help-13

[high coyote]

$\sin x\leq x\leq \tan x$ is true in $\left(0,\frac{\pi}{2}\right)$

[crystal raptor]

1?

[high coyote]

yes

[wraith dagger]

jnkena

[versed fulcrum]

?

tan(π/4) = √3

sin(0) ≤ 0 ≤ √3 ??

[high coyote]

??

x, x and x

[versed fulcrum]

Oh

[high coyote]

You have to use same x always because is the same letter x

[versed fulcrum]

Why did you choose sin x and tan x though

[high coyote]

Because it works

[versed fulcrum]

Why not cos x though

[high coyote]

Because that does not work

[versed fulcrum]

This feels like intuitive learning

[high coyote]

I have sin(x)/x so I want lower and upper functions that will give me inequations involving that by transforming them

Yes, there's not an algorithm for proofs

Most of the proofs consist on lucky ideas

[versed fulcrum]

Oh

Are there any other that I have a memorize?

[high coyote]

proofs?

yes, infinite

XD

That's mathematics, learning and developing proofs from previous results

[versed fulcrum]

I heard that sin(ax)/sin(bx) = a/b

How does that work?

[high coyote]

when x≈0, sin(ax)≈ax

This is what's called "equivalent infinitesimals"

And "substitution principle" for limits

[versed fulcrum]

Uhhh

Is this high school level?

[high coyote]

One can substitute multiplying or dividing factors by equivalent infinitesimals

[high coyote]

Some equiv. infinitesimals are, not all of them. At least not in my country

[versed fulcrum]

For this one do I substitute?

[high coyote]

This being 1 is exactly what means for two functions to be equivalent infinitesimals

(or equiv. infinites)

[gleaming cloud]

try that, what do you get?

[high coyote]

0/0

Maybe mult. and divide by 1+sin(x) works

[versed fulcrum]

How does this work?

[high coyote]

$\lim_{x\to\frac{\pi}{2}}\frac{\cot^2x}{1-\sin x}=\lim_{x\to\frac{\pi}{2}}\frac{\cot^2x(1+\sin x)}{1-\sin^2 x}=\lim_{x\to\frac{\pi}{2}}\frac{\cos^2x(1+\sin x)}{\sin^2x(1-\sin^2 x)}=\lim_{x\to\frac{\pi}{2}}\frac{\cos^2x(1+\sin x)}{\sin^2x\cos^2 x}=\lim_{x\to\frac{\pi}{2}}\frac{1+\sin x}{\sin^2x}=\frac{1+1}{1}=2$

[gleaming cloud]

which step

[high coyote]

That was exactly what I was doing

[versed fulcrum]

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

How does this work?

[gleaming cloud]

expand (a-b)(a+b)

do it

[versed fulcrum]

a^2 - b^2

Oh

lol

What is sin^2(π/2)

How do I get it?

[high coyote]

Uh

Yes

my bad

[wraith dagger]

jnkena

[high coyote]

How can you ask about the squeeze theorem if you don't even know what sin²(π/2) ??

[versed fulcrum]

hm

[high coyote]

π/2 is 90° sin(π/2)=1 so sin²(π/2)=1²=1

[gleaming cloud]

$\mathrm{M\ddot{o}b}(\hat{\bC}) \cong \mathrm{PSL}(2, \bC)$

[wraith dagger]

giannis_money

[versed fulcrum]

so sin^2(π/2) = (sin(x))^2?

[high coyote]

Yes...

[versed fulcrum]

Okay thanks

[high coyote]

with x

[versed fulcrum]

Oh yeah, right

[versed fulcrum]

?

[gleaming cloud]

sup?

[versed fulcrum]

.close

[cedar kiln]

Channel closed

Closed by @versed fulcrum

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.

[stable tendon]

hey

[stable tendon]

what are the pre requisites for category theory

[hazy minnow]

There are no essential prerequisites but familiarity with the basic theory of groups, rings, vector spaces, modules and topological spaces would be very useful, and other topics such as Algebraic Geometry, Algebraic Topology, Homological Algebra and Representation Theory are relevant.

Taken from google.

Try asking in #category-theory instead of here.

You don’t see category theory questions in this part of server.

[cedar kiln]

@stable tendon Has your question been resolved?

[cedar kiln]

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.

[crimson sedge]

What does A^c mean?

[crimson sedge]

in set theory

[upper abyss]

Everything that isn't in A

And they're letting A = U, which probably refers to a set that contains "everything"

[crimson sedge]

so c basically means "Everything not in a set" o.o?

[upper abyss]

A^c is the set of things that aren't in A

[crimson sedge]

the set of elements that aren't in A? would that just be 0 then?

[upper abyss]

There are 0 elements in A^c, if that's what you mean, yes

A^c is empty

Sorry, A^c I mean

[crimson sedge]

so any variable raised to c is pretty much just gonna result to 0 then right? when would it not result to 0?

in set theory

[upper abyss]

These are sets, not variables

[crimson sedge]

sorry meant to say sets

[upper abyss]

A^c is the set of things that aren't in A

We're letting A contain everything

So A^c has to contain nothing

[crimson sedge]

Ah i see

[upper abyss]

In most other cases, A^c might contain something

[crimson sedge]

Could you help me with one more? the third one has a ' by it and it's confusing me

[upper abyss]

I think they're using ' as ^c here

So A ∩ B' is the set of things that are in A and not in B

[crimson sedge]

Ah! okay thanks Kaynex, does the c have a specific term that I could look up and learn more about just in case? it seems to be denoted with different things like ^c and '

[upper abyss]

Complement

Set theory notation is just kinda everywhere haha

[crimson sedge]

❤️ you're the best in this discord, my opinion, but I stand by it

thanks

.close

[cedar kiln]

Channel closed

Closed by @sweet pulsar

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.

[wide star]

can someone check my work?

[wide star]

.close

[cedar kiln]

Channel closed

Closed by @wide star

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.

[wide star]

can someone check my answer?

[simple shale]

correct

[wide star]

always a life saver, thanks again!

.close

[cedar kiln]

Channel closed

Closed by @wide star

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.

[limber bolt]

Hii I'm new here btw I'm a Highschool student,I got problem with this question hope anyone can help me with it

[upbeat dune]

The ratios of the speeds in both directions and distances in both directions must be the same

[limber bolt]

I'm very confused with it tho but yea I'm stuck at the calculation of the distance of an eagle to a rat obliquely..the rest of it I start confused

<@&286206848099549185>

[cedar kiln]

@limber bolt Has your question been resolved?

[limber bolt]

Anyone?

[cedar kiln]

@limber bolt Has your question been resolved?

[cedar kiln]

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.

[opal sierra]

How would you know exactly what x is approaching in limits?

[opal sierra]

<@&286206848099549185>

[tropic oxide]

unless i misunderstand your question, it is always specified what x (or other variable) approaches

or it is otherwise obvious from context and omitted for brevity

[opal sierra]

thanks

https://tenor.com/view/smart-so-sosmart-gif-15534259

bye!

.close

[cedar kiln]

Channel closed

Closed by @opal sierra

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.

[buoyant latch]

When you are trying to find at most x events happening do you sum the binomial from 1 or from 0?

[buoyant latch]

in n draws (of a card), with at least r of the set, k is the deck size
$$1-\sum_{i=0}^{r-1}\binom{n}{i}\left(\frac{i}{k}\right)^i\left(\frac{k-i}{k}\right)^{n-i}$$

Like this

[wraith dagger]

Frosst

[buoyant latch]

Well here it’s 1-at most for at least so same thing

Here I’m running into a problem where wolfram sees 0^0 for i=0 in the 2nd bracket

Oh never mind I figured out the problem that number shouldn’t be i

.close

[cedar kiln]

Channel closed

Closed by @buoyant latch

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.

[grand raft]

Hello! I have a question, how do you solve differential equation from second order?
I have a question:
I wanna solve the equation
x'' + x' + x = 0

[grand raft]

I've been thinking to say:
Let x = e^sx and solve for s

[amber ridge]

don’t they use the variable y?

[amber ridge]

yeah I think the usual way to do it is setting y=e^(rx) and solve for r

[cedar kiln]

@grand raft Has your question been resolved?

[cedar kiln]

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.

[loud flare]

anyone able to explain the part I put a red box over a bit?

i never really worked with pi and am confused

how they got 11

[dire geode]

,calc pi

[wraith dagger]

Result:

3.1415926535898

[dire geode]

Pi is just a number represented by a symbol

So when you see 22pi, that means

,calc 22*pi

[wraith dagger]

Result:

69.115038378975

[dire geode]

Nice

[unkempt aspen]

Worth mentioning if he’s not familiar, that number is an approximation

For exact answers you’ll want to put in 22pi

[cedar kiln]

@loud flare Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.

[buoyant latch]

What have u tried

[cedar kiln]

@tribal token Has your question been resolved?

[tribal token]

dont know how to start

[tough aurora]

do you have an idea of what kind of number W is, that would be a good start

[buoyant latch]

Think of the ℂ number plane

And now imagine starting from the position of z you have an arrow to a new point

This arrow ends at a point let’s call it p

So |p| must be within 10 units of the origin

So can you imagine an arrow from z that goes inside a circle with radius 10 cantered around the origin?

How long can this arrow be?

Where is it pointing?

[buoyant latch]

This isn’t necessary but it can help you find how long it can be

[tough aurora]

are the coordinates of z even important here ?

[cedar kiln]

@tribal token Has your question been resolved?

[tribal token]

the opposite direction of z?

[buoyant latch]

Uh huh

[buoyant latch]

Yea

[tribal token]

how can I align a vector with the same direction as -z?

[buoyant latch]

Find it’s direction

Or slope

Pretend it’s x y plane

[tribal token]

ok I solved it thank you

[buoyant latch]

👍

[cedar kiln]

Channel closed

Closed by @tribal token

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.

[fickle trellis]

Alr its good now

[crimson sedge]

yahh

[livid hound]

whats your issue with this question

[crimson sedge]

idk whats the answer is

[livid hound]

not what I meant

what do you think is preventing you from reaching the answer

[crimson sedge]

idk its so hard

[livid hound]

do you understand all the words in the question etc...?

[crimson sedge]

lol

[crimson sedge]

no

[upbeat dune]

Always try giving the unknown a name
And try making an equation with it

[livid hound]

which word(s) don't you understand

[crimson sedge]

all of them

[upbeat dune]

What is the sum of 100 and 100 ?

[crimson sedge]

yah

[livid hound]

do not over-exagerate

it doesn't help

[crimson sedge]

ok

i just want wt is the answer

[livid hound]

try to be as specific as possible

[crimson sedge]

cuz my friend gave it to me lol

🥲

[upbeat dune]

Do you know what sum means ?

[crimson sedge]

no

i math in bangla

lol

[upbeat dune]

Sum means to add

[livid hound]

because if you're implying that you don't know what "the" means,
a word that you've been using and reading then I'm gonna dip

[crimson sedge]

ohhhh

[crimson sedge]

o

[obsidian coral]

What grade/math level are you in?

[crimson sedge]

class 9

bro i read in bangla language

this math isnt mine

[upbeat dune]

Now that you know what sum means can you solve it now?

[crimson sedge]

ok imma try

[obsidian coral]

Then you could have used a translation tool

[crimson sedge]

maybe the answer is -60

[crimson sedge]

hmm

[crimson sedge]

right?

[upbeat dune]

Are you sure ?

[livid hound]

no

[upbeat dune]

I would recheck that

[crimson sedge]

yahh

i think so

[upbeat dune]

I would still recheck that 😅

[crimson sedge]

but idrk

[livid hound]

let's start with what's the sum of 100 and 100

[crimson sedge]

ok

[crimson sedge]

200

[upbeat dune]

...

200 = ??
Can you make the rest of the equation ?

[crimson sedge]

200=200

[upbeat dune]

Im out
Bye

[crimson sedge]

I think they are trolling

[upbeat dune]

Yea most definitely

[crimson sedge]

ik the answer

[calm hedge]

[crimson sedge]

its 60

[upbeat dune]

🥳 🥳
You have successfully added 2 numbers

[crimson sedge]

yahh

lolllllll

thanks for helping me bros and sisters

.close

[cedar kiln]

Channel closed

Closed by @south plover

Use .reopen if this was a mistake.

[cedar kiln]

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.

[crimson sedge]

-16+22-4/5+9-10

[left parrot]

https://lmgtfy.app/?q=-16%2B22-4%2F5%2B9-10

[crimson sedge]

can you help me with the process

[left parrot]

just add and subtract in numerator and denominator separately and then divide 💀

lol this server is becoming schooling server or what 🤣

[foggy merlin]

you must be 13 years old to be on discord, and your question is like 3rd grade or 4th

i do believe that people can learn maths later tho, its never late to learn

[crystal raptor]

come on guys

[foggy merlin]

.

[foggy merlin]

the lack of give me pain, try to well write the operation

[reef venture]

I think they meant
$\frac{-16+22-4}{5+9-10}$

[foggy merlin]

like, i dont know if its -16 + 22 - (4/5) + 9 - 10
or (-16+22-4)/(5+9-10)

[wraith dagger]

Swas.py

[crimson sedge]

Exactly, sorry

[reef venture]

but again

yeah use () from the next time

[reef venture]

This ^

[crimson sedge]

ok

[reef venture]

You know how to add numbers right?

do the thing on the top and bottom

(numerator and denominator)

[crimson sedge]

which comes first, addition or subtraction?

[foggy merlin]

[bitter reef]

$a - b = a + (-b)$ so they are the same thing

[wraith dagger]

Doggo

[bitter reef]

as long as you do it right at least

[reef venture]

yeah

its the same operation

[sonic thistle]

@crimson sedge

did you solve it?

[crimson sedge]

2/4 I got

[sonic thistle]

ok

but

2/4

it can be simplified

[crimson sedge]

OH 1/2

[sonic thistle]

yes

[crimson sedge]

how can I know when it can be simplified?

[sonic thistle]

both the numerator and the denominator are divisible by a number

then it can be simplified

[velvet mortar]

charlie pie's dog is disgusting

[crimson sedge]

ok thanks

[sonic thistle]

np

in this case both 2 and 4 are divizible by 2

[crimson sedge]

sorry

[sonic thistle]

so you can simplify the fraction

by 2

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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.

[twin coral]

how do i find the other direction vector?

<@&286206848099549185>

.close

[cedar kiln]

Channel closed

Closed by @twin coral

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.

[silk saffron]

How to solve after this ? I need to find x

[ember dagger]

is x meant to be n

[silk saffron]

Yeah

I write it that way , doesn't matter though

N or X .. i just have to find it 💀

[eternal pendant]

if I'm not wrong, no value of x satisfies this expression

anything raised to x can be anything from more than zero to infinity and never negative

[ember dagger]

no real number, yes

[eternal pendant]

can you send the exact question slav

[ember dagger]

n would be a complex number, no?

[silk saffron]

The exact question
Wait Imma send it

[dim thunder]

help

[ember dagger]

this chanel is occupied.

[obsidian coral]

#❓how-to-get-help

[eternal pendant]

i don't assume they've asked that

[dim thunder]

whoops sorry

[ember dagger]

i guess, still, n would have to be a complex number unless i'm missing something

[silk saffron]

E part

[eternal pendant]

you're right

[silk saffron]

I can use a calculator

If that helps

[eternal pendant]

you missed the minus after 2

[silk saffron]

Oh .. yeah 💀💀

[ember dagger]

.

[silk saffron]

Still

Like what do I do after these steps

To find x

[obsidian coral]

What did the graph look like?

[eternal pendant]

even i can't find x that easily, I'll try hit and trial

[silk saffron]

Well i couldn't plot the graph either .. so i thought of solving these first ngl

I didn't think the graph would matter

[obsidian coral]

But it does matter

Plot it

Then see if it ever reaches y = -10

[silk saffron]

Well i couldn't figure out the y axis points .. after taking the x values as 1,2 i got x=2.5 and 2.8

Do I take the y axis point 0 ?

[ember dagger]

if this helps, it does

[obsidian coral]

I know how to use graphing utilities. And I wasn't asking you to do it. It was more for the OP to do it themselves

[ember dagger]

if you say so

[silk saffron]

I don't even think this graph is in my course ..

So I wanted to solve the equation at least ig

[obsidian coral]

And FYI, it's not a complex number

[obsidian coral]

Try to isolate (3/4)^x, then apply log properties

To solve for x

[silk saffron]

Oh .. i Haven't learnt log yet

So ig this question is not in my syllabus

.close

[cedar kiln]

Channel closed

Closed by @silk saffron

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.

[cedar kiln]

Please don't occupy multiple help channels.

@thorny bramble Has your question been resolved?

[thorny bramble]

.close

[cedar kiln]

Channel closed

Closed by @thorny bramble

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.

[blissful stirrup]

im not sure what to do

like i dont get it

<@&286206848099549185>

[cedar kiln]

@blissful stirrup Has your question been resolved?

[manic acorn]

Do you know binomial expansion

And how to evaluate nCr?

Just google it and i think ull get it

[blissful stirrup]

i know ncr

[manic acorn]

And binomial?

[blissful stirrup]

nopoe

[manic acorn]

Ah just google it, these questions are all from there only

[blissful stirrup]

oh yes i know this

but like for a its 70a^4b^m and m is 4

[manic acorn]

Its just saying whether the statements are true or false

[blissful stirrup]

how do i know if that is or not how do i check?

[manic acorn]

What is the power of a

And power of b

Both are 4

[blissful stirrup]

no clue

[manic acorn]

I meant like exponent...

[blissful stirrup]

oh

[manic acorn]

Its 4 right?

[blissful stirrup]

yea

[manic acorn]

And what is the general way to write say (a+b)^n

[blissful stirrup]

thats the power of 8

[manic acorn]

I know...

Im just asking the general way to expand (a+b)^n

[blissful stirrup]

add the inside then power it?

[manic acorn]

Bruh

What you dont know a and b

How would u expand them using the binomial theorem

[blissful stirrup]

70a and b is unknow

[manic acorn]

Dont concentrate on your question for now...

Just think of (a+b)^n expansion

Everything will be cleared if u understand this

[blissful stirrup]

is it the trangle thing

[manic acorn]

(a+b)^n = nC0. a^n. b^0 + nC1 a^(n-1).b^1 +.....+ nCn. a^0.b^n

[blissful stirrup]

it will be a 2 and b2

[manic acorn]

Do you agree?

[manic acorn]

What is the triangle thing

[manic acorn]

Do u agree with this?

[blissful stirrup]

like the higher the power the more unbers it adds to and it just expnads from there iot forms and trangle

[manic acorn]

Are u talking about pascals triangle?

[blissful stirrup]

yea

i think

[manic acorn]

Damn i barely remember that lmao, but this question can be done without it

[blissful stirrup]

but ncr or something

oh ok

[manic acorn]

Do u recognise this???

[blissful stirrup]

kinda

i get it till half way

[manic acorn]

What do you mean by that

[blissful stirrup]

i dont get the last part

[manic acorn]

It means theres a lot of terms in between

And the last term is that

[blissful stirrup]

ohhh

0k

[manic acorn]

Like if i write the sigma notation

(a+b)^n = sigma (r=0 to n) for nCr.a^(n-r).b^r

So now if ur question you only have (a+b)^8, if you want more intuition id say just expand the entire thing

And see what it comes out to be

[manic acorn]

All the answers of your questions will come from this

[blissful stirrup]

oh

would i need to replace anyhting?

[manic acorn]

What do you mean

[blissful stirrup]

like for a

what do i do with the power of 4 and 70?

[manic acorn]

No just expand (a+b)^8

[manic acorn]

Power of 4 will come in the expansion

[manic acorn]

For r=4 u will get 8C4. a^4.b^4

[blissful stirrup]

yea

[manic acorn]

💀 then find 8C4

And see if ur statement true or not

[blissful stirrup]

what u mean find it?

[manic acorn]

U said u knew ncr...?

[blissful stirrup]

yea it just a line

[manic acorn]

I mean how to evaluate nCr

[blissful stirrup]

8N0 8N1 8N2

[manic acorn]

What line

[blissful stirrup]

like i mean it will just added on like anumber line in ordr

1,2,3,4,5,6,7,8 lik,e that

[manic acorn]

But what is say 2C2= ?

[blissful stirrup]

1

[manic acorn]

Now find 8C4

[blissful stirrup]

70

[manic acorn]

Yes so is statement a true or no?

[blissful stirrup]

ohhhhh

damn im stupid lOL

im overthinking it

true

[manic acorn]

It also does say explain how you arrived at this conclusion so i think do write some stuff

I will go now, i think u can do the rest

[blissful stirrup]

yea thanks

[blissful stirrup]

what does c mean tho the leading coe is 256 shouldent it be 1 or 0?

[manic acorn]

Im not sure how u arrived at 1 or 0..., Infact i myself have forgotten about what leading coefficient exactly means, cuz its been like 6 months i did this💀, but i think its just asking you to sum all the nCr from (a+b)°8, like 8C0 +8C1 +8C2 +....+8C8

[blissful stirrup]

oh

leading is the number in front

70A

70 is

[manic acorn]

Im so sad i cant remember the direct answer to this wth 😭😭

But there was a way to directly get an answer instead of finding all the individual ones

[blissful stirrup]

so i do ur way

add it all up>

[manic acorn]

The direct answer is 2^8

nC0+nC1+nC2+...+nCn = (1+1)^n, here n was 8 so 2^n

2^8*

[blissful stirrup]

ok

[blissful stirrup]

by any chnace you know how to do this

i made 38 words

[manic acorn]

Ive forgotten a lot of my pnc, so theres a very high chance ill be wrong

Better if someone else helps you with it

[blissful stirrup]

oh ok

would i make a new chat?

[manic acorn]

Nah someone wud probably come here only

[blissful stirrup]

oh ok

[marsh frigate]

Explain your reasoning

[blissful stirrup]

I put the worm things in

I got like 5074

[marsh frigate]

Worm things?

What are worm things?

[blissful stirrup]

Wrong

Number

[cedar kiln]

@blissful stirrup Has your question been resolved?

[marsh frigate]

[blissful stirrup]

?

[high coyote]

Worm things??

🐛🐛

[blissful stirrup]

wrong things

[high coyote]

HAHA

[blissful stirrup]

LOL

[high coyote]

Ah, hahaha

okay

[cedar kiln]

@blissful stirrup Has your question been resolved?

[cedar kiln]

@blissful stirrup Has your question been resolved?

[cedar kiln]

@blissful stirrup Has your question been resolved?

[tough aurora]

easy, get a dictionnary, write a python script and let it run

x)

[cedar kiln]

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.

[quasi goblet]

https://media.discordapp.net/attachments/903430332324405288/985054858031800350/IMG_20220611_110514801.jpg

[quasi goblet]

Need some help with the circled questions. Can't figure them out

<@&286206848099549185> ? Help pls ?

[cedar kiln]

@quasi goblet Has your question been resolved?

[cedar kiln]

@quasi goblet Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.

[wide light]

heres mark scheme

im not rly sure

[crimson sedge]

I believe oatloard has the same question

[cedar kiln]

@wide light Has your question been resolved?

[cedar kiln]

@wide light Has your question been resolved?

[cedar kiln]

@wide light Has your question been resolved?

[cedar kiln]

@wide light Has your question been resolved?

[cedar kiln]

@wide light Has your question been resolved?

[wide light]

https://cdn.discordapp.com/emojis/840773475119136788.webp?size=64

[quiet jewel]

#help-0 message

read that

they didn't get a solution but maybe it will help you

[wide light]

i read it

it did not help 😦

[astral crown]

umm basically, this is like saying "how many black panthers (or normal jaguars) do you need to get in a row before you conclude that the probability is not 6%"

although i don't agree with this test, it is one way

[dire geode]

.close

[cedar kiln]

Channel closed

Closed by @dire geode

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[cedar kiln]

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.

[still holly]

can someone give me some pointers on this one

[sturdy finch]

How do I do this? It won't let me use T as a variable for some reason.

[bright river]

#❓how-to-get-help

[bright river]

You have to express y in function of x without using t

[still holly]

wtf

[shut reef]

eugene was here first tho

what happened

[still holly]

what i do wrong

[bright river]

Then why the room has name blank ?

[still holly]

confusing man

[stuck jolt]

bot was restarted

[bright river]

Maybe a problem from the bot tho. Sry if you did it the right way

[shut reef]

idk but if blank had deleted the first message this channel would have closed

[bright river]

Oh, okay

[shut reef]

so is this blanks or eugenes

[still holly]

blanks can have i

[bright river]

Can u open new room for your question?

[sturdy finch]

Sure

[bright river]

[sturdy finch]

.close

[bright river]

So, the informations in the question are supposed to give you enough information for A and for k

[cedar kiln]

Channel closed

Closed by @sturdy finch

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[velvet mortar]

.close

[cedar kiln]

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.

[crimson sedge]

How?

[crimson sedge]

the answer is 36.027

[livid hound]

no

[crimson sedge]

isnt it like this?

[livid hound]

the calculation of that angle will be involved,
however it isn't quite the final answer

[crimson sedge]

isnt the bearing 53.97 then

[livid hound]

no

[dusty hazel]

Bearing means the angle from north, right?

[livid hound]

note that the bearing is the angle measured clockwise from north

[crimson sedge]

yeah

[dusty hazel]

Yeah.

[livid hound]

what you calculated was the angle clockwise from east

[crimson sedge]

which angle would I be looking for then?

[livid hound]

the angle measured clockwise from north

it would be helpful to draw a compass axis at point A

[crimson sedge]

im confused

[livid hound]

consider the line north of A

[crimson sedge]

the mark scheme says its correct??!?!

[livid hound]

draw a clockwise arc from that to AB

the calculation of that angle will be involved,
however it isn't quite the final answer

[crimson sedge]

oh alr

so which angle is it

on the diagram

[livid hound]

consider the line north of A
draw a clockwise arc from that to AB

that's the angle you want

[crimson sedge]

ohhh ok

90 + 53.9

[livid hound]

yes

[crimson sedge]

180 - 90 + 53.9 = 143.9

makes sense now

[livid hound]

actually, the value of 53.9 wasn't rounded properly

[crimson sedge]

oh

but yea I get it now

thanks

[livid hound]

in the mark scheme 53.9**(...)** was indicating that more numbers were written after the 9

[crimson sedge]

oh okay

I will just probably round to 3 significant figs next time

-close

.close

[cedar kiln]

Channel closed

Closed by @light lantern

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[mossy flower]

cot $\frac{33 \pi}{4}$ is equal to ?

[wraith dagger]

LoneliestSoul

[dusty hazel]

Do you have any idea?

Like you could start by changing the angle into a smaller angle in which you know the value of cot at that angle.

[mossy flower]

wait

after simplifying

i get the 33pi/4 part as

[mossy flower]

$8 \pi + \frac{\pi}{4}$

[wraith dagger]

LoneliestSoul

[mossy flower]

so the expression becomes

cot $(8\pi + \frac{\pi}{4})$

[wraith dagger]

LoneliestSoul

[mossy flower]

the solution says that the final answer is 1.

I understand that by converting $\frac{\pi}{4}$ to degrees we get it as 45

[wraith dagger]

LoneliestSoul

[mossy flower]

and cot of 45 = 1

but where does the 8 pi go ?

[manic acorn]

One complete round takes 2pi, so the 8pi gets used up in doing 4 rounds, and then just cot (pi/4)

[mossy flower]

ohhhh

now i get it

Thonxe so much man u saved my day

.close

[cedar kiln]

Channel closed

Closed by @mossy flower

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[plucky holly]

I understand all the options, except for the third option. Can anyone please tell me what does the sign of the third option mean?

[fiery whale]

i believe it's that AD is perpendicular to BC

[slate nest]

pythagoras

[slate nest]

confused between A) and B)

[plucky holly]

Confused of what?

I know that BD = CD

[sonic thistle]

is this a test?

[slate nest]

confused that which one is correct

cause bd = dc

and

ad is perpendicular to bc

oh wait the question is select all the correct

then A and C are correct @plucky holly

[plucky holly]

but isn't the triangle isoceles?

[rugged palm]

They just asked what ⊥ meant

[slate nest]

so?

[plucky holly]

so can AD = BC?

cause BC is the base, AD is the height

[slate nest]

yes cause the mentioned that the two triangles are equal

firckkkkkkkk

my bad

C

is correct

no wait even a is correct

dude

[slate nest]

im talking about bd=dc

@plucky holly

[plucky holly]

Ohh, i know that's true

[slate nest]

yes

than

[plucky holly]

i'm just asking what the sign mean

[slate nest]

A and C

are correct

[plucky holly]

for the third option

[tight sun]

For some reason I got a ping here that I can't see?

[slate nest]

it means that ad is perpendicular to bc @plucky holly

[slate nest]

my bad wrong ping

[sonic thistle]

lol

wrong ping again

[plucky holly]

So option number 1 and 3 is correct?

[slate nest]

yessir

[plucky holly]

Okay, thanks.

.close

[cedar kiln]

Channel closed

Closed by @plucky holly

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

Channel closed

Closed due to the original message being deleted

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[cosmic steppe]

Bro

[vapid orbit]

I'm sorry I sent the wrong image

I meant to send this image

I don't know how to ingrate a function with given points or x

<@&286206848099549185>

[balmy apex]

!15m

[balmy apex]

read this

[vapid orbit]

Oh my bad, just new to the server

[balmy apex]

lmao that's not an excuse

1. you got a popup

2. there's a rules channel

3. there's a how to get help channel

4. there was a bot message

[vapid orbit]

I'm really sorry

[balmy apex]

$$\int_a^b f(x)dx = \left.\left ( \int f(x)dx \right ) \right\vert_a^b$$

[wraith dagger]

illuminator3

[balmy apex]

where

$$\left.f(x)\right\vert_a^b = f(b) - f(a)$$

[wraith dagger]

illuminator3

[vapid orbit]

Is this the formula for the problem?

[cedar kiln]

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.

[crimson sedge]

how?

[crimson sedge]

is this correct or wrong

I thought it would be cos

[velvet mortar]

yes cos

[hazy minnow]

x/9 = cos(72).

[crimson sedge]

thanks 😂

my teacher made some mistakes then

.close

[cedar kiln]

Channel closed

Closed by @light lantern

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[crimson sedge]

d/dx[(x+1)/(x-1)]

[crimson sedge]

I get 2X/(X-1)^2

Can anyone check

Wait nvm

.close

[cedar kiln]

Channel closed

Closed by @onyx ether

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[green skiff]

hi

[green skiff]

this is kinda simple but how do i do

16^1/4 x 125^1/3

[unreal pendant]

you could just plug it into a calculator

[green skiff]

my questions are supposed to be non calc

so im kinda stuck

[unreal pendant]

but the proper way to do it is realize 16^1/4 is the quartic root (idk) of 16

ie what number to the power of 4 is 16

[mighty drift]

fourth power, not times 4

[unreal pendant]

yeah

then the same for the other one

[green skiff]

2 to the power of four is 16 right

so that would be

wait uh

2 x 5?

great

thanks

.close

[cedar kiln]

Channel closed

Closed by @green skiff

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[final horizon]

I think I know how to solve this

[stable plinth]

f(x) is a monotonically non-decreasing function and g(x) is a monotonically non-increasing function prove that f(g(x)) is a monotonically non-decreasing function

[final horizon]

F = 15cos(20)i + 15 sin(20)j

G = 11cos(50)i - 11sin(50)j

correct so far?

set H = x i + y j

then 15 cos(20) + 11cos(50) + x = 0

and

15sin(20) - 11sin(50) + y = 0

we solve for x and y right?

[left parrot]

just take x1 and x2 where x2>x1 then take g of them and according to concavity change the inequality then take f of g and again change sign of inequality

[final horizon]

is this to my question?

[left parrot]

oh!, no

let me answer yours too

[stable plinth]

thanks

[final horizon]

Thank you

[left parrot]

solve for x( i) and y( j) = 0 separately

rest are correct

[final horizon]

okay one think I am confused about though

so I got x = -17.40728253519

and y = 7.9029964237712

the magnitude is easy but since we want angle with respect to vertical

it is arctan(x/y) right?

[left parrot]

I am not sure about that one 😓 , let me check once

[final horizon]

https://www.wolframalpha.com/input?i=+15cos(20)+%2B+11cos(50)+%2B+x+%3D+0+solve+for+x

[left parrot]

not sure bro( don't want to guide you wrong), let the channel be open, someone will help you

[final horizon]

https://www.wolframalpha.com/input?i=+15sin(20)+-+11sin(20)+%2B+y+%3D+0+solve+for+y

[final horizon]

sounds good!

guys any help with my question?

[cedar kiln]

@final horizon Has your question been resolved?

[final horizon]

anyone?

[crimson sedge]

since H makes an angle with the vertical, you have the right idea finding the y components of each force

[final horizon]

so is my answer correct?

[haughty surge]

It is arctan(x/y) as we are measuring angle from vertical

yes

[crimson sedge]

i checked it and yea

[final horizon]

I have one extra question.

.close

[cedar kiln]

Channel closed

Closed by @final horizon

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[fringe escarp]

How would i solve this algebraically step by step? Online calculator are giving way to complicated ways to solve

[dire geode]

Show their complicated ways

[fringe escarp]

Ok

Pic 4

Pic 3

Pic 2

Pic 1

I moved the /(.8-2x)^2 to the left and then put it in calculator but it is the same problem (look at pic 1 beginning)

[fringe escarp]

^

[dire geode]

It's just the quadratic formula. The numbers are complicated because of your initial equation

[fringe escarp]

When i tried to make it into a quadratic i got this

[dire geode]

Check that this is what you're supposed to solve

[sonic thistle]

1st step is wrong

from your last photo

[fringe escarp]

The bottom part?

[sonic thistle]

yeah

[fringe escarp]

Oh

+4x?

[sonic thistle]

no

[fringe escarp]

Cause (-)^2 becomes +

[sonic thistle]

$(8-2x)^2$

[fringe escarp]

Its .8

On top

[wraith dagger]

Master Oogway

[fringe escarp]

^

[sonic thistle]

still wrong

what is $(a+b)^2$ ?

[wraith dagger]

Master Oogway

[fringe escarp]

(A+b)(a+b)

So it would be

4x^2

Oh

Then a^2 + b^2

[sonic thistle]

no

$(a+b)^2=a^2+2ab+b^2$

[wraith dagger]

Master Oogway

[fringe escarp]

Oh right foil

Wait did i foil wrong

[cedar kiln]

@fringe escarp Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[shy garnet]

Aight
I need help for the entirety of this
cuz idk how 2^{x-y} finna help solving the expression above 💀

[obtuse wedge]

?

[obtuse wedge]

this the question?

[shy garnet]

N a a a h

ofc it is lol

but ye, im thinking the denominator finna turn to 2^{x+1}

since both terms have the same base

deduct the y's from eachother

[obtuse wedge]

you need to find x and y right?

[shy garnet]

mhm

[obtuse wedge]

aight wait

fuck bro

[shy garnet]

along with the answer to that expression obv

[obtuse wedge]

okay so the numerator if the frac is in ap , with common difference d and final term 2a

find number of terms

[shy garnet]

if the frac is in advanced placement?

wha

d???

2a?!

Bruh what is this harry potter shit

[obtuse wedge]

x , x+ 1 ,x+2 is in ap with final term as two x

you know sequences and series?

ap is arithmetic progression

[shy garnet]

Thank you

[obtuse wedge]

every term is 1+ the other term

find number of terms with it

[shy garnet]

Boy i know summation

Well you need to know what x is
to know the limit

of the summation

[obtuse wedge]

find number of terms , im lazy to do calculation

bruh

[shy garnet]

...

[obtuse wedge]

the limit is 2x

thats the last term

[shy garnet]

Yeah
but what's
x
ffs

[obtuse wedge]

dude you will get a simple equation form it

[shy garnet]

x could be 10^100 ffs

[obtuse wedge]

just find it in terms of x

[shy garnet]

2x(2x-1)/2

?

[obtuse wedge]

and youll get two easy linear equations and solve

[obtuse wedge]

no waiy

ffs ill do it myself

kids these days man , what grade u in?

[shy garnet]

I'm a freshman

this is AP material

[obtuse wedge]

9th?

[shy garnet]

yep

[obtuse wedge]

yeah its a good question

[shy garnet]

no shit that's why i came in here

[obtuse wedge]

wait gimme some time ill need a pen and paper

[shy garnet]

bet

$\sum_{i = 1}^{x}x+i = x(2x-1)$

[obtuse wedge]

dude

[wraith dagger]

Javaan T

[shy garnet]

this is what im thinking

[obtuse wedge]

its the easiest fucking question

[obtuse wedge]

no

just take 2^x common

youll get 1 * 2 * 3

so on

[shy garnet]

tf dym common

you mean factorization?

[obtuse wedge]

factor $$ 2 ^x ( 2^ 1 + 2^ 2...) $$

[wraith dagger]

Zyzzbrah

[shy garnet]

uh... continue on?

[obtuse wedge]

upto 2^x

bruh im not typing all that

[shy garnet]

😐

[obtuse wedge]

wait do u even understand what im saying?

[obtuse wedge]

dude there are more than 10 terms

[shy garnet]

Dude

you suck at explaining shit 💀

[obtuse wedge]

ik i mostly do math in my head

[shy garnet]

You're just doing random operations and expecting me to understand each one

[obtuse wedge]

wait ill try to

[shy garnet]

and then shitting on the table aswell

[obtuse wedge]

have you studied exponents?

[shy garnet]

Ofc

[obtuse wedge]

do you know that you can split $$ 2^x = 2^x * 2^ 0 , 2^x+1 = 2^x * 2^1 $$

[wraith dagger]

Zyzzbrah

[obtuse wedge]

man i cant use latex

[shy garnet]

Hol up

nah

you did sumn wrong

[obtuse wedge]

but u can split $$ 2 ^ (x+1 ) = 2^x * 2^ 1 $$

[wraith dagger]

Zyzzbrah

[obtuse wedge]

💀 im in 12th grade bro

[shy garnet]

$2^{x+1} = 2^{x}(2^{1})$

[obtuse wedge]

yeahhhh

[wraith dagger]

Javaan T

[shy garnet]

there we go

[obtuse wedge]

yes , so once u factor two out

youll get some numbers

$$ 2^1 + 2^2 + 2^3 ... $$

[wraith dagger]

Zyzzbrah

[shy garnet]

Oh

makes sense

yeah

[obtuse wedge]

you get it?

[shy garnet]

Indeed

but like

.... what next 💀

[obtuse wedge]

now do the same in denominator and factor $$ 2 ^x $$ out

[shy garnet]

But

2^y ain't got no x in it

[wraith dagger]

Zyzzbrah

[shy garnet]

Ohh

Hold up

lemme try this

[obtuse wedge]

write it as $$2^ y - x $$

[wraith dagger]

Zyzzbrah

[shy garnet]

.

...

[obtuse wedge]

bruh

i cant use latex fr

but u get what i mean?

once u multiply , x cancels out

[shy garnet]

so ur saying $2^{y} = 2^{y-x}$

[wraith dagger]

Javaan T

[obtuse wedge]

yes

2 ^x

just factor and cancel 2^x out

youll get something simpler

[shy garnet]

...

smth's hella sus rn bruh

lemme see this for myself for a sec.

[obtuse wedge]

actually like im probably using much more complex but simpler steps so you cant understand it fast

sorry for that bro

idk how to solve it using only 9th grade knowledge but i can write u an answer once i have a pen and paper

youll have to wait bout 30 min