help-13

[vast cedar]

sorry guys

[ancient valley]

ahh ok

well 9 can be rewritten into 3^2

[fair mortar]

it is uh $\pm \sqrt{3}$ and some imaginary roots

[wraith dagger]

Bettim

[ancient valley]

thus giving $\sqrt[4]{3^{2}}$

[wraith dagger]

Judgemental Snail

[ancient valley]

we can convert that to a fractional exponent giving $3^{\frac{2}{4}}$, which further simplifies to $3^{\frac{1}{2}}$

[wraith dagger]

Judgemental Snail

[ancient valley]

and finally, $3^{\frac{1}{2}}=\sqrt{3}$

[wraith dagger]

Judgemental Snail

[vast cedar]

ooooh that makes so much sense tysm!!

[ancient valley]

np :)

[vast cedar]

.close

[cedar kiln]

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[obsidian coral]

np 🙂

[cedar kiln]

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[last trench]

I’m how many ways may four men and four women be arranged around a circular table, if no two men are to be seated next to each other?

[last trench]

in*

[glossy pasture]

3,024

[last trench]

the answer says it’s 3! * 4!

why?

[cedar kiln]

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.

[glossy pasture]

Start by placing the four women around the table. There are 4! ways to do this.

Now, we have five slots between the women where the men can sit.

Arrange the four men in these slots, making sure no two men are next to each other. To do this, you can think of it as arranging four men (M) and five empty slots (E):

E M E M E M E M E

There are 126 different ways to arrange the men in this pattern.

Multiply the number of ways to arrange the women (4!) by the number of ways to arrange the men (126).

The total number of arrangements is 4! * 126 = 24 * 126 = 3024 ways.

[last trench]

wouldn’t there be 4 slots between the women where the men can sit?

[glossy pasture]

yes

But imagine the women as empty seats

because we are only focusing on the men

ohhhh

wait

[last trench]

yes

[glossy pasture]

its 144 ways

[last trench]

yea that’s the answer why?

3!*4!

[glossy pasture]

Pick any one of the 8
positions to seat one of the men. There are 3!=6
ways to permute the remaining three men in the three remaining positions available for men. Then there are 4!=24
ways to assign the women to the four remaining seats. That makes 1152
possible ways.

If you are only concerned with the order (i.e., rotating does not change what we are interested in), then remove the factor of 8
to get 144
ways.

[last trench]

cause (4-1)!

?

[glossy pasture]

let me simplfy real quick

You have 8 positions to seat 4 men and 4 women.

First, choose any one of the 8 positions to seat one of the men. There are 8 ways to do this.

After seating one man, you have 3 men left to seat. Since we've already placed one man, there are now 7 positions left (8 - 1) to seat the remaining men.

Calculate the number of ways to permute the remaining three men in the three remaining positions available for men. This is 3! (3 factorial) since there are 3 men to arrange. 3! = 3 x 2 x 1 = 6 ways.

Now, you have 4 women to seat. There are 4 positions left (8 positions - 4 men already seated), so you have 4! ways to assign the women to the remaining seats. 4! = 4 x 3 x 2 x 1 = 24 ways.

To find the total number of possible ways, multiply the number of ways to seat men (step 2) by the number of ways to permute the remaining men (step 4) and then multiply this by the number of ways to assign the women (step 5):

Total ways = 8 (ways to choose the first man's seat) x 6 (ways to permute the remaining men) x 24 (ways to assign the women) = 8 x 6 x 24 = 1152 possible ways.

However, if you're only concerned with the order and rotating doesn't change the outcome, you can remove the factor of 8 (since there are 8 equivalent starting positions) to get the reduced number of ways:

Reduced ways = Total ways / 8 = 1152 / 8 = 144 ways.

So, there are 144 possible ways if you only consider the order and rotation doesn't change what you're interested in.

[last trench]

chat gpt merchant

[ancient valley]

are you using chat gpt?

[junior dome]

<@&268886789983436800> GPT

[dire geode]

Don't use chatgpt for math

[last trench]

😂 still helpful

or not

[glossy pasture]

To simplfy

[ancient valley]

still, its against the rules of the server

[glossy pasture]

and make easier to understand

oh

[glossy pasture]

good

[dire geode]

Wrong

[last trench]

.close

[cedar kiln]

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[wanton sail]

GPT is not allowed here.

Please stop using GPT; this is your final warning.

Explain concepts in your own words

[cedar kiln]

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[naive juniper]

How do I solve this I did 5x-3 + 13 = 40 to solve for x and it was still wrong what should I do

[solemn quail]

your equation looks good

I think you just made an arithmetic mistake when solving for x

[naive juniper]

Do u know what my mistake was her? (Sorry for messy handwriting)

[crystal raptor]

you added 3 to the 13 instead of the 40

[naive juniper]

O

Alr thanks guys

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[worn tapir]

okay so the hint just tells me to follow the steps above and the solution just tells me the answer

but I am not quite sure I follow

So to me, the first step would be to make 1 into a fraction with a common denominator to 1/x+2

wait

Okay I see what I did wrong

nvmd

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[vapid dove]

problem 17

[vapid dove]

I have an integral from 0 to 10 of 42(8pi)(10-x)dx

im taking the fact that the cross sectional area is a semi circle and the plane begins at the base

should it be solved like this or by using a rectangular cross sectional area?

because my work shows the answers not even close to each other but should they not be the same regardless?

[half zenith]

The semi circle should be the cross sectional area

Did you forget to include 9.8 in your integral for gravity?

[vapid dove]

my class hasnt gone over including gravity constant yet

[vapid dove]

i thought so, but theres some other examples of this problem where they take the rectangle so i was just curious

[vapid dove]

yea not yet

we have it as f(x) representing work

not work

uhhhh

force

which grav is included ig

but we never outright include 9.81

for now at least lol

well thanks youuu

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[clever jacinth]

is integration by parts necessary here? or can i just u sub

[dire geode]

Try both!

[clever jacinth]

could i get some help with that? Ill send in my work in a secx

im stuck now

i feel like i did something wrong

[dire geode]

Blurry pic but that looks right

Just sub back in for x and do +C

[clever jacinth]

but would i want to multiply everything together before i do so?

like the 5/2 * 2/5

and the -2 * 3/2 * 2/3

if i dont, my answer will be

(x+2)^5/2 * 2/5 -2(x+2)^3/2*2/3 + C

[rain drift]

nah that answer is acceptable imo, you could combine like terms to make it something like

[clever jacinth]

oh really?

i wasnt sure if i was supposed to sub back the u before i multiplied everything out

[obsidian coral]

Or you need your eyes checked

[rain drift]

$\frac{2}{5}(x+2)^{\frac{5}{2}} - \frac{4}{3}(x + 2)^{\frac{3}{2}} + C$

[wraith dagger]

MellowDramaLlama

[clever jacinth]

would my answer be equivalent to that?

[rain drift]

you could also find a common denominator between the two but that might be overkill

[rain drift]

yes. All I did extra was multiply -2 by 2/3rd

[clever jacinth]

sweet thanks!!

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[sleek storm]

How does the first one become the others? I know you use the euler's formula, but I still can't write the first one as the others.

[sleek storm]

<@&286206848099549185>

[thorn lotus]

Let's focus on just one

Which one do you want to work on first

[sleek storm]

The second one, would be useful

[thorn lotus]

Okay. There are two ways to go about doing this. One is if you already know the definition of cos and sin in terms of exponentials. The other is by plugging in numbers for t

[sleek storm]

Well, yeah, I know the euler's formula

[thorn lotus]

Right, but you said you want to turn the first into the second, right?

Or is it the other way around

[sleek storm]

Wait, no im sorry, I figured out the second one, I would like to see the 3rd one

From first to 3rd

[thorn lotus]

Okay

Try writing the exponentials into sines and cosines

[sleek storm]

Wait a sec, imma send it

[thorn lotus]

no rush

[sleek storm]

So I get here. Bur how do I turn this into the 3rd equation?

[thorn lotus]

Cool

do you know the formula for angle sum

cos(x+y) = ?

[sleek storm]

Yeah, I do

[thorn lotus]

Cool. You want to choose your alpha and beta, so you can fit that formula in there

You want to turn that into the cosine angle sum formula

[sleek storm]

Wait.. Lemme try..

Is this how it is? @thorn lotus

[thorn lotus]

Almost

[sleek storm]

Then you just attach a constant?

[thorn lotus]

By making that substitution, you're implicitly assuming that E = 1

You want to allow for E to be general

[sleek storm]

Ahh

i see

[thorn lotus]

But yes, you got it

[sleek storm]

This is supposed to be a solution to a diff. eq so that makes sense....

Alright thanks a lot for your help!

. close

how do I close

[thorn lotus]

space

remove the space

[sleek storm]

.close

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[cedar kiln]

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[glossy fossil]

aplace transform e ^t t cos2t

[cedar kiln]

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[atomic steppe]

can someone help me find the derivative of this function

[slate lintel]

does it help if i write it like this

$f(x) = (1 - x^3)^{\sfrac12}$

[wraith dagger]

hayley!

[atomic steppe]

oh wait hold on

i kinda got in but i’m also kinda lost

[crimson sedge]

have you done chain rule?

[atomic steppe]

nope

can u explain it to me?

this is what i’ve done so far

[crimson sedge]

that is the first half of the chain rule, but I think you've done it a bit wrong. it should be -1/2, not -3/2.

1/2 - 1 = -1/2

and you've dropped the 1 in the parentheses, which you should not do -- keep it as (1 - x^3)

[slate lintel]

and the thing on the inside (the 1 - x^3) stays as it is; then you multiply the whole thing times the derivative of that

[atomic steppe]

i haven’t learned the chain rule yet so i don’t think my teacher wants me to use that method

is there another way i can work around this?

sorry i thought i just forgot what it was but turns out we aren’t going over that until next week

[crimson sedge]

I can't think of easier ways than chain rule, personally

[slate lintel]

yeah neither can i

i mean

you could go back to the limit definition of derivagtive

but that won't be easy

[atomic steppe]

i’ll give it a shot rn 🥲🥲

[crimson sedge]

maybe some weird binomial expansion thingy but it just seems so unlikely they'd set it that way

you sure you didin't pick up her next class's homework sheet xD

[wanton grove]

could maybe do y^2 = 1 - x^3 then do implicit differentiation and solve for dy/dx

but that's still kinda using the chain rule? idk

[crimson sedge]

yeah, still chain rule on the y^2

$\frac{1}{2}(1 - x^3)^{-\frac{1}{2}} \times \dv{x} (1 - x^3)$ I think, should you have chosen chain rule

[wraith dagger]

f1dbefdd4de64fb49c77b14e7029

[cedar kiln]

@atomic steppe Has your question been resolved?

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[hidden hound]

can someone help me understand geometric proofs better

[hidden hound]

like i dont understand this stuff

well i know some basics ig

but yeah

so question

like

you see how we use LETTERS to label stuff

like A, B, C, D

when referring to them in angle (example : <DCA)

or even with that triangle thing

does it matter which order we write them in

like the letters

and would it always not matter or

what

[peak minnow]

what is ur question?

[cedar kiln]

@hidden hound Has your question been resolved?

[cedar kiln]

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[timid pawn]

It does matter that you use specific formats in some instances, like proving figures congruent.
If ABCD is congruent to PQRS, then ABCD is not congruent to any other configuration (ex:SRQP).
Letters are chosen succesively, that is, they are chosen one after the other.
The measures of angles, like <ABC and <CBA are the same.

Hope this helps.

[cedar kiln]

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[last trench]

A committee of 6 is to be chosen from 8 men and 6 women so as to contain at least 3 men and 2 women.

In how many ways can it be done if 2 particular men refuse to serve together?

[brave tree]

show work

[tropic oxide]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@last trench Has your question been resolved?

[last trench]

1

[last trench]

wdym i haven’t started that’s why i’m asking the question

[brave tree]

i mean whats ur approach to begin with

were not ggonna sppoonfeed u

[cedar kiln]

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[last trench]

maybe using complementary so the two men serve together

[cedar kiln]

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[last trench]

.close

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[dense locust]

Heya

[dense locust]

Could someone check if my graph is correct

And if it was -x^7, would it just be flipped right (Upsidedown)

[cinder venture]

Looks so

,w graph (x^2-1)(x-7)^3(x+9)^2

[wraith dagger]

Results provided by WolframAlpha

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

Requested by nairamarley

[dense locust]

Yeah

looks right

lol

Thanks :>

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[peak bough]

Where did I go wrong?

[peak bough]

oops. it's "ln y ="

[crimson sedge]

first step

[crimson sedge]

oh

[thorn lotus]

You multiplied by 2x twice

[crimson sedge]

okay

[thorn lotus]

You over chainruled

[peak bough]

oh wait really?

[thorn lotus]

3rd line

[peak bough]

so it's just u' / u even with composite functions?

[thorn lotus]

it's just a lump inside if you chain rule. You don't care what the argument is until you chain it to the next derivative

[peak bough]

if d/dx ln u

[thorn lotus]

So it's just d/du ln u

[peak bough]

I see tysm!!

wait

so if the given is ln (x^3)

the answer would be

[thorn lotus]

Well that one is a bit too simple since ln (x^3) = 3ln x

[peak bough]

$2x^3 / x^3$

[wraith dagger]

ren

[thorn lotus]

But yes

Wait no

[peak bough]

oh wait

[thorn lotus]

3x^2*

The other way around

[peak bough]

yepyep my mistake lol

[thorn lotus]

But yeah you got the idea

[peak bough]

I see. I really find chain rule confusing but I'm practicing

thanks again!

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[olive stag]

I dont understand how did we get the pink area

arent we supposed to use conjugate pairs?

[dim tiger]

What is the question

[dim tiger]

The original question of this

[tropic oxide]

this looks sus to me

[olive stag]

We get the common denominator

Then I tried conjugate pairs but it leads me no where

[dim tiger]

Try multiplying by just the conjugate of num

[olive stag]

This is what I got

<@&286206848099549185>

[dim tiger]

Why did you expand

Your problem in the main limit is having 0 in num and denom which leads to indeterminate form

If you get rid of a term in num or denom it may solve your problem

That's why you multiply by conjugate

[olive stag]

Conjugate of num or deno?

[dim tiger]

You are seeking to simplify some term(s)

[dim tiger]

The same as you got above but don't expand

So conjugate of num

@olive stag

[olive stag]

So here I didnt expand

How do continue from here?

[dim tiger]

Now can you simplify

[olive stag]

Simplify what

[dim tiger]

Look if you can simplify something from num and denom

[olive stag]

Like this?

@dim tiger

[dim tiger]

You have mistakes

Notice that a 7t can be cancelled from both num and denom

[olive stag]

But I did that

Or wait

Where is the 7t in denom

[olive stag]

Here

Aaaaaaaa

Now I got it

My bad I was slow

@dim tiger thanks

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[safe dragon]

Please help

[cinder venture]

You already seemed to be getting it

Why did you stop?

@safe dragon

<@&268886789983436800> 😊

[thorn lotus]

<@&268886789983436800>

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[placid nacelle]

The computer program myPgm produces different types of output depending on which (if any) of the parameters
-a, -f, -h and -k it has been called. The order in which the parameters are specified is irrelevant.
(a) How many different types of output can be obtained from myPgm?

[placid nacelle]

I got 16 but i'm not entirely sure if thats correct. Any ideas?

[crystal raptor]

From 2⁴?

[placid nacelle]

Yes

Since each parameter can either be there or not be there it should be 222*2 wich yeah is 2^4 = 16

did i think correct?

[tropic oxide]

yes

[placid nacelle]

!close

[cedar kiln]

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[cedar kiln]

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[errant wasp]

What is an elimination matrix

[dire geode]

Needs more context

Otherwise, probably
https://en.m.wikipedia.org/wiki/Gaussian_elimination

[errant wasp]

this was a good article, but is the elimination matrix what you mutliply by the original matrix to get the result of gausian elimination?

[tropic oxide]

idt anybody else knows what an "elimination matrix" is

did you see that term in a problem?

[errant wasp]

yes

[crimson sedge]

I think they may be confusing "elimination matrix" with elementary matrix

[dire geode]

again, needs more context

[errant wasp]

is the context

[crimson sedge]

yeah elementary matrix

so what do you know about elementary matrices in general?

[errant wasp]

I can guess?

its probably how you manipulate the matrix in gausian elimination to get the upper triangular matrix?

[crimson sedge]

an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation

so for example
1 0 0
1 1 0
0 0 1

[errant wasp]

oh because you added 1 to the 2nd row col 1?

[errant wasp]

for lu decomposition you can use gaussian to find both the lower and triangular matrix right?

[crimson sedge]

because I performed the operation R1 +R2

sry rly can't type atm m

[cedar kiln]

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[errant wasp]

no problem thanks for helping!

[cedar kiln]

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[empty locust]

can someone please help with b part

[thorn lotus]

Are you allowed to use identities for the levi-civita? or do you have to prove that too?

[empty locust]

we can use these since i proved these in earlier parts

[thorn lotus]

Ok good

So you're aware of how to write the cross product in terms of the levi-civita, yes?

[empty locust]

like this?

sum sign but we can skip that due to enstien's convention right

[thorn lotus]

Yes!

So just do that twice

You're going to want to use 1(b) I think

[empty locust]

yeaa i am kind of stuck there

this is what I am doing

which i am pretty sure is wrong

[thorn lotus]

I had to refresh myself but I was able to rederive it. You do only need 1(b) for this one

Let's start with b x c

write that in levi-civita form

[empty locust]

okay done. it should just be

this right?

[thorn lotus]

Good. That gives you the i-th element of bxc

Now do the same but for axd. I'll tell you why later

use different indices

[empty locust]

this??

[thorn lotus]

good. That the l-th element of axd

now we want to replace d_n with the bxc stuff

so the nth element of d

will act as the ith elementh of bxc

[empty locust]

yeaaa

[thorn lotus]

so you should have to epsilons: one with lmn, and one with njk

from there, you can exploit the cyclic property of levi-civita and use 1(b)

[empty locust]

this??

[thorn lotus]

i'm guess that's an n on the second epsilon.

but yes

from there you can use 1(b) but make sure you get the indices on the proper ordering

you can play around their order using the cyclic property

[empty locust]

yeaaa

[empty locust]

okay i will try that

[empty locust]

can we rewrite this like this

is this allowed?

[thorn lotus]

Those are all constants so you can rearrange them. The ordering in the epsilon seems preserved as well. You're doing good.

[empty locust]

okay so we can further rewrite this like this?

using 1b

[thorn lotus]

Yes

Looks right

Now simplify the kronecker deltas

[empty locust]

okay i got this

now what do i do for del lj and del lk?

[thorn lotus]

What happened to your other stuff?

For example, B is missing from your first term

C on your second

[empty locust]

Like I tried further simplifying this. Del mk is same as A dot C since in our sheet it was given that Del ij is same as Ei dot Ej

So I just subsituted that. Do we have to do it differently?

[thorn lotus]

That's right

But your expression up there is missing some factors

[empty locust]

Yeaa I don't know how we can simplify del lj. I mean what vector does l represent??

[thorn lotus]

d_{lj} is simplified by letting l = j

choose whichever you want to keep

[empty locust]

Oh

Why are we doing that?

[thorn lotus]

because l not equal to j contributes nothing

you want to keep the nontrivial terms

[empty locust]

Aaah

[thorn lotus]

Remember, there's a sum there that we're hiding

[empty locust]

So we can rewrite del_lj as del_jj ?

[thorn lotus]

I'm not really comfortable of thinking about it that way. I just immediately say that j = l and remove the delta symbol altogether

Doesn't really matter, as long as it doesn't hurt your calculation

But I get confused sometimes so...

Maybe not you

At any rate, that's just 1

[empty locust]

So this just becomes A dot C - A dot B(B dot C)?

[thorn lotus]

Uh no

What happened to you B_j

on the first term

Look at the formula you want to prove. You're supposed to get a vector back

you should have indices left at the very end

[empty locust]

Yeaaa

Okay

So

[empty locust]

wait i am getting confused. if we let l = j then wont this become 0?

Del_jjDel_mk - Del_jkDel_mj
Del_mk - Del_mk

and all of this multiplied by AmBjCk

Q

[thorn lotus]

Those are independent terms

if it helps, I suggest evaluating them separately

what you're doing is doing evaluating the delta but your choice on the first sum is affecting the other sum. It shouldn't

these are dummy indices

To see why it shouldn't cancel focus on just the first term. Forget the second term entirely

Anyway, I have to go. I'll be back in like 2 hours, so if you need help just send me a message. Or, hopefully, someone else can help you.

[cedar kiln]

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[errant wasp]

I am having trouble finding the lower triangular matri

[crimson sedge]

are you trying to LU factorise

[errant wasp]

yes

i tried row combinations and none of it worked

is this where i like pivot

[crimson sedge]

going Back to Ur usage of elementary matrices earlier

\dm
suppose $A$ can be reduced to the echelon form (upper triangular matrix) using only row replacements that only add a multiple of one row to another below it

\vs{3 mm}
In that case, there are a series of elementary matrices $E_p \dots E_1$ such that [
(E_p \dots E_1)A= U
]

[crimson sedge]

\dm
then [
A = (E_p \dots E_1)^{-1}U = LU
]

[crimson sedge]

\dm
this means that [
L=(E_p \dots E_1)^{-1}
]

[errant wasp]

right

Wait why cant i juse swap R2 and R1

and then perform the math to isolate

[crimson sedge]

because swapping kind of fucks up the above process a bit

[errant wasp]

like makes it more difficult, or completely wrong

[errant wasp]

I do not get this definition

[cedar kiln]

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[errant wasp]

.close

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[bright karma]

i got 1 but it doesnt feel right

hi pigeon

oh or is it -1

[solar hemlock]

1 should be fine i think

[crystal raptor]

Since all those limits exist, you are fine to just do them all individually

[bright karma]

how do i find c

[junior dome]

i told you earlier

[south tundra]

You are not told to find c

[junior dome]

check in the neighbourhood

dont sub in the value

[south tundra]

Even if you were, there is not enough information regarding c to do that

[bright karma]

so its basically 1/1-2?

[crystal raptor]

You seem to be plugging in f(c) and g(c), which is not what they want

[junior dome]

x is tending to c

not actually c

[south tundra]

No, like mentioned, [ \lim_{x\to c}\frac{f(x)}{f(x) - g(x)} = \frac{\lim_{x\to c}f(x)}{\lim_{x\to c}f(x) - \lim_{x\to c}g(x)} ] Thanks to the fact that $\lim_{x\to c}f(x)$ and $\lim_{x\to c}g(x)$ exist and that $\lim_{x\to c}(f(x) - g(x)) \ne 0$

[wraith dagger]

A Lonely Bean

[bright karma]

uh

so -3 / -3 - 0?

which is 1

ok thx

idk why i doubted my first answer

[viscid karma]

Hi everyone, will someone help me solve math examples?

[crystal raptor]

Stop going into other peoples channels, you have one already #help-3

[bright karma]

.close

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[viscid karma]

No one answers there

[crystal raptor]

Just be patient and wait, if someone wants to help you they will

[cedar kiln]

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[wintry roost]

do i split it into 2 integrals or do i make one u? idk how to start this problem

[crimson delta]

just try something

if it doesnt work then try something else

[wintry roost]

ok i got it

.close

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[dusk cairn]

dπr^2 + 2πrh? factorize

[surreal cave]

first off what do you notice is common?

[dusk cairn]

ehm

pls I don't know the pie 😭 ?

[surreal cave]

the pi is just a number

[dusk cairn]

3.14 then

[surreal cave]

yes pi is approximately 3.14, but pi is just so important we give it's own symbol

so it's standard and better to keep it as just pi

[dusk cairn]

pi

okay

but is that the common thing?

[dire geode]

yes

[surreal cave]

very

[surreal cave]

hello riemann!

[dusk cairn]

so pi is the one standing outside of the ()?

[surreal cave]

yep so what does this expression become now?

[dusk cairn]

d is diameter I think

[surreal cave]

no mein freund what does dπr^2 + 2πrh turn into if you pi out of both :)

[dusk cairn]

dr^2 + 2rh

????

[surreal cave]

very close but you forgot your pi!

$\pi(dr^2+2rh)$

[wraith dagger]

MrFancy

[dusk cairn]

oh, it's that simple???

[surreal cave]

yep! :)

but do you think we can simplify this any further?

[dusk cairn]

no

😘

[surreal cave]

I disagree

[dusk cairn]

THANK YOU

[dusk cairn]

😟

[surreal cave]

im sorry

but do you notice the r?

[dusk cairn]

yes

[surreal cave]

do you know what r^2 means?

[dusk cairn]

r*r=diameter

no, that's wrong, no I don't know

[surreal cave]

you have it right mein freund r^2=r*r

so we get $\pi(dr\textcolor{red}{r}+2\textcolor{red}{r}h)$

do you see now how we can simplify? :)

[wraith dagger]

MrFancy

[dusk cairn]

3R

r^3?

[surreal cave]

you see the gold but you're still mining iron

both are being multiplied by r

so we can just do the exact same thing we did with pi mein freund

[dusk cairn]

what are we playing minecraft suddenly pls 😭

[dusk cairn]

pi r?

[surreal cave]

it's an expression I just decided to make up on the spot :)

[surreal cave]

that's going to be on the outside

so what's going to be inside the parentheses?

[dusk cairn]

pi r (dr + 2h)?

YEEES

ONG THANK YOU I WANTED TO DIEEE, 😘

[surreal cave]

$\textcolor{red}{\pi r}(dr+2h)=(dr\textcolor{red}{\pi r}+2\textcolor{red}{\pi r}h)=d\pi r^2+2\pi rh$

do you see it now? :)

[dusk cairn]

yes

omg tysm

[wraith dagger]

MrFancy

[dusk cairn]

👩‍❤️‍👨

LOVE YOU

.close

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[surreal cave]

thank you actually listening lol

[cedar kiln]

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[surreal cave]

.close

mf

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[surreal cave]

.reopen

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✅

[surreal cave]

actually while I have a channel

if I have 12 cards that I flip over what are the odds they sum to 50?

I'm new to this combinatorics stuff so sorry if I'm like being dumb here

note I flip over the 12 cards randomly and are independent of each other

so the number of possibilities if 52 choose 12 ik that but how do I compute the number possibilities that cards sum to 50?

[silent finch]

What are the specifics of the cards?

Like are they numbered?

[surreal cave]

yea just like playing cards

[silent finch]

What happens to face cards

Is Jack 11 etc

[surreal cave]

blackjack values ace=1

jack=11

queen=12

king=13

[silent finch]

Ok

Let me try it

I don’t believe there is a nice way to do this, because we can only use a card at most 4 times and 13 is our maximum

Otherwise, we could use stars and bars

[surreal cave]

mhmm ok then thanks, just a little problem I came up with!

.close

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[silent finch]

Maybe 4 cards will be nicer if you want to make a problem

Since there’s a nice way to do it

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[zenith sail]

If possible can you translate to english?

[ivory walrus]

It’s just asking the X nothing to translate

[ivory walrus]

<@&286206848099549185>

[cedar kiln]

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[mild carbon]

Determining the Divisibility

[mild carbon]

WITHOUT THE CALC

i want to know

if there is a way to determine it without using calc

[crimson sedge]

Sorry!

[mild carbon]

np

is there an efficient way to find out ?

or is using a calc the only option i have

.close

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[crimson sedge]

i need these 2 blanks to be filled in, can anyone help me?

[thorn lotus]

what's the value from 3 to 6

[crimson sedge]

0?

[thorn lotus]

good, so that one is 0

for the 2nd line it's possible to do it visually, but unless you're comfortable with that, it's best to use point-slope form of a line

You see from the plot that that piece of the curve has two points (2, 2) and (3, 0)

You can calculat the equation of the line using those two data points

[cedar kiln]

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[crimson sedge]

Can anyone link me a website where they have proofs for how calculus is used to derive these kinematics formula?

[thorn lotus]

Do you just want the proof or are you interested in proving them yourself?

You can try this https://www.muncysd.org/site/handlers/filedownload.ashx?moduleinstanceid=2437&dataid=4035&FileName=Kinematic Eqns.pdf

[errant bluff]

facts about math

[crimson sedge]

thanks

.close

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[echo anvil]

a bit confused on this how would one graph this

[brave pike]

Follow the top graph from x= inf to 1 (excluding 1)

and then follow the bottom graph from 1 to inf (including 1)

[echo anvil]

?

[brave pike]

What is 2x-1

Is it liner? (mx+b)

[echo anvil]

yes

[vestal bear]

linear

[brave pike]

Ok so then how would the graph of that specific funtion look like @echo anvil

What is the slope and y intercept

[echo anvil]

heres also what the thing said to do also

[brave pike]

Ok, so answer my question

how would hte graph of the spesific equation on top look like

[echo anvil]

as a line

[brave pike]

Ok

Is it going up or down

[echo anvil]

a horizontal line

[brave pike]

No, there is a slope

[echo anvil]

ah mb I dumb

ok so I got a increasing line

ok and the rest of the problems are possibly use a calculator

so thanks

.close

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[echo anvil]

.reopen

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✅

[echo anvil]

.close

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[crimson sedge]

Need the answer to this linear algebra problem

[cedar kiln]

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[crimson sedge]

.reopen

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✅

[crimson sedge]

<@&286206848099549185>

[modern compass]

use their observation to write a vector equation using those three vectors.

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[formal lynx]

what does it mean if a limit "exists at every c"

[stark quest]

depends on context here

[formal lynx]

ok then lets say what does this mean: "limf(x) exists at every c in (-1,1)"

[stark quest]

im assuming it means -1 < c < 1, where lim x to c f(x) exists

whats the context of this?

like what unit is this/subject

[still swan]

i think this means that if you pick any number c where -1 < c < 1, then the limit of f(x) as x approaches c exists

[formal lynx]

limits and continuity

it shows a graph and it says to pick all the statements that are true

[formal lynx]

what does c stand for

[still swan]

just any number between -1 and 1

[formal lynx]

does it just mean continuity?

[still swan]

its a variable

[formal lynx]

oh

ohhh ur right

[still swan]

so the limit exists for all values of c in (-1, 1)

[formal lynx]

bc the limit says limit from x--> c at every c in (-1,1)

[still swan]

if there is a point in (-1, 1) where the limit doesn't exist then that statement won't be true

[formal lynx]

ok

[cedar kiln]

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[silent creek]

hello i dont understand where they get 70 degrees from

[cedar kiln]

@silent creek Has your question been resolved?

[silent creek]

<@&286206848099549185>

the vector with magnetude 10 N is 160 degrees the one on the right which is 8 N is 100 degrees

<@&286206848099549185>

[austere tundra]

@silent creek

oh wait you were asking about the 70 one sec

idk looks made up is there more context?

[cedar kiln]

@silent creek Has your question been resolved?

[silent creek]

hey sorry for lat eryply

but they are asking to find resultant vector

i was wondering how they get 70 degrees in the inner angle

[celest sentinel]

Note that the 10N vector is oriented 160 degrees counterclockwise from North

[silent creek]

yep

[celest sentinel]

that means it would dip 70 degrees below the west-pointing axis

hence why there's 70 degrees noted

[silent creek]

oh okay its a bit confusing but i think i e ti

[celest sentinel]

yeah, it's not completely clear where it's getting these numbers from

[dusk cairn]

😘 np

[silent creek]

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[brave pike]

Hi, Im just curious as to where I keep messing up, ive checked the math a couple times and can not seam to figure out my error

[brave pike]

I know there is a better way to rewrite the equation but im just hoping to find my mistake in this type of equation

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[brave pike]

nvm yeah I still cannot seam to figure it out

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[dark arch]

I have a point for example (173.000,110.000).
It's projected on a 3d space that has orientation,
[h: ( 1.000, 0.000, 0.000), v: ( 0.000, 1.000, 0.000), n: ( 0.000, 0.000, 1.000)],
by adding those coordinates to the origin each multiplied by the spacing which results in a 3D Vector for example (-1740.050,-786.901, 177.183)
I have another space with a different orientation for example: [h: ( 0.796, 0.605,-0.003), v: (-0.170, 0.220,-0.960), n: (-0.580, 0.765, 0.278)]
I need to get the 3D vector of that same point in the second space

[dark arch]

u should ask ur question in a channel that hasn't been claimed

[unborn gull]

aa sorry didn't noticed !

[cedar kiln]

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@dark arch Has your question been resolved?

[dark arch]

<@&286206848099549185>

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@dark arch Has your question been resolved?

[cedar kiln]

@dark arch Has your question been resolved?

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@dark arch Has your question been resolved?

[vernal shell]

Hello. How are you obtaining (-1740.050,-786.901, 177.183) from (173.000,110.000)? Or is it just an example

[dark arch]

it's just an example, it is a real usecase because we have an origin with coordinates x,y,z so I'm adding that point to the origin but it's only because I also need to multiply the x and y with the column and row spacing

[vernal shell]

Mmm ok what I understand about the problem so far:
You have a point P expressed in coordinates of space A, that vector is Pa.
There's also a space B, and you want the coordinates of P in that space (vector Pb)

is that correct? 🤔

[dark arch]

Yes

[vernal shell]

ok great

first you have to find each axis of A with respect to space B

For example. We want to ha in terms of space B.
That is the projection of ha on hb, the proj of ha on vb, and on nh

You can use dot product for that

ha in space B = bha = [ha.hb, ha.vb, ha.nb]

then you multiply the h component of Pa by bha, that's the h component of Pb

[dark arch]

ohh, thank you

[lean ether]

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[median galleon]

Can someone explain me A part

[median galleon]

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[median galleon]

Can someone explain me with ( A ) part

.

.

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[full wasp]

There were some students in the library. The number of girls was twice the number of boys after 8 boys left. The number of boys was twice the number of girls after another 15 girls left. How many boys were there at first?

[full wasp]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[full wasp]

2

[crimson sedge]

note everything down

[full wasp]

Mhm I did

[crimson sedge]

show your work

[full wasp]

Okay so

I did g=x2 (-8 boys)
B=x2 (-15 girls)

B-2(2) (b-8-15)
=2 (-2b-16-15)
B=2(2b-31) x2

[crimson sedge]

wait let's pause a bit

what does x2 mean

[full wasp]

Twice

[crimson sedge]

You'd probably end up confusing yourself the way you are writing this lol

[full wasp]

Ik I'm confused ngl

[crimson sedge]

Start like this and then try ig
Let there be b boys and g girls in the beginning

From the first statement
g = 2(b-8)

From second

[full wasp]

Ah ic

[crimson sedge]

b-8 = 2(g-15)

Try now

Actually the second statment is unclear to me

It could be either
b-8 = 2(g-15)
Or
b = 2(g-15)

Idk

[full wasp]

I think it's stating after the boys left

[crimson sedge]

Alright

Imma head out now

[full wasp]

But like someone is gonna explain it to me like physically so

[crimson sedge]

Okay I'll go after explaining then

Do you know how to solve equation with 2 variables btw?

[full wasp]

Eh I'm learning ig

I don't use equations that much though

[crimson sedge]

To learn the methods to solve equations with 2 variables just YouTube search

There are plenty of khan academy videos explaining it

[full wasp]

Alr

[crimson sedge]

And to physically explain the equation i got

We have b number of boys and g number of girls

From the first statement we know that when 8 boys leave

the number of girls left is twice

if we have b boys and 8 of them leave, we are left with b-8 boys

number of girls is twice that so

g = 2×(b-8)

Similarly when the 15 girls leave, the number of boys is twice as much so

if we have g girls and 15 leave we r left with g-15

And hence

b = 2×(g-15)

[full wasp]

Yea I get that bit

Nvm it's fine I'll solve it

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[keen nova]

I think I have the answer here, but I want to get an explanation on when to use AND and when to use OR, signs

in my head, AND signs are used if both conditions need to be true. This is impossible here. I guess it would only be used if we're doing something like 0<x<1 , but then why use AND ?

I guess I always think the answer is to use the OR sign?

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[blissful silo]

I got stuck again can someone help

[strange mauve]

,rccw

[tropic oxide]

doubtless you are expected to do 6^2 + 7^2 + n^2 = (n+1)^2

with the value of n yet to be found

[blissful silo]

Missed last

[frozen dust]

,rccw

[slate lintel]

this is a step up from those "guess the pattern" questions

[blissful silo]

Uh i dont realy understand can u send me u tube link

whats this (^)

[frozen dust]

power

[tropic oxide]

exponent symbol

[wraith dagger]

Ann

[blissful silo]

Ohh

Its square

[tropic oxide]

no, square is ^2 specificlly

but ^ is for all powers

for example n^3 means n cubed

[blissful silo]

Ohh right

Tyy

dang shade giving it alot of thought

[frozen dust]

,tex 6^2+7^2+42^2=43^2

[blissful silo]

idk what ur doing but it sure looks like a headache

[frozen dust]

trying to figure out how this bot works

[wraith dagger]

Shade

[frozen dust]

this should be the second to last line @blissful silo

the last one is just an explenation of what you have done before, just fill it out with variables, like this

,tex $x^2+y^2+(xy)^2=(xy+1)^2$

[wraith dagger]

Shade

[frozen dust]

and this is the last one

[tropic oxide]

what's that asterisk supposed to be tho

[frozen dust]

times

whats the times symbol

@tropic oxide

[tropic oxide]

\times or \cdot

[frozen dust]

oh and how do write pi

[tropic oxide]

but also x^2 + y^2 + (xy)^2 ≠ (xy+1)^2 generally tho

[tropic oxide]

\pi, but other latex questions go in #latex-help

[frozen dust]

tyty

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[inner elbow]

If I have the system of equations x=3y+2, 2x=4p+5, how can I find the value of x, y and p?(they’re all integers too)

[turbid lynx]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[barren canopy]

you cannot find all three with 2 equations

[inner elbow]

Hmm as I thought

Then how do I solve linear congruence systems?

Say we have x ≡3(mod 4) and 2x ≡5(mod 7)

That gives x=4y + 3 and 2x=7p + 5

If we want to find x, we have to know all the unknowns

[barren canopy]

yes

[inner elbow]

So now what?

[barren canopy]

yeah... you need atleast another equation in either x and y, x and p or p and y to solve this

[barren canopy]

btw, here mod = "%" (modulus function) or absolute value?

the modulus function returns the remainder right?

[cedar kiln]

@inner elbow Has your question been resolved?

[slate lintel]

remainder yes

[barren canopy]

in some asian countries, modulus is used to mean the absolute value of

and modululo is used to mean the remainder

[slate lintel]

yes

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[inner elbow]

Modulus function?

[inner elbow]

I think that

[inner elbow]

How is it proven that a=a1/a2, b=b1/b2 and so on?

[barren canopy]

no, these are conditions
a≠ a1/a1 and so on

we can say two linear equations have a unique solutions, infinitely many solutions or no solutions using these conditions

[inner elbow]

Oh I get it now

But what’s the proof for this rule/theorem?

[barren canopy]

no idea 🥲

[inner elbow]

Lmao

[barren canopy]

but you can easily infer them using graphs

[inner elbow]

But how do I find the solution?

[barren canopy]

for what

[inner elbow]

The system of linear congruences

The x

[inner elbow]

For example in this

<@&286206848099549185>

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[lyric narwhal]

The product of two numbers 231 and ABA is BA4AA in a certain base system (where base is less than 10),
where A and B are distinct digits. What is the base of that system?

[lyric narwhal]

no idea where to start

setting up equations doesn't do me much good

[dull oxide]

I would work it out like an elementray multiplication

[lyric narwhal]

isn't that the same as making equations?

[dull oxide]

i dunno. I haven't gone further than this

if base is less than 10, the 4 as a digit also tells you base is at least 5

That's helpful