help-23

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[timber echo]

i got no clues to solve this

[timber echo]

well i think i can do prime factorization on 316 first

and 2025

[open wedge]

$2025 = 45^2$ btw if you didn't know

[flat frigate]

1 divided by 0 equals Infinity

[timber echo]

nvm i got the ideas

.close

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[balmy sky]

is it mandatory tha each day will have a class for sure?

can there be days with no classes?

[arctic snow]

I dont think so, if we consider days with no classes, the total possible arrangements could be 5^7 i think. Since, each class has 5 options.. and if we say, she has a class everyday, that means 5 classes are already arranged. The rest 2 can be arranged by 5C2. I am not sure about this though.

[balmy sky]

"and if we say, she has a class everyday" yes this is true regardless. Because she is choosing the classes. There could be a case that the 7 classes that she chose are all scheduled on the same day

[arctic snow]

ohh yea... and she cant have 7 classes in a day, max is 6..

[balmy sky]

oh i didn't notice that

i thought 6 classes total for a week

[arctic snow]

its not true regardless though, she can choose 6 in one day, and one on some other day, rest days free

[balmy sky]

this makes sense now. i misinterpreted the line "There are 6 classes to choose from for each
day of the week"

yea this is an easy question now

[arctic snow]

oh great

[balmy sky]

you're in college?

[arctic snow]

this year, I will be

at the end of the year

[balmy sky]

jee?

[arctic snow]

yea

[balmy sky]

cool cool

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[hasty wagon]

do tell, not sure if i can help though

[undone jungle]

istg

[winter whale]

Uh

O7

I'll remember you when you're gone

Actually nah I'd probably forget

[delicate shore]

Nvm

it's a troll question

Don't troll in help channels @waxen spruce

[winter whale]

We are letting him off easy?

That's a bummer

[undone jungle]

@delicate shore while youre here

can you delete the three compile errors in #help-6

[delicate shore]

I do not have delete message perms

.close OP is a troll

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[scenic ridge]

is this ight

[lone void]

Could u send the whole question

[sharp tangle]

This is completely a physics question...???

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[errant hearth]

a problem i have with functions in calculus is that a lot of times questions asking you to draw the graph of a functions won`t give you specific points they will just give you the function and idk how to draw the graph tbh

[errant hearth]

here are some examples

[zealous ingot]

convert it to a known form if you can

[errant hearth]

what does that mean

[zealous ingot]

do you know the equation for a circle?

$x^2+y^2=r^2$

[flat frigate]

donkey

[errant hearth]

yea

what abt it

[zealous ingot]

well f(x) is essentially just the y coordinate right

[errant hearth]

yup

[zealous ingot]

so that eqn is equivalent to $y=\sqrt{4-x^2}$

[flat frigate]

donkey

[zealous ingot]

note that y must be positive cuz the range of radical is only positive

square both sides, take x^2 to the lhs

you'll have $x^2+y^2=2^2$ and you only have to plot the part where y>0

[flat frigate]

donkey

[errant hearth]

i dont understand tbh

[zealous ingot]

which part

[errant hearth]

all of it

[open wedge]

so can you square both sides of this

@errant hearth?

[errant hearth]

no

why would you do that

[open wedge]

because you would want to turn it into a familiar form

[open wedge]

in this case: this

and also the roots are ugly to deal with

[errant hearth]

man

[open wedge]

?

[errant hearth]

am trying to understand it hold on

[open wedge]

take your time

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[mortal ore]

What is the next step here?

[lone void]

there isnt one..plug in x=0

there is no indeterminate form here

so u cant use l'hopital

[stoic torrent]

are you sure the Q is right?

[north fulcrum]

can they just divide both top and bottom by x^2 to show that the top is +inf

[mortal ore]

yes

[mortal ore]

the limit is +inf, I just dont know how to get there

[stoic torrent]

its pretty obvious here right?

highest index of x in numerator is 1

whereas in denominator its 2

therefore, its c/0 form, (where c is a positive quantity) and hence the limit is +inf

[mortal ore]

does it make sense to look at the limit of the numerator and the denominator separately?

[stoic torrent]

nope

they both are subject to the same limit so how can you separte the two?

[lone void]

just put x=0...ull get 2/0 which is +infinity

[mortal ore]

okay, thank you

.close

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[full ridge]

How do I do this?

[red raft]

So

Gx will be inverse of fx

You get this?

[full ridge]

I know that

[red raft]

So if k,-4 ) lie on gx

Then -4,k must lie on fx

So just substitute

[full ridge]

Okay I got it

[red raft]

🫡

[full ridge]

So k=14 then

[mellow lodge]

You make the function f(y) = x and then solve for y

[red raft]

Yup

[full ridge]

.close

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[modest thistle]

.close

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[plush mountain]

.close

[modest thistle]

Whys -2*-2 = 4. I can understand that

I assume I start at position 2, then I get brought to position -2 but then I get brought back to the negative position of -2

[modest thistle]

But without that, I wouldnt understand.

[vague phoenix]

Well i can only use the axiom of real numbers

Which a number x can be only: x>0 in P, x=0, and -x in P

Where P is positivet set

If x in P such at 2 multiplies y (also in P) will have the product in P, else not

[modest thistle]

[vague phoenix]

Well any number in P is positive

[modest thistle]

[vague phoenix]

Let -2 and 2 you say, 1 positive, 1 not

[modest thistle]

Yws

Yes

[vague phoenix]

The product of it will not be positive (not in P as definition)

[modest thistle]

Since I go back -2 two times

[royal parcel]

Because when multiplying, you always carry over the sign of each variable.

understandable?

[modest thistle]

Ie

In example?

[vague phoenix]

What are you explaining

Pain, you know -2 = -1*2 right?

If not you can use prove to prove it

[modest thistle]

I mean but what you saying with that?

[royal parcel]

for example: you have +1*+2, it is?= +2, because you take the + with it, so if you multiply with -, you take from the first variable the - and then form the second

[vague phoenix]

For any real numbers x, such that -x = (-1)x

[modest thistle]

That theres no -2 and only a -1 is valid?

[vague phoenix]

You agree?

So -2 is basically a (-1)2. Then $-22=-122=-14=-4$

[flat frigate]

Minhh

[modest thistle]

Real number x <= 0?

And x>=0

[modest thistle]

Yeah but

[vague phoenix]

For all real numbers

[paper haven]

to me i just visualize it like this
if there are 2 -s i imagine they merge to make a +
and if there's a + with a - the - knocks out the + and so on

[modest thistle]

If I have a debt of 2 (-2), ive got it two times (not?) Why have +4 balance?

[vague phoenix]

So you debt -4

[timid ridge]

that's -2 * 2

you would have double your debt

[modest thistle]

But I dont do it

[timid ridge]

not doing it is not doing anything

[paper haven]

that's -4. double the debt

[modest thistle]

I mean not 2 (-2). I mean

Having a debt not two times

[vague phoenix]

You said double your debt which id 2 times bigger?

[paper haven]

to elaborate on this so

2 * -2 which is basically +2 * -2,
the - knocks out the +.
so the answer comes out negative no matter what

[vague phoenix]

When 2 time bigger is multiply by 2

[modest thistle]

So yeah, the statement is "having a debt not two times" = -2 * -2 = 4 . But why

[modest thistle]

Bruh

[paper haven]

i was just about to do that

[royal parcel]

dud

[modest thistle]

That is a cool explanation

[paper haven]

good job prime

[red raft]

This is the simplest way i can explain that to you

[red raft]

🤝

[modest thistle]

Not sure how to abstract this to real life sense atm. But thats a pretty explanation

[paper haven]

the concept of negative numbers in on itself is kinda hard to abstract irl

understanding this on paper will allow you to apply it irl tho

[modest thistle]

yes, I hope so.

thx

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[hidden ivy]

im unaware its unlikely someone can help, but if you're out there (this is for a practice MT)

[red raft]

So whats the problem?

[tardy mango]

discord.gg/physics

wrong server

.close

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[void barn]

If 8 cats can catch 10 mice in half an hour, how many minutes will it take 3
cats to catch 18 mice?

how would this be represented as a indirect proportion?

[timid ridge]

more mice = more time (direct)
more cats = less time (inverse)

oosp wait

ok

[void barn]

so it would be like this?

[timid ridge]

$t \propto \tfrac{m}{c}$

[flat frigate]

tten ʚɞ

[void barn]

ohh i c

[timid ridge]

we are tryna find the time

[void barn]

it wouldnt work with m or c being the on the left hand side

right?

[timid ridge]

m propto ct ?

i think it will work but there would be another step before solution

and the multiplier is not a clean number anyway

[void barn]

oh ok

the wordings just confuse me sometimes

[timid ridge]

$t = k\tfrac{m}{c}$

[flat frigate]

tten ʚɞ

[void barn]

ok i got 144 minutes

k thx

🙂

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[twilit cargo]

so is this what this questions means? solved it and got ~0.33

[twilit cargo]

so the area inside those two curves is essentially ~0.33

[quiet plume]

,w integral sin(x) - sin^3(x) from x=0 to x=pi/2

[flat frigate]

Results provided by WolframAlpha

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

Requested by azyrashacorki

[quiet plume]

Looks good

[twilit cargo]

oh i see,

but the graphing part that i show on desmos, is that what it essentially means right?

[quiet plume]

Yes it's the area you shaded

[twilit cargo]

perfect thanks

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[kindred pier]

im stuck on y^4

[kindred pier]

Oh wait its +

sorry

was'nt helpful

[granite quartz]

uhm let me see

[kindred pier]

see

[elfin comet]

what u have is right

[kindred pier]

what?

[kindred pier]

and wth is that username

arent you a boy?

HELP

https://youtu.be/IXmF4GbA86E?si=2sN72_FEjvhlz51D

o wait i can post pics haha

just relised

[kindred pier]

Nothing?

[kindred pier]

??

[elfin comet]

its 12 dude

and u dont need to do that either

[elfin comet]

no im a girl

[kindred pier]

he/him??

[kindred pier]

hhow

[elfin comet]

its so people stop dming me thats why

i get a lot of weird messages

[kindred pier]

Still not solved yet

[elfin comet]

these 2 triangles in ur picture are the same

i just redrew cos ur pic has too much writing already

that means the area of ABCD is going to be 2(4+2)

which is 12

[elfin comet]

make sense?

[kindred pier]

ahh yes

thank you

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[graceful lichen]

The solution says since the triangle is isosceles triangle the desired point is centroid and hence the coordinates of R are (3,4/3)

I didn't understand why the point is centroid if the triangle is isosceles

[halcyon meadow]

Because a median divides atriangle in ratio 2:1

[graceful lichen]

Yes centroid is the point of concurrence of medians and centroid divides it in 2:1

[graceful lichen]

How do you verify that's the case here?

[halcyon meadow]

MPT

[graceful lichen]

R is mid point?

[halcyon meadow]

Median..

You draw a line paralell to median and yu solve it

its a standard proof look it up

[graceful lichen]

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[desert pasture]

I'm confused as to how I'd find the conditional dist here

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[warm hull]

Yeah something is wrong with the LaTex code I don't know

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[ripe crystal]

How would you write the domain? I've tried splitting it such that is -inf<x<-9 and 9<x<inf

[hard crest]

maybe they want (-oo, -9), (9, oo) or something

[ripe crystal]

i've tried that too

[broken forum]

Typically with these kind of things it's better to look at the documentation for whatever website you are working with. It could want some kind of set notation $(\infty, -9) \cup (\dots)$ or something else. There's too many different notations to know what it could be

[flat frigate]

Nyxzore

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[north orbit]

how do we know that the horizontal acceleration is 0?

[quiet plume]

In those examples you'll usually be assuming that there is no friction, so once the ball has left the racket there is no force acting on it other than gravity, which pulls it down

It also says that the ball travels "freely under gravity," so no air friction is assumed

[manic patrol]

assuming no drag / air resistance, there is no net force on the ball horizontally; hence no acceleration.

[north orbit]

okay

i just thought they would've said that there is no air resistance

or friction

.close

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[eager junco]

Hi, does anyone know how matrix multiplication relates to linear regression?

[cerulean grotto]

Like this. There some matrices multiplying on the RHS

Here are x and y. Beta is the matrix of line coefficients

[eager junco]

Ok, May I know if those matrices are the data points?

[cerulean grotto]

indeed, they are given points (x1, y1), (x2, y2), etc.

[eager junco]

Got it. So far I have learned what the least squares method is, but haven’t gone much in depth in to other things related to statistics. May I know how this formula works and what it is used for please? Thanks for helping!

[cerulean grotto]

It works exactly like it's written: so you organize your data points (x1, y1), (x2, y2), etc. in matrices x and y, calculate the right hand side, and obtain 2x1 matrix beta that gives you the coefficients of your linear regression line (y = beta_1 * x + beta_0).
It is used for the same thing as the least squares method, but more suitable for matrix-optimized calculations

[eager junco]

I think I get it now! So is this matrix equation just a generalization of the least squares method, as it works for lines with high polynomial degrees?

[cerulean grotto]

yes. For example, for the quadratic regression you need to add the column $x_1^2, x_2^2, ... ,x_n^2$ to the x matrix (and, of course, the coefficient $\beta_2$ into the beta matrix).

[flat frigate]

Dedekind

[eager junco]

That makes sense now! Thank you so much 🙂 I will go learn about this. Have a good day

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[stoic raptor]

yo how is this wrong bruh

[stoic raptor]

their final answer was just my first step but cant it be simplified or nah?

[dusky totem]

Bunch of errors

Numerator was x denominator was x^2 but you still canceled it out fully

In your second step

And then everything after that falls

Also how did x^2+1 became x^3+1

[stoic raptor]

oh

its supposed to be x^3 + x

i see my error

thanks for the pointing that out

[dusky totem]

Yup

[stoic raptor]

ok so it cant really be simplified eh?

[dusky totem]

Idk maybe

[stoic raptor]

alr that makes sense then

thanks robin dabanc

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[dusky totem]

Can you add “for” before my name please

@stoic raptor

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[topaz furnace]

i need yall help again 😞

[topaz furnace]

The pyramid S.ABCD has a base that is a right trapezoid at A and D, with AB = 2CD.

M is the midpoint of AB

I, H, K are the projections of A onto SB, SM, SD respectively.

thats it

so
AI ⟂ SB
AH ⟂ SM
AK ⟂ SD

prove that AI ⟂ HK

<@&286206848099549185>

[ebon hatch]

!status

[safe radish]

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

[topaz furnace]

im on 1

[fiery fractal]

i dont get paid enough for ts

[topaz furnace]

ts is so harddd

[safe radish]

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[deft gorge]

I think its about adding the square root 5 with the other square root 5 and same with 3

[bronze sentinel]

Yes but they never really taught how to do it

[deft gorge]

Oh

But well you know it now

Think its like x and y

You can add x togethef

Together

[bronze sentinel]

OK ty

[deft gorge]

But not an y with a x

[bronze sentinel]

So it's A since you add the numbers before the square root that have the same number inside it

[deft gorge]

I think so

[safe radish]

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[deft gorge]

@bronze sentinel close it

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[lavish skiff]

for part c, im assuming that i need to set dy/dx at x = 3pi/4 to solve. derivative is 2cos x/sin^3 x, whats the fastest way to solve without calculator

[plucky elk]

quotient rule probably

oh nevermind you have the derivative

[lavish skiff]

yeah

i just need to do c

[plucky elk]

,w diff csc^2(x)

[flat frigate]

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[lavish skiff]

b was pretty obvious since cos at pi/2 = 0

[plucky elk]

are you having trouble finding cos(x) and sin(x) at 3pi/4

uhhhh go back to trig and remember your unit circles

,tex .unit circle

[flat frigate]

riemann

[lavish skiff]

well like, is evaluating the cos, multiplying by 2, dividing that by the sin^3, the fastest way to do it

like im asking since my prof usually asks us not to use calculator for trig stuff, with some exceptions

so i was wondering if there was a more obvious way to do it

[plucky elk]

i don't know what's difficult about what you're describing

[lavish skiff]

ok

😭

[plucky elk]

the amount of time it takes for you to ask is longer than the actual calculation

[lavish skiff]

ill memorize unit circle

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[safe radish]

Please don't occupy multiple help channels.

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[wintry cedar]

why when i search up the answer what i got is drastically wrong?

[median vigil]

can you show what answer you're supposed to get

[wintry cedar]

yeah

[median vigil]

it would be worth double checking whether or not your answer is equivalent before immediately concluding it's wrong

[wintry cedar]

i tried

[median vigil]

so which part is not equivalent?

[wintry cedar]

wait

sorry it is equivalent

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[lament vigil]

Hello! I'm here to ask a question about my process for doing this trig function problem
Here are my steps so far! I'm stuck on what to do next, since I'm not sure what DeltaMath means by "plugging in and evaluating"

[glacial cairn]

Yes, arccos(1) = 0

[lament vigil]

Since it's 0, should I just turn it into
-π - 2 • 0?

[glacial cairn]

Yes

[lament vigil]

Okay

That makes sense
Sorry if the question seemed kind of silly, I just got confused by DeltaMath's wording

Tysm!!

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[tame zephyr]

to determine whether a pitchfork bifurcation is subcritical or supercritical, do you just check from the bifurcation diagram (if the two splitting branches are unstable then its subcritical and stable being supercritical?)

[tame zephyr]

the direction of splitting branches doesnt matter and the stability at the other fixed point doesnt matter? (in terms of determining whether its sub or supercritical?)

[safe radish]

@tame zephyr Has your question been resolved?

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@tame zephyr Has your question been resolved?

[plucky elk]

Can also try #odes-and-pdes

Or maybe #dynamical-systems

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[graceful lichen]

While writing the final intersection of solution. The positive interval (-1,2) will not contain in final solution right? because the quadratic inequalities are +ve and -ve respectively?

I wanna Confirm it

[olive cloud]

yeah its correct according to me

just take intersection b/w these 2

[graceful lichen]

Thx

I was making mistakes in taking intersection

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[silver current]

What is an uncommon solution

Can sime1 pls help

[thin bridge]

different

e.g if the first polynomial has real roots
2, 3
and the second has 2, 5
the uncommon roots would be 3 and 5

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[serene sequoia]

welp.

[hasty wagon]

find x?

[supple pagoda]

What is written to the left of the alpha corner?

[zealous ingot]

2 alpha ig

[gusty flicker]

I thought those were x

[zealous ingot]

i'm confused what x is

nothing is labelled

[gusty flicker]

I think it’s the angles and that small side

Not the whole line

[open wedge]

Trig exercise?

[zealous ingot]

huh, alr

@serene sequoia assuming x=ED, have a look at triangle ABE and triangle ABD. And find a relationship between tangents of 3$\alpha$ and 2$\alpha$

[flat frigate]

donkey

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[serene sequoia]

.reopen

[safe radish]

✅ Original question: #help-23 message

[serene sequoia]

yep.

[serene sequoia]

2 alpha.

[hasty wagon]

im still finding the answer

[hasty wagon]

do you have the answer btw?

[serene sequoia]

i can't remember, unfortunately.

[hasty wagon]

ouch

what i found is around 8.60 (to 3 sig.fig.)

not sure if it's good enough though

or if i made a mistake or something

kinda really long work comparing to the information given by the graph

[merry remnant]

i think ive got it but 3 alpha is really ugly

or no

wiat

[serene sequoia]

[hasty wagon]

hmmm... did you try anything yet? maybe i can give you some hint (and check if I'm doing in the right path lol)

[merry remnant]

what have u tried till now?

[lean otter]

is ABC a right angle

[merry remnant]

oh my

[serene sequoia]

90°.

[hasty wagon]

yea, I assumed it is

or else it will be too hard for me

[serene sequoia]

İ tried to calculate both areas of triangle ABD and ADC then equalised them.

[merry remnant]

BRO WHAT

[serene sequoia]

But got nothing.

[hasty wagon]

cuz there's a black square at the tip

[hasty wagon]

and thought it's a sign for 90°

[hasty wagon]

lemme see

[merry remnant]

wait mb i thought u were saying eql triangle

sorry

💀

[hasty wagon]

ah...

do you need the answer to be in closed form?

like something with squareroots?

[merry remnant]

tan 3 alpha = 2 tan 2 alpha, @serene sequoia ?

[hasty wagon]

if not, it will be much easier

[lean otter]

what expression did you get

[serene sequoia]

we will able to figure it out if we found the answer :)

[hasty wagon]

i wanna know too

[hasty wagon]

oh

what i got is soemthing like.... (I'll type)

[merry remnant]

it has to be this

[serene sequoia]

hmm.

[merry remnant]

wait ill type

[hasty wagon]

$x=\frac{\sqrt{1+\frac43(\sqrt5+\sqrt3)^4}-1}{2}$

[flat frigate]

Biscuity

[lean otter]

crazy

[hasty wagon]

i have 2 more answers tooo

but they are 0 point something not sure if they're correct

must be rejected somewhere (especially when alpha < 30°)

[hasty wagon]

and yes @serene sequoia , this is a very big hint to this question

[merry remnant]

wasnt it findig the relation biscuity

[hasty wagon]

sorry i don't get what you mean

[merry remnant]

see the qn

wasnt ti uh

[hasty wagon]

yes?

[hasty wagon]

btw, I don't think finding areas would be useful in this problem

what I used are

• similar triangles
• Phy. Theorem
• tangent
• quadratics

[safe radish]

@serene sequoia Has your question been resolved?

[hasty wagon]

Anyways it's a fun question!
I'm guessing you'll need Grade10 or 11 to do it (if you have to find the exact form)
Definitely worth 1 hour working on it, thanks! @serene sequoia

[zealous ingot]

it is a little nasty yeah

that part is very mechanical tho, dw abt it

[zealous ingot]

pretty sure it's 8 😂

what'd u get

[safe radish]

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[magic vale]

Don't rlly understand how to think about solving part iv, other parts are fine tho

[zealous ingot]

triangle law of vector addition

you'll get a force perpendicular to the ground, and one parallel to the ground

you js need to find their resultant's magnitude

[mossy lotus]

Think Newtons 3rd law. yk the force the block exerts on the floor already, use that

[waxen hound]

^

[magic vale]

oh yh got it now

thnx every1

.close

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[stuck plank]

How to find the number of onto functions? This is a 12th ques. (Please ping me if you're giving the answer)

[covert yoke]

Surjective?

[stuck plank]

yepp

[covert yoke]

So how many total functions are there?

[stuck plank]

what..i didn't get it

[covert yoke]

Disregarding surjectivity

How many functions in total exist A -> B?

[stuck plank]

umm..i am not getting ur question but the image i have provided is the complete question

[covert yoke]

The question is intended to help you answer your question

It's a first step

[stuck plank]

do you mean, injective function, bijective function?

[covert yoke]

No, any function from A to B

[stuck plank]

i dont know..

[covert yoke]

How many functions in total? Then we can subtract away the ones that aren't surjective

[stuck plank]

ohh

T-T idk

[covert yoke]

Well, we have six members of the domain, yes?

[stuck plank]

yess

[covert yoke]

And each of these six members of the domain can map to any of the 3 members of the codomain yes?

[stuck plank]

yes

[covert yoke]

So this is a combinatorics problem

[stuck plank]

heard this term for the first time, no idea what's that

Are you asking total number of relations or functions?

[covert yoke]

Ok, consider just the first of the 6 members of the domain, how many possible mappings of this value are there?

[stuck plank]

18..

[covert yoke]

Let's call A = {1, 2, 3, 4, 5, 6} and B = {a, b, c}

And our function is f

f(1) can be what values?

[stuck plank]

I'm feeling so dumb, idk

[covert yoke]

Well, can f(1) = a?

[stuck plank]

maybe, we dont know the function

[covert yoke]

We are trying to list all possible functions

(between these two sets)

[stuck plank]

then, yes

[covert yoke]

Ok, so how many total values can f(1) take

[stuck plank]

3

[covert yoke]

And f(2)?

[stuck plank]

3

[covert yoke]

So if we consider just f(1) and f(2), i.e. the restriction of the function to the set {1, 2}, how many total functions would there be?

[stuck plank]

6

[covert yoke]

Why 6?

[stuck plank]

3 + 3

[covert yoke]

Why would adding be appropriate here?

Let's list out the functions:

f(1) = a, f(2) = a
f(1) = a, f(2) = b
f(1) = a, f(2) = c
f(1) = b, f(2) = a
f(1) = b, f(2) = b
f(1) = b, f(2) = c
f(1) = c, f(2) = a
f(1) = c, f(2) = b
f(1) = c, f(2) = c

How many are there in total?

[stuck plank]

9

[covert yoke]

So why are there 9?

[stuck plank]

multiplied..

[covert yoke]

Yes

What if we let f accept the value 3 as well?

How many functions would there be now?

[stuck plank]

give me 1 min..

27

[covert yoke]

So how many total functions from A to B?

[stuck plank]

6^3 = 108?

sorryyy

3^6

[covert yoke]

Now what if we restrict the outputs instead?

How many functions map A to the set {a, b}?

[stuck plank]

2^6

[covert yoke]

Good! And how many functions map A to the set {a}?

[stuck plank]

1

[covert yoke]

Cool, now, if a function is not surjective, then there is some a, b, or c that is not mapped to, yes?

[stuck plank]

what..

[covert yoke]

That is to say f(A) = {a, b}, or f(A) = {b, c}, or f(A) = {a, c}, or f(A) = {a}, or f(A) = {b}, or finally f(A) = {c}.

(where f(A) = {f(k) | k ∈ A})

[stuck plank]

yess

[covert yoke]

So we will use the inclusion exclusion principle to count the total number of functions.

We have the surjective functions = all functions - all functions mapping to at most 2 elements + all functions mapping to exactly 1 element.

Do you understand why this will give you the value you seek?

[stuck plank]

I need 1 minute to think

[covert yoke]

("no" is an acceptable answer here, and an invitation to ask questions)

[stuck plank]

No, please explain

[covert yoke]

Better if you ask

That way I can get an understanding of where the gaps are

[stuck plank]

all functions - all functions mapping to at most 2 elements (because there can only be a single image right for onto functions? )

[covert yoke]

Specifically, the single image is the entire codomain

Damn. I got to go, sorry

[stuck plank]

alright!

[safe radish]

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[vagrant ether]

square root of 10947

[hasty wagon]

you need to do it by hand or you can use calculator?

[vagrant ether]

can use calculator

[lone void]

then why are u asking here..

[vagrant ether]

just testing

[lone void]

testing what

[hasty wagon]

i see

[lone void]

our patience?

[vagrant ether]

the helpfulness

[hasty wagon]

i guess it's that

[normal moss]

||translated: wasting people's time||

[delicate shore]

,calc sqrt(10947)

[flat frigate]

Result:

104.62791214585

[normal moss]

!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.

[normal moss]

🙂

[open wedge]

,w calculate sqrt(10947) to 1000 decimal places

[flat frigate]

Results provided by WolframAlpha

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Requested by iaminfinityiq

[open wedge]

now try nosolsing me

i gave a more accurate answer

tbh this channel seems like a troll to me

[covert yoke]

Please don't try to "stress test" the helpers on this server by asking for pointless calculations. They're people, and you're wasting their time.

If you have an actual question, feel free to ask.

[lone void]

also checkout #help-39

[vagrant ether]

alright i guess

[hasty wagon]

so, do you have any other math questions that you need help with?

[vagrant ether]

nothing, I'll come back when i need help

.close

[safe radish]

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[covert yoke]

Dummit and Foote 4.1.7 part (d)

Prove that the transitive group $G$ is primitive on $A$ if and only if for each $a \in A$, the only subgroups of $G$ containing $G_a$ are $G_a$ and $G$ (i.e., $G_a$ is a \emph{maximal} subgroup of $G$, cf. Exercise 16, Section 2.4). [Use part (a).]

2.4.16 part (a) reads as follows

A subgroup $M$ of a group $G$ is called a maximal subgroup if $M \ne G$ and the only subgroups of $G$ which contain $M$ are $M$ and $G$.

(a) Prove that if $H$ is a proper subgroup of the finite group $G$ then there is a maximal subgroup of $G$ containing $H$.

My doubt here is can we say that just because $G$ is transitive on the (said previously in the problem to be finite) set $A$, can we demonstrate that $G$ is finite to use the result of 2.4.16.a? My gut says no.

Recall that a transitive action is an action for which there exists some $g \in G$ that for any $a, b \in A$ we have $a = g \cdot b$.

My concern is there may be multiple such $g$ that satisfy this. (Consider for instance the action of the real numbers under addition on the real numbers modulo 1, clearly if a = 0.5 and b = 0.75, then any of g = 0.25, 1.25, etc will satisfy this).

May I consider a finite quotient group of $G$ such that we have a single $g$ that will satisfy this property and allow us to use 2.4.16.a? How could I formalize this in the general case?

[flat frigate]

OmnipotentEntity

[covert yoke]

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[graceful lichen]

I sent wrong images of question

.reopen

It's closed so opening new

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[floral sonnet]

can anyone help

with this

question

[worn pollen]

🤔

[open wedge]

oof

[brave wolf]

<@&268886789983436800>

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@floral sonnet Has your question been resolved?

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[modest thistle]

@drifting sierra

Add first term with first term second term with second term and so on

but thats s = 6 + 4 + 2 not 4 +4 +4 , what happend

#help-6 message

[drifting sierra]

No

S=1+2+3

S=3+2+1

[modest thistle]

its the same?

[drifting sierra]

Yes

But this is just an example

It's easier to explain with a small case

So we add S and S

2S

1 and 3

[modest thistle]

oh

[drifting sierra]

2 and 2

So 2S = 4+4+4

2S = 4*3

S= 4*3/2

Now try do this for a larger ap

You'll get the formula

[modest thistle]

ill do it later. I cant rn

but thx

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[slim swallow]

Yo guys I need an opinion. So I'm a university student who cheated his way thru high school and now I gotta learn mathematics for real there's no running away from it anymore. Gemini suggested me this path -

Here is the exact order you should read them in. Think of learning math like building a house: you have to pour the foundation before you can build the roof!

Phase 1: The Foundation
Start with: Basic Mathematics by Serge Lang

Why: This is your primary textbook. It starts from the very beginning (numbers and basic rules) and builds up your logical thinking.

How to use the "For Dummies" books right now: Keep Technical Math For Dummies nearby as a backup. If you are reading Lang's book and his academic English gets confusing, open the Dummies book to the same topic. It will explain the exact same math, but in simpler, everyday English.

Phase 2: The Bridge
Next read: Trigonometry Workbook For Dummies

Why: Toward the end of Serge Lang's book, you will encounter geometry and trigonometry (shapes, angles, triangles, and circles). Trigonometry is the "bridge" between basic math and calculus. This workbook will give you the practice you need in plain English before you move on to the hard stuff.

Phase 3: The Roof (Your Goal)
Finally read: The Calculus Lifesaver

Why: Do not open this book until you have finished Phase 1 and Phase 2! Calculus uses all the algebra and trigonometry you learned in the previous books and mixes them together. If you start here, you will feel completely lost. But if you read the other books first, this modern, easy-to-read book will guide you through calculus beautifully.

Summary of your reading order:

Basic Mathematics (using Technical Math For Dummies if you get stuck on the English)

Trigonometry Workbook For Dummies

The Calculus Lifesaver

[safe radish]

@slim swallow Has your question been resolved?

[vague phoenix]

Dont think you ask here but ask in #study-discussion

[tardy mango]

#book-recommendations would be better, but help channels are for specific questions - questions about book recommendations go in well ... #book-recommendations lol.

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[thorn junco]

how can a line go through -1 on the x axis if the y is 7 and it's horizontal?

[glacial cairn]

That's not what this says

The line goes through the point (-1,7)

That point is not on the x-axis

[thorn junco]

disregard my question, thank you 💀

.close

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[ionic matrix]

i need help on this mechanics question. ive checked the mark scheme and i understand how they took moments about A and how they got Mga + 3Mgx but i dont know how they got T2asin(alpha)

i think i also need help on the diagram because im assuming they need an X and Y force somewhere but i dont know where

[inner parrot]

what are all the labeled forces you have on your diagram so far?

[ionic matrix]

let me send a photo… super cute pfp btw !

the other bits are different subparts to the question so theyre not relevant to the 1st part

<@&286206848099549185> sorry!!!

[visual linden]

Have you tried conserving torque?

[ionic matrix]

i dont know what that means

:((

[visual linden]

I mean this looks like a rigid body problem

If system is in Equilibrium then sum of torque should be zero where the axis is the base of the rod

What topic is this from, can you check that?

[inner parrot]

torque is another word for moment btw

[ionic matrix]

ohh

[visual linden]

Oh yeah, moment of Force

[inner parrot]

yeah some ppl use moment some use torque

[ionic matrix]

forces and moments

i dont really know anything about mechanics icl im so lost

[visual linden]

Yeah yeah then you have to conserve the moment of force here

[ionic matrix]

as in anticlockwise = clockwise ?

[inner parrot]

yes essentially

[visual linden]

Yes, in case of Equilibrium

(Basically the rod isn't moving, it's fixed)

[ionic matrix]

but

[visual linden]

Do you know about conservation of force?

[ionic matrix]

im getting 6aTsin(alpha)/4

[ionic matrix]

errrmm

remind meee…?

[inner parrot]

can you show your work for that

also aren’t you solving for T?

T shouldn’t be in the equation

[visual linden]

I mean it's not relevant here, I thought if you knew that then you could relate it here

[ionic matrix]

uh

[visual linden]

I'll solve this real quick and get back to you (yk, verify the answer and get a clear path)

[ionic matrix]

i did tan(alpha) = 3/4 = o/2a so 6a/4 = o

okay

[ionic matrix]

my workings are all there, theyre just kinda nonsensical 😭😭😭

[inner parrot]

okay gotcha

[inner parrot]

so what you did here is just finding the length of AC but we need T

the only way we can pull T into an equation is either through newton’s 2nd law or its equivalent form with moments

have you tried analyzing the moments of the plank?

[ionic matrix]

?

[ionic matrix]

i have not a clue what any of this means

wait no

i did that didnt i

Mga + 3Mgx

[inner parrot]

mhm yes

[ionic matrix]

and thrn i just need the other side of the equation

somehow

[inner parrot]

yeah

[visual linden]

Okay yeah, it needed like 4 steps

[inner parrot]

so those moments move the system in which direction

[visual linden]

Just apply conservation of moment of force here, and you should get the answer very quickly, you'd just have to fiddle around with the tan(alpha) = 3/4 a bit

If you want I can tell you how many terms there are whose moment we'll use here, so that'll give you an idea

[ionic matrix]

but i cant get the other side of the equation

[visual linden]

Well it's 0

Or wait, you mean the anti-clockwise one

[inner parrot]

what other forces are there acting on the plank other than the gravity of the two objects

the only other force that is producing a moment

[visual linden]

Well I'd suggest break the angles into components and use the vertical component of T

[ionic matrix]

i mean i tried that and i dont know how to do that

thats how i got some bs answer

[ionic matrix]

yes

[visual linden]

Are you facing trouble in components?

[ionic matrix]

i guess ?

[visual linden]

I mean what I do is try to think logically, like in this case, if you're confused between cos(alpha) and sin(alpha), then think logically, if the string was in such a manner that it was parallel to the rod (so the angle was 0), then would the value of T be maximum or minimum

And if it was in such a manner that it was absolutely perpendicular to the rod (or the angle was 90), then would tension be maximum or minimum, if it's maximum at 90, then use sin, if it's maximum at 0, then use cos

[ionic matrix]

i have not a flipping clue what you just said

[visual linden]

Yeah not very effective trying to convey tricks over chat tbh

Okay so basically, vertical components you use sin, for horizontal components you use cos, if the angle of elevation is given

[ionic matrix]

but i did use sin

[visual linden]

But you didn't use conservation of moment

[ionic matrix]

no i just didnt write it because i wasnt getting the answer that it asked for

[visual linden]

You can't solve it directly by components

[ionic matrix]

so there was no point me writing it = my wrong answer, knowing its a wrong andwer

i dont see what world i should be using 2a in the same equation as sin(alpha)

[visual linden]

In the world of moment conservation

(Cue shimmering music)

Okay no but, tell me, what's the first thing you see you can find moment of?

Basically where the axis is the y-plane of the wall the rod is attached to

[ionic matrix]

what wdym

[visual linden]

What's the moment of the block?

[ionic matrix]

i feel like i dont understand enlgish

[ionic matrix]

3Mgx

is that what ur on abt

[visual linden]

Okay

[ionic matrix]

if i was to take moments from A

[visual linden]

What's the moment of the rod?

[ionic matrix]

what rod

[visual linden]

That's it

[ionic matrix]

the one with tension ?

[visual linden]

Plank

[ionic matrix]

oh right

Mga

[visual linden]

God I'm used to questions with rod, plank is kinda new wording

[visual linden]

Nice

[ionic matrix]

LOLL well its just context. it says plank = rod right ? 😭

[visual linden]

What's the vertical component of the moment of the tension?

[ionic matrix]

that i dont know

[visual linden]

I mean technically yeah

[ionic matrix]

because

i got this bro

i have not a clue in the world

[visual linden]

Yeah you got Tsin(alpha) yeah, that's the vertical force

And now that you have the force, just multiply it with 2a and you get the moment

You get this?

[ionic matrix]

why am i multiplying by 2a

[visual linden]

Well, Tsin(alpha) is the force, like mg

[ionic matrix]

OHHH

OH MY GOODNESSS

[visual linden]

You multiply it with the distance from A to get torque

[ionic matrix]

TIMES IT BY THE DISTANCE

YEAH

OMFG

[visual linden]

Your excitement gives me hope

[ionic matrix]

thank you

i was

freaking tf out

icl

[visual linden]

No problem mate

[ionic matrix]

i got more questions though so see you soon ? 😭😭

[visual linden]

Okay so the other two moments were acting down, so they go on one side of the equation, and this one is acting up, so it goes on the other

[visual linden]

Well I gotta go somewhere in a few minutes, but I'll try if I can be here

[ionic matrix]

thank you

[visual linden]

You got the answer?

[ionic matrix]

YES

THANK YOU

SORRY I WAS BEING DUMB

THANKS !!!

[visual linden]

Aren't we all

[visual linden]

No problem mate, anytime🫡

[ionic matrix]

.close

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[fringe dock]

i need help with part a

i dont really understand it

[sonic jungle]

isnt this just subbing in formulae

you are trying to show that themodel is correct

[fringe dock]

i struggle to label the diagram

i am doing another question and im also finding it hard to label the diagram

please can you help

anyone?

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@fringe dock Has your question been resolved?

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@fringe dock Has your question been resolved?

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[exotic crystal]

I don't get the definition of convolution of two sequences given here

[exotic crystal]

is it so that the term ck is this one?

or is it the multiplication of both generating functions?

[solar hazel]

it's just like polynomial multiplication

[exotic crystal]

okay so for example if I got the function 1/(1+x) which generates the sequence 1,-1,1,-1, and want to convolute it with itself and get a formula, do I just do (1/(1+x))^2?

and then get the coefficient of each term?

[solar hazel]

what does 'just doing (1/(1+x))^2' mean? like yes that would be the generating function

but are you asking how to compute the corresponding sequence?

[exotic crystal]

yes

how can I get the convolution of that sequence with itself?

[solar hazel]

yes you can use this

when we take an x^i term from one generating function and an x^(k-i) term from the other and multiply them, we get a x^k term

[solar hazel]

this captures all the ways you can do that

[exotic crystal]

oh okay

and it's basically the same as multiplying both generating functions?

[solar hazel]

yes

when the generating functions are polynomials it is literally just polynomial multiplication

for 'infinite polynomials' it is still similar

[exotic crystal]

oh okay

ty so much

.close

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[rocky pivot]

Hello. May someone please tell me what I did wrong here? Thank you for your time.

[safe radish]

@rocky pivot Has your question been resolved?

[plucky elk]

Why do you think it's wrong

[rocky pivot]

I don’t know on the answer sheet it says (2xy-3e^y)/(3xe^y-x^2)

What steps am I missing may you please tell me

It’s d/dx( 3xe^y -4 = x^2-y)

Thank you for the tip

I don’t see anything I did wrong though to me

[plucky elk]

Check a few points to see if they're actually different

Show your full work then

[rocky pivot]

Demos says they’re different I made a mistake for the answer sheet answer but even after fixing it it’s different

[rocky pivot]

It’s uptop

[plucky elk]

What does "Fixing it" mean then

[rocky pivot]

Oh I meant for the answer sheet answer key answer I accidentally mistyped something not my answer

I still don’t know what’s wrong with my answer

[rocky pivot]

<@&286206848099549185>

[plucky elk]

Show what you put in Desmos

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@rocky pivot Has your question been resolved?

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[rocky pivot]

.reopen

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✅ Original question: #help-23 message

[rocky pivot]

Sorry thank you for your help

.close

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[young shale]

can someone help me with derivative applications and tutor me now ill pay good pls msg

[severe pond]

not really

[thin bridge]

people are willing to assist within the server for free
if you want help you can simply ask your questions here

[severe pond]

he offered to pay

it would be different if it was the other way around

but nonetheless you can just ask here for free

[lethal oasis]

pay to help?

[severe pond]

no if people were advertising their tutoring services to him

[thin bridge]

ideally you shouldn't be asking but
participate in compensatory transactions outside the server at your own risk

[lethal oasis]

offering to pay is ok, but if someone accepts it and receives money, isn't that technically illegal?

[severe pond]

why?

how is that illegal

[lethal oasis]

the person receiving the money is against the server's rules

[severe pond]

it's just that the server isn't responsible for it

you do it at your own risk

[lethal oasis]

well anyways what is your quesion, buddy

[severe pond]

where does it say that

huh

they changed it?

Do not offer money for doing homework assignments, and vice versa.

when was this changed

[thin bridge]

always like that

[severe pond]

or maybe that's just homework

and not tutoring in general

[safe radish]

@young shale Has your question been resolved?

[lethal oasis]

what is your question? people will help you for free here 😀

[safe radish]

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[torpid acorn]

could someone give me a rundown on basic trigonometry we went over it in class today but i had a late night and slept through my first period (math)