help-28

[restive geyser]

(oh lol I forgor the dx of (2x -1) being TWO 🤣)

[torn jolt]

lol

[restive geyser]

yh, got -5/12 too then

[ancient folio]

Could have check it using desmos

[torn jolt]

i idnt

didnt

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[umbral dome]

what have you tried?

[valid spear]

Is this correct?

[umbral dome]

yes

[valid spear]

Yay

So the magnitude is the square root of (-10²+4²

)

[hot lily]

$$\sqrt{(-10)^2 + (4)^2}$$

[glossy valve]

King Leo

[umbral dome]

make sure you have parentheses around the (-10)

[valid spear]

Ok

So root 116

Simplified to 2root29

Thanksss

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[placid shell]

Can someone check me

[hot lily]

!1c

[full forum]

Please stick to your channel.

[placid shell]

halloooo

[hot lily]

AB length is wrong, so bottom left is wrong almost entirely

Check your rounding in top left

[placid shell]

I think I figured it out

[hot lily]

And top right

[placid shell]

5 correct?

[hot lily]

✅

Did 798 help you on this btw

[placid shell]

HUH?

Ab is 5 and ac is 5.7?

[hot lily]

How did you get 5.7

[placid shell]

I don’t know i thought since ab is 5 then it would be 5.7

[hot lily]

Use the pythagorean formula

Subtracting 1 from the leg doesnt necessarily mean subtracting 1 from the hypotenuse

[placid shell]

Okay hold up im tryna figure ts out

5.831

[hot lily]

Sry im back

[hot lily]

✅

Now you need to change your trig functions

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[tall parcel]

confused

[hearty plover]

Why did you say it's 7 when x tends to 1

It does not mention any handedness

Also the white points mean a hole in the graph

[hearty plover]

The limit only exists if the left hand limit and right hand limit exist and are equal

Here the lhl ≠ rhl

[upper valley]

The function is not continuous at that point.

[long sky]

Limit of the function at a point be different from the actual value of the function at that point

[tall parcel]

what's up y'all 😭

[long sky]

Eg. Even though for b.) f(0) is DNE, approaching from both sides you still get the value 8

[tall parcel]

oh okay i understand it now

preesh @long sky

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[long sky]

I was using b.) as an example

Mb cuh

Thought I said that already

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[tawdry grove]

I got stuck

[nocturne shard]

As simple as it seems, start by u-sub: u=√x

du = dx/[2√x]
dx = 2udu

By then, you can IBP

[tawdry grove]

i dont understand

[nocturne shard]

what makes you not understand this

[keen vector]

do you know about integration by substitution

[nocturne shard]

2√xdu = 2udu

Then you can IBP

[tawdry grove]

Like how do you recognize a case like that. I would have never seen/thought of that

What did you look for/see/analyze

[nocturne shard]

uhh

u-sub is kinda obvious bro

why would u want √x stuck in that function

[tawdry grove]

Hm? So you look at the sqrtx and thought of taking it out? Was that the recognition?

[nocturne shard]

Yea

Plus, u = √x then 2udu = dx which is also pretty convenient

There are lots of cases where u-sub is that convenient
u = cbrt(x) -> 3u²du = dx
u = tan(x) -> du/(1+u²) = dx

[spiral spindle]

basically if you ever see something inside of a trig function like that in your class thats gonna be u sub

(im assuming this is calc 1)

[tawdry grove]

this is calc 2

[spiral spindle]

oh

well

same rules applies

i guess

kinda atleast

if it looks hard to integrate

thats probably u

if your doing a usub

[tawdry grove]

i see, maybe a trig sub too

oh how to recognize trig sub cases?

[spiral spindle]

trig sub is only when

u see smth like

ill just send a pic

its really obvious

when you see something like sqrt of 9-x^2

[tawdry grove]

alright

thanks

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[spring vigil]

ive factored so far

(x+6)(x-2)

then ended up with x+6

how would i do this

[hot lily]

So you know that $\frac{x^2 + 4x - 12}{x - 2} = x + 6$ for all $x \neq 2$.

[glossy valve]

King Leo

[spring vigil]

ok

[hot lily]

Since you only care about near x = 2, just make a table of x + 6

[grim skiff]

I don't think you need to do this. The instructions says to see the behavior near x = 2 so you need to use the original expression

[spring vigil]

woops

[grim skiff]

Because using x + 6, near x = 2, you don't get undefined values

A table of values is somethig like this

And you want near x = 2, so 0, 1, 1.9, 1.999, 2.0001 etc

[spring vigil]

can i do this well without calculator?

[umbral dome]

i think you are expected to use a calculator for that sort of problem

[spring vigil]

this specific is ok?

cuz its only x + 6 anyway

[grim skiff]

.

As I said, I think it's expecting the original function

Not the simplified

Because the problem wants to see the behavior near x = 2

With x + 6, nothing fancy happens near x = 2

[spring vigil]

ii plugged in 1.9

then got 7.9

[grim skiff]

What exactly are you questioning?

You just do what the problem says and the values I gave

[spring vigil]

so

i got
1.9 1.99 1.999 2 2.001 2.01 2.1
7. 9 7.99 7.999 0 8.001 8.99 8.9

[grim skiff]

Plugging in 2, does not result that

[spring vigil]

its undefined

[grim skiff]

Also it says near 2, at 2

Near means you don't plug in 2

[spring vigil]

ok

so i just take out 2

[hot lily]

Even with the original expression, does anything fancy happen near x = 2?

[grim skiff]

Yeah, it's undefined

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[mystic tapir]

do you know how to do the limit of sin(x)/x

[spring vigil]

i want sin(x)/x

i just need a nudge on how to manipulate it

[mystic tapir]

let x = 8 theta

write the limit in terms of x

[spring vigil]

before that

i want to show some example

[mystic tapir]

you want to show an example?

[mystic tapir]

yeah

its the exact same idea as this one down here

[spring vigil]

none of these deal with theta

[mystic tapir]

theta is just another variable name

you can pretend its x

[spring vigil]

yeah i was gonna ask why u wanted theta as x

[mystic tapir]

what do you mean

[spring vigil]

u wanted to substitute theta to x?

[mystic tapir]

no because i thought you're not allowed to just do it like this

but if you are then you don't need to substitute anything

[spring vigil]

okay thanks

i just put 8/8

then 4/8 then 1/2

[mystic tapir]

yeah

[spring vigil]

can you explain why sin (8 theta) times 8 theta is 1

[mystic tapir]

$\frac{\sin(8\theta)}{8\theta}$ is $1$

[glossy valve]

DiamondPanda16

[mystic tapir]

as in the limit as theta goes to 0 is 1

for the same reason as sin(x)/x

[spring vigil]

okay

thanks diamond panda 1

6

[spring vigil]

can u look over my worksheet so fat

far

i answered all

[mystic tapir]

i think you messed up the last two columns

should be 8.01 and 8.1

[spring vigil]

wow great thank you

ive been missing small points like this because i didnt have someone look them over

[mystic tapir]

also im pretty sure for this one the answer is just -1 because the limit from the left and the right is the same

they're both -(x-2)²

[placid sapphire]

maybe try with small values on calculator and saw that happen?

[spring vigil]

i got the ans already thanks

without calculator

[spring vigil]

huh

[placid sapphire]

oh sh-

[spring vigil]

u mean 1+ is not 1 so we dont need to use the bottom one?>

[mystic tapir]

x = 1 is not 1- or 1+, so you don't care about the value at x = 1

you ignore the 5

[spring vigil]

must be something wrong with my arithmetic

[spring vigil]

isnt it -( -1 - 2 ) ^2

[mystic tapir]

yeah, thats -1

its the same from both sides though, so the answer is -1, not DNE

[spring vigil]

can you go over the solution rq

ik its very basic

but i might be confusing my signs here

[mystic tapir]

$f(x)=-(x-2)^2$ at $x\ne 1$ \
If you sub in $x=1$ into this, you get $-(1-2)^2 = -(-1)^2 = -1$

[glossy valve]

DiamondPanda16

[spring vigil]

-1- 2 is 1 then carry the - from outside

(-1)^2 = -1

oh its not (-1)(-1)

but (-1)(1) ?

[spring vigil]

ok

[mystic tapir]

no

the square of (-1) is 1

(-1)(-1) = 1

therefore -(-1)(-1) = -1

[spring vigil]

then just take the negative sign from outsidwe

okay

is there anything else?

[mystic tapir]

i don't think so

[spring vigil]

thank you

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[wise wharf]

You have the numbers 1-n and want to make a string of these numbers. There are 3 rules. Each number must be used exactly once. A number i cannot be the ith number. Going left to right, the numbers increase in value until reaching n, where they start decreasing in value.

[mystic tapir]

so whats the question

[wise wharf]

oh

how many possible strings of numbers are there for a value of n, and what are these strings (this second one matters less)

[mystic tapir]

ok

[wise wharf]

obv doesnt work for n=1, just ignore that

[mystic tapir]

well n = 2 and n = 3 have one way im pretty sure

2, 1 and 2, 3, 1

[wise wharf]

yes

never beengood at combinatorics

[mystic tapir]

this looks hard tho

[wise wharf]

yep

<@&286206848099549185>

[jagged raptor]

Wsp

[wise wharf]

ye idk what im doing with this problem

just wanna solve it and hopefully prove my solution is correct

[grave ledge]

hi

[jagged raptor]

Whats the question

[wise wharf]

.

[jagged raptor]

It would start out with

$\sum_{n=1}^{i-1}k$

[glossy valve]

Marshall The Gamer

[jagged raptor]

to get to i - 1

And are you trying to add these together or what?

[wise wharf]

uhh

im trying to find all possible strings

how many specifically

[jagged raptor]

Nvm

It is outside of my understanding, sorry

[wise wharf]

alr no problem

[jagged raptor]

Good luck

[wise wharf]

ty

[jagged raptor]

Wait

It is the same thing for a padlock

Search up this but simpler and for a padlock and you should get a formula

[wise wharf]

?

[jagged raptor]

I got it

(N-1)!

[wise wharf]

n=3

[jagged raptor]

2!

[wise wharf]

=2

[jagged raptor]

Or 2

[wise wharf]

theres only 1 tho

231

[jagged raptor]

213

321

*312

[wise wharf]

2 is in the 2th posiiton

it can only be decreasing after 3

[jagged raptor]

What?

[wise wharf]

think of it like a mountain

[jagged raptor]

You said increase

Making it impossible

[wise wharf]

on the left of n the numbers can only be increasing, on the right of n they can only be decreasing

[jagged raptor]

Ohh

But you can never reach n

Say 3

213

3 is in the third position

[wise wharf]

yes

[jagged raptor]

231 ohh

[wise wharf]

^

[jagged raptor]

The answer is 1

For all values

[mystic tapir]

what

[wise wharf]

n=4, 2341, 3421

[mystic tapir]

2431 doesn't work

ok yeah that looks good

[jagged raptor]

Do 5

[wise wharf]

23451, 25431

uhh

[jagged raptor]

23451, 34521

[mystic tapir]

n = 1: no sol
n = 2: 21
n = 3: 231
n = 4: 2341, 3421
n = 5: 23451, 25431, 35421

[wise wharf]

23541, 23451, 35421, 34521

[mystic tapir]

24531

[wise wharf]

thats all 5 i think

nvm

im so cooked

[mystic tapir]

ok so theres:

23451
24531
25431
34521
35421

[wise wharf]

23541

[mystic tapir]

hey 1 has to always go at the end

i mean of course it does but like

[jagged raptor]

$\sum_{k=1}^{n}k(2)$

Maybe

[wise wharf]

forgot $

[mystic tapir]

k(2)?

[glossy valve]

Marshall The Gamer

[mystic tapir]

that literally fails for n = 2

[wise wharf]

lets start from n=4 for these ok

[jagged raptor]

It doubles from the last si it wiuld increment by 2 not one, i messed up

[wise wharf]

the first few are funky

[mystic tapir]

doesn't work

4 is 4th

n = 5 has five solutions:

23451
24531
25431
34521
35421

im pretty sure

[jagged raptor]

Yeah

This is tricky

[wise wharf]

OH MY GOD

[mystic tapir]

ok so far we got 1, 1, 2, 5 sols

[wise wharf]

ok wait holdon

[mystic tapir]

maybe you could just find a numerical pattern

xD

[wise wharf]

look a the numbers before 5

for every solution

[jagged raptor]

Fibinnacy?

[mystic tapir]

234
24
2
34
3

yes but it skips "23" and "4"

because 23541 and 45321 don't work

[jagged raptor]

We hit 2

[wise wharf]

nonono

i mean just like

the first 2 numbers of each

23

24

25

34

35

its legit just like counting n stuff, i think this is kinda on to something

im probably trippin fr

[jagged raptor]

Do 6

[wise wharf]

aaaaaaaaaaaaaaand im stuck again

[jagged raptor]

234561
345621
456321
564321
654321

Any more?

[wise wharf]

465321

[jagged raptor]

6

Thats it yeah?

[wise wharf]

346521

[jagged raptor]

5 > 4

[wise wharf]

again, only needs to increase on left, decrease on right

[jagged raptor]

We discounted 3 for that i think

[wise wharf]

?

no

231

[jagged raptor]

On one of them we did

[wise wharf]

no

if we did its not part of the question

[jagged raptor]

Do 4 again

2341
3421
4321

[mystic tapir]

coincedence

[jagged raptor]

Thats 3

[mystic tapir]

OOPS

right

2 -> 1
3 -> 1
4 -> 3
5 -> 5

ok lets do 6

[jagged raptor]

Already done

[mystic tapir]

yes there's more i think

[jagged raptor]

465321

6 so far

236541

7

[mystic tapir]

654321
465321
564321
236541
246531
346521
456321
235641
245631
345621
234561

that's literally 11 that work

and I think that's all of them

[jagged raptor]

Check 5 again

[mystic tapir]

25431
35421
24531
34521
23451

five

[jagged raptor]

Ok

[mystic tapir]

I feel you can calculate it based on the position of n

[jagged raptor]

Yeah

I am graphing it

[mystic tapir]

like if its _ 5 _ _ 1 then you know that 3 can't come after 5, so #1 can't be 4

[jagged raptor]

I feel like there is a function

[wise wharf]

the goal is to find a fucntion

[jagged raptor]

IT IS FIBBINACI

Nvm jacobsthal

[wise wharf]

11 isnt fibonacci

[jagged raptor]

Jacobsthal

Add all prior numbers to get next

[mystic tapir]

do you actually know what Jacobstgal is

[jagged raptor]

Just said it

[mystic tapir]

no

its f(n) = f(n-1) + 2 * f(n-2)

[jagged raptor]

Twice prior plus one before prior?

7 should have 21

[mystic tapir]

it should

lets check

[jagged raptor]

8, 43

WE DID IT

[mystic tapir]

um

not confirmed

lets check 7

[jagged raptor]

Ok

Wt

[mystic tapir]

2765431
3765421
4765321
2576431
3576421
4576321
2675431
3675421
4675321
2347651
2357641
2367541
2457631
2567431
3457621
4567321
2346751
2356741
2456731
3456721
2345671

that is indeed 21

it seems that this is correct

[jagged raptor]

@wise wharf we found it

[wise wharf]

ok i chat gptd some code

it should give me all sequences for a given number

LETS GOOOO

7 is indeed 21

[jagged raptor]

GG

[wise wharf]

8 is 43

guys we did it

ok now

...

wanna see if we can at least reason why it would be this pattern?

forget a proof just a reason

[mystic tapir]

ok so we need to show f(n) = f(n-1) + 2f(n-2)

[jagged raptor]

The fact that it acendes then descends maybe

[mystic tapir]

what happens if you take all the sequences for n, and then remove the n from all of them

[wise wharf]

the mountain aspect works but not the position aspect

ok wait

maybe it has something to do with the fact that theres different patterns for odd and even numbers

so both are kind of needed for the next thing in the sequence?

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[wise wharf]

.close

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[bitter coral]

can someone answer my #1336210000867098656 ?

[bitter coral]

<@&286206848099549185>

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[little badge]

i need help

[little badge]

i need help can someone help me to solve this?

[hot lily]

A guy who created his acc today is able to understand the concept of individual channels 👏

[nocturne shard]

imagine the feeling when they know how to get help

[little badge]

i cant understand what are you saying i just want to sort this assesment can you guys tell me where i get this solution

[gritty rose]

Too bad they didn't read the rules about getting help

[little badge]

tell me the rules please

i am new here

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@little badge Has your question been resolved?

[crystal spruce]

@little badge #❓how-to-get-help he's probably referring to limit yourself to one question

Also I assume it's cuz it looks like ur asking someone else to do your homework for you

you also don't have any work done or started yet

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@little badge Has your question been resolved?

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@little badge Has your question been resolved?

[royal charm]

Also this

https://discord.com/channels/268882317391429632/1336224009771159563

[crystal spruce]

huh

[royal charm]

Matthew, you said you didn't know how to do any questions, then you did one. Then your said again you didn't know how to do them, and then you said you did know how to do two of them.

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[shut totem]

Ceiling within an inequation

Background of the problem
I was trying to come up with a formula to calculate the win chance of a combat in a videogame. To do that I tried a lot of different things like calculating the best and worst case damage of the player and cpu, the average amount of turns both of them require to beat the other, the best and worst case amount of turns etc, but nothing really came to an end. After that I tried to just do one example by hand which was very time consuming sadly and didn't help much.

The actual problem
After some back and forth I came up with the solution of taking the minimum damage and then adding the range of damage multiplied by a factor x (or 1-x ) for which: 0 ≤ x ≤ 1
to have a value to solve for as a sort of percentage "How much has to go right for me to win" kind of value. I then wanted to put that into a formula to calculate the turns required by both the player and cpu: ⌈ enemy_hp / damage ⌉
For both the player and the cpu those are basically the same, just that the damage calculation is slightly different due to the player having it calculated with 1-x
min_dmg + (1-x) * (max_dmg - min_dmg)
and the CPU having it calculated with x
min_dmg + x * (max_dmg - min_dmg)

I did it that way so if I win in a worst case scenario (my own damage always being the minimum damage (the inside of the bracket muliplied by 0)) would equal an x value of 1, or 100% to get the winrate of that scenario or a lose in the best case scenario would equal an x value of 0, or 0% winrate.
I then put both of the turn calculations into an inequality to see for which x values the player turns are less than the CPU turns to calculate the win rate.
But that is where I ran into the problem. I have looked at inequalities and understood them with no problem and I looked at ceiling and floor functions and think I understood them well enough.

But I don't see how I can combine both, the inequation and the ceiling. How could I go about solving that for x?

[mystic tapir]

this looks the kind of problem that would be easier to solve with code rather than math

[shut totem]

I mean kind of, at least for smaller number
But the numbers get rather high which would require a lot of computing power to simulate sadly

I was trying to find a formula so I can calculate it easier for 20-30 different levels to be able to use the winrate alongside the reward for winning to calculate which fight is most profitable and I don't think my computer could handle that if I solved it with code

[royal charm]

This question is quite hard and will not have a formula. The difficulty is not the inequalities or the rounding functions.

Try this with a simple case of something like 1-5 damage each, 30hp versus 32 hp.

[shut totem]

Yea I already tried it with low numbers and it was a ton of work, but I thought maybe if I could find the x there I would have at least an approximate winrate ^^
And if I can isolate the x, I thought I could use that as a way to calculate the x with a formula

[royal charm]

You can see pretty quickly that no such x can exist. Let's say you need x is 0.6 to win a certain fight. If you and opponent both have double hp, x will be 0.6 again. But the win rate will be very different.

[fallow thunder]

i think u could prolly solve this by introducing another var n=number_of_turns
then u could ditch the ceilings
u get some nice bounds like this:
enemy_hp/player_damage(x) < n and,
player_hp/cpu_damage(x) >= n

then u could only consider integer values for n

that might result in a good approximation

i got this:
(playr_hp / n - min_c) / (max_c - min_c)<= x <1 - (enemy_hp / n - min_p) / (max_p - min_p)

[full forum]

@shut totem Has your question been resolved?

[shut totem]

Would I then have to calculate that for many n values to see for which one that is correct?

[fallow thunder]

yeah i mean u could go mos plausible ones like u cant expect the battle to end in 1 turn unless the boss is super strong

u need to set a goal for number of turns

but going over multiple values of n is better

[shut totem]

Hmmm alright, I'll try that ^^
I have been sitting on this problem for like... 4 weeks now and my brain is thoroughly fried lol

Thank you!

[fallow thunder]

see if it works lol

[shut totem]

I gotta implement that once I am done with school
Gotta somehow integrate it into my excel sheet, but now I at least have something to work with

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[hallow walrus]

How do I find which zeros stay zeros in L and U?

[hallow walrus]

A=LU is the way this book has done decomposition, where L is lower triangular and U is upper triangular

for A, I believe L will keep the three zeros in the bottom left

since while eliminating we aren't doing anything to those, so the inverse of our row operations also won't have terms there

not sure about U

[fast peak]

U is the result after all the row operations

will you at some point during the row operations possibly add some nonzero number to these zeros in the top right half

[hallow walrus]

in the top right?

you mean the one in the second row?

yes, it will turn into -x

[fast peak]

those x's arent all the same value

[hallow walrus]

hmm actually I'm not even sure how you can write A as LU without doing a row switch

[fast peak]

they are just a placeholder

[hallow walrus]

oh

[fast peak]

its just nonzero vs zero

[hallow walrus]

hmm

still, the zero in the second row won't remain a 0

[fast peak]

yes

[hallow walrus]

so L retains the zeros in the bottom left but U doesn't retain the zeros in the top right

will it be the same for B?

[fast peak]

you'll have to check

[hallow walrus]

Ok so the bottom left 0 definitely remains in L

I think what I'm getting is that only the largest triangular 0 matrix remains in the decomposition

but that seems like a difficult thing to prove

[fast peak]

if you mean the correct thing then its obvious just from the way row operations behave

writing it out properly is just annoying at that point

[hallow walrus]

it does seem obvious

it's easier to visualise what U looks like than what L looks like

[fast peak]

you can just do induction for example and then you only have to do one layer and thats very doable

[hallow walrus]

right

[hallow walrus]

instead of multiplying all the inverse row operations I can also just row reduce in the opposite direction to get L right?

like bottom to top

[fast peak]

uhm

[hallow walrus]

or will that give me a different L

[fast peak]

L is just the coefficients of the row ops, no?

[hallow walrus]

yeah

[fast peak]

ignoring row switches which are a bit annoying

[hallow walrus]

we haven't dealt with row switches much yet

[fast peak]

so you dont have to imagine it as multiplying the inverse row ops

that makes it harder

[hallow walrus]

right

I can think about it heuristically

like "add row 1 to row 2, then add row 2 to row 3" becomes "subtract row 1 + row 2 from row 3, then subtract row 1 from row 2"

this one is just 5 and 9 right

[fast peak]

uhh, how are you doing row ops

in the first step you should only use row 1 for everything

in the second only row 2

and so on

[hallow walrus]

not like that

yes

that's how I'm doing it, I just gave a bad example

[fast peak]

yes. that almost seems too easy. not sure why they are calling that exercise important

[hallow walrus]

yeah I thought I might've missed something

[fast peak]

I suppose just the general idea that certain steps are independent of others?

[hallow walrus]

perhaps

I guess it also means that submatrices have a subset of the same eigenvalues

that also seems obvious actually so idk

[fast peak]

nonono

row reduction and eigenvalues are separate

do not mix them up

[hallow walrus]

are the pivots not the eigenvalues?

[fast peak]

row operations completely destroy any eigen-related stuff

no

[hallow walrus]

I assumed because the product of the pivots gave us the determinant, just like the eigenvalues that they were the same

[fast peak]

1*14=2*7=...

tells you nothing

[hallow walrus]

true

[fast peak]

all invertible matrices are row equivalent

do you think all of them have the same eigenvalues?

[hallow walrus]

what does that mean?

[fast peak]

row operations can translate one into the other

[hallow walrus]

right, but each one's diagonal matrix will be different right

or atleast there will be invertible matrices with different diagonal matrices

[fast peak]

under row operations you can make those all equal

scaling of rows is very obviously dangerous for eigenvalues

but the other operations also destroy eigenvalues

[hallow walrus]

so do the numbers in the diagonal matrix mean anything apart from "their product equals the determinant"

[fast peak]

no

[hallow walrus]

sad

M^T will be [A^T, C^T ; B^T, D^T] right?

not sure what conditions it wants me to say though

[sick vortex]

sorry maybe unrelated question but this is strang, right?

[hallow walrus]

yes it is

are you doing the same book?

[sick vortex]

yeah i was! i decided to review older concepts tho and come back to this

[sick vortex]

okay thanks

[fast peak]

presumably A=A^T, B=... and so on

[hallow walrus]

that doesn't sound right...

A doesn't have to be a square matrix for M to be symmetric

[hallow walrus]

oh interesting

[fast peak]

good catch I automatically assumed you would choose A as quadratic

I would assume strang also means that

its strange to not choose it as quadratic

[hallow walrus]

quadratic?

do you mean square?

[fast peak]

jeez

fuck me

quadratisch = german for square

[hallow walrus]

oh lol

yeah so that question seems weird

[fast peak]

second time I've made that mistake

its not like there is only one way to choose to write it as a blockmatrix

wlog you can always assume A square and so on

[hallow walrus]

right

[fast peak]

its very cursed to not choose it like that in a context where you want to transpose

[hallow walrus]

aren't rectangular matrices cursed in general

[fast peak]

more or less, yeah

[hallow walrus]

Like what kind of linear transformations are even practically studied

[fast peak]

🤷‍♂️

[tropic hill]

Hii kheeri

You probably don't recognize me but I remember you from last year

[hallow walrus]

Hello

[hallow walrus]

Oh, from this server?

[full forum]

@hallow walrus Has your question been resolved?

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[torpid pier]

How would I solve this? It's for a review and I can't find my notes on it. I know how to do [g o f] but idk how I would solve the first one

[leaden ermine]

f o g means g in f

[grave elm]

I'm suspecting it could be a typo

[grave elm]

they wrote f o x

[leaden ermine]

oh

haha

f((x))

[torpid pier]

Yeah cuz idk what x is

[grave elm]

if it's this, then the way they wrote it is absolutely terrible

[torpid pier]

Would it just be the original function?

[leaden ermine]

99 % it's not that

surely a typo

[grave elm]

Yeah, so it's a typo

[torpid pier]

Ok so it's probably f of g

[grave elm]

they most likely meant f o g

[torpid pier]

Ok cool

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[final wing]

what happened to the d/dx?

[fast peak]

what the hell is happening here anyway

[fast peak]

the y in the first integral is a dummy variable, its name doesnt matter

[honest hill]

hmmm, this format looks awfully familiar

[final wing]

ye i dont understand it at all

i love the part that i have been looking at 15 slides of differental equations and she hasnt shown 1 example so far

[honest hill]

which part is confusing

[final wing]

this part

[honest hill]

try this

[final wing]

swap d/dx by dy/dy?

[honest hill]

dy/dy is just 1

there definitely is some magic going on though

but this is the only thing i can see

[final wing]

aaah

@honest hill alright tahkn you i think i got it now

you understand why this is even allowed?

[honest hill]

you can multiply left and right hand side with anything, doenst matter

as long as its not 0

$\frac1{g(y)}\frac{\dd y}{\dd x}=f(x)$

[glossy valve]

Bonk

[final wing]

aaah

we now multiply by both sides

[honest hill]

this is what they have, they multiply LHS and RHS by g(y) to get y'=f(x)g(y)

[final wing]

i thought only from 1 side

[honest hill]

what uni is this btw?

[final wing]

erasmus

[honest hill]

ah, thats why it looks familiar

[final wing]

why?

[honest hill]

i didnt know they used the same template

i study at TUD

[final wing]

Aaaah what study?

Wait so you are dutch or international?

[honest hill]

dutch

[honest hill]

mathematics server, guess 🙂

[final wing]

Toegepaste/technische wiskunde

1 of those 2

i suppose

[honest hill]

its the same

[final wing]

oh really?

didnt know

[honest hill]

afaik they only have one maths program lol

[final wing]

aaah alright

[honest hill]

ah i think i understand, toegepast is the old one

they swapped to a new program and w/e this or last year

so now i think its called technische

[final wing]

aaah what year are you in?

[honest hill]

5....

[final wing]

damnn

what master?

or did you fail a year so had to redo it?

that is also possible ofc

[honest hill]

i started in the covid years

[final wing]

aaah that sucks

[honest hill]

its a miracle i made it past the first year tbh

and atm it looks like its going to be 6 years 🙂

[final wing]

aah shi

u like TUD tho?

[honest hill]

yeah definitely

wouldnt wanna go anywhere else

[final wing]

nice

[honest hill]

i just had bad work ethic

[final wing]

ye i was considering TUD or erasmus

[honest hill]

and discipline

just a bad student in general lol

[final wing]

same :(

[honest hill]

youre 2nd year?

[final wing]

1st

[honest hill]

ODE is 1st year?

hmm

[final wing]

ODE?

[honest hill]

ordinary differential equations

gewone differentiaal vergelijkingen

[final wing]

ja blijkbaar

we have first order, seperable first order and second order

[honest hill]

did you ever consider leiden?

[final wing]

not really

[honest hill]

based

[final wing]

cuz the only interesting thing about leiden for me was AI

[honest hill]

ew

[final wing]

but AI seemed too boring

and for TUD it was either the double bachelor

or for erasmus econometrics

[honest hill]

oh delft has it in first year program now too

[final wing]

AI?

[honest hill]

i know someone who does both

double bachelor AND econometrics

[final wing]

naaaah

[honest hill]

no, ODEs

but Q4

[final wing]

aaah

[final wing]

this is crazy work

[honest hill]

yeah it is

hes quite busy

[final wing]

quite!?

[honest hill]

hes smart AF though

in my first year i also had a kid who was 16

and did like 14 HS subjects

9 nines or smth crazy like that

[final wing]

ye some kids are just crazy

they have them here too

[honest hill]

no clue where hes now though

[final wing]

probably hong kong or something

earning millions

you already know what master u want to do?

[honest hill]

nope

havent rly thought about it tbh

[final wing]

aaah alright

anyways imma close this one

thank you man

and gl with your study :p

[honest hill]

np

[final wing]

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[fallow hamlet]

is this proof of rolle good? weiss stands for weierstrass i just think of weiss from nier replicant

[fallow hamlet]

of course excluding when m=M

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[prisma relic]

Hello, how can I solve this?

[prisma relic]

I tried to substitute various parts

But I always end up with very impossible calculations

[gritty rose]

does $z\bar{z} = |z|^2$ help

[glossy valve]

riemann

[prisma relic]

Not really, I end up with something as messed up

I tried that and also simplifying the z^4 with the z in the denominator or simply substituting everything with the corrispondent (x+iy), (x-iy) etc

[gritty rose]

did you use z^4 must be real

so that tells you some information about the the arg(z)

so maybe polar coordinates is a better approach than cartesian

[prisma relic]

I will now try, thank you

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[faint karma]

anyone know how i can frame x/y ?

[hybrid zephyr]

Just shade the region where x is between -1 and 3 and y is between -3 and 5

x/y can be anything tho

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[torn bane]

i wrote this as my answer but that wouldnt make sense

because if I meant k in (Z/NZ)* I could take k to be 2 and N to be 8, then gcd is not 1

so no inverse

lol then my answer was wrong? i guess?

wait i thought (Z/NZ)*={1,...,N-1}?

[full forum]

@torn bane Has your question been resolved?

[torn bane]

ohh i see

ahh

remembered wrong def

mixed up w F_p*

ahhhh

ok

[torn bane]

ahhh thats only is N is prime

ok!

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✅

[torn bane]

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[hot forge]

hey can you help me with this

[hot forge]

is it necessary for image to have the same dimension as the R3

[gritty rose]

you can try just using 1s and 0s

of course all 0s won't work because that'll give you the 0 vector

[hot forge]

the solution says that it doesn't exists, because dimension of im(T) cannot be 2

but i have trouble understanding why

any ideas?

[gritty rose]

can you show the full solution

[hot forge]

i asked chatgpt

[gritty rose]

[gritty rose]

can you not call AI "solution"

[hot forge]

sorry((

[gritty rose]

don't use ai for math

and don't use it to waste helpers' time

[hot forge]

sorry

[honest hill]

!nogpt

[full forum]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[hot forge]

desperate needs call for desperate measures

[gritty rose]

absolutely waste of time

[hot forge]

is there any way you can help me understand the problem?

or hint you might have

[gritty rose]

i tried

then you just ignored me

[leaden ermine]

just like ai 😂

[honest hill]

can you find $T:\R^2\to\R^2$?

[glossy valve]

Bonk

[hot forge]

can you be more specific? should i express R2 with 0 and 1

[hot forge]

what do you mean

[honest hill]

i dont understand how you cannot understand my question

[hot forge]

sorry guys im not very competent in this field, i just started studying it at uni and my questions might sound dumb to you

[honest hill]

you have seen this notation before right?

[honest hill]

ah.

have you seen stuff like $f:\R\to\R$?

[glossy valve]

Bonk

[hot forge]

i understand the transformation

but what do you mean by findind the transformation

i think we have no info about what sort of mapping it is

[honest hill]

you just have to give a T

like if its asking: Find a function $f:\R\to\R$ such that $f(x)=0$. Then an example of $f(x)=x$ would suffice

[glossy valve]

Bonk

[leaden ermine]

actually i am wondering how Im(T) = R² i kinda get the point of gpt lol

[honest hill]

||i was thinking T(x1,x2,x3)=(x1,x2,0) or does that not work??||

[gritty rose]

(1,1,0) is not in R^2

[leaden ermine]

yea i get that but it's not R^2 but really

[gritty rose]

such a dumb interpretation of the question though

[leaden ermine]

it's a subspace of R^3 a plane that resembles R^2 in R^3

[gritty rose]

should say isomorphic to R^2

[hot forge]

is image always in R^n where n is the R^n of matrix

wait no

it can be just R

[honest hill]

so question phrasing is bad?

[leaden ermine]

image of T refers to the space spanned by the column vectors of your transformation matrix

[gritty rose]

yea technically

[hot forge]

T(x1,x2,x3)=(x1,x2) is this possible?

ah the dimensions wouldnt work for multiplying

[honest hill]

then its not R^3->R^3

[leaden ermine]

it's even undefined

2x2 matrix times a 3x1 vector

[hot forge]

yea yea

[leaden ermine]

3x1 -> 3x1 is only possible with a 3 x 3 matrix

[hot forge]

so there is none?

or if not how do you prove that

[leaden ermine]

the question would make more sense if it were T : R³ -> R² because then you can actually make Im(T) = R²

with a 2x3 matrix

[honest hill]

mby theres a typo?

[leaden ermine]

or as riemann stated they meant isomorphic to R² which for you just means "similar"

[hot forge]

ok thanks guys i appreciate it a lot

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[chrome elbow]

Can someone please help me and tell me how to answer these questions

[chrome elbow]

<@&286206848099549185>

[safe trench]

!15min

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

[steel solar]

!15min

[full forum]

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

[steel solar]

Reminder that you're pinging thousands of people all at once; with great power comes great responsibility.

[chrome elbow]

its my first time here so not fully sure how it works

[steel solar]

Do you know the general equation for a circle, represented by it's center and radius?

[chrome elbow]

as in y^2 + x^2 = r^2

[steel solar]

More general. Note that for this equation, the center would be at (0,0).

[chrome elbow]

umm

am not sure tbh

[steel solar]

Okay.

Well, it would be (x-h)^2+(y-k)^2=r^2, where (h, k) is the center of the circle, and r is the radius.

Consider drawing a radius from that point of tangency at the y-axis to get the circle equation (the center, really).

I got to eat dinner, I'll be back.

[chrome elbow]

alright

thats fine

[chrome elbow]

ill do this and see where to go from that

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[primal root]

hello, can someone verify a solution i have for a question? its calculus 3 related

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[narrow shadow]

anyone know how to do 74c?

[narrow shadow]

answer is -1.3 x 10^2 J

[hot lily]

First, do you understand why the answer is negative?

[vestal moat]

You have to compute the total force normal to the plane, that will allow you to figure out the friction component parallel to the plane using the friction coefficient. Once you do that, you just apply the formula for the work

[narrow shadow]

negative because it's opposites

[narrow shadow]

why can't I just do 93 times sin(36.9) times 5 times 0.2

5 being the displacement

[hot lily]

Yes, the work by the friction is negative, because the friction opposes the box's movement

[hot lily]

How did you get 5 as the displacement

[narrow shadow]

because the 5 is the length

of the hypotenuse

[vestal moat]

Cause 85 will also have a normal contribution

[hot lily]

No, that is merely the length of the inclined plane

Wait

Is it

[narrow shadow]

yeah

right?

[hot lily]

Uh

Shakigras will help you :)

[narrow shadow]

idk what i put in my calculator

to get

the answer

of -130 J

• what to put

[vestal moat]

@narrow shadow, read what I wrote again.

[narrow shadow]

alr

oh

lemme see

[vestal moat]

you calculated the normal component of 95 by multiplying it by sin

you also need the normal component of the "85 force" which you will probably obtain by multiplying by cos

once you sum those normal components, then you can use the friction law to determine your total friction force

[narrow shadow]

i got 339.9 for that

hmm

[narrow shadow]

I got 85cos(36.9) times 5 for this

so the total frictional force is 619 J?

OHHH

I got it

ty

lmaoo

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[ashen grove]

Heyo. I was wondering if somebody could help me figure out if I did this correctly? I did 1) correctly, but I'm not very confident with #2

[ashen grove]

Lim x->1 sqr root(x+3)-2/(x-1)

Please ignore the 0/0 for now. I know that's not the correct way to show that

[hot lily]

Looks good

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[hearty sleet]

I cant even begin to prove this lol

[leaden ermine]

Maybe consider the sets Z_n* and Z_n\Z_n*

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[plain depot]

how to prove that -x^5 + 2x^2 - x -1 has exacly one real root ?

[plain depot]

I tried to use Bolzano-Cauchy theorem

since the function is contineous and f(0) = -1 and f(-1) = 3 therefore it must exist at least one root between [-1,0]

to prove that it has exacly one root i tried to go by contradiction and assume that the function has 2 roots so i can use Rolle's Theorem but it doesent work here

[fast peak]

there are results like descartes rules of signs which tell you stuff about the number of roots, which may be enough here

[plain depot]

i never heard of that but i will look it up

[fast peak]

you can also for example show that it is decreasing in that interval, giving only one root. and then show in some other way that everywhere else it cannot be zero

[plain depot]

i thought about that "method"

and i think it works but i was looking for an easy way

maybe there isnt one idk

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[torn jolt]

hey

[torn jolt]

just a quick question

when the exercises asks about the value of an variable lets say m, for which an system is compatible.

does it mean compatible determinated or undeterminated

or in both cases i have to check det(A) != 0

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[hardy void]

This is what I’m getting

Actually nvm it’s probably wrong

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[lament wagon]

just working on part a for now

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[torn jolt]

I need help on the 3rd problem. I tried finding x by 5√3/2 and its already in its simplest form and its decimal is 4.33. So idk what Im doing wrong.

[hot lily]

Uh, x = y/2

[river saddle]

side opposite to the 60 deg angle is always x * root 3, so what would x be

hint its 5

[viral ore]

For 3 you wanna use the the special right angle triangle for 30/60 degrees, the sides are multiples of 1, sqrt(3), and 2

[torn jolt]

yea ive been trying to divide the hypotenuse by 2 to get the short leg