help-19

[steel notch]

hmmm

but isnt this more complicated

[crisp wadi]

More complicated than what?

[steel notch]

thant the previous one

how can i find the radius from this

[crisp wadi]

What's the previous one

[steel notch]

the one i sent

the original one

[crisp wadi]

What condition on a geometric series makes it converge?

[steel notch]

i only know 2 ways to find the radius root test and an+1 / an

limit as n goes to inf for both

[crisp wadi]

.

[steel notch]

i am not sure

[crisp wadi]

$\sum_{n=0}^\infty r^n$ converges if and only if $\abs{r} < 1$

[clever fjord]

孤独な豆

[steel notch]

oh ok

it converges to 1/1-r

[crisp wadi]

So you would want $\abs{e^{x^2 - 4}} < 1$ for this to converge

[steel notch]

yes i remember

[clever fjord]

孤独な豆

[crisp wadi]

But $e^anything$ is positive anyway so you just need to solve $e^{x^2 - 4} < 1$

[clever fjord]

孤独な豆

[steel notch]

makes sense

can i keep this cahnnel open for a few more minutes

as i test the 2 limits

-2 and 2

for convergence

[crisp wadi]

Surely

[steel notch]

does it mean that i doesn't converge for x=-2,2

since they lead to 1^n

[crisp wadi]

Yeah

[steel notch]

so the interval of convergence is (-2,2)

[crisp wadi]

Yes

[steel notch]

thank you very much for your help

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[deep turret]

$$\text{Suppose that } f(0) = -3 \text{ text and } f'(x) \le 5 \forall x \text{. }$$ $$ \text{How large could f(2) possibly be?}$$

[stark elbow]

Do you mean f'(x) <= 5?

[deep turret]

yea

[clever fjord]

Nerdy_Coder

[tame tulip]

guys what is 0/0 value

[stark elbow]

#❓how-to-get-help

[deep turret]

Infinity

[stark elbow]

That is also false

[formal oriole]

Does not exist

[frigid canopy]

what do you think?

[somber zealot]

what the fuck typa questions u be doing

whys the A reversed

ciggerettes+math>>>

[frigid canopy]

That's a symbol that means "for all"

[deep turret]

$$\text{Suppose that } f(0) = -3 \text{ text and } f'(x) \le 5 \hspace{1cm}\forall \hspace{1cm}x \text{. }$$ $$ \text{How large could f(2) possibly be?}$$

[clever fjord]

Nerdy_Coder

[somber zealot]

oh shet

[deep turret]

oh nooo

NOOO ahh

just wanted 1 space

Well that's the problem

It's ripped right from my Calulus textbook

Then james stewart one

Hopefully copying word for word via text rather than images is more sympathetic in the courts....

[frigid canopy]

pretty sure you'd be safe under fair use laws

anyway, what do you think the answer is

[deep turret]

The book gave me the answer but I don't understand the solution

[deep turret]

Would I be safe if I took a partial screenshot?

[frigid canopy]

spoliers || the function must increase as fast as possible for the function to be maximised use that ||

[frigid canopy]

no idea

[deep turret]

Maximized? I'm only given 2 values

[frigid canopy]

That's enough, the derivative must be 5 everywhere on this interval

for the value of f(2) to be as largeas it can be given the constraints

[quiet wing]

Uh, can't we apply lagrange's mean value theorem on the open interval 0,2.

[deep turret]

That was the point actually

[quiet wing]

That will give an upper bound.

[deep turret]

Idk why that works though

[dapper canyon]

just integrate both sides

[quiet wing]

I actually never thought about such problems this way.

Very interesting.

[deep turret]

I'm confused idk how to integrate this...and the mean value theorem seems to lead toa. dead end.

f(2) isn't given

[frigid canopy]

Yes, so asume a linear function joining 0 and 2

as the derivative is less than or equal to 5

for the function to be as large as possible at 2, the derivative must be 5 everywhere

[deep turret]

We have no slope

[frigid canopy]

we do

we have been given f'(x)'s maximum value

[deep turret]

oh

[frigid canopy]

can you do it now?

[deep turret]

Trying

Same answer as the book 7

Wow...wonder why this works?

Ahh it does a similar thing but uses the mean value theorem.

[frigid canopy]

it does? TIL

[deep turret]

So it's about the fact that maximizing allows us to assume f'(x) is 5?

[frigid canopy]

essentially , yes

[deep turret]

I assume minizing does the same thing?

but in reverse?

[frigid canopy]

there is no minima given the constraints , but if you were given f'(x)>=5 , yes, it would

[deep turret]

Thanks

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[jovial coral]

can somebody explain how they got a 1/25 as a common factor?

[cursive field]

just factorized it out

[cursive field]

hang on why am i the owner of this channel?

anyway 1/25 times 5x = x/5

so yep

that answers it @jovial coral ?

[jovial coral]

i do not see it..

[cursive field]

...

wdym

it's just distributive

the first one is just x/5 so that turns into 5x times 1/25
the second is -1 times 1/25 so that stays

[jovial coral]

how did the x even get a 5 ??

[cursive field]

wh?

what-?

$x\frac{e^{5x}}{5}-\frac{e^{5x}}{25}+C$ turns into $5x\frac{e^{5x}}{25}-\frac{e^{5x}}{25}+C$ since it's 5x/25 in this case

[clever fjord]

ren

[cursive field]

then that turns into, factorizing, $\frac{e^{5x}}{25}\left(5x-1\right)+C$

[clever fjord]

ren

[cursive field]

@jovial coral got it?

or ru trolling

[jovial coral]

OHH Equality of denominators?

[cursive field]

yes-

[jovial coral]

seriously you arent forced to help.

[cursive field]

!vol

[odd edge]

Helpers are just people volunteering their time to help you. Be polite and patient.

[cursive field]

i've seen 3 trolls in the past 2 days

so yea

sorry if that offended you

[jovial coral]

but should we really do the Equality of denominators before factoring?

[cursive field]

i mean yes

simplifies it

why not give it a shot

[jovial coral]

but when i factored it without the Equality of denominators , wasn't semplified enough?

[cursive field]

well it was pretty untidy

[jovial coral]

:0

[cursive field]

with the 0.2 on the outside AND inside

[cursive field]

lol

in calculus you tend to mix stuff up

it's good to keep constants outside

that's it?

done?

[jovial coral]

i see, thank you for taking your time to help me out :>

ye

[cursive field]

okay

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[finite pivot]

Could someone please help me with parts b, c, and d?

[odd edge]

@finite pivot Has your question been resolved?

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[wintry jetty]

There’s too many words for my brain to process this, can anyone tell me what the answers are?

[cursive field]

!noans

[odd edge]

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

@wintry jetty Has your question been resolved?

[wintry jetty]

i worded it terribly oops can someone help me find out the answers

[odd edge]

@wintry jetty Has your question been resolved?

[wintry jetty]

can i please get some help

[odd edge]

@wintry jetty Has your question been resolved?

[wintry jetty]

i really need help

[odd edge]

@wintry jetty Has your question been resolved?

[wintry jetty]

NO

can someone please help omg

it’s due soon

[odd edge]

@wintry jetty Has your question been resolved?

[shell solstice]

What words are you finding difficult to understand?

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[lethal willow]

for (a) tryna prove by contradiction, assuming x0 is a natural, if n<= x0, then x0 is the lub of naturals

idk what to do bruh fr

[odd edge]

@lethal willow Has your question been resolved?

[lethal willow]

i feel like it has to do something with adding 1 to both sides but i cant put it into words

<@&286206848099549185>

like if another natural is x0 + 1

idk

[upper onyx]

if x0 is a natual number, then x0+1 would also be. but what property has x0?

[lethal willow]

that its the least ubber bound?

[upper onyx]

yes, so you have your contradiction.

[lethal willow]

ohhh

my brain is not functioning frfr

tysm

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[solar burrow]

|A||B|sin(theta) = |AxB|
|B|sin(theta) = |AxB|/|A|
how can i manipulate this to get to the formula
|AxB/|A||```

[brittle beacon]

|A| is just a scalar

[solar burrow]

ok so the magnitude of v in the following example can stay outside of the other magniute

not sure why it's written like this, with the abs value encompassing everything

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[subtle heron]

hi, i just completed my complex analysis course and i have a bit confusion in my head. my main question is on what differential ueqations is good to use fourier transform and on which laplace transform. I know, that for differential equations with initial conditions, you should rather use laplace, but thats pretty much all i know. thank you

[mystic saffron]

initial conditions: Laplace
boundary conditions: Fourier

i guess thats the most clear cut way

[subtle heron]

that kinda makes sense, i see why we used laplace mostly on like systems and fourier for waves, thank you

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[burnt gazelle]

$2.$ Let $hk \in HK$, then since the set of distinct left cosets form a partition of $G$ and $hk \in G$, so it must be that $hk \in h_i(H\cap K)$ for some $i=1,..,r$. Finally since $h_i(H\cap K) \subseteq h_iK$ so $hk \in h_i K$ as desired.

[clever fjord]

Iusgnol

[burnt gazelle]

Could anyone check my proof? Did i miss anything, I feel like the suggested proof in the picture is abit indirect so im wondering if I made an error in mine

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[burnt gazelle]

.reopen

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✅

[burnt gazelle]

okay nvm

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[short oasis]

Does anyone know why
$$
(g^T g)^2\leq g^T Bgg^T B^{-1}g \\
B\text{ symmetric & positive definite}, g\text{ is the downward gradient vector of some function}
$$
I tried to write it out as a sum, using the symmetric eigenvalue decomposition with all eigenvalues positive, and I tried a simple example with g being ones(5, 1) and B being diagonal of 1:5, and I see that if one term is larger, the other will be smaller, but both together will make the right hand side larger.

[clever fjord]

Memiya#9800
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[short oasis]

I can't get line breaks to work...

[odd edge]

@short oasis Has your question been resolved?

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@short oasis Has your question been resolved?

[clever fjord]

spq_64_t

[torpid shore]

Hope that's right

I'm not sure why it would matter if g is a downward gradient of something or not

[odd edge]

@short oasis Has your question been resolved?

[odd edge]

@short oasis Has your question been resolved?

[short oasis]

that looks right to me, thanks! I think I was missing the step to reduce it to a unit vector, which would let me easily compare left and right hand sides.
The gradient thing is because it's from Nocedal's numerical optimisation book.
My linear algebra is unfortunately kinda crap, so easy things like these elude me.

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[mystic saffron]

Areas and Perimeters of Circle, Regular and Irregular Shapes.

[mystic saffron]

the equation how to do them

[hollow meadow]

Area of Circle : pir^2

Perimeter: 2pir

[mystic saffron]

and if its a half circle i just divide it by two?

[south pecan]

Yes, as you see the concept of area is very intuitive.

[mystic saffron]

ok thanks for your time!

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[lavish laurel]

how can a confidence interval be from a larger number to a smaller one?

[green elm]

can you show an example of what you mean?

[lavish laurel]

this problem here, the values for the chisquare (0.975, with 40 degrees of freedom)

is 24.43

https://www.danielsoper.com/statcalc/calculator.aspx?id=12

why did they flip it ?

<@&286206848099549185>

[runic swift]

is it a left tail or right tailed test

[lavish laurel]

ugh

damnit

its a Right tailed

wait

so L tail for X^2(0.975) and R tail for X^2(0.025)?

I got it, thanks @runic swift

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[lavish laurel]

.reopen

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✅

[lavish laurel]

same problem

unless the image of the chi square distribution is wrong

<@&286206848099549185>

[runic swift]

i think i got it

they're both left tailed

[lavish laurel]

hmm

so the solutions manual is wrong?

[runic swift]

¯_(ツ)_/¯

[lavish laurel]

looks like it to me

its just confusing bc of this:

[runic swift]

i think you have to calculate chi(0.975) and chi(0.025) seperately

[lavish laurel]

but theta is in the denominator

and we are looking for it wrt theta

so everything should be backwards ?

[runic swift]

damn sorry i dont think i know anything about that

[lavish laurel]

eh you tried

<@&286206848099549185>

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[devout silo]

what is it that you are having trouble with?

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@lavish laurel Has your question been resolved?

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[magic quail]

help pls

[magic quail]

this is my work so far

question

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[mystic saffron]

how would i solve for BC? is it a centroid?
since BT is 12 then is BC 18?
or is it not a centroid

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[bold saddle]

the way my teacher "explained it" worked until the last question, tutiorals arent helping either

pls help!

[honest quest]

Basically take any trig function e.g. sine. You want find the value of theta such that sin(theta) = |sin(-11pi/3)|

Where theta is an acute angle

[hot dome]

I like to start by adding multiples of 2pi

[bold saddle]

it would be 5pi/3 you would think right?

[honest quest]

If you add 2pi once then -5pi/3

[hot dome]

Add twice lol

[bold saddle]

says its incorrect

[hot dome]

-11pi/3 + 4pi

[bold saddle]

how did you get 4pi?

[hot dome]

$\sin\theta=\sin(\theta+2\pi n)$

[clever fjord]

Miyagi

[hot dome]

So you just add an appropriate multiple of 2pi which happens to be 4pi

Because you're getting the value above 0 and below pi/2

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[bold saddle]

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[desert marlin]

Why does this go to 3/e?

[signal carbon]

if you write n/(n+1) as 1/(1 + 1/n)

then raising that to the n gives you 1/(1+1/n)^n

[desert marlin]

which is 1/e? and a constant 3

[signal carbon]

taking the limit to infinity is one of those definitions of e

[desert marlin]

Ty, long time no see

I was just missing the n/(n+1) = 1/(1+1/n))

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[mystic saffron]

guys, is the part ii of this question really this simple?

[mystic saffron]

Is there something I'm missing?

[low locust]

(could be even easier with difference of squares)

[mystic saffron]

Yeah I wrote the thing out

I coulve just skipped the second line

[low locust]

yeah just wasnt sure if you noticed that this is what is going

[mystic saffron]

But I know that these two functions are representations of some trig functions

thought maybe there's something extra to it which makes it not as straightforward

[low locust]

sinh and cosh

no it really is that simple

[mystic saffron]

ok cool

@low locust also can you maybe explain to me this other question?

I'm unfamiliar with the content its refering to

[low locust]

you mean binomial coefficients?

[mystic saffron]

no

this one

[low locust]

taylor series?

[mystic saffron]

that

I have a rough idea as to what taylor series are

[low locust]

sadly I actually have to go. sorry

[mystic saffron]

ok thanks eitherways

[boreal crag]

Do you know the power series' for e^x and for 1/(1-x)

[odd edge]

@mystic saffron Has your question been resolved?

[mystic saffron]

hey

sorry I'm back

[mystic saffron]

no i don't

[boreal crag]

Well then you are probably in over your head with this problem

[mystic saffron]

so I gotta combine the taylor series of the numerator and the denominator?

[mystic saffron]

100%

[boreal crag]

Well the Taylor series for 1/denom

which is just the geometric series formula

1/(1-r)

[odd edge]

@mystic saffron Has your question been resolved?

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[silk ibex]

differentiate, is this 9x^2-4x-3

[runic swift]

yes

[crisp wadi]

The derivative of that is 9x^2 - 4x - 3, yes

[silk ibex]

ok thanks!

was just making sure i got it right 😄

.close

[odd edge]

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[cursive field]

use partial fractions, i think

[odd edge]

@shut turtle Has your question been resolved?

[shut turtle]

yeah i did

[cursive field]

okay

hang on

im solving myself

[shut turtle]

i got a=b=1/2

[cursive field]

wait wait wait

solving

hang on

yep same

[shut turtle]

what happens next

[cursive field]

...

so we know

that we can split that integral

hang on, imma use latex

[shut turtle]

yeah

[cursive field]

$\int_{ }^{ }\frac{1}{z\left(2-z\right)}dz=0.5\int_{ }^{ }\frac{dz}{2-z}+0.5\int_{ }^{ }\frac{1}{z}$

[clever fjord]

ren

[cursive field]

i think that should work

yep

[shut turtle]

yeah

[cursive field]

okay

so just solve

[shut turtle]

but i need to apply cauchy?

[cursive field]

??

[shut turtle]

I need to apply Cauchy integral formula?

[cursive field]

no...?

idk what that is

but you definitely dont use that

[shut turtle]

I have to use it now

[cursive field]

no u dont

its just ln

[shut turtle]

No bro this is complex analytics

[fluid tundra]

yes use residue theorem lmao

no partial fractions please

[shut turtle]

Can’t I use Cauchy?

[fluid tundra]

but it is not defined at z = 0

[shut turtle]

Indeed

[fluid tundra]

and z = 0 is inside |z| = 1

[shut turtle]

Yeah

But z=2 is outside

[fluid tundra]

right but this automatically means cauchy does not apply

[shut turtle]

Are you sure?

[fluid tundra]

are we talking about the same cauchy?

i am referring to "Cauchy's Integral Theorem" for complex analysis

[shut turtle]

Yeah me too

Here is the answer

[shut turtle]

They applied Cauchy bro

[fluid tundra]

that's

not

ok so we were talking about a different cauchy

[odd edge]

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[fluid tundra]

ok so this is different from "Cauchy's Residue Theorem"

[odd edge]

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[compact owl]

How do i simplify this?

[cursive field]

distribute the two

and write both one and cotangent in terms of sine and cosine

$2\left(\frac{\cos^{2}x}{\sin^{2}x}+\frac{\sin^{2}x}{\sin^{2}x}\right)$

hang on-

[clever fjord]

ren

[cursive field]

@compact owl

[compact owl]

what does distribute the 2 mean?

[cursive field]

...

distributive property

like take it common basically

[compact owl]

ohhhhh wait i think i get it

[west merlin]

factor out the 2

[fluid tundra]

they mean factor

not distribute

[cursive field]

yes sorry

my mistake

@compact owl done?

[compact owl]

why would we do sin2x/sin2x and not 1

[cursive field]

like solved it?

[cursive field]

helps to simplify

can we add the fractions?

[compact owl]

i got it but like i dont think id be able to come up with that in a test or something

[cursive field]

well

you just gotta... see it

in my opinion maths is about thinking creatively

but not much i can do im afraid

[compact owl]

Okay wait

so we first factor out the 2 so that it becomes 2(cot2x+1)

[west merlin]

whenever you want to add 1 to a fraction, like (a/b)+1, then you just turn 1 into b/b

then you get (a+b)/b

and boom. simplified

[compact owl]

ohhh okookko

[cursive field]

yep

[compact owl]

then we do 2(1/tan2x +sin2x/sin2x)

then 2(cos2x/sin2x +sin2x/sin2x)

[west merlin]

yessir

[compact owl]

then we add cos2x+sin2x=1
over sin2x so that it becomes 2(1/sin2x)

[west merlin]

yess

and finally...

1/sin2x is what

[compact owl]

which is then 2cosec2x

[west merlin]

perfect

[compact owl]

ohhhhh okayyy

[west merlin]

2(cosecx)^2

[compact owl]

thank youuu

[west merlin]

cosec2x makes it look like its cosec(2x)

[compact owl]

I was never gonna figure that alone 💀

[west merlin]

but we know what you've been meaning

well now you know for next time

[cursive field]

btw

@compact owl

we usually write it as csc^2 x

[compact owl]

i dont oftenly type up math questions on computer 😭

[cursive field]

is fine

btw

!done

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[cursive field]

@compact owl

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[odd edge]

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[desert dome]

Does ajyone know how to do thsi

[frigid canopy]

!status

[odd edge]

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

[mystic saffron]

do yk the domain of the sqrt(x) function normally

[desert dome]

No

[mystic saffron]

ok this is going to be a bit difficult to explain then

i can link you some resources on this first lmao

[odd edge]

@desert dome Has your question been resolved?

[odd edge]

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[mystic saffron]

May I please have help?

[cold urchin]

You may.

[mystic saffron]

Thank you!

So I'm doing a graphing project

And I have to make up questions for a provided situation

That part is already done

The situation was given by my instructor

I came up with the questions as part of the assignment

BUT

We have certain requirements that I'm not sure how to meet

We have the context and the story

But I don't know how to make equations out of these questions and proceed to graph them

And every question needs an equation and a graph, I think

Wait

Unless it only needs an equation for the situation

I'm not sure, I'm so confused and my instructor isn't here today to help me

😭

And I'm required to graph it in the desmos calculator

online

[odd edge]

@mystic saffron Has your question been resolved?

[thorn palm]

You can solve, but cannot visualize it?

or do you also need help in solving them?

[mystic saffron]

Both

Please

I'm so confused, I feel so stupid because I've done this before but it's so hard to grasp the concept

<@&286206848099549185>

[thorn palm]

I personally want to ask what does 4th question means

probabilities in every hour?

[mystic saffron]

The one the instructor assigned?

Oh

[mystic saffron]

In one hour

[thorn palm]

for initial vampire to bite?

[mystic saffron]

Yes

In the first hour, what is the probability of a female getting bit if there are 30 females and 50 males that the Vampire can choose from?

[thorn palm]

ah ok

idk if it is possible to "graph" that question though

[mystic saffron]

Oh

[thorn palm]

Having problem with all 4 question?

[mystic saffron]

I'm not sure

My teacher wasn't very specific

I'm sorry

[thorn palm]

So not sure about where you got stuck?

[mystic saffron]

I've been stuck

All I have are the questions we had to make

We had to make four questions, and I made them all

I just don't know where to go from here

[thorn palm]

you need to solve them right?

[mystic saffron]

yes

and create an equation for them

and put that equation in a graphing calculator

[thorn palm]

Are there any specific topics you learning right now?

any topic of lecture

I'd like to know what kinda approaches are valid

[mystic saffron]

no not rlly

um

yeah idk.

[thorn palm]

ok

[mystic saffron]

sorry

[thorn palm]

For 1st question

has any clue?

any ideas/approach you thought

[mystic saffron]

well, all i rlly have to do is count lol

i can try to figure it out

[thorn palm]

Can you give it a try?

[mystic saffron]

yes

[thorn palm]

not with actually counting them all

[mystic saffron]

oh

😭

[thorn palm]

ah ok dont worry

So idea is that each vampire will bite 1 person, so there will be same number of new vampires

[mystic saffron]

so it would start with 1 in the first hour

in the second hour, there would be two, and they each bite someone, so four in the second hour?

[thorn palm]

I think first hour vampire bites one, so two vampire in total

so 0h 1
1h 2
2h 4

[mystic saffron]

yeah

3rd hour is 8

[thorn palm]

So if we say $a_n$ is vampire population in n hour, $a_n=2a_{n-1}$

and $a_0=1$

[clever fjord]

Dri111

Dri111

[mystic saffron]

what

😭

well i counted for the 24 hours

[thorn palm]

What i wanted to say was

there is $2^n$ vamp in n hour...

[clever fjord]

Dri111

[thorn palm]

This way much easier to calc

[mystic saffron]

for u maybe

this is so complicated for me

i'm in my junior year of high school and i cant even do simple math ;(*

😭

[thorn palm]

you know powering?

[mystic saffron]

yes

[thorn palm]

idk foreign education courses

[mystic saffron]

like

[thorn palm]

ok then

[mystic saffron]

x to the second power and stuff

im in the USA rn

[thorn palm]

in 0 hour, there is 1 vamp

[mystic saffron]

yes

[thorn palm]

after 1 hour, vamp doubles

so 1×2=2

[mystic saffron]

yeah

and then they both infect someone, so there's 4

and then 8

and so on

[thorn palm]

after another 1 hour, vamp doubles

[mystic saffron]

yes

[thorn palm]

so 1×2×2=4

and 1×2×2×2=8

[mystic saffron]

yeah

and then 16

32

64

?

[thorn palm]

so you can express it as $2^n$

[clever fjord]

Dri111

[thorn palm]

after 24 hour

2^24 vamps

you choosed 3 day when making question?

3day=72hour

2^72 will be enormous

,w 2^72

[clever fjord]

Results provided by WolframAlpha

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

Requested by dri111

[thorn palm]

Can you use calculator when solving question?

[mystic saffron]

yes

u can use any resource that might help

sorry im in a class rn lol

my responses might be a bit slow

[thorn palm]

What I wanted to show you was
0h ->$1=2^0$
1h ->$1\times2=2^1$
2h ->$1\times2\times2=2^2$
3h ->$1\times 2\times 2 \times 2=2^3$
and goes on n hour ->$2^n$

[clever fjord]

Dri111

[mystic saffron]

oh my

I think I'm not gonna be able to get this

I'm sorry

Your help is greatly appreciated!

But I'm too slow to figure this out.

[thorn palm]

I believe some else can make you understand

that's what this server is good at

I'm sorry

[mystic saffron]

it's ok

I just don't know who will be able to help

[thorn palm]

I think you can call helper one more time

its been 15 min

[mystic saffron]

oh ok

<@&286206848099549185>

tho i dont think they'll be able to help

i'm genuinely stupid 😭

[pliant quartz]

no ur not

lets see

pls reply to the message that contains ur question

[mystic saffron]

oh ok

[mystic saffron]

here and the picture below

[odd edge]

@mystic saffron Has your question been resolved?

[arctic idol]

Can u not use arithmetic/ geometric sequences to form the equation?

[mystic saffron]

if i could, i would.

[arctic idol]

Such as this?

Is there a specific way you need to do it

If u use these questions and do something similar using arithmetic/ geometric/ quadratic sequences it might help?

[arctic idol]

I don’t understand why can’t you? 😭

[mystic saffron]

bc im dumb

[odd edge]

@mystic saffron Has your question been resolved?

[arctic idol]

Geometric, quadratic and arithmetic

Nth term in all of them is the one you’re trying to find

[odd edge]

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[steel yoke]

need help determining relative angle of impact between two objects, using only the object's own bearing, and the X and Y coordinates of both objects. Pictured below.

[steel yoke]

In this example, the projectile is originating from the bottom left rectangle in each example and is hitting the top right rectangle which has its own bearing from a cardinal. Trying to find theta or "angle of impact", which changes based on the bearing of the target and the angle from the origin ship and the target ship

ive already been able to determine the firing angle from the origin ship by using arctan(Δy/Δx), its just a matter of determining the relative angle of impact with one or multiple formulas, can be conditional.

i imagine something like this has been done before but I dont even know how to google it. So im not entirely sure how to determine this. Using 45 degrees as an example in these problems at first for simplicity sake, but the idea is that a formula can handle any origin angle

[odd edge]

@steel yoke Has your question been resolved?

[odd edge]

@steel yoke Has your question been resolved?

[odd edge]

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[hard crown]

linear algebra anyone? <@&286206848099549185>

[stark elbow]

Don't ping helpers immediately

!15m

[odd edge]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[stark elbow]

Also, what have you already tried?

[hard crown]

oh sorry

thought you just do it to start off

but what I've tried is that the inverse of the matrix is (5/2, 3/2) for row1 and (2,1) for row two

[stark elbow]

It literally says right here

[ivory raven]

the hint says to not calculate A

[stark elbow]

"Hint: Can you do this without calculating A?"

[hard crown]

sorry I was going to explain it more

so I tried not calculating A

getting the top answer

but then got that wrong

so THEN I calculated A

[ivory raven]

what did you do to get those vectors?

[hard crown]

sorry I didn't know that it affected the server this much 😭

[hard crown]

I applied the vector for inverse A and just straight up calcualted it here because I thought that it would give me the uninverted vector

[toxic smelt]

Listen... multiply both sides with A inverse
LHS will vanish out and you will be only left with u, v or W
On the rhs multiple A inverse with the followings 1×2 matrix

You didn't have to calculate A

[hard crown]

yeah, that's what I tried before, it didn't work, prob just calculation error?

[hard crown]

yeah I know I only did that afterwards

[toxic smelt]

Prob

[stark cloak]

9j^14/2j^4?

I already know that I need to subtract and be left with 9j^10 but I'm not sure what happens with the 2 under. Is the variable just removed and i'm left with 9j^10/2?

[hard crown]

wrong chat or something?

also, just solved the problem!

[stark cloak]

ok thanks

.close

[ivory raven]

.close

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[dapper hollow]

Hello

[lavish jackal]

helo

[sterile blaze]

hlo

[fervent hound]

lo

[cold sage]

o

[quasi sparrow]

[odd edge]

@dapper hollow Has your question been resolved?

[dapper hollow]

Nope

[quasi sparrow]

Use Pythagorean theorem

[dapper hollow]

How I’m not good at that

I am so confused

[quasi sparrow]

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/v/pythagorean-theorem-2

[dapper hollow]

What is that ?

[odd edge]

@dapper hollow Has your question been resolved?

[odd edge]

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[fringe flame]

for part b

[fringe flame]

i got all the cos terms correct

including the a0 1/pi term

but idk where the 1/2sin came from

as the bn term is 0

[quasi sparrow]

It's not

[fringe flame]

i got this for the bn term

and wouldnt it simplify to just 0

[stone cipher]

why would it simplify to 0

[fringe flame]

cause you get -sin(npi)/pi(n^2-1)

and isnt that just 0?

[stone cipher]

probably this is only if n != 1

if n = 1 then you have integral sin^2

which is certainly nonzero

which is probably why you just have this one sin term

[fringe flame]

i see i see alr tyty

.close

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[chrome arrow]

my bad, I figuered it out

sorry

[odd edge]

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[grave barn]

Not sure where the mistake is?

[shut flower]

Why 3x-2?

In the first line

[grave barn]

The dirivitive of square root (x-1)

[shut flower]

Are you sure?

[grave barn]

Ok lemme recheck

[shut flower]

I think it is 1/(2(x-1)^(1/2))

[grave barn]

Ye I think ur right

[shut flower]

The rest seems to be correct, so just change that

[grave barn]

Ok 👍 thanks alot

.close

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[round loom]

Could someone help me with this?

[round loom]

I know the derivative of cot(x) = -cosec^2(x)

The derivative of -tan(x) = -sec^2(x)

However I'm still a bit confused on how to progress with the question

does (theta)^3 represent a variable like x or a constant?

<@&286206848099549185>

[upper onyx]

as it starts with h(theta) = ... i would assume that theta is a variable not a constant.do as if it would be an x.

[round loom]

Oh I see, so I would need to use product rule?

[upper onyx]

yes.

[round loom]

Alright, thanks.

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@round loom Has your question been resolved?

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[tacit eagle]

Am I correct?

[odd edge]

@tacit eagle Has your question been resolved?

[tacit eagle]

.close

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[torn stump]

Yoooo help i dont wanna redo all this 😭

[torn stump]

it wasn't 3.01 or 3.00

no way im rounding this wrong

wish me luck

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[fallen cedar]

how would I know to put the highlighted 5 ?

[fallen cedar]

it is because it asks for T < so you put the value thats lower/

[orchid torrent]

T is at least 5

so it's rlly asking $P(5 \leq T \leq 15)$

[fallen cedar]

gocha

[clever fjord]

Civil Service Pigeon

[fallen cedar]

thank you

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[odd edge]

@sick bluff Has your question been resolved?

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[distant yew]

Simple question about including probability in an average between 2 numbers.

[distant yew]

174,562.50 is the base number that will be selected 70% of the time

with a 30% chance to be 279,300

how do i calc the average incl probability.

[green elm]

what do you mean by average incl probability

the expected value?

[distant yew]

just a number inbetween that accounts for the margin of error

not sure if that makes sense

Basically im trying to calculate a number that has a margin of error and Compare it to a static number without probability

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[plush root]

How do i simplify

[true wave]

(a+b) (a-b) = a(square) - b(square)

And then it turns into an identity

Yea

[plush root]

oh wait thats easy. i didnt realise the first one was tan

mb

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[plain nacelle]

I got a

For b I want to make sure that this setup is correct

and idk how to do c

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[hoary halo]

how would i solve for r?

i think i need to find CE, but idk how to

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[pulsar hedge]

I was working on this problem:

[pulsar hedge]

And I got this far

[desert marlin]

congrats

[pulsar hedge]

dy/dx = 7 + e^y / e^(7x) * e^9

but I couldn't make the y's go to dy and the x's go to dx

so we can't seperate this

And then I was confused on how to proceed

[pulsar hedge]

haha thanks

[pulsar hedge]

any idea how to solve this?

[desert marlin]

How did you solve it

above

you have the answer

I'm confused

[pulsar hedge]

I solved it a couple of days ago

and now I am confused how I solved it (when revising the problem RN)

hence why I posted the question & answer, as well as my current work

my mind was much smarter a couple of days ago haha

[cedar geyser]

Are u trying to seperate them?

[pulsar hedge]

I failed

[pulsar hedge]

I got this far!

dy/dx = 7 + e^y / e^(7x) * e^9

[desert marlin]

I think

[pulsar hedge]

but I can't seperate it due to the PESKY 7 +

[desert marlin]

you should write it as

[pulsar hedge]

mhm

[desert marlin]

something with e^(y/x)

and do a substitutioon

[pulsar hedge]

how would I convert y - 7x + 9 to y/x

[desert marlin]

algebra

probabyl

[pulsar hedge]

😭

I don't think it is possible

because if we divide by x

wait NVM

hahahha

y - 7x + 9 -->

y/x - 9 + 9/x
(y-9x+9)/x

it won't work

because x will be in the numerator still

[pulsar hedge]

I think there must be another way, I vaguely remmeber not having to do any substutition

[desert marlin]

let me grab my notebook

let u=y-7x+9

this will be seperable after substituting

[pulsar hedge]

AHHH YES

genius

that worked

[pulsar hedge]

Thank you so much austin!!!

[desert marlin]

no problem

[pulsar hedge]

so is it like every time I see ax + by I should like

[desert marlin]

it's over the form dy/dx=F(ax+by+c) I think that's how you say it

[pulsar hedge]

do u = ax + by

[pulsar hedge]

got it

[desert marlin]

and never ask chatgpt

[pulsar hedge]

where did chatgpt come from haha

[desert marlin]

I was curious if it had gotten any better at math

figured this would be a good test problem

it hasn't

[pulsar hedge]

LOL

they should make a chat gpt

that is trained PURELY on math problems

mathgpt

[desert marlin]

they have one of those

[pulsar hedge]

optimized for math problems

[pulsar hedge]

wait what

[desert marlin]

,w wolframalpha

[pulsar hedge]

what is it called

[clever fjord]

Results provided by WolframAlpha

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

Requested by austinu

[pulsar hedge]

is it fire or nah?

[desert marlin]

hah I'm slightly joking, it's not AI, it's a calculator, but one of the best

does a lot of stuff

,w dy/dx=7+e^(y-7x+9)

[clever fjord]

Results provided by WolframAlpha

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

Requested by austinu

[desert marlin]

beats chatGPT here

lol

[pulsar hedge]

Wait just to confirm

a differential equation is autonomous if

the derivative can be expressed without the X variable right?

[desert marlin]

well

the variables not always X

[pulsar hedge]

or T

[desert marlin]

if it can be expressed without the independent variable

[pulsar hedge]

bet

[desert marlin]

which normally is x or t

yea

[pulsar hedge]

Thank uuu

[pulsar hedge]

Alrighty, i'll try it on my HW haha

[desert marlin]

well

do ur problems dont use the calculator

u got this

[odd edge]

@pulsar hedge Has your question been resolved?

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[edgy stag]

Hello, I am having trouble understanding some proofs of limits using its formal definition. My question is, why exactly can we say that |x| < ε? And apparently in some other proofs I have been trying to study, |x| can be smaller than... anything? This confuses me the most, and I would be grateful for any explanation!

[odd edge]

@edgy stag Has your question been resolved?

[edgy stag]

@dusk warren

[odd edge]

@edgy stag Has your question been resolved?

[stark turret]

The main idea behind of the formal definition of limit is related to the concept of a Cauchy succession , which says that the distance between elements of converging sucession gets smaller and smaller when you approach the limit value

A Cauchy sequence is a sequence of real numbers that gets closer and closer together as the sequence goes on. More formally, a sequence ( {$a_n$} ) is Cauchy if for every positive number ( $\epsilon$ ), there exists a number ( N ) such that for all ( m, n > N ), we have

$$ |a_m - a_n| < \epsilon $$

In other words, for any given positive number ( $\epsilon$ ), we can find a place in the sequence beyond which all of the terms are less than ( $\epsilon$ ) apart.

Cauchy sequences are important in analysis because they are used to define the completeness of a metric space. A metric space is a set of points with a distance function defined between them. A metric space is complete if every Cauchy sequence in the space converges to a point in the space.

The real numbers are a complete metric space, which means that every Cauchy sequence of real numbers converges to a real number. This is one of the reasons why the real numbers are so useful for doing mathematics.

[clever fjord]

The Mad Pirate

[stark turret]

So then, the main idea behind limits is that the distance between terms becomes smaller and smaller the more you approach the limit value.

That allows to define convergence in terms that are not in the usual real numbers sense, like mean limits in functional spaces ( Hillbert spaces). As long as you have a definition of a metric, you can define the concept of a limit.

[edgy stag]

Wow thanks so much for the explanation, I will read it in depth after dinner, and hopefully I will finally know how the formal definition works 😭

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[fast ivy]

i was given some hints

i set it u p like this:

0.02x=0.18(800-x)

and got x=722