help-42

[magic fable]

what site is this

?

looks good

[sinful lion]

Webwork

No it isn't

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[calm coral]

@remote mural Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[fresh jewel]

(This is for a program I'm writing, not anything school-related)
((Also I've been out of school for years so my standard math knowledge is quite rusty))

I need to find a function (any function) that fits some specific requirements and I'm unsure of how to go about it.

1. This line only goes from x=0 to x=a, none of the following requirements matter outside of that range. a can potentially be any value between 1 and ∞.
2. The first derivative at the point (0, 0) must be exactly 1, all higher derivatives must be 0.
3. All derivatives at x=a must be exactly 0.
4. The second derivative must always be less than or equal to 0.
5. There must not be discontinuities in any derivative (first, second, third, so on).
   I don't know enough about math to know if avoiding discontinuities in this many derivatives is possible. If it isn't possible, I'm satisfied with a lack of discontinuities up until at least the eighth derivative, if possible.
   Aside from these requirements, the function can be anything (unless I forgot something...), but I don't know how I can find something that fits those requirements.

[fresh jewel]

Here's an example of my first attempt (the red line). The white line is the first derivative and the green line is the second derivative. This red line satisfies all the requirements, except #5, because there is a massive discontinuity in the second derivative (at the end at x=a when it snaps back to 0).

(Oh, the screenshot uses k instead of a, my bad)

[calm coral]

@fresh jewel Has your question been resolved?

[fresh jewel]

A much simpler (and probably better) example would probably be something like this (x-(x^2)/2a), but the second derivative (bottom red line) has discontinuities at x=0 and x=a (since it needs to be exactly 0 at those points). Maybe it would be possible to fix this for more and more derivatives by adding higher and higher exponents into the function somewhere?

[calm coral]

@fresh jewel Has your question been resolved?

[fresh jewel]

I made more progress and managed to remove the discontinuities from the second derivative via pure guess-and-check. I'm not sure if I can spot what the pattern is yet though.

[calm coral]

@fresh jewel Has your question been resolved?

[tulip veldt]

I am wondering if a bump function might be of assisstance?

https://en.wikipedia.org/wiki/Bump_function

[fresh jewel]

Thanks, this isn't quite the solution on its own (though it's probably fairly close, haven't finished reading the page yet) but it led me to some pages that can probably help a ton. Seems like what I'm looking for is:

1. a C-infinity function
2. with first derivative of 1 at (0, 0), all other derivatives being 0
3. with all derivatives being 0 at x=a with any a >= 1
4. with a non-positive second derivative from x=0 to x=a
   That significantly simplifies my question.

[fresh jewel]

Thanks a ton, I was able to get it figured out by modifying some of the things from here!
I noticed one of the recommended functions had a derivative of 1 partway through it, so I thought that maybe if I made that point the origin (therefore making it no longer a bump function, but should hopefully still remain continuous beyond that first derivative starting point) it would fit my requirements, and it appears to work perfectly.

.close

[calm coral]

Channel closed

Closed by @fresh jewel

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

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!

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

[remote mural]

Find the coefficient of $x^{10}$ in the expansion of[
\p{\sum_{n=0}^\infty x^{2n}}\cd\p{\sum_{n=0}^\infty x^{4n}}\cd\p{\sum_{n=0}^\infty x^{6n}}
]

[remote mural]

this translates to [
\p{1-x^2}^{-1}\cd \p{1-x^4}^{-1}\cd \p{1-x^6}^{-1}
]

[remote mural]

what do u do from here tho

[clear delta]

not that i think

actually maybe

do a taylor series

[remote mural]

Not possible

[clear delta]

wait that'd be the tenth derivative

ok dont do that

[remote mural]

[clear delta]

what i (dumb) would do

is just enumerate cases

starting with that x^6n

wait yeah do that, that takes no time

[remote mural]

there is like

this thing my teacher did where you evaluate some binomials

i really forgor but it was shit like this according to my old notes

[oblique current]

Yeah just write out a few terms of each binomial and think about all the ways you can multiply 3 terms to get x^10

[remote mural]

hmmge

[fluid flame]

when the solution to the dm problem is “just count lol”

[remote mural]

ok yeah this makes sense now

thanks .clsoe

.close

[calm coral]

Channel closed

Closed by @quick snow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[neon pine]

please help…

[neon pine]

I have an online final exam that is starting soon, for calculus. I’m not sure where else to look for help. Tho I’m sure you guys probably aren’t allowed to help, even tho it’s not an assignment.

[fringe reef]

we can't help on tests

you can ask and study tho!

[visual nimbus]

^

[neon pine]

I don’t think I’d have the time to do that during the exam

😭

[visual nimbus]

study?

[neon pine]

nor would I have time to have the question explained

idk where else to get help

[hushed tartan]

this should be done from the very start not some mins before the exam

[neon pine]

I’m aware, thanks

.close

[calm coral]

Channel closed

Closed by @neon pine

Use .reopen if this was a mistake.

[hushed tartan]

gl

[calm coral]

Available help channel!

Send your question here to claim the channel.

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!

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

[strange pier]

Yes but i dont think IS that because my Initial exercice IS :

In an orthonormal coordinate system (O;I;J) we consider the center O passing through I. Let M be a point on the circle and H the orthogonal projection of M onto (OI).
Where should we place point M so that the air in the IHM triangle is maximum?

[strange pier]

How i place the H point?

Please

[fluid flame]

that’s a whole lot of fluff to describe R²

form an equation on θ then maximise that ig

[calm coral]

@strange pier Has your question been resolved?

[strange pier]

So i need to found the best angle ?

[fluid flame]

well yeah you’re trying to maximize the area no?

[strange pier]

Yes @fluid flame

[fluid flame]

so form an equation for the area then maximize that

[strange pier]

So (OH * HM)/2

Ro calculate the area

@fluid flame

Oups nop

HI*HM

All /2

[fluid flame]

that’s a nice start, now rewrite it in terms of variables
you will need some trig for this

[strange pier]

Okk

@fluid flame

IS this good ?

[fluid flame]

i don’t think cos α is representing the correct length?

[strange pier]

Oops

So cos(a) - 1

@fluid flame

[fluid flame]

still not it but i guess pretty close

[strange pier]

you're holding me back, because that's precisely where I'm stuck

[fluid flame]

this is either 0 or negative

so figure out what’s wrong and fix it

[strange pier]

IS √2/2?

[fluid flame]

what

[fluid flame]

im telling you that cos(α)-1 is never positive

[strange pier]

Oh

So cos(a)+1

[fluid flame]

and if you’re constructing triangles where one of the sides is never positive something going wrong

[strange pier]

Mmh ok

So i need to Change thé Position of the triangles?

[fluid flame]

take α=0. are you sure you’re supposed to get a length of 2?

try staring at your diagram for a few seconds

[strange pier]

No

Okkk

[strange pier]

Bro i See nothing

X)

[fluid flame]

the geometric interpretation of the length IH is right there

[strange pier]

So the point M is equal to cos a ? @fluid flame

Is thiz true ?

[fluid flame]

wait, M? then no

[strange pier]

M is equal to sin a

[fluid flame]

M is a point in your 2D space so you should probably describe it with 2 values

[strange pier]

But my teacher tell me that we are going just to set variable on length and find function

To calculate the d/dx

And find the solution

@fluid flame

[fluid flame]

yes and that’s what we’ve been doing and you just haven’t set the correct length yet

[strange pier]

Arghh im so bad 😭

M(Sin(a);cos(a))

[fluid flame]

ye now we’re back on track

[strange pier]

Ok fine

[fluid flame]

look at OI, you’be already set it to be 1 which makes everything else nice.

then look at OH = cos α
now OHI are always collinear so express HI in terms of OH and OI

[strange pier]

Ok i see

@fluid flame

HI = OI - OH.

So

1-cos a

[fluid flame]

ye we finally got there

now you can solve

[strange pier]

Lets goooo

@fluid flame

[fluid flame]

you forgot about brackets but sure

then just maximize that and solve for α

[strange pier]

I need to d/dx? @fluid flame

The area

To get maximus ?

[fluid flame]

when you maximize/minimise something you always take the derivative yes

[strange pier]

Maximum*

[fluid flame]

but there’s no x in your equation

[strange pier]

So

d/da

[fluid flame]

ye

[strange pier]

@fluid flame

IS thiz good ?

I have say that let a = x

And f(x) = Area

[calm coral]

@strange pier Has your question been resolved?

[strange pier]

<@&286206848099549185>

[calm coral]

@strange pier Has your question been resolved?

[calm coral]

Channel closed

Closed by @strange pier

Use .reopen if this was a mistake.

[strange pier]

@fluid flame i have found 3/5

Ty

[calm coral]

Available help channel!

Send your question here to claim the channel.

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!

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

[true canyon]

Solve the system

[true canyon]

$x’=y$

$y’=(\alpha -(x-1)^2-y^2)y-x$\
$\alpha\leq0$

[potent lotus]

jsidind810

[true canyon]

<@&286206848099549185>

(I asked my question before )

<@&286206848099549185>

I actually have to determine if the above is lyapunov stable at (0,0)

For alpha leq 0

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[calm coral]

@true canyon Has your question been resolved?

[true canyon]

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185> ODE problem

[true canyon]

<@&286206848099549185>

[calm coral]

@true canyon Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[deft flax]

!status

[calm coral]

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

[past zinc]

write the definition of a sequence diverging to positive infinity

[deft flax]

this ?

so

there exists no for all n>no sn>H

and then

the same for tn with a diff letter

[past zinc]

yes but i prefer this way:

$\lim_{n \to \infty } s_{n}=+\infty \Leftrightarrow \forall _{M>0}\text{ }\exists {n}\text{ }s{n}>M$

[potent lotus]

Joanna Angel

[past zinc]

but it is the same

[deft flax]

okay sure

[past zinc]

and next thing is super easy, yoru secodn sequence

t_n

is greater than s_n

for all n

[deft flax]

so

M<sn<tn?

[past zinc]

yes )

[deft flax]

awesome

thanks

[past zinc]

yw 🙂

[deft flax]

.close

[calm coral]

Channel closed

Closed by @deft flax

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[torn hemlock]

I am supposed to find the volume of the described solid, but I don't even know where to start. I am having trouble comprehending what the question is even describing, and I don't know how the cross sections can be equilateral triangles when the graph is a right triangle?

[tidal grotto]

Picture you are looking down at the solid

if cross sections are perpendicular to the y-axis, they are parallel to the x-axis

again, picture you are looking DOWN at this solid, without any like, depth perception. The green lines represent the bases of the equilateral triangles

does this make sense?

there's infinitely many of these equilateral triangles, but they're base and height is purely determined by the length of the green line (it's because they're equilateral)

@torn hemlock

[torn hemlock]

Ohh I see, that makes more sense

So I need to take the integral of √3/2x?

*X^2

[tidal grotto]

i believe the area formula is sqrt(3)/4 x^2

[torn hemlock]

Oh yeah over four

Thanks a lot

.close

[calm coral]

Channel closed

Closed by @torn hemlock

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

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!

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

[fresh mist]

I saw my friend struggling on this fr idk how to do omg can u guys teach me fr he is in a higher math class fr

[calm coral]

@fresh mist Has your question been resolved?

[fresh mist]

<@&286206848099549185>

[next hound]

area is base * height

next question you have to maximize A(x) by finding critical points, and testing them and the endpoints

E is the same as D but its x value instead of area

[fresh mist]

Is b correct

[next hound]

not sure why the y is there but looks right

[fresh mist]

so 2x(9-x^2) right fr

and liek u multiply it out fr

[fresh mist]

Wats a critical poin

@next hound

[next hound]

maximize the A(x) function however your friend learned

if it's a calc class (it probably is) they need to learn critical points

[fresh mist]

precalculus

waht does maximize the function mean fr

@next hound

[next hound]

I'm not doing your friends hw for them

at least have them come ask themself

[fresh mist]

😭

[fresh mist]

Teach me fr🙏

[fresh mist]

<@&286206848099549185>

[simple plover]

I have to ask; What is "fr"?

[edgy oasis]

area will be hxb --> 2x(9-x^2)

[fresh mist]

For real

[fresh mist]

Fr

Idk the next ones

[edgy oasis]

differentiate

[fresh mist]

Idk wat that means

[edgy oasis]

f(x) = 18x-2x^2

[simple plover]

Those who speak your language would be best to help you.

[fresh mist]

Isn't it cubed

[edgy oasis]

ohh ya dumb mistake

18x-2x^3

f'(x) = 18 - 6x^2

[fresh mist]

wat

[edgy oasis]

do you know differentiation?

[fresh mist]

no

I'm doing algebra 2 stuff and this is pre calc thingy paper

😭 😭 😭

[edgy oasis]

lol that sucks

x=sqrt(3)

[fresh mist]

so true

[edgy oasis]

will be maximum point

was it like in precalc paper or in an algebra one?

[fresh mist]

precalculus

[fresh mist]

now wat

[edgy oasis]

i dont really know any other method to do this without calculus

well if you graph the A(x)

[fresh mist]

this one or the other

Idk

[edgy oasis]

18x-2x^3

[edgy oasis]

ignore this I was being stupid

[fresh mist]

wahr

[edgy oasis]

I was just saying if you graph it but obv graphing isnt a option

[fresh mist]

umm wat do I do

[edgy oasis]

Broo, its written on the paper calculus is required

[fresh mist]

nah

[edgy oasis]

the title

[fresh mist]

teach me the necessary calculus rn

I'm 'him' it's ok

https://tenor.com/view/luke-skywalker-green-lightsaber-mandalorian-jedi-luke-gif-19627631

That's me

[edgy oasis]

do you just want the steps? or like learn it?

[fresh mist]

uhh

Steps

I think

[edgy oasis]

like what you want to write in paper right?

[fresh mist]

Fr

[unreal viper]

Ong nocap rizzler fr

[edgy oasis]

A(x) = 18x-2x^3
A'(x) = 18-6x^2
A'(x) = 0 for maxima point
18-6x^2=0
x=sqrt(3)

then put x in area function and thats the area

[edgy oasis]

lol

[fresh mist]

I didn't even notice he was being sarcastic for 2 min 😭

[unreal viper]

Oof sorry I didn’t mean to be rude

I was mostly mocking that guy for saying that slang is a different language

[edgy oasis]

thats why i said lolol

[unreal viper]

The paper says calculator not calculus

[fresh mist]

Is this it for D

[unreal viper]

Unless youre referring to a different document

[edgy oasis]

I am going to die, with my stupidity

[unreal viper]

It’s okay lol you’re not stupid

Simple mistakes happen

[edgy oasis]

but i have never seen a paper that ask for a calculator lol

[unreal viper]

But he definitely won’t need calculus

[fresh mist]

Ez

[edgy oasis]

my school so strict

[unreal viper]

Yeah it depends on the teacher

[edgy oasis]

how to do it without?

[unreal viper]

I used a graphing calculator a lot in grade twelve

[fresh mist]

uhh me and my friend are in 10th grade

[unreal viper]

I mean it could be as simple as graphing the function and use your TI-84 graphing calculator to solve for maximum

[edgy oasis]

https://tenor.com/view/new-girl-witchcraft-winston-sorcery-gif-22394282

[unreal viper]

Graphing calculators have max and minimum functions built in

[fresh mist]

can I use desmos

[unreal viper]

So if you’re allowed a calculator then why not a graphing calculator lol

[fresh mist]

He qas

[unreal viper]

Yeah desmos is a graphing calculator

[fresh mist]

He had some Texas thing

Instrument

[edgy oasis]

I thought graphing wasnt a option

[fresh mist]

Graphing

Calc

[unreal viper]

Yep TI-85 probably

Those have graphing capabilities

[fresh mist]

how find answer

[unreal viper]

And you can find maximum using it

[fresh mist]

how

[edgy oasis]

graph it

the point that is at maximum val

[fresh mist]

(1.5, 13.5)

[fresh mist]

Wahr

[edgy oasis]

the graph

[fresh mist]

I JUST HAVE A PARABOLA

[edgy oasis]

plot -- 18x-2x^3

lol

[fresh mist]

Oh

Do I say the relative max or idk

Infinity

😭

[edgy oasis]

relative max

[unreal viper]

Yeah don’t forget you need to find the graph of A(x) not the parabola

And that is b times h

Not just h

[edgy oasis]

the point close to y=+20

[unreal viper]

You probably just graphed y

[fresh mist]

(0.577, 6.928)

[edgy oasis]

no

(1.732, 20.785)

[fresh mist]

😔

[edgy oasis]

do you know how to use TI-85?

[unreal viper]

It’s been a hot minute

But if I had one in my hand I could figure it out again

I don’t think I could teach it though

Not over discord at least

[edgy oasis]

https://tenor.com/view/we-all-bus-infinity-war-gif-21386170

[edgy oasis]

can you graph it on on desmos?

[fresh mist]

That's what I meant

Fr

Typo

[edgy oasis]

?

[fresh mist]

Now wat

[edgy oasis]

.

[fresh mist]

Meant to say this trust

[fresh mist]

Yes

[edgy oasis]

bro how is that a typo

[fresh mist]

Now wat

[edgy oasis]

you got this?

[fresh mist]

yuh

easy

[edgy oasis]

(1.732, 20.785)

[fresh mist]

fr

then wat

[edgy oasis]

thats the answer

[fresh mist]

Oh

[edgy oasis]

x = 1.732

A = 20.785

[fresh mist]

oh

the x one is for

E

Right

[edgy oasis]

yes

[fresh mist]

So cool

Wat is this called

[edgy oasis]

and A is for before that

[fresh mist]

Does it have a cool name

For wat we did

[fresh mist]

Ez

https://tenor.com/view/the-mandalorian-luke-skywalker-mandalorian-star-wars-lightsaber-gif-19622893

[edgy oasis]

its called doing shit to be honest

you just graph it, I mean lol

[fresh mist]

was that this or just graphing

[edgy oasis]

that was somethin else

that is cool af

calc i mean not differenation

[fresh mist]

why did it even say round to three decimal places😭 😭

[unreal viper]

Because desmos did it for you but it didn’t have to

[edgy oasis]

you alerady have 3 decimal places

[edgy oasis]

yes

[unreal viper]

It could be that on a different calculator it gives a different answer with more decimal places

Either that or the prof just wanted you to keep all 3 and not round to 1

“Prof” lol I mean teacher

[edgy oasis]

miss directed respect

[fresh mist]

how is the maximum point even an area fr

[unreal viper]

Yeah most HS teachers haven’t earned that title lmao

[edgy oasis]

so true

[fresh mist]

Omg wat the highest level math a highschool teacher can do

[unreal viper]

Some are pretty good

[edgy oasis]

what class are you in?

[fresh mist]

integrated math 2 irl

[edgy oasis]

obv there are exceptions

[fresh mist]

But on Khan I'm about halfway through integrated math 3

I've surpassed the class above me

I'm a god amongst them

[unreal viper]

Depends on the person my uncle is a English major who went to be a very successful hs mathteacher

But then I also know a guy at my HS who had a master in pure maths and taught math at HS

So there’s lots of variability on what levels they can do

[edgy oasis]

Worst teachers that dont eveen answer questions, but finally I have some good teachers

[edgy oasis]

god

[edgy oasis]

what didnt you understand in this?

[fresh mist]

uhh the the y axis a(x)

[edgy oasis]

@unreal viperyou are in college?

[edgy oasis]

Area will be anumber

[fresh mist]

is this good fr

[edgy oasis]

you just plot all those numbers

for all values of x

[fresh mist]

Is this good fr

[edgy oasis]

yes

[fresh mist]

So cool

Ty

[edgy oasis]

Np

[fresh mist]

omg

Wanna see my roadmap

rn I am working on integ math 3 but trig and algebra 2 will complete itself automatically as I go through it

Fr

[edgy oasis]

whhhhyyyy

[fresh mist]

I wanna be a master

[edgy oasis]

joking pretty good

[fresh mist]

Fr

[edgy oasis]

probably do number theory a little before calc in my opinion

[fresh mist]

Nah

it's ok

.close

[calm coral]

Channel closed

Closed by @fresh mist

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[narrow ore]

I have a right triangle ABC with the right angle at C. Then there are points A¹,B¹ and C¹ which are reflections of A,B,C. A¹ is reflected about C, B¹ about A and C¹ about B.

[narrow ore]

Then I have to prove that

[calm coral]

@narrow ore Has your question been resolved?

[calm coral]

@narrow ore Has your question been resolved?

[narrow ore]

<@&286206848099549185>

[calm coral]

@narrow ore Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

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!

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

[inner delta]

I think so, yes

2sqrtx / x = 2/sqrtx

As x tends to inf, that tends to 0

$\frac{2\sqrt{x}}{x}$

[potent lotus]

Lorentz

[inner delta]

You mean this?

Yes that's the same

2/sqrt x

Coz sqrt 1 = 1

Yeah well

You didn't have to write 2 as sqrt 4 really

But it's all the same

Nothing wrong

Just multiply 2 directly over here

Sqrt 1 is 1

2*sqrt(1)/sqrt(x)

Anyway yeah that's not the main thing rn is it

Just put lim x to infinity and it becomes 0

Good.

Yes

Np

[calm coral]

Channel closed

Closed by @gloomy galleon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[scarlet comet]

how do i show this

i tried setting 1= (x-1)^2 ....

which is the level curve

but idk what to do from here

[fathom shuttle]

What shape does the equation make?

[scarlet comet]

uh not sure lemme find out

weird egg looking thing

[fathom shuttle]

Yeah its an ellipsoid

[scarlet comet]

yes

[fathom shuttle]

Is the point inside or outside the ellipsoid

[scarlet comet]

inside

oh so no tangent planes would go through the inside of the ellipsoid huh

.close

[calm coral]

Channel closed

Closed by @scarlet comet

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[weak rapids]

why can we take 1 to the otherside rather than taking the x and y term to the otherside, also the question is there on the top

[warm solstice]

I don’t know what you mean? It doesn’t matter which you move across

And in this case they actually have moved the x and y terms across since they’ve flipped signs

[weak rapids]

yea because like this we are getting theta as 7pi/6

but if we take

dont take*

x and y to other side we will get theta pi/6

and also p=-1

but like this we are getting different answers

[warm solstice]

I don’t really feel like working though it to verify it, so I would advise that you do, but they should come out to be the same thing

Yeah that will actually

They differ by pi

And cos(0)=1 cos (pi)=-1

[weak rapids]

is it because they showed p here positive?

[warm solstice]

I would work through it anyway to clear up any doubts you have but they should be equivalent

[weak rapids]

this is dumb ik

[warm solstice]

Without them specifing the set p comes from you can’t in general assume it to be positive

[weak rapids]

yea right

[warm solstice]

But work through it and verify that they’re the same

I assure you they are, it doesn’t matter how you rearrange the equation, and as I said cos flips sign with multiples of pi

[weak rapids]

oh ok

nope thanks

.close

[calm coral]

Channel closed

Closed by @weak rapids

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[lone gust]

Can someone help me with a certain question

[lone gust]

I never learnt this so can someone pls teach me

[calm coral]

@lone gust Has your question been resolved?

[lone gust]

Figured it out bymyself

Cant figure this out

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[pure kayak]

thoughts

[deft fulcrum]

i am stuck on finding the angle

is it 135 or 225

the answer says 225 anticlockwise but i dont know how they got 225, i keep getting 135

[pure kayak]

what does the rotation matrix look like in terms of sin and cos

[deft fulcrum]

costheta sintheta minus sintheta costheta?

[pure kayak]

yeah, its constructed that way for a anticlockwise
if you go clockwise just swap the sign of the sines

anyway

you know that sin theta = 1/sqrt(2)

sin135=-1/sqrt(2), so it must be the 225 if youre going anticlockwise since sin225=1/sqrt(2)

if you were going clockwise then yeah, 135

you can describe it either way

theyre both valid

[deft fulcrum]

when i do inverse sin -1/sqrt2 i get -45 how would i know that it is 135

[pure kayak]

youre not inverse sin of -1/sqrt(2) but rather inverse sin of 1/sqrt(2)
remember the top right entry is +sin(...)

in which case you get the angle to be 45 or 135

you then have to check the cos, we know cos(...)=-1/sqrt(2)
so the angle then is either 135 or 225

you know what, you may be correct, should be 135 anticlockwise

one moment

just gotta check something

aha ive got my stuff backwards

top right is -sin, mb, been a while

one sec

alright, so sin=-1/sqrt(2), then the angle is either 180+45 or 360-45
so 225 or 315

cos=-1/\sqrt(2) so the angle is either 135 or 225

the only consistant one is 225 anticlockwise

you did the same thing as me, thats why you got 135

you used the clockwise rotation matrix

[deft fulcrum]

whyd you add and subtract 45

[pure kayak]

if arcsin of -1/sqrt(2) is -45 right

[deft fulcrum]

yes

[pure kayak]

let me pull out a graph for this

,w graph (y=sin(x) , y=-1/sqrt(2)) from x=-pi to 2pi

need more range

one sec

[potent lotus]

Results provided by WolframAlpha

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

Requested by aldrnari_

[pure kayak]

okay

so if there is a solution sin(x)=y
then there is also a solution sin(2pi+x)=y
and another sin(pi-x)=y
these are represented by the two intersections in the positive side of the x axis

sin(2pi+x)=y is one because sin repeats every 2pi
the other is due to the symmetry of sin

[deft fulcrum]

is that the same for cos as well

[pure kayak]

kinda

,w graph (y=cos(x), y=-1/sqrt(2)) from x=-pi to 2pi

[potent lotus]

Results provided by WolframAlpha

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

Requested by aldrnari_

[pure kayak]

cos has symmetry around pi instead

if cos(x)=y then cos (2pi-x)=y, the +2pi also works though

since it also repeats every 2pi

[deft fulcrum]

okay yeah

thanks

[pure kayak]

dk why i said instead

they both have symmetry around pi lol

the point is, if you draw a graph its easier to see other solutions

[deft fulcrum]

okay thank you

.close

[calm coral]

Channel closed

Closed by @deft fulcrum

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[pallid halo]

!status

[calm coral]

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

[pallid halo]

where are you stuck? can you show what you did so far?

[vocal goblet]

yeah so basically, i know the formula is the summation of x * P(x)

where x is the money, and P(X) is the probability of rolling a certain event

im stuck on finding the probability of rolling two of the same values

sorry im trying to send a photo rn

it's not loading

[pallid halo]

one way to do it is as follows..
first suppose that the two same values occur on the first two dice, so there are 6 possibilities for the first two dice, then 6^3 for the remaining three

now multiply that by the number of ways to rearrange the rolls

[vocal goblet]

it cant be 6^3 tho, because then we would have the possibility of getting the same number again

[pallid halo]

oh right sorry

[vocal goblet]

which would make it a 2+ of the same value

[pallid halo]

5^3

[vocal goblet]

there we go

[pallid halo]

so it'd be something like 6 times 5^3 times (number of ways to choose which two dice match)

all over 6^5

ah wait

not 5^3

5x4x3 ig

since they can't match each other either

[vocal goblet]

okok

so would the number of ways to choose 2 dice match be 5c2?

[pallid halo]

yep

[vocal goblet]

ahh okay

that makes a lot of sense

okay i think i got it from here then

thank you!

[pallid halo]

cool

[vocal goblet]

.close

[calm coral]

Channel closed

Closed by @vocal goblet

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

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!

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

@hasty crag Has your question been resolved?

[calm coral]

@hasty crag Has your question been resolved?

[calm coral]

@hasty crag Has your question been resolved?

[calm coral]

Channel closed

Closed by @hasty crag

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

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!

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

[halcyon creek]

how do i convert 2log3 (x+1) + 4 into exponential form

[halcyon creek]

<@&286206848099549185> urgent

[cloud topaz]

[next hound]

unclear question

also

!15m

[calm coral]

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.

[halcyon creek]

how

[next hound]

can you show your original problem?

[halcyon creek]

Determine the equation of the asymtote of y = 2log3 (x+1) + 4

but im just curious

how i would convert it to exponential form

[cloud topaz]

why woukd you convert it to exponential form

[halcyon creek]

i just want to know how i can

[fading crater]

2 * (3^(x+1)) + 4. I think that would be it best guess

[halcyon creek]

why are you guessing

what

i need an exact answer

⁉️

[cloud topaz]

[ y = 2\log_3 (x+1) + 4 ]

[potent lotus]

Pure

[halcyon creek]

yes

[cloud topaz]

wym by expoential form

solve for x?

[fading crater]

it is that waht it would be rewritten as

[halcyon creek]

convert to the form 3^x

dawg

the inverse of this equation

basically

😭

[cloud topaz]

okay thats what you shoulve said

[halcyon creek]

my bad gango

[cloud topaz]

[ x = 2\log_3 (y+1) + 4 ]

swapping x and y

[potent lotus]

Pure

[halcyon creek]

how do i get rid of the log

⁉️

[cloud topaz]

[ x - 4= \log_3 ((y+1)^2) ]

now do 3^lhs = 3^rhs

actually

[\df{x-4}{2}= \log_3 (y+1) ]

[potent lotus]

Pure

[cloud topaz]

now do 3^lhs = 3^rhs

[halcyon creek]

how can you just do that

theres a log

on one side

[cloud topaz]

?

[\mr 3^{\frac{x-4}{2}}= \mr 3^{\log_3 (y+1)} ]

wow

thats so bad

[potent lotus]

Pure

[halcyon creek]

okay

how do you get rid of log

on RHS

[cloud topaz]

,, \loglaws

[potent lotus]

Pure

[halcyon creek]

which one is it

[cloud topaz]

look trhough and think

[halcyon creek]

product of powers

[cloud topaz]

no

[halcyon creek]

inverse property?

[cloud topaz]

yes

[halcyon creek]

okay

can you finish the

solution

[cloud topaz]

no you do it

[halcyon creek]

3^((x-4)/2) = y+1

[3^((x-4)/2) = y+1]

@cloud topaz

[cloud topaz]

Yeah just isolate y

[halcyon creek]

y = [3^((x-4)/2) + 1

but i just need to find the asymtote

[cloud topaz]

-1

[halcyon creek]

so why am i doing all this

⁉️

[cloud topaz]

Good question

Ur a waste man

[halcyon creek]

LMFAOOOO

[halcyon creek]

can i ask u antoehr question

[cloud topaz]

maybe

[halcyon creek]

does free will actually exist

[cloud topaz]

imagine the world is a piano

and im playing mozart 2053

isnt that concerning

[halcyon creek]

is math real

⁉️

[cloud topaz]

Are you real

.close

[calm coral]

Channel closed

Closed by @cloud topaz

Use .reopen if this was a mistake.

[cloud topaz]

Bruh

[calm coral]

Available help channel!

Send your question here to claim the channel.

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!

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

[gritty jasper]

do anyone know how to get act exams?

[calm coral]

@gritty jasper Has your question been resolved?

[leaden thunder]

Don't use math help for getting exams

.close

[calm coral]

Channel closed

Closed by @leaden thunder

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

@junior fern Has your question been resolved?

Channel closed

Closed by @junior fern

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

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!

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

[icy flame]

Does anyone know what I would put for my third reason I don’t know the proper way to say that they are congruent through right angles

[icy flame]

Oh so I don’t even gotta

Alr thanks

.close

[calm coral]

Channel closed

Closed by @icy flame

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[past zinc]

hint: please note that a necessary condition for differentiability is continuity

$\text{f is a continuos function at a point }\text{ }x_{0}\text{ }\overset{def.}{\Leftrightarrow }\text{ }f\left( x_{0} \right)=\lim_{x \to x_{0}} f\left( x \right)$

[potent lotus]

Joanna Angel

[past zinc]

however, to ensure the existence of the limit, we must ensure the equality of one-sided limits at this point

your function is not

lol

what youre talkign ab

come on

i give you a link to it, i wrote defintion for you above

so oyu must check this condtion i wrote

hte most improtant is the limit

to fidn it

you need to compute onde sided limits

from left and from right side of x = 0

exactly

and ow

becaue f is not continuos at x = 0

then cant be differentable

at x = 0 either

and that explains, lack of tangent line

37 ?

no, plz sketch the graph

fidn a tangent line

at x = 0

A vertical tangent touches the curve at a point where the gradient (slope) of the curve is infinite and undefined. On a graph, it runs parallel to the y-axis.

and that is not the case here

mayeb author means something different, to justiy him/her 🙂

or mistake

in printing

book has not been made by the God 🙂 so .....

🙂

becasue tangent line exists when derivative exists in htis point

and i shwoed it

it was zero

so tanget line is

y = 0

do oyu remeber equation of the tnagent line ?

$y-y_{0}=f'\left( x_{0} \right)\left( x-x_{0} \right)$

[potent lotus]

Joanna Angel

[past zinc]

f ' ( 0 ) = 0

hence

y = 0

and if it coems to 36, f is continuol;s but is not differentiable in x = 0, hence no tangent line

i shwod you limit

do you remember ?

$f'\left( x_{0} \right)\overset{def.}{=}\lim_{\Delta x \to 0} \frac{f\left( x_{0}+\Delta x \right)-f\left( x_{0} \right)}{\Delta x}=\\\lim_{\Delta x \to 0} \frac{f\left( 0+\Delta x \right)-f\left( 0 \right)}{\Delta x}=\lim_{\Delta x \to 0} \frac{\Delta ^{2}x\cdot sin\frac{1}{\Delta x}}{\Delta x}=\\\lim_{\Delta x \to 0}\left( \Delta x\cdot sin\frac{1}{\Delta x} \right)=0\\\text{because}\\0\le \left| \Delta x\cdot sin\frac{1}{\Delta x} \right|\le \left| \Delta x \right|$

[potent lotus]

Joanna Angel

[past zinc]

the first line is the defintion

of differentiability at the point

that is sandwitch theorem for limits of fucntions

its applikcaiton ofc

it is vey rknown trick

absolute value destroyrs ugly sine

on left we have zero

and on right we have expresiosn that goes to zero too

so middle goes to zero as well

pzl write it in yout exercise book

to ot forget such a trick

yes

formulation si easy but using of it reauores practises

to establish proper habits

some problem book with solutions as well, do oyu have any ?

btw: why are you reading it ? yoru hooby ? or ?

i see ok

i have a link to pdf

do you study if not a secret ?

36 no tangent since f' ( 0 ) does not exist

do oyu study at the uinversity or some school ?

because

$\lim_{\Delta x \to 0} sin\frac{1}{\Delta x}\text{ }\text{ }\text{ doesn't exist}$

[potent lotus]

Joanna Angel

[past zinc]

look =

no

$f'\left( x_{0} \right)\overset{def.}{=}\lim_{\Delta x \to 0} \frac{f\left( x_{0}+\Delta x \right)-f\left( x_{0} \right)}{\Delta x}=\\\lim_{\Delta x \to 0} \frac{f\left( 0+\Delta x \right)-f\left( 0 \right)}{\Delta x}=\lim_{\Delta x \to 0} \frac{\Delta x\cdot sin\frac{1}{\Delta x}}{\Delta x}=\\\lim_{\Delta x \to 0}\left( sin\frac{1}{\Delta x} \right)\text{ doesn't exist}$

[potent lotus]

Joanna Angel

[past zinc]

and it does not exist

due to Heine's definition of the limit at the point

that means

it is possible to find two diffeernt sequences, convergent to zero

but

if you plug them into this ugly sine function

they give you diffeernt limits

hence the limit doe snot exisist

and hence

f is not diffeerntiable at x = 0

thus, no tnagent line

but that is nice example

that continutiy at x = 0 is satisfied

so you have exampel fo the function

which is continous at x = 0

but not diffeertnaible at x = 0

worth to memorize it

Detlax is the same as your letter h

but if you study hig maths

we do not use such school letter like h

we prefer deltax

in 35, deltax was sqaured

so even if twas reduced by oen delta

the othe deltat was in nomiantor

and caused limit = 0

due to squeeze thereom

but here, in 36

delta is reduced by delta x form denomiatnro

and you ar eleft with ugly sine

multiplicaiton is not rule i thappens here, becasue you have multiplicaiton in yoru ufcntions

but osmetimes you do not have multplication, but addition

or other form

yes sine oscialates

as an exericse you shud prove :

$\lim_{\Delta x \to 0} sin\frac{1}{\Delta x}\text{ }\text{ }\text{ doesn't exist}$

[potent lotus]

Joanna Angel

[past zinc]

no difference

k

well 🙂 such grpah is rather not proof

i told you , you need to use Heine;s defintion of the limit

have you eve rheard about it ?

The Heine definition of limit: f limx→af(x)=L if and only if for all sequences xn (with xn not equal to a for all n) converging to a the sequence f(xn) converges to L.

and now

if there exists even oen sequeence

and when we plug it into function and we get different limit than we go form other sequences, then limit doe snot exist

but it is not

both defintions

heien and cauchy are equivalent

i shwo you some easy

example

look:

$\lim_{x \to \infty } sinx\text{ }\text{ }\text{ doesn't exist.}\\\text{Solution:}\\$

[potent lotus]

Joanna Angel

[past zinc]

we will choose two sequences that diverge to plus infinity, for example:

$x_{n}^{'}=n\pi\text{ } \text{ }\text{and }\text{ }\text{ }x''_{n}=\frac{\pi}{2}+2n\pi$

[potent lotus]

Joanna Angel

[past zinc]

and then, fo rour function f(x) = sinx, we create two sequences like:

$f\left( x'{n} \right)=f\left( n\pi \right)=sin\left( n\pi \right)=0\to 0\\
f\left( x''{n} \right)=f\left( \frac{\pi}{2}+2n\pi \right)=sin\left( \frac{\pi}{2}+2n\pi \right)=1\to 1$

[potent lotus]

Joanna Angel

[past zinc]

and because

$\lim_{n \to \infty } f\left( x'{n} \right)\neq \lim{n \to \infty } f\left( x''_{n} \right)$

[potent lotus]

Joanna Angel

[past zinc]

then we receive that:

$\lim_{x \to \infty } sinx\text{ }\text{ }\text{ doesn't exist.}\\\\$

[potent lotus]

Joanna Angel

[past zinc]

that is very easy example but your thing relatyed to sin(1/x) is very alike

[calm coral]

@remote mural Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[scarlet helm]

$(x-2)^2$ is equal to (x-2)(x-2) or (x-2)(x+2)

[potent lotus]

odokawa

[remote mural]

It’s equal to having two x-2’s

@scarlet helm

[scarlet helm]

the first one

.clsoe

.close

[calm coral]

Channel closed

Closed by @scarlet helm

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

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!

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

[remote mural]

For part (c), i get [
f =\f1{2\pi R}\s{\f{gR}{\m\sin\theta}}
]

[remote mural]

where theta is like

would that be correct

.close

[calm coral]

Channel closed

Closed by @quick snow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[reef crest]

Two circles C(O1,R1) and C (O2,R2) intersect at two points I and J.
Show that the line (O1,O2) is perpendicular to the line (IJ)

In the figure below, the lines (AB) and (CD) are perpendicular in I.
Let J be the middle of [B, D]. The line (IJ) intersects [A, C] at H.
This involves showing that (IH) is the height of triangle IAC.
1° Justify the equalities of the marked angles
Indication Also think about the inscribed angle theorem

2° We are only interested in the AIC triangle. Justify the ehalities of the marked angles: Deduce the desired result

[reef crest]

I need help 👹

[calm coral]

@reef crest Has your question been resolved?

[calm coral]

@reef crest Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[haughty smelt]

i would just like someone to confirm if im right and what to improve

[haughty smelt]

i am in data management 4u

[calm coral]

@haughty smelt Has your question been resolved?

[calm coral]

@haughty smelt Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[torpid wind]

I am trying to create a context-free grammar corresponding to a DFA. The DFA is for a language which accepts an even number of 0’s followed by an even number of 1’s. I need to write all the elements of the grammar, not just the production rules. This was my attempt, would anyone be able to let me know if it's correct. DFA transitions:

q0 --(0)--> q1

q1 --(0)--> q2

q2 --(0)--> q1

q2 --(1)--> q3

q3 --(1)--> q4

q4 --(1)--> q3

The grammar

S -> ABA | CDC | ε

A -> 0B | ε

B -> 0A | ε

C -> 1D | ε

D -> 1C | ε

Explanation: S -> ABA | CDC | ε: Represents an even number of 0's followed by an even number of 1's or an empty string.

A -> 0B | ε: Generates an even number of 0's.

B -> 0A | ε: Helps maintain an even number of 0's.

C -> 1D | ε: Generates an even number of 1's.

D -> 1C | ε: Helps maintain an even number of 1's.

[calm coral]

@torpid wind Has your question been resolved?

[torpid wind]

<@&286206848099549185>

[calm coral]

@torpid wind Has your question been resolved?

[calm coral]

@torpid wind Has your question been resolved?

[torpid wind]

<@&286206848099549185>

[calm coral]

@torpid wind Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

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!

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

[calm coral]

@soft orbit Has your question been resolved?

[calm coral]

@soft orbit Has your question been resolved?

[tidal grotto]

use the definition of periodic function, i.e. f(x+T)=f(x)

try to rewrite/plug in nice values so you can rewrite f(x+2alpha)+f(x)=0 as f(x+T)-f(x)=0

by plug in, i mean plug in for x, like for example, I can plug in x-2alpha in for x, and this should still be valid f(x)+f(x-2alpha)=0 (this doesn't help, but it's the general approach you can take. :) )

@soft orbit

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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!

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

[worthy comet]

Can someone explain pythagorean relations to me with sin cos tan csc etc

[hasty kite]

sure

[hasty kite]

wht do u wanna know

[worthy comet]

I dont quite know how to best explain the difficulty but heres what i do know

That ones like sin and csc cancel each other out because y/r and r/y respectivly

equaling out to 1

therefore if sin csc and cos then cos will be the only one left standing

but

im supposed to express cos in terms of sin

and they dont quite explain it well

[hasty kite]

so u know how we get sin,cos...etc

[worthy comet]

ye

[hasty kite]

so wht do u wanna know

[worthy comet]

Just how to work it out

[hasty kite]

theres many things

t ratios

complimentary angles

and identities

[worthy comet]

I think its identities

[hasty kite]

so basically first one

sin^2theta + cos^2theta =1

r u taking abt these?

[worthy comet]

Yeah like that

[hasty kite]

theres nothing to explain

only to remember

[worthy comet]

Im supposed to simplify them though

[hasty kite]

wdym

[worthy comet]

How do i simplify something like this

[hasty kite]

1+cot2x = cosec2x

thts an identity

so its cosecx

[worthy comet]

still confused

[hasty kite]

wait

im sending a pic

[worthy comet]

im sorry but i cant quite make out your handwriteing in the picture

[worthy comet]

much better thx

[hasty kite]

did u understand

[worthy comet]

sort of let me talk it to you to correct me if im wrong

cot2 plus 1

is equal to cosec2 because

[hasty kite]

yes

its an identity

[worthy comet]

cot is x/y

and csc is r/y

and r is radius and typicly the greater number

is that right?

so the plus 1 is so it is equal to R

Then you unsquare it