohh

so 3d/200 = 2d

but u just said tis their sum

[round tusk]

avg speed = total distance/total time

total distance = 2d

total time = d/100 + d/200

https://tenor.com/view/think-mark-invincible-omniman-gif-21416554

[topaz raft]

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

https://media.discordapp.net/attachments/268882317391429632/1223598233763319819/1192815796490080286.gif?ex=665bb1e8&is=665a6068&hm=8d1a33b02c2a4cc715df7b25a815565b1098e5afb0e75426618f65e5f991b142&=&width=120&height=120

[topaz raft]

https://media.discordapp.net/attachments/268882317391429632/1223598233763319819/1192815796490080286.gif?ex=665bb1e8&is=665a6068&hm=8d1a33b02c2a4cc715df7b25a815565b1098e5afb0e75426618f65e5f991b142&=&width=120&height=120

[round tusk]

problem solved?

[topaz raft]

https://tenor.com/view/aww-yeah-yoda-star-wars-dancing-chill-gif-16743902

[graceful dust]

the end of the lifecycle for a water beam help channel

[cerulean cradle]

https://tenor.com/view/stephen-colbert-popcorn-3d-glasses-watching-eating-gif-17602628

[topaz raft]

rahhhhhhhhhhhhhhhhhhhhhhhhhhh

.close

[calm coral]

Channel closed

Closed by @topaz raft

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[calm coral]

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[pale panther]

hi I know how to do 10 but I tried to do 11 the same way and got stuck

I just ended up back at the start idk

[wide jewel]

When q(x) is divided by x, it gives the remainder 16. What do you get from that?

[pale panther]

q(x) = 16?

[wide jewel]

X would be 0

[wide jewel]

Put that into the q(x)

[pale panther]

how do you know

how do you know that X is 0?

sry

[wide jewel]

?

Ok for example if it is divided by x+6, then how do find x’s value?

[pale panther]

-6

[wide jewel]

Yeah cuz you do x+6=0 right

[pale panther]

yea

oohh

[wide jewel]

So we divide by x

So x = 0

[pale panther]

there's no constant here so x=0

[wide jewel]

Yeah

[pale panther]

Alright

[wide jewel]

So put that value here

[pale panther]

q(0)= 16

h² + k = 16

[wide jewel]

Yeah

[wide jewel]

Now here, right after you expand the bracket

There’s h² + k here

Put the value in that, 16

[pale panther]

SO 16-4H + 4 =0

[wide jewel]

Yeah

Find h

[pale panther]

3

[wide jewel]

How?

[pale panther]

oh lol mb

5

[wide jewel]

Yeah

[wide jewel]

You can find k from here

[pale panther]

-9

wow

[wide jewel]

Yeah

[pale panther]

thanks ❤️❤️

[wide jewel]

Np

[pale panther]

I didn't get the divide by x th9ng

ty

.close

[calm coral]

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[calm coral]

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[grizzled temple]

how to do d)

[winter elbow]

If a number for example 1000a+100b+10c+d is divisible by 3

a+b+c+d is divisible by 3

This may help you

[calm coral]

@grizzled temple Has your question been resolved?

[calm coral]

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[eternal stirrup]

What have you tried so far?

[calm coral]

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[thick sinew]

why does this property hold?

[thick sinew]

Or rather does someone find an online proof for it?

present functions are Gamma(s) and Dirichlet-Eta(s)

[calm coral]

@thick sinew Has your question been resolved?

[spare beacon]

Rewrite 1/(e^x+1) as e^-x / (1 + e^-x), apply the geometric series formula and pull apart eta and gamma

[obtuse pendant]

https://www.youtube.com/watch?v=06OO9597ZeI

[thick sinew]

ooh

yeah have it

but how does one see that so quickly :c

I often get 80% of the way

in this case I did it the other way, from gamma * eta to the integral

[spare beacon]

The gamma function has an integral, and eta has an infinite sum

[thick sinew]

yeah I got fairly close up to a substitution where my sum index was shifted oddly

[spare beacon]

You know gamma has an e^-x in it, so it's just a matter of going down a very finite list of reasonable taylor series expansions

[thick sinew]

kk, thank thees! 🐛

.close

[calm coral]

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[flint wind]

Help

[flint wind]

How do i do this question

[cerulean cradle]

Property of logarithms

[flint wind]

?

[cerulean cradle]

Log a - log b = log a/b

[flint wind]

Yes

[cerulean cradle]

log a + log b = log ab

[flint wind]

Log4 x/x-1

[cerulean cradle]

So log( base 4) x/((x-1)×3) = 1/2

[cerulean cradle]

Also bring that log 3 to same side

So we have 4^(1/2) = x/(3(x-1))

@flint wind There ?

[flint wind]

Yes sorry i was trying to understand

[cerulean cradle]

Ok np

[cerulean cradle]

Did you understand ?

I can re-explain

[flint wind]

Not really

Yes pls

[cerulean cradle]

See bring all log4 terms to one side

Then what will you get ?

[flint wind]

Log4 x/x-1 - log4 3

= 1/2

[cerulean cradle]

to thia

[cerulean cradle]

Apply this

[flint wind]

Log4 X/x-1 all over 3

Or

[cerulean cradle]

To get this

[flint wind]

Log4 x/x-1 /3

Why is it x3

[cerulean cradle]

Think like x/x-1 × 1/3

[cerulean cradle]

Can you do this ?

[flint wind]

X/ 3(x-1)

X/3x - 3

[cerulean cradle]

yeahh

[flint wind]

Why do you multiply by 1/3 tho

[cerulean cradle]

So log x/3x-3 = 1/2

[cerulean cradle]

Ok see

-log x = log 1/x

[flint wind]

Okay

[cerulean cradle]

,rotate

[cerulean cradle]

,w x/(3x-3) = 2

[potent lotus]

Results provided by WolframAlpha

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

Requested by itzmecairo

[cerulean cradle]

Correct !

[flint wind]

I’m lost 😭

[cerulean cradle]

Why ?

[flint wind]

?

[cerulean cradle]

You solved it

[cerulean cradle]

Ok see we have log x/x-1 - log 3

[flint wind]

Mhm

[cerulean cradle]

-log 3 = log 3^(-1) = log 1/3

log x/x-1 + log 1/3

[flint wind]

Ah

[flint wind]

I understand

[cerulean cradle]

= log x/x-1 ×1/3

[summer iris]

Won't it be minus

[cerulean cradle]

I applied minus on power

To make her understand

why its like it

[summer iris]

My bad

Just being a dumbass

[cerulean cradle]

Np

Happens sometimes !

[cerulean cradle]

Hey any more doubts

?

[flint wind]

No

Thank u sm

[cerulean cradle]

Welc.

[flint wind]

.close

[calm coral]

Channel closed

Closed by @flint wind

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[calm coral]

Available help channel!

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

(a + 1) * x/(1!) + (a + 2) ^ 2 * (x ^ 2)/(2!) + (a + 3) ^ 3 * (x ^ 3)/(3!) +...

[idle fractal]

Test convergence

[glad parrot]

what's a ?

[idle fractal]

No idea

I guess some constant?

[lyric ravine]

You can use hadamards formula for the radius of convergence(hadamard cauchy theorem)

[bronze adder]

this series looks very suspicious

do you recognize it

[glad parrot]

i think it will end in cell e when we caught it

[lyric ravine]

What series is it?

Doesnt look like any of the standard expansions

[glad parrot]

it's because he has a good mask on him

[bronze adder]

Oh we're mistaken quickdoom is right

[lyric ravine]

Did you think e^x?

[glad parrot]

yes i did

[lyric ravine]

The coefficients are (a+i)^{i}/(i!)

If you had (a+1)^k/(k!), then youd have the series for e^{(a+1)x}

[stone flax]

Whats the question? Whats the possible range of x?

[lyric ravine]

They say "test convergence", so im asssuming they want us to find the radius of convergence

[calm coral]

@idle fractal Has your question been resolved?

[idle fractal]

The question is which series is convergent

[lyric ravine]

There is only one series

[idle fractal]

Given answer is x>1/e convergent

And x<=1/e divergent

And written lograthim test

[stone flax]

Can you send a snapshot of the complete question itself?

[idle fractal]

Sure

[stone flax]

Picture is too low resolution

Send a better quality pls

[idle fractal]

Download it @stone flax

[stone flax]

Did you try using ratio test?

@idle fractal

[idle fractal]

Nope

🙈🙈

[stone flax]

Then use it

Solving the limit will give you the answer

all the best for bsc

[idle fractal]

Acutually i am graduated

But poorly without knowledge

[stone flax]

Ohkay get it

respect it

[potent lotus]

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

Jun 1, 2024, 1:36 PM

[stone flax]

You missed an x

You missed a (a+n) tern

Rest is okay

@idle fractal bro with me?

[idle fractal]

Yes

I am doing it again

Bro?

🙄🙄

[cerulean cradle]

'Bro' gender neutral

[idle fractal]

I guess i kissed only x

[idle fractal]

I see

[stone flax]

Do females come on discord even 😂

My girlfriend doesn't know about discord

[remote mural]

I apologise for the disruption but I never got to ty for the help yesterday I ended up getting it right ty for the help!

[stone flax]

No issues bruv glad i could help

[remote mural]

I tried looking for the channel but it disappeared or something 😭

[stone flax]

You missed an a+n yet again

Wait so blue dots mean males and pink dots mean females

oh okay

🤣

[idle fractal]

[stone flax]

sorry im new guys

[idle fractal]

It is okay sir

[reef nimbus]

"male" and "female" should only be used as adjectives, not nouns

[idle fractal]

But where

Which step

[stone flax]

You took a+n common in 2nd to 3rd step

But it was from a power of n+1

[idle fractal]

Ohhhhhhhhhh

I got it now

🙈🙈🙈

[stone flax]

why

male is a noun

too

[reef nimbus]

it's not correct usage

[stone flax]

There were two males in that house

Is it an adjective here?

[reef nimbus]

look at the definition of the noun form. animal or plant. in typical usage (in the US, at least), it is best not to use either male or female as nouns

[idle fractal]

Hmm what next

[stone flax]

IDK what you guys on but we were taught male is a noun as well as an adjective bruv

Humans are animals too

[stone flax]

,rotate

[stone flax]

What do you think 😂
limit as n goes to infinity

a is a constant

What happens to 1/(a+n) as n goes to infinity?

[idle fractal]

Infinity/infinity

Ohh wait

[stone flax]

[idle fractal]

e.x

[stone flax]

Yup

For x = 1/e you will need to check separately I guess

Since then the limit is 1

[calm coral]

@idle fractal Has your question been resolved?

[lyric ravine]

So what is your conclusion

[idle fractal]

For x>=1/e divergent

X<1/e convergent

@lyric ravine

[stone flax]

How for x=1/e?

@idle fractal

[idle fractal]

Because ratio test fails at x=1/e

[stone flax]

So it means you cannot tell if its divergent or convergent

ratio test fails for 1/n, and 1/n^2 both

But one diverges and other converges

@lyric ravine what do you think

[idle fractal]

Here ratio fails but p test

Works

[stone flax]

@idle fractal how? For p test you need a constant power if I am not mistaken

[idle fractal]

1,2 are constant no?

They do not need base constant

[stone flax]

Not sure what you mean, but for x=1/e not sure how p test works

[calm coral]

@idle fractal Has your question been resolved?

[idle fractal]

No i am saying about 1/n and 1/n^2...here power of n is 1,2 so we can decide about convergence with p test

@stone flax

[stone flax]

Yup, but what are you using for your problem? At x=1/e?

[idle fractal]

@stone flax

Log test

.close

[calm coral]

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[azure thorn]

In parametric integration, why can't I just do ∫y dt if y is in terms of t? I can change the limits and everything, but if y is in terms of t, what's wrong if I do ∫y dt straight away without multiplying by dx/dt?

[potent igloo]

Can you give an example of what you mean?

[azure thorn]

sure one sec

[azure thorn]

In this example, I can't just integrate 2sin(2t) + 3sin(t) with respect to t, I need to multiply it with dx/dt

[potent igloo]

Why are you trying to integrate y with respect to t? To find the area R?

[azure thorn]

Yeah

[potent igloo]

Recall how integral area is defined: A riemann sum of rectangles

The area is the limit of the sum of the area of each rectangle. The area of each rectangle is $y\times\Delta x$. As you approach the limit, the differential area become $ydx$ (height $\times$ width)

[potent lotus]

SWR

[azure thorn]

yes, but what would that imply?

[potent igloo]

Area of R would be $\int ydx$

[potent lotus]

SWR

[azure thorn]

But if I change the limits, why can't I just do ∫y dt?

[potent igloo]

Because that is not how area is defined

geometrically, $\int ydx$ is the sum of all infinitesimally small rectangles of height $y$ and width $dx$. But $\int ydt$ is the sum of $y$ and $dt$, but $dt$ has no geometric meaning.

[potent lotus]

SWR

[azure thorn]

ok thank you

.close

[calm coral]

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[calm coral]

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[remote mural]

If I have a right angle triangle with side b = 5√2, c = 4√2 and I want to solve for side a. I understand that applying the pythagorean theorem means I end up with 5√2 - 4√2 = side a which is √2.

However, I know √2 is 1.414213562 as shown on my calculator, but when I take the numerical values of 5√2 and 4√2 which are 7.071067812 and 5.656854249 respectively then I get ‘a’ as 4.24264.

What am I missing please?

[ancient helm]

It's a^2 + b^2 = c^2

[normal current]

its (5√2)^2 - (4√2)^2 = a^2

[remote mural]

Oh ofc, thanks -_-

🙏

.close

[ancient helm]

SIR

[calm coral]

Channel closed

Closed by @errant pine

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[normal current]

yes?

[ancient helm]

https://cdn.discordapp.com/attachments/1232936403319521312/1246221295364997150/MV5BNzE1OTY3OTk5M15BMl5BanBnXkFtZTgwODE0Mjc1NDE.png?ex=665c4246&is=665af0c6&hm=608b9d786c07b90854204881cdfbf4063dc222b582a3d6787d25328828fe85e7&

are you familiar??

[normal current]

NOT AGAIN

STOP SHOWING ME THIS

I AM NOT THAT GUY

[ancient helm]

SO YOU ARE FAMILIAR??

[normal current]

YES

[ancient helm]

EXCELLENT

[normal current]

fire first episode btw

[potent igloo]

#❓how-to-get-help

[ancient helm]

I thought it was a movie

is it a series

[normal current]

someone forced me to watch 10 minutes of this

[normal current]

yes

you should watch the covid 19 one

[ancient helm]

say less

[calm coral]

Available help channel!

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[real sentinel]

i dont know where to start for this

[sharp narwhal]

maybe find first r(x,y)^2

the distance to the line

squared

[calm coral]

@real sentinel Has your question been resolved?

[real sentinel]

im guessing that would be like (x-a)^2 + (y-a)^2 or something along those lines?

would i be going along the sides or do i include the area as well

[sharp narwhal]

i'm guessing it means the interior as well

[sharp narwhal]

this is true for some (x,y) but not all

i mean for the distance to the line you take a perpendicular line passing through that point

[calm coral]

@real sentinel Has your question been resolved?

[real sentinel]

yh im still lost

how would u find an expression that describes the distance from every point to the line for that area if both points can change

[calm coral]

@real sentinel Has your question been resolved?

[calm coral]

@real sentinel Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[frosty mica]

I need help with this. My teacher is being wildly unhelpful when I ask for help.

[brittle isle]

Okay so first prove the direction: If there is a bijection from T_1 to T_2, then T_1 is finite

if a bijection exists between two sets, they have the same cardinality

you can probably just take that as a fact/theorem

so if there's a bijection from T_1 to T_2, the cardinality of T_1 is the same as the cardinality of T_2, and since T_2 is finite cardinality, T_1 has a finite cardinality and is therefore finite

To prove the other direction, namely that if T_1 is finite then there exists a bijection from T_1 to T_2

list the elements of T_1 as t1, t2, ..., tn

and construct T_2 as having n unique elements a1, a2, ..., an

[potent igloo]

How are you definining finite in your class?

[brittle isle]

then consider the bijection from T_1 to T_2 that maps t_i to a_i for i from 1 to n

clearly T_2 is finite by construction

[frosty mica]

That's a great question

[potent igloo]

One you'll need to answer then

[frosty mica]

I will see what I can do with the above info.

.close

[calm coral]

Channel closed

Closed by @frosty mica

Use .reopen if this was a mistake.

[slate field]

you need to tell us what your teacher is saying specifically

ik the channel was just closed but if they’re trying to say something it might be good stuff