help-4

[sharp whale]

as a result, there is no such thing as a "lowest" or a "highest" number for this set

mathematicians respond to this by defining a different kind of lowest and highest

they are called "infimum" and "supremum" which in this case is the 0 and 1 you expect

[edgy meteor]

always nice when you talk about sequential compactness and your limit is actually in the set though

[pine prairie]

as richard feynman once said Mathematicians can do what they want to do, one should not criticise them because they are not slaves to physics

[cunning ruin]

I regard mathematics as a higher form of thinking as compared to physics

[sharp whale]

physics also doesnt need to care about indivisible quantities when they act vague about the radius of a particle, or that forces never seem to end but only diminish in size across large distances, or that the planck length and such are commonly defined because "our math cannot accurately support what the world may do at these scales," or...

[sharp whale]

do you want to hear the proper way to show that the function is discontinuous

[pine prairie]

physics is not mathematics and mathematics is not physics

[river adder]

Lets not get there
Let's talk bit more about "they don't even know what's pi value" (no ill intended )

[cunning ruin]

I know it already.

At a point of discontinuity of a function, any two of the left hand limit, right hand limit and the functional value do not match.

[sharp whale]

how is a limit defined?

[cunning ruin]

It is the expected value of the function at a point

[sharp whale]

...expected?

define expected?

[pine prairie]

E[f(x)]

[cunning ruin]

we assume a small interval near a point and check the functional values in this interval.

[sharp whale]

"let him cook"

[cunning ruin]

we then make a prediction about the expected value at the point by assuming that the function will not behave in an unexpected manner and that it will keep on behaving in a predictable manner in this small interval

@pine prairie

[sharp whale]

predictable?

define predictable

[pine prairie]

okay this is nonsensical

[sharp whale]

shouldnt there be a clearer condition or formula that we can check?

let him cook

[pine prairie]

we have very rigorous definitions of continuity in math because it works for our purposes

trying to reimagine the definition will lead to lots of issues because there's a reason why everyone's settled on the standard definition of continuity

[cunning ruin]

I am defining the limit

[pine prairie]

every other definition will cause some issue here or there

[cunning ruin]

It will behave at the centre of the interval as it does on the edges of the interval.

[sharp whale]

other problems include:

• it can be too similar to the current definitions so you dont gain any new information
• it's too unwieldy to work with for most cases, so not many insights can be gathered

[cunning ruin]

@pine prairie what is your definition of limit?

[sharp whale]

I did ask about the proper way instead of any new way, do you know what the proper way is?

it begins with "e"

[pine prairie]

there are 2 main ways to define the limit, in open sets and as a metric

[cunning ruin]

Please teach me

[sharp whale]

there we go

[pine prairie]

for your purposes i believe a metric definition will be sufficient (the open sets one is more general)

Formally, we'd start with let $(M, d)$ be a metric space, this means we need to be able to measure distances in $M$, informally, we can just consider the real numbers $\mathbb R$ and the distance between two points $a$ and $b$ to be $|a-b|$ using the absolute value function

[rocky lotus]

frosst

[pine prairie]

A function $f$ is said to be continuous at $a$ and equal to $L$ if for all $\varepsilon > 0$, there exists a $\delta > 0$ such that $|x-a|<\delta \implies |f(x) - L|<\varepsilon$

[rocky lotus]

frosst

[pine prairie]

that's what one calls the "epsilon-delta" definition of continuity

one sees this usually in first year of university

[sharp whale]

occasionally its also taught in around 11th to 12th grade if your math class is forward enough

thats around when I learned this definition of continuity

[cunning ruin]

I have read this definition

I got a picture

but I haven't got examples to solve using this definition so

[sharp whale]

you might as well practice on one

[cunning ruin]

I use my definition for solving problems

[sharp whale]

your definition may not align with the definition they want you to use

[cunning ruin]

It works well enough, although I face troubles visualising using that

[sharp whale]

its not exactly a strong definition, thats the definition most people use

[pine prairie]

it's very scary to imagine things in maths, because what you imagine may not be the same thing as what others are imagining

[sharp whale]

you might as well accustom yourself to the epsilon-delta definition since thats most likely what they'll want going into university

to imagine something is to assume you know all there is about it

proofs avoid this pitfall

here go practice on a limit:

[cunning ruin]

I'll have to understand this epsilon delta definition

@pine prairie how would you define the limit?

[sharp whale]

the limit was already defined as shown

[pine prairie]

i would define limits using open sets because that's the most general definition of continuity that i know of

but for your case they are equivalent

[cunning ruin]

The epsilon delta definition defines continuity, doesn't it?

[pine prairie]

it does

[cunning ruin]

Can you please teach me the proper definition of limit?

[pine prairie]

i just did

[sharp whale]

I can show you a way to understand how to use it

[pine prairie]

i would argue that sequential limit is far easier to understand than epsilon delta

perhaps you should start from there

[sharp whale]

that is true, I forgot about that definition

part of the usefulness of epsilon-delta is that there are other ways that act the exact same way as epsilon-delta

[pine prairie]

i rather like the decreasing epsilon and increasing N, the constrast makes it easier to grasp imo

[cunning ruin]

How can I use this definition to solve some problems?

Do you have a pdf on hand that I may go and solve?

[pine prairie]

show that x^2 is continuous at 0 and is equal to 0

[cunning ruin]

Please share the solution as well, so that I can understand the definition

[sharp whale]

you can also search up "epsilon-delta proofs" to see more examples

if you want I can show you an easier limit and how it would be solved

[dusky pulsar]

Sorry a bit off topic but I need a movie on this channel conversation

[sharp whale]

doesnt seem angry or eventful enough to require one

there are worse ones

this just seems reasonable

[cunning ruin]

@pine prairie how would you argue that

[pine prairie]

https://www.youtube.com/watch?v=kVQNhAIFZYc this video looks pretty good

i just skimmed it but it looks like they go through the ideas well

[cunning ruin]

the greatest integer function(thanks for sharing the video link) is continuous at non integral points?

[pine prairie]

integer*

yes

[cunning ruin]

We look at the graph(which is a series of steps), and consider one step and leave it's integer to the side, we get an open interval.

How should I argue that the function is continuous in this open interval...?

[sharp whale]

you should get a good sense of epsilon-delta before trying to attack this problem

[pine prairie]

your function is in fact very easy to show continuity even

[cunning ruin]

Please show me how to do it

[pine prairie]

the fact that constant functions are continuous is very easily shown

you should watch the video first otherwise you won't understand what im saying even if i write you a proof

[sharp whale]

you just need a sense, it wont require much work as soon as you get the sense

[cunning ruin]

Please do, even if I have to do more work in the end

[sharp whale]

you might as well consider the work of watching the video

[pine prairie]

watch the video first

[sharp whale]

this isnt a movie, youll have to sludge through the entire video but its a necessary pain we have to go through

one of the benefits for a commonly accepted definition is that there's videos and explanations for epsilon-delta everywhere if you search for them, we showed you an example up there

[cunning ruin]

Thank you for the help.

@sharp whale do you accept dms?

[sharp whale]

sure, but I cant guarantee Ill be up to answer questions

[cunning ruin]

We gotta talk some things through, you and I

.close

[vale dock]

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[sharp whale]

right

[vale dock]

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[waxen berry]

given a unit circle, consider a convex polygon which contains the unit circle, if the area of the polygon is A, what is the maximum possible perimeter? if there is no maximum possible perimeter, what is the supremum possible perimeter

[waxen berry]

i am basing this off a question i have seen earlier which showed if a convex polygon has area A and perimeter P, then there exists a circle of radius A/P completely inside the polygon, the proof involves drawing rectangles of width A/P on each side of the polygon

if that helps

[late helm]

Hey anyone wants to work with me on a theory that explores symetries and prime numbers?

[safe fulcrum]

wrong place to ask

[shadow moss]

do you mean one that is contained within the unit circle?

otherwise i could just make a very large square

[late helm]

could you direct me?

[safe fulcrum]

#math-discussion

[late helm]

I do not have access.

[safe fulcrum]

ah go to id:browse

it's math-discussion

[karmic bloom]

the area is fixed, its A

[shadow moss]

ah

[karmic bloom]

so one thing is its upper bounded by 2A i think
suppose the sides are s_i, distances from centre of circle to the sides be d_i then
A=sum of 1/2(s_i)(d_i) and P = sum of s_i
now d_i>=1 gives P<=2A

[waxen berry]

you have bounded area

[waxen berry]

hm

[karmic bloom]

now if u can construct somethin with 2A perimeter then

hm

[waxen berry]

how did you prove d_i >= 1, i know it make sense, but idk how to prove it

[karmic bloom]

it contains the unit circle so d_i has to be more than radius=1

[pure patio]

uh but if you take an equilateral triangle of area A

[waxen berry]

well, if convex was not there i culd give you a counter example

[pure patio]

oh frick

[karmic bloom]

what is P/A

for this

[waxen berry]

it is that thing multiplied by root(A)

so you have to divide this thing by root(A) to get the answer

minimum value of A in which this works is

P/A is exactly 2 in this case

[karmic bloom]

oh nice

[waxen berry]

for minimum A

[karmic bloom]

so you just constructed an example with P=2A

thats the max then yeah

[waxen berry]

not for all A

only for one particular value of A

[karmic bloom]

oh

what is the triangle btw

[waxen berry]

also, we havent proven di >= 1

[karmic bloom]

the circle is inside it

so every d_i will exceed radius

is that not a satisfactory argument

[waxen berry]

no

[karmic bloom]

why

[waxen berry]

here

EF is outside the circle

but it is closer to C then 1

[karmic bloom]

hm

but that wont make a convex but I get your point

[waxen berry]

ik, but how would we prove it?

[karmic bloom]

let me think

[waxen berry]

oh i proved it, assume such a line exists, then all other points must be on one side of that line, but the circle must be completedly contained in the convex hull of all points, this is a contradiction

[karmic bloom]

oh yes

[waxen berry]

this actually solves the qn for areas under 3root(3)

because for that i could just make a shape always tangent to the circle

so we have A<=3root(3) P_max = 2A

but what about for A higher then 3 root(3)

oh this is wrong

i cant always make a shape tangetnt to the circle

for A <= 3root(3)

i can do it for A higher then 3 root(3) though

[karmic bloom]

how?

[waxen berry]

just by shifting one line slightly

oh actually i can do it for A lower then 3root(3) as well

i can just consider a n sided regular polygon

and i can shift the sides smoothly

hm

so we have a maximum of 2A for all A > pi

what about this, interms of A and P, what is the maximum size of circle we can fit into any convex polygon with area A and perimeter P

[karmic bloom]

again r<=2A/P by same summation

but is it attained or not

[pure patio]

it works if you consider an equilateral triangle i think

.

[vale dock]

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[fair wing]

If the D of a quadratic eqn is D > 0 and not perfect square then roots are irrational and occur in conjugate pair similarly for D < 0 roots imaginary and occur in conjugate pair. What makes them occur in conjugate pair? why

[stark wedge]

well if you think about the quadratic formula

you get x = -b/(2a) ± sqrt(D)/(2a)

[fair wing]

Yes

same thing goes here?

±

[stark wedge]

if D is negative it's in the form of u ± iv for u, v real

these are by definition a conjugate pair

you can prove a more general result concerning complex roots: for a polynomial of any degree with real coefficients, all its roots are either real themselves, or come in conjugate pairs

[fair wing]

How do i come to know any random polynomial has the roots your talking about

[stark wedge]

basically prove this: for a polynomial P with real coefficients, if some complex number z is a root of P i.e. P(z)=0 then z* will also be a root

this can be proved via $P(\overline{z})=\overline{P(z)}$

[rocky lotus]

Ann

[fair wing]

z* is another new root?

[stark wedge]

no

z* is conjugate of z

[fair wing]

Ok

[stark wedge]

i usually write conjugate with overline but it is not plain text friendly

[fair wing]

What does the bar means

I don't understand overline thing

[stark wedge]

... i just said

please read my messages

[fair wing]

Kk

[stark wedge]

i do not want to repeat the same things many times

[fair wing]

Mb

[vale dock]

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[hearty garnet]

Can anyone solve this for me

[hearty garnet]

All multiple choice questions

[crimson crow]

this isnt a feeding answers/crunching problems server, you can ask to be explained a fundamental concept that may apply to a wider section. Read #info

[gleaming kindle]

@hearty garnet we're not chegg

[vale dock]

@hearty garnet Has your question been resolved?

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[stray jewel]

What is the definition of intramolecular forces and intermolecular forces

[verbal badger]

intramolecular: forces within molecules
intermolecular: forces between molecules

[stray jewel]

Thanks

Oop I just realized this is the math discord not the science

Mb y'all

[safe fulcrum]

Google it lmao next time

[stark wedge]

intra- means inside ie within one thing
inter- means between things

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[peak heath]

Can someone explain to me why for a) you use the numerator and for c) you use the denominator??

Other way round even

But u know what I mean

[daring orbit]

do u guys learn about difference equations in math?

[distant galleon]

Your answer for c is wrong so

,w (3 ln x-7)/(ln x-2), x=1

[peak heath]

Its not

[rocky lotus]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[peak heath]

Oh

Strange I copied it from a mark scheme

Thanks tho

[distant galleon]

Whoever made it is a muppet then

[peak heath]

Yup

Wait but they're getting rid of the denominator

That's the thing

They're only looking at the top part

So 3lna - 7 > 0

So it is right

[distant galleon]

????

And when ln a - 2 is negative?

Then you’re multiplying both sides by a negative quantity but not flipping the direction

Look at what I sent above

[peak heath]

Hmm

For part a they use the denominator to deduce k

And here the numerator so like what idk

[distant galleon]

Idk what to tell you other than that c is wrong

Whatever floats your boat

[peak heath]

Lol ok I'll look at it again 😔😭

Thanks

. close

.close

[vale dock]

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[peak heath]

.reopen

[vale dock]

✅

[peak heath]

Wait u are right lol can u explain what I would do then

[distant galleon]

Consider what you can multiply by for this to not be an issue

Alternatively use some common sense to determine when a quotient is positive

[peak heath]

Ah ok I get it now

Thanks

.close

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[serene jetty]

The Golden Gate Bridge is an iconic structure spanning the neck of San Francisco Bay, connecting the city of San Francisco at the northern tip of the San Francisco Peninsula with Marin County near the town of Sausalito in the south. The spans of the bridge are 1,280 meters, and the towers are 230 meters above the water. The cables between the towers are in the shape of a parabola. The parabola is located in the Oxy coordinate system as shown in the figure, with the vertex of the parabola coinciding with the center of the road. Point A on the parabola is shown in the figure. Find the height of the cable at a position 200 meters from the towers (round the result to the nearest unit).

[serene jetty]

help me

help plss

[vale dock]

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

[serene jetty]

1

The Golden Gate Bridge is an iconic structure spanning the neck of San Francisco Bay, connecting the city of San Francisco at the northern tip of the San Francisco Peninsula with Marin County near the town of Sausalito in the south. The spans of the bridge are 1,280 meters, and the towers are 230 meters above the water. The cables between the towers are in the shape of a parabola. The parabola is located in the Oxy coordinate system as shown in the figure, with the vertex of the parabola coinciding with the center of the road. Point A on the parabola is shown in the figure. Find the height of the cable at a position 200 meters from the towers (round the result to the nearest unit).

[pure mirage]

Well, it's a long text, for these, the best thing is to just take the minute and quickly read through it

In the end, all that is needed is the diagram

There might still be some additional info that is relevant, which is not really the case here

[serene jetty]

i dont know how to find the height

[pure mirage]

Can you mark the position that you want the height of

(Just approximately)

[paper verge]

you could try to sketch it in a more clean place aswell, might help u see points

[serene jetty]

alright

thanks

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[ember trellis]

In case that there is a Vector-space, with the dot product $\langle\cdot,\cdot\rangle$. For all subspaces $U,W\subseteq V$, the direct sum $U+W$ is defined as.
$[U+W={u+w|u\in U,w\in W}]$
how can I show, that $V=U+U^\bot$?

[rocky lotus]

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

[ember trellis]

In case that there is a Vector-space, with the dot product $\langle\cdot,\cdot\rangle$. For all subspaces $U,W\subseteq V$, the direct sum $U+W$ is defined as.
$U+W={u+w|u\in U,w\in W}$
how can I show, that $V=U+U^\bot$?

[rocky lotus]

McMake

[ember trellis]

there we go

[rough jacinth]

Good job

[ember trellis]

ty

[rough jacinth]

I can't help you though, bcz i can't make a head or tail out of it 😅

[ember trellis]

alright. thank you tho

this is university math

[rough jacinth]

OoO, that's what i thoughhhh

[spark sluice]

Well thats not the definition of direct sum

[ember trellis]

ive translated from german. im sorry if some terms are incorrect

[spark sluice]

V is a direct sum of U and W if V= U + W and U intersection W = {0}

[ember trellis]

its the case in the end of the qeustion anyway, since I am using the orthogonal complement

[spark sluice]

Yes

[ember trellis]

but ty

[spark sluice]

Okay so you want to show that for any vector $v \in V$, we have $v = u + u'$ where $u \in U$ and $u' \in U^{\bot}$

[rocky lotus]

Herbert

[spark sluice]

What have you tried?

[ember trellis]

ive tried showing that via orthogonal projection, but I cannot finish the calculation

since $\langle v-u,u\rangle=\langle v,u\rangle-\langle u,u\rangle$ but that doesn't get me to anything

[rocky lotus]

McMake

[spark sluice]

Okay, so I would try taking a specific basis for U and U^{\bot}, and showing that their union is a basis for V and so we get our result (since you say you have shown U intersection U^{\bot} = {0})

[ember trellis]

u

uhh

how do I make a basis out of both, that fulfills that definition?

i haven't done anything like that before

[spark sluice]

Do you know gram schimdt orthogonalisation?

[ember trellis]

yes

[spark sluice]

Ok, so take an orthonormal basis for U, say ${e_1,e_2,...,e_n}$ and define the projection onto U $\pi : V \rightarrow V$ by $$\pi(v) = \sum_{i=1}^{n}\langle v,e_i\rangle$$
Then any vector $v = \pi(v)+ (v-\pi(v))$. Then if you show $\pi(v) \in U$ and $v-\pi(v) \in U^{\bot}$, you are done

[rocky lotus]

Herbert

[ember trellis]

this only gives one point and makes me concerned for my future

I thank you very much

i think that works

.close

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[spark sluice]

Yes, but i hope you showed it

[ember trellis]

"it"?

[spark sluice]

I mean the statement that pi(v) in U and v - pi(v) in U^{\bot}

(To complete the proof)

[ember trellis]

yes

tyvm

[vale dock]

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[green shore]

Can anyone help me? I have dyscalculia and have been stuck on this one problem for a few days because i dont really understand the material

[pine prairie]

!da2a

[vale dock]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[green shore]

I guess im just not sure how to differentiate? can someone explain the difference to me?

I read the material provided but it didnt really make sense to me, is their a simpler way this could be explained to me?

Every "rule" im given to find the difference seems to also apply to the other 2???

any help is appreciated

[broken orchid]

do you know what a derivative is?

[green shore]

Yes, i do however have a math disability that makes this super hard for me

I know its a dumb question

[broken orchid]

no it's alright

it's not a dumb question

okay, lets start with putting the question into our own words to understand better

[green shore]

alright

[broken orchid]

could you repeat to me, in your own words, what the question is

[green shore]

Well theres 3 curves that are showing the motion of a particle along a coordinate axis at t (which i think is seconds) They are all polynomials and related, but i need to pick drag S(t) and A(t) and V(t) to their respective graph lines

Its just that the rules to differentiate them make no sense to me

[broken orchid]

ahh I see

[green shore]

It refers to hills and valleys like they all dont have that

[broken orchid]

your understanding of the question is fantastic

[green shore]

Thank you

[broken orchid]

do you know what a derivative is?

[green shore]

Im very rusty on this so im a little foggy on how to find them without power rule or like L'Hopitals

[broken orchid]

L'Hospitals is not nessacary

okay

let's start with the power rule

[green shore]

alright

[prisma nova]

Shouldn't the acceleration graph be straight @broken orchid

Any one of them ?

[broken orchid]

no

[green shore]

Thats what i thought!

[broken orchid]

This question actually tests your understanding of polynomial functions and their graphs more than your physics or calculus knowledge

[prisma nova]

Ok I need an understanding too

[broken orchid]

the acceleration graph should not be a line

Hint: the position function is actually a polynomial to the fourth power

[prisma nova]

Position function Can't be to an even power but yes any odd power

[green shore]

I assumed the parabola was the s(t) but a friend said i was incorrect

[broken orchid]

?

what are you talking about?

[broken orchid]

your friend is right

[green shore]

I thought so…

[prisma nova]

Oh so any higher odd power polynomial can look like cubic function am I right?

[green shore]

If thats not the position function then im not sure how to tell which of the other 2 is? what am i looking for?

[broken orchid]

Remember my hint

[prisma nova]

Nvm

[broken orchid]

remeber that the power rule is that d/dx ( x^n) = nx^(n-1)

[green shore]

so by that logic s(t) would be the solid line?

Wait no

The dotted one i think

[broken orchid]

that's beyond the scope of this question. Maybe some series expansion of odd power functions could approximates a cubic near 0, but I'm not sure.

[broken orchid]

👍

[broken orchid]

I'm assuming you mean the round dot line

[broken orchid]

👍

[green shore]

with your help i think i got it

[broken orchid]

not quite

[green shore]

MANNN

[broken orchid]

very close

remeber that d/dx (x^n) = nx^(n-1)

each derivative decreases the power by 1

[green shore]

Im writing this down hold on

[broken orchid]

Hint: odd functions can be negative, even functions can't (unless it has a negative coeffiecient)

[green shore]

I have one more of these left , lemme try to use that rule

[prisma nova]

@broken orchid the little irregular change in gradient of dotted graph indicates it maybe with highest degree or is there any other logic?

[green shore]

I think i did it right this time

[broken orchid]

note that the general shape of a polynomial function will adopt the shape of the highest power polynomial as abs(x) increases. It is not possible of a O(x^2 ) function to have such a bump becuase all x^2 functions can be factored into y = a(x-b)^2 + c

[broken orchid]

not quite

[green shore]

damn it

Im really trying

[broken orchid]

actually, every answer is wrong

[green shore]

REALLY??

[broken orchid]

trying is what matters

[green shore]

is a(t) represented by the straight Line? i thought about that

[broken orchid]

I think the real problem is that you don't have a solid understanding of how polynomial functions can be graphed

[green shore]

Is very hard to explain anything like this to me in a way where i understand, Dyscalculia is a horrible thing to have

Im really trying to get the rules

[broken orchid]

indeed

[prisma nova]

Maybe he first needs to know how position, velocity and acceleration correspond to each other and then with help of derivatives question can be crack

[broken orchid]

I think we should start from the basics of polynomials

There are a few rules about polynomials that will help you deduce the answer:

even power polynomials will only trend towards one infinity as x increases or decreases

[green shore]

okay..

[broken orchid]

odd power polynomials will always trend towards both infinities as x increase or decrease (the particular positive or negative slope isn't import in this case)

[green shore]

Arent they all trending towards infinity?

[broken orchid]

polynomial functions to the second power will always be a bumpless parabola as all functions of x^2 can be repersented as a(x-b)^2+c

[broken orchid]

by both infinities, I mean positive and negative infinity

by one infinity, I mean only positive or only negative infinity

[green shore]

second power meaning a(t)?

[broken orchid]

second power meaning any polynomial functions of the form ax^2+bx+c

where the highest power is 2

[green shore]

Can you explain this in laymens terms? i have no idea

[broken orchid]

you know what the general form of a polynomial function is yeah?

[green shore]

Not sure how to type it but vaguely

[broken orchid]

a polynomial function of the second power, is that but the highest power is 2

[green shore]

Alright

Ket me see if i can apply this to something rq

So a(t) is most often represented as a straight line correct?

I might be confusing it with v(t)

This is so confusing man

[broken orchid]

yes and no

[green shore]

oh?

[broken orchid]

given that you have three lines, s(t) v(t) a(t)

the lines v(t) a(t) are most likely to be lines, if your teacher isn't devious with making the questions

however, all three lines could be straight

if your teacher is a devious person

[broken orchid]

However, this does not mean that it is like for v(t) and a(t) to be lines.

like with the first example, all three could be curvy

alright, I have to go now

[green shore]

I understand

Thank you for trying to help

[broken orchid]

there should be other people here to help you, @ the helpers if no one comes for a while

[green shore]

<@&286206848099549185> I need help, i dont know how to do graphing questions and im not sure how to continue

[static birch]

ok, ask on.

so, you want to mark the main details

asymptotes, extremum

whatever they asked

[green shore]

Kinda? i have a bunch of questions i dont know how to answer, i understand derivatives when used numerically, but graphically i just dont get it

Like this for example, if this was not a graph question i could work it out but Derivatives of graph lines just dont make sense

This was an easy one i actually knew how to answer but you get the gist

[green shore]

I tried using the x-x/y-y rule but i dont think im doing it right

I followed the tan line to choose a point but im not sure how to determine WHICH point i should use

Does it matter?

<@&286206848099549185> The answer is 1 right? Partner is telling me its 2

[static birch]

no rules.

[green shore]

oh alr

[static birch]

1.5 to 2

use a compass.

[static birch]

just hard done practice.

[green shore]

Wait which point was i supposed to use??

i knew (-1,-1) but the other?

[static birch]

x=-1

[static birch]

for each x theres one y.

[green shore]

it was 1

the answer was 1

[static birch]

i dont know. i didnt use a compass

[green shore]

I get cha

Trying to learn how to use this

[static birch]

just practice parabolas.

[green shore]

Not sure how to work out when the point is at the peak?

[static birch]

f'(x)=0

meaning, the slope is 0!

you can see here, x=-1

and y=3

max {-1,3}

[green shore]

Alright, now i just gotta find the derivative for x+-1

x=-1

[static birch]

thats how you write it.

[green shore]

mb

[lyric sundial]

y= -(x + 1/2)² - 3/4

y' = -2(x + 1/2)

So yes it's 1

[static birch]

no, x=-1±1

[green shore]

hm?

[static birch]

or, you can even use x=1±e

but 1 is nice

so you check one for 0, one for -2

[green shore]

im so lost

[static birch]

because we already know that f'(-1)=0

[static birch]

you go right and left to it

x=5.31 isnt nice

go for x=5

or x=-10

those are nice numbers.

[green shore]

huh?

How would i choose those?

[static birch]

choose an x, nice to work with, smaller than -1.

maybe, -2

maybe -10

[green shore]

-10 isnt on this graph...

How would i use that?

[static birch]

then use -2

you wont put there a million, bc thats too big

its dumb

[green shore]

I though to find deriv, i needed to use the tan line?

[static birch]

so go close

[static birch]

is it desmos?

geogebra?

i dont know those systems

i work on paper

[green shore]

Stupid ass site called "knewton" i had to pay to use

[static birch]

YOU PAID?

god damn bro.

[green shore]

Yep,

[static birch]

god save you lol

[green shore]

Im really trying man

[static birch]

use desmos

its free and better

[static birch]

no no, if you are trying

hit the notebook!

[green shore]

I just dont know how to find the deriv of this, im trying but everyone is telling me different things

[static birch]

ok, so theres a formula

a general formula

f(x)=ax^b

you know this form?

2x^2, 5x^4, 3x^2.5

[green shore]

yes

[static birch]

in this case, the derivative is

f'(x)=ab x^(b-1)

@green shore just ask for practice anytime

[green shore]

sorry, trying to work this one out

[static birch]

the skills you really want, are quadratic formula

basic algebra (dont need to know 7^7, its useless)

[green shore]

Im using a weird formula

[static birch]

mx+d=ax^2+bx+c?

[green shore]

no a fraction one

[static birch]

huh.

[green shore]

this one i believe

[static birch]

thats...

so unrelated

who taught you this?

[green shore]

I have dyscalcula man, they all genuinely look the same to me

I have trouble telling the difference

[static birch]

i dont remember formulas

i remember how to do it

its muscle memoru

[green shore]

no no, i mean the LOOK the same to me

Its hard to explain'

[static birch]

i dont know the formula, it takes a lot of thinking for me

[static birch]

use markers.

[green shore]

i just.. dont know how to do this, and eveyones using these big math words and formulas i dont understand

I have a math disability man, and this is very tough for me

[green shore]

im trying to use this

[halcyon lintel]

anyone here know autocad?

[prisma nova]

What's that?

[lyric sundial]

!occupied

[vale dock]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[green shore]

thank you

[halcyon lintel]

the 2d drawing software

by autodesk company

[prisma nova]

@green shore you know the function of the curve given?

[green shore]

sadly no, only the curve

[prisma nova]

Ok so can you plot any desired straight line on the graph

[green shore]

I have to move the black point wheres its deriv is 5

[static birch]

i know the problem

i had equations longer than the width of the page

the solution, mark in colors

[prisma nova]

It's impossible to do it manually either you have to have an equation of curve or be able to draw a line with slope 5 so you can drag the point and make parallel to it

[static birch]

hahaha autodesk. i hate autocad.

[halcyon lintel]

@static birch why?

Q

[static birch]

solidworks>autocad

[halcyon lintel]

Do you know how to find the downward angle of G using polar coordinates?

[static birch]

kinda bad comparison

but for that kicad>autodesk

[green shore]

Dude, all I’m given is this graph and the question of which point makes the derivative equal to five

[static birch]

360-alpha

[lyric sundial]

!occupied

[vale dock]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[halcyon lintel]

Is kicad open source version?

[halcyon lintel]

That's what I tried

[static birch]

theres freecad, freescad too.

[halcyon lintel]

Yea but my course teaches autocad

It's industry standard

[static birch]

what can i do?

[static birch]

solidworks is.

[halcyon lintel]

But I did 360-alpha

[static birch]

solidworks is far more expensive tho

5000 dollars a year

[halcyon lintel]

But my drawing is wrong

[static birch]

im the god of 3d modelling, not 2d

[halcyon lintel]

Isn't it basically 270+25?

[static birch]

but for 2d i know of freecad, freescad, kicad

[halcyon lintel]

115-90=25

Then to get the downward line it's basically 270+25

[static birch]

i have like 500 to 900 hours modelling

[halcyon lintel]

295deg?

[static birch]

and algebra, 2000 hours

[static birch]

the calculation is

[static birch]

wait what

[green shore]

I genuinely think my help session got hijacked

[static birch]

it was.

[halcyon lintel]

Yea 115-90

[static birch]

want in dms?

[halcyon lintel]

Cause the given inside angle is 115

[prisma nova]

Dudes

Get out

[halcyon lintel]

Why?

[static birch]

not yours.

[lyric sundial]

!occupied

[vale dock]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[halcyon lintel]

Oh is this help channel?

[lyric sundial]

For the 3rd time!!!! @halcyon lintel

[halcyon lintel]

I thought it was main chat

[static birch]

for specifically little e

[green shore]

no, no you have to go to the other chat to ask for help

[static birch]

ask on little one

[green shore]

There’s a bunch of ones on top they should say available

[halcyon lintel]

My bad...I don't know why i auto joined this room

[static birch]

i can handle 10 people too

[halcyon lintel]

Can you help in dm

[static birch]

yes

[halcyon lintel]

K let's do it

[vale dock]

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[stark wedge]

mate just post the question(s) you need help with

dont beat around the bush

yes we can help you

[vale dock]

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[fresh isle]

how to simplify this imaginary number :

(cosθ + isinθ)/(cosθ - isinθ)

[spark sluice]

multiply the denominator and numerator by the conjugate

[fresh isle]

i tried and i got some expression but i can't tell if it's correct or not

[spark sluice]

show your work

[fresh isle]

can i send a pic and u tell me?

my handwriting sucks

i hope u can understand

[spark sluice]

thats correct

[fresh isle]

there's no more simplified expression of it then?

[spark sluice]

THERE IS

do you know $\cos ^2 \theta - \sin ^2 \theta = \cos 2\theta$ ?

[fresh isle]

nope i don't..

[rocky lotus]

Herbert

[spark sluice]

do you know any identity for cos 2\theta?

[fresh isle]

naah i didn't memorize any of these

i only know cos² + sin² = 1 lol

[spark sluice]

well you need to know atleast one identity for cos 2theta and sin 2theta

[fresh isle]

i see

[spark sluice]

do you know any identity for sin (a+b) and cos(a+b)?

[fresh isle]

nope either 😅

[spark sluice]

okay then this is as much as you can simplify it

[storm perch]

Have you considered writing in exponential form?

[fresh isle]

no i didn't

do i need to?

[storm perch]

Do you know it?

[spark sluice]

do you know exponential form?

[storm perch]

It'll help with the simplification.

[fresh isle]

yeah

[spark sluice]

okay then write them in exponential form

[fresh isle]

re^iarg right?

[storm perch]

Oh, great! Try to write it in exponential, then.

[fresh isle]

okay

[thin nebula]

hello guys I apologize for the suddent cry for help

[storm perch]

!occupied

[vale dock]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[thin nebula]

I'm sorry I'm kinda new to the this discord channel but I'm kinda missing the help channel even after following the steps do you mind pushing me in the right direction

basically I can't do step number 1

[storm perch]

https://discord.com/channels/268882317391429632/908078008609431674

Message there.

[fresh isle]

i ended up with e^iθ

[storm perch]

Show your work.

[fresh isle]

ohh wait i made a mistake

ill do it again and send u the pic

sorry id I'm taking too long

[storm perch]

Ok.

[storm perch]

,rccw

[storm perch]

Good.

[fresh isle]

so in this case

Z = cos(2θ) + isin(2θ)

okay ty for help

appreciate it

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[heavy iris]

ello

[heavy iris]

i need to find the derivative of sqrt 2x

[midnight pier]

using the limit definition ?

[heavy iris]

or power rule

[tepid wind]

First, you can recognize that $\sqrt{2x} = \sqrt[2]{2x} = (2x)^\frac12$.

[rocky lotus]

@tepid wind

[tepid wind]

From here, it becomes easy to apply the Power Rule of Differentiation.

[heavy iris]

and i keep getting 1/sqrt x

[tepid wind]

Can you show your work?

[tepid wind]

You can't change $(2x)^\frac12 \implies 2x^\frac12$.

[rocky lotus]

@tepid wind

[heavy iris]

oh i c

but then i’m getting 1/2• 1/2sqrt x

[polar oxide]

what happend to the sqrt2 ?

,, (2x)^\frac{1}{2} = \sqrt{2} \cdot x^\frac{1}{2}

[rocky lotus]

<rajel />

[polar oxide]

it should be $\frac{\sqrt{2}}{2\sqrt{x}}$

[rocky lotus]

<rajel />

[heavy iris]

i don’t see it

[polar oxide]

wdym ?

,, \frac{\dd}{\dd{x}} \left(\sqrt{x}\right) = \frac{1}{2\sqrt{x}}

[rocky lotus]

<rajel />

[heavy iris]

you dont need chain rule?

[polar oxide]

you do

[heavy iris]

oh

she hasnt taught us yet

taught us that*\

[polar oxide]

,, \frac{\dd}{\dd{x}}f(x)^n = n\cdot \frac{\dd}{\dd{x}}(f(x))\cdot f(x)^{n-1}

[rocky lotus]

<rajel />

[polar oxide]

you can apply the same thing for: $\frac{\dd}{\dd{x}} x^{\frac{1}{2}}$

[heavy iris]

wtf\

[rocky lotus]

<rajel />

[heavy iris]

my teacher has legit taught "the power jumps down and leaves behind one less than itself"

[polar oxide]

well thats true , *for simple functions *

i.e for any x^n

[heavy iris]

but it doesnt work here?

[polar oxide]

it does

i just wrote the general rule

that works for any function

[heavy iris]

but based off of this alone can you not find it?

[polar oxide]

try it

,, \frac{\dd}{\dd{x}}x^n = n \cdot x^{n-1} \cdot \frac{\dd}{\dd{x}}(x)

[rocky lotus]

<rajel />

[polar oxide]

it works without adding the derivative because its just 1

but for any other function it wouldnt

[heavy iris]

how is it just one

its 2x

wouldnt it be 2?

[polar oxide]

thats because of the constant

the constant doesnt matter when its about derivating , we keep it aside and we work with main function

i.e the result would be multiplied by that constant

,, \frac{\dd}{\dd{x}}(3x^3) = 3 \cdot \frac{\dd}{\dd{x}}(x^3)

[rocky lotus]

<rajel />

[polar oxide]

it is 1 , but became 2 cuz of the constant

just try to derivate it and you'll get what im saying

[heavy iris]

i got it

but like how are you supposed to do that only knowing that na^(n-1)

because when you blindly apply that you get smth weird

[polar oxide]

i dont follow

you shouldnt apply anything blindly anyways

[heavy iris]

I know but thats the only context she gave us

see what im saying?

anyways

ty

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[charred fulcrum]

Given a point P and a line r in space, with P not on r. How many lines in space pass through P and are perpendicular to r?

[charred fulcrum]

in 2d it's quite easy, it's a unique line

in 3d when looking for orthogonal lines we do cross product, with the lines' directional vectors

so it should be infinitely many lines?

if the lines dont intersect with the line r

idk tbh

[vale dock]

@charred fulcrum Has your question been resolved?

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[analog harbor]

How do i solve this question? Investigate graphically and show with a simple sketch whether there any v such that 2sin(v+12°) = cos(v+23°) for 0° < v < 180°

[analog harbor]

I put it into geogebra but i don't know how to make the x axis into degrees

[shadow moss]

do you know how to convert radians to degrees?

[analog harbor]

yes 180/pi

[steady charm]

in the geogebra keyboard there should be a degrees symbol somewhere

[shadow moss]

you can multiply by that on the inside of the sin to convert to degrees

or that

[steady charm]

(although all the degrees symbol does is multiply by 180/pi)

[analog harbor]

it looks like this

[shrewd marten]

you can just plot your bounds as well

since 0 deg = 0 rad and 180 deg = pi rad

you can plot x = 0 and x = pi

and see if there are any intersections between the two vertical lines

[analog harbor]

like this?

[shrewd marten]

yes

so now we can tell if there are any intersection points within the given bounds

[analog harbor]

so the answer would be 0.211*(180/pi)

[shrewd marten]

yes, 0.211 * 180/pi degrees

or just 0.211 radians

although if you're rounding it should be 0.212

[analog harbor]

alright thank you very much!

[analog harbor]

yup ill fix

have a nice day

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[acoustic laurel]

where do i start

[frozen ledge]

look where the tangent line changes from above the curve to below the curve or the other way around

[acoustic laurel]

i think im dumb

[frozen ledge]

happens

[acoustic laurel]

just that i dont know what your talking about

[frozen ledge]

you don’t know what a tangent line is?

[acoustic laurel]

like graph of a tangent or slope of a tangent line thing?>

[frozen ledge]

no like literally a tangent line

when the line changes from above —> below or below —> above you have a point of inflection

[acoustic laurel]

i think im just dumb

[frozen ledge]

damn

what’s your 2s rank though

[acoustic laurel]

um like plat to diamond

[frozen ledge]

tough

😭

[acoustic laurel]

you

[frozen ledge]

i was gc2 back in the day

gc1 in 1s and 3s

i played from like

2020-2022

[acoustic laurel]

i started in like 2016

[frozen ledge]

yea i played in 2015

but like played fr during 2020-2021

i played here and there from 2015-2019

[acoustic laurel]

ive just been on and off

[frozen ledge]

i was like all star back in the day

you might remember that

rising star

[acoustic laurel]

didnt pay that much attention

[acoustic laurel]

i dont remember

id be down to play eventually

if you are

[frozen ledge]

maybe

maybe over the weekend or something

[acoustic laurel]

ok

could i dm you

[frozen ledge]

yea idc

[acoustic laurel]

that?

im an idiot i think i need to see examples of it to understand

[frozen ledge]

not quite

[acoustic laurel]

any of them right?

[frozen ledge]

basically it’ll look like a line when there’s a point of inflection

looks like x = -0.5 and x = 1.5 to me

[acoustic laurel]

oh its where it turns from one concave to the opposite pretty much

[frozen ledge]

yea

[acoustic laurel]

i feel stupid

[frozen ledge]

happens

[acoustic laurel]

i litterally didnt understand

where oit changes from concave up to down

.close

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[ornate dragon]

#help-21｜아리스킨충1 message

Asked this earlier. Had to leave

"Check that the following implicitly defined function are solutions of the corresponding differential equations"

Solving a)

I'm not sure what it is I'm supposed to do. Do I find the derivative for the implicit solution?

a) is not homogeneous. I've checked

[frozen ledge]

i mean you can literally just find dy/dx

from implicit differentiation

you need to verify that

$\dv{y}{x} = \frac{-2xy}{x^2 + 2y}$

[rocky lotus]

knief

[frozen ledge]

which follows immediately basically

[ornate dragon]

i'm not really following

sorry

[frozen ledge]

what don’t you understand

[ornate dragon]

hm

"A relationship G(x,y) is an implicit solution of an ODE F(x,y,y',...y^(n)) = 0 with x in I if phi exists such that G(x,phi) = 0 and F(x,phi,phi',...,phi^(n)) = 0"

so phi is x^2y + y^2 - c = 0?

plus c i guess if it's just a constant

F(x,y) = 2xydx + (x^2*2y)dy

[frozen ledge]

this makes it all over complicated tbh

[ornate dragon]

maybe

[frozen ledge]

you have the relation x^2y + y^2 = c

[ornate dragon]

i'm just trying to understand whats going on

yeah

[frozen ledge]

you need to show that you get 2xy dx + (x^2 + 2y)dy = 0

[frozen ledge]

so just differentiate both sides

[ornate dragon]

in relation to what?

[frozen ledge]

i mean i don’t think it matters?

if you assume y is a function of x it works

if you assume they’re both functions of something like t it’s fine too

not sure how rigorous this needs to be

[ornate dragon]

its the second exercise in the first ODE exercise guide

probably not too rigorous

@frozen ledge

this okay?

[frozen ledge]

yea

[ornate dragon]

alright neat.

thanks!

.close

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[frozen ledge]

you’re welcome

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[versed sedge]

is this correct?

[versed sedge]

also small mistake at the start i just saw it should just be r not r^2

im mostly asking about the integer, cause idk if its the correct one

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[versed sedge]

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[open thistle]

does anybody know how to do quadratic regression with the T1-84 Plus calculator?

[steady charm]

stat -> calc -> 5: QuadReg

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[subtle crane]

Hi

[subtle crane]

I need the formula for the perfect square trinomial

<@&286206848099549185>

<@&268886789983436800>

@safe fulcrum

[gleaming kindle]

@subtle crane dont ping individuals or mods for math help

[subtle crane]

Ok

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@subtle crane Has your question been resolved?

[static birch]

hi.

(ax+b)^2, yes?

a^2 x^2+2abx+b^2

[subtle crane]

Could you give me a picture?

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[unique pasture]

how do u do this

[viscid spade]

Euler formula

sin²(x) = 1 - cos²(x) = (1-cos(2x))/2

[unique pasture]

.close

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[stark wedge]

Ann Gets Rekt By 8th Grade Geometry: Part 3

all given info is on the picture. my progress is basically just working out the lengths i marked. and i worked out that angle PAB is 54°. but once again ive hit a big fucking snag.

[stark wedge]

well like also AD=a if it matters at all lmao

and DAP is 90°

and ADM is isosceles

but idk how that helps either

[rough talon]

wait if ABCD is a parallelogram then AB=CD no?

how is it AB=2DC

[ebon glade]

2BC. typo

[rough talon]

o

[stark wedge]

yeah this

[ebon glade]

god thats a normal 8th grade problem?

it feels like it would help to draw AM and MB. and then maybe something with AMBP ? but I dont know

ann you are not alone

[stiff fossil]

I suppose AD and BC are parallel to each other because BAD and ABP are alternate interior angles, arent they?

[ebon glade]

its a parallelogram

[silk coral]

The helper gets helped 🗣️🗣️🗣️

[stiff fossil]

Fr

[silk coral]

Not throwing shade btw

[rough talon]

ikr i dont think an eight grade even knows what a bisector is

[stiff fossil]

I think they would

[ebon glade]

not like you need that word

[stark wedge]

🇧🇬

[stiff fossil]

Bulgaria was one of my least expected countries with school curiculum as tough as that

Oh wow

[stark wedge]

yeah ngl i am actually hardcore skillissueing at this problem

like ive even given it to a colleague and she can't solve it

fun times!!!!!!!!!!!! (not)

[paper verge]

maybe its about 36 54 90 triangle properties? its not an exact match but in simple physics you just assume triangle's lengths are 3k 4k 5k

[stark wedge]

????

no

that's pretty wrong mate

a 3-4-5 triangle does NOT have angles 36 and 54 degrees

i can tell you for a fact this ain't it

[paper verge]

i might be remembering wrong my bad

[rough talon]

a more accurare diagram might help?

[stiff fossil]

I drew it on a paper geometrically accurate