help-23

[mint veldt]

oh

lmao

I give up

[obtuse plover]

u still have 3x^ (1/3)

its not ^(1/3)

@mint veldt

[mint veldt]

ohhh fs

ffs

It should be 3 * x^1/2

there we go boyz

ty

.close

[safe radish]

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[signal dagger]

I have a problem as follows: 2x^2+kx+3=0, solve for k while k is a constant above 0. I believe that this is impossible if k has to be positive

[spiral bane]

factor it out and see

[young nexus]

2(x+3)(x+1/2)=0 has solutions at x = -3 and x = -1/2 and a k > 0.

[spiral bane]

!nosols

[safe radish]

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.

[spiral bane]

how did you get helpful without learning that

[young nexus]

this isnt a solution as the example asks for "solve for k", its just a counterexample for the "believe" of the op.

he/she has still to solve the example for himself/herself.

stop playing block captain

[obtuse jackal]

I think helpful is automatic anyways

[spiral bane]

wdym automatic

you still have to help a lot

[obtuse jackal]

I think I remember one of the mods saying it's a certain secret condition that the bot can automatically verify

[spiral bane]

huh

how did they even get helpful with only 2000 msgs

I'm at 7000

[obtuse jackal]

I won't pretend to have a clue as to what the criterion could be

[safe radish]

@signal dagger Has your question been resolved?

[safe radish]

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[silent roost]

You can do this?!?
This is allowed??

https://youtube.com/shorts/0ymGn7hhu44?feature=share

[silent roost]

How does he set them equal to each other, why does that work? Huh

[neat kiln]

Same base

Law of indices

[frank glen]

Yep it's allowed

You can rewrite exponents

[silent roost]

Oh really?

What law/rule is that?

[frank glen]

$(\sqrt{a})^b = (a^{\frac 12})^b = a^{\frac b2}$

[flat frigate]

VulcanOne

[silent roost]

How many laws/rules should I make sure I know for something like the SAT how many of those exist up to precalculus

[frank glen]

Understand the general rules

[silent roost]

woah interesting I didn't know that worked

[frank glen]

Don't memorize anything

[silent roost]

so the b distributes into the exponent?

[frank glen]

Yep

[silent roost]

yeah I wanna understand all the rules but i want a list so i can make sure id know all of them 😂

lol

anyway yeah cuz like ik general rules but then when i get given complex or tricky problems i just lose sense of them

[frank glen]

@neat kiln ah you deleted your message. Okay.

[silent roost]

cuz we barely use a lot of the fundamental rules half the time

at least not in creative ways and stuff

but i wish i used rules more to simplify math and be able to do a lot more stuff in my head and stop relying on technology

[frank glen]

You need a lot of experience to be able to get creative

[neat kiln]

Lemme ask you a question nino

[silent roost]

go ahead

[neat kiln]

Do you call your parents by their name?

[frank glen]

What

[silent roost]

uh lol

no i don't

[frank glen]

What question is that

[neat kiln]

Then why don't you forget their name since you rarely use them

[silent roost]

because other people call them their name idk?

it's also family and like

kinda different

i understand what u mean

[neat kiln]

That's why fundamentals of math is very important, treat it as you treat your family, you never know

[silent roost]

i just wanna either find weird complex problems to work with to test and create more algebraic intuition or understand everything fundamentally

since most things are intuitive when it's a weird or tricky problems it throws that out the window and stops making sense

[neat kiln]

Try reading principa mathematica 💀

[silent roost]

omg that is actually such a good idea

but there's probably better ways to learn calc 💀

[frank glen]

Most tricky problems need a small piece of information to change it

Then it becomes familiar

[silent roost]

right

i wanna find ways to work on those things

but im not ever exposed to them nor know about the roles i don't know about

if i did then id know xD

[frank glen]

Well the best way is to play around with the rules yourself

[silent roost]

yeah i thought so but what about the ones i just don't think about and might forget

[frank glen]

I'd say to have a math expert give you a problem and you try poking it with what you know

[silent roost]

Where can I find a math expert 💀

[frank glen]

Usually your teachers are a good source

[silent roost]

I wish all experts of every field were easily accesible and they could just help but like

nahh it's uncomfortableeee

[frank glen]

Mood

[silent roost]

yeah XD

[frank glen]

Second would be the internet.

[silent roost]

mhm that's why im here

[frank glen]

You could search for hard SAT problems and the way they get solved

Also the books you have for math should be sufficient too

[silent roost]

ehhh most problems in both of those sources aren't crazy

I'd say only math competition problems are usually crazy

cuz im in mu alpha theta and yeah those are hard

[frank glen]

Math competition questions are really hard and they usually need actual math experts

[silent roost]

😂 facts

no but they're actually fundamentally simple half the time

[frank glen]

But they need a small twist

And then yeah I'd say they become simple afterwards

[silent roost]

i mean there's this guy which works with like more complex simple numbers and actually helps quite a bit

https://youtube.com/shorts/zZIrIs1l1sM?feature=share

[frank glen]

Well some stuff gets easily recognizable from the amount of times you worked on them

[silent roost]

but yeah it's too time consuming to try to find resources so i don't ever know how to find things that rlly help me and don't take all my time looking for stuff

[karmic hedge]

to a certain degree of competition math

[silent roost]

well at least in high school XD

no advanced stuff here yet

[karmic hedge]

I’m talking about high school comp math

late aime and above isn’t necessarily fundamentally simple lol

[silent roost]

late aime?

[karmic hedge]

https://artofproblemsolving.com/wiki/index.php/American_Invitational_Mathematics_Examination

You know amc10? If you score well enough you qualify for aime, then you can qualify for usajmo, etc

[silent roost]

oh lol

well ive only competed in mu alpha theta

i wish i did more of that too

[karmic hedge]

ah cool

[silent roost]

yeah ive only done stuff in regional level, we could also go to states but it's expensive

there's different levels like algebra 1 algebra 2 precalc stats and calc

[karmic hedge]

Does the school not pay for you?

[silent roost]

not for states ;(

but yeah idk how to prepare and increase my intuition with all this stuff

like i wish i could solve logs in my head and stuff and simplify things easily to work with complex problems and use calculators less

[silent roost]

how do you prepare for it?

[karmic hedge]

for what

[silent roost]

the exam

[karmic hedge]

mu alpha theta? I recommend past exams. Really, for any math competition doing past exams and doing corrections is going to help you improve a lot.

[silent roost]

yeahhh for the most part

i still struggle with dumb things sometimes i rlly just wanna get better with my intuition

[safe radish]

@silent roost Has your question been resolved?

[silent roost]

Like this crazy trick

https://youtube.com/shorts/bTy_jkSn8RI?feature=share

[safe radish]

@silent roost Has your question been resolved?

[safe radish]

@silent roost Has your question been resolved?

[silent roost]

https://youtube.com/shorts/zXNx5Sn6m0c?feature=share

[safe radish]

@silent roost Has your question been resolved?

[safe radish]

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[royal arch]

can someone explain these notes to me in simple words

wtf do the +- represent

[safe radish]

@royal arch Has your question been resolved?

[fossil shore]

those are the quadrants

and they indicate positive or negative

so like cos is inverse is positive in quadrant 1

but negative in quadrant 2

[royal arch]

what about quadrants 3 and 4?

[fossil shore]

cos is x

so x is positive in quadrant 1 and 4

negative in quadrant 2 and 3

but since the bounds are being set from 0 to pi

it's only focusing on those 2 quadrants

sin inverse is focusing on quadrants 1 and 4 because you have +90 degrees and -90 degrees

or in this case +pi/2 and -pi/2 since it's in radians

[royal arch]

oh its just for x

than whats the difference between tanx cosx and sinx

[fossil shore]

no it's for cosine

not for x

for sin it's for y

[royal arch]

what about tan

[fossil shore]

tangent is y/x

[royal arch]

ah yes

[royal arch]

so like... why are these "bounds" being shown

[fossil shore]

idk

that's just where they set it to

do can do cosine from 0 to 2pi as well

[royal arch]

ok so right after these notes these are the example problems

just pretend the work and answers isnt there, like for example on a), why are we adding 26.7 to 180, and how do we know not to just subtract it from 270

[fossil shore]

here you go

that's for cosine tho

[royal arch]

I see

[fossil shore]

you always start from quadrant 1 and go counter clockwise

from quadrant 1 to quadrant 2 there is 180 degrees

[royal arch]

yes yes yes i know othat

[fossil shore]

okay so to find your theta, you know it's gonna be 180+x

now you need to find x

since your sin (y value) is -0.45, you can inverse it and that's where the 26.7 comes in

[royal arch]

ok this sounds dumb but like

lets take example d

what if instead of cos

it was sin or tan

what would the difference be

[fossil shore]

sin inverse

or tan inverse

[royal arch]

lets just say sin

[fossil shore]

arcsin(0.82) and then you add it to 180

[royal arch]

wait i think im understandin where im trippin

theta isnt always the reference angle, correct?

i notice that on each example theres theta, and theres theta prime

[fossil shore]

theta prime is theta inverse

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[frosty granite]

if a graph is being transformed from ln (x+4) to ln (2x+4)

[frosty granite]

is that a stretch?

[faint seal]

,w graph ln(x+4), ln(2x+4)

[flat frigate]

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[frosty granite]

thanks

so its a normal stretch sf 1/2 im assuming

fair enough

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[left willow]

can i get help with c

[left willow]

ik K=Kern(phi), where phi is the homomorphism from G to Sym(G/H)

K={g| g(aH)=aH for all (aH) in G/H}

[safe radish]

@left willow Has your question been resolved?

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@left willow Has your question been resolved?

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@left willow Has your question been resolved?

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@left willow Has your question been resolved?

[left willow]

anyone there

nvm

.close

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[broken wagon]

i dont really need help, im just wondering if theres a place where i can find tasks that a 15/16 year old can do at home to get better at math and things i should learn before studying for engineering

[brave wolf]

khan academy

https://www.khanacademy.org/math

Includes articles videos and is in lots of languages

[broken wagon]

at what stage is a normal 15/16 year old?

[brave wolf]

When you click on courses, pick something from high school section

Algebra 1 e.g.

https://www.khanacademy.org/math/algebra

You can then try course challenge

https://www.khanacademy.org/math/algebra/test/subject-challenge?modal=1

[broken wagon]

right, thank you

how far does this go

does it go to a level you have when studying for engineering?

[brave wolf]

Well it goes far enough to take you 2 months

I am not sure what level you need to study engineering

[broken wagon]

right okay

[brave wolf]

It covers whole high school + some slightly more advanced topics

[broken wagon]

right ill give it a try, thank you

[novel crescent]

when doing engineering you will have to do calculus 1 and 2 which is also in khan academy

[broken wagon]

great

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[ruby nebula]

Could someone help me to prove this
Theorem: Suppose that f and g are analytic on A, where A is subset of ₵ is an openset.
Prove a f + b g is analytic on A

[lean otter]

use the definition of analytic

this is different to your original question, right?

but looks fine

[ruby nebula]

no

it is the result of the original question

isn't that right?

[ruby nebula]

if f and g is an analytic function then f and g are differentiable functions

I tried to show that

[lean otter]

the original question is to show that they are analytic, not differentiable

analytic => differentiable, but converse is not nessesarily true

[ruby nebula]

Could you show that for me

[lean otter]

show what?

[lean otter]

this should be a standard result in your notes

[ruby nebula]

if f and g are analytic functions, could you show that af+bg is also analytic function

[lean otter]

whats your definition of analytic?

[ruby nebula]

An analytic function is a complex-valued function that is defined on an open set in the complex plane and is differentiable at every point in that set. In other words, an analytic function is a function that has a well-defined derivative at every point in its domain.

[lean otter]

ah ok

forget what i said then

this is fine

[ruby nebula]

are you sure

[lean otter]

yeah

the definition i know was based on power series

[ruby nebula]

Yeah there is also a definition for this

thank you Toby

[lean otter]

np

[ruby nebula]

.close

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[twilit garden]

Hi does anyone know how to walk me through this

im having some trouble with these types of questions

nvm

.close

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[karmic hedge]

divide 639027 by 111*101

that yields AB*C

,w 639027/(111*101)

[flat frigate]

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Requested by kappa#4417

[karmic hedge]

now you should be able to do the rest

[safe radish]

@fossil vine Has your question been resolved?

[fossil vine]

how did u get those numbers tho

[young nexus]

CCC = something divisible by 111 -> Cx111.
ABAB = AB*101

[fossil vine]

wait why 101

[young nexus]

ABAB=AB00+AB=ABx100+AB=ABx101

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[coral ruin]

I need some help on an easy mechanics question pls

[coral ruin]

Mass of a cyclist and his bike is 140kg. He's going along a straight road experiencing resistitive force of 50N. Find the work done when he goes from 6ms^-1 to 9ms^-1, travelling 30m

I get 2 different answers

I can't use F(distance) here can i?

Do I have to use ½mv²-½mu²

[misty bay]

why can't you use F dot distance

you just need to know the right F lol

it's not like these definitions magically don't hold in special situations

[coral ruin]

because force changes depending on speed no?

[misty bay]

I mean sure, it can

[coral ruin]

If I use ½mv²-½mu² then take off 50 I get 3100

if I use F(D) I get 41160 J

[misty bay]

what F did you use?

[coral ruin]

1322N

140(9.8)

[misty bay]

why 1332 N

[coral ruin]

Then take off 50

[misty bay]

so you just multiplied a bunch of shit together

[coral ruin]

so 1322

[misty bay]

and hoped that it would work

[coral ruin]

F=ma

;-;

[misty bay]

yeah you need to review

like

force diagrams and all that

you're just multiplying random things

[coral ruin]

How is force due to gravity not mass x acceleration

[misty bay]

the force due to gravity is the guy's weight

[coral ruin]

Yeah

[misty bay]

what does that have at all to do with the situation here?

he's not accelerating downward

the road is pushing up and keeping him from falling through the planet

[coral ruin]

but depending on his weight it'll be more work done no?

[misty bay]

uh not really

I mean sure, but that's only because weight is positively correlated with mass

but it has very little to do with weight

[coral ruin]

So why is F(D) wrong with F of 1322

[misty bay]

because you just randomly multiplied stuff?

it's like asking why 100x100x10 is wrong

why would you expect it to be right

that's the real question

[coral ruin]

F=ma is the equation id been given for force

Ty for being condescending tho

[misty bay]

okay so the force of gravity on the dude is 1372 N or whatever

why does that matter

[coral ruin]

Yup

because it'll be more work done for the dude to go 6 to 9 ms^-1 across 30m?

[misty bay]

why would it be

[coral ruin]

Bc more weight?

[misty bay]

why does the value of the gravitational field matter

it's not like gravity is pulling the guy backward

[coral ruin]

Idfk

I know I use ½mv²-½mu² now

[misty coral]

you can use this

[misty bay]

stop memorizing procedures and formulae

set up some equations involving energy and work

also learn the proper definitions of work and energy

[coral ruin]

My hw is on energy work and power lol

[coral ruin]

;-;

[misty bay]

work is defined as F dot d

[coral ruin]

Yes...

[misty coral]

you should get the same energy value if you use consv of energy or F=ma ^^

[misty bay]

yeah so you can see that the force of gravity is downward while the distance traveled is horizontal

so how is gravity doing any work on the person

[coral ruin]

Idfk

sorry for asking a question then

I know which one to use now

Cheers ig

[misty coral]

what would this be equal to ?

[coral ruin]

3100J

[misty coral]

sorry I mean the relationship

in general

what are you actually working out

if you have 1/2mv^2 - 1/2mu^2 = ?

[coral ruin]

work done by a biker as he accelerates from u to v between distance s

u is 6

v is 9

s is 30

[misty coral]

right, however there is a resistive force here

[coral ruin]

Yeah*

[misty coral]

so it does calculate the work energy Fs but we have a resistive force R so it would be more (F-R)s

[coral ruin]

Yeah

I don't know F tho

[misty coral]

we calculate Fs

Rs would be the work done by the resistive force over the integral from a->b

[coral ruin]

It would indeed

[misty coral]

setup your relationship then

and solve it for Fs

[coral ruin]

wdym relationship

[misty coral]

without the putting in the numbers

[coral ruin]

There isn't direct proportion

It isn't a linear relationship

[misty coral]

im sorry im lost what you mean

[coral ruin]

Wdym relationship

[misty coral]

relationship like a =b

10 = 2 * 5

[coral ruin]

Relationship is like Fαx for spring extension in my country

[misty coral]

ok

[coral ruin]

fαx=>f=kx

[misty coral]

anyway

[coral ruin]

I'll assume u mean equations tho?

[misty coral]

it doesn't matter.

[coral ruin]

so Fs-50s=½mv²-½mu²

[misty coral]

good

well

I wouldn't plug in the R

[coral ruin]

well we know s

That makes it easy?

[misty coral]

I would just solve it for Fs

then you can plug stuff in

[misty coral]

yes it is quite a simple problem

[coral ruin]

30F=½(140(9²))-½(140(6²))-150

[misty coral]

Fs is the work done.

I wouldnt solve for F specifically

[coral ruin]

Yg

Yh*

[misty coral]

Fs = W = ½(140(9²))-½(140(6²))-150

,calc ½(140(9²))-½(140(6²))-150

[flat frigate]

The following error occured while calculating:
Error: Syntax error in part "½(140(9²))-½(140(6²))-150" (char 1)

[misty coral]

,calc 1/2 * (140(9^2))-1/2 * (140(6^2))-150

[flat frigate]

Result:

3000

[misty coral]

huh

uh disgusting syntax problems

also it should be + Rs

not minus

which gets me 4650J

,calc 1/2 * 140 * 9^2 - 1/2 * 140 * 6^2 + 50 * 30

[flat frigate]

Result:

4650

[misty coral]

now we can do the net force method if you want

[coral ruin]

@misty coral I have a different question now mb

I did get 3000J

[misty coral]

For this problem? That is wrong

[coral ruin]

?

won't the biker's force go down if he's experiencing resistitive force

[misty coral]

$\sum F = ma$

[flat frigate]

Clarkie

[misty coral]

$F_{\rightarrow}-F_{\leftarrow}=ma$

[flat frigate]

Clarkie

[misty coral]

$F{\rightarrow}=ma+F{\leftarrow}$ so presumably the forward force must increase if our motion periods remain constant, aka the cyclist must push harder to across a larger resistance

[flat frigate]

Clarkie

[misty coral]

I mean think of it as cycling across sticky stuff that is resistive versus a nice smooth road ig

gotta put more effort in if you wanna travel the same distance across the same period

[coral ruin]

@misty coral

I'm really stuck on a question rn

[misty coral]

you could post it

[misty coral]

this is quite literally the same principles

[coral ruin]

but we don't know F or s

[misty coral]

well we certainly know s

just takes a second to get there

[coral ruin]

I'm so confused

I've always used F=ma where a is -9.8

[misty coral]

why

[coral ruin]

But now I'm being told its all wrong

[misty coral]

why MUST a be -9.8

its not at all

its completely fine

[coral ruin]

Idfk

I genuinely feel so stupid rn

[misty coral]

confusion is the most uncomfortable pain

understandable

it helps me to talk over with my profs or teachers with this stuff

if im ever in a pit of confusion

I would recommend doing the same.

Especially if you've been told that a must be some value

but hiding the formula behind abstraction generated by levels of 'this must be this value' is pretty painful

[coral ruin]

I'm just autistic as fuck and absolutely hate not understanding it

[misty coral]

that is consistent throughout all of academia

best to get familiar with the feeling now

[coral ruin]

Genuinely rn i feel like I could cry

I've taken hours

To do 2 questions

[misty coral]

yep

[coral ruin]

One probably wrong

and it was meant to be a 20 minute task

[misty coral]

and the worst part, nobody cares

[coral ruin]

To do 10 questions

[misty coral]

mhm

[misty coral]

this is brilliant later on btw

just recently spent three weekends on a problem and once you solve it the feeling is very addictive

[safe radish]

@coral ruin Has your question been resolved?

[safe radish]

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[safe radish]

Please don't occupy multiple help channels.

[worn sandal]

o ok

mb

[junior smelt]

#help-20 please and thank you 🫶

.close

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[frigid plinth]

Can anyone help explain this to me?

I tried finding the lengths of the triangle to find the ratios

But the points aren't in exact spots

[rugged trench]

it is only a and e

sub to me friend pls

https://www.youtube.com/@namitvernekar762/videos

help him

[safe radish]

@frigid plinth Has your question been resolved?

[safe radish]

@frigid plinth Has your question been resolved?

[frigid plinth]

It's a practice test

I need explaining please

The guy above didn't even give an explanation

<@&286206848099549185>

Guy above didn't even help he just posted his friend's yt chnl and advertjsed

[safe radish]

@frigid plinth Has your question been resolved?

[safe radish]

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[bold temple]

For what reason would someone use method 2 for

Instead of 1

[faint seal]

they are equivalent methods

the second method is just a shortcut

[bold temple]

The second one is just confusing

So I don’t need to know it?

[faint seal]

yes you do

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

[flat frigate]

kheerii

[bold temple]

Why do I need to know it

[faint seal]

because it's a shortcut

• in the future you will need to know it as well

[bold ferry]

I mean method 1 is literally doing method 2 just not showing it

[bold temple]

I like method one

[safe radish]

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[calm comet]

x-15+1/2x

[calm comet]

For some context in trying to add the length of to rectangles

[slate sky]

if ur doing the math like that

you won’t get an exact answer for x

[calm comet]

wdym

[slate sky]

it’s going to be another equation

as your answer

(x + 1/2x) - 15

[calm comet]

lemme send a pic

[slate sky]

3/2x - 15 would be ur answer

[calm comet]

Ignore the other 2

[slate sky]

u said ur just adding them?

[calm comet]

well I need to get the area of both rectangles combined so I need the length of both of them

[slate sky]

it’s just Area = length x width

[calm comet]

yep

[slate sky]

you don’t need 2 lengths to find the area

u need one

[calm comet]

why?

[slate sky]

too lazy to explain

[calm comet]

so if I have two other those on top of eachother

[slate sky]

it’s just that the opposite sides are = because of the right angles

[calm comet]

they both have different areas

I need to add their lengths

[slate sky]

u wanna send the full picture

[calm comet]

I need to find the area of agility part and re energize area

[serene bobcat]

In this case I guess yes

You have 2 different areas to work on

[calm comet]

so i need to add their lengths right? then just multiply the result by 2x-50?

ohh cmon dont leave me now it would be the second time. We got so far

[calm comet]

^

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[sudden sparrow]

can someone help me with b

[faint seal]

notice the figure is a semicircle

what's the radius?

[sudden sparrow]

1.9?

[sudden forum]

No, that's the diameter

[frank glen]

hey so

@sudden sparrow

How much did you do till now?

[deep depot]

1/2×πr² ☠️

[frank glen]

Ideally we'd want elpims to figure out how to calculate the area

But looks like they are gone

[sudden sparrow]

hello

i know how to calculate area

[fair delta]

Okay so

Do you know the formula $\pi r^2?$

[flat frigate]

ether

[sudden sparrow]

ya

[fair delta]

ight so what would the first one be?

I'll give you a hint
||you know radius is 7 so we use our formula pi * r^2||

||which would be pi * 7^2
which simplifies to 49pi||

[sudden sparrow]

ya

it would equal to 154

thats question a

[fair delta]

That's good

okay so

in b we see that we got the diameter and its a semi circle

@sudden sparrow you here?

[sudden sparrow]

yup

[sudden sparrow]

yea

[fair delta]

okay so

we know diameter = 2 * radius

$d = 2r$

[flat frigate]

ether

[fair delta]

$r = 2/d$

[flat frigate]

ether

[fair delta]

basically we got the radius of the circle now but the thing is

we have a semi circle

$\frac{\pi r^2}{2}$

[flat frigate]

ether

[fair delta]

We can sub r into that

[safe radish]

@sudden sparrow Has your question been resolved?

[fair delta]

@sudden sparrow helllloo

[quasi bison]

@sudden sparrow didnt you post that exact semicircle problem before?

like, with the same diameter of 1.9m

and then our convo died somehow when you asked a weird question and got an equally weird answer from me lol

[fair delta]

It's just subbing in 😭😭😭

It's quite 'trivial'

[safe radish]

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[quasi bison]

it sure is. but some ppl either don't want to or cannot communicate clearly.

[safe radish]

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[lean otter]

Hello, just a quick vector question

[lean otter]

consider those two vectors

<siunitx>
you would have [
\abs{A \cross B} = 4.6 \textsx{cm}^2
]

[lean otter]

the cross product would be in the -z-direction by the right hand rule

so is it correct to say
[
\vb{A} \cross \vb{B} = -4.6\vc{k}
]

but it isnt is it

[split ether]

Isn't cross product of two-dimensional vectors a number?

[split ether]

Or the z axis just isn't shown here?

[gentle niche]

Yeah it is

[lean otter]

what do you mean?

[lean otter]

oh is it simply -4.6k?

[split ether]

As I remember, cross product is a vector when you have 3 or more dimensions

But in two dimensions its a number

[gentle niche]

Uhhh idk about the negative sign but if k is the unit vector orthogonal to A and B in the right direction using right hand rule then you simply scale it by the magnitude of the area between A and B

[gentle niche]

That number is called the determinant

[lean otter]

yeah but like thats

[zinc token]

oh no its lix again

[lean otter]

the magnitude

of the cross product

[lean otter]

hey derpzy

[zinc token]

surely not

[sand minnow]

2D can always be represented as 3D with the 3rd dimension supressed so that doesnt really matter

you can treat it as either a number or a vector with magnitude of that number in 2d

[lean otter]

oh huh

[zinc token]

TIL

[split ether]

So my calc 3 course was wrong

[misty coral]

well

it is the determinant multiplied by the k component

if you have ai bj

you find the det between the two vectors then multiply it by k

that's what i've always done anyway

[lean otter]

so if i got what duh hello said, either
[
\vb{A} \cross \vb{B} = -4.6\vc{k} \
\vb{A} \cross \vb{B} = -4.6
]would be correct?

[sand minnow]

ehh, depends on what you are using it for

if you are trying to find the area these 2 span

then the 2nd with the proper units will also be right

but for the definition of the cross product i would say its not really right

[lean otter]

the question is simply this haha

[misty coral]

top one then

makes more sense to me

[lean otter]

okay TIL, i never realised this

[sand minnow]

magnitude is just a number but the cross product is a vector

[lean otter]

yeah

[gentle niche]

And anyone who says it's a number is a liar

[lean otter]

yeah i guess the second would be more about the magnitude, but you still have that - for the direction so idk

[sand minnow]

but again it just depends on what you are using it for. the cross product can be used to find the area of the parallelogram of the 2 vectors, but that doesnt mean that the cross product is the area of this parallelogram

[lean otter]

yeah i get the idea

thanks lots

.close

[safe radish]

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[sand minnow]

👍

[lean otter]

.reopen

[safe radish]

✅

[lean otter]

wait actually before that

i have a continuation question with the actual question

so now, if I were to find [
\vb B \cross \vb A
]
I know that would just be equal to $-\vb A \cross \vb B$, but how are you meant to calculate that?

[lean otter]

like is the angle now theta = -120?

[sand minnow]

yeah basically, you are just starting from B checking how large the angle to A is, you can either go "backwards" 120, aka -120 or forwards 240 degrees

[lean otter]

ohh i see i see okay

so like

u just start from the first vector and go to the other

wait

but wait

like

[sand minnow]

yeah i think you are actually wrong

first one should be negative

[lean otter]

going from B to A would be counterclockwise

[sand minnow]

and this one positive

[lean otter]

yeah!

exactly

[sand minnow]

can use right hand rule to verify

[lean otter]

yeah amazing

but wait like thats the formula for magnitude right

so how are we retrieving the direction too with the signs too

[sand minnow]

well in a right hand coordinate system the z axis would be pointing out of the paper

so the sign just tells you whether its out of the paper or into it

[lean otter]

Using the unit vector n cap

If you look at the formula of cross product, its actually absintheta ncap

Here n cap is calculated as said by Duh hello using the right hand thumb rule

[sand minnow]

i mean it comes from the determinant definition of cross product

$$A\times B=\det{\begin{bmatrix}
\hat{i}&\hat{j}&\hat{k}\
a_1 & a_2 & a_3\
b_1 & b_2 & b_3\
\end{bmatrix}}$$

[flat frigate]

Duh Hello

[sand minnow]

the n cap or $\hat{n}$ you are talking about gets defined after the fact, its just the normal to the plane that the parallelogram that these vectors make

[flat frigate]

Duh Hello

[lean otter]

Well that is the direction right?

[sand minnow]

yeah but the way you are phrasing it makes me think that you are using this thing that gets defined by the cross product to define the cross product

but yes you are correct, the normal vector and the sign of the cross product will tell us which direction it is pointing, but i think lix was wondering how this direction gets chosen in the first place. and its from the determinant definition which follows the right hand rule, and hence why the cross product also follows it

[lean otter]

no but like

oh wait

hmm

okay never mind haha i got it i think

i was just confused because like

from what i know

[
\norm{\vb A \cross \vb B} = \norm{\vb A} \cdot \norm{\vb B} \map \sin \theta \
\vb A \cross \vb B = \norm{\vb A} \cdot \norm{\vb B} \map \sin \theta \cdot \vc n
]
if this makes sense?

[sand minnow]

ah yeah

thats right

[lean otter]

like what i calculated was the first

[lean otter]

Oh no i was just reminding the fact that ncap is responsible for the direction

so in my mind, the negative sign should've not came up with that, because it is just the magnitude

but rather you have to find what the direction is using the right hand rule

thats what my confusion is i guess

[sand minnow]

hmm, ok now im a bit unsure as well. i guess the first one isnt actually the magnitude

since sin can be negative

[lean otter]

yeah so like

we can totally recover the direction seemingly

[lean otter]

No

Not here

[toxic stratus]

looks like we need a couple more | | s

[lean otter]

oh right

what was the command for that again

\Vmap ~ x time

[lean otter]

Vectors lie between 2nd and 1st quad only

[lean otter]

Where sin is always positive

[sand minnow]

im talking in general

[toxic stratus]

[lean otter]

updated

[toxic stratus]

thats not what i meant lix

[lean otter]

oh

[sand minnow]

around sin

[toxic stratus]

but if you want it like that

[lean otter]

Well in general sin could be negative but not here i guess

[toxic stratus]

[
\norm {\vb a \cross \vb b} = \norm {\vb a} \norm {\vb b} \abs {\sin \theta}
]

[lean otter]

already did it

smh

[toxic stratus]

where the angle θ is measured according to the right hand rule

meaning it can be negative

(looking at you twerkingbee 👀)

[lean otter]

so why this distinction then since seemingly they are identical

they both give you the direction and magnitude

[lean otter]

👁️👄👁️ no

[sand minnow]

$\hat{n}$ is a unit vector thats why

it has length 1

[flat frigate]

Duh Hello

[lean otter]

As far ss i remember

[lean otter]

Our physics teacher said theta is the lesser angle

We have not done vectors in mathematics yet

But this is my memory from basic mathematics lectures

Which is required for physics and all

[sand minnow]

no idea what you mean by the "lesser angle"

depending on which way you are going, i.e with the clock or against the clock will decide which sign the angle will have, but it doesnt matter whether you choose -120 or 240, both are the same

[lean otter]

By lesser angle i mean that if alpha and beta are the angle btw two vetors clockwise and anti clock and alpha>beta in magnitude we will take beta and disregard alpha.

[sand minnow]

excuse the horrible drawing. if we are taking the cross product between A and B we have the blue angle 120 degrees and red angle 240 degrees. what are we supposed to use here?

[lean otter]

Blue one

[lean otter]

I guess he said this because in physics vectors only lie between 0 to 180 not sure about mathematics tho as we are yet to study that in the next grade

[sand minnow]

oh actually i made the example wrong, ok instead we are taking the cross product $B\times A$ which angle are we using then?

[flat frigate]

Duh Hello

[sand minnow]

kinda weird that we are supposed to go with the clock with cross products instead of against it

but anyways, in the case of $B\times A$ we are supposed to use the red one

[flat frigate]

Duh Hello

[sand minnow]

now the red one is equal to the negative of the blue one

so you can of course use that one instead

but then you need to use -120

[toxic stratus]

👁️ 👁️

what the heck

[toxic stratus]

it doesnt matter which angle you use so long as you measure counterclockwise according to the right hand rule 😐

[lean otter]

This is what i mean

[sand minnow]

no apparently you are supposed to measure it going with the clock if you think of it as going from the first arrow to the 2nd arrow

if you are thinking of it as starting on the 2nd and going to the first then yes its counterclockwise

[toxic stratus]

i have no idea what you're on

[sand minnow]

going from a to b is a clockwise rotation

[toxic stratus]

in an ordered basis, take a as your first basis vector, b as your second, then that defines a coordinate axes

the angle is measured counterclockwise just like in the xy plane

[sand minnow]

if you go counter clockwise you would get 360-θ

[toxic stratus]

it doesnt matter which angle you take

because itll be signed measure

counterclockwise being +

[sand minnow]

uhh, in the example of θ=30 then we would have 330 which is -30 so you would get opposite sign no?

aka $B\times A$

[flat frigate]

Duh Hello

[toxic stratus]

what example

[lean otter]

I get it now lol we were not told about negative and positive angle conventions, i guess that statement of his was probably for the students not to get confused as we barely knew any trigonometry at that time

[toxic stratus]

for a x b

hell, you can even go around the circle 42069 times if you want

doesnt matter

[sand minnow]

oh wait, i thought the cross product of this would be positive

i think im dumb

[toxic stratus]

lol

[sand minnow]

[toxic stratus]

triggered the bot

[sand minnow]

ok mb, been ages since ive been working with the non determinant cross product

[safe radish]

@lean otter Has your question been resolved?

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[candid wolf]

Need help ehhm

[candid wolf]

Thomas ang gerry are on opposite sides of a building and are 50m apart. From thomas position, the top of the building has an angle elevation of 50 degrees. From gerrys position the top of the building has an angle of elevation of 60 degrees. How high is the building?

[vagrant sinew]

I have a dumb answer

50-x/√3

Sorry mate

I'm dum

[candid wolf]

welp

[vagrant sinew]

I mean

I think you can divide it in the ratio of 3:2 by seeing the diagram

But what i see isn't always true

So idk

If that turns out to be true then the answer could be 20√3/3

[candid wolf]

Wha the answer has smth to do with the six trigonometric ratios or smth

idk man

[burnt dew]

Have u tried sine law?

[candid wolf]

nope

how would i apply sine

[hasty wagon]

actually i would just use tan(50°) and tan(60°)

let the height be h, and then use tan(50°), tan(60°), h and 50 to make a equation

[candid wolf]

What?

I mean how can i make an equation with that

.close

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[tardy burrow]

Someone readyy

[tardy burrow]

seee

The figure below shows a cross section through a pool triangle, which has the shape of an equilateral triangle and is drawn in red.

Each ball has a diameter of 57mm.

(a) Argue that angle v is 30°
(b) Determine the distance |P S|
(c) Determine the perimeter of the red triangle

[safe radish]

@tardy burrow Has your question been resolved?

[tardy burrow]

help...

[hasty wagon]

hi

is QSP a right angle?

yea, i think if we can prove QSP is a right angle, then we can find v is 30°

[safe radish]

@tardy burrow Has your question been resolved?

[tardy burrow]

yea

I think soo

what we do know

[safe radish]

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[lean otter]

why take the limit and not just plug it in

[safe radish]

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[viral current]

im not sure how to solve this

[safe radish]

@viral current Has your question been resolved?

[safe radish]

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[burnt spindle]

I need help

[safe radish]

@burnt spindle Has your question been resolved?

[safe radish]

@burnt spindle Has your question been resolved?

[safe radish]

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[leaden scaffold]

Can someone help me understand how to evaluate this?

[mortal sandal]

looks like a substitution is in order

[leaden scaffold]

This was my answer. I double checked with calculator and it says I'm right though..not sure if im putting it in wrong

[mortal sandal]

you didn't include the +C right

because it's at the end of the box too

[leaden scaffold]

It's just telling me syntax error..

[mortal sandal]

probably because of the powers on the cosine but

I think you might have forgotten to actually increase the powers

you integrated u^3/2 - u^7/2, right

ah no

ok it's good

[leaden scaffold]

from u^5/2 to 2/7u^7/2

[mortal sandal]

Just try writing cos(x)^(3/2) instead

[leaden scaffold]

and radical u to 2/3u^3/2

[leaden scaffold]

ok

[mortal sandal]

like not as the whole answer just in that format

keep your answer just reformat

[leaden scaffold]

maybe the 3/2 and 7/2 should go in front of x?

[mortal sandal]

what does it look like reformatted now?

[leaden scaffold]

Okay I understand..my powers were in front of (x) which is illegal..

[mortal sandal]

yeah sometimes it's fine

idk if it doesn't like it with fractions or what

maybe they just never happened to build it in

would make it harder to detect correct answers

(though not really much)

[safe radish]

@leaden scaffold Has your question been resolved?

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[oblique badge]

Hello

[oblique badge]

Help?

[winter pivot]

let's look at a simpler example

5/10 = x/2

how do you solve that?

[oblique badge]

hmmm

1

5/10 = 1/2

[sharp venture]

cross multiply then simplify

[oblique badge]

just like what i did?

kz+kw?

[winter pivot]

so what you did was:
5/10 = x/2
2 * 5/10 = x

right?

[oblique badge]

mmmm

i still dont get it

[sharp venture]

no dont expand the bracket

cross multiply with the bracket

to remove the fraction

[oblique badge]

lemmme try

Like so?

[sharp venture]

yes

[oblique badge]

what now?

[sharp venture]

now how do u get k to be by itself

[oblique badge]

taking out the xy and (z+w)?

[sharp venture]

yes

[sharp venture]

so divide both sides by that

[oblique badge]

like the whole left part by xy?

[sharp venture]

divide both sides by xy(z+w)

[oblique badge]

HOLY FUCK I MASTERED MATH

so with equations like this it's always the same procedure?

[sharp venture]

p much

[oblique badge]

hold on a second there's something weird

[sharp venture]

try do a diff question like that

[oblique badge]

why did it give out x(z*w)/y

whereas

the 4 answers are

[sharp venture]

number 2

[oblique badge]

oh nvm i mistakenly fd up the multiplication

thank you so much

[sharp venture]

yea it should be - not x

[oblique badge]

yes

[sharp venture]

np

[oblique badge]

there's another issue

[sharp venture]

u need to find x?

[oblique badge]

it asks what's the smallest value of x

[sharp venture]

can you use your calculator?

[oblique badge]

nope

[sharp venture]

oh damn

[oblique badge]

this is a < one minute quiz during the exam that includes three math seasons that include one which consists of 20 quizes with a timer of 20 mins before flipping the page

[sharp venture]

hm

i guess u do

put everything on one side

[oblique badge]

and leave out the x

?

[sharp venture]

no

try put everything on one side first

[oblique badge]

hmm how so

[sharp venture]

x^2 - 7x + 10 = 0

[oblique badge]

yes

[sharp venture]

now put it into brackets

[oblique badge]

how so?

the x^2 - 7x?

[sharp venture]

no all of it

like

( )( )

[oblique badge]

i see what you did there

[sharp venture]

you should get (x-5)(x-2)

so x= 5,2

smallest value of x is 2

[oblique badge]

wait what how

which parts do i put in the brackets

[sharp venture]

x^2 - 7x + 10

u put that into brackets

if you expand (x-5)(x-2)

you get x^2 - 7x + 10

[oblique badge]

so (x^2)-(7x+10)?

[sharp venture]

no

do u know how to simplify x^2 - 7x + 10

[oblique badge]

i can learn

[sharp venture]

you need to basically put it into a format like (x- ) (x- )

think of 2 numbers that add to -7 and multiply to +10

[oblique badge]

so 5+2 is 7

and both can be multiplyed to 10

damn nice method

[sharp venture]

yeah