help-0

[alpine sable]

is gonna be easier than trying to explain it

[vivid heath]

i dont have a pic

im trying to figure out a processing time

if i takes someone 37.5 hours

to complete these processes

but it takes 3x as long to do the middle proces

[tepid fulcrum]

Think abt ur question

[vivid heath]

because there is a bottleneck

[tepid fulcrum]

And repost

[alpine sable]

lmao

yea

[vivid heath]

.close

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[lone heart]

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[primal token]

just don't know how i'm supposed to use trig on this

[lone heart]

@primal token Has your question been resolved?

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[pastel jasper]

Is there a notation for natural numbers that distinguishes between having 0 or not?

[pastel jasper]

Maybe N_0? to include 0

[alpine sable]

in general they use "*"

to denote 0 isn't in the set

[hot snow]

since when 0 was a natural number?

[oak perch]

I use
$Z_{\geq 0}$ for former
$N_{\geq 1}$ or $Z_{\geq 1}$ or $N^{+}$ or $Z^{+}$ for latter

[ocean seal]

Cogwheels of the mind

[alpine sable]

$(\mathbb{N^*})^n$

[pastel jasper]

I see @alpine sable thanks

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[thin pivot]

.close

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[little berry]

this is my progress so far

I'm stuck

ping me

[serene junco]

I drew in an extra line segment here

You have enough information to know the length of the red line segment I added

and if you can find that, you can use pythag to find x

@little berry

[little berry]

is this right @serene junco ?

[serene junco]

No, that distance isn't 6

notice that it's a radius of the sphere

[little berry]

oh

yeah

18/2 = 9?

and thennn

[serene junco]

um, 9 is correct for the hypotenuse but I'm not sure where 18/2 came from

[little berry]

becase the problem said the diameter of the sphere is 18

or

[serene junco]

oh ok

yeah that's good

[little berry]

alr

then

9^2 = a^2 + 6^2

[serene junco]

yep

[little berry]

3sqrt(5)

alr thanks!

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[serene junco]

no problem 👍

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[median oar]

.coose

[median oar]

I’m so fast

[vapid shuttle]

True

Could anyone tell me if my work so far is valid?

like fair reasoning and such

and I think the problem would conclude as follows: Then either one of the arcs between a and b works as the continuous function to show that the unit circle is arcwise connected. And as such, for any unit sphere in R^n (for n>2) we can deduce it into the great circle in R^(n-1) and show that this is arcwise connected instead, which at the end of the day just comes down to the R2 case.

<@&286206848099549185>

[lone heart]

@vapid shuttle Has your question been resolved?

[oak perch]

Detailed omitted but it’s correct

If you use this path from (x,y,z) to (x’,y’,z’) : (x,y,z) to (kx’,ky’,z) for some k then to (x’,y’,z’) you can see a pattern of induction going on (move it first in S^(2-1)=S^1, then adjust one remaining component)

Similarly (x(1),…,x(n-1),x(n)) to (y(1),..,y(n)) in S^(n-1): since S^(n-2) is path connected we have a path (x(1),..,x(n-1),x(n)) to (ky(1),…,ky(n-1),x(n)) for some k, then this point is in the same “vertical” cycle with (y(1),…,y(n)). Second half path can be constructed (spheres with different radius are homeomorphic, like radius 1 and sqrt(1-x(n)^2)

[vapid shuttle]

I don't really understand that. Could you maybe try rephrasing? What details am I omitting exactly?

[oak perch]

Just the existence of the big cycle

We know it’s true, so I think omitting it might not be a problem

[vapid shuttle]

of the great circle you mean?

[oak perch]

Yeah

[vapid shuttle]

ah okay

yeah that is like a geometry thing I'm not sure it is important here to prove

[oak perch]

Oh wait a min

For any dimension we have a far easier way:

We just show that any point is arc-connected to (0,0,…,0,1)

Because a connect to p, b connected to p, together a is connected to b

Any point (x_1,…,x_n)

F(t)=

$F(t)=(k(t)x_{1},…,k(t)x_{n-1}, x_{n}+t(1-x_{n}))$ where $k(t)=\sqrt{\frac{1-(x_{n}+t(1-x_{n}))^{2}}{x_{1}^{2}+…+x_{n-1}^{2}}}$

[ocean seal]

Cogwheels of the mind

[oak perch]

Oh he didn’t recommend induction in the first place, just generalization

This is a more direct approach right

[vapid shuttle]

I'm not sure what you are asking

but anyways I must go to bed now, ty for the help cogwheels

.close

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[alpine sable]

[2\textwidth] <newpxmath, newpxtext>[
\parens{
\bracks{\bigvee_{1 \le x_1 < \hdots < x_k \le n}\quad \bigwedge_{i=1}^k p_{x_i}} \wedge \bracks{\bigwedge_{1 \le y_1 < \hdots < y_{k+1} \le n}\quad \bigvee_{j =1}^{ k+1} \neg p_{y_j}}} \iff \parens{\txs{exactly}k\tsx{of the prepositions are correct}}
]

[alpine sable]

is there any simpler/compacter way to rewrite the left side of this logical equivalence

💀

[vale wigeon]

probably not

what do you need this for anyway

[alpine sable]

this is just the general case I guess

I'm trying to prove both directions of the equivalence

why do u need order x1< x2<...?

well it is kind of misleading

they just have to be different

x_k are naturals less or equal to n?

yes all of them being different

if so just put $k \in \mathbb{N}_{\leq n}$

[ocean seal]

IllIIIllIlIIl

[oak perch]

I think you can but it’s not necessary for the question itself. aΛb being true <-> a and b being true, aVb being true <-> a or b being true already can make you take off V, Λ layer by layer

[lone heart]

@alpine sable Has your question been resolved?

[oak perch]

@alpine sable

[lone heart]

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[oak perch]

Therefore it equals RHS

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[formal rune]

Please help me find the surface area

[noble geyser]

you can split the rocket up into different shapes

[formal rune]

283 (Cone) + 942 (Cylinder) = 1230 (rounded to 3sf)

But this is wrong

Which did I do wrong ?

1070 is correct answer

[noble geyser]

let me compute

[formal rune]

Unless the textbook is wrong

It’s IGCSE second edition IG maths

Sometimes it’s wrong but very rarely

But it’s only been wrong in this section

[noble geyser]

i think found it

you might need to find the bottom of the cylinder as well

[formal rune]

Ohhhhh

Wait

[noble geyser]

doing gets 340π

[formal rune]

OHHH

I’m forgetting to remove

The top part of the cylinder

[noble geyser]

nice

good luck!

[lone heart]

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[alpine sable]

what 4E means and -1?

[vale wigeon]

E means the identity matrix, $\bmqty{1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1}$

[ocean seal]

Ann

[vale wigeon]

the ^-1 means inverse

[alpine sable]

can u give me example?

like all 1

[vale wigeon]

the all 1's matrix doesn't have an inverse.

,w inverse {{3, 1, 4},{1,5,9},{2,6,5}}

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by ann_dec

[vale wigeon]

something like this

[alpine sable]

.close

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[dim matrix]

Is my solution correct?

Suppose A and B are two independent events, associated with a random experiment. If the probability of occurrence of either A or B is 0.6; while probability that only A occurs is 0.4, then determine the probability of occurrence of event B.

Sol: Since events A and B are independent, we can express the probability of occurrence of either A or B as the sum of the probabilities of A and B minus the probability of both A and B occurring.

[vale wigeon]

why write P(B) as 0.3333 and not 1/3?

correct other than that

[dim matrix]

okay thanks @vale wigeon

.close

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[lethal belfry]

could someone please explain what this question means?

[lethal belfry]

I'm not sure I understand it

[lone heart]

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

[lethal belfry]

6

[vale wigeon]

f(x) = max{ 1(1-|x-3|), 2(1-|x-5|), 3(1-|x-7|), ..., 10(1 - |x-21|) }

[lethal belfry]

oh, so the function which has the maximum output out of all those? Thanks

[vale wigeon]

yes

[lethal belfry]

.close

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[small tapir]

Hello everyone. Does anyone know what this symbol is.
At first I thought it is integral... but why does it have the letter c on it?
The symbole: ⨐

[mellow knoll]

its an integral along a curve

eg in the complex plane

like how with normal integrals you're integrating over a line on the real axis

[worn fox]

are you sure you don't mean $\oint$?

[ocean seal]

ΣΑCu

[small tapir]

no

I think @mellow knoll is right

[small tapir]

I think that is counter integral

[worn fox]

He's describing a line integral, which is what the symbol I put is for

[small tapir]

I don't know.
this is the textbook page:

[worn fox]

Yeah its a line integral it's meant to be a circle not a C

[small tapir]

what is a line integral?

[worn fox]

Integration along a curve basically

[small tapir]

when I google integral with a circle on it; I'll usually find results that mention counter integral with is used in complex analyzing

[worn fox]

That's because they're very similar and related

Not everyone puts the little circle anyway if it's clear from context

[small tapir]

thank you a lot

but I still have doubts...
I believe circle one is strictly for complex numbers . And its called counter integral 🤔

[vale wigeon]

contour, maybe?

[small tapir]

yes. my bad

[worn fox]

People also put the circle for line integrals sometimes

[lone heart]

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[cinder charm]

Hi i really need help with the first step that ℹ circled

[near apex]

,rccw

[near apex]

Hint: You can write $a^m$ as $\left(a^{\frac{m}{2}}\right)^{2}$.

[ocean seal]

Enemagneto

[cinder charm]

I am not sure if I understand that where did the the whole square go to?

[near apex]

Umm.. What whole square?

[cinder charm]

The ( )^2

[near apex]

Here?

Or in your image?

[cinder charm]

At here

[rancid jay]

@ionic garden

[near apex]

Well, You have $x^m - y^m$ in numerator. You wrote that as $\left(\left(x^{\frac{m}{2}}\right)^{2} - \left(y^{\frac{m}{2}}\right)^{2}\right)$.

[cinder charm]

Ohh aight thank youu

[ocean seal]

Enemagneto

[near apex]

Well, You have $x^m - y^m$ in numerator. You wrote that as $\left(\left(x^{\frac{m}{2}}\right)^{2} - \left(y^{\frac{m}{2}}\right)^{2}\right)$.

[ocean seal]

Enemagneto

[near apex]

Ignore this. This has a typo.

[lone heart]

@cinder charm Has your question been resolved?

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[proper chasm]

Change quadratic equation into standard form?

[nimble fern]

looks like the same q from yesterday

[proper chasm]

To?

Yk?

[alpine sable]

ez

[vale wigeon]

yeah, it is the same exact one.

[proper chasm]

🙄🙄🙄

[vale wigeon]

what's "ez" for you is not necessarily also easy for everybody else.

[alpine sable]

do i need to provide solution?

[vale wigeon]

!nosols

[lone heart]

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.

[proper chasm]

Nah

[vale wigeon]

so no, don't do that.

[proper chasm]

Give me full solution

Wtf

Ok now tell me

😁

[vale wigeon]

do you... want to start completely from scratch?

[proper chasm]

Ye

From total basicc

[vale wigeon]

and we should assume you have erased ALL the progress you made earlier on this problem too?

[proper chasm]

Yep

[vale wigeon]

k

[proper chasm]

Mhm

[vale wigeon]

so our equation is: $$\frac{x+4}{x-2} - \frac{x-2}{x} + 4 = 0$$

[ocean seal]

Ann

[vale wigeon]

this equation has some fractions in it, which complicate matters.

what can we do to make it so there are no more fractions?

[proper chasm]

Mhm

[vale wigeon]

(don't do it yet, only say what it is)

[vale wigeon]

this was not a yes-no question.

[proper chasm]

Yes

Oh sorry

I didn't understand what r you saying actually before

I thought you r saying to give answer in yes or no 😅

[vale wigeon]

i cannot imagine why you would think that.

[proper chasm]

Nvm sry

[vale wigeon]

ok, again:

what can we do to make the fractions go away?

[proper chasm]

Ye

Yes

We can

Take lcm

[vale wigeon]

i give up

[proper chasm]

Ugh ok

I am leaving

It's my fate for math

[somber owl]

U need to have same denominator first

[proper chasm]

Give me a sec

[alpine sable]

Will solve it, just a moment

[proper chasm]

Ok

@vale wigeon

[steep wren]

why make it so complex

[proper chasm]

Mhmm

[steep wren]

u from

india or us

[proper chasm]

Can you tell me a simple method

[proper chasm]

Pakistan

[steep wren]

oh

[vale wigeon]

do you know of any simpler method than that?

[steep wren]

simplex method is

[vale wigeon]

this is fine so far

[proper chasm]

Gtg outside byee

[vale wigeon]

now collect like terms

[steep wren]

ya it works

[vale wigeon]

k

[steep wren]

no simple ig

[proper chasm]

Try again and again will make you succeed

I going ill be backk

.close

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[flint belfry]

in a path do you need to visit all vertices? or is it just the fact that no vertex is visited more than once?

[flint belfry]

because for a graph like this how would you visit every vertex without repeating one?

[vale wigeon]

do you mean just a path

or do you mean something like a hamiltonian path maybe

[flint belfry]

idk what that is

just a path i assume

[vale wigeon]

why "assume"

ok lets see

do you have a problem statement in writing

[flint belfry]

yes

[vale wigeon]

how would you visit every vertex without repeating one?
for the graph you showed that's impossible

ok show the problem statement in full please

[flint belfry]

give me 2mins

to connect my pc to discors

@vale wigeon

5b

[vale wigeon]

ok alright so the definitions of walk, path and trail are all written clearly here.

don't troll + open your own channel if you need actual math help ( #❓how-to-get-help )

[flint belfry]

OH WAIT

[vale wigeon]

5b? or 5c

[flint belfry]

I MISREAD THE QUESTION

[alpine sable]

do you mean an Euler path or something

[flint belfry]

Pn is for paths anyway

so its juts n-1 right

[vale wigeon]

yes

[flint belfry]

just*

ty ann 🙏

.close

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[faint lantern]

I was wondering what I am supposed to do now? 2x doesn't go into 21x.

[vale wigeon]

sure does

ten and a half times

[faint lantern]

oh wait I've done it wrong haven't I. I was meant to do -24x + 45x wasn't I

[vale wigeon]

but that is what you didd.

[faint lantern]

Wait no thats what I did do

[velvet summit]

yeah

[vale wigeon]

assuming everything else up to this point is correct

[velvet summit]

use adecimal

he did do everything correctly

use a decimal or fraction

[faint lantern]

so 10 remainder 1?

[vale wigeon]

no

21/2

[faint lantern]

sorry 2 remainder 1

[vale wigeon]

no

the constant term in your quotient will be 21/2

yes it's a fraction no there's nothing wrong with that

[faint lantern]

so its 10 - (-5 * (21/2))

is the final sum I need to do?

I've got my 21x + 10 and I need to write what 2x needs to be multiplied by to get to 21x

I need to write that on the line at the top right?

so I write + 21/2?

ohhhh

hang on I think I'm getting it here

dang it I ended up with -32 as my last number and that isn't even close

[faint lantern]

Somehow the answer is supposed to be +10 but I have no idea how that is reached

[lone heart]

@faint lantern Has your question been resolved?

[lone heart]

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[tawny imp]

should i be using this same formula for the problem above?

cause i got (6.9,-5.6) and it says it's wrong

<@&286206848099549185>

[delicate hearth]

show how you solved

[tawny imp]

i=-5cos30+4cos50=6.9
j=-5sin30-4sin50=-5.6

[delicate hearth]

Do you know how to find out if the component is negative or positive?

[tawny imp]

no, i was only given the example above

[delicate hearth]

first multiplying by cos you get component on X axes. Look, if it lying on left side of Y axes then you put '-' sign before it. Same for sin but you get component on Y axes and if below X axes then it's negative

understand?

[tawny imp]

i do, but im still getting the same answer

nvm i got it

thanks for the help

.close

[lone heart]

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[alpine sable]

anyone know what 5a - 3a + 4a
2a + 4a
6a is

[winter light]

Do you think we can know it with only this information?🙃

[gray isle]

well that's pretty much you could do

6a
is the simplified result

[vale wigeon]

a poorly written line of work for a problem that was not written at all.

[alpine sable]

oh i mean like

simplifying 1 - 2 + 3 -1

mybad

[gray isle]

what's your issue with that

[alpine sable]

simplifying it

1a - 2a + 3a - 1a

[gray isle]

addition and subtraction have the same precedence
the basic approach would be to go from left to right

[alpine sable]

so the answer would be go from left to right

[gray isle]

simplify from left to right

[alpine sable]

1a + 2a
3 a

[gray isle]

where's 1a + 2a coming from

in what you posted, you had
1a - 2a

[alpine sable]

you add them right

[gray isle]

you do what the signs tell you

here the sign between the
1a and 2a is a
MINUS SIGN

and you would subtract

[lone heart]

@alpine sable Has your question been resolved?

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[split sundial]

Can someone help me understand this question? I used the simulation to find that it was in the 2nd percentile, but i dont get part b, i guessed that it came from a different population but i dont have any reasoning behind it

[lone heart]

@split sundial Has your question been resolved?

[tacit arch]

,rotate

[lone heart]

@split sundial Has your question been resolved?

[lone heart]

@split sundial Has your question been resolved?

[lone heart]

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[crimson tundra]

Hello, how do I determine without calculation in the joint distribution table if the correlation will be greater than 0 or less than 0

For the third one I understand but not for the first two : it says that if one variable that is growing results in the growth of the other it will be positive but if one variable that is growing results in the fall of the other it will be less than 0. So how do I apply this?

[alpine sable]

sta je to?

[crimson tundra]

Pozdrav, vjerojatnost

[alpine sable]

statistika i vjerovatnost?

[crimson tundra]

Dvodimenzionalni slucajni vektor

Da

[alpine sable]

ja treba sad da spremam calculus al mrzi me

imas mozda neku dobro izbirku?

[crimson tundra]

E jbg ja se isto sa ovim jebem

Ne znam ja sam sve ucio iz materijala od fakulteta

[alpine sable]

a koji s faks

[crimson tundra]

Fer

[alpine sable]

uvatime danas da prepisujem

fuj sve mi bodove skinuli

[crimson tundra]

Jbg

[alpine sable]

kad je tebi ispit sutra?

hahha kakav sa madzionicar znam da polazes sutra

[crimson tundra]

Petak

<@&286206848099549185>

[earnest pawn]

mhm

[crimson tundra]

Sorry for the chat, a guy that speaks my language tried to help

[deep elm]

hallo

[crimson tundra]

I've sent a pic and an english text

[earnest pawn]

jebem ti sunce sta pingas onda @crimson tundra

[crimson tundra]

Jer mi treba pomoc

Eto

[earnest pawn]

pa de reci

sta treba

[alpine sable]

pitaj onu Anu onda dobro zna

[crimson tundra]

Kako cu znat pod a i b predznak koeficijenta korelacije

Ovo je dvodimenzionalni slucajni vektor

<@&286206848099549185>

[lone heart]

@crimson tundra Has your question been resolved?

[crimson tundra]

.close

[lone heart]

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[dense garden]

what is wrong with this

[ancient saddle]

Mmm I think problem c is wrong. Could you explain why you chose that option? 🤔

[dense garden]

well it doesn’t have no solution

or infinite

oh is it unique?

[ancient saddle]

Mmm if it's unique, what's the solution?

[dense garden]

x = 5

z = -1/2

y = 0

[ancient saddle]

What if y=100

Is it still a solution?

[dense garden]

wdym

no?

why is it infinite?

is it because it is a 2x3

[ancient saddle]

Yeah at leat in this case where the system isn't inconsistent

You can plug in any value for y, and the solution will always be correct as long as x=5 and z=-2

[ancient saddle]

(it's -2)

[dense garden]

ah I see now

thank you

.close

[lone heart]

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[vale storm]

confused

[echo forge]

You have to replace all the k with 3k when doing h-p

[vale storm]

huh

[echo forge]

Where are you stuck?

[vale storm]

everything

[echo forge]

You have two functions h and p right?

[vale storm]

yea

[echo forge]

k is the variable

[vale storm]

ok

[echo forge]

in each function

So now

They ask for h-p of 3k

Let’s do h-p first

[vale storm]

ok

[echo forge]

What’s h-p?

[vale storm]

function-function

[echo forge]

Sure but in terms of k

[vale storm]

im confused wdym

[echo forge]

Think h as h(k) and p as p(k)

[vale storm]

ok

[echo forge]

h-p is what expression

[vale storm]

h(k)-p(k)

[echo forge]

And what are h(k) and p(k)

[vale storm]

functions

[echo forge]

Yes but what’s the explicit formula which depends on k

[vale storm]

i dont get it

[echo forge]

Look at the exercise

[vale storm]

h(k)=9k^2-6?

[echo forge]

Yes

[vale storm]

ok what about it

[echo forge]

replace h(k) with this in h-p

[vale storm]

(9k^2-6) - (k-11)

[echo forge]

With parentheses

Yeah

[vale storm]

ok

[echo forge]

Now develop

[vale storm]

how

[echo forge]

Distribute the -

[vale storm]

to the k-11?

[echo forge]

Yeah

[vale storm]

-k+11

[echo forge]

Yes

Now simplify

k-p

[vale storm]

how can u simplify more then this

[echo forge]

The whole expression

[vale storm]

ok

9k^2-6-k+11

[echo forge]

Which is

[vale storm]

11-6 5

9k^2+5-k

[echo forge]

Yes

[vale storm]

then what

[echo forge]

Nos you have (h-p) of k right

[vale storm]

i think

[echo forge]

(h-p)(k)

That’s the thing you have

[vale storm]

where did the 3 go'

[echo forge]

It has never been there

[vale storm]

what

[echo forge]

So we want (h-p)(3k)

[vale storm]

i thought you said the 3 wasnt there

[echo forge]

You have to replace all the k’s with 3k

[vale storm]

isnt there supposed to be a 3 here

[echo forge]

Read again

[vale storm]

its the excat same thing exact without the 3

[echo forge]

Ok let’s start again

[vale storm]

ok

[echo forge]

You have your expression

What is it

The thing which depends on k

[vale storm]

h(k)=9k^2-6

p(k)=k-11

[echo forge]

Yes

[vale storm]

ok

[echo forge]

Now h(k)-p(k)=(h-p)(k)

It’s just two different notations

[vale storm]

why is the three dissapearing though

[echo forge]

You have never had a three in your expression did you

[vale storm]

wait nevermind

i get it

[vale storm]

ok i understand this

ur just rewriting it

[echo forge]

Good

[vale storm]

ok

[echo forge]

What’s (h-p)(k)?

[vale storm]

9k^2-6+k-11

thats the h-p

[echo forge]

Which is

Simplified

[vale storm]

9k^2+5-k

[echo forge]

Yeah

[vale storm]

ok

[echo forge]

So

[vale storm]

so then its 9k&2+5-k(k)

[echo forge]

Now we want (h-p)(3k) that’s the question right

[vale storm]

yes

[echo forge]

The second parenthesis means that we want the unknown to be 3k instead of k

So you have to replace every unknown k you have in the simplified expression into 3k

[vale storm]

ok

so then its

so then its 9*3k&2+5-3k(3k)

[echo forge]

That’s not right

[vale storm]

but i replaced it with 3k

[echo forge]

This expression

Is h-p

[vale storm]

so what am i supposed to replace with 3k

[echo forge]

k

You added a (3k) at the end for mo reason

[vale storm]

in what equation

[vale storm]

cause before it was 9k&2+5-k(k)

so i replaced all ks i saw with 3k

[echo forge]

There were no (k)

(k) is for a function this is just an expression

[vale storm]

so then its

so then its 9k^2+5-k

[echo forge]

Yes that’s h-p

[vale storm]

ok

[echo forge]

Now replace k with 3k

[vale storm]

9k^2+5-3k

[echo forge]

Don’t forget the other k

You have to replace every unknown

[vale storm]

9*3k^+5-3k

[vale storm]

but why

[echo forge]

You change the variable of the function so that’s how it is if you don’t do that only half of the function’s variables would change which is nonsense

[echo forge]

Parenthesis for the power of two

[vale storm]

ok

9*3k(^2)+5-3k

[echo forge]

Because 9x3k^2≠9x(3k)^2

[vale storm]

its 93k?

it increases that much?

[echo forge]

Look again discord did weird things

[vale storm]

ok

[echo forge]

x is *

[vale storm]

9*3k^2

where did the +5 go

[echo forge]

Nooo

Ok just listen

[vale storm]

ok

[echo forge]

h-p is $9k^2-k+5$ right?

[ocean seal]

MatFous

[vale storm]

yes

[echo forge]

h-p depends on the variable k

[vale storm]

yes

[echo forge]

Now we want to make it depend on 3k which is now our variable

So we replace each k with 3k instead

[vale storm]

why are we substituting 3k

i mean substituting k for 3k

why though

[echo forge]

That’s what the question on your paper asks

[vale storm]

ok

[echo forge]

We have (h-p)(k)

The paper asks for (h-p)(3k)

[vale storm]

why did the k from the outside get there

i thought we have h-p

which is the 9k^2 stuff

[echo forge]

Do you know what a function is?

[vale storm]

to the most part

[echo forge]

That’s the problem

Let’s say h-p=f

[vale storm]

ok

[echo forge]

You now have f(k)

[vale storm]

f is the function

[vale storm]

ok k is the function

[echo forge]

No???

f is the function which depends on k

[vale storm]

ok

[echo forge]

so f(k)=9k^2-k+5

[vale storm]

ok

[echo forge]

Are we ok with this?

Good

[vale storm]

i think so

[echo forge]

Now we are looking for f(3k)

That’s the question on your paper

[vale storm]

is k=3k

[echo forge]

You can think of it that way

[vale storm]

arent we looking for f(k)

not f(3k)

[echo forge]

We already have f(k)

[vale storm]

oh ok

is h-p f(k)

[echo forge]

(h-p)(k) is f(k)

[vale storm]

ok

[echo forge]

h-p is 9k^2-k+5

But f(k) is defined by this expression too

Anyway

[vale storm]

ok

[echo forge]

We want f(3k) which is 9(3k)^2-3k+5

[vale storm]

ok

then what do we do

[echo forge]

Which is 81k^2-3k+5

That’s your answer

That’s f(3k)

[vale storm]

ok so can u summarize it

[echo forge]

Which is (h-p)(3k)

[vale storm]

from the beginning

[echo forge]

Well

You try to do it and i’ll tell you if it’s right

[vale storm]

ok

the exersize

is 9k^2-6

and k-11

[vale storm]

p=this

[vale storm]

h=this

[echo forge]

First we want to know (h-p)(k) which is

[vale storm]

then we do h-p

[echo forge]

Yeah

[vale storm]

9k^2-6+k-11

which is

9k^2+5+k

[echo forge]

Minus

[vale storm]

then

[echo forge]

Minus k

[vale storm]

why minus

[echo forge]

-(k-11)

-k+11

[vale storm]

where did the outside minus come from

[echo forge]

p=k-11

h-p

=

[vale storm]

oh ok

[echo forge]

h-(k-11)

[vale storm]

so its 9k^2+5-k

good?

[echo forge]

Yes

[vale storm]

then

its 9k^2+5-k(k)

[echo forge]

Nooo

[vale storm]

and k=3k

[echo forge]

Ok

[vale storm]

so then you substitute

[echo forge]

So h-p is the same as (h-p)(k)

No need to add (k)

[vale storm]

ok

k=3k

so you substitute

[echo forge]

(k) doesn’t mean you multiply by k it means you have a function which depends on the variable k

[vale storm]

its 9(3k)^2+5-(3k)

[echo forge]

Yes

[vale storm]

simplify

[echo forge]

Now simplify

[vale storm]

81k^2+5-3k

[echo forge]

Yes

Done

[vale storm]

can u define function for me rq

[echo forge]

What level

[vale storm]

precalc level

[echo forge]

Ok

A function is a relation between a group of number and an other group of number

You assign for example to 4 the number 2

That’s a function

[vale storm]

so then 4=2?

[echo forge]

A sort of magical box that you put numbers through and it gives you an other number

[vale storm]

where you substitute

[echo forge]

If the function is called f you say f of 4 is 2 which is written f(4)=2

[vale storm]

ok

[echo forge]

Now let’s say you don’t want particular values

You just want a formula

For example the function that two a number gives the number times two can be the function f(x)=2x

x is a variable

You can change x to be any number

Choose one

[vale storm]

3

[echo forge]

So f(3)=3*2=6

[vale storm]

ok

[echo forge]

So that’s where the substitution comes from

[vale storm]

so in this situatio

[echo forge]

Your k was the variable

[vale storm]

i still dont understand why we substitute k for 3k

[echo forge]

We have f(k)

And if you want to know what happens when you three times the k in the function

You have to find f(3k)

Which is f(k) but you replace k in the expression by 3k

[vale storm]

ok

can u help me with 1 more problem

[echo forge]

Show me

[vale storm]

ok

[echo forge]

You have f(x)

[vale storm]

yea

[echo forge]

What’s f(m-4)?

[vale storm]

thats x

[echo forge]

Nooo

[vale storm]

because f is the function

[echo forge]

It’s a function

Yes

So the thing in parenthesis after f is the unknown

The variable

[vale storm]

so then do we substitute the x in 6 to m-4

[echo forge]

try it yes

[vale storm]

ok

6(m-4)-5

[echo forge]

Yes

That’s f(m-4)

[vale storm]

6m-24-5

6m-29

[echo forge]

Yes

Now they ask for f(m-4)+2

Which is

[vale storm]

what is 6m-29 = to

[echo forge]

f(m-4)

[vale storm]

ok

so then we substitute 6m-29 in the thing

and its 6m-29+2

6m-27

[echo forge]

Yes

You got it

[vale storm]

f(6m-27)

final answer?

[echo forge]

???

Why f

[vale storm]

oh

ok

[echo forge]

You found f(m-4)+2

[vale storm]

6m-27 final answer?

ok

[echo forge]

Yes

[vale storm]

lemme write it down

[echo forge]

Now go watch a video or two about functions on youtube and try to understand the notation when you use it and when you don’t

[vale storm]

ok

[vale storm]

i understand better

can u help me with another question though

[echo forge]

You’ll have to ask somebody else im about to go to sleep or you can try solving it by yourself which is in my opinion the best choice

[vale storm]

ok

how do i close this

[echo forge]

,close

[vale storm]

,close

.cose

.close

[lone heart]

Channel closed

Closed by @vale storm

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[languid plaza]

help pls

[lone heart]

@languid plaza Has your question been resolved?

[languid plaza]

<@&286206848099549185>

[primal creek]

Let's first find the direction vectors for both lines:

For line l: Direction vector = (−9, 3, 9)
For line r2: Direction vector = (3, −1, −3)
Now we'll check if the direction vectors are proportional. Two vectors are proportional if one is a scalar multiple of the other. In this case, the direction vectors are not proportional since their components are not scalar multiples of each other.

to find out which is the case, we can set the parametric equations for the two lines equal to each other and solve for the parameter t to see if there is a common point of intersection:

lei(t) = r2(t)

K - 9t = 3t
3t + 1 = -t
9t + 5 = 5 - 3t

Solving these equations, we get t = 0 for all three equations. This means that the two lines intersect at the point where t = 0:

Intersection Point: (K, 1, 5)

Since the lines intersect at a point, they are not parallel or skew. Thus, the lines are neither parallel nor distinct parallel. Therefore, the answer is DNE for distinct parallel lines.

As for the equation of the plane containing these lines, since they are not distinct parallel lines and are not skew, they must lie on the same plane. We can use the point-slope form to find the equation of the plane. We have the point of intersection (K, 1, 5) and the direction vectors of the lines:

Point: P(K, 1, 5)
Direction Vector 1: (−9, 3, 9)
Direction Vector 2: (3, −1, −3)

The equation of the plane in point-normal form is given by:
n · (r - r0) = 0

Where n is the normal vector to the plane, r0 is a point on the plane, and r is a general point on the plane.

The normal vector n can be found by taking the cross product of the direction vectors of the lines:
n = (−9, 3, 9) × (3, −1, −3) = (24, 72, 24)

Now we can write the equation of the plane:
24x + 72y + 24z - (24K + 72 + 24 * 5) = 0
24x + 72y + 24z - 24K - 72 - 120 = 0
24x + 72y + 24z - 24K - 192 = 0

So, the equation of the plane containing the lines is:
24x + 72y + 24z - 24K - 192 = 0

[tacit arch]

Is this some chagpt

#chill for trolling

[lone heart]

@languid plaza Has your question been resolved?

[lone heart]

Channel closed

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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[tight girder]

I need a little help with this one, the main issue is the X's grade, I dunno how to do this limit with equations of grade 3, I tried to reduce it with Ruffini and while it worked and I got x^2 - 3x + 2/ x^2 - 1 ((x-1)(x + 1)) but I can't get the factors for x^2 - 3x + 2 but this is all is assuming reducing the grade is even a good move in this instance

[wide sierra]

$(x-2)(x-1)&= x^2-3x+2$

[ocean seal]

binibini
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tight girder]

Wow I'm stupid, thanks

.close

[lone heart]

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[real dagger]

how do i derive this

[real dagger]

yeah but

how would you do

the derivative of the natural log

[alpine sable]

(lnx)' = 1/x

idk how to do it

[real dagger]

oh

so would it just be

[alpine sable]

I forgot how to do it

[real dagger]

ln(x)(e^x)+(e^x)/x

[alpine sable]

but maybe you'll need to use exponencial

[alpine sable]

that's right

[real dagger]

that does not seem right

[wide sierra]

f(x)=lnx
e^f(x)=x
dy/dx(f(x)×e^f(x)=1
dy/dx( f(x) ) = 1/x

[sonic ridge]

why doesnt it?

[real dagger]

Ohhh

nvm i dont understand

[real dagger]

how is f(x)=lnx

[wide sierra]

lnx is a function

and you asked about the derivative of the function?

f(x)=lnx
e^f(x)=x
f(x)'×e^f(x)=1|÷e^f(x)
f(x)' = 1/x

[lone heart]

@real dagger Has your question been resolved?

[real dagger]

OH

[lone heart]

@real dagger Has your question been resolved?

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[eternal hornet]

Hi so I have question about “e” why is it 0 instead of 1? Isn’t it increasing until 1?

[eternal hornet]

Also for f.. trying to figure out how to interpret that

[wary stream]

Because it's asking for the interval for the x values

Not y

You probably saw the f(x) and went straight into thinking the interval for y that it increases on

[eternal hornet]

So where x is increasing basically?

[wary stream]

Yes

[eternal hornet]

Wait but x is increasing until… oh wait so (-infinity,0) is just the domain..?

So just find where it’s increasing in the domain?

[wary stream]

Yeah

[eternal hornet]

Oh.. wow why did I think it was y instantly

[eternal hornet]

Can u also help this this

[wary stream]

It's just asking for where g(x) is greater than 0

[eternal hornet]

this time g(x) IS y

?

[wary stream]

g(x) is that given function and it wants you to identify where it's above the x axis

[eternal hornet]

Only thing above the x axis is (-1/2,1) tho

[wary stream]

Then that's it

[eternal hornet]

But the answer says [-1/2,0)

If it’s “0” it’s not greater than 0

Im so confused

[wary stream]

You still did it in terms of y

It's still suppose to be in terms of x

What is the interval of x values where it is above the x axis?

[eternal hornet]

Above also includes “on”…?

[wary stream]

Yes

[eternal hornet]

Bruh

[wary stream]

That's why it's [-1/2

[eternal hornet]

I get it 😭

[eternal hornet]

Wait question, if it’s below does that also include 0? Like f(x) <0

[lone heart]

@eternal hornet Has your question been resolved?

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[alpine sable]

Vi = 16m/s
Vf = ?
Gravity is pushing down on the ball by 9.8 ithink

[alpine sable]

Use the G.U.E.S.S Method

but what would grav

what the

????????

time = 2s

solving for Vf?

[wary stream]

Given
Unknown
Equation
Solve
Solution
I think is what GUESS means

[alpine sable]

ah

Well unknown is Vf

i state dmy knowns already

what does the 9.8 do in this situation?

where does it apply

[wary stream]

What formula has vi, vf, t, and gravity aka acceleration

[alpine sable]

ah

gravity = acceleration

air resistance doesnt apply btw

idk if that was obvious

Gravity is a force that accelerates an object.
The acceleration on earth being ~9.8 m/s^2

it prob is

oh -

because it pulls it down

right

isnt it m/s^2

You are correct

Anyways

You did the G.U part of G.U.E.S.S.
Now do the E part

?

Equations

i think

its

this one

2nd equation

because i dont have Vf

so i need to reorganize the equation right

WRONG

[wary stream]

No

No vf means vf isn't a given a known value

[alpine sable]

The unknown variable will be in the equation

You are using the equation to solve for the unknown variable

so the unkown variable must be in the equation for you to solve for it

so its just the last one then

delta x =

WRONG

bruh

uhhhh

[wary stream]

What formula has vi, vf, t, and gravity aka acceleration

[alpine sable]

You have three knowns

and one unkown

Known: $$ v_i$$ $$a$$ $$t$$ Unknown: $$v_f$$

[ocean seal]

MBI Agent Sigma-6 (σ-6)

[alpine sable]

2nd to last one then

CORRECT

🆘

how do i know whether i need to reorganize an equation or not?

[alpine sable]

By looking at it

clarify

* equation *

and if none of them fit

i have to reorganize?

If the variable you are trying to solve for isn't on it's own side of the equation then you would reorganize it to be so

[wary stream]

Plug in all the info you have, then see if you need to reorganize it

[alpine sable]

i see

so if i need to reorganize i would have one unknown on the other side

interesting

ill understand it sooner or later

@alpine sable what song would you like me to play on the piano in return for you helping me?

[alpine sable]

Blue bird

or i can do a quick sketch of a character for you

okay

naruto

?

https://musescore.com/user/29234930/scores/5520783

you had that up rather quickly

but Ill play Animez Modified Version

👍

[scenic falcon]

hi can someone pls help me

[lone heart]

Please read #❓how-to-get-help

[scenic falcon]

for som reason theres no help channels on my screen

only the taken ones

[wary stream]

Make sure that arrow is pointing down

[scenic falcon]

it is

it wasnt like this before i dont know what happened

[wary stream]

Refresh discord

[alpine sable]

got to id:browse and opt into all of the help channels

[scenic falcon]

thank you so much!

wait i do not have permission to send message