help-49

[ocean dune]

So to prevent this the wise men need to ensure that every corridor has at least one wise man at one of its ends?

And since there are 100 rooms the wise men should place themselves so that each room has at least one wise man

And that way no matter wich corrider she chooses she'll lose

So the number of wise men is 100? Isn't that logic?

[nova pike]

Yes

[ocean dune]

So I believe the right answer is 100?

[nova pike]

Btw it’s not just 100, it’s finding all possible values

[ocean dune]

But they said the mininal

Minimal*

[nova pike]

Also you need to make sure that there are exactly 1000 corridors too

[ocean dune]

Develop?

[nova pike]

Sorry wdym?

[ocean dune]

I asked u wdym here

[nova pike]

Oh, it’s specified in the problem at the beginning. That there needs to be 1000 connecting corridors

[ocean dune]

oooh yep 1000 corridors and 100 rooms

[nova pike]

Yes, and not only just that, but there are many ways to connect the rooms by the corridors which is why there should be more than one magic number that exists. Because there can be different constructions just with the same 1000 corridors and 100 rooms

[ocean dune]

Yeah..I get it now ..

[fervent ember]

why cant it be 99?

[livid summit]

wait

do exactly 1 wise man go through a corridor each minute?

[nova pike]

yes

[nova pike]

because then at least there is a room with 0 people, from which Merlin can definitely make a series of iterations such that there are two connecting rooms with 0 people

[livid summit]

so for example when theres 3 rooms and 2 corridors

like a cherry

then the magic number has to be 3?

wait

mb

2

[fervent ember]

... can definitely make a series... are you sure?

[nova pike]

Oh wait, I actually retract what I said before. 99 works I think

[livid summit]

i think if 3 vertices and 3 edges

then 3?

[nova pike]

yes that should be it

[livid summit]

ok got it

i dont think the graph has to be connected right?

[nova pike]

I think it’s just a simple graph. that’s what someone else told before

[fervent ember]

for the win of merlin he must achieve such a situation:

then he could choose te connection AB and the wise man from B as to move to A.

[nova pike]

yes ofc he can

[nova pike]

yeah or similarly BC, so the wise men cannot act accordingly

[fervent ember]

so you do not need a wise man in every room

[nova pike]

nope

[fervent ember]

so i guess the minimal number is much lower than 100.

[nova pike]

the problem is that there could be more than one minimal number depending on your construction. ofc for smaller numbers like n=2 and n=3, theres only one, however for n=100 (this problem), there probably is more than 1 depending on the construction

[livid summit]

ah

[fervent ember]

how should there be more than one minimal number?

[livid summit]

its different every construction

there are 100 rooms and 1000 corridors

so depending on the construction of the rooms and corridors the minimum may vary

[nova pike]

we actually would have to list out all possible minimal numbers

[livid summit]

yeah

[fervent ember]

and what is the relevanz for my statement that i guess the mimimal number is lower than 100?

[livid summit]

my guess is that its 1000 for any construction

[nova pike]

i dont think so

[nova pike]

honestly, idk, im still working on the problem

[livid summit]

i think regardless of the number of vertices

the answer can be the number of edges

i think

thats what you can try to prove

i mean

its only a guess

and its true on sum smaller cases lmao

[nova pike]

yeah i can see so far

[livid summit]

i think this is true

@nova pike

[nova pike]

is there a rigorous proof behind it?

[livid summit]

idk

but hear me out

ive created an outline for the solution

you induct on the number of edges

assume that you have 100 rooms

and you just keep on adding an edge to an already existing graph

so the induction thesis would be that you need at least k wise men when theres k edges right?

[fervent ember]

so you would say if the castle has 4 rooms and 4 corridors (formed as rectangle) and you have only 3 wise man than merlin would win?

[livid summit]

yeah

[fervent ember]

show.

[nova pike]

yes, i would like to see how your idea works

[livid summit]

how do i even begin

[fervent ember]

take a rectangle A, B, C, D assume the wise man are on A, B, C than show the moves from merlin to win.

[livid summit]

ok

take A and B

then wise man of B has to go to A

[fervent ember]

no.

[livid summit]

or else A and D would be empty

now take C and D

[fervent ember]

no. on A and B are wise men. if merlin choose AB, A could go to B or B could go to A, the wise men decide.

[livid summit]

im saying if A goes to B

A and D would be empty

and merlin can simply choose AD

[fervent ember]

you said "has to go".

[nova pike]

also the wise men decide tactfully

[livid summit]

im saying that cuz if you dont, merlin would win

[nova pike]

im pretty sure merlin wins here

[nova pike]

ok, how does your induction work exactly?

[livid summit]

i was thinking of doing something like

its so hard to explain lol

like

taking a subgraph where the number of men in that subgraph is less than the number of edges

but this idea kinda sucks

[nova pike]

thats fine

[livid summit]

you should do somethin like

if the minimum is k

and k men are placed in the rooms

then there exists a sequence of moves for merlin such that

he can empty a given room

this gotta be something

[nova pike]

hmmm

[midnight plank]

@nova pike Has your question been resolved?

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@nova pike Has your question been resolved?

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[ionic magnet]

.close

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[glossy compass]

I don't think I'm doing this correctly 😭

[tribal temple]

And the question is turning points of y = ... in said interval, and if they're max/min?

[blissful summit]

Nice handwriting

Wats the question?

[glossy compass]

Analyze and sketch the graph

Label intercept relative extreme points of inflection and adymtops

Asymptotes

[blissful summit]

Ah so concave up down type stuff?

[glossy compass]

Yes

[blissful summit]

Ah

Im watching vids on how to sketch using concavity since its been a while

Brb

[glossy compass]

Help 😭 alr

I think (?) I derived it correctly

But idk how to find the points of inflection ans critical point

[blissful summit]

Check with the actual answer

Points of inflection i remember happen where the second derivative is zero

[glossy compass]

I did that but I think it's wrong

[blissful summit]

Y do u think its wrong

[glossy compass]

When i try to graph it it's not correct

But i got the critical point correct somehow

[blissful summit]

Dang this is hard. I was seeing what should x be at the critical points but idk if u can solve for it since we r dealing with trig functions

Im seeing if there are other ways

If another <@&286206848099549185> can help thatd be great

[midnight plank]

@glossy compass Has your question been resolved?

[blissful summit]

Im watching this rn hopefully something will click https://youtu.be/dIY86WqvGjw?feature=shared

[midnight plank]

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[finite jolt]

im a little confused how to go about finding a set of vectors that are linearly independent that span U

[finite jolt]

I know you need to set up a matrix, solve using gaussian elimination to put it in rref, then put the solution in vector form

but not sure what matrix to set up?

[runic hamlet]

have you found some vectors in U?

[finite jolt]

Yeah

Can I just use any of them to create a matrix

[midnight plank]

@finite jolt Has your question been resolved?

[surreal moon]

As long as they're independent, yes

[trim quest]

well if you polynomials are ax^2+bx+c then U contains all those with a+b=0. So they are of type ax^2-ax+c. It's a two dimensional space given by vectors (a,c). So you can take a base (1,0), (0,1) which gives polynomials x^2-x and 1. These are clearly linearly independent.

[midnight plank]

@finite jolt Has your question been resolved?

[finite jolt]

I would still need to set up a matrix though right

To get it in vector form

Also I thought the polynomials themselves were the vectors, not (a, c)? I think I'm missing something notationally

[surreal moon]

A vector is just an abstract representation of a polynomial. (a, b, c) is just an abstract representation of ax^2+bx+c

[finite jolt]

ok so I don't have to set up a matrix right because if I do x^2-x and 1, then a and b can be anything and will describe anything in U? unless I'm tripping

[midnight plank]

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[calm quest]

i need a little help with part d

[calm quest]

i thought that i could do this:
3P2 * 4! / 5!

3P2 is to select 2 vowels from the 3 in a particular order, then i group them

then I multiply by 4! which is the number of letters + group -1

but this gives me a probability of 6/5 which is > 1 and i dont know what I'm doing wrong

[distant vigil]

I reckon it's better to do the probability of 1-(no two vowels are next to each other)

[calm quest]

oh do u have any idea why this isnt working?

[midnight plank]

@calm quest Has your question been resolved?

[misty carbon]

Because ur double counting 3 vowels together

[calm quest]

how so?

[misty carbon]

Your 3P2 could be AE, AI, EI and your 4! Includes permutations where the last vowel is next to your other 2

So your over counting

[rugged oriole]

Dawg can someone teach me two step inequalities I still dont understand it I'm literally crying I am a straight a math student in highschool somebody fucking help

[calm quest]

but isnt that okay because it just needs at least two vowels

[misty carbon]

no you are counting AEI once in AE

and AEI again in EI

[calm quest]

ohhhhh i get it

thanks for explaining!

.close

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[calm quest]

can someone help me with d)

[calm quest]

i dont know where to start

[midnight plank]

@calm quest Has your question been resolved?

[calm quest]

<@&286206848099549185>

huh

im not really sure what that means

[wet phoenix]

search it up

[calm quest]

💀

what do i search up

[agile cliff]

take the number of integers you have and apply the formula (n-1)!

[last slate]

wtf guys don’t say that

It’s highly inappropriate

[calm quest]

oh

[agile cliff]

so you have 8 integers, and so you want to do (8-1)! = 7!

[last slate]

Ya please don’t look it up. They’re probably just playing a prank or smth….listen to @agile cliff’s explanation

[calm quest]

yes

[agile cliff]

i only remember the formula, I can read and find an intuitive explanation for you

[calm quest]

thanks for letting me know

[agile cliff]

If you would like

[calm quest]

omg that i would really appreciate that

[wet phoenix]

just do the math and dont rely on other people

[agile cliff]

you’re being a poor helper rn

[agile cliff]

give me 5 minutes tops and i’ll get back to you okay?

[calm quest]

....

[last slate]

<@&268886789983436800>

[calm quest]

thank you so much!!! :)

[last slate]

@calm quest basically you have to consider the odd numbers as one unit

Lemme draw that for you

[olive matrix]

do not say things like this here.

[calm quest]

right so there's 4 odd numbers

but i only want at least 3 together

[last slate]

No not really. It says ATLEAST 3

So that means 3 or 4

[calm quest]

ahh ok yep

so i need to find the arrangments where 3 or 4 of them are together

but no less

[last slate]

Now the easy thing to do is to add the permutations for 3

Add the permutations for 4

Add em together
Voila!

But can you see the problem here?

The problem here is that some permutations in 3 would automatically contain permutations where 4 of them are together

[calm quest]

yesss

i see that

[agile cliff]

it would seem @last slate has tackled the problem

i leave it to him.

[calm quest]

thanks for trying anyways, I really appreciate it!!

[agile cliff]

if you would like my help, feel free to message or @ me. but i have faith he can help you.

[agile cliff]

no problem, good luck!

[calm quest]

ty!!

[calm quest]

so does that mean we only need to consider the ones with 3 together?

[last slate]

Yes I think that should work

Since the permutations of 3 together automatically contain permutations of four together

[calm quest]

okay so do i have to choose 3 of the 4 odd numbers, consider it a group and then arrange it around a table?

[last slate]

Yeah

U would have to do 2 cases

3 together

And 4 together

[calm quest]

but the 4 is already considered in the 3 together?

[last slate]

But the one with 3 together should be ONLY 3 together and not cases with 4 together

[calm quest]

oh but dont we want both of them together

[last slate]

Yeah but when we apply the factorial to inside the odd numbers unit, we would still be arranging using 3!

[last slate]

Exactly

We have to do

ONLY 3 + ONLY 4

[calm quest]

so what is the difference between 3 and 4 TOGETHER and ONLY 3 + ONLY 4

[last slate]

We miss out on the in-unit arrangements

[calm quest]

wait sorry could u explain that?

what is a in unit arrangment

[last slate]

Inside the block we are considering as one unit

[calm quest]

ohhh ok let me try it

[last slate]

(block),remaining odd,2,4,6,8.

This is what I mean by exactly 3 together

Now the remaining odd number has to be kept AWAY from the block

[calm quest]

yess i see

[last slate]

And you would have to do

$${}^4 \mathbb{C}_3$$

[grand pond]

Edmund Cloudsley

[last slate]

To select the items in the block

[calm quest]

ah!! yes i see

[agile cliff]

i saw similar notation. this is indeed true

[calm quest]

okay so for just 3 arrangement i did this:

[last slate]

,w 4C3 * 5N2 * 3! * 4!

[calm quest]

4C3 * 3! * 5! - 4! * 4!

[last slate]

,w 4C3 * 5N2 * 3! * 4!

[stable dawn]

Use \binom

Maybe that'll work

[last slate]

Cheers thanks mate

[calm quest]

hey cold te!!

[stable dawn]

Hello

[last slate]

,w solve \binom{4}{3} * 5N2 * 3! * 4!

[grand pond]

Results provided by WolframAlpha

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

Requested by alison_burg3r5

[last slate]

How do I do the permutation

Screw that ill just use a calculator

[stable dawn]

4C3 × 3!

[calm quest]

wait so is this correct for just 3 arrangements

[last slate]

,w 4203!*4! + 4! *5!

[grand pond]

Results provided by WolframAlpha

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

Requested by alison_burg3r5

[last slate]

@calm quest

[calm quest]

yes

[last slate]

Is this the final answer

[last slate]

⬆️

If you have the marking scheme or smth

[calm quest]

ohoh

wait sorry

yes

thats correct

[last slate]

It is right?

Great

[calm quest]

yes

[last slate]

Now I’ll explain it to you

[calm quest]

wait hang on

[last slate]

Okay

[calm quest]

its 2304

sorry i was reading the wrong one

[last slate]

Huh

2304

That’s really weird

[calm quest]

yeah! :(

we doing d so yeah thats the answer

[last slate]

,w solve 4!*5!

[grand pond]

Results provided by WolframAlpha

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Requested by alison_burg3r5

[lavish venture]

<@&268886789983436800> i’m not sure why no one pinged for this

[olive matrix]

ugh i missed that ty

[lavish venture]

you’re welcome

[midnight plank]

@calm quest Has your question been resolved?

[midnight plank]

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[blissful drum]

i am very confused...

[midnight plank]

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[bright grail]

How to simplify this?

[bright grail]

am i right that it's like this

i am trying to get a general expression for V

but i need help i am stuck

in cartesian the laplacian operator is very simple and im able to get this

iam stuck with this i dont know what to do

can anoyne help me

someone did this

how did he get this last line

dv = A dr/r^2

like huh?

please @ me if you know

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[grim tusk]

help how do i solve this

[lofty girder]

y=a*b^x what are the variables

[grim tusk]

the data table is all the questions given

[lofty girder]

What I mean is in this expression a and b are constants and y and x are variables right?

[grim tusk]

yeah, sorry

[lofty girder]

So let y be thousands of transistors and x be years since 1980 and find a and b

[grim tusk]

ahh okay thanks

.done

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[gaunt nimbus]

could someone help me start no. 6 and no.8

it'll also be great if u can check my induction for no.7

[gaunt nimbus]

also im completely lost for this

[midnight plank]

@gaunt nimbus Has your question been resolved?

[lethal path]

no 7 looks good

[gaunt nimbus]

Thank u 🙏

[lethal path]

ah for question 8, can't you do $F_{kn + k} = F_{kn + 1} F_k + F_{kn} F_{k - 1}$

[grand pond]

south's secret twin brother

[midnight plank]

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[lethal path]

.reopen

[midnight plank]

✅

[lethal path]

so by the induction hypothesis $F_{kn} F_{k - 1}$ already divides $F_n$

[grand pond]

south's secret twin brother

[gaunt nimbus]

Huh

[lethal path]

kn + k = (k + 1)n

[gaunt nimbus]

Oh

Why are we doing

F kn + k

Not F kn tho

[lethal path]

assume F_n, F_2n, ... F_kn divide F_n

then we want to show it for F_(k + 1)n

[gaunt nimbus]

Ok

[gaunt nimbus]

Then don’t u have to prove that the remainder is less than F kn + 1

Too?

[lethal path]

IDK yeah this approach seems not to work

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[chilly cobalt]

where can i find proofs of calculus rules/theorems? (like definition of integral, derivative rules, limit rules)

[runic hamlet]

any real analysis book

[chilly cobalt]

hmm, any online stuffs? cause real analysis books in my country are hard to find

[runic hamlet]

most classic books are available online

some even legally

[chilly cobalt]

alright, thanks

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[south heath]

for deriving pi^x

[south heath]

what is pi^x equal in terms of e^ln

and why

[dreamy lichen]

e^ln(pi) = pi

[south heath]

is it rly outside the brackets i.e. here

[south heath]

but pi^x

e^ln(pi^x)

?

OHHHHH

OHHHHHHHHHHHHH

[dreamy lichen]

$\pi^x = (e^\ln{\pi})^x $

[south heath]

cuz then u move the pi^x to x * ln(pi)

[south heath]

so it is this

[dreamy lichen]

yes, this

[south heath]

$\pi^x = (e^\ln{\pi})^x$

[grand pond]

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

[dreamy lichen]

$\pi^x = (e^{\ln{\pi}})^x = e^{\ln{(\pi)}x}$

[grand pond]

MæthIsAlwaysRight

[south heath]

woudlnt the derivative of e^(ln(pi) * x) be ln(pi) * pi^x

why this?

[dreamy lichen]

yes

ln(pi) * pi^x = pi^x * ln(pi)

it's the same thing

[south heath]

oh mb

im went delulu with eyes

thanks

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[subtle nimbus]

how do i do "c" and "d"?

[boreal ocean]

Upper or bottom?

[plain osprey]

bottom

[boreal ocean]

When you have something like $\frac{a}{b}x = c$, multiply both members of the equation for $\frac{b}{a}$ and simplify the left member

[grand pond]

cristorenzo99

[boreal ocean]

So, in the first one, multiply both members of the equation for $\frac{11}{6}$ and do the multiplication in the second member

[grand pond]

cristorenzo99

[midnight plank]

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[tame shoal]

I wanna learn how to calcculate minecraft stronghold coordinates via just 2 ender eye.

[dreamy lichen]

Lmao

okay

you'll need the x and y coords of both throws

[tame shoal]

Ok

[dreamy lichen]

make one throw, record x and y coords and the direction of the pearl

[tame shoal]

@dreamy lichen can you explain me with example like i am nuub in math ;-;

[dreamy lichen]

okay

you can make a throw at e.g. (0, 0)

then you'll need to record the direction of the throw

does minecraft show you your orientation?

or not

[olive matrix]

yes you can see it with f3

it's in degrees

[dreamy lichen]

okay, cool

[tame shoal]

Yea i got it like ik the basics like have to press F3 and take a ss of direction in F3

[dreamy lichen]

so there will be some triangle like this one

2 points with known coordinates

the third point will be the stronghold

so you'll need to calculate its coordinates

for simplicty, move only in the x-direction.
So make your throws e.g. at (0, 0) and (500, 0)

then the angles will be just your orientation

[olive matrix]

the way speedrunners do it is they either use a program to calculate this stuff or they look at the difference in angle and use a table to tell them how far to go https://www.reddit.com/r/MinecraftSpeedrun/comments/lkthsk/navigation_tips/

but yeah this is the basic idea

[dreamy lichen]

they move perpendicularly to it?

interesting

[olive matrix]

that's one way yeah

[dreamy lichen]

that's probably the fastest way to get accurate result

one needs to calculate the point in perpendicular direction tho

[olive matrix]

i know some people can get an estimate in their heads

it means you only need to care about the difference in angle

[dreamy lichen]

yeah

[olive matrix]

there's also some weirdness with chunk boundaries

[dreamy lichen]

if you moved perpendicularly to the direction of first throws like this (for x blocks) and the difference in directions was A, then you would need to move x / sin(A) blocks in the direction of 2nd throw, from the place of the 2nd throw

this looks pretty estimate-able actually

https://docs.google.com/spreadsheets/d/1h4v5rhDopz4VFgpq2DQ4vZ10wNpYThr6y0yRzXST7Yw/edit?gid=0#gid=0

Here is a calculator btw

just make a copy of that

so you can edit it

https://www.strongholdfinder.com/

here is another one

[dreamy lichen]

this one is probably even easier to use

the math behind it is just making a triangle and then using some trigonometry

[tame shoal]

Btw i also thought that same graph

@dreamy lichen i have mod to find and calxulate automatically but i wanna learn the calculations

As i am noob

[olive matrix]

hmm well you probably should learn some basic trigonometry first, this will be a good goal but probably not the best way to jump into it

[sinful trout]

ninjabrain bot is way faster tbf

[tame shoal]

Yes

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[chilly cobalt]

why is the allowed values of the statement(?) (a^b)(c^b) = (ac)^bhold for only a,c >= 0 is there a proof why?

[median gust]

wait... are you sure it only holds for m,n >= 0

it holds for negative values too right

[chilly cobalt]

ive heard it doesnt

wait

[median gust]

????

[chilly cobalt]

wrong thing lmao help

[lethal path]

you could have (-1)^(1/2) for example

and that's complex number territory

[chilly cobalt]

changed it

[lethal path]

also you need to change m, n >= 0

[chilly cobalt]

ive studied a little of that, is there a proof?

[lethal path]

yeah then (-1)^(1/2) still applies

[lethal path]

$\sqrt{-1} = i$ is the definition of $i$

[grand pond]

south's secret twin brother

[chilly cobalt]

yeah

[lethal path]

should be a,c >= 0 btw

[chilly cobalt]

oops

😭

[lethal path]

exponents can be negative no problem

[chilly cobalt]

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[wise bough]

(a to b) integration of floor(x) + (b to a ) integration of floor (-x)

[wise bough]

a to b integration(floor x - floor(-x)

a to b integration (x-{x}+(x+{-x}))

(a to b integration)(2x-({x}-{-x})

so I am stuck at this part what should I do for integartion of fractional part (x) or (-x)

Rest it will be (b^2-a^2)

[midnight plank]

@wise bough Has your question been resolved?

[frail edge]

You're basically finding the area of a rectangle and since it's a piece wise function I'd recommend you break the Integral into multiple pieces wherever it changes definitions (at every integer between a and b)

[wise bough]

Of course I did the same

{x} gives 1/2

[frail edge]

Can you send an image of what you've done, it's really hard to read the typed out version

[wise bough]

@frail edge

[frail edge]

That fractional part thing will evaluate to 1

They both offset each other (you can see that if you use some random numbers)

[grand pond]

xd_senBugha

[wise bough]

Can you show me how it gives 1?

Do you meant....1/2-(-1/2) =1?

if it is true then integration will be ....x^2/2 .....(b^2-a^2)/2

????

[midnight plank]

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[jolly roost]

for this question

why does this equation not make sense

[grim vector]

Literally saying that v-3 = v+ 3

[jolly roost]

so how would we approach this

[grim vector]

Let me read rq

[fickle oriole]

Isn’t it just saying any velocity

Except for 3 and -3

satisfies the equation

[grim vector]

Ive no idea tbh

[midnight plank]

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[rugged pumice]

.close

hi

[rugged pumice]

.close

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[rugged pumice]

sorry i just really wanted to do that

[dawn dagger]

lucky

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[olive herald]

How does one prove that a given function is not a tangent for another given function?

[olive herald]

/ prove it is not

[formal rampart]

im guessing you need to have a point a where f(a)=g(a) and f'(a)=g'(a)

[olive herald]

I have two functions

[formal rampart]

if one of these conditions cannot be satisfied th functions aren't tangent

[olive herald]

that's all

And now

[lavish venture]

!xy

[olive herald]

I need to prove that it isn't a tangent/is a tangent at any point

[lavish venture]

!xy

[midnight plank]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[formal rampart]

yea, i believe you need to show that f(a) = g(a) or f'(a) = g'(a) cannot be satisfied for any x = a

[olive herald]

How does that work

[formal rampart]

if f (a) = g (a) that means that they have the same point

and f'(a) = g'(a) shows they have the same slope

[lavish venture]

this is how it works

cant be any clearer

[formal rampart]

so if they have the same point and same slope they are tangent

if they have the same slope but not the same point they aren't

[olive herald]

Sure, but I'm not given a point

[formal rampart]

and if they have the same point but not the same slope they aren't tangent either

can you please show us the functions

[lavish venture]

you show there exists a point such that either of the conditions isn’t satisfied

the negation of it being true for all x, is it being false for at least one x

[olive herald]

f(x)= 9x

f1(x)= x^3 -3x^2 +3x+18

[lavish venture]

what did you get for f’

we could also just choose any point where the functions are equal, such as x = 0

[formal rampart]

f'(x)=9 and f1'(x)=3x^2-6x+3

[olive herald]

3x^2 - 6x + 3, no?

ye

[lavish venture]

i don’t need you to tell me man

but yes

[formal rampart]

i mean he probably did it right

just wanted to save you some time sorry

[lavish venture]

^

[olive herald]

tangent means it only touches at 1 point as far as I know

So I can't just take any point

[lavish venture]

as oak dining table said earlier, for one function to be the tangent line of another function, the two functions must be equal at that particular point, and their derivatives must also be equal

what point in particular are they asking for

[olive herald]

And is equal to the derivative at that point

[lavish venture]

or are they saying for all points

[olive herald]

I'm supposed to check

if it is a tangent for that function

[lavish venture]

but where

it can’t be a tangent everywhere

are you supposed to find where?

[olive herald]

if it is one, yes

[lavish venture]

or do they ask you if it is at a particular point

[olive herald]

they don't

[lavish venture]

ok

then set the derivatives equal

[lavish venture]

^

solve for x

[olive herald]

oh shit

that sounds about right

[lavish venture]

yep

[olive herald]

alright give me a second

[lavish venture]

in the future please just take a picture of your question

it leaves out the ambiguity

[olive herald]

It's not in english

[lavish venture]

then translate it

the entire question

[olive herald]

Sure

I'm gonna be back in a sec anyway

With something that has to be translated

x is

two solutions here right

[lavish venture]

$3x^2-6x + 3 = 9$

[grand pond]

knief

[proper kernel]

Hey knief 👋

What’s happening here

[lavish venture]

$x^2-2x-2 = 0$

[grand pond]

knief

[lavish venture]

what’s up gigagoat

[proper kernel]

Wassup

[lavish venture]

marties doing calculus

[proper kernel]

cool

[lavish venture]

did you get this @olive herald

[olive herald]

yes

[lavish venture]

and what did you get

[olive herald]

quadratic formula

simplified to 1+- root of 3

[lavish venture]

$x = \frac{2\pm \sqrt{12}}{2}$

[grand pond]

knief

[lavish venture]

x = 1 \pm \sqrt{3}

[olive herald]

yeah

[lavish venture]

yea

now you evaluate each function at those points

if they are equal, then it is the tangent line

[olive herald]

sure, but if it is 2 solutions

Doesn't that mean

This isn't a tangent

Since like it touches at 2 points

[formal rampart]

it doesn't touch 2 points

it has the same slope at 2 points

[lavish venture]

no, this just means the slopes are equal at two points

[formal rampart]

now you check if they touch

where they have the same slope

[olive herald]

Ahhh

right

[lavish venture]

it will touch if the functions themselves are equal at these points

[olive herald]

How do I make sure it doesn't touch at any other point though? Are tangents allowed to do that if the slope isn't equal?

[lavish venture]

no

if the slope isn’t equal it may intersect sure, but it won’t be a tangent line

[olive herald]

So it is allowed to intersect

[lavish venture]

if the functions are equal yea

[olive herald]

Alright getting to check the functions now

[lavish venture]

🦆

[olive herald]

13,803

[lavish venture]

a bit large

[olive herald]

So

for 1-root 3

[lavish venture]

13 thousand?

[olive herald]

Not true

[lavish venture]

or is that 13.8

[olive herald]

Oh no, in my country we use that instead of 13.803

Lol

[lavish venture]

ahh

[olive herald]

I get -6.5

[lavish venture]

,calc 9(1+sqrt(3))

[grand pond]

Result:

24.58845726812

[olive herald]

So checking for positive now

[lavish venture]

,calc (1+sqrt(3))^3 - 3(1+sqrt(3))^2 + 3(1+sqrt(3)) + 18

[grand pond]

Result:

24.196152422707

[lavish venture]

,calc 9(1-sqrt(3))

[grand pond]

Result:

-6.5884572681199

[olive herald]

seems right

Is it allowed to touch at 2 points with the same slope btw

[lavish venture]

,calc (1-sqrt(3))^3 - 3(1-sqrt(3))^2 + 3(1-sqrt(3)) + 18

[grand pond]

Result:

13.803847577293

[olive herald]

Well, now we have proven it is the case for 24.588 etc

anything else to do or?

[lavish venture]

two functions "touch" at a point if the functions are equal at that point

well it isn’t tangent at either point

because the functions are equal at those points

[olive herald]

so it isn't tangent?

But why

The functions are not supposed to be equal for that?

[lavish venture]

suppose f(x) = 9x and g(x) = x^3 - 3x^2 + 3x + 18

[olive herald]

yep

[lavish venture]

then there does not exist a value of x such that f’(x) = g’(x) and f(x) = g(x)

you can also see this graphically

[olive herald]

So both the derivative

And value have to be the same?

[lavish venture]

yes

[olive herald]

And this isn't the case because if I put 1+root of 3 into the derivative function

The Derivative isn't the same?

value* ig

Because we solved for Derivative

[lavish venture]

well, the slopes are the same at those points, but the functions themselves aren’t equal

we need both to be true

one being true is insufficient

[olive herald]

ahh

I get it

[lavish venture]

https://tenor.com/view/duckinhand-duck-duckpfp-gif-25731273

[olive herald]

next one

I need to translate

Will take a second

oh btw

Does this way always work?

the one we just did

[lavish venture]

yes, though you could’ve also done it in reverse, first find the values where the functions are equal, then test if the derivatives are equal at those points

[olive herald]

Ok

The next ones kinda fucked cause ngl what this is even asking hahah

[lavish venture]

just show it

[olive herald]

Movable Pedestrian Bridge

To allow for smooth passage of ships in the harbor basin, a movable pedestrian bridge was designed in Duisburg. When needed, it can curve to varying extents, forming an arch. The pylons (pillars of the suspension bridge) are pulled further outward by four hydraulic cylinders, which tensions the two main suspension cables, raising the footpath connected to them. The structural support and the footpath each form parabolas with different curvatures.

When the bridge is positioned at its median height, the vertex of the footpath reaches approximately 4.50 meters above the normal level. At its maximum height, the vertex reaches 9 meters, with the slope angle α\alphaα of the footpath reaching nearly 45°.

Check the given statements about the angle a(alpha) through own calculations

[lavish venture]

have you tried anything

[olive herald]

So

9m is in the middle

Half of 73,72m

something about trigonometry

not rlly

Idk what this is even saying ngl

Hold up

I'm actually on to something, no?

just make a triangle at that point

[lavish venture]

well you’ll need more than what you had

the tangent line doesn’t touch the vertex

so you cant just do tan(alpha) = 9/36 ish

[olive herald]

huh

That's it?

,calc 9/(73,72/2)

[grand pond]

The following error occured while calculating:
Error: Parenthesis ) expected (char 6)

[olive herald]

:(

[lavish venture]

i meant can’t

[olive herald]

Ah

How can you tell the tangent doesn't touch the vertex? What tangent even?

[lavish venture]

have you tried finding the equation of the parabola and setting up a coordinate system

[lavish venture]

the tangent on the right side drawn

where alpha is

[olive herald]

Oh

[lavish venture]

you should know that tan(alpha) = slope

[olive herald]

nearly 45 degree

Probably that?

[olive herald]

yep

[olive herald]

I only know ax^2 + bx+ c is the parabole formula

I don't even know what a b c are in that formula tbh

[lavish venture]

well what about vertex form

$ax^2 + bx + c = a(x-h)^2 + k$

[grand pond]

knief

[lavish venture]

h = -b/2a

k = f(h)

[olive herald]

Vertex means...

Highest point?

[lavish venture]

sure or lowest

[olive herald]

ahh

[lavish venture]

turning point for parabola

[olive herald]

I didn't even know you could calculate that

🦆

[lavish venture]

(h,k) is the vertex

[olive herald]

what is k and h?

[lavish venture]

^

[olive herald]

ah

So

[lavish venture]

^

[lavish venture]

^

[olive herald]

It's like

wait what are a b c in a parabole btw

[olive herald]

So how do I find out what a b c are

[next urchin]

The best way to visualize this is by playing around with desmos for a while, so I'd suggest doing that. C is where the y-value where the line crosses the x-axis, or (0, c); b affects the slope by whatever magnitude its value is, and a essentially tightens it even more quickly than b

[olive herald]

f(0) is c

k

Next

how do I get them from here

[next urchin]

Is there any other information given in the problem

[olive herald]

No

[next urchin]

I'll get back to you in a minute, then. If there's an answer key or something you could find, that would be cool; if not, I'll play with the numbers & stuff and see what comes of it. It seems that it's just asking you to prove that a(alpha) is nearly 45°, and I don't know what else. It doesn't seem like you actually need to worry about the parabola, though

[olive herald]

pretty much

But I'd like to learn how to do the rest while I'm at it

[next urchin]

Well, I don't think there's much to learn from it; the question is intentionally very vague, just complex problem solving

[olive herald]

In the end

It's just a parabole with like a couple given values and the rest to calc ig

[next urchin]

yeah, I don't know how to do this. Sorry

[olive herald]

@lavish venture

I need your help buddy

[lavish venture]

use the coordinates of the vertex

[olive herald]

36 ish and 9, yeah

[lavish venture]

,calc (73.72)/2

[grand pond]

Result:

36.86

[olive herald]

yep

but put them where

[lavish venture]

h and k

[olive herald]

Is h

x or y

[lavish venture]

you need to define your coordinate system

you can do it many ways

[olive herald]

basically a(x-36.86)+9?

[lavish venture]

we can say the left point is (0,0)

[lavish venture]

^2

but yea

[olive herald]

Oh yeah

[lavish venture]

we need another point on the parabola to find a

we can use (0,0) or (73.72,0)

[olive herald]

yep

now?

[lavish venture]

yep

plug them in and solve for a

$f(x) = a(x-36.86)^2 + 9$

[grand pond]

knief

[lavish venture]

plug in either

for (x,y)

[olive herald]

don't know where

[lavish venture]

brother

[olive herald]

Oh nvm

Lmaooo

[lavish venture]

i’m not going to hold your hand

[olive herald]

0/73 on the left side ig

Ok

[lavish venture]

pick one

[olive herald]

73.72= a(x-36,86)^2+9?

[lavish venture]

what about x sir

[olive herald]

ah

[lavish venture]

you didn’t substitute a value for x

[olive herald]

right right

73.72= a(0-36,86)^2+9?

[lavish venture]

yep

wait so how do you express larger numbers

if you use , for decimals

do you use .

[olive herald]

you mean coordinates?

[lavish venture]

no like

13,808 to me is 13 thousand 800 and 8

how would you write that

if not with a ,

[olive herald]

yeah, we use . if at all

[lavish venture]

hmm

interesting

what country

[olive herald]

Germany

[lavish venture]

🇩🇪

[lavish venture]

you like flammable maths?

[olive herald]

hans get ze flammenwerfer

[lavish venture]

i don’t speak german

[olive herald]

Anyway, a= -8.9457

[lavish venture]

,calc (-9)/(36.86)^2

[grand pond]

Result:

-0.0066241757685295

[lavish venture]

hmm

[lavish venture]

how’d you get this

[olive herald]

hmmm

I did

73,72/(-36,87)^2-9

[lavish venture]

you have to subtract 9 first

[olive herald]

makes sense

anyway, now we got a

[lavish venture]

or no

[lavish venture]

this should be 0

[lavish venture]

the x value is 73.72

you switched them

[olive herald]

oh lol

[lavish venture]

instead of 73.72

[olive herald]

-9/73.72^2

[lavish venture]

nope

73.72 - 36.86 = 36.86

[olive herald]

ah ye

Realized

A sec after sending

[lavish venture]

^

[olive herald]

yup

[lavish venture]

so we have

$f(x) = \frac{-9}{(36.86)^2}(x-36.86)^2 + 9$

[grand pond]

knief

[lavish venture]

differentiate

find the slope at x = 73.72

then tan alpha = slope

alpha = arctan(slope)

[olive herald]

why differentiating though

[lavish venture]

to find the slope

at that point

[olive herald]

ah ye

[lavish venture]

^

[olive herald]

arctan was 1/tan

Right

[lavish venture]

nono

arctan is its own function

1/tan is cotan

hence why i didn’t use the shitty notation

$\tan^{-1}(x) = \arctan(x)$

[grand pond]

knief

[lavish venture]

it’s the inverse function of tan

[olive herald]

ah

what confuses me is

is that the slope for the entire or just for the point

[lavish venture]

what

[olive herald]

And if it is just for the point, why does it let me get the angle

[lavish venture]

the derivative is a function that tells us the slope at a particular point

[lavish venture]

because $\tan(\alpha) = \frac{\Delta y}{\Delta x}$

[grand pond]

knief

[olive herald]

yeah...because sinus= x or y and cosinus equals x or y, right

ok this might sound stupid but

how does one differentiate this? I've never done it with numbers

I mean it is like

[lavish venture]

power rule

[olive herald]

yeah

I know that rule

differentiating as I know is

doing it for every x in f(x)

but now we don't have x

[lavish venture]

🤔🤔🤔

huh

am i going to have to put you on my shoulders

🍼

i’ve essentially done the whole problem for you

[olive herald]

maybe x^2 - 2x36,86 + 36,86^2 first ig

now we got like -0,0066241 * x^2 -73,72x + 73,72

-0,0066241 * 2x - 73,72 is f'(0)?

where x= 73,72

so like -0,0066241 * 73,72

[lavish venture]

$f’(x) = \frac{-18}{(36.86)^2}(x-36.86)$

[grand pond]

knief

[lavish venture]

$f’(73.72) = \frac{-18}{(36.86)^2}(36.86)$

[grand pond]

knief

[lavish venture]

,calc (-18)/(36.86)

[grand pond]

Result:

-0.488334237656

[olive herald]

oh hey

I got the same

😎

[lavish venture]

,w arctan(-0.488334237656)

[grand pond]

Results provided by WolframAlpha

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

Requested by c.knief

[olive herald]

it shouldn't be negative though

[lavish venture]

,w arctan(0.488334237656)

[grand pond]

Results provided by WolframAlpha

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

Requested by c.knief

[olive herald]

anyway, mind explaining why this works

[lavish venture]

hmm wait

something must’ve went wrong

[olive herald]

That is the exact solution from the solution book lol

[lavish venture]

they said 45 degrees?

[olive herald]

yep

[lavish venture]

oh so it’s right

[olive herald]

not negative

but yeah

I think

[lavish venture]

this is correct?

[olive herald]

The vertex formula

Depends on

[olive herald]

It only goes to 45°

but seems about right

[lavish venture]

hmm this isn’t 45 degrees though

[olive herald]

I think because it opens up downwards

[lavish venture]

this is like 25 degrees

something must’ve went wrong

send the problem again

[olive herald]

oh yeah nvm

About 26 degrees

According to book

So yah

Correct

[lavish venture]

oh ok

[olive herald]

I get confused about radiants

[lavish venture]

why did it say 45 degrees?

[olive herald]

radiants and degree

anyway

Why does this work

[lavish venture]

ok so we found the equation of the parabola

[olive herald]

We use the formula for vertex calculation

[lavish venture]

you’re fine with this yea

[olive herald]

wdym

[lavish venture]

like you know why we found the parabola equation

and you’re fine with how we got it

[olive herald]

no