help-27

[restive river]

Actually...

Nevermind

[mint orbit]

God damn yo u gotta chill

u nearly gave me a heart attack

lol.

[restive river]

Actually no it's not

wait

no it is

Nah I'm just playing with you at this point

[mint orbit]

Lol.

Yea its a stupid question but I jus wanna be sure

[restive river]

I thought it was slightly increasing to its right but I'm just now realising it's actually perfectly flat so it counts

[mint orbit]

because maximum and minimum is finite so as the end behavior approaches infinity well infinity is non-stop so that can't be our max or min.

so then I guess my question is answered where we can choose to constrain a function at a certain interval and observe the maximum and minimum values

or we can just observe the function in terms of a broad scale and also observe the maximum and minimum values.

[restive river]

Maybe my brain is just not braining right now but what exactly is the problem?

[mint orbit]

Wait hold up Labyrinth would u mind taking a look at this rq

[restive river]

I'm already here to help so I might as well

[mint orbit]

sending a pic

[restive river]

Glad I'm not the only one to write in print

[mint orbit]

I love pen and paper.

Anyways.

I was wondering for maxima and minima do I need to constrain it to a closed interval? Or can it be an open interval, but if its an open interval couldn't it lead to the possibility of the argument below?

[restive river]

Do you need to constrain it... for what?

[mint orbit]

I'm asking when determining a maxima or minima does it have to be constrained to a set interval or can the interval be open as well. But the only problem is if we make an open interval then we can have the argument below which would be wrong?

[restive river]

Are you asking about showing that it's a maxima or minima?

[mint orbit]

If I wanna show something is a maxima or minima does the x values need to be constrained to a set interval or can it be an open interval?

[restive river]

If x is contained within an open interval such that for any x' in the interval we have f(x') >= f(x) or f(x') <= f(x) then there must be a smaller closed interval contained entirely within that open interval such that this holds

This logic goes both ways

So unless I'm missing something, it shouldn't matter whether you use a closed or open interval

@mint orbit Does that answer your question? If so, you can .close this channel

[devout snow]

@mint orbit Has your question been resolved?

[mint orbit]

So what your saying is that in both the open and closed interval we know that by definition of local maximum and minimum holds for either scenario. As long as there is nothing that impedes that fact then we know it holds for both open intervals and closed intervals. But my question to you is when you say smaller interval that is not a rigorous statement to me for the definition of local maximum and local minimum to me, because I'm thinking mk well in what specific range do I have to be to ensure that the statement is true. Maximum point c (Local) If point c is a relative maximum if f(c) >= f(x) for all x e ( c - h, c + h) where h > 0 (our tolerance level measure).

[devout snow]

Channel closed

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[mint orbit]

.reopen

[devout snow]

✅

[sand dove]

This function is not concave upwards

[mint orbit]

what makes u say that?

[sand dove]

I can find two points on the curve such that, if I draw a segment between them, the segment is not above the curve

[mint orbit]

wdym

[steel halo]

that's a cool property for visualizing concavity

[mint orbit]

mk tell me why that is

[sand dove]

The true definition of "$f$ is concave upwards", that doesn't rely on the second derivative, is : $\forall x,y\in D, \forall \lambda \in [0,1], f(\lambda x + (1-\lambda)y)\leq \lambda f(x) + (1-\lambda)f(y)$

[woven radish]

rafilou2003

[mint orbit]

do you really think i am gonna know that what the fuck lol

teach me professor

[sand dove]

well it surprises me that you haven't been taught this. So usually when $f$ is differentiable twice EVERYWHERE, then $f$ is concave upwards if $f''(x) \geq 0$

[woven radish]

rafilou2003

[sand dove]

However, notice than on your light blue point, f is not differentiable twice

[mint orbit]

I usually just picturize a bowl and align it with the curve

[sand dove]

well that doesn't always work as seen here

[mint orbit]

hmmmm

[sand dove]

the only visual way to see if a function is concave upwards is this line trick

[mint orbit]

thats rlly interesting cus that is essentially the bowl idea but is better. equipped for more functions

[mint orbit]

OHHHH THAT MAKES SENSE NOW

yea i purposefully made the fist derivative at that point not differentiable at that point

but since that point would not be differentiable for the second derivative

it violates the fact that f”(x) must be positive in terms of magnitude for every point for every point to be considered concave upwards?

[sand dove]

yep

[mint orbit]

interesting because i initially presumed that u were saying somewhere was concave downwards and thus we had a f”(x) < 0, which I found confusing as I know the f”(x) > 0 for every point on there except for the non-differentiable point. This line basically indicated that.

Is there a proof I can see that would be around my level? Also question rafilou when determining maxima and minima does it have to be a closed interval or can we have an open interval as well. Intuitively both should be true, and Labyrinth’s explanation does make sense, but I want ur thoughts in case I am missijg anything.

[sand dove]

what are the conditions regarding extrema?

I don't think I understand the part for maxima

[mint orbit]

Well according to extreme theorem if a function is continuous over the closed interval [a,b] then we have one local maximum and one local minimum

[sand dove]

ok so, just draw any concave upwards function on a closed interval?

[mint orbit]

well in my function its an open interval

(-infinity, +infinity) for our x values

[devout snow]

@mint orbit Has your question been resolved?

[devout snow]

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[autumn crest]

need help with homework: the question is a 19.5% discount on a flat screen tv amounts to $560. what is the list price?

[autumn crest]

do i just add 19.5% towards the $560?

<@&286206848099549185> new question

im stuck

.close

[devout snow]

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[whole wharf]

does this look good?

[quaint citrus]

,w x^2 - x + 1 = 0

[woven radish]

Results provided by WolframAlpha

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

Requested by northsteve

[quaint citrus]

Looks good Gomez

[rapid merlin]

The answer in one statement wow

[whole wharf]

nice thanks

🫡 🤝

[quaint citrus]

Ur free to use the bot btw

[whole wharf]

oh ok

[quaint citrus]

Anytime in #bots

[whole wharf]

i never learned to use it

i guess i should

.close

[devout snow]

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[quaint citrus]

For wolfram bot just do ,w (problem)

For simple calculations like

(16*12)-202^2

U can use wolf or calc

,calc (16*12)-202^2

[woven radish]

Result:

-40612

[main gull]

You can always just go to the site itself

wolframalpha

[quaint citrus]

,w (16*12)-202^2

[woven radish]

Results provided by WolframAlpha

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

Requested by northsteve

[whole wharf]

oh ok

thanks for the example

[whole wharf]

🫡 sure thing 🤝

[devout snow]

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[barren halo]

can someone explain to me how tf this is right

[barren halo]

i mean i get the first one is the power of the power rule so that would end up being 6 to the 5th right

[lyric hornet]

$\frac{a^b}{a^c}=a^{b-c}$ :)

[woven radish]

FancyBredFries

[barren halo]

i understand that one

but whawt is the difference between that *second and last one

[lyric hornet]

different exponents

you either need to have the same bases and exponents, or have one be the same to do anything with it†

†you can do some other things to it with logs but that's more advanced

[barren halo]

what

alright alright alright

so the last one would be what

because i mean you're supposed to multiply the numbers and add the exponents right

so that should be right then the last one

but it says its incorrect so how tf does that make logical sense

this is certainly helpful

i am getting so much knowledge

BY TALKING TO MYSELF

WOW

hey how are you doing today

good how about you

im doing pretty good

thats nice to hear

yeah especially these days, the world is so screwed up right

yeah i know as of right now i need help with math but no one is here to help me

wow dude that kinda sucks

yeah i know i kinda wish someone would help me

well good luck with that buddy i hope you find someone that can help you

yeah me too i really hope i dont fail my math quiz

ah good luck with that math quiz buddy

thanks good luck with whatever challenges you in life

ah thats nice of you, i better get going

ok, see you around

"Be patient and wait for someone to answer."

lets see how long ill wait

lets set a timer and see how long the wait is

waiting patiently

https://tenor.com/view/byuntear-sad-sad-cat-cat-meme-gif-25617057

[obsidian raptor]

yeah

how about cleaning this out

well can you send it again?

so it's easier

[barren halo]

6 minutes, 33.67 seconds

[obsidian raptor]

epic

[barren halo]

i've already solved the problem

.close

[devout snow]

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[barren halo]

so much for help huh

[devout snow]

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[wraith pike]

hi can you help me the equations of this graph?

[devout snow]

@wraith pike Has your question been resolved?

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[light sable]

Is this the right approach?

[wicked turtle]

what are you doing on the second line, did you take the derivative of a(t)?

[light sable]

yea

[wicked turtle]

you need to go the other way

a(t) is the derivative of v(t)

so you need to integrate a(t) to get v(t)

[light sable]

so integrating a(t) that would be the v(t)?

[devout snow]

@light sable Has your question been resolved?

[devout snow]

@light sable Has your question been resolved?

[light sable]

<@&286206848099549185>

[charred zodiac]

yes this is v(t), now use v(0) = 9i+2j to find c

[light sable]

which is by putting 9 into sin and 2 for cos?

[charred zodiac]

mmm no, you just plug t=0

[light sable]

oh

so i got 5

[charred zodiac]

you have v(t) = -5sint i + 5cost j + c

what's v(0) ?

[charred zodiac]

according to this

[light sable]

v(0) = 5 right?

[charred zodiac]

mmm just 5?

don't forget the constant c

[light sable]

5 + C ?

yea

[charred zodiac]

yess

also don't forget the base

i or j

[light sable]

how do i get r(t) then?

[charred zodiac]

wait what did you get for v(0) then

[charred zodiac]

you have to find c first

[light sable]

v(0) = 5 + C

[charred zodiac]

you forgot i and j bases here 🤔

[light sable]

i got that

[charred zodiac]

For example
the integral of 2i is
2t i + c

you should keep the base too

[light sable]

and that would be for the 5 + C or ?

[charred zodiac]

it's an example of how you should keep the bases after an integral

[light sable]

oh ok i understand that

then i would keep i as the base for 5?

[charred zodiac]

here you have
integral of -5cost i
= -5 sint

it should be

-5 sint i

[light sable]

yea i got that part

[charred zodiac]

the same for the other term

ok great

then considering that, what's v(0)

[light sable]

9ti + 2tj + C?

[charred zodiac]

no

Please write again v(t) so we can start from there 🤔

[light sable]

v(t) = -5sin(t)i + 5cos(t)j + C

[charred zodiac]

great. Now according to the problem v(0) = 9i + 2j

so

v(0) = 9i + 2j
-5sin(0)i + 5cos(0)j + C = 9i + 2j

does that make sense?

[light sable]

yea

[charred zodiac]

ok now you can find C

after that, you can find r(t) which is the integral of v(t)

you'll get a constant of integration again, which you can find in the same way because you're given r(0)

[light sable]

ok so i got 16 for C

so then the r(t) = -5sin(t)i + 5cos(t)j + 16?

[charred zodiac]

did you find 16 from this?

[light sable]

yea

[charred zodiac]

here everything has i and j, so C must have i and/or j too

I mean, C is a vector

otherwise the function wouldn't make sense

[light sable]

nvm

i got 6

[charred zodiac]

could you please show your work? So I can suggest how you should operate these equations

[light sable]

yea hold up

Nvm my 6 I wrote the equation wrong

[charred zodiac]

wait why do you write 9i + 2j... for v(0) ? 🤔

[charred zodiac]

you got this for v(t), so v(0)...
v(0) = -5sin(0)i + 5cos(0)j + C

and that must be equal to 9i + 2j because v(0) = 9i + 2j according to the problem, so

-5sin(0)i + 5cos(0)j + C = 9i + 2j

[light sable]

its cuz of this

i see then

[charred zodiac]

oh I see. Well it's on a different line

it was another equation

[light sable]

would it still be 5j though?

from cos(0

5cos(0)j

[charred zodiac]

yes 5cos(0)j = 5j

-5sin(0)i + 5cos(0)j + C = 9i + 2j
solve this eq.

[charred zodiac]

yes, so c = ...

[light sable]

am i able to subtract everything?

do i end up with c = 9i - 3j?

[charred zodiac]

yes that's correct

i and j are like "constants"

so sure you can subtract and add them as usual

Now you have the complete expression for v(t) without an unkown C 'cause you already found it

r(t) is the integral of v(t)

[light sable]

Like that and then I find the integral of it for r(t)?

[charred zodiac]

yes

When you write the answers, you should probably put all the same basis together:
for example: -5sin(t)i + 9i = (-5sint + 9)i

[light sable]

like that?

[charred zodiac]

yess great

now find c

[light sable]

have it = to r(0) right?

[charred zodiac]

yes

[light sable]

is this right?

[restive river]

yes

[light sable]

ty

.close

[devout snow]

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[limpid citrus]

could someone solve this equations in terms of sinx? the video did it in cos but I want to see if mine one is right

[frosty nebula]

I don't believe the first line you've written here is correct

[limpid citrus]

why

oh no thats the teachers one

[frosty nebula]

Oh shoot sorry

[limpid citrus]

i haven't submitted mine because I think i did it wrong

[frosty nebula]

I misread the question.

[limpid citrus]

but I want to see what this would look like if you made sin the main unit you want to convert

[frosty nebula]

I'm thinking through the trig identities and I'm not sure if there is a way to rewrite the right hand side of the equation in terms of sin while getting rid of cos

[limpid citrus]

so only cos?

[frosty nebula]

The solution shown here is the only one I can think of. What is your approach?

[limpid citrus]

hold on

let me take a picture

sorry for taking so long

@frosty nebula

[frosty nebula]

That's valid!

[limpid citrus]

yea but where do I go from this?

[frosty nebula]

Sorry, I thought you were asking if there was a way to rewrite everything in terms of sin

[limpid citrus]

yea thats what I have in mind

[frosty nebula]

Now you can multiply both sides by 1/2 and factor a sinx out from the terms on the left side

So you have sinx(cosx + sinx) = 1

[limpid citrus]

you're genius

I didn't think of that

[olive ledge]

it would be better if u write cos2x as 1-2sin^2 x

[limpid citrus]

I did

[olive ledge]

oh yeah

[limpid citrus]

lol

[frosty nebula]

Unfortunately this is a tricky equation to solve

[limpid citrus]

I see

oh I see... yea it is harder

[limpid citrus]

but thank you for the help

I'll do the rest now

.close

[devout snow]

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[magic tapir]

The answer is B but can someone please help me understand it

also pls tag me if soeone answes

[frosty nebula]

How do we generally find the roots of a quadratic equation?

[magic tapir]

squadratic formula

i subtracted the 2 roots from the squasdratic formula and dquaster to 2

didn't work - was too complex

[frosty nebula]

Exactly!

[frosty nebula]

You're on the right track! If we let $x_1$ and $x_2$ be the solutions to the quadratic equation, and since $|x_1 - x_2| = 2$, we can then find an equation relating $m$ and $n$

[woven radish]

thedude365

[frosty nebula]

What do you mean by "didn't work"?

[magic tapir]

oh waiiit

i did the exact same thing i did yester again now and got the answer

thank you so so much

got the ans now

[frosty nebula]

Of course, I'm happy to help!

[devout snow]

@magic tapir Has your question been resolved?

[magic tapir]

@frosty nebula could you guide me with this ques too , please?

[frosty nebula]

Since we want to see what $f(x)$ outputs when we plug in $3p$, we first need to find out what the constants $a$ and $b$ are

[woven radish]

thedude365

[frosty nebula]

Plugging in the given points, $(p, 4)$ and $(2p, 76)$, gives us two equations with which to solve for $a$ and $b$

[woven radish]

thedude365

[devout snow]

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[magic tapir]

.reopen

[devout snow]

✅

[magic tapir]

I did try this but don’t know how to solve further

[devout snow]

@magic tapir Has your question been resolved?

[magic tapir]

@frosty nebula what do i do next?

I did this and got the answer

you know of any better method?

[devout snow]

@magic tapir Has your question been resolved?

[devout snow]

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[forest lily]

idk how to do this

[pseudo basin]

do you know the binomial theorem?

@forest lily

[forest lily]

yeah

[pseudo basin]

ok then can you write out the coefficients of x^1 and x^2 in (2 + x)^n?

[forest lily]

with (n C 1) and (n C 2) ?

[pseudo basin]

not gonna instruct you either way on that one.

[forest lily]

(n C 1)(2)^n-1 is coefficient for x

then (n C 2)(2)^n-2 for x^2

right

[pseudo basin]

yes

now write down the equation that says one is twice the other

[forest lily]

uh huh

then

[pseudo basin]

write it down

send it here

[pseudo basin]

ok, great.

now solve this for n.

you might want to know that $\binom{n}{1} = n$ and $\binom{n}{2} = \frac{n(n-1)}{2}$

[woven radish]

Ann

[forest lily]

alright

i try

ah ive got it

thank you @pseudo basin 😄

.close

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[mystic rune]

what skew is this

the first graph

[jolly latch]

Skewers is variance difference types

Do u wanna know formula?

@mystic rune

[mystic rune]

no

is it positive skew or sum

is that your feet

nvm

.close

[devout snow]

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[fair osprey]

guys I need help with the 2nd question

for the first one this is what I did

so there are n bins

there is 1/n probability for ball to go to first bin

thus it's complement is 1 - 1/n

so that's my answer for the first

is it wrong?

<@&286206848099549185>

I already posted it

<@&268886789983436800> he is trolling

WTF

<@&268886789983436800> he is racist

[topaz axle]

also not trolling

you have to troll to be on this server

[fair osprey]

WTF

[topaz axle]

i think this is right

[fair osprey]

can you help me with 2?

also why are you guys allowing n-word

[placid rover]

theres a filter on it, but that doesnt mean people cant try bypassing it.

[fair osprey]

oh ok

okay anyways

so in 1

the bin is empty right

and I got the probability for it

I was thinking in 2, I would just do complement trick again and do 1 - my answer in 1

raised to k

what do you guys think?

[devout snow]

@fair osprey Has your question been resolved?

[devout snow]

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[deep kiln]

doing a project which will involve making a continuous approximation via a function and some constants to some discrete data. I will need to compare it to the already existing mathematical models for these discrete points. Is there a way of statistically calculating how "good" of an approximation a curve is to discrete points?

[devout snow]

@deep kiln Has your question been resolved?

[stone stump]

for each point you could calculate the distance to the curve and then sum up all the distances

or if your points are of the form (x,y), then you could take the difference f(x)-y.

usually you would then either square the difference or take abs, then sum

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[tribal peak]

.close

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[uncut blade]

Solve the system to prove that Ox aka x axis equation does not touch any point of the circle equation

[devout snow]

@uncut blade Has your question been resolved?

[uncut blade]

Noooo

HELPPP

NOW

[uncut blade]

What are the 2 values of Coefficient in a C euqation like 3y+4x=C with circle center 2;6 a point of 8;1 and a radius of 5

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[vivid torrent]

The height of the base of a regular triangular prism is 2√3cm. Find the area of ​​the lateral surface of this prism if the diagonal of the lateral face of the prism forms an angle of 30◦ with its lateral edge.​ need help with a solution

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<@&286206848099549185>

[vivid torrent]

<@&286206848099549185>

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[pulsar phoenix]

(This is where I’m at)

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[pulsar phoenix]

ugh

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[devout snow]

@pulsar phoenix Has your question been resolved?

[pulsar phoenix]

<@&286206848099549185>

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[devout snow]

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

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[uneven ledge]

<@&286206848099549185>

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[terse notch]

i need help

[terse notch]

can someone explain to me how to do these two problems?

this is for calculus ab by the way

[long pasture]

what have you tried?

[terse notch]

nothing :( i don’t really know how to do these type of problems

but their the last 2 for the assignment

[long pasture]

oh okay

first one, very typical chain rule problem

[long pasture]

consider g'(x)

what is g'(x)

i bet @terse notch must be sleepy 😛

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[nova basin]

idk how to differentiate this

[nova basin]

like sec = 1/cos and tan = sin/cos

not sure what to do from there

[arctic temple]

you can do product rule

[arctic temple]

this won’t really help, this is sinx/cos^2x

which is again quotient rule

[nova basin]

um

so i do product rule first?

[arctic temple]

yes

you can try first

[nova basin]

i dont think ik how to do this correctly ._.

its u'v + uv' so u'(tan(theta)) + sec(theta)v'

i think

so i need to derive sec(theta) and tan(theta)

[arctic temple]

sure

[nova basin]

how do i do that

[arctic temple]

you haven’t did derivative of secx before?

[nova basin]

um i dont think so

[arctic temple]

secx= 1/cosx right?

$\sec x = (\cos x)^{-1}$

[woven radish]

.doc

[arctic temple]

take the derivative of the right side

Hint:, power rule

[nova basin]

yes

[arctic temple]

try this?

[nova basin]

ohhhhhhhhhhhhhhhh

i love power rule

[arctic temple]

take the derivative of this

great

[nova basin]

so d/dx sec(x) = -1(cos(x))^-2

i think

which = -1/cos^2(x)

also i think

[arctic temple]

are you done?

recall chain rule

[nova basin]

um no

[arctic temple]

do you see cosx is a function sitting inside an outer function

so you should take derivative of the inside

[nova basin]

um

[nova basin]

not particularly

[arctic temple]

I think you should revist chain rule

It’s used to take derivatives when we have a composition of function

which is the case here, we have cosx composed into x^-1

[nova basin]

so inner = cos(x) and outer = x^2-1?

[arctic temple]

Do you know how to compose functions? f(g(x))?

[nova basin]

uh no

what does compose mean

[arctic temple]

$f(x)= x^{-1}, g(x)= \cos x$ thus $f(g(x))= (\cos x)^{-1}$

[woven radish]

.doc

[nova basin]

oh

yes that thing

[arctic temple]

the output of a function becomes input of another

[nova basin]

so what do i do with that

f(x) = x^-2
g(x) = -cos(x)

ohhhhhhhhhhh

do i do product rule

if we have f(x) and g(x) we can find derivatives

i think

f'(x) = -1x^-2
idk what to do with g(x)

idk im lost

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[mild yoke]

so thats what i did so far

i just need

to compare my function m(n)

to another one

and show why its better due to a contradiction

but i cant think of one

log2n - 1 gives contradictions in the base cases and such

so i dont think its a good example

<@&286206848099549185>

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[ashen carbon]

Yoonie is a personnel manager in a large corporation. Each
month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately
four hours each to do with a population standard deviation of 1.2 hours. Let Χ be the random variable representing the time
it takes her to complete one review. Assume Χ is normally distributed. Let X
¯
be the random variable representing the mean
time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.

[ashen carbon]

what's the mean, standard deviation, and sample size

Complete the distributions.
a. X ~ (,)
b. X
¯
~ (,)

also what is this even mean

[livid geyser]

Sample size is..... number of samples (usually denoted by $n$

[woven radish]

992qqoloy

[livid geyser]

SampleMean is $\frac{\sum X}{n}$

[woven radish]

992qqoloy

[livid geyser]

Sample Variance is $\frac{\sum X^2 - \frac{\left(\sum X\right)}{N}} {N - 1}$

[woven radish]

992qqoloy

[livid geyser]

And sample standard deviation is the square root of that

I assume you wanted the sample ones since it asks for sample size

The true mean and stsnadard deviation are the expected value and square root of variance

[devout snow]

@ashen carbon Has your question been resolved?

[ashen carbon]

oh ok

how do i complete the distributions?

[livid geyser]

Can u show the full problem

Maybe it says something like "complete the distribution table"?

[ashen carbon]

that is the full problem

Yoonie is a personnel manager in a large corporation. Each
month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately
four hours each to do with a population standard deviation of 1.2 hours. Let Χ be the random variable representing the time
it takes her to complete one review. Assume Χ is normally distributed. Let X
¯
be the random variable representing the mean
time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.

Complete the distributions.
a. X ~ (,)
b. X
¯
~ (,)

[devout snow]

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[ashen carbon]

.close

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[woven citrus]

Can someone help me understand this matrix

I have no idea where to start

[main gull]

If it was (x + (a))(b) = c, what should you do?

[woven citrus]

(x+a)(b)=c?

And (bx+ab) = c?

[main gull]

No you don't need to distribute

You are solving for x

[woven citrus]

Then my first step is to?

[main gull]

(x + (a))(b) = c
The b is multiplied with (x + a) so what should you do?

[woven citrus]

bx + ab?

[main gull]

.

Why are you distributing

[woven citrus]

x+ab?

[main gull]

No

As a different example, if you have 2x = 6, what should you do to find x?

[woven citrus]

Divie3

Divide

X=3

[restive river]

is division defined for matrices ?

[main gull]

Yes

(x + (a))(b) = c
Same logic is applied to this

[woven citrus]

But its (x+a)b = c

[main gull]

Yes and it's no different

You can treat x + a as one term

[woven citrus]

x=c/ab ?

[main gull]

No

Where did ab come from?

[woven citrus]

a*b= ab

[main gull]

No

Stop distributing that b

[woven citrus]

b=c/x+a?

[main gull]

No

What if I gave you something like (x + 4) * 5 = 20?

And used actual numbers

[woven citrus]

X+4 = 20/5

[main gull]

Yes

[woven citrus]

X+a = c/b

[main gull]

Yes

But in a matrix case, you apply the inverse

[main gull]

This is just a standard, non matrix example, where the first step is to divide by d

[woven citrus]

So like this?

[main gull]

For your problem, instead of dividing by b, you apply the inverse

Do you know how to find inverses?

[woven citrus]

yes

i think so

[main gull]

So you want to multiply both sides by the inverse of B

[main gull]

That's not the B matrix

[woven citrus]

Inverse of B is -4 right

[main gull]

No

[restive river]

the inverse should be a matrix with the same dimension

[main gull]

It's suppose to be a matrix

[main gull]

Where did -4 come from?

[woven citrus]

13 * 3-5 * 8 =[B]

[main gull]

Recall that the original problem is (x + (a))(b) = c

[restive river]

i think it is the determinant

[main gull]

No

It's still not -4

[woven citrus]

Yes

How do u find inversion

[main gull]

You can apply this shortcut

[woven citrus]

B matrix is (13,8 5,3) right

[main gull]

Yes

[woven citrus]

So i need to inverse B matrix?

[main gull]

But use a semicolon to separate rows

[main gull]

Yes

(13,8; 5,3)

[woven citrus]

1/-4(3,-8; -5,13)

[main gull]

You're missing one more step

[woven citrus]

?

[main gull]

.

Do you see how you have to multiply by 1/(ad-bc)?

[woven citrus]

I have to multiple by 1/-4 right

@main gull

[main gull]

Find the det of B again

[woven citrus]

OHH

1/-1

So its

(-3 8 5 -13)

[main gull]

Yes that's the inverse of B

[woven citrus]

Okay

[main gull]

So you multiply by the inverse on both sides

So you will end up with (x + a) = c * b^-1
Where b^-1 is the inverse of b

[woven citrus]

Yeah

[main gull]

Can you find what c * b^-1 is?

[main gull]

Do you know how to multiply matrices?

[woven citrus]

Yrs

Yes

[main gull]

Then can you explain how you got that result?

[woven citrus]

Did i multiply wrong

(2 * -3, 1 * 5; 3 * 8, 2 * -13)

Right?

[main gull]

Nope

You go across the row of the first matrix, and down the column of the next

[woven citrus]

Oh

So

So from this we found cb-1

[main gull]

So you have (x + a) = c * b^-1

What should you do with a?

[woven citrus]

X= cb^-1 - a

[main gull]

Yep, you subtract a on both sides

[woven citrus]

Both?

On the other side right

And we find the x right

@main gull

[main gull]

Yes

[woven citrus]

Okay thank u

.close

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[weary kestrel]

how can i approach this problem

[devout snow]

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[weary kestrel]

<@&286206848099549185>

[dense barn]

what

[weary kestrel]

oh so sorry I thought i could ping the helpers

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[brisk raft]

Why is my formula for simpson's rule approximation incorrect?

l=delta x or (b-a)/n

[devout snow]

@brisk raft Has your question been resolved?

[supple knot]

It's an approximation

[brisk raft]

The approximation is too off

It should be much closer

[supple knot]

Then you're entering it wrong

[brisk raft]

I know. I want to know why it's wrong

[supple knot]

Show the formula you're following

[brisk raft]

I based my summation on this

I took the two endpoints out and then incremented the 4 2 pattern

At least, that's what I was trying to do

[supple knot]

These x_k alternate 4,2,4,2, yours are always odd

Try changing 2k-1 to 2k on one of them

[brisk raft]

Oh I see

I forgot to remove that part when I pasted it in for x

Thanks

.close

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[dry loom]

Hello can somebody explain to me when I should use permutations, variations and combinations? I generally know what they do but I do not know when to use them in a problem. Last year I variantions instead of permutations or something and the problem went to hell

[wheat pebble]

@dry loom stay put imma help you out

[dry loom]

Ok

[restive river]

you have 4 fundamental questions you want to answer

how many options for chosing:
1.with order without repetition
2.with order with repetition
3.without order without rep
4without order with rep

most commonly you will use 3

[wheat pebble]

https://youtu.be/KbB0FjPg0mw?si=VxU7Zhxh_Bbkgvt6

[dry loom]

I don't think we have ever used repetitions

[restive river]

which's answer is n choose k

[wheat pebble]

@dry loom minute 34:25

[dry loom]

I will see it thank you

[wheat pebble]

the YouTube video i sent is precisely what hadarS mentioned

[dry loom]

I am in 11th grade just starting and we are doing and exam with all the stuff we did last year so I need to revise this

[wheat pebble]

there are 4 scenarios and depending on what you want to find you pick one out of those

[restive river]

good so the only things relevant are permutations and sets

[restive river]

yea im also doing college and high school combined

im 11th grader also

[dry loom]

Nah, there are all 3 types

I understand permutations and combinations but variations I don't see what they are used for

[restive river]

also multisets and sets in order with repetition?

[dry loom]

I have never seen these words bro tbh I do not know what they mean they don't teach in english here

Multiset

For example

[restive river]

i guess the words are variations and tuples

i see on wikipedia the words in english

[dry loom]

.close

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[distant lion]

need help with this

[distant lion]

dont understand how to balance this

[pseudo basin]

x : 6 + 1[???] = z + 2[???]

what are these symbols meant to be

[distant lion]

the one shaped U is "MU"

the other i bhelive is landa the symbols do matter as much but dont geet what i have to do to make them balance

x : 6 + -1[Lambda] = 2 + 2[MU]

i need to do something to balance the Lambda for x and y if both numbers where positive i could times but becausse its negitive im stuck

@astral elk

[woven radish]

riemann

riemann

[supple knot]

are those your two equations

[distant lion]

not exactly

[distant lion]

this should be 10+-2?

[distant lion]

yes but for the second one shouldnt it be 10+-2Lanbda?

[supple knot]

$10 \pm 2 \lambda = 0 + 2\mu$

[woven radish]

riemann

[distant lion]

yes that looks correct so how would i cross the two exuations balance them out to get value of lambda and mu?

@astral elk

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@distant lion Has your question been resolved?

[distant lion]

@astral elk

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[worldly vale]

how do i find the slope of the tangent line?

[worldly vale]

they dont give me a point to use or an equation

[devout snow]

@worldly vale Has your question been resolved?

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[slim token]

How can you tell what the period of a sinusoidal graph is? I'm having trouble recognizing when a graph is one third or one half of its period?

[slim token]

Like this graph for example

I can't tell if the graph is 1/3 of it or 1/2 of it or 1/4 of it

So it would be appreciated if I could get a tip or trick on this^

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<@&286206848099549185>

time to go to bed

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[twin grove]

Linear Algebra Question:
If I say that the last column, B, is just all 0s, would it be in span {v1, v2, v3} ?

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[mental carbon]

How's it possible for a solution to satisfy both conditions

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@mental carbon Has your question been resolved?

[terse shale]

@mental carbon what can x be if {x, 20} is a subset of {2, 7, 20}?

[mental carbon]

Well its not directly stated

So its impossible

[terse shale]

so, if {x, 20} is a subset of {2, 7, 20}, that means that all the members of {x, 20} are also members of {2, 7, 20}

so that tells us x is 2, 7, or 20

which one of those also lets us have {x, y} a subset of {2, 11}?

probably the question also is assuming that they're not listing repeat elements so in that case we'd have x is 2 or 7

[terse shale]

I think in your diagram you're saying that y = 20 since you're accustomed to thinking of ordered pairs (x, y) right

[mental carbon]

So 2,2 doesnt workc

[mental carbon]

Ya

[terse shale]

so these are not ordered pairs, but just sets of numbers

[mental carbon]

Yes

[terse shale]

so {x, 20} being a subset of {2, 7, 20} places no restrictions on y

since the variable y doesn't show up in there at all

[mental carbon]

Y is given to be 20 in this example

[terse shale]

it is not

[mental carbon]

The question is really odd

[terse shale]

{x, 20} is the set containing the numbers x and 20

y is another variable unrelated to these

it would probably be easier if they used variables like m, n because then you wouldn't be thinking of ordered pairs

[mental carbon]

Ohhhhhh so x = 2 and y = 11

[terse shale]

yep that'd work

[mental carbon]

Hahaha i get it now

[terse shale]

easy mistake to make!

[mental carbon]

The question restriction is quite odd and unlike others tho

Ty griff

[terse shale]

np

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[signal drift]

Hello,

Y is the midpoint of XZ. Find XY if ZY = 3x - 13 and XZ = 4x + 7

could someone explain to me how to find X? I have the line drawn out just stuck on finding X

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@signal drift Has your question been resolved?

[eager lodge]

notice that XY+YZ=XZ

[signal drift]

mhm

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[worn harbor]

Hello

[worn harbor]

I got a formular to calclulate the Multiplicative digital root

How would i be able to make ist a function?

[pseudo basin]

wdym by "make it a function"?

[stone stump]

the image describes a function

a function doesnt have to be something you can just write down like f(x)=2x

that said, you could just write down $$F_b(n) = \prod_{i=0}^{k-1} \frac{n \bmod b^{i+1} - n\bmod b^i}{b^i}$$

[woven radish]

Denascite

[worn harbor]

Ok thanks

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[rugged jewel]

A vector $\vec{v}$ is perpendicular to $\vec{a}=(2,3,-1)$ and to $\vec{b}=(1,-2,3)$. Also, $\vec{v} ( 2*\vec{e{x}} - \vec{e{y}} + \vec{e_{z}} ) = -6 $
Determine $\vec{v}$

[rugged jewel]

so I know a X b is perpendicular to V

But how do I continue?

[jaunty mantle]

Use () for vectors

{} is for sets

And if you want to use { or } you need to add a \ before them in latex

[rugged jewel]

Yeah my latex isnt the best yet 😅

[eager lodge]

first find any vector c that's perpendicular to a and b

[jaunty mantle]

I said, use ()

{} is usually for sets which are unordered

Vectors are ordered

[eager lodge]

then we know v=tc

[rugged jewel]

Aaaaaaaaaah

wait

[jaunty mantle]

You don’t need \ before brackets

[woven radish]

rainy

[jaunty mantle]

What is vec{e{x}}

[rugged jewel]

So cross product of a and b?

[eager lodge]

yeah

[eager lodge]

I think they mean the basis vectors for x y z axis

[rugged jewel]

Yes

[jaunty mantle]

I’d suggest subscript but it’s up to you

[jaunty mantle]

I also see multiplication of vectors on the last row

That’s not defined

Used \cdot for dot product

[rugged jewel]

Okay, so that vector is (7,-7,-7)

Whats the next step?

[eager lodge]

v=t(7,-7,-7)

we just need to solve (t(7,-7,-7)) dot (2,-1,1) = -6

[rugged jewel]

Wait I dont get it

Where does 2, -1, 1 come from

Its v.(2ex - ey + ez)

Not v(2ex, -ey, +ez)

Or doesnt that matter>

[eager lodge]

?

[rugged jewel]

This is what i tried to do in latex

I dont get how you got (2,-1,1)

[eager lodge]

aren't they basis vectors

so e_x = (1,0,0) e_y = (0,1,0) e_z = (0,0,1)?

[rugged jewel]

yes

So isnt it then v dot (2 - 1 + 1)

--> v dot (2)

[eager lodge]

what

[rugged jewel]

💀

[eager lodge]

how do the basis vector turn into scalars

????

[eager lodge]

this should be my reaction

[rugged jewel]

Wait

I think i get it

hold up

[eager lodge]

writing the basis vectors is just another way to notate vectors

$(a,b,c)=a\vec{e_x}+b\vec{e_y}+c\vec{e_z}$

[woven radish]

WhereWolf(ping if needed)

[rugged jewel]

You want me to do this

right

[eager lodge]

forgot the t

[rugged jewel]

yeah

[eager lodge]

should be easy to solve

[rugged jewel]

lets see

Now just distribute the t {...} over the 3 vectors?

Got -3 3 3

which apperantly is correct

[eager lodge]

-3 3 3?

[rugged jewel]

Yes

[eager lodge]

what have you done

[rugged jewel]

Long story short

You saying i needed a 't' really helped me

Thanks

Now still gotta work on my latex

🫡

.close

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[restive river]

Need with epsilon-delta limit proof

[restive river]

Ive gotten to this point however Im now stuck

I need it to be the other way around

[fair gazelle]

Wht do u exactly wanna prove?

I din get the question

[restive river]

Im supposed to prove the limit

by appealing to the definition of a limit

Im trying to find a delta in terms of epsilon

[long pasture]

try another delta, e.g. 0.5

[restive river]

ah right I see

I tried 2 and ran into same problem

didnt think to go smaller

@long pasture thanm you that worked

.close

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[solemn carbon]

What method to solve this?