help-10

[fathom harbor]

ok

[balmy mortar]

But if you owe someone those assets

Its like you own a negative amount of them

so that is like multiplication by -1

ok?

So you own this piece of paper that says you owe someone all this stuff

[fathom harbor]

ok

[balmy mortar]

Now if you owe someone this piece of paper

[fathom harbor]

ok

[balmy mortar]

That is like multiplying by -1 again

[fathom harbor]

ok im never gonna understand these stuff

[balmy mortar]

You should give them this piece of paper

[fathom harbor]

ok

[balmy mortar]

And they owe u stuff

so actually you own a positive amount of stuff

[timid silo]

ngl that explanation is kind of complicated

[balmy mortar]

-1 x -1 = 1

[fathom harbor]

ok i dont understand anything that u just said

[balmy mortar]

well no ones succeeded in giving a good intuition

[fathom harbor]

i dum

[timid silo]

true

[fathom harbor]

ill just ask my math techer i guess

ok ty for help everyone

byee

someone is typing

ill wait

[slate zephyr]

@burnt narwhal Maybe there is one that is less confusing but I like it in that it is the first here that actaully explains a reason "why" without just saying "do this".

[fathom harbor]

ok

have a good day

.close

[obtuse pebble]

Channel closed

Closed by @fathom harbor

Use .reopen if this was a mistake.

[timid silo]

yeah good idea

[nocturne minnow]

That was a rabbit hole

[slate zephyr]

welp lol he left

[timid silo]

truly

[slate zephyr]

yeah

I think too many people explaining at once

[timid silo]

yeah

[nocturne minnow]

That and the lack of knowledge with negatives

[timid silo]

lmao

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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[balmy mortar]

asking the right questions at least heh

[balmy mortar]

.close

[obtuse pebble]

Channel closed

Closed by @balmy mortar

Use .reopen if this was a mistake.

[timid silo]

heheheha

[unique solstice]

[slate zephyr]

I think you would be surprised how many grown ups working in the industry would be having trouble.

[timid silo]

negatives always have been annoying for me

[slate zephyr]

It's just that a lot of people memorize things get through school

[balmy mortar]

but rlly, why does -1 x -1 = 1 D:

[unique solstice]

Theres a reason why negative numbers werent discovered for a hot minute

[balmy mortar]

Dont gimme ring theory bs

[slate zephyr]

and throw it ouf the window immediately once they are done with school.

[fathom harbor]

why r u guys still talking

[nocturne minnow]

I would understand more complex topics that isn't used daily but if it's something applied on a daily basis, that's different

[timid silo]

does that mean its not really useful

[spiral maple]

R is a R vector space

[balmy mortar]

its fun

[fathom harbor]

ok

[slate zephyr]

I agree, but that that is the voice of a mathematician. For us this is so fundamental that we see this everywhere. But for other people it's different.

[spiral maple]

also vector spaces aren't rings afaik shuri smh

[balmy mortar]

fields are rings

vector spaces are modules

[nocturne minnow]

I'm not a mathematician but I apply negatives a lot

[unique solstice]

-1 * -1 = i^2 * i^2 = i^4 = 1

[slate zephyr]

modules and rings are semi groups

[spiral maple]

Fields only have 1 set of elements, VS has 2

[slate zephyr]

I should not have said mathematician maybe. I meant it more broadly.

[unique solstice]

Negative numbers arent that useful in terms of counting and trading cows

[balmy mortar]

owing cows

[slate zephyr]

If you are a cashier you can multiply but never need to multiply negatives.

[balmy mortar]

.reopen

[obtuse pebble]

✅

[unique solstice]

Its more for financing and physics and stuff

[nocturne minnow]

I always count using negatives \s

[balmy mortar]

but if u owe someone who owes you who owes someone... idk

[timid silo]

when you owe the ower

[unique solstice]

"Jimmy you owe me 40 bovines"

Not "jimmy I currently have -40 bovines entrusted to your care"

"Multiply those there bovines by -1 right this instant"

[slate zephyr]

@fathom harbor Why did you do this to us. lol

[unique solstice]

🐄

[fathom harbor]

i was just asking question

[slate zephyr]

I know but...

[nocturne minnow]

It was a rabbit hole question

[fathom harbor]

ok cool

[balmy mortar]

a rl application of multiplying negatives, have we really none?

[slate zephyr]

I think it's always a bit contrived.

[wraith gazelle]

Money?

[nocturne minnow]

If you owe money at a constant rate

[balmy mortar]

I dont see anything obvious on google

[slate zephyr]

We did that already but it was confusing admittedly.

[balmy mortar]

at a glance

You could do directions/physics

but i dont think thats as good as money

[unique solstice]

One person mentioned like

[slate zephyr]

Hm

[unique solstice]

Somethign along the lines of

"Every time I eat a chicken nugget there is one less chicken nugget on the planet"

Assuming chicken nuggets are not being produced

[balmy mortar]

uhuh...

[unique solstice]

chicken nuggets = previous chicken nuggets + -1 * chicken nuggets eaten

If I barf up a chicken nugget

[balmy mortar]

wtf

[unique solstice]

chicken nuggets = previous chicken nuggets + -1 * -1

Bam

Real life application right there

[balmy mortar]

if money was contrived

[unique solstice]

+1 chicken nugget

[slate zephyr]

Very natural explanation

[balmy mortar]

I think I can safely conclude we shouldn't be taught to multiply negatives until uni then

[slate zephyr]

lol

[unique solstice]

Until you learn complex numbers

[balmy mortar]

'normal' people shouldnt need this...

[unique solstice]

Multiplying -1 being equivalent to a 180 degree rotation in complex space

[slate zephyr]

I mean people often say "complex numbers are made up" or something like that.

In reality all numbers are made up.

It's just that we learn negatives so early that it seems natural to us by the time we get to the complex numbers.

[nocturne minnow]

But complex numbers are made up, they're imaginary

[balmy mortar]

people seem to be more comfortable with negative/fractional exponentials than complex

[slate zephyr]

All numbers are imaginary

numbers just model real phenomens.

Sometimes it's just positive integers like people in a room.

[unique solstice]

The names of numbers are imaginary

[slate zephyr]

Sometimes it's complex like points in a plane.

[unique solstice]

Not numbers themselves

[fathom harbor]

why r u guys still talking

ok

[slate zephyr]

Idk tbh

[balmy mortar]

im sad there is no good explanation for multiplying negatives

[unique solstice]

I mean complex numbers fit way to perfectly into all math for them to be made up

Theyre an integral part of the basic nature of everything

[slate zephyr]

I am a formalist, I think you are a platonist.

It's a very old debate.

[unique solstice]

Idk what that means

[slate zephyr]

It means exactly this point of view

[balmy mortar]

R isnt algebraic in R. C is tho :D

[nocturne minnow]

It's not your channel anymore so it doesn't matter

[fathom harbor]

ok

[slate zephyr]

"numbers are real in an abstract way/created by god/etc" vs "it's definition pushing, we just define something and it must be that way because that's what we defined"

platonist vs formalist

viewpoint

[balmy mortar]

f(x) = 1-x
ff(x) = 1-(1-x) = -(-x)

Surely we can tack this onto something . . .

[unique solstice]

I mean basic numbers have stayed the same since the beginning of time

And everything of basic math even though undiscovered has fit perfectly with it

[slate zephyr]

Yeah because it's a very useful tool.

[unique solstice]

Like people didnt know about complex numbers when they counted cows

But theres that hidden layer underneath counting cows

[slate zephyr]

Yes, they extended the definition later to do more interesting stuff.

[unique solstice]

That fits like a glove

Every time the "definition was extended" it fit perfectly with not only what already existed but with what would exist

[slate zephyr]

The way to go from natural numbers to integers to rationals to reells to complex numbers

[unique solstice]

Theres no other way to express numbers really

[slate zephyr]

are general algebraic concepts that work in other monoids/rings/topologies

[unique solstice]

As hard as you might try

Yeah other bases and stuff

[slate zephyr]

I don't really mean bases.

[unique solstice]

But bases just represent value

[slate zephyr]

Bases are just a way to format large numbers.

[unique solstice]

Which is what Id call a definition

[slate zephyr]

I thinking of numbers as sets in ZFC.

[nocturne minnow]

Base 128 is the best base to exist

[unique solstice]

Perhaps

[unique solstice]

If youre french

[slate zephyr]

?

[unique solstice]

Dont the french use base 6 or smthn weird

[slate zephyr]

Idk

I am pretty sure they use base 10 for writting numbers

[balmy mortar]

Ahahahaha I've found a good one.

You owe 10 people 2 dollars.

So thats 10x-2 = -20 dollars.

You pay 3 ppl back. Thats 3 less people you owe, so you gain -3x-2 = 6 dollars.

Now you are on -14 dollars.

[unique solstice]

They do but with some exceptions afaik

[slate zephyr]

yeah

[balmy mortar]

@fathom harbor

[fathom harbor]

wut

[slate zephyr]

I have no idea about french so... 😮

[fathom harbor]

ok

[timid silo]

yall are still on this haha

[unique solstice]

Neither

[balmy mortar]

u wanted to know why and i found a better example

[unique solstice]

Ive just heard that

[slate zephyr]

apparently

[fathom harbor]

uh

[nocturne minnow]

We pretty much turned this channel in a discussion channel

[unique solstice]

https://tenor.com/view/cat-funny-bed-gif-19641468

[fathom harbor]

but u dont gain any dollars because u still owe them

[timid silo]

great

[fathom harbor]

like u dont get any money back

i mean

like

ur networth wont go up

[slate zephyr]

@fathom harbor The real power is not really that specific example though. It's just an example where we see how it applies.

[nocturne minnow]

But you owe less though

[balmy mortar]

Lets say someone pays them back for you

[fathom harbor]

dont understand but ok

[balmy mortar]

Or they uh die ig

then u stop owing them

[nocturne minnow]

Like student loans

[unique solstice]

$40k of debt for PhD in cats

[slate zephyr]

cats important

[unique solstice]

#❓how-to-get-help

[slate zephyr]

Should we ping helpers?

[nocturne minnow]

Why?

[timid silo]

damn i thought i was gonna get some of you with that image

[unique solstice]

I mean its been 15 minutes

[slate zephyr]

ye

[timid silo]

didnt fall for it though

[slate zephyr]

Easy with bright theme 😄

[unique solstice]

[timid silo]

[nocturne minnow]

The ratio is wrong too

[slate zephyr]

I think some people here dislike light themes lol

[timid silo]

okay you guys dont have to bully me for my screenshotting skills

i think i rather did pretty well

[unique solstice]

https://tenor.com/view/cat-gif-22968526

[timid silo]

https://imgur.com/a/qG8K54D

[unique solstice]

https://tenor.com/view/cat-catslap-cats-slap-gif-5628396

[timid silo]

we love cats

[idle thunder]

You guys want this closed

[slate zephyr]

is it a general thing that mathematicians like cats?

[nocturne minnow]

Nah

[slate zephyr]

Nooo

[timid silo]

well im not a mathematician but i do like cats a bit too much

[nocturne minnow]

#cats

[timid silo]

perfect

[unique solstice]

https://tenor.com/view/kitty-cat-calculating-poor-calculations-bad-math-gif-16946752

[timid silo]

i regret

[unique solstice]

Cat doesnt know how to eat

[timid silo]

you think thats food?

[unique solstice]

Yes

[unique solstice]

Looks like some kinda cat formula

[timid silo]

i really hope not

looks really bad

[unique solstice]

Cats dont require fine cuisine

[timid silo]

they deserve it though

[unique solstice]

Despite what the fancy feast ads make you think

[timid silo]

i mean, humans dont either

now that i think about it most humans dont

[balmy mortar]

Alright to #chill you all go

bye bye

[unique solstice]

No

[balmy mortar]

.close

[obtuse pebble]

Channel closed

Closed by @balmy mortar

Use .reopen if this was a mistake.

[unique solstice]

Chill is a horrible place

[timid silo]

nao

[obtuse pebble]

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Channel closed

Closed due to the original message being deleted

[unique solstice]

Nothing to see here

[obtuse pebble]

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

please

help

[slate zephyr]

What is the question?

[brittle swan]

csc² = cot² + 1

[slate zephyr]

Find the solution set?

[idle sail]

find theta

ye

thats the answer

[brittle swan]

use this

afterwards let cot θ = x

[idle sail]

okay 2cot i presume

[brittle swan]

wdym

[slate zephyr]

btw the solution set is incorrect.

[idle sail]

wait fr

wtf this teacher giving me ;-;

[slate zephyr]

because it certainly must be 2pi periodic

so 11pi/4 must do as well

etc

19pi/4

[idle sail]

ohh we havent gotten that far

[slate zephyr]

Ah okay

[brittle swan]

i think the answers are limited to from 0 to 2π

[slate zephyr]

Maybe

[idle sail]

yes

i tried doing it and i believed i needed to factor

like csc(2cos+csc)=0

[slate zephyr]

You should start how Chromium said.

[idle sail]

oki

[slate zephyr]

note that

cot² + 1 = cos²/sin² + 1 = (sin² + cos²)/sin² = 1/sin² = csc²

[idle sail]

oki ty

.close

[obtuse pebble]

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[marble sable]

Can someone teach me find the equation to Thea table

[obtuse pebble]

@marble sable Has your question been resolved?

[marble sable]

<@&286206848099549185>

[marble sable]

<@&286206848099549185> can you help?

I have been here for almost 50 minutes

[scenic sundial]

no idea what are you trying to do

are you trying to find the equation of a line? @marble sable

[noble berry]

Seems like it since I don’t think it can be like direct variation or smth

[marble sable]

Yeah

[ebon token]

<@&286206848099549185> Can you help?

[noble berry]

Chat being used

[timid silo]

#❓how-to-get-help

[noble berry]

You’d need to find the slope

[timid silo]

parabola im guessing?

[noble berry]

Yeah seems like a curve of sorts since the rise/run aren’t the same. Idk about those

[timid silo]

wait

its the same

yeah i got the equation

i probably shouldnt say the equation but yeah its linear

[noble berry]

They are?

[timid silo]

technically yes

[scenic sundial]

okay, draw a graph using the points

[marble sable]

Ok I found the slope

[noble berry]

Do you know how to find equation of a line?

[marble sable]

No

[obtuse pebble]

@marble sable Has your question been resolved?

[obtuse pebble]

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[timid silo]

So $A$ and $D$ are similar iff $A = CDC^{-1}$. Then the columns of $C$ satisfy $A\vec{v} = \lambda \vec{v}$. So the columns of $C$ are the eigenvectors of $A$? And $D = C^{-1}AC$?

[warm shale]

leadersheir

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[slate zephyr]

Yes if D is a diagonal matrix.

This is usually how one construct this.

You use the eigen vectors for C

and the eigen values for D.

[obtuse pebble]

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[obtuse pebble]

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[static bluff]

What are the damains? Help

[short spruce]

do you mean domains?

[obtuse pebble]

@static bluff Has your question been resolved?

[obtuse pebble]

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[potent compass]

6/2 (1+2) =

[pliant heart]

3(3)

=9

@potent compass

[potent compass]

Thanks

A lot

8/2 (2+2) =

[gaunt rain]

8÷2(4)
4(4)
16

Perenthesis first (2+2)
Then 8÷2(4) is the same as 8÷2x4
so from left to right
4x4
16

@potent compass

[potent compass]

Ok got it thanks

[pliant heart]

Which grade are you in

[brittle swan]

siohgfuoghdfgi jfg

this question is notorious to have stirred unneeded shitstorm over rarer-than-hell ambiguities

so yea, don't ask that

[short spruce]

it's improper notation

[potent compass]

I’m in grade eight I’m just doing extra stuff

[brittle swan]

wdym 'extra stuff'

[brittle swan]

questions like these have no meaning

none

zero

nil

[potent compass]

Yeah just bored

[short spruce]

nada, zilch, zip, if you will

[wide vigil]

Hey can someone help me answer a quick geometry question?

[short spruce]

#❓how-to-get-help

[obtuse pebble]

@potent compass Has your question been resolved?

[obtuse pebble]

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[rare bloom]

How did you not know this one

[brittle swan]

????

[rare bloom]

Nvm

.close

[obtuse pebble]

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[timid silo]

am i doing this right?

[brittle swan]

no

[timid silo]

explain

[brittle swan]

how did you obtain the right angle

[brittle swan]

don't rush

[timid silo]

well, there is a theorem, which says taking ends of a diameter line and connecting it to any point on the circle will give a right angle

https://youtu.be/5WB1911rBz4?t=164

timestamped link

wait no...

lemme process this

ohh its not an issoceles triangle

but the theorm stands correct

[timid silo]

this seems about right?

[brittle swan]

slight error

at AOB

[timid silo]

180-61=119?

[timid silo]

?

[brittle swan]

wait

shit

yea, you should be right

sorry

thought you wrote 19

[timid silo]

alright, thanks

appreciate it

.close

[obtuse pebble]

Channel closed

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[kindred mango]

Suppose 10 students are to be grouped into teams. Order doesn't matter. If each team has either two or three students, how many ways are there to form teams?

[kindred mango]

I understand everything, but I'm confused on where the 2!2! came from

[obtuse pebble]

@kindred mango Has your question been resolved?

[kindred mango]

<@&286206848099549185>

[obtuse pebble]

@kindred mango Has your question been resolved?

[kindred mango]

pls help i have an exam today very simple question

[timid silo]

got it, thanks! 🙌

[royal solar]

because the order doesn’t matter. each time you double count divide by 2

first 2! is to remove all double counting in teams of 2

second one is for teams of 3

2! is literally 2 tho, you count them all twice in total so you divide by 2

[kindred mango]

wdym by double count

shouldnt it be 2!3!

[worthy comet]

The order doesn't matter. This implies also that there is no "first group of two" and no "first group of three". One 2! is for the order of the two groups of two persons and the second 2! is for the order of the two groups of 3 persons

[kindred mango]

ohhh ok that makes sense now

thank you

so you're eliminating duplicate groups by dividing the 2!2!

ex: groups of 2 being a,b. groups of 3 being c,d

it can be abcd, bacd, etc.

[kindred mango]

.close

[obtuse pebble]

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[drowsy viper]

what does "is not equal to" sign means

[drowsy viper]

Example: {Y e R | x ≠ r}

[daring rock]

It means, literally, x is not equal to r

Do you have some more context for this set? Or did you just make this one up?

[drowsy viper]

@daring rock

[daring rock]

Ahh okay

okay my latex isn't working but whatever

It's saying the domain is all real numbers, except for 0

same for the range

[drowsy viper]

Oh so it's just a undefined

?

what if it's going to be 1, not 0

so it will be {x e R | x =/ 1}?

[daring rock]

Don't mix up x and y like that

[drowsy viper]

yea

[daring rock]

Yeah, domain is for the x values, range is for the y values

And yes, what you wrote means all real numbers except 1

[drowsy viper]

mhm, thanks

[daring rock]

Literally "the set of real numbers x such that x is not equal to 1"

[drowsy viper]

Got it

thank you so much

.close

[obtuse pebble]

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[signal cobalt]

Given AB = AC, C' D = CD, AREA ABC'E = AREA C' DE, Proof C'D = DE

[neat flare]

help

oh shoot

sorry

[signal cobalt]

||7Y - 42|| 7 * y - 7 * 6

[neat flare]

oh

thanks

[short spruce]

don't do people's work for them

[signal cobalt]

Help

[daring rock]

this channel is occupied

[soft marsh]

oh sorry

im dumb

[signal cobalt]

Given AB = AC, C' D = CD, AREA ABC'E = AREA C' DE, Proof C'D = DE ( isosceles right triangle ABC)

[daring rock]

So, you basically are asked to prove that triangle C'DE is an isosceles right triangle

[signal cobalt]

yea

[daring rock]

And we know that triangle BAC is an isosceles right triangle

So if you can prove that these triangles are similar, you're set

[signal cobalt]

yes

how'

[daring rock]

Actually wait, I guess it's not given that these are right angles

[signal cobalt]

it is

isosceles right triangle ABC

[daring rock]

Is it given that DE is perpendicular to BC?

[signal cobalt]

** An isosceles right triangle ABC with legs of length 2 cm is cut from a sheet of paper that is cross-hatched on one side and is solid gray on the other. The triangle is folded by moving the vertex C to position C ′on side BC.**

[daring rock]

Okay then yes, the crease (DE) would be perpendicular to BC

So angle C'DE is congruent to angle A because they're both right angles

angle DC'E is congruent to angle C. They are both the corner of the paper

That's two congruent angles between triangle DEC' and triangle ABC

[signal cobalt]

okay

[daring rock]

Two congruent angles is sufficient to prove that two triangles are similar

[signal cobalt]

😮

ok

ty

.clos

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[obtuse pebble]

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[daring rock]

sure thing

[obtuse pebble]

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[little cove]

Hey, i have some problems with 1.d on this question, i've tried applying the variance formula

[little cove]

https://media.discordapp.net/attachments/452922871656742942/942831922818723940/unknown.png

I tried to solve it by applying the variance formula to only the concerned data and i get those results but they're wrong
Var(Y|X=0) = 0.16245

Var(Y|X=1) = 0.00225

Var(Y|X=0) should be equal to 0,1056

[obtuse pebble]

@little cove Has your question been resolved?

[obtuse pebble]

@little cove Has your question been resolved?

[obtuse pebble]

@little cove Has your question been resolved?

[tardy epoch]

Can you share a sample of the data here

[little cove]

https://media.discordapp.net/attachments/903430332324405288/942864767519973446/unknown.png

Check the 4 points given in the table

[tardy epoch]

Do you know the individual x_i values?

[little cove]

wdym?

oh no i dont

only the couple (x,y)

[tardy epoch]

These x_i

Try using this formula instead
https://en.m.wikipedia.org/wiki/Conditional_variance

https://wikimedia.org/api/rest_v1/media/math/render/svg/d0ec2a666702bb70daec781b5fa8e52533fd72d4

[little cove]

hm i see, for the conditional mean, i would just have to do the mean the data that has x=1 for example?

[little cove]

Thanks for the help, imma loop into it more in depth 😄

[tardy epoch]

yea. in fact, parts b and c set you up to do part d's calculations.

[obtuse pebble]

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[tardy epoch]

what do you think?

apply things you learned in class

one way a function is discontinuous is when the denominator are zero

[slate zephyr]

From the rules: "When asking for help, do not insist with getting just the answer; we are here to help you learn, not do the work for you. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer." 😮

[tardy epoch]

can the denominator be zero?

why not?

[slate zephyr]

Not really, usually one sees the point 0 as just undefined. Thus it's neither continous nor discontinous.

[tardy epoch]

oh shit you're right

[slate zephyr]

Which point do you think would be discontinous @timid silo?

[obtuse pebble]

@timid silo Has your question been resolved?

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[wintry stream]

how do i convert this

[wintry stream]

to smth like this

[slate zephyr]

I don't think you should or can.

It's to different.

I would suggest to try substitution to solve the earlier integral.

[obtuse pebble]

@wintry stream Has your question been resolved?

[wintry stream]

how about these?

basically, my teacher wants us to choose one of these to solve

by converting 244 into smth in this table

[slate zephyr]

I think they are all different.

Read the heading

a² + u² is not something we have.

[wintry stream]

i think i found one

[slate zephyr]

Nope

Do you know how to substitute?

[wintry stream]

oops forgot the sqrt

yeah

but my teacher wants to do smth diff

aka finding one from the table and plugging values

[slate zephyr]

I don't think there is much differnet you can do.

[slate zephyr]

Ok, if you want. 😄

Idk what the teacher wants to teach with that but I guess you have to follow his plan.

[obtuse pebble]

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[unborn nebula]

for b would it be (1/3+h-1) - (1/3-1) / h

[strong vale]

Did you mean $\frac{f(3+h) - f(3)}{3+h-3}$

[warm shale]

azeem321

[strong vale]

If so yes, that's good

[unborn nebula]

oh my

thank you haha

where would the 3+ h - 3 come from?

what about the -1?

[strong vale]

This is the limit definition you learned?

[unborn nebula]

yes sir

[strong vale]

The limit definition is actually $\frac{f(x+h) - f(x)}{x+h-x} = \frac{f(x+h)-f(x)}{h}$

[warm shale]

azeem321

[strong vale]

So same thing really

[unborn nebula]

oh

[strong vale]

$f(3+h) = \frac{1}{3+h-1}$

[warm shale]

azeem321

[strong vale]

So it seems what you did above was right

[unborn nebula]

ohh

how do i carry on there from there

[strong vale]

So you have $\frac{\frac{1}{3+h-1}-\frac{1}{2}}{h}$

[warm shale]

azeem321

[strong vale]

Get it over common denominator

[obtuse pebble]

@unborn nebula Has your question been resolved?

[obtuse pebble]

@unborn nebula Has your question been resolved?

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[tardy crater]

yo

[tardy crater]

so im at this final step in my derivative

but i have no idea how to attack it

any help?

[mental solstice]

what do you mean, 'attack it'?

what do you need to do?

[tardy crater]

lol attack it just meant like approach the problem

just a jokey way of saying it

alright so let me update you. I managed to find the next step. it looks like this

how do I simplify this further?

thats all i need to do

[flat anvil]

mult. top and bottom by sqrt(x)

for one thing

[tardy crater]

oh got it

wait why sqrt x?

out of all things

like not -2sqrtx for example

[flat anvil]

you see the 1/(sqrt(x)) right?

i mean you could do that

but then you would have that on the bottom as well and it wouldn't look that nice

[tardy crater]

oh i see

[flat anvil]

actually

2sqrt(x) would prob be best

then you remove all the fractions

[tardy crater]

oh ok i see. ill try it and lyk

-2sqrtx or 2sqrtx

@flat anvil

[flat anvil]

whichever you see fit

[tardy crater]

hm

ok

[flat anvil]

do you want a negative on the bottom?

[tardy crater]

ok so

i got this

but

this is the answer on the online calculator

im a little confused lol

@flat anvil

[flat anvil]

why did you not multiply everything by 2sqrt(x)

you left the 3 hanging

[obtuse pebble]

@tardy crater Has your question been resolved?

[obtuse pebble]

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[brittle swan]

here

why isn’t it
$R_n > \int_{n + 1}^{\infty} f(x) \dd x$ instead

[warm shale]

Chromium

[brittle swan]

isn’t it guaranteed to overestimate

[mental solstice]

it's an infinity thing, you can't say $R_n > \infty$

[warm shale]

Camilleone

[mental solstice]

so if the thing on the right diverges to $\infty$

[warm shale]

Camilleone

[mental solstice]

then you end up with $R_n = \infty$ also

[warm shale]

Camilleone

[mental solstice]

there's also a second case, when $f(x) = 0$ for all $x$, in which case $R_n = 0$ and the RHS is also $0$, so it must be an equality

[warm shale]

Camilleone

[brittle swan]

but the integral test wouldn’t apply

[brittle swan]

aren’t we assuming the integral test is applicable here

and that the series (hence the integral) converges in the first place

[mental solstice]

what is the exact statement of the integral test?

[brittle swan]

for +ve cont. dec f, series of f converges iff integral of f converges

[mental solstice]

i'm going to write that in words cause it's painful to read

in fact the true statement is somewhat more

[brittle swan]

wdym

[mental solstice]

Let $N\in\bN$ and $f$ be a monotonically decreasing function on some unbounded interval $[N,\infty)$. Then, $$\sum_{n=N}^\infty f(n) < \infty \iff \int_N^\infty f(x) dx < \infty.$$

[warm shale]

Camilleone

[brittle swan]

not strictly decreasing?

[mental solstice]

no need

continuity isn't strictly needed also, but in anywhere before advanced real analysis, you will assume continuity

[brittle swan]

any examples?

[mental solstice]

$f\equiv 0$

[warm shale]

Camilleone

[brittle swan]

what’s the integral of 0 😦

[mental solstice]

0

[brittle swan]

alright

.close

[obtuse pebble]

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[obtuse pebble]

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[mental mortar]

Is there any way of solving this problem withhout guessing?

[timid silo]

algebraaaaa

variables are THE tool for replacing unknowns, so you can use em here where there are unknowns

[mental mortar]

ok

[flat anvil]

could also be a constant (general antiderivative of 0 would be a constant as a constant has a slope of 0)

[mental mortar]

aight coolio

I just said

for 1.

you can put in variablpes

cause it didnt specify to solve it

[timid silo]

woah what do you mean?

I mean, it at least asked for one solution right? Although it's true it didn't ask for all of them

I think the problem is a little poorly worded, but it seems to be heavily implied that there are some numbers that could go in those blanks that you can find

[mental mortar]

these math questons for real got me doing english analytical essays

I'm just going to tell my math teacher to help me on this because he's got the explanations on the teacher guide

Thank you zd for the help

[timid silo]

Did you try what I mentioned? I think you might find it cool @mental mortar

and yw

[mental mortar]

yea i filled it in with variables but im skipping it for now because i dont know what to do after that LOL

[timid silo]

what did you call the variables? I can help you out

[mental mortar]

just a b and c

[timid silo]

cool so you have (a-2i)(b+2i) = c - 10i right

[mental mortar]

Yes

[timid silo]

Well you may know every complex number is of the form a real plus an imaginary right

[mental mortar]

of course

[timid silo]

so you can simplify that left hand side into such a form

and equate it with c - 10i

[mental mortar]

Ok

so i basically use foil

[timid silo]

sure!

[mental mortar]

ok

wait

what would the answer be when you multiply a * 2i

[timid silo]

precisely that

[mental mortar]

makes sense

[timid silo]

but written more cleanly would be 2ai

[mental mortar]

Oh fr

i just add the variable

sweet

[timid silo]

if by "add" you mean "add to how it's written" then yeah!

[mental mortar]

yes

i got ab + 2ai - 2bi - 4 is

is this correct

[timid silo]

what's -2i(2i)

which is one of the terms you get from multiplying everything out

I would look at that one closely again

[mental mortar]

oops

ab + 2ai - 2bi +4

[timid silo]

looks good

[mental mortar]

ab + 2ai - 2bi - 4 is= c-10i

oops

ab + 2ai - 2bi - 4 = c-10i

[timid silo]

I think you meant to put +4 but that's just a nitpick at this point

so to proceed with anything useful here we will have to assume a b and c are real: we're going to use the fact that two complex numbers are equal exactly when their real parts are equal, and their imaginary parts are equal.

[mental mortar]

probaly cause i copy and pasted

[timid silo]

lulul

all good

[mental mortar]

bro if im being honest

[mental mortar]

can you say this in caveman words

[timid silo]

two thing same when left parts are same and when right parts are same

Basically writing (ab+4) + (2a-2b)i = c + (-10)i we can make some inferences

you'll see I pulled out a factor of i on some terms on the left, lmk if I did anything too fast

[mental mortar]

i see

[timid silo]

So if a,b,c are real, then ab+4 = c, and 2a-2b = -10

[mental mortar]

oh

[timid silo]

from there I think you got this, try solving for one of the variables

[mental mortar]

kk

I'm going to comeback to this question because my homework due in like 8 minutes 😢 but its light work quetsions from there

[obtuse pebble]

@mental mortar Has your question been resolved?

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[tardy crater]

sometimes I surprise myself too

[tardy crater]

😂 thanks

[flat anvil]

you're welcome

use .close if you have no more questions

[tardy crater]

actually

so i have question still

i just went to eat food this whole time so thats why i lagged on you

i got this now

but it still isnt this:

and idk what I did wrong

@flat anvil

[obtuse pebble]

@tardy crater Has your question been resolved?

[obtuse pebble]

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[covert comet]

The first few rows were hard to follow due to missing/misplaced brackets, but it's fine - the last line was correct

[covert comet]

However, this does not follow from the last line of the previous picture

Compute correctly and you may find the desired result

.close

[obtuse pebble]

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[obtuse pebble]

Please don't occupy multiple help channels.

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[surreal moth]

why is the angle pi/4

[obtuse pebble]

@surreal moth Has your question been resolved?

[surreal moth]

<@&286206848099549185>

<@&286206848099549185>

[covert comet]

Let the angle be $\theta\in(-\pi,\pi]$. Then
$$\text{Re}(a+ai)=a>0\implies\theta\in(-\frac{\pi}{2},\frac{\pi}{2})$$
and
$$\text{Im}(a+ai)=a>0\implies\theta\in(0,\pi).$$
Hence $\theta\in(0,\frac{\pi}{2})$. In addition,
$$\tan(\theta)=\frac{\text{Im}(a+ai)}{\text{Re}(a+ai)}=\frac{a}{a}=1;$$
hence $\theta=\frac{\pi}{4}$.

[warm shale]

Rafain

[surreal moth]

ohh

thank you sm

.close

[obtuse pebble]

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[vestal flame]

help

[vestal flame]

can anyone solve this

[royal basin]

which part

[vestal flame]

1 - 7

[royal basin]

...

[vestal flame]

im really struggling

[royal basin]

okay so like, do you want help or do you want someone to do this for you

[vestal flame]

both

[royal basin]

we don't do other ppl's homework here

okay so like

as far as helping you goes

[vestal flame]

ok

[royal basin]

do you understand what "___ property of equality" means

where the blank is one of the four arithmetic operations

[vestal flame]

no i am having a hard time understanding

[royal basin]

has your teacher not explained such concepts as "adding the same thing to both sides", "multiplying the same thing to both sides" etc?

[obtuse pebble]

@vestal flame Has your question been resolved?

[obtuse pebble]

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[abstract magnet]

may i know if the question is changed to -7854, 2772, do we still have the exact same steps? since gcd(-7854,2772) = gcd(7854, 2772)? or we cant do it with the exact same steps because this is finding the linear combination

[rigid kestrel]

Yes. The same step.

The quotient should be taken such that the remainder is non negative and smaller than divisor.

[rigid kestrel]

I don't mean "same" . I mean "Similar"

[abstract magnet]

sorry which part ya, i dont get it

[rigid kestrel]

In the third line of solution. That is first equation.
Here you put - 7854 in place of 7854. Now you should select a quotient with 2772 ( in the solution quotient is 2) so that the remainder that comes out should be positive and lesser than divisor (that is 2772)

[abstract magnet]

why do we need to put -7854? cant we just put 7854?

since gcd(-7854,2772) = gcd(7854, 2772)

[rigid kestrel]

Yes. That is also absolutely correct.

But I was talking for the situation when you don't know about this Relationship.

In that case you will go through fundamentals only.

[obtuse pebble]

@abstract magnet Has your question been resolved?

[rigid kestrel]

@abstract magnet did you get it?

You can close the channel if you have no doubts remaining

[obtuse pebble]

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[abstract magnet]

.reopen

[obtuse pebble]

✅

[abstract magnet]

@rigid kestrel do you mean like this bro
?

[rigid kestrel]

Yes that is also correct.

[abstract magnet]

So the whole thing is correct? Because in the end i change the 191 to become -191

[rigid kestrel]

Yes. You changed -8 . And that is acceptable. Because all you need to care about is that "the coefficients should be integers"

[abstract magnet]

Sorry what do you mean by i changed 8 ya?

Im confused

[rigid kestrel]

In the last line where you have changed 191 into - 191

You also had to change coefficient of 191 ( before it was - 8 now it has to be 8 because you have given its minus sign to 191)

[abstract magnet]

So if my final ans is + (-8) x 191

Then it will be wrong right?

[rigid kestrel]

Yeas.

Your question is for - 191 not for 191

So you should write in terms of - 191

At the end.

[abstract magnet]

Oh i seee so we just need to change the sign based on the question

[obtuse pebble]

@abstract magnet Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[flat minnow]

help pls

[loud egret]

What exactly u need help with ?

Simplify it or ?

[obtuse pebble]

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[onyx fog]

hi, im very confused about this question. i don't have any work yet cuz i am completely stumped. my professor isnt the best and teaching these things

[brave bramble]

I don't know what your book may mean by "type I" "type II" "type III" these aren't standard afaik

Happen to have those anywhere?

[onyx fog]

§2.2, §3.1 from Linear Algebra with Applications, by Steven J. Leon, Pearson, 9th or 10th Ed.

(i dont have the textbook on hand)

[spiral maple]

Well we can't help if you can't tell us which elem matrix is which

[onyx fog]

i dont know what it means either

._.

[spiral maple]

Since it's required to know which is swapping, which is scaling, and which is adding a scaled version

[onyx fog]

i guess its equivalent to I1, I2, and I3 types

[spiral maple]

Welp, come back when you have your textbook to look them up

[onyx fog]

ive seen those

[spiral maple]

No clue what I1,2,3 types are

Nor what you would be referring to

[onyx fog]

Definition: An n × n elementary matrix of type I, type II, or type III is a matrix obtained from the identity matrix In by performing a single elementary row operation (or a single elementary column operation) of type I, II, or III respectively. Theorem 2.5: Let A be an m × n matrix.

there

[spiral maple]

Ok.... which ERO is "Type 1,2,3" then?

[onyx fog]

any ERO

identity matrix I1 for example is a 1 x 1 matrix

[spiral maple]

....

[onyx fog]

I2 would be a 2 x 2 matrix

[spiral maple]

Can you answer what I asked??

What ERO is a "type 1 ERO"?

cause identity matrices don't have "types"

[onyx fog]

this??

idk

[spiral maple]

finally

So yeah, E_1 swaps rows, E_2 scales rows, and E_3 adds scaled rows

so det(E_1)= what? det(E_2)=what? (Given it scales the 2nd row by 3) and det(E_3)=what?

[onyx fog]

ummm

ok i think i understand

!close

oh.

.close

[obtuse pebble]

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[iron nymph]

Mason had $40 in his bank account when he started to save $15 each week.
Write an equation to represent the total amount, A dollars, he had in his account after w weeks.

[obtuse pebble]

Please don't occupy multiple help channels.

@iron nymph Has your question been resolved?

[nocturne minnow]

@iron nymph

[iron nymph]

.close

[obtuse pebble]

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[verbal ermine]

From what I understand a is 1 and 3 because those are the 0’s of s’(t)

I am very confused on the rest

I would think b is s(3) - s(0) but the answer makes no sense to me

[obtuse pebble]

@verbal ermine Has your question been resolved?

[brave bramble]

,w graph -x^3 + 6x^2 - 9x - 4

[warm shale]

Failed to get a response from Wolfram Alpha.
If the problem persists, please contact support.

Feb 15, 2022, 2:39 PM

[brave bramble]

,w graph -x^3 + 6x^2 - 9x - 4

[warm shale]

Failed to get a response from Wolfram Alpha.
If the problem persists, please contact support.

Feb 15, 2022, 2:39 PM

[brave bramble]

Huh okay then

So I remember you getting something like -8 for b. Are you still getting that?

Looking at the graph, what are s(0) and s(3)?

[obtuse pebble]

@verbal ermine Has your question been resolved?

[verbal ermine]

s(0) and s(3) = -4z
s(3) - s(0)
-4 - (-4) = 0

wait no so its 0?

that still doesn’t feel right tho

Actually nvm it kinds makes sense

x = t(time)

So according to displacement from 0 to 3 seconds it did not change from -4

So displacement would be 0

and distance?

[obtuse pebble]

@verbal ermine Has your question been resolved?

[tardy epoch]

$s(t)$ is distance. for a time delta between two times $t_2$ and $t_1$ with $t_1 < t_2$
$\textrm{displacement} = s(t_2) - s(t_1)$

[warm shale]

riemann

[obtuse pebble]

@verbal ermine Has your question been resolved?

[verbal ermine]

.close

[obtuse pebble]

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[short forum]

https://www.wikiwand.com/en/Factorial read this and you should be fine

[obtuse pebble]

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[untold cave]

Can someone interpret this for me? Why's the result not directly e^3 and why's there no absolute value around k?

[balmy mortar]

complex integration for wolfram.

[untold cave]

In other words?

[balmy mortar]

You are integrating in R

Wolfram is integrating in C

[untold cave]

Yes

This is what I'd do: $\int_{k+1}^{2k} \frac{dx}{x-k} = \ln\abs{x-k}\Biggr|_{k+1}^{2k} = \ln\abs{k} = 3 \Rightarrow k = \pm e^{3}$

[warm shale]

JSGF

[untold cave]

@balmy mortar

[balmy mortar]

???

well no comment rlly

havent done the Q or anything

[untold cave]

I'm lost, what do you mean by Q?

[unique solstice]

Question prob

[obtuse pebble]

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[rose sandal]

Just need help figuring out 6 on this one

I understand the rest, just not sure how to get a manageable equation on 6

[drowsy girder]

y = 2tan0 - x?

Probably wrong

[obtuse pebble]

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[prime goblet]

How do you find the sum of a finite geometric sequence

[prime goblet]

I am having trouble with sigma

On the top it’s 7, n=1

4x4^n-1

[unique solstice]

$\sum_{n=1}^7 4 \cdot 4^{n-1}$

That?

[prime goblet]

Yeah

[long sinew]

oh sigma notation kk

[warm shale]

PapaBread

[unique solstice]

Sorry had y at the top instead of 7

[prime goblet]

How do I do it?

[unique solstice]

Hmm

Well multiplication distributes over addition

So you can pull that 4* right out

Im assuming that much makes sense?

If not I can explain it more

[prime goblet]

Would you take the 4^n-1 or the 4

[unique solstice]

Just the 4

[prime goblet]

Ok

[unique solstice]

Because theres still an n in the 4^(n-1)

[prime goblet]

Ok

[unique solstice]

You cant take it out because its something different each iteration

So then uhh

[prime goblet]

Ok

[unique solstice]

Another step that might make it a tiny bit easier

How would you get rid of the -1 on the n?

[prime goblet]

By making the n=1 so then it would be 4?

It wouldn’t be powered by the nth power

[unique solstice]

Hmm

Wdym by that?

[prime goblet]

Because if n = 1 like it says at the bottom, wouldn’t they cancel?

[unique solstice]

Oh I see what you mean

For the first term yeah absolutely

But Im talking more in terms of the entire sum

Because soon enough n will be 2

Then 3, 4, 5, 6, then finally 7

Where it wont cancel out

[prime goblet]

Square root?