help-39

[sonic mist]

K + a !!!

[timber tartan]

Now join points A and D

[sonic mist]

I made a mistake

[timber tartan]

Fair, correct it please

It should be 90 - k + a

[timber tartan]

Do you see that triangle AED is right angled

[sonic mist]

We got 45 degrees for each side then

[timber tartan]

Yep

[sonic mist]

Right angled?

[timber tartan]

Yeah

[sonic mist]

Should i translate that

[timber tartan]

One angle of triangle AED is 90 degrees

@sonic mist

That is, angle DEA = 90°

[sonic mist]

Yea!!

Give me a second please

[timber tartan]

You are writing down all the angles in a neat figure, right?

[sonic mist]

Yeah!

But I'm lost now

What am I supposed to look for

[timber tartan]

I'm also trying to figure that out

[sonic mist]

The answer is C if that helps

Euhh it sent it sideways

[timber tartan]

Oh I got it

So now do you have angle ADE

[sonic mist]

135-k ?

[plush bramble]

,rotate

[timber tartan]

Notice that the sum of angles ADE + CDE + BDA = 180°

[timber tartan]

Maybe you can calculate alpha from this

[sonic mist]

Oke >:3

[timber tartan]

It should be 180 - (90+45-k) = 45+k

Oh it doesn't work

You just get 180° = 180°

[sonic mist]

No

You get k=30

I think

[timber tartan]

Huh, can you show your work

[timber tartan]

Angle ADE isn't 135-k though

It is 45+k

[sonic mist]

I think it should be

If I'm not wrong

[timber tartan]

Wait lemme work it out

Gimme two minutes

[sonic mist]

I think i made a mistake because if i reverse solve it from the answer it doesn't work

I'm sorry for stealing your time :<

[timber tartan]

yeah u just get 180 = 180

sadge

u were right, dwai

k isn't 30 though

[sonic mist]

I won't be able to sleep peacefully if i dont solve this >:(

[sonic mist]

Yeah

I realized :s

[timber tartan]

let's use the fact AB = BD

we can do this

let AB = R

[sonic mist]

Oke

Can we use the similar triangle thing

With edc and abc

[timber tartan]

oh wait

[sonic mist]

Is it any useful

[timber tartan]

im thinking

[tardy zinc]

A suggestion if you dont mind

Sum of angles in ABE is 180 and angle AEB is 90- alpha

That should get you k

[sonic mist]

Lets try!!

[tardy zinc]

@timber tartan you can stop thinking im sorry

[sonic mist]

But doesn't it give you

[timber tartan]

blud it cancels k out

[sonic mist]

180=180

[timber tartan]

anyways now we use trig

[tardy zinc]

Oh sheet

Keep thinking

[sonic mist]

Sjnfksnfoenf

Oh trig oke

Lets think

Ed/ec?

[tardy zinc]

/cd

[timber tartan]

yep

oh yeag

dude

[tardy zinc]

Im thinking of something else but i dont have anything to write on

[sonic mist]

Tell me i can write

Ig

[tardy zinc]

What about finding BE using law of sines then trying to find alpha also using law of sines

Do you think that would work flux

[timber tartan]

ok now it makes sense

[tardy zinc]

It's too long even if it did work theres defo a shorter way (talking about mine not working)

[sonic mist]

[tardy zinc]

Gotta avoid confrontations yk everythings open to interpretation lol

[sonic mist]

You said eb

How would you find if with sinus

I'm sorry my brain is foggy rn its midnight I might talk stupid

[tardy zinc]

Mark point A

O*

[sonic mist]

Mhm

[timber tartan]

,w a√(1-a^2) - a^2 = 1

[jolly parrot]

Results provided by WolframAlpha

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Requested by _nofluxgiven

[timber tartan]

i see

[tardy zinc]

Find OE first then BO

Then try alpha

But this long ad

Af*

[sonic mist]

Finding oe and bo is the same as finding be tho

[tardy zinc]

Yeah you asked how to find be i told

[sonic mist]

I'm sorry i didn't mean to sound rude

[tardy zinc]

Nm you can just find it from the bigger triangle

[tardy zinc]

No no you werent

I'm just so confused how to work on this lmal

Theres too many unknowns

[sonic mist]

Flux what were you trying to solve it from

The path i mean

[timber tartan]

uh trig -> algebra

turns out k ain't real

[sonic mist]

Lmfao

[tardy zinc]

Working please i wanna see for myself, the only hard triangle question in existence this would be if k was imaginary

[sonic mist]

I think all 3 of us are high

Im gonna try to add another unknown

All the 90-k stuff is hurting my brain

[tardy zinc]

Is there something secret written in your language that we could never read

That would be hilarious fr

[sonic mist]

Lmfao give me asec

Better safe than sorry

[tardy zinc]

Ok no secrets there

Disappointment

[sonic mist]

Why don't we do reverse engineering

The answer is 45

[tardy zinc]

Rsink/cos alpha =BE
sink/ BE= sin alpha/ R
cosalpha/R=sinalpha/R
Alpha is 45

Am i a genuis or am i a genuis

[tardy zinc]

I didnt even see this lmao

[tardy zinc]

Spelled it wrong both times what the hell

[sonic mist]

I need a second to comprehend

Brb

[tardy zinc]

Ok

[tardy zinc]

@timber tartan

[sonic mist]

U really don't have any paper around im too slow for this rn

[timber tartan]

fine

that's nice

[tardy zinc]

I used sin rule both times

[sonic mist]

Thank you so so so much

And you too executor

But I'm not letting you off the hook till i make sure I get this shit in my brain

[tardy zinc]

I kept trying angle sums lmao it didnt work at all

[tardy zinc]

Yeah im waiting

Unless my mom comes to whoop me

Then im gone

Cos its 2 am

[sonic mist]

Lmao

I think I get it

[tardy zinc]

Nice

[sonic mist]

I'll try again tomorrow morning, can I dm you if I struggle?

[tardy zinc]

Ok

Dm

[sonic mist]

Kk good night and ty so much:3

[tardy zinc]

Gn

Yw

[sonic mist]

Bro we're been struggling on this shi for the last 52 mins

Gn everyone

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[wicked quartz]

How do I get 2yy’ from this equation?

I understand that the derivative of x^2 is 2x, but why is it different when it’s y^2?

[tardy zinc]

Because you're differentiating wrt x

So y=f(x)

[runic shoal]

differentiate with respect to x

so you have to use the chain rule

[wicked quartz]

Can you please show it step by step?

[tardy zinc]

It's shown already...

[runic shoal]

you can replace y with f(x)

[buoyant panther]

dy/dx is y'

[earnest finch]

$$\begin{aligned}
\dv{x} \qty(y^2) &= \dv{y} \qty(y^2) \times \dv{y}{x} \
&= 2y \times y' \
&= 2yy'\end{aligned}$$

[jolly parrot]

@earnest finch

[wicked quartz]

Thank you very much! However, where is the dy/dx coming from?

[earnest finch]

It's like the chain rule. You can also kinda-sorta visualize it as the y cancelling out.

$$\begin{aligned}
\dv{x} \qty(y^2) &= \frac{\dd}{\cancel{\dd y}}\qty(y^2) \times \frac{\cancel{\dd y}}{\dd x} \
&= 2y \times y' \
&= 2yy'\end{aligned}$$

[jolly parrot]

@earnest finch

[pearl pond]

@wicked quartz Has your question been resolved?

[pearl pond]

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[magic ruin]

i don't get the correct answer

[autumn fossil]

Can you show your work?

[willow hawk]

15280 + 0.25x + 0.15(15280-x) = 18248

can you tell how I got that equation?

[verbal whale]

!occupied

[pearl pond]

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

[tardy zinc]

?

He's answering the question

[verbal whale]

Ups lol I've just realised 🙈

[tardy zinc]

Lol

[willow hawk]

🌚

[pearl pond]

@magic ruin Has your question been resolved?

[magic ruin]

.close

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[exotic gale]

please help i got the answer 15/64 but it was wrong

[toxic fractal]

!show

[pearl pond]

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

[exotic gale]

there are 6 faces on a cube and each face could either be red or blue so there are 2^6=64 total possibilities

and for the numerator

there are 4 faces out of the 6 that we want to choose to have the same color

so 6 choose 4 = 15

but i think that overcounts

but that's how i got 15/64

[toxic fractal]

you can land the cube on 6 different faces

lets say the cube landed on face A

one of the vertical faces is gonna be one of the colors, let's say face B

the chance of faces C, D and E to be the same color as B is 1/8

repeat for each face the cube can land at

[exotic gale]

how did you get 1/8?

[toxic fractal]

three faces, (1/2) chance for each to be the same as the fixed one

so (1/2)^3

[exotic gale]

so (1/8)^6

?

[toxic fractal]

no

[exotic gale]

oh wait that's overcounting

[covert quiver]

A lot yeah

[exotic gale]

(1/8)^3 i think

[covert quiver]

There are some colorings where multiple faces could be on the bottom to satisfy this so you will overcount if you count that way

But you could account for them

[exotic gale]

can you elaborate on this please

[covert quiver]

If all 6 sides are the same (6 red or 6 blue) any face being bottom would work
If 5 sides are the same (5 red 1 blue or 5 blue 1 red) the different colored face and the one on the opposite side of that would work as the bottom
If 4 sides are the same (4 red 2 blue or 4 blue 2 red) such that the different ones are opposite, either of the different ones would work as the bottom one
If 4 sides are the same but in some other way no side being bottom would work
If you have 3 red - 3 blue no side being bottom would work

You can actually just think of these 5 categories and count how many colorings are in them (they need to add up to 64)

[exotic gale]

(1/8)^3? i think i was overcounting earlier

[covert quiver]

You could do 6 times 1/8 because 6 sides but you’d have to later account for the overcounting

You can still get to the same answer you would get some other way but it is honestly more work

[covert quiver]

Id recommend this

[exotic gale]

why do we need to work out the choices that don't work?

there are only 3 cases that work in here

[covert quiver]

Oh yeah you could count the amount of colorings in the 3 cases that work and divide by 64 too

I counted the amount of colorings in all 5 cases so i could make sure they added up to 64 so i didnt count a coloring in two of them or smth

or missed one

[exotic gale]

oh okay

[covert quiver]

But you only need the ones that work you’re right

[exotic gale]

so is it (30+10+2)/64=42/64=21/32

if you want me to explain my cases then i can

@covert quiver

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[covert quiver]

You should because the answer is wrong

[pearl pond]

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[eager jewel]

im getting the general term as
tan inverse
(n^2+3n)/(2n^2+6n+5)

which im not able to simplify

by simplify i mean write as a difference of two tans

[rustic tendon]

so you have a - b = n^2 + 3n and 1 + ab = 2n^2 + 6n + 5

[eager jewel]

1+ab

[rustic tendon]

yeah

mb

[eager jewel]

yea

oh wait let me try something 1 sec

[rustic tendon]

did that reveal anything

ab = 2n^2 + 6n + 4

2(n^2 + 3n + 2)

2(n + 1)(n + 2)

[eager jewel]

yeah..how do i go from this

[rustic tendon]

Hmm

[eager jewel]

when i have n^2+3n in numerator

or did i write the wrong general term?

[rustic tendon]

Maybe

I didn't check that

[eager jewel]

i dont think its wrong tho

for n^2+3n i got it as difference is in AP

and the other one i wrote term as

1+(n+1)(2(n+1)+2)

@rustic tendon this is the soln given

[azure kite]

yo

[eager jewel]

Hi

[azure kite]

yeah its diverging

the term is getting bigger and bigger , if you keep adding big term to big term , the series wont give good answer
i didnt check values tho , im going what the solution wrote

[toxic lichen]

what kind of textbook has you work with infinite series but is allergic to sigma notation tbh

[azure kite]

jee likes to make questions look complicated than it has to be

[dusty flame]

If general form is given, they think it’ll be too easy 🥀

[toxic lichen]

??

oh so just deciphering the general term is intended as part of the difficulty??

[eager jewel]

ohh alr alr

[eager jewel]

yeah lmao

[dusty flame]

Ye😭

[toxic lichen]

christ

[eager jewel]

its a way of including sequence and series as part of the q

ty anyway

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[eager jewel]

im not able to get option D

[eager jewel]

fuck we just have to add options a and b

.close

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[eager jewel]

(sorry)

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[rustic tendon]

.I didn't even see the last option 💀

[nova osprey]

What formula was I supposed to use for questions that look like > 2x³+2x²+4 < ?

[tardy zinc]

!xy

[pearl pond]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[nova osprey]

I don't have the original paper but I'm mostly certain that's how the question was

My problem was that the first unit was x³ and second unit was x² and I think I vaguely remember a formula used for those equations

[runic shoal]

if you don't have the original problem we can't help you

what does it ask you specifically to do

[nova osprey]

Oh right I forgot to say that

Told me to solve for x

And it all equaled 0

So 2x³+2x²+4=0

[azure kite]

for solving cubic equation
you will have to use trial and error to find 1 root , and then eprform polynomial division with the factor on the orignal cubic

[nova osprey]

Okay thanks

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[eager jewel]

oh lmao

[tardy zinc]

Me when all my roots are through RRT 🤓

[pearl pond]

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[dusky spire]

how do i do i find the intergral for dx in 3d geo shapes like this https://www.desmos.com/3d/sllhp2cn58

[pearl pond]

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[dusky spire]

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[red drift]

cant seem to find an answer, im basically stuck after carrying x and 90-x angles throughout the the 3 triangles

[carmine zinc]

dont you need the pos of E

whats DE

[warm current]

You want to consider similar triangles

[carmine zinc]

this question cant be solved without further info

[warm current]

Actually, that's right. Some info is missing somewhere

[pearl pond]

@red drift Has your question been resolved?

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[red drift]

fuck me im sorry i accidentally undid that

[red drift]

something came up, had to go somewhere for a while. im back

[carmine zinc]

1?

[red drift]

yep

[carmine zinc]

in that case

you just need one triangle

construction

do you see how you can make AE the hypotenuese of 1 triangle?

[red drift]

1 big triangle yeah

[carmine zinc]

draw it

Let's call the vertex you construct "F"

[red drift]

are we talking about this?

[carmine zinc]

yup

[midnight haven]

excuse me for my bad english, as I am not a native I will have struggles explaining this,

so you see we have BC edge that is 5 units long and CD edge that is 6 units long. As long as we keep the real measurements right, we can move the edges to turn this shape into a big triangle, this means the floor of the triangle is 3 + 6, thus 9 and the side is 1 + 5 thus 6

tan alpha is the edge alpha sees an infront of it divided by the side edge (except hypothenus)

so, 9/6

simplified 3/2 should be the answer if I didn't mess up something

[carmine zinc]

Labelling that vertex F

What shape is CDFB?

[red drift]

okay lets label that f

rectangle

5 6

[carmine zinc]

Yup

whats the property of rectangles regarding opposite sides?

[red drift]

god this makes so much sense

[red drift]

yeah i can just carry them

which makes 1 big triangle and easy to find whatever trigo function it asks

thanks so much

[carmine zinc]

you can close the ticket if that's all

[red drift]

give me a sec

yep

again thanks a lot

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[midnight haven]

I am glad you understood my statement, have a nice day!

[pearl pond]

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[grand bough]

This is the circular convolution formula

[grand bough]

but i don't understand why is there a mod

unlike the linear convo

[waxen agate]

Think of the signals arranged around a circle of length N. When you shift h[n] by m, instead of extending beyond the circle (as in linear convolution), you wrap the overlap around to the beginning, hence “circular” convolution.

[grand bough]

please if you can explain more this circular convo because at this point i'm lost

[waxen agate]

In circular convolution, both signals x[n] and h[n] are assumed to be periodic with period N. In other words, x[n + N] = x[n] and h[n + N] = h[n].

So, when you compute the term h[n - m], you might get indices outside the range 0 <= n-m <= N. The mod N is there to wrap the index back into that range, ensuring it “wraps around” as if the sequence repeats indefinitely.

Does this make sense to you?

[grand bough]

yeah yeah i get

no mod means we can get n-m outside the range as if it was a linear convolution

[tropic saddle]

with things like this you should always do an example

take for example N=3 and write out the sum

then you will see where you run into problems without the mod

[grand bough]

yeah yeah i get it

[grand bough]

we'll get terms like h[-1] and h[-2] which is a problem with the mod h[1] h[1]

thank you @waxen agate and @tropic saddle

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[worldly turtle]

I am stuck on the part where I have to solve algebraically because I thought that you couldn’t solve the system if the 3 variables are different and not on the same equation

[worldly turtle]

<@&286206848099549185>

Help

<@&286206848099549185> its about vectors if you need more info let me know

[frail zephyr]

I think you missed an equation

[worldly turtle]

Wdym

[frail zephyr]

wait

[worldly turtle]

If you need the file I can upload it to you

[frail zephyr]

sure

i need more context

[worldly turtle]

Do you have an email I can send it too

[frail zephyr]

you can dm me no ?

or is the file too large ?

[worldly turtle]

It’s not letting It says my orginizations data cannot be accessed

Nevermind i got it

[frail zephyr]

you mean you solved it ?

[worldly turtle]

no the file sorry

[frail zephyr]

oh ok

[frail zephyr]

what were the 3 equations you found in 3.b ?

[worldly turtle]

i found
[-300] + 15.56t = 500 + Xvt
[-300] + 15.56t = -300 + yvt
[300 ]+ 15.56t = 300 + Zvt

[frail zephyr]

yeah, the 3rd one ( [300 ]+ 15.56t = 300 + Zvt ) isn't that

[worldly turtle]

its not why would it just be 300

[frail zephyr]

you're supposed to have a 0
[300 ]+ 0 * t = 300 + Zvt

[worldly turtle]

okok that makes sense because he doesnt move correct

[frail zephyr]

yeah, and if you look at you're equation in 3.a, you can just take the lines for your equations

[worldly turtle]

okok

thats how I would solve 3.c

and what do you mean take lines

[frail zephyr]

wait, i'm taping it out

[worldly turtle]

ok

[worldly turtle]

ok Im following

[frail zephyr]

notice that, if you only care about the x component, you only take the top line of ecah vector

same for the y component, you only take the middle line

same for z, the bottom line

[worldly turtle]

yes then you solve for it correct like a normal equation

[frail zephyr]

yeah

[worldly turtle]

so -800 + 15.56t = x

[frail zephyr]

x * t yeah

[worldly turtle]

okok so -300 +15.56 = 500 +(-800 + 15.56) t

then I would go down the line filling in everything like that

[frail zephyr]

tbh, you don't even need to do that, because you can find z and y without doing the line filling

and also you can't replace y with what you found for x

[worldly turtle]

but arent they differnet equations

[frail zephyr]

it's 3 independent equation

each with 1 variable

x, y and z

you're just looking for x y and z in term of t (idk if that's understandable)

well t* if we want to be picky

[worldly turtle]

yeah so I dont have to find all that just what it equals to

[frail zephyr]

yeah, just isolate x, y and z

[worldly turtle]

okok

i get what you are saying

[frail zephyr]

also, it's supposed to be Vx, Vy and Vz, but whatever

[worldly turtle]

but thgen what about t

[frail zephyr]

well, that's for the next question

[worldly turtle]

okok hold upo I have company formation ill be back

[pearl pond]

@worldly turtle Has your question been resolved?

[pearl pond]

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[steady wolf]

for a second order differential equation, why is it true that after doing the y = e^(rx) and i use the discriminant, if D>0 then the solution is in the form y = c1e^(r1x) + c2e^(r2x)? i dont get why thats true

[meager solstice]

do you know any algebra ?

the general proof is easier to understand with algebra tools

if not then plug in y=exp(rx) and suppose that it's a solution to the equation

then you will find that a (r^2) + b r + c = 0

then if you suppose that the general solution is of this form

with phi and psi two different functions of x

then you'll have your result

[meager solstice]

but to prove this you need algebra

or there is another proof but it's completly unintuitive

[steady wolf]

huuuuuuuuhhh

[steady wolf]

lmao what

what level of algebra is required

cuz ya i understand algebra lol

[meager solstice]

ok idk how to say this in english wait a sezc

do you know what an eigen value is ?

[steady wolf]

np

and nope

[meager solstice]

search diff equation of order 2 wronskian

maybe

well anyway it's too hard to explain like that so it's prob better if you search for yourself

but I think it would be better if you wait a little before trying to understand everything about it

till you know more about algebra in general

[pearl pond]

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[orchid pendant]

wdym

[wet osprey]

Draw it

Sketch the region then use your multivariate calculus knowledge to find the bounds of integration and integrate

Go learn it first

[orchid pendant]

it is f(x) or f(x,y) ?

you'd have 2 integrals

[wet osprey]

https://youtu.be/lv_awaaT6gY?si=AI2TFAsUZ60otPaL

[orchid pendant]

euh not sure tbh

pretty sure the bounds are 57 for each

5 to 7*

sike

hang on

yeah actually i think that would work

well if its z=x+y

no

0=x+y yeah

actually yeah that would work

in all

overall

do it

nah dont even do dx dy

just do dx

y=-x

you can do single variable

[pearl pond]

@naive marlin Has your question been resolved?

[limber nimbus]

if this is your only bound, then you can let x be unbounded -inf to inf, and then 5 - x < y < 7 - x

a general algebraic method for these types of problems is to pick an ordering for the variables, and iteratively find the range for each variable given values for the previous ones

this might be harder or easier depending on the ordering you pick and the region itself, but often times you will be able to do it purely algebraically (although it can be a lot simpler to just graph)

[pearl pond]

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[worldly turtle]

can someone check my work up until the point I am stuck and help me plase

[worldly turtle]

<@&286206848099549185>

[ivory basin]

!nopdfs please

[pearl pond]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[ivory basin]

Send screenshots

[worldly turtle]

<@&286206848099549185>

I am on using equation 3d and 3c i dont really know if I am right and I am having a hard time understanding what the problems are asking for

<@&286206848099549185>

[pearl pond]

@worldly turtle Has your question been resolved?

[worldly turtle]

no

<@&286206848099549185>

.CLOSE

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[void scaffold]

can someone tell me if this is right?

[white estuary]

How is there a cube there

[void scaffold]

ye there's supposed to be a cube in the upper circle you drew

[white estuary]

Ohk

[void scaffold]

original q

@white estuary

[white estuary]

Put upper limit first

Then lower limit

[void scaffold]

i just learnt calculus basics so my brother decided to bomb me with ts 😭

[void scaffold]

i did???

[white estuary]

Lol i relate

U put pi/4 first

Which is lower limit

[void scaffold]

????

how

pi/4 is 90 deg

pi/12 is 30 deg

are you ok

[white estuary]

Pehle pi/12 dalo then minus karke pi/4 dalo

[ivory basin]

Honestly bruh why

[white estuary]

Oh

[midnight haven]

pi/4 > pi/12

[void scaffold]

older brothers are like that

[ivory basin]

Fair

[white estuary]

This is wromg

[void scaffold]

but you flip it during the brackets tho

[white estuary]

Yes but he put the wron lim8ts in the last step so i got confused

[white estuary]

No not the lim8ts

[void scaffold]

then?

[white estuary]

U flip the position where u write limits

[void scaffold]

yes

ik

[midnight haven]

oh

[void scaffold]

aren't you supposed to do that during integ?

😭

[white estuary]

This is what u should do

[white estuary]

Nope

[void scaffold]

oh im stupid

thanks

[white estuary]

Its cprrect

The answer is cprrect

[white estuary]

No ur not stupid

U just leanrt integration

Ur answer is absolutely correct

[void scaffold]

ok thanks

.close

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[pearl pond]

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[formal tiger]

hi can someone explain how to solve this? just not sure how to approach

[formal tiger]

what i thought is that car s would be appearing to move in the negative direction at t4 bc thats when car t would pass car s but chatgpt says otherwise

[viscid shale]

!nogpt

[pearl pond]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[viscid shale]

Also, lets go over what the question is basically asking

[trail swallow]

you're right

when T's speed exceeds S's speed

[viscid shale]

Imagine for a sec you are in Car T, under what circumstances youll see the car S moving backwards

[formal tiger]

when car t passes car s?

[steep hawk]

car s is basically ahead of car t from t1 until t4?

[viscid shale]

Not really needed

[formal tiger]

huh

wdym?

[viscid shale]

Imagine youre 1km away from me

And im moving slower than you

Youll be closing in to me from my perspective

But havent crossed me yet

[steep hawk]

mhm

[formal tiger]

ohh

so it would be when car t is faster than car s

[viscid shale]

Okay, arguably is when its slower

Faster would mean that its going into the positives from our perspective

Now, in a position-time graph, what does the velocity/speed represent?

[formal tiger]

derivative

[viscid shale]

So, we are looking for what thing?

In respect of both cars

[formal tiger]

oh so it would be equal slopes?

[viscid shale]

equal slopes means we are moving at the same speed

from the perspective that the derivative (slope) is the velocity/speed

[formal tiger]

o wait so then when car t is steeper than car s

[viscid shale]

What would a steeper derivative mean?

[formal tiger]

higher derivative

[viscid shale]

Yeah, but in terms of speed

[formal tiger]

faster

wait isnt it car s going backwards

[viscid shale]

mb

[formal tiger]

npnp

[viscid shale]

Well, you could try to approximate the actual derivative of both functions since they are quite elementary

But you could also find the point at which the slope is tangent to the line

anything beyond that, has a bigger slope (faster)
anything before that, has a smaller slope (slower)

[void scaffold]

t4

basically

imagine two people are running

one is faster than the other

so for the faster person

it seems like the slower person is moving negatively

appears to

not is

so same thing here

once car t moves faster than car s

which is at t4

[viscid shale]

This is wrong, it asks the first point at which the Car S seems to move backwards, not at any point

[void scaffold]

yes...?

[viscid shale]

Try to draw yourself the tangents

also

[void scaffold]

oh shit wait this is d-t not v-t

[pearl pond]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[viscid shale]

wrong factoid lmao

[void scaffold]

what

wiat no t4 is still right

[viscid shale]

!nosols

[pearl pond]

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.

[viscid shale]

This one

[void scaffold]

oh al

new here so

thanks for letting me know

[viscid shale]

np

[void scaffold]

can i just ask a quick q since you're already here

[viscid shale]

t4 is a point at which the carS seems to move slower

we are looking for the first point

[void scaffold]

yep

t3

[viscid shale]

go ahead

[void scaffold]

the integral of 1/(a+x) is just ln (a + x)

right?

[median bronze]

ln(abs(a+x))

[void scaffold]

ok so look for where the tangent to the graph of car t becomes steeper than that of car s

[void scaffold]

okay thanks

[pearl pond]

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[final ember]

I had a quick question regarding if my working out for part b is actually valid

$x^\mu = (ct,x,y,z) \implies \frac{dx^\mu}{dt} = (c,u_x,u_y,u_z)$

[jolly parrot]

Katrro

[final ember]

and if you rearrange dt in terms of gamma and d tau you can substitute it in and get the right expression but is that valid?

[pearl pond]

@final ember Has your question been resolved?

[fringe goblet]

thx bro

[pearl pond]

@final ember Has your question been resolved?

[pearl pond]

@final ember Has your question been resolved?

[final ember]

<@&286206848099549185>

[pearl pond]

@final ember Has your question been resolved?

[nocturne plover]

you mean you calculate $\frac{d x^{\mu}}{d t}$ and then multiply by $\gamma(u)$ to get $\frac{d x^{\mu}}{d \tau}$?

[jolly parrot]

Katharine

[final ember]

I meant like I calculated $\frac{dx^\mu}{dt}$ then from part a I rearranged the expression to get $dt = \gamma(u) d\tau$ and subbed it in for dt $\frac{dx^\mu}{\gamma(u)d\tau}$

[jolly parrot]

Katrro

[final ember]

like a treating it as an object

[nocturne plover]

that's fine, it's basically the same thing as what i said but just different order

i think technically mathemathically it's iffy

but for physics it's fine and the result is correct

[final ember]

I just realised it's basically just using the chainrule but skipping a step

but thank you

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[vagrant briar]

f(x) = { x<0 : -1 , x=0 : 0, x>0 : 1}, g(x) = cos(2x)-2sinx+3, h(x) = f(g(x))
i calculated and found that g(x) = 0 at x = pi/2 +2npi, and LHL and RHL of h(x) at pi/2 + 2npi= 1 but h(pi/2 + 2npi) = 0... i had difficulty plotting the graph of h in desmos. i wanted to check the nature of the discontinuity

[toxic lichen]

f(x) = sgn(x)?

so h(x) = sgn(cos(2x) - 2 sin(x) + 3)

[vagrant briar]

yess!

[toxic lichen]

so your h is equal to 1 everywhere except at pi/2 + npi

and at those points it's 0

that makes it a jump discontinuity

[vagrant briar]

i need to determine what type of discontinuity there is in the function h(x). i was hoping desmos would help but it seems to fill in the discontinuities in the graph

[toxic lichen]

where it jumps down by 1 and then immediately up by 1

[vagrant briar]

ohk. my module says its a "isolated point discontinuity". whats the difference between those two

[toxic lichen]

ehhhhhh the difference is i didnt know what to call it.

[vagrant briar]

so it will categorised as isolated?

[toxic lichen]

if isolated point discontinuity is what they want you to call it then thats what they want you to call it

nothing deeper than that

[latent sage]

It’s an isolated removable discontinuity not a jump both side limits are 1 but the function’s value there is 0

[vagrant briar]

oh yeah. i was just typing that out. i should have looked over at the definitions once more lol

tysm everyone

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[sweet willow]

For listing all the partitions of {1, 2, 3, 4, 5} that have 2 non-empty sets, I really have no clue how to go about this by this point. I know about Bell numbers but not sure how that's gonna help me find all the possible combinations? I was also trying to look at the programming example below too. But I feel like I'm not thinking about this correctly. How would you break this down and keep track of everything? Thank you.

https://www.geeksforgeeks.org/dsa/generate-all-partition-of-a-set/

[median bronze]

Well, do you know how many partitions you should expect?

[sweet willow]

I'm gonna be honest, I'm not sure. We only briefly covered it, and I've tried looking it up. You have to start by making a triangle, from what I understand.

So it would be:
1
1, 2, 3, 4
... (not sure how to calculate the rest)

I think, in my case?

[sonic geyser]

you need techniques from combinatorics

I'm not sure how much you know about that though

[sweet willow]

I'm in a Discrete Maths I class, and unfortunately I don't remember learning about this back in high school. Sorry. rubs temples Should I be looking into combinatorics then?

I think it's this?

[sonic geyser]

only if you want to actually learn how to count the number of possibilities. upon first glance it seems like the stars and bars method might be useful here?

[sonic geyser]

yeah

[sweet willow]

Ah I see, ok. Give me a bit to look at that. Yea, I've just been having issues following along with what professor was doing.

[sweet willow]

Thanks for telling me about Stars and Bars. I'll try figuring this out using it, gonna take a break, this has been tiring. 🙂

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[stoic imp]

I need some help with this exercise, I have some progress

"Determine all the tuples (a,b) in Z^2, such that it is satisfied simultaneously "4|a", "8|b" and "33a + 9b = 120"

ok, so for example if 4 | a then a = 4x for some x in Z
similar with 8 | b then b = 8y for some y in Z
I place this in the last equation and we get
33(4x) + 9(8y) = 120
and we get
132x + 72y = 120
and if you divide by 12 both sides

we get
11x + 6y = 10
after this is where I get stuck
we might need to use fubini
like, first solve 11x + 6y = 1

so
gcd(11,6) = 1
11x + 6y = gcd(11,6)
11x + 6y = 1
this is where I get stuck
I forgot how to solve linear diophantine equations
ok. now I remember
just, first find a particular solution
then after we found one particular solution we can find all the solutions to the linear diophantine
so for example
11(-1) + 6(2) = 1
because -11 + 12 = 1
so we got that one solution to the linear diophantine is (-1,2)
now, its simple
11(-6) + 6(11) = 0
so
all the solutions to 11x + 6y = 1
are of the form
11(-1 -6k) + 6(2 + 11k) = 1
where k in Z
so all the soltuions to 11x + 6y = 1 are (a,b) = (-1-6k, 2 + 11k)
the issue is that we were trying to find all the solutions to 11x + 6y = 10

[toxic lichen]

you need to find any solution at all

you dont need to go through =1

unless you feel stuck or unable to spot one for 11x + 6y = 10 right away

[stoic imp]

care to elaborate?

[toxic lichen]

22 - 12 = 10

11*2 + 6*(-2) = 10

this one i spotted just now

[stoic imp]

I need to find all of them

ahh you say (2,-2) is a solution to the original diophantine?

[toxic lichen]

to 11x + 6y = 10

[stoic imp]

33a + 9b = 120

[toxic lichen]

once you have one you can find them all with this same technique

all the solutions to 11x + 6y = 1
are of the form
11(-1 -6k) + 6(2 + 11k) = 1

[stoic imp]

,w 33(2) + 9(-2)

[jolly parrot]

Results provided by WolframAlpha

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

Requested by renatoxbz

[toxic lichen]

ok well a=4x and b=8y

first find all (x,y) and then translate them to (a,b)

[stoic imp]

wait a minute

[stoic imp]

help please

can we start from scratch

we have 33a + 9b = 120

a = 4x and b = 8y

for some x,y in Z

we now divide by 12

33(4x) + 9(8y) = 120

132x + 72y = 120

we divide by 12

11x + 6y = 10

[stoic imp]

ok, one solution to this 11x + 6y = 10 diophantine is (2,-2), hard to spot by eye though

now we use the same techinique for finding all the solutions to this diophantine

11x + 6y = 10

[toxic lichen]

not very, you just list the first few multiples of 11 and 6 and see if there's any which are 10 apart

[stoic imp]

11(2 -6k) + 6(-2 + 11k) = 10

[toxic lichen]

yes so you've got x = 2-6k, y = -2+11k

now find a and b again in terms of k

[stoic imp]

yeah so (x,y) = (2-6k, -2 + 11k) for some k in Z

and (a,b) = (4x, 8y)

so (a,b) = (8-24k, -16+88k)

[stoic imp]

is it me or this exercises are nasty?

you have to follow a certain procedure, but it feels like black magic and out of the blue to me? this diophantine equations

[toxic lichen]

diophantine equations are a little bit black magic yes

[stoic imp]

I appreciate the help as always, though this elementary number theory is biting my ass, I can feel the pain in my body everytime I do one of this exercises

is nothing like the past math I have done, this intro to proofs class is hard for me ngl

.close

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[stoic imp]

so true bro

nothing, been catching up with my math courses

just watched some rise of the shield hero and thats it I am at second season

well when the turtle arc starts like it gets a little bit rough, like not as fun as the other eps in the second season

yeah same, I will finish it, is just that I havent had the time

yeah

well, the other heros are fucked up, they are literal douches

at least the shield hero is not stupid

but yeah he might be a loser or whatever

good luck on your exam ^^ btw

[pearl pond]

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[desert plaza]

Does anyone know where I messed up?

[desert plaza]

the bottom is right, just the top it sees like something went wrong

[plush bramble]

why do you think it's wrong

[pearl pond]

@desert plaza Has your question been resolved?

[desert plaza]

i checked my answer and it isn’t equipment

equivalent

It got flipped signs on the numerator

[marble wadi]

hi i need help with a calclus question

[desert plaza]

Ask in #help-6

[marble wadi]

thanks so much

I did

[lone bison]

uhh idk about dy/dx but u can factor to obtain xy(x+y) = -2 and then express x as a quadratic

[autumn ravine]

wdym

[ripe lantern]

Was your answer inputted online?

[pearl pond]

@desert plaza Has your question been resolved?

[desert plaza]

wait is mine correct?

maybe I just put into into chegg wrong

[dense jasper]

,w x^2 y+y^2 x=-2

[jolly parrot]

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[dense jasper]

It's fine

also you can check this in #bots as shown above

[desert plaza]

Oh okay I must of typed it in wrong

[desert plaza]

just do ,w?

[pearl pond]

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[pearl pond]

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[dusky crane]

i need some help in completing my stoichiometric guide because im preparing for organic chem

[dusky crane]

i plan to balance and i decided like similar to cramer's rule, i can just make a generalized form

$P(x) \Longleftrightarrow { [ a_{ij} ] }^{k, \ \ c}_{i=1, \ \ j = 1 } = M \in \mathbb{Z}^{k \times c}, x \in \mathbb{Q}^c.$

Let P(x) be the system of linear equations of a given chemical equation. Assign coefficients $x \in \mathbb{Q}^c, [a_{ij}]$ as P(x)'s matrix equivalent denoted by M, where indices i and j imply rows and columns. k and c are the dimensions of the matrix. How M can be formatted is based on user preference.

[jolly parrot]

しもた

[dusky crane]

can anyone verify if this will work as a generalized form?

$P(x) \Longrightarrow M, M \Longrightarrow P(x), \therefore P(x) \Longleftrightarrow M$ is how i would do it, P(x) can be just for verification and M for matrix version, i think both can be solved at the same time

[jolly parrot]

しもた

[dusky crane]

if RREF, it is normal the matrix gives out rational numbers which is in $\mathbb{Q}$, where we multiply all resulting constants with the LCM such that $x_n \in \mathbb{Z}$. Dividing by GCD of all components for the yielded coefficients is another option

[jolly parrot]

しもた

[dusky crane]

ill try to use a chemical equation and update because i need help

[pearl pond]

@dusky crane Has your question been resolved?

[pearl pond]

@dusky crane Has your question been resolved?

[dusky crane]

i need help if my formula is actually mathematically correct

i want something compact for my tests soon

anyone?

[pearl pond]

@dusky crane Has your question been resolved?

[dusky crane]

i tried reconstructing this and i think it should be conditional in terms of stoichiometry and not pure linear algebra

the things i wanted in one single line

flexible methods
one-liner matrix form so i know how it can be formatted in either smiths or RREF gauss jordan
system of linear equations' logical equivalence to its counterpart matrix

<@&286206848099549185>

[dusky crane]

anyone?

[pearl pond]

@dusky crane Has your question been resolved?

[dusky crane]

it has been hours, i'll do it alone. thanks

@cobalt quest

.close

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[buoyant fulcrum]

21st
I'm stuck here is my work

[toxic lichen]

,rccw

[crimson valve]

As [x] is an integer, and 4 is an integer, 2x should also be an integer. So x is either an integer, or an integer plus 0.5.

[buoyant fulcrum]

x=1.5
Then?

[crimson valve]

|[1.5]-2x1.5|=|1-3| = 2

[buoyant fulcrum]

Oh sorry 💀

[crimson valve]

When x is an integer, [x] =x ; when x is an integer plus 0.5, [x] = x-0.5. Solve x in these two conditions.

[buoyant fulcrum]

Ohk i see
x=+-4

[buoyant fulcrum]

Now ive got x=+-3.5 too

Now any?????

@crimson valve am I right till now?

[crimson valve]

[-3.5]=-4

[buoyant fulcrum]

Oh

I really don't see any more

[crimson valve]

Well, for [x]=x-0.5, we have |x-0.5-2x| = 4, or |-x-0.5| = 4 . It should have two solutions.

[buoyant fulcrum]

4solutions

[crimson valve]

-x-0.5=4 or -x-0.5 = -4

The other two are +-4

[buoyant fulcrum]

??

[buoyant fulcrum]

How is this for sure?

[crimson valve]

if |a| = 4, a = 4 or a = -4

[buoyant fulcrum]

Ik thar

But that 0.5's

Is it for every time?

[crimson valve]

if x is some integer plus 0.5, then [x] = x - 0.5. The integer can be less than zero.

like [-3.5]=-3.5-0.5=-4

It is true for every integer.

[buoyant fulcrum]

No

I didn't mean that

I meant about 2 solution
For x= Z +- 0.5

[crimson valve]

It is x=Z+0.5, then [x] = Z . If you use x=Z-0.5, then [x] =Z-1.

You get [x] = x-0.5 for both of them.

[buoyant fulcrum]

I mean for the solution of such equations in the question man

Is it always that such equations will have 2 solutions when x=Z+- 0.5
😭

[buoyant fulcrum]

U understand what I mean @crimson valve

[split void]

hint: divide it into two subcases: if [x] > 2x or if [x] < 2x
also use the fact that x = [x] + {x} ({x} is the fractional part function, so {1.5} = 0.5}), and then 0 < {x} < 1

[crimson valve]

These two solutions comes from the absolution || .

Because |a| = 4 can be written as a=4 or a=-4 .

It does not come from the [] sign.

[buoyant fulcrum]

Oh is see

Thank You
@crimson valve
@split void
U appreciate ur efforts

.close

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[versed lake]

I know the power rules but don’t know how to solve this, could someone walk me through.

[glass meadow]

Do you know the log rules

[versed lake]

Yeah

[glass meadow]

Alright, what's ln(a/b) ?

[versed lake]

Ln(a)-ln(b) iirc

[glass meadow]

Yes, so start with that

[versed lake]

So we can eliminate options c and d

[glass meadow]

Don't try to eliminate options, just simplify the expression without even looking at the options

[versed lake]

The denominator would be (1/2)ln(x), im not sure how to get e with ln though

[glass meadow]

Ok sure, can you write what you get so far?

As in what expression you get after applying the simplifications that you know

[versed lake]

It would be ln(5)+ln (something)-(1/2)ln(x)

[glass meadow]

Well, you do know what the something is

[versed lake]

Huh?

[glass meadow]

Write down the steps

[versed lake]

I’m not sure im following, what i just wrote was the step i took

[crystal dew]

where did you get the ln(5) from?

if you can think about this, you can probably get what that something is supposed to be

[versed lake]

Is the something supposed to be e^2?

[crystal dew]

correct.

[versed lake]

Ohhh so it simplifies to 2

Thanks

.close

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[wind robin]

Let H(2n) - H(n) = f(x) with n = natural number. H(x) denotes the xth harmonic number.

1. I showed that 0.five <= f(x) < 1
2. I also showed that f(x) increases as the input increases.

Now, cannot I conclude that there is a finite value which f(x) tends towards as x->infinity

[pearl pond]

@wind robin Has your question been resolved?

[dense jasper]

Consider bounding $\sum^{2n}_{k=n+1} \frac{1}{k}$ by integrals.

[jolly parrot]

Civil Service Pigeon

[spiral pivot]

.close

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[daring valley]

let x be the actual weight of millets, and let y be the cost

[fading ledge]

Sure

[daring valley]

if for 1000 grams of millet he gets 1.3y dollars

then how many grams of millet do the customers actually get, if they pay y dollars which is the actual cost

[fading ledge]

1.3?

Kg?

[daring valley]

no

[fading ledge]

Y dollar

Then

1000×y/1.3y

1000/1.3

[daring valley]

yeah

[fading ledge]

I didn't get this line properly

But he gets 1.3y right

[daring valley]

i actually dont know how to explain it

[fading ledge]

Hmm true

Complicated sentence

In real market🤣

.close

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[native sentinel]

@robust lynx

[robust lynx]

all our progress is gone nooo 😭

[native sentinel]

I realized the correct way to do this was to swap the integrals lmao

It makes it so much easier

since u = 1 + xy^3 then du = 3xy^2dy

ez plug in

[robust lynx]

does that mean you got it?

what answer did you get and are you sure it’s right?

[pearl pond]

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[pearl pond]

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[kind forum]

D4.7 I don't know how they got the part (a) answer, i know that we can approximate the field by finding the difference in voltage divided over the distance that is normal to the equipotential surface (from less potential to higher) and the field is the opposite of that $$E \approx - \dfrac{\Delta V}{\Delta N} \textbf{a}_n$$

[jolly parrot]

Ænema

[kind forum]

From what i see the normal direction is basically a straight line in the y direction and it goes up two squares, hence 2mm

And the delta V is 106-104 = 2

Dividing i get 1000, and because the electric field is the opposite of that, -1000 a_y

[pearl pond]

@kind forum Has your question been resolved?

[pearl pond]

@kind forum Has your question been resolved?

[lilac jackal]

@kind forum its better to treat a as the midpoint between the 106 and 102 curves

then we have 4V over say 3.7mm which is closer to the given answer

[pearl pond]

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[pearl pond]

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[thorny lagoon]

here do we eliminate the - by changing a to -a and -b to +b?

[dire tapir]

<@&268886789983436800>

[thorny lagoon]

?

[dire tapir]

someone spammed

[ocean wagon]

can u explain the question a bit more

[pearl pond]

@thorny lagoon Has your question been resolved?

[thorny lagoon]

??

how

[ocean wagon]

in which parenthesis

are the a and b

[thorny lagoon]

do u understand me?

theres - so i have to change the fomr

[warped violet]

What is your goal

[pearl pond]

@thorny lagoon Has your question been resolved?

[thorny lagoon]

Complete the sentence. Choose the correct answer from the options given.

The expression
2(a - 2b) - (a - b)(2 - b) + b^2
can be equivalently transformed into the form

A. ab
B. ab - 2b
C. b^2 - 2b - ab
D. b^2 - 6b + a - 2
E. b^2 + ab

[thorny lagoon]

.close

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[minor pebble]

Hello, I don't want help regarding a specific question but more so with a whole topic (if that is possible), It's linear algebra:Vectors and there are a bunch of tutorials on the internet but my uni teacher wants me to answer very specific questions which I can't find concise help on, I'd appreciate any form of response