help-49

[hard shard]

guys please my run-escape buddies are making fun of me

[tawdry laurel]

yayayayaya

bro ts so nice

[pearl hull]

LMAO

[wintry knot]

Hello

[pearl hull]

Orange’s sus

[tawdry laurel]

also what is this channel for again

[pearl hull]

[tawdry laurel]

[wintry knot]

Wait this isnt general

[hard shard]

no, this is #help-49

[tawdry laurel]

imagine hat on this

[pearl hull]

It’s the place to celebrate Christmas

[tawdry laurel]

[olive matrix]

it does not

[bold peak]

Gotta backstab my previous highest role the moment I get a higher one

[rancid wolf]

Happy birthday

[hard shard]

nobody is explaining this to me

i thought this server was helpful

[tawdry laurel]

Welcome to mathcord @rancid wolf

[bold peak]

No you're helpful

[wintry knot]

Im the 831Santa

[tawdry laurel]

wrong place blud

[bold peak]

The server is mathcord

[olive matrix]

because it scales by 73 up to 2277

[tawdry laurel]

#「helpers-lounge」 for help

[tawdry laurel]

it has help in its name

[rancid wolf]

Thx

[hard shard]

ohhh ok

[olive matrix]

wait it's not 2277 anymore it's 2376

gross

[bold peak]

So does this channel lmao

[pearl hull]

:((

[tawdry laurel]

[hard shard]

why do they call it o/srs, why cant they call it o/j

[pearl hull]

Time to rename this channel specifically

[tawdry laurel]

💀

[bold peak]

If I was mod I'd do it for the meme

[slow thorn]

this is why

[bold peak]

My mod nomination thread just got auto rejected

[hard shard]

i have also met a committee why dont i get the role?

[pearl hull]

Were I a Smod, I’d archive this channel and create a new one

[hard shard]

this server is food-ist

[bold peak]

You're a garlic with three visible cloves

[flat spire]

merry

[pearl hull]

[bold peak]

I love this one so much

[hard shard]

that guy could use one of these

[pearl hull]

Sharing today’s wordle

[bold peak]

I clicked it before I read the description

Lmfao

[modern sapphire]

no hard mode 🥀

[pearl hull]

I would die 💀

[modern sapphire]

you already speedran it

[pearl hull]

Precisely speaking, perish

[bold peak]

I did yeah

[lyric charm]

tf is this

[modern sapphire]

Cant let the corporate know the business is down, so we are posing as customers ourselves

[twilit field]

stock buybacks

[bold peak]

Hlounge breaching containment

[pearl hull]

hlounge, Christmas edition

[slow thorn]

more active than hlounge

[sharp coral]

,tex the channel id is \bigfactor*{1018703621841494076}

[slow thorn]

awesome

[frail carbon]

[bold peak]

Okay now there's a legit help channel

Who wants to close this

[hard shard]

alright channels are back in swing

time to close up

[tawdry laurel]

[pearl hull]

.solved

[midnight plank]

Channel closed

Closed by @pearl hull

Use .reopen if this was a mistake.

[grand pond]

cloud ☁

[tawdry laurel]

💀

[paper prism]

. What was that

[tawdry laurel]

Helpful shenanigans

[midnight plank]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[native epoch]

how to do this im kinda in a rush

[native epoch]

man i cant even sleep

gotta stay up for 26 hours just to do this

[vapid nacelle]

whats your specific question

[native epoch]

i keep dragging it and stuff but its not working and tells me to drag it again 🙉

it says "compare angle dab and angle bcd as you drag the vertices in the figure above. update your asnwer to reflect this relationship"

[vapid nacelle]

hmmmm, wont ask it from a technical issue then, i suppose you need to determine what are always true and what isnt?

[native epoch]

yes

deltammath wouldnt bug like that

im probably just doing something wrong

[lyric charm]

why are you committing such reckless acts of sleep deprivation

[native epoch]

10 point bonus bro

[vapid nacelle]

do you have any specific statements which you are unsure is true and what isnt always true?

[native epoch]

i got like 2 projects for other classes too

might stay up an extra 2 hours

[native epoch]

well i mean im pretty sure my answers are mostly correct

[vapid nacelle]

ok lemme take a look

[native epoch]

hmm

im pretty sure opposite sides are always congruen

oh man i didnt get enouugh sleep for this

class is in like 2 hours

[vapid nacelle]

if you have a quadrilateral form some more irregular ones

[native epoch]

it says 93% done

[vapid nacelle]

do a trapezium for example

[native epoch]

what is that 🙉

[vapid nacelle]

drag D and A out diagonally

are opposite lines always parallel?

try these for example

[native epoch]

yes

it is a "parallelogram"

[vapid nacelle]

a parallelogram is part of a quadrilateral, but not all quadrilaterals are parallelograms

[native epoch]

C doenst let me drag 🤷‍♂️

it only moves the shape around

[vapid nacelle]

what can you drag then

[native epoch]

every other point

it goes in and out

for a b and d

[vapid nacelle]

ok so anything but c?

[native epoch]

ye

[vapid nacelle]

drag D and A into a trapezium or trapezoid and verify whether opposite lines are always parallel

[native epoch]

i refreshed it and it works 🤷‍♂️

ok

oh its back to it again

[vapid nacelle]

yep because quadrilaterals are just anything with 4 sides

[native epoch]

guess i cant drag c

[native epoch]

i dont think i can make a trapezoid wth this

its onlly turning into squares and rectanges and the parallelogram shape

[vapid nacelle]

hmm, alright, i will work with the assumption that you can only form squares, rectangles, and parallelograms instead

[native epoch]

yes

[vapid nacelle]

would love to help but perhaps opening another ticket would be better 🙂

[real delta]

Alright

Omg I didnt even see it that I was commenting here

sorry

[native epoch]

well theres a drop down menu

[real delta]

No I thought I clicked on the prealg channel

I wanted to ask there

[native epoch]

it says four side lengths, four angle measures (vertices), four slopes of sides, lengths of diagonals, measures of angles cut by diagonals, measure of angles, intersection of diagonals

idk what it wants me to do though

[vapid nacelle]

when they mean diagonals are congruent they mean the length?

[native epoch]

probably the line

around the shape

[vapid nacelle]

consider this

[native epoch]

idk mines doesnt have markings like that

bro like lowkey

i need to get this done asap

[vapid nacelle]

<@&286206848099549185>

[native epoch]

ts gonna be late and im not gonna get my 10 bonus points 😭

[vapid nacelle]

the restriction to quadrilateral but only allows parallelgrams squares and rectangles really confuses me

[native epoch]

what kind of teacher sets the due date at 7 am 🙏

[slow thorn]

well it asks the user to drag the point until it turns dark

[vapid nacelle]

. for helpers

[native epoch]

ye i did

[slow thorn]

and i really dont know if it works

can you possibly send a recording of dragging it or sth

[native epoch]

it physically wont let me turn it into something else 🤷‍♂️

[native epoch]

nah i dont think i can do that on a school laptop mb

[native epoch]

yeah well the diagonals are the things that connect to the center point, e

idk if they bisect eachother though

99% they are congruent though

[vapid nacelle]

if you know that opposite sides are congruent, then lets take a parallelogram for example

have you learnt the concept of hypertenuse

[native epoch]

ye in algebra

[vapid nacelle]

you have two parallel horizontal and two parallel vertical lines

[native epoch]

a^2+b^2=c^2

[vapid nacelle]

both hypertenuse are from one horizontal and one vertical line

[lilac finch]

eh did you try rhombus?

[native epoch]

well yes i learned that in 5th grade math 🤷‍♂️

[vapid nacelle]

yeah so diagonals are congruent in that case

[native epoch]

yeah i already put that there

[vapid nacelle]

therefore it will be always true if you only working with parallelograms, squares and rects

[native epoch]

im tryna see if the diagonals bisect eachother

maybe it ends at e and each one is just a new one extending from each poiint

[vapid nacelle]

do u want me to tell you the answer or guide you to it

[native epoch]

i kinda do need the answer and i think i understand the concept well enough 🤔

[vapid nacelle]

yes they do

for squares rects and paras

[native epoch]

alr this is kinda what i have so far

[slow thorn]

maybe try dragging it a bit more once again and sending another screenshot of it?

[vapid nacelle]

anything else?

[native epoch]

not always true:
all four sides are congruent, all four angles are congruent, diagonals instersect at a right angle, diagonals bisect interior angles,
always true: opposite sides are congruent, oppositie sides are parallel, opposite angles are congruent, diagonals are congruent, diagonals bisect eachother

[vapid nacelle]

ok looks fine to me

[vapid nacelle]

ok then, should be fine

[native epoch]

doesnt let me submit

"compare the length of diagonal AC and the length of diagonal BD as you drag the vertices in the figure above. Update your answer to reflect this relationship"

[vapid nacelle]

hmm

do you know the angle then

[lilac finch]

mm..diagonals of a parallelogram are not always congruent

[slow thorn]

yeah this is perfect (not meaning the answer table)

[vapid nacelle]

oh yes you are right

they arent equal but does bisect

[native epoch]

ead is 45, eba is 37, ecb is 45, edc is 37, eab is 27, ebc is 72, ecd is 27, eda is 72

measurement

of the angle

(degrees)

[native epoch]

oh lets go i got it right

[native epoch]

yk cuz im actually doing a project on oppenheimer

[lilac finch]

https://tenor.com/view/nuclear-explosion-nuclear-fission-warhead-meme-dog-puppy-gif-17955887116502039290

[native epoch]

🥶 these questions are hard

they technically are correct for the answers

but the system doesnt like it

would a paralellogram always add up to 360

[lilac finch]

yes

[native epoch]

is it becuase it has 4 sides

[lilac finch]

every quadrilateral

[native epoch]

hmm

so

[lilac finch]

yes a closed figure with 4 sides

[native epoch]

every side adds 90 degrees

cuz like in a square

[lilac finch]

nah

[native epoch]

you annotate it with 90 degree marks

90+90+90+90 = 360

[lilac finch]

yeah only in squares and rectangles

[native epoch]

ok

wait what

slope?

https://tenor.com/view/sweating-nervous-gif-21041319

[lilac finch]

?

[native epoch]

how am i supposed to do this

[lilac finch]

ts same question?

[native epoch]

its different structure though

they change the measures

[native epoch]

theres lik 3 questsions on this section

[lilac finch]

hmm.. slope of a line = tantheta

if slopes are equal then lines are parallel

[native epoch]

only the parallel slopes are equal thoough

they arent the same 🙉

[slow thorn]

you can change the dropdown here and experiment

[native epoch]

yeah i was doing that

but the thing is

i dont have time to experiment

its almost 5 am 😭

[lilac finch]

lmao

[lilac finch]

sleep

[native epoch]

cant ill only get an hour of sleep

and im a heavy sleeper

[lilac finch]

you are cooked

[native epoch]

ill just sleep during math class

[slow thorn]

is there an option to measure the angles?

[native epoch]

yes

it gives you the measures of the angles

theres 2 options though

measure of angles, cut by diagonals and measures of angles, intersection of diagonals

[lilac finch]

wdym

[slow thorn]

then maybe you can drag and check opposite angles again first

[native epoch]

yes and i still have 2 projects i gotta turn in when i walk into the room

[native epoch]

which option do i pick

[lilac finch]

1

[lilac finch]

mm diagonals bisect each other should be true

[native epoch]

its 23 and 67

ok

i have

in not always true

all four angles are congruent

opposite angles are congruent

diagononals are congruent

diagonals intersect at a right angle

always true

all four sides are congruent

opposite sides are congruent

sum of all angles equals 360

diagonals bisect interior angles

diagonals bisect each other

and opposite sides are parallel

[slow thorn]

this one first

[native epoch]

what

[slow thorn]

here the opposite angles

[native epoch]

well they are congruent

[slow thorn]

yeah

[native epoch]

alr now it says

[slow thorn]

and you can try with another quadrilateral too

[lilac finch]

den check dis

[native epoch]

"look at the angles formed by the diagonals of the figure as you drag the vertices in the figure aboe. update your answer to rflect this relationship"

[slow thorn]

actually not this option

what about just the "measures of angles" option

[native epoch]

the "four angle measures (vertices) one?

[lilac finch]

yes

[graceful sleet]

what's 6 + 7 + 6 + 7 + 41

[native epoch]

alr it says

dab is 94

abc is 86

bcd is 94

cda is 86

[graceful sleet]

wow u smart

[lilac finch]

!occupied

[midnight plank]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[graceful sleet]

im js a 7th grader

[slow thorn]

yeah

[graceful sleet]

okay

[slow thorn]

you can see the opposite angles being equal

[native epoch]

yeah they are

[slow thorn]

it should be equal for other such quadrilaterals you form here too

[native epoch]

well the shape itself should kinda share the characteristics between its forms

[slow thorn]

so that should be in the other section

[slow thorn]

yeah

[native epoch]

this is what i have rn

[slow thorn]

i mean uh in this example

[native epoch]

lemme get a screenshot

[slow thorn]

ok just two more

now about the sides of the shape

if thats in one of the options

[native epoch]

do i select the four side lengths option

[slow thorn]

yeah

[native epoch]

all of them are the smae

same

2.63 for all

[slow thorn]

ok alright..

so thats a rhombus

[native epoch]

interesting indeed

[slow thorn]

then only one more to clarify

this one

not sure what option allows you to check this one though

[native epoch]

idk if thats a right angle

[slow thorn]

hmm do you have the option list or something?

like everything the dropdown shows

[native epoch]

wait what

it lets me

submit now

🤔

do i do it

[paper prism]

The diagonals of a rhombus do make right angles, you put it in not always.

[native epoch]

oh i did

[paper prism]

nvm then

[native epoch]

oh yeah i think if all of the measures of the diagonals are exact

it means its a right angle

cuz its straight

[paper prism]

hmmn, that reasoning seems off but you could either show it with congruence or interior angle sum rule by this image

[native epoch]

wha is interior angle sume rule

[paper prism]

The sum of all angles in a triangle sums to 180 degrees

all interior angles*

[native epoch]

but its not a triangle

[paper prism]

it makes four small triangles

[native epoch]

😲

[paper prism]

the two angles add to 90, so the angle made by the diagonal has to be 90 so that their sum is 90

[native epoch]

it actually does

[clever sedge]

<@&268886789983436800>

Of course they will let someone with no roles mention over 300,000 people

[olive matrix]

it doesn't actually mention anyone

[clever sedge]

Yes I know

Sarcasm

😂

[midnight plank]

@native epoch Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

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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.
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• 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.

[long geyser]

hey guys! i just need help on c

[long geyser]

i know it's t'(2) but could someone help explain why?

[bold peak]

What does the derivative represent

[gaunt jetty]

erm am i having deja vu or

[long geyser]

lmaooo i asked this question already hehe but only for a and b

i came back for c

[long geyser]

umm im actually not sure

[gaunt jetty]

do you remember what T'(h) was

[long geyser]

how would i know? NOT SARCASTIC but like how would i figure that our

[gaunt jetty]

okay actually imma just circle back to what xavier said

like

the derivative is meant to tell you the instantenous rate of change of a function, right?

[long geyser]

isnt it seconds over meters

yap

[gaunt jetty]

ok so

The derivative T'(h) reprsents the rate of change of time with respect to distance. In simpler terms, it is basically asking "How much extra time does it take to fall if we add a tiny bit more distance to the drop?"

does this make sense @long geyser

[long geyser]

$T'(h) = \frac{2^{\frac{1}{2}}{|g|^{\frac{1}{2}} * \frac{1}{2}h^{-\frac{1}{2}}$

[grand pond]

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

[long geyser]

wow i worked so jard

[gaunt jetty]

ignore the equation

dont worry about it

[long geyser]

ohh okay

[gaunt jetty]

i dont think they want you to use it at all which is why i deleted my message

[gaunt jetty]

So let me give you a question

assume you drop a ball from the top of the building you are on

[long geyser]

yes yes i love when ppl do this

[gaunt jetty]

would it be falling faster right after the moment you dropped it, or after maybe 5 seconds?

[long geyser]

maybe after 5 seconds? cuz of accelaration?

[gaunt jetty]

yeah!

exactly :D

[long geyser]

yes!

[gaunt jetty]

so

for your question at 2 metres, the ball hasnt been falling for very long right

so would it take a noticeable amount (relatively) to travel an extra metre or not?

@long geyser

[long geyser]

ohh yeah it would right? compared to when its been falling for a long time it wouldnt really matter

[gaunt jetty]

yeah

but at 20 metres

the ball has been falling for a while and gravity accelerated it a lot

[long geyser]

mhm

[gaunt jetty]

so, same quetion again

would it take a noticeable amount (relatively) to travel an extra metre or not

[long geyser]

at 20 meters?

[gaunt jetty]

yeah

[long geyser]

i would guess not cuz its been traveling for so long

[gaunt jetty]

yeah!!

you nailed the intuition :)

so now its time to tie it back to the mathematical jargon

Can you make any conclusions from what we said so far or do you need additional help

[long geyser]

mm i think i can answer it, so like it would be like
"bigger at T'(2) since the derivative represents times over meters, that means its looking at time in respect to distance. T'(2) indicates it hasn't been moving for very long so that extra distance is more significant than if it were at T'(20)"

[gaunt jetty]

the wording is a bit off

but you more or less got it yeah

[long geyser]

ohh shoot

could i ask how you would word it?

[sturdy prairie]

could you answer ??

[bold peak]

!occupied, use #help-7｜zen1thxyz pls

[midnight plank]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[bold peak]

Fix the grammar really

Other than that it looks good

Also sorry for dipping

[long geyser]

lmao! no worries

okay thanks guys

.close

[midnight plank]

Channel closed

Closed by @long geyser

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[long geyser]

okay nvm i need more help

[long geyser]

i have 1-3 already i think

f(t) is -2 - (1/2)sin(u)+ (1/2)sin(1) and g(t) is 1-t^2

used chain ruled for 2

units of v(t) is meters per second

but i have a hard time with 4? like how would i know

[lilac finch]

is it 1/2 (sin(1)) or sin(t)

[long geyser]

1

[lilac finch]

what will be p'(t)

[long geyser]

$tcos(1-t^{2})$

[grand pond]

evan

[lilac finch]

so there exists value of t between where expression becomes zero

you will have one zero in the graph

[long geyser]

ohh

how did you know that?

cuz its cos?

[lilac finch]

yeah cos(-pi/2)

[long geyser]

wait what is the -pi/2?

[lilac finch]

-pi/2 is approx -1.57

t^2 = 2.57 exists in the interval

[long geyser]

ohh

ok

so p'(t) must be the red graph

[lilac finch]

yes

[long geyser]

nice! thank you

[lilac finch]

np

[long geyser]

okay what about 5

[lilac finch]

p'(t) is the function of velocity

if we consider right as positive then it will move towards right when graph is positive

will stop when graph is = 0

and left when graph goes negative

[long geyser]

so red would be one moving right to left then stopping?

sorry could you explain it more i dont understand

hellur?

[lilac finch]

yes

if we assume moving right is positive

red shows the velocity , when it goes from positive to negative it means it stopped moving in a direction(positive ) and then started moving in opposite direction(negative)

@long geyser you there?

[long geyser]

lmao yes im just processing

oh okay, so it moves from right to left once it crosses 0?

but when does it stop?

[lilac finch]

yes

[long geyser]

at x=2?

[lilac finch]

when it crosses x axis

here

[long geyser]

wait but i thought it moves from right to left here?

@lilac finch sorry to ping u

can i ping helpers? i feel like i havent gotten help for 15 min

[lilac finch]

yes to move from right to left you have to stop

like when you move forward and want to go reverse you have to stop moving forward first then go backwards

[lilac finch]

you can if i'm not there

[long geyser]

ohh okay alright thank you

noo i just didnt want to get introuble

thank you!

.clos

.close

[midnight plank]

Channel closed

Closed by @long geyser

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[midnight plank]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[unkempt sluice]

<@&268886789983436800>

[olive matrix]

gone

[unkempt sluice]

A scam like ad posted originally

[midnight plank]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[heady wedge]

A pine tree (BC) grows on a hillside (AD) with a slope of 34 degrees as shown in the figure. At a certain time of day, the shadow on the ground is measured to have a length of CD = 2m and an angle BDC = 100 degrees, knowing that BK is perpendicular to AD at K. Calculate BK and BC.

[lilac finch]

do you have the figure?

[heady wedge]

wait a min

sending

[cerulean oyster]

Are we allowed to use trigonometric functions / projections?

[heady wedge]

like sin cos and tan?

[cerulean oyster]

while technically, yes, but there is a useful technique for finding lengths of right triangles just by a side and an angle.

[heady wedge]

my teacher says that as long as you can prove it, then it can be used

just don't make it too complicated

[cerulean oyster]

You havent seen the unit circle ever right? 🥀

[heady wedge]

sadly no

[cerulean oyster]

sadge

Well, its still somewhat easy once you know what to do.

Ill somewhat spoil it, the problem is basically solved when you find BD

[heady wedge]

i've found some angles, but not sure what I can do yet

[cerulean oyster]

Try to show which you found.

[heady wedge]

triangle BCK and ACH are congruent => ∠CAH = ∠CBK = 34

∠KDB = 180 - 100 = 80 => ∠DBK = 10 => ∠CBD = 24

∠DCB = HCA = 56

[cerulean oyster]

CDB = 24º?

I suppose you meant CBD yeah

[heady wedge]

so now what?

[cerulean oyster]

Remember Sine Rule?

[heady wedge]

the Law Of Sines?

[cerulean oyster]

yep

[heady wedge]

CD/∠CBD = BD/∠DCB

[cerulean oyster]

with sin*

Also, given you already found a lot of angles, you could skip the step of finding BD

Try to work a relation for BC

which is one of the sides of our interest.

[heady wedge]

i'm only in grade 9, and although i've learnt it, my teacher prob won't let me use it in homework or future tests

bcs in his words they're "too far from the currciculum"

[lilac finch]

how do they expect you to solve?

[heady wedge]

from other similar problems, using pytha, basic sin cos tan and triangle relations

[cerulean oyster]

okay, to clarify, SOH is basically Law of Sines for Right triangles

But yeah, we can do it with just that.

[lilac finch]

the equation would be messy

[cerulean oyster]

to do it without law of sines, youll have to transform all triangles into right triangles.

[heady wedge]

(round up to tenth)

[cerulean oyster]

Given, 2/3 already are

[heady wedge]

btw can I submit my sol in my native language?

[lilac finch]

what is your native lang?

[heady wedge]

vietnamese

[lilac finch]

you can

[heady wedge]

i need to submit these so might as well

any hints to do it the basic way?

[vivid yoke]

Which tools are we allowed to use that're considered "basic"

[heady wedge]

.

[lilac finch]

find angle BDK

[heady wedge]

80

[lilac finch]

tan 80 = BK/DK

[heady wedge]

and what can DK bring exactly?

[lilac finch]

tanBCK = BK/2+DK

make equation in terms of DK

[heady wedge]

*tan 80

[lilac finch]

mb

[heady wedge]

can you explain your thought process and why you chose DK?

i don't quite get it just yet

[lilac finch]

we are given 2 and we have to find Bk so using CK is easier

[heady wedge]

i've found a sol that works for me but i;m not sure if it's the optimal one

[soft stone]

can you send your solution?

[heady wedge]

am writing it down rn

wait a min

[soft stone]

yeah that works but the same problem can be solved using just one sine in triangle BDC to get BK and one cosine to get BC

[heady wedge]

i didn't know sine can be used on normal triangles too

[junior flower]

you are so pretty

[heady wedge]

well ty everyone

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[inland patio]

I've been going in circles with this proof for some time now. Recall Abel's theorem, namely if $S:=\sum_{k=0}^\infty c_k<\infty$, then $f(z):=\sum_{k=0}^\infty c_kz^k$ tends to $f(1)$ if $z\to 1$ within a single Stolz sector. The author says without loss of generality, assume $S=0$ (for we can always add a constant to obtain this). \

Like, if $S\neq 0$, how do we proceed? How do we define $f(z)$?

[grand pond]

psie

[marble hedge]

out of my league 💔

[soft stone]

you don’t change abel’s theorem or redefine the power series

if the sum of the coefficients is S ≠ 0 you simply subtract S from the function

prove the result when the sum is 0 then add S back at the end

that is what “without loss of generality assume S = 0” means

[inland patio]

Ok, thank you.

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[heady wedge]

I'm back

,rccw

[heady wedge]

Need help w last ques

,rccw

[heady wedge]

Rough translation: Draw (O; R) and A outside with tangents AB and AC. H is the intersection of BC and OA. Draw diameter CD of (O), AD intersects (O) at E. Draw OK perpendicular to DE at K. AD intersects BE at F. Knowing that R = 6 and OA = $6\sqrt{5}$, find KF.

[grand pond]

Thomas

[heady wedge]

<@&286206848099549185>

[soft stone]

since AB and AC are tangents to the circle the line BC is the chord of contact (polar) of point A

so BC is perpendicular to OA and H is the foot of the perpendicular from O onto BC

[heady wedge]

that's proven in question a

[lilac finch]

AD intersects BE at F?

or BC?

[soft stone]

oh sorry you need help in c?

[heady wedge]

do you have any ideas?

[soft stone]

use the fact that BC ⟂ OA and that O is the midpoint of CD

try to locate K and F using right triangles with vertex O then you can use the given lengths R = 6 and OA = 6√5

[heady wedge]

i can't seem to see any connection

<@&286206848099549185>

[fluid yacht]

Maybe using that triangles KFB and BOH are similar?

[heady wedge]

O, K, and B aren't meant to be on a straight line

gtg

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[woeful turret]

.

[woeful turret]

i have to calculate A^10

but im not noticing any pattern

[main current]

Right. Taking high powers of matrices is only easy if your matrix is in the form of PAP^-1

But you've got PAP^T here, so that's not the same.

... I mean, they're not the same, right?

[woeful turret]

oh wait

[echo crystal]

Hello

I'm newbie in Math world, can anyone help me with a resource?

[tawdry kraken]

!occupied

[midnight plank]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[woeful turret]

P^T P = I

[echo crystal]

What?

[tawdry kraken]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[woeful turret]

wait guys

[main current]

Oh but I am missing that A is not diagonal

[woeful turret]

which diagonal are they talking about

[woeful turret]

?

[main current]

The diagonal elements of a matrix are those from the top left to the bottom right

[woeful turret]

oh bruh 😭😭

i was doing the other diagonal

[main current]

Or, they're the elements preserved under ^T

[woeful turret]

alr alr

then i got it

thank u

[main current]

Np! Feel free to ask if you have anything else

[woeful turret]

i didnt understand this tho

[lyric charm]

where do you get these questions from where the typesetting is this eye-wateringly bad

how tf do you have the text in like 14 point type while all the math is in fucking 48 or 72

[woeful turret]

😂

[tawdry kraken]

My homework in Desire2Learn (D2L, brightspace) looks like that too

[echo crystal]

Ok

@tawdry kraken Are you the adm?

[tawdry kraken]

I think it's the MathJax sizing

[lyric charm]

what incompetent bhenchod made this shit

[tawdry kraken]

You can scale it by right clicking on it though

[woeful turret]

oh nah

ann has learnt the hindi slurs

💀

[tawdry kraken]

No

[echo crystal]

@tawdry kraken What concepts in Math did you know?

[main current]

Taking the 10th power of A is also somewhat difficult here, but I think you might have figured it out yourself!

[woeful turret]

yea we have to find the pattern

[main current]

If A were a diagonal matrix (all non-zeros are on the diagonal) then it would have been easy.

[woeful turret]

ohhh

alr alr

i calculated A^2 and A^3 and there was a pattern which we could extend

[main current]

As you just take the 10th power of every element

[woeful turret]

got it

thanks again

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[midnight plank]

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[bronze wigeon]

Well that was quick lmao

[tribal temple]

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[small jasper]

mods good

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[echo crystal]

yo

[hard shard]

whaddup home boy

[echo crystal]

I have a question

[echo crystal]

What kind of question?

[tender trench]

The question you need help with

Do you have a specific problem?

[scenic wyvern]

hi OP, do you have a specific question you need help with?

[echo crystal]

General Math?

[scenic wyvern]

so can you show us the problem?

[echo crystal]

Yes I have a doubt in this situation lemme show

[scenic wyvern]

please directly send your question next time - makes it easier and faster for everyone

[echo crystal]

Example
6x² / 3x² =
12x² / 8x =
-24x² / 12x =

[echo crystal]

Ok sorry

[scenic wyvern]

hint: do the numbers and the variables separately

[echo crystal]

6x² / 3x² = 2x?

[scenic wyvern]

x^2 divided by x^2 leaves x?

[echo crystal]

So it's 2?

[scenic wyvern]

yes

[echo crystal]

12x² / 8x = 1.[something]x?

1.48x?

[scenic wyvern]

well yes, or you can leave the answer in fraction form

it should not be 1.48 anyway

[small jasper]

hi

[echo crystal]

Really

[echo crystal]

Hello

[scenic wyvern]

12/8 has a definite answer

[echo crystal]

and this question
-24x² / 12x =

[scenic wyvern]

orz

[scenic wyvern]

same technique

[echo crystal]

-2x?

[scenic wyvern]

yes

[scenic wyvern]

so get back to fixing this one and you'll be all good

[echo crystal]

ok

1.32?

x

[scenic wyvern]

no

the final answer has only one decimal place

[echo crystal]

@scenic wyvern Do you have some resources for me?

[scenic wyvern]

Khan Academy

[echo crystal]

Thanks

12x² / 8x = 1.5x?

[scenic wyvern]

still no, even if you include the x

there we go

please don't say that, and you're welcome.
any other questions?

[echo crystal]

I think this is all

Thanks

[scenic wyvern]

aight

!done, if you are done

[midnight plank]

If you are done with this channel, please mark your problem as solved by typing .close

[scenic wyvern]

.close by OP agreement.

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[twilit field]

I've asked this in #groups-rings-fields but not really sure I fully understand this. Why do we care about discrete valuations. And what's the intution for it.

[midnight plank]

@twilit field Has your question been resolved?

[twilit field]

<@&286206848099549185>

[twilit field]

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[onyx tide]

Task 6. (0–1)

The number x was increased by 7, and then the obtained result was multiplied by 4.
The number y was multiplied by 5, and the obtained result was increased by 3.

Which pair of algebraic expressions correctly describes the performed operations?
Choose the correct answer from those given.

A. 4(x + 7) and 5y + 3
B. 4x + 7 and 5y + 3
C. 4(x + 7) and 5(y + 3)
D. 4x + 7 and 5(y + 3)

[onyx tide]

Wouldn’t that be B?

[bold peak]

Explain your thought process

[hard shard]

a neat trick to check your understanding is to try it with a number

say x=1

what happens

[bold peak]

That too

[onyx tide]

(1+7)5

But like

A. for example would be 4x + 28

[hard shard]

gud 4 u, ur are smrt

[scenic wyvern]

!nosols, please.

[midnight plank]

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.

[mortal socket]

oh
i forgot the rules xd

[pearl hull]

:((

[onyx tide]

But wouldn’t you need to multiply the brackets?

[mortal socket]

yeah it applies to the x

[onyx tide]

No

[slender walrus]

you aren't obligated to expand / get rid of all parentheses you see
4(x+7) does expand to 4x+28
but that isn't the point of the question

[mortal socket]

the task tells you to increase the value of the x

then you multiple the result by 4

[onyx tide]

It would be 4x + 28

[mortal socket]

its not to multiple the value of x

[scenic wyvern]

by 4*

[onyx tide]

It’s 28 not 7

[mortal socket]

mistyped xd

[mortal socket]

but that is not what the task requires

though 4(x+7) is 4x+28 itself

make it simple

[onyx tide]

Fine

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[twilit field]

Part(a)

[bold peak]

What's ℤD_8

[twilit field]

$(-3r^2+rs)(r^2+r-2s) = -3r^4-3r^3+6r^2s+rsr^2+rsr-2rs^2$

[twilit field]

one min

[bold peak]

Is it a group ring

[twilit field]

it's a group ring

yes

[bold peak]

Cool

What's your definition of r and s for a dihedral group

I've only ever used x and y

[twilit field]

generators(r^4=s^2=1)

and rs=sr^{-1}

[bold peak]

Ah cool r is rotation and s is reflection

[bold peak]

Third term should be r²s

[grand pond]

wai

[twilit field]

now to simplify it a bit

[bold peak]

Yup

[twilit field]

-3r^4=-3

[bold peak]

Yes

[twilit field]

and -2rs^2 is -2r

[bold peak]

Ye

[twilit field]

after which I'll factorise to see if I can simplify it any further

[bold peak]

Hold on

There's more you can do before that

So far you've only used the first property

[bold peak]

Now use this

[twilit field]

rsr=s

[bold peak]

Yes

[bold peak]

Also idt they want you to factorize

You should probably leave it in the ℤD_8 form

[twilit field]

so $-3-3r^3+6r^2s+rsr^2+s-2r$

[grand pond]

wai

[midnight plank]

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[tawdry kraken]

It's nice to see you coming back all the time with these algebra questions 😆

[twilit field]

tq

Have a quick question

So I need to show $Nrg_k=rg_kN$

[grand pond]

wai

[twilit field]

right

where r is in R and g_k is in G

My question is N is really 1_{R} N right

[tawdry kraken]

Back

[tawdry kraken]

Yeah

[twilit field]

oh, then I just need to show Ng_k=g_kN

which is true

[tawdry kraken]

Yes 👍

[twilit field]

(As we exhaust all the elements and addition is commutative)

[tawdry kraken]

That's the reasoning ✅

[twilit field]

cool

thanks!

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[tawdry kraken]

No problem 😆 didn't even have to do anything really

[twilit field]

.reopen

[midnight plank]

✅ Original question: #help-49 message

[twilit field]

Really silly question given I just finished by group theory course

but could I be reminded of what a conjugacy class is

a and b are conjugate if a=gag^{-1} right

[scenic wyvern]

b = gag^-1

[tawdry kraken]

gagged

[twilit field]

aren't both equivalent

[tawdry kraken]

Okay I knew I wasn't crazy somehow our book never defined conjugate for elements

But only for groups

O.o

[scenic wyvern]

I mean, you are defining conjugacy on a and b, but your definition only uses a

all you did was to seemingly show a is conjugate to itself

[twilit field]

ah

I see

thanks

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[twilit field]

.reopen

[midnight plank]

✅ Original question: #help-49 message

[twilit field]

on second thought this is sus

[tawdry kraken]

XD I knew it was gonna be reopened again

What's the isse

[twilit field]

There's no reason $(g_1+g_2+ \dots + g_n)g_k = (g_1+g_k)+ \dots + (g_n+g_k)$ Has to be equal to $(g_k+g_1)+ \dots + (g_k+g_n)$, Unless addition has to be commutative in the group

[grand pond]

wai

[tawdry kraken]

Mmmm

[twilit field]

Wait a minute...

🤦

[tawdry kraken]

XD

[twilit field]

They ARE the same, the pairs don't need to be the same

[tawdry kraken]

There we go 👏

[twilit field]

SO SORRY

[tawdry kraken]

n elements in the group, you have n distinct elements there

[twilit field]

How did I miss that

[tawdry kraken]

(distinct being the key word)

[twilit field]

they don't NEED to be distinct, do they

like g_2+g_k= g_6+g_k is possible

[tawdry kraken]

If I only have n-1 distinct then the equality becomes fishy

But they will be distinct because it's a group

[tawdry kraken]

Right cancel this and tell me what g2 equals

[twilit field]

g_2=g_6 by cancellation laws

[tawdry kraken]

Exactly

[twilit field]

ah

cool

binary operations in finite groups are bijective then[ this can be proven I suppose]

[tawdry kraken]

That

No

If you fix an element

yes

Because it becomes a permutation of the group

Cayley's theorem or something like that

[twilit field]

Like a+b=c+b iff a=c

[tawdry kraken]

Right

Fixing b now it's a bijection

[twilit field]

got it

thanks

[tawdry kraken]

np 👍

[twilit field]

One more question

[tawdry kraken]

(If you've every had to draw a cayley table this is why all the rows and columns must have exactly 1 instance of every element <-> the binary operation is associative)

[twilit field]

why do we define discrete valuations over fields the way we do

more specifically why (iii)

[tawdry kraken]

You asked that before, unfortunately I've never heard of the term 😂

[tawdry kraken]

That's interesting though

I guess that's to say it must satisfy the triangle inequality

Oh actually it doesn't mean that

Wait what does that imply then 😂

I guess the value of doing two things must be at least the value of doing the easier of the two

But yeah maybe you'll figure out why from the theorems that follow

[twilit field]

Cool, will have to wait for field theory for that I suppose

thanks!

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[tawdry kraken]

No problem !

[midnight plank]

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[floral ruin]

i converted this into standard form of LDE and then got stuck in the integrating factor

$\int \frac{e^x(x-2)}{x^3 + xe^x}dx$

[grand pond]

Prathmesh

[floral ruin]

how to integrate this?

ohh no I found another way to solve this

.close

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[tawdry kraken]

!status

[midnight plank]

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

[near geyser]

1

Obviously

@tawdry kraken

By the way solution available on MSE

[lethal path]

can you send the link?

[near geyser]

https://math.stackexchange.com/questions/1659502/determine-x-such-that-lim-limits-n-to-infty-sqrt1-sqrtx-sqrtx2-sq

[midnight plank]

@near geyser Has your question been resolved?

[silent dock]

Why is this still unsolved if that's your solution?

[midnight plank]

@near geyser Has your question been resolved?

Channel closed

Closed by @near geyser

Use .reopen if this was a mistake.

[midnight plank]

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[tawdry kraken]

Jesus

[near geyser]

I didn't understand the question properly

[pearl mist]

differential coefficient means the derivative

[near geyser]

suppose we do differentials normally with respect to x

[pearl mist]

coefficient

[near geyser]

I don't understand how to start the problem

[tawdry kraken]

Yes but we need respect to e^cos(x), so we have to sub

[pearl mist]

do you know how to differentiate a function with respect to another function?

[midnight plank]

@near geyser Has your question been resolved?

[near geyser]

I don't know

That's what I need to know and curious

[pearl mist]

bruh what took you so long

[tawdry kraken]

Literally

XD

[pearl mist]

$\frac{df\left(x\right)}{dg\left(x\right)}=\frac{\frac{df\left(x\right)}{dx}}{\frac{dg\left(x\right)}{dx}}$ take a look at this

[grand pond]

Xerxes

[tawdry kraken]

Oh that's a much nicer way to do it than the substitution method I learned

[near geyser]

Do you mean dy/dt/dx/dt?

Actually I was outside

For bringing brinjal

[pearl mist]

well your functions are in x variable right

[near geyser]

Yeah

[pearl mist]

this is parametric differentiation

[near geyser]

d(sin^2x)/dx/(d(e^cosx)/dx)

Is this correct?

[pearl mist]

you need the functions in parametric variable and then just eliminate the t variable completely if this was the case

[near geyser]

2sinx.cosx/(-e^cosxsinx)

2cosx/-e^cosx

[pearl mist]

yes

[tawdry kraken]

I should compare to my answer

$$u = e^{\cos(x)}$$
$$ln(u) = cos(x)$$
$$\sin^{2}(x) = 1 - \ln^{2}(u)$$
$$\frac{d}{du}(1-\ln^{2}(u)) = -2\ln(u)\cdot\frac{1}{u} = \frac{-2\cos(x)}{e^{cos(x)}$$

Useless thing

[grand pond]

Coolempire93
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tawdry kraken]

How am I supposed to compare the answer if I can't see it bozo

[pearl mist]

just type in your final result no need to show your work

[tawdry kraken]

\begin{align*}
u &= e^{\cos(x)} \
\ln(u) &= cos(x) \
\sin^{2}(x) &= 1 - \ln^{2}(u) \
\frac{d}{du}(1-\ln^{2}(u)) &= -2\ln(u)\cdot\frac{1}{u} = \frac{-2\cos(x)}{e^{cos(x)}}
\end{align*}

Foudn it

[grand pond]

Coolempire93

[tawdry kraken]

Sorry it was gona bother me forever 😭

But yeah same answer

[pearl mist]

oh its similar to a substitution in integrals

[tawdry kraken]

Yep

Sometimes I write integrals as $d(e^x)$ instead of $du$ to throw people off

XD

[grand pond]

Coolempire93

[pearl mist]

but what do you do when the functions arent related in any way? here we have a sin cos identity

[lusty python]

[tawdry kraken]

is there a such thing?

Every function is related by the identity function

And you'll never see a non invertible function in a calc class

That is to say

If you can u-sub it in an integral (even if it doesn't give you a nice integral)

You can differentiate respect to it by substitution method

What you have given me though is a very interesting way to sub my integrals

If I can't calculate the differential

Oh wait multiplying du/dx by the whole integral and multiply and hope everyone else fits their way in is already what we do

XD

[pearl mist]

i mean here it was a trig function and the exponent also had a trig function which had an identity what if one was trig and the other was say algebraic

[tawdry kraken]

Could you give an example 😅

[pearl mist]

say differentiate the same function but with respect to e^x^2

[tawdry kraken]

sin^2(x) respect to e^(x^2)

\begin{align*}
u &= e^{x^2} \
\ln(u) &= x^2 \
\sqrt(\ln(u)) &= x \
\sin^2(x) &= \sin^2(\sqrt(\ln(u)))
\end{align*}

[grand pond]

Coolempire93
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tawdry kraken]

That's what I mean when I sayit matters than the function is invertible

Noting that I leave off the negative branch because it gets cancelled with the sin^2 anyway

[pearl mist]

wait oh now i get what you mean

switching the original function domain with the intermediate u variable is still valid

[tawdry kraken]

What's that mean

😅

[pearl mist]

i mean the x input

you changed it to sqrt(ln u ) for substitution as it is x

i get it how it works out

[tawdry kraken]

Yeah 👍

[tawdry kraken]

Oh I remember why this works now

It's chain rule

$$\frac{df(x)}{du} = \frac{df(x)}{dx}\frac{dx}{du}$$

[grand pond]

Coolempire93

[pearl mist]

oh yeah it is chain rule

[midnight plank]

@near geyser Has your question been resolved?

Channel closed

Closed by @near geyser

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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 pine]

i’m assuming if the integral turns out positive then it converges, and diverges when it’s negative. is that true?

[tawdry kraken]

An integral to infinity has you evaluate $\displaystyle \int_1^{\infty}f(x)dx = \lim_{x \rightarrow \infty}F(x) - F(1)$. We say the integral diverges if that limit doesn't exist or goes to infinity, and the integral converges if that limit gives you a number to work with

[grand pond]

Coolempire93

[tawdry kraken]

In general convergence and divergence of integrals is just like series - do you get a number? converges. do you get unknown/undefined/goes to infinity/not converges? then it diverges

[fringe pine]

oh i see

so for this test, as long as i get a real value then it converges

[tawdry kraken]

Essentially

[fringe pine]

if i get plus or minus infinite it’s diverging

i got it now

.close