help-10

[timid silo]

-1

[jagged onyx]

no

-1 - 1

[timid silo]

what

[jagged onyx]

-1 to 1

sin^2 belong from 0 to 1

[timid silo]

thats what i wrote😭😂

[timid silo]

still it cant be equal to 4

becoz

0,1

[jagged onyx]

type .close if your doubt is solved

[jagged onyx]

yes

[timid silo]

i have another’s

another*

[jagged onyx]

ok

[timid silo]

@jagged onyx the

question

i have another doubt

[jagged onyx]

63?

[timid silo]

yes

yes

sir ne bataya tha kuch 28 hoga

but kyu

[jagged onyx]

yes

graph

you'll have to draw

no other choice

[timid silo]

i did

[jagged onyx]

integal values are 2

[timid silo]

but im really bad

at plotting graph

of

mod of fx

fmodx

im confused

[jagged onyx]

desmos

[timid silo]

can you haelp

[jagged onyx]

desmos?

[timid silo]

no but

theres some rule

about flipping graph along x axis

and y axis

[jagged onyx]

yes

[timid silo]

about particular mod

[jagged onyx]

for mod

[timid silo]

just tlel when to flip from where

[jagged onyx]

you flip the graph along x axis usually ( you just draw what is in the negative on the positive side)

[timid silo]

no

but

its differnet

[rare crane]

Hello can anyone help me with data management

[timid silo]

for different mods

[timid silo]

dude this is my channel

pls

[jagged onyx]

you'll have to open another one

[rare crane]

I’m new to this how do I do that

[timid silo]

#help-22 put ur doubt there

[jagged onyx]

go to how to get help channel

[jagged onyx]

no

[timid silo]

not in my channel?

stop disturbing bro😭

[jagged onyx]

continue

your doubt

[timid silo]

.

read

[jagged onyx]

for log yea

depends on the function

for log since negative of a log doesnt exist

x can take negative values becuz of mod

ok?

is your doubt cleared

?

uhh

hello?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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.

[versed cave]

Hi! I keep getting the same wrong result, is it set up correctly?

[warm shale]

Nonna

[tardy epoch]

x(t=0) is 1, not 4

oh you're going in reverse?

[versed cave]

Yes haha

[tardy epoch]

is your answer off by a - sign?

[versed cave]

No

I get -211/2, the result should be 109/2

[tardy epoch]

"from" means the starting point should be 4, -1, 2 though

oh jeezus your limits make it work tho

[versed cave]

What? Isn't that just how it's supposed to be done?

Like, I just parametrize the curve and then choose the limits

[tardy epoch]

,w int 1 to 0 [(1+3t)^2 (-8) - (7-8t)(-1+3t)3] dt

[warm shale]

Results provided by WolframAlpha

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

Requested by rie.mann

[versed cave]

[tardy epoch]

not that i think it'll help, but try parametrizing it with x = 4 -3t, y = -1 + 8t, z = 2 - 3t from 0 to 1

if that gives you 109/2 still, then the answer is probably wrong

[tardy epoch]

oh wait it is right. you just made a mistake in your t integral somewhere

,w int 0 to 1 of (4-3t)^2 8 - (-1+8t)(2-3t)(-3) dt

[warm shale]

Results provided by WolframAlpha

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

Requested by rie.mann

[tardy epoch]

yea same answer, just different parametrization

[obtuse pebble]

@versed cave Has your question been resolved?

[versed cave]

I made the same mistake three times, just found it

[versed cave]

With this other integral I got it right

[tardy epoch]

yea both wolframs outputs gave 109/2

[versed cave]

I just started with this topic and was worried I didn't set it up properly

Thanks riemann!

.close

[obtuse pebble]

Channel closed

Closed by @versed cave

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[lusty yarrow]

#help-10 I was trying to use implicit differentiation to find $\frac{dy}{dx}$ in the function $e^{x+2y}=1$ so I used $e^{u}*u'$ to get $e^{x+2y}\cdot(1+2\frac{dy}{dx})=1$ but I dont know how to do the rest of the algebra

[warm shale]

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

[lusty yarrow]

the answer is -1/2 but I dont know why

[versed stratus]

try taking the log of both sides

[lusty yarrow]

natural log

[versed stratus]

and then differentiating

[lusty yarrow]

oh ok

[versed stratus]

yes

[lusty yarrow]

thanks

.close

[obtuse pebble]

Channel closed

Closed by @lusty yarrow

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.

[strong atlas]

hepl

[obtuse pebble]

@strong atlas Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[urban patrol]

is this enough to prove that p(t) is not a subspace of P_2

or is this wrong

[karmic fog]

The notation is a bit fishy, but the reasoning seems correct

[south cargo]

Yep this is enough

[urban patrol]

yeah probably a bit messy

I did the ? over the is an element of and then decided to just do the is not

and im writing in pen

[karmic fog]

I'd just make sure you write out your explanation in words if you need to turn this in somewhere, not just symbols

[urban patrol]

alright

thanks you two

.close

[obtuse pebble]

Channel closed

Closed by @urban patrol

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.

[fringe cedar]

for this one i tried to connect af and cf, i also tried extending bc and af so they intercept but i couldnt figure it out

i tried angle bisector serum but also no help

[fringe cedar]

i used similar triangles aeh and abc, and solved for square side with similar triangle ratio but keep getting wrong answers

,help

[warm shale]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[fringe cedar]

<@&286206848099549185>

[obtuse pebble]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[timid silo]

hello

which question?

[fringe cedar]

those 2

[timid silo]

pick one

[fringe cedar]

first

[tranquil sonnet]

you need to know AC

[fringe cedar]

how ;

[tranquil sonnet]

i can pick any triangle with sidelengths 3 and 4 and construct the figure

they should give you the length of AC

[fringe cedar]

so i choose onee?

💀

[tranquil sonnet]

wait no i got it one sec lemme solve

[fringe cedar]

ohh ty

[tranquil sonnet]

Ok heres a hint: let BF intersect AC at X. EF/BC=EX/XC

you know BC and you can find EX/XC

so try to find that ratio

[fringe cedar]

wait lemme solve

can u give a hint on how to find ex/xc

[tranquil sonnet]

ok

Let AC=x. EX=AC-AE-XC. Use similar triangles to find AE in terms of x, and use the angle bisector theorem to find XC in terms of x

[fringe cedar]

ae=x/3

[tranquil sonnet]

mhm

[fringe cedar]

x/ae=4/3

[tranquil sonnet]

what

x/ae=3

[fringe cedar]

oh shot

no it was

oh soo

xc/ax=4/3

[tranquil sonnet]

yea

[fringe cedar]

and ax=x/3 +ex

[tranquil sonnet]

yea

[fringe cedar]

heh

and then uh

wait why does ef/bc=ex/cx again

[tranquil sonnet]

DF and BC are parallel so EFX is similar to CBX

[fringe cedar]

oh O HOW DIDI NOT SEE THAT 💀

[tranquil sonnet]

lol

[fringe cedar]

i blind

wait so

what i do after i get cx/ax=4/3

;-;

help;

[tranquil sonnet]

rewrite them in terms of AC=x

[tranquil sonnet]

and then use this equatio

[fringe cedar]

ok

[fringe cedar]

so its like

xc/x/3 -ex

[tranquil sonnet]

what

[fringe cedar]

can i just have the rewritten equation

i gotta go like in 3 minutes

[tranquil sonnet]

ok

EX=x-x/3-3x/7

for the second problem just focus on the top triangle

[fringe cedar]

wait whats this

[tranquil sonnet]

EX in terms of AC

[fringe cedar]

ok

[tranquil sonnet]

AC=x, AE=x/3, XC=3x/7

[fringe cedar]

cx is 3/7x?

ohk

ty

bro this is suppose to be 8th grade math

how is this so hard

ty

[tranquil sonnet]

np

[fringe cedar]

also

how did u find what cx equals

3/7x

[tranquil sonnet]

by angle bisector theorem AX/XC=3/4 and AX+XC=x and solving the system gives the result

[fringe cedar]

ohh ok ty

i gotta go

ty bye

.close

[obtuse pebble]

Channel closed

Closed by @fringe cedar

Use .reopen if this was a mistake.

[tranquil sonnet]

cya

[obtuse pebble]

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.

[urban patrol]

I dont really understand this problem and how to use coordinate vectors

[warm canopy]

take the standard basis of P_3, {1,t,t^2,t^3}, then you can write a general element of P_3 a + bt + ct^2 + dt^3 as the coordinate vector (a,b,c,d) with respect to the standard basis

[urban patrol]

but how would that compare to the set given?

coordinate vector times standard basis I understand

[obtuse pebble]

@urban patrol Has your question been resolved?

[urban patrol]

<@&286206848099549185>

[obtuse pebble]

@urban patrol Has your question been resolved?

Channel closed

Closed by @urban patrol

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.

[solid crane]

idk why but some things just dont make sense to me

[solid crane]

So im converting from m/s to kilometers per hour and cant understand why the math is done the way it does

im doing this in more of a stochiometric way cause it is for chem

[tardy epoch]

1 km = how many meters?

[solid crane]

1000

[tardy epoch]

And 1 hour= how many seconds

[solid crane]

3600

[tardy epoch]

Convert one unit at a time

[solid crane]

this is how i set it up but its not correct

although the units cancel correctly

[civic zealot]

how are your 'seconds' unit canceling?

[solid crane]

oh wait

yea

its m/ s

im stupid

thanks

.close

[obtuse pebble]

Channel closed

Closed by @solid crane

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.

Please don't occupy multiple help channels.

Channel closed

Closed due to the original message being deleted

[obtuse pebble]

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.

[misty lintel]

Guys what is a reciprocal graph?

[misty lintel]

Initial graph I meant initial relation and reciprocal

God dam I found it “the inverse of a value or a number”

.close

[obtuse pebble]

Channel closed

Closed by @misty lintel

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.

[green sphinx]

Angle LMP and Angle LNP same, x = 10, angle LMP = 31, the arc is 2x inscribed angle, meaning PL is 62?

[obtuse pebble]

@green sphinx Has your question been resolved?

[sacred root]

Looks fair..

[obtuse pebble]

@green sphinx Has your question been resolved?

[shadow tangle]

@green sphinx looks good to me 👍

[obtuse pebble]

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.

[urban patrol]

Whats the formula for change of basis? either google and everything isnt giving me a set formula or im stupid

[violet sentinel]

you mean this?

[urban patrol]

no, for linear algebra

[violet sentinel]

oh change for basis

lul nvm

misread that

This might be what you're looking for

looks like the formula is B = V^(-1)AV

or somethin along those lines

[urban patrol]

yeah I had that written down but it doesnt make sense because wouldnt the Vs cancel out?

so i disregarded it

[karmic fog]

Matrix multiplication is not commutative

[urban patrol]

oh

[karmic fog]

ie, you can't reorder the multiplication to cancel the V's

[urban patrol]

so whats V supposed to be then

[karmic fog]

tbh I can't remember; it's been quite a while since i've done computational linear algebra

sorry

[urban patrol]

its okay

it looks like its supposed to be the change of basis matrix but thats what im trying to figure out

for the example its obvious since one of the basis is the standard plane

[obtuse pebble]

@urban patrol Has your question been resolved?

Channel closed

Closed by @urban patrol

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.

[amber dome]

Ok ima be afk for a while bc its 12 am for me

[amber dome]

but

if b(x) is the probability for winning a standard game of bingo where x is the amount of numbers called, what is the formula for b(x)

I figured out that if b is 4 it could look like 1/nCr(74,4)

but what about 5,6,7 up to 75

This assumes the board is 5x5 and has a free space

So someone help pls bc i want to get progress in my project beforeninsleep

[urban patrol]

the channel will automatically close if you do not check up on it every hour or so

[amber dome]

Oh

great

perfect

whatever

[urban patrol]

you can just put your question in another channel

[amber dome]

Ig

But anyways can u help

[urban patrol]

that matches what your question is about

#probability-statistics

[amber dome]

Ok thanks

.close

[obtuse pebble]

Channel closed

Closed by @amber dome

Use .reopen if this was a mistake.

[urban patrol]

im not sure how to do this

[obtuse pebble]

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.

[burnt bear]

Prove the second identity in De Morgan's Law. That is, suppose A and B are subsets of R (real numbers). Using U as our universal set, (A ∩ B)^c=A^c U B^c.

[burnt bear]

I just want to make sure the proof is right sorry for the bad quality

[royal basin]

too grainy to read

[burnt bear]

Is this better?

[royal basin]

ok yeah i can read this now

theres a nonzero amount of typos but the logic is there and it holds water

[burnt bear]

Ok ty

[obtuse pebble]

@burnt bear Has your question been resolved?

Channel closed

Closed by @burnt bear

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[frozen quest]

i am very confused

[frozen quest]

first i am confused if bernoulis distribution will be used here or not

can someone help me with this one

and killing the bird should be 1/3 so why is the answer 19/27

[timid silo]

yes sir. 1/3 and 19/27 have the same value

[frozen quest]

what?

[timid silo]

the fractions have the same value

[dusk widget]

?

[frozen quest]

19*3 = 57 not 27 bruh

[leaden ginkgo]

clearly they don’t..

[timid silo]

wait

[limber quartz]

he must be destroyed

[timid silo]

i thinks my brain is broken

[limber quartz]

🍴

[timid silo]

oof

right

then is should be 1/3

is it a math program?

cause its broken

[limber quartz]

I think this is a conditional probability question

[timid silo]

yeah (._.)

[limber quartz]

ah, let it go

[leaden ginkgo]

sorry

[frozen quest]

in some website it is 1/3 in some it is given 19/27. i am very confused

[timid silo]

there is no way you guys are typing this many messages for this problem

[timid silo]

yeah the website is broken

it happens

[timid silo]

Anil has a 1 in 3 chance to kill a bird.
What is the probability he kills a bird if given three chances?

[frozen quest]

bro leave please

[timid silo]

?

[frozen quest]

yeah he fires 3 shots

[timid silo]

Also get better questions

This one is gross

[frozen quest]

i have to get better questions to get my doubt solved?

[timid silo]

he fired three shots given that it takes 1 bullet to kill

Literally just reading comprehension problem not even math

💀

chance of killing bird in one shot = 1/3
chance of not killing in one shot = 2/3
chance of not killing in all three shots

mathematicians do not like comprehension

[frozen quest]

i am just asking, the answer given is 19/27

[timid silo]

no

yes

[timid silo]

@frozen quest tell this

[frozen quest]

then?

[frozen quest]

2/3 * 3?

[timid silo]

bruh

[frozen quest]

sorry i meant cube

not multiply

[timid silo]

yes write

2/3 * 2/3 * 2/3

$$ 1 - P(x)$$ Where P(x) is the probability of it not happening

[warm shale]

Brandon H

[timid silo]

which is 8/27

[frozen quest]

but my doubt is why not 1/3? i mean he is shooting 3 times and he can get the target 1 time

[timid silo]

it's a probability

not guranteed to happen every three times

a coin has a 50% probability to land on heads

doesn't mean it has to land on heads the 2nd or first time

[glossy basalt]

side note: poor bird🐦

therefore I'm guessing it's 19/27

[timid silo]

yea so suppose he gets it in the first time then probability is 1/3
but let's say he missed the first time and got the second time then probability is (2/3)(1/3)
then let's say he missed twice and gets it in third time which will be : (2/3)(2/3)(1/3)
Now you add all three of these cases

[glossy basalt]

it's like
first shot:
Case 1: dead bird
Case 2: alive bird
second shot
Case 1: dead bird
Case 2: alive bird
third shot
Case 1: the bird must be dead

[frozen quest]

ok noice and thanks

got it now

.close

[obtuse pebble]

Channel closed

Closed by @frozen quest

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.

[north anchor]

help

[quaint glen]

help with what

[north anchor]

i dont understand

[glossy basalt]

which part?

[north anchor]

I apply

[glossy basalt]

you might have to use "double angle formula" for convenience

[glossy basalt]

although this is also do-able

[north anchor]

yes i apply but i dont know howw continue

[glossy basalt]

1-2sin²x=cos(2x)

[glossy basalt]

do you mean this?

[north anchor]

is 1/2 squared?

[glossy basalt]

yes

[north anchor]

where

[glossy basalt]

(sin(2x)cos(2x))²

(½ sin(2x+2x)+ sin(2x-2x) )²

therefore the ½ is squared

[north anchor]

okay

oh and comes out?

[north anchor]

a i traslate wrong sorry

how i can continue

[glossy basalt]

oh

(sin(4x))² this?

[north anchor]

yes

[glossy basalt]

have you learnt these?

[north anchor]

no

[glossy basalt]

so anything you've learnt about cosine so far?

cos(a+b)=cos(a)cos(b)-sin(a)sin(b) this?

[north anchor]

i have super heagon

yes

[glossy basalt]

we need something more than that

[glossy basalt]

use this

take a=4x, b=4x

[north anchor]

a i dont understand

why you use that formula

[glossy basalt]

it's for the next step

try first

[north anchor]

with this formula?

[glossy basalt]

yes, with a=4x, b=4x

[north anchor]

cos16x - sin16x?

[glossy basalt]

nope

be careful

[north anchor]

cos^2(4x) - con^2(4x)

[glossy basalt]

cos(8x)=cos²(4x)-sin²(4x)

next, use
sin²a+cos²a=1
to change cosine² to sine² and 1

[north anchor]

o okay

[glossy basalt]

how is it so far?

[north anchor]

I'm confused sin^2 can be other formulas as I know which is more convenient.

[glossy basalt]

ok

[glossy basalt]

is this ok?

if yes, I'll continue

[north anchor]

How do I know which one to use? if i have more formula

[glossy basalt]

to be honest, it is by experience

but of course, the more you know and practice you make, you can easily found which to use

[north anchor]

ow

use 1- cos^^2 (x)

[glossy basalt]

,align
\cos(8x)&=\cos²(4x)-\sin²(4x)\
\cos(8x)&=(1-\sin²(4x))-\sin²(4x)\
\cos(8x)&=1-2\sin²(4x)\
\cos(8x)-1&=-2\sin²(4x)\
1-\cos(8x)&=2\sin²(4x)\
\frac12(1-\cos(8x))&=\sin²(4x)\
\sin²(4x)&=\frac12(1-\cos(8x))

[warm shale]

Biscuity

[glossy basalt]

using this would not get to the result we want

[north anchor]

i get the answer thx for the help

[obtuse pebble]

@north anchor Has your question been resolved?

[obtuse pebble]

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.

[slate kayak]

Hey, how would i do this with inclusion exclusion

as in

|A U B| = |A| + |B| - |A ∩ B|

[errant lark]

You will still have to think somewhat as it says at least 2 are in set A.

[errant lark]

Of course, this still works.

So tell me. What do you make of this: At least 2 of the members in set A are not in set B.

[slate kayak]

|A| has to be greater than or equal to 2

[errant lark]

Nope.

[slate kayak]

wait

|A| means everything

[errant lark]

|A| is given as 50.

[slate kayak]

right sorry

[errant lark]

No problem. just think more.

[slate kayak]

i mean |A| - |A ∩ B| = <2 (greater than 2)

[errant lark]

Yes

[slate kayak]

yeah i just forgot that |A| is everything including the intersection 😭

[errant lark]

So, you can find a lower bound on |B-A|.

[slate kayak]

is |B-A| the same as |B| - |A|

i guess it shoul dbe

[errant lark]

I don't think so.

See this: A = {1,2,4} B = {a,b}
|A| - |B| = 1

While |A-B| = 3

[slate kayak]

oh yeah cool

|AUB| = |B| + <2 = <55

but i guess i dont need |AUB| hmm

i'm thinking about |B-A|

|A-B| = <2 as well right?

[errant lark]

Here, also, what you have written only works for this question.
If you look closely, that condition translates to this: There are at least two people in A who are not in B. Now, Set which has all the elements of A which are not in B is (A-B).
So, you should say that |A-B| >=2

However you are correct here as well, since A - (A ∩ B) = A-B.

[slate kayak]

oh yeah we have the same rationale

<2 in my definition means more than 2

[errant lark]

You have this wrong. Sign should be inverted as i just explained above.

Also, A-B is not same as B-A. So be careful.

Why don't you try making a venn diagram ?

[slate kayak]

isn't it the same thing?

i defined my own definition of numbers greater than 2

<2

so wouldn't this just mean |A-B| = <2 -> |A-B| is a number greater than 2

[errant lark]

|A-B| = <2 and |A-B| >=2 are same things ?

[slate kayak]

which with inequalities is |A-B| >= 2

[slate kayak]

no

i mean like

this would be |A| - |A ∩ B| >= 2 mathematically right

i just used this symbol of <2 to denote greater than 2

therefore whole new definition

anyway i should probably stick to mathematical definitions lol

btw i'll be back, and then can we continue the problem then? @errant lark

i'll ping you

[errant lark]

Sure.

[errant lark]

Ah. Well, stick to mathematical notation. Lol

[obtuse pebble]

@slate kayak Has your question been resolved?

[obtuse pebble]

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.

[pearl aurora]

Hello quick question: -2m^3+8m^-8m is not a quadradic equation right

?

[high lily]

not even an equation

also what's with the
^"

[chrome crypt]

Ram can you take a look at my question if you can?

If not no worries and have good day or night.

[pearl aurora]

how can I find a quadratic equation?

[chrome crypt]

A quadratic equation is to the degree of 2

x^2

The function you listed is x^3 with a degree of 3.

Quadratic functions are parabolic in nature, like an arc.

We can perform some transformations to the function

(x-2)^2 + 8

still a quadratic function always remember the leading degree dominates.

[pearl aurora]

ok

thanks

.close

[obtuse pebble]

Channel closed

Closed by @pearl aurora

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.

[tulip steeple]

hows it 1 + 1/sqrt(2) --> that (2nd line)

[tulip steeple]

$innit ((2 + {\sqrt2})/2$

[warm shale]

™Vlad The Lad

[tacit scarab]

??

[tulip steeple]

what?

[tacit scarab]

^

what you trying to type

[tulip steeple]

that

u can make sense of it cuz of brackets

[tacit scarab]

$\frac{2+\sqrt{2}}{2}$

[warm shale]

WhereWolf

[tacit scarab]

it should be this

[tulip steeple]

so hows they get this

[tacit scarab]

it's wrong

,w 1+(1/(sqrt(2)))

[warm shale]

Results provided by WolframAlpha

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

Requested by _wherewolf_

[tulip steeple]

does the rest of the working make sense or is it all wrong - could be typo
i cant tell tho

[tacit scarab]

there's another mistake

[tulip steeple]

might need context

[tacit scarab]

the minus sign is missing in the last line

[tacit scarab]

what trashy site is this

[tulip steeple]

cambridge

[tacit scarab]

two mistakes in one question

[tulip steeple]

textbook

[tacit scarab]

bruh

[tulip steeple]

lol

idek what they tried to do here

[tacit scarab]

pi/2 is 90 degrees

so use Pythagoras theorem

[tulip steeple]

so why find the magnitude of op oq

whatever imma ignore it - i doubt imma do smth like that on a test, is why

main thing was the typo ig

🙂 ty

.close

[obtuse pebble]

Channel closed

Closed by @tulip steeple

Use .reopen if this was a mistake.

[tacit scarab]

bro the magnitude are the sides of the triangle POQ

[tulip steeple]

how

.reopen

[obtuse pebble]

✅

[tulip steeple]

dot product or smth

[tacit scarab]

draw the triangle POQ

[tulip steeple]

ye i drew it

[tacit scarab]

PO and QO are the shorter sides

PQ is the hypotenuse

[tulip steeple]

well u cant assume its 90 degrees?

until answer?

or

[tacit scarab]

it's the converse of Pythagoras theorem

if a^2+b^2=c^2 then it is a right triangle

[tulip steeple]

ah ye

ag

.close

[obtuse pebble]

Channel closed

Closed by @tulip steeple

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.

[tulip steeple]

for this question why cant you just do pi/2 - a = sin^-1(0.4)

[tulip steeple]

i get pythagoraron identity works but should that also

,w solve sin(2x+pi/3) = 0.5

[warm shale]

Results provided by WolframAlpha

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

Requested by vladthelad69

[wet moss]

because then you are saying that sin(pi/2 - a) = 0.4

[tulip steeple]

and is that wrong

[wet moss]

yes

[tulip steeple]

since sin(theta) = 0.4

and pi/2 - a = theta?

or not why

[tulip steeple]

thats what i see

[wet moss]

no pi/2 - a doesnt equal theta

[tulip steeple]

why

cant you set it as a variable

[wet moss]

because it just doesnt

[tulip steeple]

k then

[wet moss]

they are all constants

none of them are variables

[tulip steeple]

and how would you do these

i got x = -pi/12

but since domain is positive

that means its in qudarant 1 and 2 since sin?

[wet moss]

???

there is no x

you arent setting that sin expression equal to anything

you are trying to find the value of it, so you wouldnt set it equal to something

[tulip steeple]

the question is solve for quation for x, where 0 < x < 2pi

[wet moss]

oh

is it a different question?

[tulip steeple]

yep

[wet moss]

oh mb

[tulip steeple]

ag

i wasnt specific

since sin(x) = +ve value we infer that its in quadrant 1 and 2 since thats where sin is +ve right?

[wet moss]

first find all of the solutions to sin^-1(0.5) around that region

because there will be more than just -pi/12

[tulip steeple]

how is my issue

11pi/12 is 1. --> -pi/12 + 12pi/12

but idk rest

[wet moss]

you cant do it that way i dont think

you cant just find one value of x and then do pi - x to get the rest

you have to find what 2x + pi/3 is equal to

and then find x for each of those values

[tulip steeple]

pi/6

[wet moss]

all of them

thats only 1

[tulip steeple]

how

[wet moss]

sin^-1(0.5) = pi/6, 5pi/6, 13pi/6, 17pi/6 ...

there are infinite solutions

[tulip steeple]

how do you get the other values

tho

like, how

what formula

what i do

etc

xd

[wet moss]

sinx = sin(pi - x)

sinx = sin(2pi + x)

keep doing that and you will get enough values of x for the domain you want

[tulip steeple]

im confused wheres the sin?

whys there 2

$2x + pi/3 = sin^-1(0.5) = pi/6 is what ik$

[warm shale]

™Vlad The Lad

[wet moss]

pi/6 isnt the only solution to that

if you look at the unit circle you want to see all the places where sinx has the same value

since sinx is the height then there will be 1 place that sinx has the same value

within 0 and 2pi

and that would be with pi - x

and if you wanted to get back to the first value on a second revolution of the circle you would use 2pi + x

[tulip steeple]

nice ty

.close

[obtuse pebble]

Channel closed

Closed by @tulip steeple

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.

[hard citrus]

can someone help me with this?

[obtuse pebble]

@hard citrus Has your question been resolved?

[obtuse pebble]

@hard citrus Has your question been resolved?

[hard citrus]

.close

[obtuse pebble]

Channel closed

Closed by @hard citrus

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.

[patent zealot]

There is a rectangle of dimensions 4 × 3 and we have 6 points in the rectangle. Prove that there are two points within a rectangle of dimensions 4 × 3 are positioned at a distance no greater than √5. Pigeonhole principle should be used, but I don't have an idea how to divide the rectangle. It probably should be divided into 5 parts somehow.

[patent zealot]

there was this idea by a fellow from here

but i'm not sure

[shell wave]

split it into rectangles 2x1

[errant lark]

Sqrt(5) or 5?

[haughty coyote]

sqrt5

[errant lark]

Maybe i just don't fully understand the question.

So, end points of diagonal have distance 5. Right?

So, what's exactly the premise of question?

[shell wave]

oh there are 6 points

[haughty coyote]

how about taking 4 areas in the corners, and 1 in the middle, based on these circles ?

[patent zealot]

yess there are 6 points and because we are supposed to use dirichlet's principle

[haughty coyote]

not neccessarily rectangles, but something to make that work

[timber fox]

this was the main idea

[haughty coyote]

is it that nontrivial to actually construct them ?

[patent zealot]

but i think if we need to prove it there should be equal triangles/rectangles, if we construct it in that way we are getting one bigger part in the middle

[patent zealot]

sqrt 5

if we had 7 points it would be much easier because we could split them into 6 equal rectangles

[haughty coyote]

a sqrt(2)*sqrt(2) square in the middle
Some complementary polygons in the corners ?

it should work

it definitely works

[patent zealot]

i found this

what is this sorcery

ahahahahha

[timber fox]

the circle strategy holds true

LESSGOOO

[timber fox]

that's cool

[obtuse pebble]

@patent zealot Has your question been resolved?

[obtuse pebble]

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.

[tacit scarab]

for the first question

it seems ok

[open relic]

🙏 wait fr??

i cant even tell i struggle that much with this topic

[tacit scarab]

wait

isn't there 4 runners

why8C3

[open relic]

typed in wrong but good eye

Putting it like that, maybe uh. 7 * 9! for both ways?

From there (7 * 9!)(7 * 9!)....?

And considering duplicates so (7 * 9! )/ (3! * 2!)

Oh wait

[tacit scarab]

how

[lusty goblet]

Wait, I found a better solution for i

There are 8 possible slots for 3 I's right? How many possible assignments are those? Then you can fill the rest as usual.

[open relic]

Yep

[open relic]

How would we consider the duplicates then?

[tacit scarab]

we don't need to in this case

we place the I's first

then the other letters

[fickle lichen]

is it fine if i write down the solution and send it here?

[tacit scarab]

!nosols

[obtuse pebble]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[fickle lichen]

ok

[lusty goblet]

That's exactly what I mean.

[open relic]

why wouldn't we?

most examples of similar questions ive seen do consider the duplicates

[lusty goblet]

There is no duplicates when assigning 3 I's to 8 slots

and the remaining 7 slots can be determined by whatever not filled by I.

[tacit scarab]

oh I remember answering the exact question and struggle with it

do someone know how to explain

[fickle lichen]

what we can do is this D* E * F* N * N * T * O

the stars are the possible places for i

so we have 6 stars

[lusty goblet]

So something like DEFINITION is uniquely determined by DEFNTON and ___I_I_I__

[fickle lichen]

so we can do 6c3 to choose the places

[tacit scarab]

you forgot the sides

[lusty goblet]

I can be placed together

[fickle lichen]

and we can arrange rest of the letters by 7!/2!

[fickle lichen]

we dont do the sides as "i" cant come on first and last

[open relic]

but can't i be arranged together?

[tacit scarab]

oh my bad

[open relic]

my heads spinning man im sorry

[fickle lichen]

ahh

well then what we can do is use set theory

[open relic]

so minus i from the first and last positions?

• 3

[fickle lichen]

n(A u B) = n(A) +n(B) -n(A "inversection" B)

A being the cases when i is the first letter

[open relic]

1 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2

[fickle lichen]

B being cases when i is the last letter

[lusty goblet]

Well, to solve the combinatorics, you can think about how to generate the desired output. In this case, the algorithm is:

1. Fill random 3 slots with I
2. Generate a random word from DEFNTON
3. fill the rest of the slots from the word generated at step 2 left to right.

[fickle lichen]

and n(A intersection B) being cases where i is in first and last places

did i mess up?

[lusty goblet]

That's what I've been thinking, but it's longer, but the result is the same

[fickle lichen]

ahh

[open relic]

3 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

Cuh my understanding must be flawed

[fickle lichen]

so 3*9!

huh

lemme try solving this on my own

i will be back

[open relic]

and then times that by 9! * 3 for cases where i is at the end, same thing

10! - 9!x3x9!x3

[open relic]

Could you explain?

by duplicates i mean the same letter

[lusty goblet]

Oh, I thought duplicate states

First, place the I's

[open relic]

if 1 of 3 of the Is is assigned to a position, that's the same as another I being assigned there instead

up until what iunderstand the total possibilities would be 10! / 3! * 2!. 2 for the 2 ns and 3 for the 3 is.

[fickle lichen]

ya thats correct

I GOT IT

its pretty simple

idk why i was overthinking this

so we use total possiblities which is 10!/2!3!

then the possibilities of getting i in the first place is the same as getting i in the last place

which is

[open relic]

oh lord 🤲 i feel so good

[fickle lichen]

9!/2!2!

2! for i and 2! for n

we subtract this twice coz 1st place and last place

finnaly we take the last case which is i appearing at both first place and last place

which is 8!/2!

2! for n

thats it

lmk if i messed up

and also if u didnt understand sumn

2nd part of the question is very easy i think u wouldve figured it out

[open relic]

hrmm

[fickle lichen]

all 3 i come together

[open relic]

i dont udnerstand whats up with the 2! tho

division by 2!

in 8! nd 9!

[fickle lichen]

so why we divide by 2! is bcoz of duplicates

[lusty goblet]

There are 2 N's

[fickle lichen]

we have 2ns

and 2Is

[open relic]

no no as in

where did the 3! for the is go

Is

[fickle lichen]

we already arranged 1 i

so we have to arrange only 2 i s

not 3 i s

we arrange an i in the first place

and as for the case with 8! where i appears at the first place and last place we only have 1 i left to arrange which is why we divide by 2! only once for the N's

[lusty goblet]

Yeah, but we assign 3 I's at once, there are 8 possible slots, we pick 3 slots, not one-by one.

By deciding that the assignment is _I__I___I_, we don't have to worry which I is on which slot.

[obtuse pebble]

@open relic Has your question been resolved?

[obtuse pebble]

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.

[nocturne laurel]

hi

[nocturne laurel]

can anyone help with the hint?

[royal basin]

8 or 9?

[nocturne laurel]

9

[royal basin]

oh ok 9

[proper kelp]

Using product to sum

[royal basin]

the hint is typo'd

they meant $\sin(\alpha)\sin(\beta) = \frac{\cos(\alpha-\beta) - \cos(\alpha+\beta)}{2}$

[warm shale]

Ann

[royal basin]

apply this formula to what's under the integral

[nocturne laurel]

oh ok

thx for the help

.close

[obtuse pebble]

Channel closed

Closed by @nocturne laurel

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[heavy zephyr]

How is this done?

[royal shard]

you want to solve for x?

[heavy zephyr]

yes

[royal shard]

i would first combine the fractions on the left

therefore we need a common denominator

[heavy zephyr]

yeah I did cross multiplying

3x+4/(x+1)(x+2)

[urban patrol]

the right fraction can be simplfiied

[heavy zephyr]

then I changed the 3 on the rhs to 3x^2+x-30

but somehow all of this leads me to some really high numbers that don't look like an answer

[timid silo]

you would want to make sure if that 3 is 3 + the fraction or 3 times the fraction

[heavy zephyr]

it's 3+ the fraction (in germany we normally denote it like this)

[timid silo]

https://math.stackexchange.com/questions/3084571/mixed-fractions-and-multiplication-with-variables

[heavy zephyr]

ahhh shit

I found it

its the third binomial

now it says: 3x+4/(x+1)(x+2) = 3x+4/x+3

and since it has to be 0 I just do the nominator

[timid silo]

wait where does that (3x+4)/(x+3) come from

shouldn't it be (3x+10)/(x+3) instead?

[heavy zephyr]

3+ (x-3/(x+3)(x-3)) so we can cancel the x-3 and have 3+ 1/x+3

so we do (3*(x+3) +1)/x+3

I hate not being able to do latex because im too lazy to learn

[timid silo]

yea and 3*(x+3) + 1 = 3x+10

[heavy zephyr]

oh yeah

oop

thanks

doesnt change too much tho

[timid silo]

well it gets ugly with a 3-degree polynomial tho

if you don't mind solving it then cool

well actually if you interpret the right hand side of the original equation as 3 * fraction then you can get a much more pleasant solution

[heavy zephyr]

why 3rd degree polynomial? isn't it 3x^2+10x+2=0? If you ignore the denominator and check later if answers are even useable?

[timid silo]

no you cannot reduce the denominators because they are not equal

LHS = (3x+4)/(x+1)(x+2)

RHS = (3x+10)/(x+3)

[heavy zephyr]

oh right. I mean I thought about that and just did *(x+3) but obviously if you do -3x - 10 you can't just subtract

...

[dusk widget]

wait why does the RHS have a numerator of 3x+10

[timid silo]

he interpreted it as 3 + the fraction

[dusk widget]

oh what the hell

[heavy zephyr]

you don't do that in other countries?

[dusk widget]

I never have, no

[timid silo]

yea it's very uncommon

[heavy zephyr]

we always do it in germany lol

[timid silo]

usually we don't apply mixed fractions to fractions that contain variables

[heavy zephyr]

but okay thanks for the help!

.close

[obtuse pebble]

Channel closed

Closed by @heavy zephyr

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[obtuse pebble]

@flat tundra Has your question been resolved?

[obtuse pebble]

@flat tundra Has your question been resolved?

[errant lark]

Do you know what's the area of an ellipse ?

[flat tundra]

I worked on it a little

[errant lark]

What's c ?

Ah. c is equal to ae. Alright.

So, yeah. This is totally correct.

Along the central line.

You'll have to be precise if you wanna write just that much.

[flat tundra]

If I want to be more specific what else can I solve for ?

[errant lark]

You can also calculate actual foci. Just define a coordinate system and give coordinates of foci.

[flat tundra]

How do I do that Given what i have

[errant lark]

Well, there are infinite ways to be honest.

Some of them are easier although.

See, all it comes down to is defining origin.

For example, you can define centre(intersection point of diagonal) of rectangle to be the origin.

Origin*

Now, you just say that coordinates of foci are (15.36, 0) and (-15.36, 0)

You can define origin at one of the corners so many ways.

[errant lark]

Just go with this one. Simplest.

@flat tundra Is that clear ?

Origin is always (0,0). 😐

Just write in your answer that you are defining centre(intersection point of diagonal) of rectangle to be the origin.

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[errant lark]

This is important.

[obtuse pebble]

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.

[timid silo]

are dot products distributive

[timid silo]

why didnt i just google that

.close

[obtuse pebble]

Channel closed

Closed by @astral night

Use .reopen if this was a mistake.

[robust sleet]

💀

[dark stirrup]

[obtuse pebble]

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.

[warped violet]

i need help with these

[forest sinew]

what is the purpose of what youve written next to 9?

[warped violet]

so i can see the numbers in the inequality more clearly

[forest sinew]

ah okay

[warped violet]

can u help

[forest sinew]

well what can you say about 10/9?

is 10/9 bigger or smaller than 1

[warped violet]

bigger

[forest sinew]

if you multiply a number by something bigger than 1, does it grow or shrink?

[warped violet]

grow

[forest sinew]

okay

so you start with 10/9

which is bigger than 1

and you multiply it by 10/9

which is bigger than 1

[warped violet]

what is it

[forest sinew]

what is what?

[warped violet]

u said multiply “it”

[forest sinew]

10/9

[warped violet]

10/9 by 10/9?

[forest sinew]

can you interpret what $\qty( \frac{10}{9} )^2$ means in words?

[warm shale]

jan Niku

[warped violet]

no

[forest sinew]

so thatd be the primary issue i guess

do you know what exponents are?

[warped violet]

yes

[forest sinew]

what does an exponent of 2 mean?

when you do x^2

say i told you to calculate 4^2

how would you do that? if you didnt have a calculator with an exponent button

its just 4 times 4, right?

[warped violet]

no

[forest sinew]

no?

which part

[warped violet]

my calc has a exponent button

[forest sinew]

lets say you have no calculator at all

how can you calculate 9^2

its okay to say you dont know or arent sure

im just asking because i think this knowledge will be helpful with the problems you posted

it will make them much easier to solve

[warped violet]

isn’t it like 9x9x9x9x9x9x9x9

[forest sinew]

well were talking about $9^2$

[warped violet]

wait

[warm shale]

jan Niku

[forest sinew]

but you are on the right track

exponents mean repeated multiplication

the exponents tell you how many times to repeat

[warped violet]

ohh

9x9

[forest sinew]

right

[warped violet]

ohh

[forest sinew]

so $\qty( \frac{10}{9} )^2 = \frac{10}{9} \times \frac{10}{9}$

[warm shale]

jan Niku

[forest sinew]

I was just using the logic we were talking about on this problem

10/9 starts bigger than 1

and then you multiply it by something bigger than 1 (namely, 10/9)

so does it end up bigger than 1? or smaller?

[warped violet]

ohh

should i simplify 10/9^2 then

to like

a whole nun

number