help-13

[obsidian coral]

And today is tue/Wed, depending on time zone. That's 4 to 5 days

Plenty of time, if you properly managed your time

[upper basin]

its late

[compact junco]

average procrastinator:

[upper basin]

and I have till 11:59

[hazy minnow]

Your wasting your 30 minutes.

[upper basin]

I just need some help

whatever tho

[obsidian coral]

Cool, as I stated, it's going to take longer than 30 minutes, probably 20 minutes now, to teach you that

[crimson sedge]

ngl I kinda feel him cause i'm procrastinating on an essay in discord :_)

[compact junco]

yo just speedrun

[upper basin]

I couldnt do it for 2 days bc my religion lol

the teacher def racist

[hazy minnow]

Anything is better than 0, just have something down.

[crimson sedge]

https://tenor.com/view/alliumghosts-run-running-away-hamster-fast-gif-22915344

[compact junco]

SAME

[icy latch]

laffin

[compact junco]

bro i should be studying linalg but im on discord

[upper basin]

https://media.discordapp.net/attachments/971920360473767946/971924096294207528/caption.gif

[compact junco]

alr bro

no time to waste

just speedrun

[crimson sedge]

gotta go fast

[upper basin]

man idk most of this stuff

💀

[crimson sedge]

well shit

you got 30 min

[obsidian coral]

Less now

[crimson sedge]

[obsidian coral]

Google is your friend

[crimson sedge]

mathway.com aswell

[upper basin]

you dont think I tried

[obsidian coral]

Or just take the L

[upper basin]

teacher made it originally

[upper basin]

cant

parents finna whoop me

[obsidian coral]

You didn't try hard enough

[obsidian coral]

That's not our fault that you didn't do your work

[upper basin]

whatever virgin

💀

ty for da lecture doe

[icy latch]

what happens if you turn it in late

[upper basin]

I get kicked out of the class

💀

[obsidian coral]

Thanks for listening to my Ted talk

[crimson sedge]

he is turning it in late

[upper basin]

I told bro it was bc of my religion but he not listening

[crimson sedge]

bro

[icy latch]

you might have a million dollar lawsuit on your hands

[crimson sedge]

what happened to sunday monday and maybe tuesday?

[upper basin]

sunday work, monday I did some work

[obsidian coral]

As I mentioned, you had 4 to 5 days, time manage better instead of playing fortnite

[upper basin]

but bro giving me more school work

I cant do 2 things at once

[crimson sedge]

[icy latch]

what's your answer to number 1 btw

[upper basin]

lemme ss

first part of problem 2 aswell

man nobody helpin me

💀

fuck this Imma tell ma teacher to take it outside

squarin up wit dat bitch

[obsidian coral]

First, a few are wrong

[icy latch]

not seeing the vertical stretch by 2

[obsidian coral]

Second, you mathed wrong

Third, wtf is going on with that process?

[upper basin]

Bro the teacher not teaching he givin us work and leaving the call

I'm a smart guy but they aint teachin

💀

[obsidian coral]

If you're smart, then why can't you solve those problems?

[icy latch]

you a remote student? did your teacher specify the time zone for the deadline?

[obsidian coral]

Probably the time zone they live in

[icy latch]

just tryin to help brah out with a loophole

rigid midnight deadlines are annoying

[compact junco]

rip this guy

[obsidian coral]

What kind of teacher makes homework due at a different time zone?

[hazy minnow]

I think they 30 minutes is over now.

[compact junco]

30 minutes is definitely not enough to solve the problems and type out the solution

[obsidian coral]

It's definitely not long enough to teach q5

[icy latch]

bit insensitive of the teacher to make the deadline just 72 hours past sabbath tbh

[hazy minnow]

Wait, isn’t sabbath every week?

[obsidian coral]

But there's Monday and Tuesday, and Friday, the day it was assigned. 3 days

[crimson sedge]

for five problems...

[obsidian coral]

Did they leave the server? Their not on my mutual server list

[calm sierra]

they were auto muted for using a slur then left

[crimson sedge]

https://tenor.com/view/rip-coffin-black-ghana-celebrating-gif-16743302

[calm sierra]

.close

[cedar kiln]

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[obsidian coral]

Lmao

[cedar kiln]

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[chrome flicker]

Can someone help me with this. <@&286206848099549185>

[calm agate]

!15m

[cedar kiln]

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

[crimson oyster]

I can help in 15 minutes

Seeing you couldn’t wait to ping me so

[chrome flicker]

huh? i dont understand sorry

[calm agate]

#❓how-to-get-help

[chrome flicker]

oh sorry

[crimson oyster]

Alright!

so now I will help

Rectangles have opposite sides that are congruent. So VA = ER.

Every angle in that rectangle is congruent so I’m not sure what to put there

AR = AR : Reflexive

And that’s as far as I’ll take you

Do some work your self

[chrome flicker]

Thank you.

.close

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[scenic gale]

2 √(2) * √(7)

[jovial snow]

What is the question? to simplify?

[scenic gale]

That is the question

[balmy apex]

what is the question

[jovial snow]

so it would be √14

because √a√b=√(ab)

[balmy apex]

don't spoonfeed

[scenic gale]

Really?

.close

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[crude bone]

Could someone work me through solving a trigonometric equation?

[jovial snow]

post the equation

[crude bone]

I don't have one, but I could make one up

2cos((1/2)x)-sin^2(x)=3sin(x)

@jovial snow ?

[tropic oxide]

this one might be a little tricky

but one thing that comes to mind is to let t := x/2 (for convenience) then express everything in terms of sin(t) and cos(t) to see what comes of it

[crude bone]

Ok I'll rewrite it

2cos(t)-sin^2(2t)=3sin(2t)

[tropic oxide]

ok

now double-angle?

[crude bone]

There is a theorem for it wait a sec

Sin(2x)= 2sin(x)cos(x)

[tropic oxide]

misplaced parentheses but yes

apply this here

[crude bone]

Ok I'll rewrite it

[tropic oxide]

2cos(t) - 4 sin^2(t) cos^2(t) = 6 sin(t) cos(t) is what you should end up with eventually

this one looks kind of tricky to solve tho

[crude bone]

So what do I do?

[tropic oxide]

dunno. graph it i guess?

[crude bone]

That's it? I'll put it into Wolfram then

,Wolfram 2cos(t) - 4 sin^2(t) cos^2(t) = 6 sin(t) cos(t)

[wraith dagger]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Ninja456#2718

[tropic oxide]

lmao

it's just ,w

,w 2cos(t) - 4 sin^2(t) cos^2(t) = 6 sin(t) cos(t)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Ann#0413

[crude bone]

Cool thx

Any other way to do it then graphing it?

.close

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[wise plank]

Find the solutions of the equation: sin(x+(pi/4)) = (sqrt(2)) cos x within 0 < x < 2(pi)

[wise plank]

So like I thought I had this in the bag

Sorry for the messy handwriting

So I assumed the answers were pi/4 and 7pi/4

However when I plot it on desmos to double check my answers

I get pi/4 and 5pi/4

Idk how it’s possible to get 5pi/4

Cuz 2pi - pi/4 is 7pi/4

But I don’t get it

Idk where I went wrong

If anyone can help it it’ll be helpful

[torpid fulcrum]

(sinx+cosx)^2 equals 1+2sin(x)cos(x)

but in fact you dont have to square both sides

from this part:

expand the RHS and move all the terms to the left hand side

and see what you get

[wise plank]

Okok thanks I’ll do tht rn

Is this correct v

?*

Makes much more sense too

[torpid fulcrum]

yup

looks good

[wise plank]

Thanks bro

[torpid fulcrum]

np

[cedar kiln]

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[cedar kiln]

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[cedar kiln]

Please don't occupy multiple help channels.

[shut reef]

@fallow steppe

[cedar kiln]

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[analog kelp]

Hey. Can someone give me an explanation on Laplace transforms? I am currently working on calculating integrals for quantum mechanics calculations. One integral is the product of two gaussian functions multiplied by 1/r, where r is a vector. My source (https://arxiv.org/ftp/arxiv/papers/2007/2007.12057.pdf chapter 5.2) says that I should do a Laplace transform to get a product of three gaussian type functions. But all I can find is the procedure for r^n where n is a positive natural number. In school we only did the basic theory on Fourier transforms but not how to actually generate the function. We never even looked at Laplace transforms. Can anybody help me what's going on?

[cedar kiln]

@analog kelp Has your question been resolved?

[analog kelp]

Basically I am trying to solve this integral
$\int_R x^{l_1} y^{m_1} z^{n_1} e^{-\alpha_1 (x^2 + y^2 + z^2)} \frac{1}{\sqrt{(x^2 + y^2 + z^2)}} x^{l_2} y^{m_2} z^{n_2} e^{-\alpha_2 (x^2 + y^2 + z^2)} dV$

<@&286206848099549185> Just following standard procedure. Can any of you help?

[wraith dagger]

lela2011

[analog kelp]

.close

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[weak halo]

Why is only 1 and 3 correct?

I am confused, can one not manipulate any of the options to describe y in terms of x?

[cold briar]

ok so

lets start with number 2

what can x and y be

[weak halo]

Okay

sqrt of 2 and sqrt 2 ?

[cold briar]

yes

is it a pair of real numbers?

[weak halo]

Or 0 and 2?

OHH

[cold briar]

but y = f(x) ok idk tbh

[weak halo]

sqrt of 2 is irrational....?

[cold briar]

yes

so therefore it's real (said not real before)

wait

it's real too

wait im having logic issues

[weak halo]

my bad, sqrt of 2 is real

Mixed it up haha

[cold briar]

ok nvm ima just go, my brain is fried today

[weak halo]

Oh

Well thank you for atleast attempting ❤️

[obsidian coral]

Real numbers include negative numbers, correct?

[weak halo]

Yep

Everything except complex

[obsidian coral]

When you manipulate the second equation, to be equal to y, what do you get?

[weak halo]

$y = \sqrt{-x^2 +4}$

[wraith dagger]

Help

[weak halo]

so it's only defined from 0 till 2

[obsidian coral]

Meaning, negatives don't work, correct?

[weak halo]

yep

i.e y can't be negative, yes

OHH

and it states "for ALL real points""

and since it does not include negative ones... it doesn't satisify the requirement

[obsidian coral]

Yes

[weak halo]

ohh

[obsidian coral]

What about 5, same logic, right?

[weak halo]

Yes

only positive x

[obsidian coral]

Negatives can't work

Hence 5 is not an option

[weak halo]

How about 4?

ohh

Got it

@obsidian coral thank you!!

I understand it

I didn't pay too much attention to the word "all" in "all real pairs..."

now it makes more sense

Hope you have a good day ❤️

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[crimson sedge]

EFGH side length 10, WXZY side length 6, I know that the area of trapezoid for up and down is 20 and 12, how can I find the right and left?

[compact junco]

you cant solve for the individul areas of the right and left trapezoids

you can solve for the sum of them though

[crimson sedge]

Ahh I figured it out, I just need to know that the left is > than the right one

thanks!

.close

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[ivory gulch]

6:2(2+1)=9 or 1

[balmy apex]

9

[ivory gulch]

👍

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[cerulean bloom]

Help

[cerulean bloom]

Here if the zeroes are the inverse of each other then for the sum of zeroes,
a+(-a) = c/a
a-a=(-9)/4
0=(-9)/4
Is this question correct or is there something wrong in it?

[soft cloak]

You got the wrong term

[south tundra]

Sum of zeroes is equal to -b/a*

Yeah

[soft cloak]

The sum of zeroes equals (minus) the x term

Their product equals the constant term

[cedar kiln]

@cerulean bloom Has your question been resolved?

[cerulean bloom]

Oh sorry

[cedar kiln]

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[cerulean bloom]

I'm really sorry I should've been more carefull

[soft cloak]

Zero problem

Mistakes are how you learn

[cedar kiln]

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[livid fog]

Hello, I need some help on this problem 🙂

[elfin hemlock]

With?

[livid fog]

would i use

z-score

with this

[elfin hemlock]

Yes

(Otherwise also kinda weird they give you critical z-values don’t you think?)

[livid fog]

what is that again

[elfin hemlock]

Its the z value that corresponds to said significance level

[livid fog]

oh

[livid fog]

What would be my x value to plug in

or the 'observed value'

[elfin hemlock]

Says what it is in the text

[livid fog]

alright ill recheck 👍

[livid fog]

so is it set up like z=2,350-2,200/500?

[elfin hemlock]

What

[livid fog]

?

I'm confused 😂

[elfin hemlock]

Why are there commas

Where does all those values come from

I suggest you check formula for computing z-score

[livid fog]

BOOM

well i know

500 is for sure in the denominator

and i believe 2350 is the observered value

so

2200 should be the mean

right

[elfin hemlock]

Yes

[livid fog]

alright I got 0.3 👍 , what is the next step?

[elfin hemlock]

Oh wait whoops

40 samples

So you want sd of mean of 40 samples

[livid fog]

wait what

[elfin hemlock]

?

[livid fog]

so what do iI do?

i do*

[elfin hemlock]

Find distribution of mean

New sd is sd/sqrt(n)

[livid fog]

is that

0.3/√40?

[elfin hemlock]

Why do you think that?

You are told what sd is in the text

Why are you not using that?

[livid fog]

ohh

[livid fog]

I know this is wrong but

Im just confused on plugging in the numbers

[elfin hemlock]

Looks good

[livid fog]

oh

lmao

[livid fog]

so I got 4.427

[elfin hemlock]

Well 2200 not 2000

[livid fog]

oh

thats what i meant

[livid fog]

yea that's 1.897

[livid fog]

is there anything else

I need t odo

[elfin hemlock]

Compare to the critical values given

[cedar kiln]

@livid fog Has your question been resolved?

[livid fog]

well

it's close too 2.5% right

cause 1.897 and 1.96

[elfin hemlock]

Now you need to know what critical value actually mean

[livid fog]

oh

[livid fog]

what does it mean

[cedar kiln]

@livid fog Has your question been resolved?

[dire geode]

https://www.cuemath.com/data/critical-value/

[cedar kiln]

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[hot cloak]

Timmy ruby and sally share some balls between them

[hot cloak]

Timmy has 5/9 number of balls as the the other two combined

Sunny has 2/7 number of balls as the other two combined

What’s the smallest number of total balls possible

[eternal comet]

• Show your work, and if possible, explain where you are stuck.

[hot cloak]

I got this final equation

But

I don’t know how to get the smallest integer solution to this

<@&286206848099549185>

[green belfry]

Hello

This is your trusted resident helper

[hot cloak]

Hi

[cedar kiln]

@hot cloak Has your question been resolved?

[hot cloak]

😦

[compact junco]

Hello

this is your second trusted resident helper

can u find how much each person has

what fraction of the balls do the people have

[cedar kiln]

@hot cloak Has your question been resolved?

[cedar kiln]

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[crimson sedge]

So I’m totally lost as to how to graph this derivative.. I got a start I think?

Anyone have some tips

<@&286206848099549185>

[hot cloak]

I think it’s something like this

[compact junco]

noo dont give answers :(

[hot cloak]

Sorry

[hot cloak]

Hm?

[crimson sedge]

Hmm

[hot cloak]

Wait I think I see what u mean

Inthink

Let me try

[compact junco]

nicee

[crimson sedge]

that makes sense, although how come we drop down to 0 when connecting the 2 open circles here?

[hot cloak]

Bc

The gradient is 0

Lol

[crimson sedge]

oh

thank you

[cedar kiln]

@crimson sedge Has your question been resolved?

[hot cloak]

I think I got it

Does this seem correct?

[wanton sail]

because the graph is flat there

flat = slope of the tangent line is 0 = derivative 0

[cedar kiln]

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[versed spear]

Answer of 14?

[obsidian coral]

We're not here to give out answers

,rotate

[versed spear]

When i tried, answers a.
When but teacher said its b.
So.. which is the correct one?

[eternal comet]

$y = \sqrt{x-2}$

[wraith dagger]

Remavas

[eternal comet]

What is the lowest value y can ever become?

[versed spear]

Understood!

[versed spear]

0

To infinity

[eternal comet]

well there you go

[cedar kiln]

@versed spear Has your question been resolved?

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[lyric sluice]

correct me if i'm wrong, but shouldn't the n in the bottom equation be negative? thanks in advance

[dire geode]

Yes

[lyric sluice]

ok ty

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[crimson sedge]

If I'm right, f(q)=px^2+q=2 is true right?

[muted bear]

f(q)=p(q)^2+q=2

But what i would note is that the function is an even function

So we know f(-1)=2

[crimson sedge]

so what I should do next?

[vagrant topaz]

Is this function?

[fallen heath]

f(q) = p**(q)**^2 + q = 2

[crimson sedge]

yeah but idk what's the next step

[tropic oxide]

pq^2 + q = 2
p + q = 2

[crimson sedge]

and p = -1 or p = 1?

[tropic oxide]

?

[crimson sedge]

cause f(-1)=2 and f(1)=2?

[fallen heath]

so??

Do you realize that f(-1) = f(1) = p + q = 2 ... so repeating the same statement isn't really giving you any hint on what p and q are

[fallen heath]

instead if you'd realized Ann's putting out the two equations for you

pq² + q = 2
p + q = 2
you're supposed to now solve it for p, q

[crimson sedge]

oh i see sorry

so p can be 0, 3, 1

[fallen heath]

wow, looks correct

[crimson sedge]

cool, thanks for the help!

.close

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[ripe jacinth]

is it possible that for every direction u the directional derivaticve of a two variable differentiable function at 0,0 is positive

[cedar kiln]

@ripe jacinth Has your question been resolved?

[amber ridge]

yeah why not

imagine you have some sort of depression at (0,0)

then every path you take will be up

[ripe jacinth]

what would be an example of such function

[hard lynx]

you learned about quartic surfaces yet?

quadric**

[ripe jacinth]

i dont think so

[hard lynx]

like do yk what a parabaloid is

the equation for a hyperbaloid, parbaloid, etc. in 3d

[ripe jacinth]

oh yeah

[hard lynx]

alr, so visualize a parabaloid centered at (0,0)

wouldnt the directional derivative be positive in every direction?

[ripe jacinth]

oh i see

ok that actually makes sense

thanks

um another question. sorry

i am solving this but i have never solved such equation with f before

so is there any like specifics or solve it normally

[cedar kiln]

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[ripe jacinth]

.reopen

[cedar kiln]

✅

[ripe jacinth]

nvm i gues

thanks for the help for the previous problem

.close

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[dusty hazel]

$3\frac12 - 0.375 + 5\frac16$

[wraith dagger]

What the hell am I doing here?

[dusty hazel]

You CAN add those two first, but pemdas doesn't say so.

But even if you add them first, I don't see why you'd get a wrong answer.

No.

At the end doesn't mean irs prioritised last.

Addition/subtraction have same priority. So if in a problem you have both of them, you go left to right.

I mean, you can only write one of them first in any acronym. But that doesn't really mean subtraction goes last. Even if you say it goes last, then so does addition.

[tropic oxide]

note however

if you try to evaluate a - b + c by adding b and c together, that's going to be wrong

if you want to do the addition first it's going to be (-b) + c

[dusty hazel]

Yes, terms go with their signs.

[tropic oxide]

GEMA

Grouping, Exponents, Multiplication, Addition

also tbh like

taking your expression as written

the first thing i'd do is rewrite everything as vulgar fractions

i.e. $\frac{7}{2} - \frac{3}{8} + \frac{31}{6}$

[wraith dagger]

Ann

[tropic oxide]

that way you will have way less headache

PEMDAS is not gospel, and it should also not stop you from doing cleanup to the expression before doing any calculation to it

your confusion seems to have little to do with fractions, in fact. it's that you learned PEMDAS and not PE(MD)(AS).

[dusty hazel]

Better or worse depends on you doesn't it? Do you like gema better? Yes? Then it is. No? Then it is not.

Sure.

That is overall a more accurate representation.

But that is not what you get.

yeah

You know long division yet?

Yeah then do it for 1/6

yeah

yeah you do ... For that

Sure.

[tropic oxide]

it's not .16666... it's 0.16666...

you should never omit this leading zero

if you don't put this leading zero then you will eventually accidentally forget this decimal point that's just dangling there

[cedar kiln]

@crimson sedge Has your question been resolved?

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[jagged socket]

@dire geode sorry for ping. I can't write to previous channel. Do you mind if i ask some question?

[jagged socket]

I know that limit point of set A is a point that belongs to set B that shares the elements with the set A

But, i have hard time imagining this in R^2

Can you elaborate more on that figure and how it correlates to the set X?

[dire geode]

Call A the hyperbola and B the horizontal line

Find a limit point of A that's in B or vice versa

[dire geode]

This is an insufficient definition.

[jagged socket]

oh

[dire geode]

Use the one taught in class or your book

[jagged socket]

the graph below is the first subset

i thought that it was x axis

[dire geode]

y=0 is the x axis

[jagged socket]

yea

now it makes total sense

thank you

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[kind ivy]

Prove the following hold in all groups, G.: The cancelation law holds; i.e., for all a,b,c ∈G, if ac = bc then a = b.

[kind ivy]

I think this way:

Let a^−1 be the inverse element of a in G (s.t. a^−1⋅a=a⋅a^−1=e where e is the identity element), which must exist by the axioms of groups. Now consider

a^−1⋅(a⋅c)=a^−1⋅(b⋅c)

But I don't know what to do next

[south tundra]

I'd rather multiply by inverse of c tho

[kind ivy]

c^−1⋅(a⋅c)=c^−1⋅(b⋅c)

Like that?

[south tundra]

Yup

[kind ivy]

Thanks, Ohh that's right

e⋅a=e⋅b

a=b

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[crimson delta]

you need to multiply from the right

[crimson delta]

if the group is not abelian

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[obsidian coral]

What are you stuck on?

[tropic nest]

The first step

ik you have to plug in f(x)

[obsidian coral]

If you were given f(x) = 3x, and what asked, f(3), do you know how to do that?

[tropic nest]

3(3)

[obsidian coral]

That's the same logic you would apply to your problem

[tropic nest]

I get that but what do I do with the cos and shit

cos(0 + pi/2) = to cos(pi/2)?

[obsidian coral]

Do you know the unit circle?

[tropic nest]

Nope

[drowsy quartz]

cos0 is equal to 1

[tropic nest]

Why?

[drowsy quartz]

so it woud be 1+cos(pi/2) i believe

[obsidian coral]

You've never seen that?

[tropic nest]

No

[south tundra]

cos(a + b) =/= cos(a) + cos(b)

[drowsy quartz]

you should try familiar yourself with this its very useful

[drowsy quartz]

huh

[tropic nest]

So f(0) is equal to 1 + cos(pi/2)?

[tropic nest]

Just memorize it?

[obsidian coral]

I doubt that, because there's no way your teacher gave you this kind of problem, involving trig functions without teaching the unit circle first

[tropic nest]

She’s teaching just from the textbook

[south tundra]

Didn't you just imply that cos(0 + pi/2) = cos(0) + cos(pi/2)?

[balmy apex]

you'd be surprised

[tropic nest]

Little is done from her

So whatever the textbook teaches, and it’s kinda “you should know it already, if you don’t learn it yourself”

[obsidian coral]

What kind of wack nonsense is that? How could you find the exact value of cos(pi/2) without using the unit circle?

[drowsy quartz]

oh so compound formula..

[sick orbit]

Triangles

[tropic nest]

?

[drowsy quartz]

cos0cospi/2-sin0sinpi/2

[balmy apex]

a calculator

[tropic nest]

Argue the semantics of United States education somewhere else. Have a test tmmr

[obsidian coral]

That's assuming if you know that the hypotenuse is 1 unit

[tropic nest]

so is f(0) equal to what We previously said got to?

[tropic nest]

^

[obsidian coral]

Most physical calculators don't give exact answers

[drowsy quartz]

cos(a+b)=cosacosb-sinasinb

[drowsy quartz]

cos0cospi/2-sin0sinpi/2

[tropic nest]

?

[drowsy quartz]

equal to this actually i believe

[sick orbit]

I mean u just draw 1,1,root2 triangle

[tropic nest]

walk me through how?

[drowsy quartz]

but is that right lol

cos0cospi/2-sin0sinpi/2 = 1x0 - 0x1

[obsidian coral]

That's overkill, because, it's redundant

[drowsy quartz]

yeah pretty pointless

[balmy apex]

you just made the issue more complicated

0 + x = x

[tropic nest]

What’s the answer bruh

[drowsy quartz]

okay someone else help my bad

[obsidian coral]

And it still indirectly involves the unit circle

[tropic nest]

what’s the answer bruh

[obsidian coral]

The answer is, learn the unit circle

[tropic nest]

bruh

[sick orbit]

F(0)=0

[drowsy quartz]

how do u get this

[tropic nest]

Idk bruh, mans not helping

.close

[cedar kiln]

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[drowsy quartz]

i can see you can use compound angle formulae which is cos(a+b)=cosacosb-sinasinb

[obsidian coral]

As I mentioned, it involves a concept you are lacking

[obsidian coral]

That's overkill still for this problem

[tropic nest]

Yeah I’ll YouTube it and learn it

[drowsy quartz]

how do u do it then

[obsidian coral]

Unit circle

[cedar kiln]

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[drowsy quartz]

explain

[obsidian coral]

cos(pi/2) = cos(pi/2 + 0) and you still need the unit circle for cos(pi/2)

[balmy apex]

are you trolling?

have you never learned that $x + 0 = x$

[wraith dagger]

illuminator3

[obsidian coral]

It's unnecessary to use trig identities for cos(pi/2)

[drowsy quartz]

i have not unless ive seen it in a different format

[balmy apex]

what the fuck

[cold briar]

it's basic algebra @drowsy quartz
any number + 0 = the same number

[obsidian coral]

[balmy apex]

it's a field axiom

[tropic oxide]

have you learned about the number zero

you most certainly have

[drowsy quartz]

oh ure saying x+0=x yes ik that

[balmy apex]

what

[drowsy quartz]

is this relevant to the problem

[balmy apex]

yes???

[obsidian coral]

I bet they use -0 instead, that's why they never "learned" it

[drowsy quartz]

.

is this relevant to this?

[cold briar]

yes?

it's asking for f(0)

[balmy apex]

you're trying to use trig identities for $\cos(0 + x)$

[wraith dagger]

illuminator3

[balmy apex]

like what 😭

[obsidian coral]

It's to point out the fact that it's overkill to do cos(a+b)=cosacosb-sinasinb

[drowsy quartz]

cos(0+pi/2)

[obsidian coral]

That is completely unncessary

[drowsy quartz]

nevermind

[balmy apex]

$0 + \frac{\pi}{2} = \frac{\pi}{2}$

😭

[wraith dagger]

illuminator3

[drowsy quartz]

thank you

.close

[cedar kiln]

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[kind venture]

if a function is monton increasing or decreasing such as 2x + 1 which is increasing, it means its injective right ?

[kind venture]

i think there is also another definition, a function is injective when

f(x1) = f(x2) => x1 = x2

[crimson delta]

strictly monotone implies injective, yes

just monotone is not enough

for example constant function f(x)=1

[tropic oxide]

it is not "another definition"

it is a theorem that strictly monotone implies injective though

[kind venture]

whats meant by strictly monotone ?

ah f(x+1) > f(x)

so no >= or <=

but is it also the way around

if its injective => monton decreasing / increasing ?

[tropic oxide]

no

a function can be injective without being monotone either way

[kind venture]

for example ?

[tropic oxide]

for example, the function f: 1:10 -> 1:10 given by f(5) = 6, f(6) = 5, and f(x)=x for x ∉ {5,6}

[kind venture]

O.o

i dont understand that example

[tropic oxide]

what do you not understand about it?

[kind venture]

f(x) = x
how can f(5) = 6 ?

[tropic oxide]

i said f(x)=x for x ∉ {5,6}

[kind venture]

can you maybe show a different example ?

[tropic oxide]

what's wrong with this one

[gleaming cloud]

Try to sketch it

Then you will see it passes the so called horizontal line test

[crimson delta]

continuous and injective I think implies monotone. so if you want a continuous example you are out of luck

[tropic oxide]

here's the graph of my function

@kind venture what is wrong with the example i presented?

[gleaming cloud]

Haha, literally I was trying to think of something like this

[tropic oxide]

and what is this?

[crimson delta]

Ann's example is a function defined on {1,...,10} instead of the interval [1,10] in case you missed that

[kind venture]

i mean its somehow a continoius function

but its not strictly montone increasing

[tropic oxide]

what's "it"?

[kind venture]

the function f?

[crimson delta]

that is definitely not continuous

there are huge jumps in your picture

[kind venture]

but you can draw it without taking your pencil off

so its continious ?

[tropic oxide]

????

i don't understand.

[kind venture]

me neither

[tropic oxide]

are you talking about my function which i called f?

[kind venture]

yes

f

[tropic oxide]

and is your image meant to be the graph of f?

[kind venture]

yes

but i didt read correctly

instead of straight like

[tropic oxide]

well your graph is wrong

[kind venture]

it should be a dot for every f(x) = x

[kind venture]

lets take yours

we can see its not strictly increasting

[tropic oxide]

it is not increasing at all, in fact.

[kind venture]

but you still consider this as a injective funtion

[tropic oxide]

what do you mean, "consider"

injectivity is not a matter of consideration

[kind venture]

when you do this test you see its injective

bc the line gets "cut" only once

[tropic oxide]

a function is injective or not regardless of whether you "consider" it as such or not

[kind venture]

is f continious?

[tropic oxide]

depending on how much topology you know, the answer could be "yes (trivially)" or "question not well-posed"

the domain of f is a discrete set

one typically does not speak of continuity of functions on such domains

[kind venture]

so

continious + strict monton => injective
but
injective DOEST NOT => strict montone

as we have seen the counter example

[kind venture]

now this

[elfin hemlock]

You need the topological space to be connected for that to be true

[kind venture]

ah ok

so not my level 😄

[elfin hemlock]

Basically if you just have your domain be union of (two) disjoint intervals on R

You can make counterexamples

[cedar kiln]

@kind venture Has your question been resolved?

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[sharp carbon]

0 = 𝑥2 + 6𝑥 + 8

<@&286206848099549185>

[sick orbit]

easy way to find the roots

is learning the general formula

so

[gaunt hamlet]

!15m

[cedar kiln]

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

[sharp carbon]

ok

[sick orbit]

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

[wraith dagger]

D.

[sick orbit]

yes?

[sharp carbon]

yea

[sharp carbon]

this isnt the way i was taught

[sick orbit]

ok so you know the roots

is when the graph crosses the x-axis

[sharp carbon]

i need to find the roots

[sick orbit]

yeS?

[sharp carbon]

yes

[sick orbit]

so when the graph crosses the x axis the y value is 0

yes?

[sharp carbon]

yes

(x-2)(x+4)=0

is this not the answer

then i state the roots

[sick orbit]

well thats wrong

its (x+2)(x+4)

becuz if you put x=2 in the function you wont get 0

[sharp carbon]

ok

could you go on a call with me

and explain it ?

[sick orbit]

what bit

[sharp carbon]

or could you write down the answer quickly and send it to me ?

for the first two questions

[sick orbit]

a) roots=-2,-4

[sharp carbon]

i need full solution

[sick orbit]

b) x(x+11)=-18

x^2+11x+18=0

(x+9)(x+2)=0

roots=-9,-2

[sharp carbon]

and #3 if you dont mind

[cosmic steppe]

Factor or quadratic formula

[sharp carbon]

factor

[cosmic steppe]

Which I think you did

[sharp carbon]

2nd one quadratic formula

[cosmic steppe]

#3 you just complete the square

[sharp carbon]

how

[cosmic steppe]

https://youtu.be/C206SNAXDGE

[sharp carbon]

i need help with number 2

more than 3

[cosmic steppe]

Just plug into your quadratic formula

What is your a, b, and c

[crimson sedge]

shouldnt the middle term on the right side be (a+b)x?

[sick orbit]

yh my bad

[crimson sedge]

np just making sure i wasnt going crazy xd

[cedar kiln]

@sharp carbon Has your question been resolved?

[sharp carbon]

need help with #3 please

<@&286206848099549185>

Step by step solution please

[calm agate]

what did you try to do?

[sharp carbon]

not sure how to solve

first i factor out 5x correct ?

????

<@&286206848099549185>

[calm agate]

not really, since you probably make -5x^2 become x^2, not -x

you can't factor 5x anyways since you have +1

[sharp carbon]

so then

[calm agate]

what did you get?

[sharp carbon]

I dont know how to do it

[calm agate]

Have you at least tried to watch that video

[sharp carbon]

That’s what I got

Using my teachers strategy

[calm agate]

,rotate

[calm agate]

You forgot to change the sign of the -30 when you divided it by -5. Also, are you sure the square is correct?

[sharp carbon]

bro just write down the answer

with steps

[calm agate]

we're not here to give you the answer. calculators exist for that. Here we try to make you understand the problem by making you solve it. again, if you don't like it, calculators exist

[sharp carbon]

ok so where did i mess up

[calm agate]

.

[sharp carbon]

wdym i forgot to change the sign

[calm agate]

what is -30x/-5 equal to?

[sharp carbon]

+6

[calm agate]

so in the first step you should have +6x, not -6x

[sharp carbon]

ok

is everything else right ?

so i have -5 ( x^2 + 6x ) + 1

@calm agate

[calm agate]

yes, now the mistake is in the next passages, the square is wrong

[sharp carbon]

what you mean

[calm agate]

(x+3)^2 is not equal to (x^2+6x+6)

[sharp carbon]

Ik it’s wrong

I need help step by step

[sharp carbon]

Let’s start from this

Will the next line be -5 (x^2 +6x +6 -6) +1

?

[calm agate]

no, that's wrong; adding +6 is the wrong part. remember (a+b)^2=(a^2+2ab+b^2).

[sharp carbon]

So what’s the correct next line

[calm agate]

the mistake is already in this line

[calm agate]

.

why did you add 6?

[sharp carbon]

So remove the +6

[calm agate]

the problem there is that you shouldn't add 6, but another number. $$(a+b)^2=(a^2+2ab+b^2)$$

[wraith dagger]

Andrea276

[calm agate]

the 2ab in this case is -6, right (since you have x^2 -6 x)

[sharp carbon]

can we call ?

[calm agate]

no, i don't have time rn. if you try to understand what i'm trying to explain i'm sure you will get to the mistake

[calm agate]

did you understand this?

[calm agate]

and this?

[sharp carbon]

lets start from the beggining

we have the orginal equation

-5x^2 -30x +1

second line is -5(x^2 + 6x) + 1

[calm agate]

yes

now you have to complete the square

[sharp carbon]

how do i do that

[calm agate]

you should probably watch this video

or think about this:$$(a+b)^2=(a^2+2ab+b^2)$$

[wraith dagger]

Andrea276

[calm agate]

which was what i was trying to explain before

that's more similar to our situation: $$(ax+b)^2=(a^2x^2+2abx+b^2)$$

[wraith dagger]

Andrea276

[calm agate]

your expression is $$-5(x^2 + 6x) + 1$$

[wraith dagger]

Andrea276

[calm agate]

so in this case $a^2x^2$ would be $x^2$ in your expression, right?

[wraith dagger]

Andrea276

[calm agate]

if there's something you don't understand ask about it

[cedar kiln]

@sharp carbon Has your question been resolved?

[cedar kiln]

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[swift anchor]

I need to prove this
the sum of all the interior angles of a convex n-gon is 2(n-2) right angles
I'm confused on how to go about it

[crimson delta]

it is stated in that form?

instead of (n-2)*180 ?

what is the simplest shape for which you know the sum of the interior angles

[swift anchor]

triangle

[crimson delta]

can you maybe break down your polygon into triangles?

[swift anchor]

yeah

[swift anchor]

Well the thing about proving this that im confused with is that since it says ngon, how many polygons do I need to prove this for

if I prove it for just one will it not be enough proog

[crimson delta]

it depends on how rigorous you want to be

[swift anchor]

and how would I prove it for the ngon being a triangle

[crimson delta]

well hopefully you can take the triangle case as a given

although I guess it wouldn't be too hard to prove either

depending on what other stuff you can treat as given

[cedar kiln]

@swift anchor Has your question been resolved?

[swift anchor]

I'm kinda confused so could you explain from nothing being treated as given

[crimson delta]

I don't really wanna start at the beginning in proving that the interior sum of the angles in a triangle is 180

for the other step, consider this (whatever)-gon

https://i.imgur.com/luulLaG.png

and how I split it up into triangles

how many triangles are there

can you use that to calculate the total interior sum?

can you generalize that to n-gons ?

[cedar kiln]

@swift anchor Has your question been resolved?

[swift anchor]

I get it, you just use the fact that the angles in a triangle add to 180 then you just split other polygons into triangles

thanks

[cedar kiln]

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[willow lion]

which of these is a possible solution for cos^2x + sin^2x - 1 = 0 in the interval xE (0, 2pi)

[willow lion]

its all of the above right?

[south tundra]

Yeah any x satisfies that equation

[willow lion]

okay thanks

.close

[cedar kiln]

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[vagrant axle]

Can someone talk me through part (b)?

[vagrant axle]

I just don’t get how they find the equivalence class

[crimson delta]

until which step do you get it

[vagrant axle]

Part b

I just don’t understand how they find the equivalence class

Like where does the 0 come from in {0,4}?

And where does the 3 come from in {1,3}

[crimson delta]

well x is always in the equivalence class of x

so that's where the 0 comes from

$[0] = {y\in\bR: 0Ry}$

[wraith dagger]

Denascite

[crimson delta]

do you understand that?

[vagrant axle]

Yes

[crimson delta]

$={y\in\bR: (y-2)^2=(0-2)^2}$

and that?

[wraith dagger]

Denascite

[vagrant axle]

Sorry to make sure I fully understand can you explain your first one?

It’s that the equivalence class of 0 is equal to what?

[crimson delta]

the equivalence class of 0 is the set of all elements y in R with 0Ry

per definition of equivalence class

[vagrant axle]

Ah okay

So the second one is just the relation showed?

[crimson delta]

yes

[vagrant axle]

Ahhhhh

That makes a lot more sense

And so all the elements in this class are just where y fits the thing?

[crimson delta]

yes

[vagrant axle]

Okay so if I’m right there is only one element on the equivalence class of 2

Which is it 2

[crimson delta]

yes

[vagrant axle]

Okay so for the third part I don’t know where they get the 9 from

[crimson delta]

when x>=5 then x-2>=3 and therefore (x-2)^2 >= 9

[vagrant axle]

Aah

Okay thanks that’s helped me a lot with equivalence classes

[cedar kiln]

@vagrant axle Has your question been resolved?

[cedar kiln]

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[cedar kiln]

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[rare wigeon]

CAN SOMEONE HELP ME WITH QUADRATICS

[rare wigeon]

please help me with math Multiply each pair of binomials and simplify your answer.
(3x + 2)^2

thats what the question is asking me but im not sure i understand

[warm slate]

Can you explain what you think it wants you to do, and what you don't understand?

[obsidian coral]

It's asking you to expand that

[sage badge]

(3x+2) write that down 2 times and put them side by side

Then use Foil method

[rare wigeon]

okay thank u 🙂

[cedar kiln]

@rare wigeon Has your question been resolved?

[rare wigeon]

okie so i got 21x+4

im not sure if im right

[cedar kiln]

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[vast coral]

Hello i was given a question in the form of : What is the radius of a circle given the equation : x^2+y^2=r^2 ,and meets the equatio of line,segment : 3x+4y = 12

[shut reef]

why not just send a picture of the question

[vast coral]

The center is at (0,0) but i dont know how to find the radius as i was given no F( from the equation r=sqrt(-F/A)

Its not in english

I ll write it down

[shut reef]

Find the distance from the origin to the line

$d=\frac{|ax_0+by_0+c|}{\sqrt{a^2+b^2}}$

[wraith dagger]

dotcom

[vast coral]

Let me try

in this case is the distance the radius

[shut reef]

yes

but why