help-19

[undone basin]

so you do E = mc^2

neutron star can't explode on its own

[last meteor]

theres a mechanism that activates the controlled explosion

[undone basin]

you don't have any quantities to work with

[last meteor]

the mechanism itself isnt relevant in the problem tho

quantities?

[undone basin]

do we need to use E = mc ^2

cuz i don't see any other way a nuclear star would give energy

[last meteor]

yeah

sorry for the delayed replies, Im doing many things atm

[odd edge]

@last meteor Has your question been resolved?

[odd edge]

@last meteor Has your question been resolved?

[odd edge]

@last meteor Has your question been resolved?

[odd edge]

@last meteor Has your question been resolved?

[mystic saffron]

What's the question?

@last meteor

[last meteor]

this

@mystic saffron

[mystic saffron]

Bro what are you cooking💀💀💀

[last meteor]

fictional firearm brah

[mystic saffron]

Alr

I'll try

5 mins

[last meteor]

kay

goodluck (you can do it)

SHOULD just be some geometry and physics

[mystic saffron]

Wait if every part is indestructible how will the neutron star be a weapon

[last meteor]

the neutron star is the thing that flings the slug

[mystic saffron]

Ohh right

[last meteor]

i just made every part indestructible so you dont have to account for any liek

variations

so to say

[mystic saffron]

So everything is going inside of this barrel

[last meteor]

mhm

well

the neutron star is in the chamber

the slugs' bottom face is right at the beginning of the barrel

[mystic saffron]

Why would the neutron star be in a chamber

That's just limiting man

Come on

Wiggle room?

[last meteor]

0 wiggle room

we can assume all the force goes into the slug

and nowhere else

[mystic saffron]

Alright

93x93 billion lightyear chamber with nothing except the slug in it near the neutron star

How about that

[last meteor]

why that?

[mystic saffron]

Idk

It's not even gonna affect the calculations

so who cares

[last meteor]

weapon is supposed to be mobile

[mystic saffron]

Ok fine

Smol chamber

[last meteor]

i did say a miniature netron star

[mystic saffron]

im gonna actually try now

[last meteor]

that has a 3cm diameter

[mystic saffron]

How would the hypothetical neutron star burst

It can either turn into a black hole or collide with another neutron star

Or are you simply referring to the nuclear yield

[last meteor]

kay so there are two miniature neutron stars inside that collide, creating a kilonova

this happens in a controlled environment in the chamber where black holes just wotn form

wont*

that kilonova will be the thing that propels the slug

[mystic saffron]

Sorry this is outta my ability 😭😭

Theoretical af

[last meteor]

o well

[odd edge]

@last meteor Has your question been resolved?

[cinder perch]

what is a slug?

like a literal slug?

slug

also i cant help this outta my league i just wnana know

[last meteor]

a solid projectile

@cinder perch

[cinder perch]

oh

[mystic saffron]

are you still online?

[proper solstice]

!nogpt

[odd edge]

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).

[analog flume]

I know this isn't what you want but friend from other server took one an approach of exploding the star 💀

[last meteor]

sweet jesus

~16.6 million times the speed of light

[spring nacelle]

Also just wrong

There's no limit to amount of kinetic energy an object with mass can have

You have to use the relativistic formula for kinetic energy

Which is unbounded as speed approaches speed of light

[last meteor]

don't know how to translate the info i posted about the firearm into the formula @spring nacelle

[spring nacelle]

This is how you would get it's speed if you knew the energy

Although this type of ballistics is more about conservation of momentum than energy usually

This is not a well formed question

[odd edge]

@last meteor Has your question been resolved?

[toxic rose]

pretty much

Your questions impossible to answer

because most importantly

you cant have a neutron star inside a gun, let alone any fictional weapon

and if its fictionals, just whip up a random number

[last meteor]

if the materials are indestructible, and there's a thing that prevents it from turning into a black hole

then it's possible

i mean for reference

have you seen the stuff in Xeelee sequence?

[odd edge]

@last meteor Has your question been resolved?

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[idle venture]

so im a bit confused what does it mean diagram? does it want me to do a diagram on the unit circle?

[long tinsel]

yeah probably

[idle venture]

even then like what would be the best way to do it? just draw 45 degrees?

[modern gyro]

Bro cosØ gives 1/2 at 60°

[idle venture]

oh shi yeah my bad lol

[modern gyro]

In first quadrant

[idle venture]

yeah

i literally have the unit circle right infront of me

[modern gyro]

Cos is positive in 1st 4 th quad

So its cos (60°) and cos (-60° ) = cos(300°)

[idle venture]

yeah

would i write cos(60) or just that its positioned at 60 degrees?

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[haughty remnant]

i have no clue where I went wrong in this

[little tulip]

u^3 * (1 - sin^2x) = u^3 - u^3 * sin^2x

it seems you did u^3 - sin^2x

at the end, almost, one of the last lines

[weary pelican]

yes

also

the u^3sin^2 x du part won't be revertible to dx

you should find a way to express sin^2(x) in terms of cot(x)

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[mystic saffron]

this question is extremely easy but its best to make sure completely

[mystic saffron]

when it says round to one decimal place

it just means to round to the nearest tenth?

[tender bloom]

Yes

[mystic saffron]

alr ty

[tender bloom]

So 1.14 becomes 1.1

[mystic saffron]

yep ty ty

[tender bloom]

Yw yw

[mystic saffron]

(im in geo but first time i hear one decimal place)

i just used to hear like 10nths 100ths

but i could infer it was 10nth but u can never make assumptions out of the blue

.close

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[marble vale]

hello, quick question

[marble vale]

how do i show it diverges when (0,0)

[green sage]

use divergence formula (sum of partial derivatives) and plug in 0,0

[marble vale]

what is the formula?

[weary pelican]

you're rather asking lim(f(x,y)) being divergent right?

[marble vale]

yes srry

[marble vale]

i can't fing two different sequences with different limits

[weary pelican]

well you got at least 1 limit right?

[marble vale]

yes 0

[weary pelican]

ok

then what about f(x,x)?

or f(1/n,1/n)

[marble vale]

it's with this one i found 0

[weary pelican]

how?

[marble vale]

wait it's 1/sqrt(2) actually mb

[weary pelican]

1/(2sqrt2)

[marble vale]

yes

[weary pelican]

ok

then just get 0 as well

[marble vale]

yes i just tae (0, 1/n) then

thanks 👍

.close

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[proven sphinx]

Help

[proven sphinx]

Shouldn't there be 12 in the last term?

Here marked in red

<@&286206848099549185>

[tall veldt]

yea they seem to have just misread the 12 as 2

[proven sphinx]

Yeah, was thinking the same

thanks for the support

I may still have some brain cell alive till now

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[pseudo glen]

will close this straight after js tryna get the bot to convert thist text

[pseudo glen]

• Sound Calculations:
  • Speed: ( \text{Speed} = \frac{\text{Distance}}{\text{Time}} )
  • Distance: ( \text{Distance} = \text{Speed} \times \text{Time} )
  • Time: ( \text{Time} = \frac{\text{Distance}}{\text{Speed}} )

[clever fjord]

2AM O'BlockBugha

[drowsy root]

#latex-testing

[pseudo glen]

oh ok thanks

.close

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[slender nova]

Hi I have a question from the book Mathematic Proof A transition to Advanced Mathematics. Here is what I did so far. How do I precede further?

[slender nova]

I don’t know how to find the maximum cardinality 😭

<@&286206848099549185>

[upper onyx]

assume 1 is in I,which other numbers could be in I?

[slender nova]

9

[upper onyx]

is one possibility, yes.
a) if 1 and 9 are in I, could there be another number in I?
b) does there exist anouther combination with 1?

[slender nova]

For (a) there couldn’t be because the whole set of A only has 10 elements while 1,9 combined has 8 elements and the minimum cardinality for the following A subsets is 3.
(b) it could be 4

[upper onyx]

so with I = {1, 9} you have 8 as cardinality for the union. try all other possible combinations for I and count each cardinality if you get a combination greater than 8.

[slender nova]

I guess 8 is the greatest.

Anyway thanks you.

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[untold blade]

how do i get from this monster $\frac{125-5t+25\sqrt{t}-t\sqrt{t}}{25-t}$

[untold blade]

to

5+sqrt(t)

i rationalized denominator

and somehow i have to get from that to 5+sqrt(t)

[wanton bison]

you need \sqrt{} btw

[nimble blaze]

when rationalising, don't bother expanding the numerator

[clever fjord]

MWB117

[nimble blaze]

that works against you

[untold blade]

oh

OHHHH

bruh it's right there

ok thanks

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[untold blade]

this reasoning is flawed right?

not all rational functions are continuous at every number in their domain

[viscid flint]

can you name a rational function that is not continuous at every number in its domain?

[untold blade]

oh would you not count the discountinuities in its domain?

[viscid flint]

are they part of its domain?

[untold blade]

no

alr i see

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[junior raven]

Hey there, I'm trying to learn integrals and I'm not really sure what I did wrong here

[junior raven]

Either it's wrong or I'm so terrible at simplifying that I'm not recognizing it as the same answer

Ah, it should be + lnx - x because I forgot to put the parentheses

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@junior raven Has your question been resolved?

[warped grove]

Hey! Do you still need any help?

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[junior raven]

Well, I think it's still wrong

[warped grove]

Aight lemme take a look

[junior raven]

But maybe not. Honestly I can't recognize the answer that wolframalpha is giving as the same thing, I tried multiplying it out and something still seems off

[warped grove]

so just to confirm, the integral is
[-\int(\ln(x)x^2 - \ln(x)),\dd x?]

[clever fjord]

kalman_filtERIC

[junior raven]

yeah that's right

[warped grove]

I think you just distributed the minus sign wrong

[\int(-\ln(x)x^2 + \ln(x)),\dd x,]
not
[\int(-\ln(x)x^2 - \ln(x)),\dd x,]

[clever fjord]

kalman_filtERIC

[warped grove]

so that gives
[-\frac19x^3(3\ln x - 1) + x\ln x - x + C]
as the final answer

[clever fjord]

kalman_filtERIC

[warped grove]

and yup that's equal to wolfram alpha's answer

[junior raven]

yeah that's what I have (after fixing the signs). Thanks. Well I'm screwed on this exam because I have to select the right answer out of 5 options and I cannot figure out how wolframs answer is the same

[warped grove]

alright let's take a look at wolfram's answer

,w integral of (-ln(x)x^2 + ln(x)) dx

[clever fjord]

Results provided by WolframAlpha

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

Requested by erictao

[warped grove]

this is the answer it gave you right ^

[junior raven]

Yeah,

[warped grove]

okay so basically

let's just expand it out

first let's multiply everything by the 1/9 x

that gives us what

[junior raven]

sec

the inside parentheses are confusing me

[warped grove]

you can also multiply out the inside parentheses first

if that's easier

[junior raven]

...okay you're right, it is the same, I forgot to distribute that ln(x) to both terms

when i took calculus 1 (a few years ago) they never made us simplify any of our derivatives and now i'm screwed

because I have to in calc 2

anyway thanks

[warped grove]

no problem haha

type ".close" if you don't have any further questions :)

[junior raven]

.close

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[sweet veldt]

Why is x = 1 the only answer?

[grand sparrow]

bruh

[sweet veldt]

Here

The photo took too long to send

[grand sparrow]

lol

lemme see the problem

[proven beacon]

thats b

whats the problem

[proven beacon]

Its the same image

[grand sparrow]

yeah..

what is th prolem

it should be 1

[sweet veldt]

Solve

[proven beacon]

Solve what

[sweet veldt]

Why not 3?

[grand sparrow]

one sec

bro

a=3^x

[proven beacon]

That problem is

(3^x)^2 = 27 - 6 * (3^x)

?

[grand sparrow]

see

[sweet veldt]

Yes

[grand sparrow]

you gte complex numbers

cuz

wait

what should be 3?

[proven beacon]

3^x can never be -9

[grand sparrow]

yeah

[sweet veldt]

Ohh ok

[proven beacon]

3^x can be 3, but 3^x can never be -9

[grand sparrow]

you get complex numbers

[sweet veldt]

I see

Thanks

[grand sparrow]

bucause if u try to write -9 in temrs of ers of 3

you cant

becuz -3^2 is NOT 9

so, =1

did you study quadratics?

[steep mantle]

if you add brackets it is :3

[sweet veldt]

I did yes

[grand sparrow]

true

[proven beacon]

-3^2 = -9 yes

[grand sparrow]

you could solve it with the root

[proven beacon]

(-3)^2 = 9

[grand sparrow]

oml

alr close this

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[warped grove]

@sweet veldt do you still need help?

[sweet veldt]

No

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[warped grove]

Ah okay

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[crude hollow]

From the sequence of natural numbers all the natural numbers are
deleted which contain digit 7 in their decimal representation to obtain a new sequence. Find the sum of first 200 terms of this new
sequence.[

[crude hollow]

help

idk where to begin

how do i figure out the no. with 7 in their decimal representation

[warped grove]

I would just list out the general pattern

for example you know 7, 17, 27, 37, etc will all get deleted

[crude hollow]

how?

[warped grove]

what other ones will get deleted?

[crude hollow]

what i try to find which will not get delelted first?'

would that help me?

[dawn tiger]

there's a lot more numbers that don't get deleted than get deleted

[crude hollow]

wait isthe decimal representation of multiples of 7 have 7

[warped grove]

The hardest part of this question is probably just trying to figure out what the 200th term of the new sequence is.

[dawn tiger]

better to keep track of how many numbers get deleted and subtract that from the number you've reached until that net amount reaches 200, then sum all the naturals up to that number and subtract off each number you've deleted

[warped grove]

Once you know where the 200th term is, it's not too hard to add up every number up to that number, then subtract out the numbers which got deleted.

But that's just a matter of counting and keeping organized.

[dawn tiger]

for example, let's say 40 numbers get deleted by the time i reach the natural number 240, then i can add up all the naturals up to 240 and subtract off the 40 numbers deleted

[crude hollow]

yeah but idk how to find those 40

[dawn tiger]

anything with a 7? so 7, 17, 27, ..., and then everything in the 70s

[warped grove]

Is your confusion about the words "decimal representation"?

[crude hollow]

but what about 35

[warped grove]

"digit 7 in their decimal representation" literally just means numbers that have 7 as a digit

[crude hollow]

0.0285714285714286

[dawn tiger]

are you thinking 35 would get deleted because 7 divides it? you only care about a number with the digit 7

[warped grove]

Where did this number come from?

[crude hollow]

what does decimal representaion mean?

[warped grove]

That's 1/35, not 35

[dawn tiger]

it just means the representation of the number in base 10

[crude hollow]

ohh

[dawn tiger]

in other words, the way you normally think of the number

if it contains 7 as a digit, it's gone

no not mod 7

if 7 is a digit

[nimble blaze]

dunno why they went this fancy with describing it, unless they intended something else

[dawn tiger]

mod 7 has to do with 7 dividing the number

you don't need mods here

[crude hollow]

yeah my bad

so 7 17 27 37 and so on

[dawn tiger]

exactly

[crude hollow]

got is thx

so 20 terms

[dawn tiger]

so let's say you start counting up the natural numbers until you reach the natural number n, and then you've deleted m numbers that contain the digit 7, then you'd want to figure out what n has to be so that n - m = 200

[crude hollow]

so u have sum of 220 terms - 7-17-27.......-197

[dawn tiger]

are you counting every term containing 70 as well?

[crude hollow]

oh that to

[dawn tiger]

because what you've described here isn't 220 terms, you're subtracting more than 20 here

[crude hollow]

so 70 and 170

so 222 terms

• the others

-*

[dawn tiger]

are there 22 "others"?

[crude hollow]

yeah ig

wahit no

also like 71,72,,,79

right?

and 171...

[dawn tiger]

7, 17, 27, 37, 47, 57, 67, 70,71,72,73,74,75,76,77,78,79,87,97,107, 117, 127, 137, 147, 157, 167, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 187, 197, 207, 217, 227, 237, 247

now clearly you need to get past 200 since you'll also be subtracting off some terms

[crude hollow]

thx

[dawn tiger]

try checking up to 242

i'm pretty sure that might work

count how many numbers between 1 and 242 you delete

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[odd edge]

@wild hull Has your question been resolved?

[tawdry cave]

!status

[odd edge]

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

[odd edge]

@wild hull Has your question been resolved?

[odd edge]

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[vernal yacht]

How do I demonstrate " integral from zero to fifteen" in limit form?

[faint knot]

what you replace x with needs to go from 0 to 15, but 1 <= k <= n (so 0 < k/n <= 1)

so replace k/n with 15k/n instead

,,=\lim_{n\to\infty}\sum_{k=1}^n\frac1n\qty(20\qty(15\frac kn)+\frac49\qty(15\frac kn)^2)

[clever fjord]

mtt

[odd edge]

@vernal yacht Has your question been resolved?

[vernal yacht]

Alr, how about if I want to integrate from 13 to 15? Do I replace k/n with 15k/n + 13?

[faint knot]

0 < k/n <= 1

0 < 15k/n <= 15

13 < 15k/n + 13 <= 15 + 13

13 < 15k/n + 13 <= 28

No

think of what the 15 does in these inequalities

then modify the 15 correctly for an integral from 13 to 15

[vernal yacht]

Like this?

[faint knot]

yep thats the one

[vernal yacht]

Tysm

[faint knot]

np

[vernal yacht]

.close

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[outer wadi]

If we have two linear equations 3x+2y = 4 and x + 4y = 3, and we want to find the point of intersection then we must make it so they cancel and add them right. So I understand why we are allowed to multiply and still get a point of intersection. I also understand why we are allowed to add them. What I am having trouble understanding is why does the resulting linear equation after the addition also forms a point of intersection with the two lines?

[leaden karma]

Say the intersection point is $(a, b)$

[clever fjord]

kheerii

[signal oar]

We know that 3x + 2y = 4 is always true. We know that x + 4y = 3 is always true. So if we add them both, we know that (3x + 2y) + (x + 4y) = 7 is always true, because the previous two are always true

[leaden karma]

No

This logic isn’t right

[signal oar]

What about it?

[leaden karma]

What do you mean by “3x+2y=4 is always true”?

[outer wadi]

ah I think I get it now

[signal oar]

I guess the phrasing is a little bad. I meant "Always needs to hold"

[leaden karma]

You mean at the intersection point

[leaden karma]

Which is why we use different variables for that

[leaden karma]

As this point lies on both lines, we have $3a+2b=4$ and $a+4b=3$

[clever fjord]

kheerii

[signal oar]

x + 4y = 3 must hold iff (x, y) lies on the line

[leaden karma]

Now, whatever we do to these equations (adding, subtracting etc) the value of a and b will remain the same

Hence why you can find any line which is concurrent with the original two

[leaden karma]

yeah

the problem with this is that it can cause confusion as to whether (x, y) is the point of intersection or whether they are variables

which is why we usually choose to label the intersection point with different symbols

[outer wadi]

Thanks I think I got it fully now

.close

[merry finch]

it's more like

[odd edge]

Channel closed

Closed by @outer wadi

Use .reopen if this was a mistake.

[merry finch]

${(x, y)\in \mathbb R\times \mathbb R|3x + 2y = 4 \text{ and }x +4y = 3}$

[clever fjord]

Frosst

[merry finch]

this set contains all the intersections of the lines

[signal oar]

Btw use \mid to make a | with a nice space left and right

[merry finch]

what do you use when you need it to auto size for matrices etc

[signal oar]

You mean for determinants?

[merry finch]

no

when i have a vector i need the mid line to be big

[signal oar]

Ah

[merry finch]

so that it autosizes like \left( and \right) does

[signal oar]

$\mrm{1 \ 2 \ 3 \ 4 \ 5} \Biggm| something$ works I guess

Nvm

[merry finch]

\left. \right|

otherwise it's confused where the left is

but then the spacing might not be ideal so that's why i asked

[signal oar]

True

There is biggm

[merry finch]

not big enough 😦

[signal oar]

That seems to do the spacing

[signal oar]

True, a little smaller than the vector

[odd edge]

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[wary forge]

i dont know how mathematical logic works

pls ping me

[inland rover]

where are you having a problem?

[wary forge]

i havent gone to college all year and have this in my assignment

i literally dont know what anything in this question means

what does ^,~ and v mean

[signal oar]

$\wedge$ means "and", \[5pt] $\vee$ means "or", \[5pt] $\sim$ means "not"

[clever fjord]

Kepe

[wary forge]

oh its basically like logic gates

?

[signal oar]

Yes

[inland rover]

yes kinda

[wary forge]

so its like (P nand Q)OR Q OR (P` AND Q)

right?

how am i supposed to simplify this?

[inland rover]

yes kinda

[wary forge]

so...?

i dont know how to simplify

[signal oar]

Do you know the distributive property for propositional logic?

I mean these

[wary forge]

nope

[wary forge]

i have never worked with these symbols
i only understand logic in computer science terms

. for and

_(in superscript) for not

• for or

[wary forge]

these are the 2 theorems right?

i forgot the name

[signal oar]

(P + (Q.R)) = ((P + Q) . (P + R))

[inland rover]

use boolean alg

for the question

[wary forge]

uh

[signal oar]

It's the first thing under "distributive law"

[wary forge]

wait

this is the question right?

[signal oar]

Seems right

[inland rover]

yes

now you can slove this

[wary forge]

i think i got it

p+q=p v q

[inland rover]

yes

[wary forge]

tysm

lmao i learnt the whole chapter within this thread

[inland rover]

lol

[wary forge]

.close

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[odd edge]

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[rapid rivet]

Guys I need an answer to this within 20 hours (I have school and classes so can’t think about it that much):

Josie and Kevin are each thinking of a two digit positive integer. Josie's number is twice as big as Kevin’s. One digit of Kevin 's number is equal to the sum of digits of Josie 's number. The other digit of Kevin 's number is equal to the difierence between the digits of Josie's number. What is the sum of Kevin and Josie's numbers? Give full justification and reasoning to each step.

[proven beacon]

josies what is twice as big as kevins

whats a member exactly

@rapid rivet

do u mean number?

[odd edge]

@rapid rivet Has your question been resolved?

[rapid rivet]

yes

mb

<@&286206848099549185>

[lavish mural]

hi I'm trying to do this rn lol

you could probably bash

or do u need like an actual solve

[rapid rivet]

actual solve lol

i need full justification for full marks

and like

yeah

[proven beacon]

my justification: i guessed it

[lavish mural]

let Kevin's number be AB

then you have 2 cases

[rapid rivet]

ive tried modular arithmetic and algebra but might have done it wrong

[lavish mural]

Josie's is 2A 2B or 2A+1 2B-10

Then solve cases

or if you want it algebraically instead of that funny method

10A+B

Is K's

[proven beacon]

isnt it backwards

[lavish mural]

oh oops my bad

[proven beacon]

i mean josies number being twice than kevin

[lavish mural]

yeah ik

so K's is 10A+B and J's is 20A+2B

[stoic island]

what is the problem

[lavish mural]

you can do this mod 10

brb lemme solve

[rapid rivet]

similar to what i did before i think, not sure if it works well

[lavish mural]

there's 4 cases

u can just casework

[rapid rivet]

wait how did you reach the 4 cases

dont entirely understand

[lavish mural]

from the statements given

you know that j is 20A+2B and K is 10A+B

[rapid rivet]

where did the 2A + 2B come from

[lavish mural]

equal to sum means mod 10

[lavish mural]

...?

assume both A and B are less than 5

then the sum of digits is 2A+2B

[unreal quiver]

Where does A = 2A + 2B - 9 come from

[lavish mural]

A=2A+1+2B-10

sum of digits assuming b is not less than 5

A<5 by the way

[rapid rivet]

so for all cases we assume a is less than 5 or is it for some only

[lavish mural]

all

a cannot be more than 5

since then J's number would be 3 digit

[rapid rivet]

ah yes

[rapid rivet]

here, how did you get 2A+1 2B-10

[lavish mural]

if 2B>10

[unreal quiver]

Can you solve the system of equations above?

[odd edge]

@rapid rivet Has your question been resolved?

[lavish mural]

...no; I also can't find a solution trying individual numbers from 10-45

[rapid rivet]

i got it

17 and 34

i think

works

kevin number is 17
josie 34

[lavish mural]

wait I'm stupid I did it the other way

I thought Josie was the properties of Kevin 💀💀

no wonder I had no solution lmao

[rapid rivet]

lol

my strategy:
try numbers

👍

[lavish mural]

alr nice that u found it ig

[rapid rivet]

craziest strat

[lavish mural]

there's a different method

[unreal quiver]

I have been trying to solve but can't find the solution. I am about to brute-force it

☠️

[rapid rivet]

A<5 helped a lot

[lavish mural]

you could find the sum of digits then divide by 2 and check if it's mod 10 then solve

[lavish mural]

it's more stupid but it works

[rapid rivet]

i knew it couldnt be 4 because it results in a minimum of 84 for josie which is not possible

nvm i forgot how i did it

[lavish mural]

I'll see if this method works later

I'm gonna go shower now lol bye

[rapid rivet]

bye

[unreal quiver]

Btw, where does this problem come from?

algebra?

[rapid rivet]

it's some math olympiad practice problems

[odd edge]

@rapid rivet Has your question been resolved?

[odd edge]

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• Show your work, and if possible, explain where you are stuck.
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• Be polite and have a nice day!

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[elfin temple]

Why is there ambiguity in the rules of logic? That there is Contrapositive statement of negative universal statement is not equal
This is modern square of opposition logic by Venn/Boole

In the book "A concise introduction to a logic by J. Hurley 14th edition" Im learning chapter about Categorical Proposition. There is section called "Conversion, Obversion, Contrapositive" and Im learning this section now

I have some transformations of statements that are both correct:
First transformation

No A are B
No non-B are non-A - Contrapositive
No non-A are non-B - Conversed
All non-A are B - Obversed

Second transformation

No A are B
All A are non-B - Obversed
All B are non-A - Contrapositive
No B are A - Obversed
No A are B - Conversed

Have I done this transformation correctly and if Yes. How is that possible?

Obverse always equal to previous statement
Converse always equal to the previous statements like "No A are B" or "Some A are B".
Statements like "All A are B", "Some A are not B" not equal after converse

But contrapositive have different rules. It firstly doing converse, then complement of subject and predicate.

But still I don't understand why after Obversing "No A are B", contrapositive of obversed statement gonna be equal to original statement "No A are B".

But without Obversing it's not equal to original statement after making contrapositive.

• Pink means empty. There is no members at all
• X means. There is at least one member of a class
  • By the logic of Venn/Boole - particulary always means that there are at least one member of particular class
• No pink or no X. Is about existentiality. Meaning that. There can be or cannot be any members. But we can always assume that there are members
  * By the logic of Venn/Boole - universalities doesn't mean that something of a class of universal exists

[odd edge]

@elfin temple Has your question been resolved?

[elfin temple]

<@&286206848099549185>

[odd edge]

@elfin temple Has your question been resolved?

[dark kraken]

Is that diagram your work or materials? The top 4 are not what I would expect

[elfin temple]

Those diagrams are from book by J.Hurley

[dark kraken]

Do the pink lines mean not included?

[elfin temple]

Pink means empty

[dark kraken]

Ah okay

[elfin temple]

X means. There is at least one member of a class

Circles without pink or X. Is about existentiallity

Meaning that. There can be or cannot be any memebers

[dark kraken]

Yes that’s right I just incorrectly assumed pink text means pink elements

Especially since all A are B does not convey any information on the size of B\A

[elfin temple]

All A are B by author and I guess Boole/Venn logic means that "There are no members of A that is outside of B"

[dark kraken]

Yes you are understanding correctly, I’m just complaining about their notation, sorry

[elfin temple]

Ah okay

Here's a book. If you or someone needs. It's really cool and interesting to read

[odd edge]

@elfin temple Has your question been resolved?

[warped grove]

Okay I'm not sure I understood your question, but: a statement is not equivalent to its converse.

For example, "all presidents are humans" is not equivalent to "all humans are presidents"

So if a converse is involved in your transformation, you shouldn't expect to get an equivalent statement

[elfin temple]

Yes. But look at diagram about conversity

"No presidents are humans" the same as "No humans are presidents"

That's sounds logicall too, right?

[warped grove]

Ah I see what you're saying

Yeah

I still don't get what your question is. Why do you think you did the transformation wrong?

It looks correct to me

[elfin temple]

The main question. Why there is ambiguity about Contrapositive statement of negative universal statement

That "No A are B" is can be or not equal to it's contrapositive. Where main thesis in logic is it can not

Basically. Contrapositive of "No A are B" is "No non-B are non-A". Both statements are not equal

But if we replace "No A are B" with it obversity "All A are non-B" that are both logically equal. This contrapositive of obversity becomes equal to the original statement

[warped grove]

Well it's because the operation of contrapositive, as it's presented in your book, preserves the logical content when the statement begins with "All" but not when it begins with "No"

You might think of contrapositive as a manipulation of symbols. There's no reason why it should or shouldn't preserve the truth value. But it happens that when the statement begins with "All", it does, and when the statement begins with "No", it doesn't.

It's irrelevant that the statement beginning with "All" and the statement beginning with "No" are equivalent, if they are obverses.

Personally I have only learned the word contrapositive for implications. In that case, the contrapositive of "A implies B" is "(not B) implies (not A)", and that manipulation always preserves the truth value. But when you apply it in this way to statements involving "All", "No", and "Some", it's different.

I think your question is about well-definedness. Normally, we'd think that if two logical statements are logically equivalent, and we perform an operation about them, the operation should return two logically equivalent statements. That's only true if the operation is well-defined with respect to logical equivalence though.

[elfin temple]

Preserves the logical content?

Actually. Book tried to explain what is modern square of opposition. The main logic behind this that universalities preserves existentialism. Meaning that
Quantities with qualifiers like "No", "All" - called "universalities". Means that this is not 100% that member of the class exists
"Some" "Some are not" are qualifier of particularity. Means that there is always exists at least one member of that class

[warped grove]

Meaning, produces a logically equivalent statement.

All and No just behave differently under Contrapositive, in this framework, as shown by the venn diagrams. There's no reason why they ought to behave the same.

[odd edge]

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

[charred yarrow]

oops

nv

m

wrong one sry

[elfin temple]

So. I mean. Can author of the book be wrong? Or why does this happens. Or is that something new. Or I kinda not understand.

We can say for example "No qualified scientists are scientists that don't know how to be prepared"
Like this
"Scientists that know how to be prepared are qualified scientists"

With my transformations. It can be both true and false

[warped grove]

Well answer this question first: why do you think All and No should behave the same under Contrapositive? Why can't it just be the case that the Contrapositive manipulation is valid in some situations but not valid in others?

[elfin temple]

Because logic is exact science, isn't it?

[warped grove]

Logic is exact, sure. And the exact logical rule here is that Contrapositive is valid for statements that begin with All, and invalid for statements that begin with No.

I'm just asking why you object to that.

[elfin temple]

No no. I'm not objecting this

I'm trying to explain that statements that begin with No are both valid and invalid in contrapositive situation

With "All" I don't have this ambiguity

[warped grove]

Let me try to follow what you are arguing here. So you start with a statement

1. No qualified scientists are scientists that don't know how to be prepared.
   Then you take the obverse
2. All qualified scientists are scientists that know how to be prepared.
   And even though statements 1 and 2 are logically equivalent, Contrapositive is invalid for Statement 1 and valid for Statement 2, so there must be something wrong.

Did I understand your argument correctly?

[elfin temple]

I spelled this wrong. AAHHH

"No unqualified scientists are scientists that don't know how to be prepared"
"No prepared scientists are qualified scientists"

[warped grove]

Ah okay

But that's a case where Contrapositive is invalid, right? The first sentence is false when there is a scientist who is both unqualified and doesn't know how to be prepared. The second sentence is false when there is a scientist who is both qualified and knows how to be prepared.

And that agrees with our general rule that Contrapositive is not valid when you apply it to a sentence that starts with No

[elfin temple]

It's not about validity. It's about truth value btw

That. Truth Value are not the same

Yeah, sorry. From start I meant truth values

===============================
For example:
"No unqualified scientists are scientists that don't know how to be prepared" - for example true

"No prepared scientists are qualified scientists" - undefined truth value

But I discovered that truth value of statements that starts with "NO". Can have truth value both true and false

[warped grove]

Why is the latter one undefined?

[elfin temple]

That's have it spelled in the book

Let me open it w8

[warped grove]

By valid, I mean: the sentence you get after the transformation has the same truth value as the original sentence in all possible scenarios.

[warped grove]

I think by undetermined, they just mean you can't figure it out based on the truth value of the original sentence. It still has a truth value, but its truth value is not related to the original sentence's truth value.

[elfin temple]

Here's the other thing. Okay. Let's look at Venn Diagrams

[warped grove]

To give an example, let's say we live in a world where all scientists that are prepared, but some are qualified and some are unqualified. Then,

No unqualified scientists are unprepared scientists.
is true because no scientists are unprepared, but the contrapositive
No prepared scientists are qualified scientists.
is false because there are prepared scientists that are qualified scientists.

Now, let's say we live in a world where all scientists are both qualified and unprepared. Then,

No unqualified scientists are unprepared scientists.
is still true because there are no unqualified scientists, but the contrapositive
No prepared scientists are qualified scientists.
is also true because there are no prepared scientists.

So we can't say what the truth value of the contrapositive sentence is, just given the original sentence. The two sentences have no logical relation between each other.

[elfin temple]

First transformation
Second transformation

Respectively

Blacknes is pinkness in the book(Emptiness)

[warped grove]

Okay

So the first transformation is just Contrapositive, what did you do to get the second one?

[elfin temple]

Obversed and then contrapositive

Being Obversed always equal. Right?

[warped grove]

Yes.

Those transformations look correct to me.

[elfin temple]

Contrapositive of original gives one Venn Diagram
Contrapositive of obversed gives another Venn Diagram

Is something wrong with second transformation? Or is that something new in logic overall. Because I don't get it.
Maybe I'm missing the point...

[warped grove]

Your transformations are correct. It just illustrates again, that when you have a contrapositive of a "No" statement, you get a different Venn diagram, but when you have a contrapositive of an "All" statement, you get the same one.

In the second transformation, you transform the No statement into an All statement by taking an obverse, so by the time you take the contrapositive, it's already an All statement and no longer a No statement, so taking the contrapositive yields the same Venn diagram.

I think the thing you're confused about is what you get when you apply a contrapositive depends not only on the meaning/truth value of the statement, but also on what form you write it in.

You can write the same statement in multiple logically equivalent forms, one starting with "All" and one starting with "No", but Contrapositive will only work right if you give it the form starting with "All", not the form starting with "No".

[elfin temple]

Yes. Technically you are correct. Are there any practicall situations of it?

I mean im asking simple question like
2 + 2 equals 2 and not equals 2

[warped grove]

Here's an analogy. Let's say I invent a new operation called Clumping a sum where I take the first element of the sum and multiply it by two. For example, after I apply Clumping to 5 + 7, I get 10 + 7.

Now, let's say I start with the sum 3 + 4.

• Transformation 1: First, I apply Clumping to get 6 + 4. Then, the result is 10.
• Transformation 2: First, I rearrange 3 + 4 into 2 + 5, which is the same sum. Then, I apply Clumping to get 4 + 5. The result is 9.
  Why do the two transformations yield different outcomes? My rearranging was perfectly valid because 3 + 4 is the same value as 2 + 5, and I applied Clumping once in each case.

[elfin temple]

But. I mean how can I believe a person who talks like this. If we can convert statement in the way that it can give both true and false. That's nonsense, right?

[warped grove]

No. Take a look at the analogy I just posted.

[elfin temple]

Oh. Wai waa???

Wow

Okayy

[warped grove]

Yeah, you'd expect the same outcome, right? So why does it give different results?

Is math broken?

[elfin temple]

But thats weird. If we use analogy. Then clumping is obversity?

First transformations should be equal

W8 a bit

Yeah. Analogy correct. But still seems weird. But okay thanks very much

[warped grove]

No, Clumping is Contrapositive in this analogy

And rearranging is Obverse

But yeah, the point is that Clumping depends not only on the value of the sum but also the way you write it

In other words, it's not a "well-defined" operation with respect to the value of the sum

Similarly, Contrapositive depends not only on the truth value of the sentence but also the way you write it

[elfin temple]

I mean of course.
To do contrapositive statement you are doing:

Converse, then Make Complement subject and predicate. Equals Contrapositive

With "ALL" statement. Converse is not equal to original
With "NO" statement. It is equal

Yeah. Right. Okay. I just need more time to think about it. But thanks very much. I think it's solved

I wish I could be a student and in a proper math university

[warped grove]

No problem at all :) Feel free to open a new channel and ping me if you need more help thinking about it

.close

[odd edge]

Channel closed

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Use .reopen if this was a mistake.

[odd edge]

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[late tendon]

how the z transfomr of the first expression is z/z-1/4 while i have found 1/1-4z ?

[shell solstice]

how did you find 1/(1-4z)?

[late tendon]

i meant 1/(1-4z^-1)

[late tendon]

hm

[shell solstice]

actually could you type that out in latex please

[late tendon]

how

[shell solstice]

$\frac{1}{1-4z^{-1}}$

[clever fjord]

idioticbaka1824

[shell solstice]

is this what you mean

[late tendon]

$\frac{1}{1-1\frac{4z^{-1}}}$

[clever fjord]

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

[late tendon]

no

[shell solstice]

$\frac{1}{1-(4z)^{-1}}$

[late tendon]

1-1/4z^-1

1/4z^-1

[clever fjord]

idioticbaka1824

[shell solstice]

is this what you mean

[late tendon]

yes

[shell solstice]

okay multiply the top and bottom by z

[odd edge]

@late tendon Has your question been resolved?

[odd edge]

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[crisp bay]

Is this correct? I wanted to figure out formula for total conditional probability (just like we know that P(A) = sum P(A, Hi), where Hi is a partition of probability space)

[crisp bay]

The problem i have is 1. A|B isnt actually an event, its a notation
and 2. i split A | B at the last equality which i dont know if it's allowed

[ocean bramble]

you would have probability of A given the intersection of B and Hi

or probability of A intersection Hi, given B

[odd edge]

@crisp bay Has your question been resolved?

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[frigid escarp]

How can I solve this problem?

[ember oak]

Consider the axioms of vector spaces

Are they all satisfied?

[frigid escarp]

i'm having problems with distrubitve property.
assume x =1, y= -1, u = inf
when (x + y)(u) = (0) * inf = 0,
however,
xu + yu = (1) * inf + -1 * inf = inf + -inf = 0.
so it it correct?

i have checked addition, multiplication, zero vector, additive inverse, associativity they checks out correctly.

[ember oak]

All of these?

[frigid escarp]

ye

[ember oak]

oh

[frigid escarp]

for any u,v,w belongs to V.
u + (v + w) = (u+v) + w.
for real numbers, assosicaitvity holds as usual.
for inf and - inf, the provided ops do not conflict with associtivity.
(t+inf) + (-inf) = t + (inf + (-inf)) = t + 0 = t.

[ember oak]

I see something

[ember oak]

Try other example for distributive property

[frigid escarp]

for dist of scalar multip with respect to vector addition.

for any scalar a in R, and vector u,v belongs to V.
a(u+v) = au + av.

for real numbers this holds by definition.

for inf and -inf i chcked a specific cases.

for example a*(inf + (-inf))
= a * 0 = 0, and
a * inf+a * (-inf) =
ainf + a-inf = 0.

i think problem might arrise in distrbutivity of scalar multiplication with respect to field addition?

[ember oak]

Consider with respect to field addition

Think on this

[frigid escarp]

for any scalar a,b in R, and vector u belongs to V.
(a+b)u = av + bv.

for real numbers this holds by definition.

for inf and -inf i checked a specific cases.

for example (a+b)(inf) = a * inf + b *inf, and similairty for ~inf.

[ember oak]

for example (a+b)(inf) = a * inf + b *inf, and similairty for ~inf.
Okay but what ends up happening?

[frigid escarp]

if a,b signs are different?

we get different results?

wait let me think about it.

a=4, b = -3.
(a+b)(inf) =
a(inf) + b(Inf).
+inf + -inf = 0.
however, (a+b)(inf) = + inf?

i'm getting different results under inf, when I distribute.

in the first case since a+b is positive by definition.
I'll get +inf.
however, a is positive i'll get + inf, and b is negative so i'll get - inf.
and + inf - inf = 0.
so this is not true. so it's not a vector spcae?

it make sense for me, please tell me it's true x.x

[ember oak]

Tell you what is true?

[frigid escarp]

that the elements inf and negative infinity do not satasify the distv propeity of scalar multiplication with respec to field addition.
hence, it's not a vector space.

thank you! @ember oak you are the best

.close

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[whole yew]

I really need help with this question. If V= [-3 -1 4] and u=3 what is uV. This is matrices.

[frigid escarp]

the definition of scalar multiplication for a vector.
is taking each cordinate and multiplying it the scalar.
Let A = (a1,a2,a3,...,an).
and let lambda be a scalar.
lambda by A = (lambda * a1, lambda * a2,..., lambda an).

given this definition @whole yew what is the answer to your question?

[odd edge]

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[shut wedge]

hi, how would you find the asymptotes for this question?

[charred tundra]

So this function logically can't have a vertical asymptote because the denominator can't be zero

[shut wedge]

yep

[charred tundra]

You can try horizontal asymptotes by taking the limit as x approaches infinity

[shut wedge]

?

[pliant latch]

ywa

yes

your answer is?

[shut wedge]

problem is

i thought this only lead to 1

how would there be a -1?

[pliant latch]

x -> - infinity

[shut wedge]

if x approaches - infinity, would the top become negative and the bottom would remain positive due to the x^2?

[pliant latch]

ya

[shut wedge]

oki thx

.close

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[dense jolt]

he says x intercept is x = 4 and y intercept = y = 2

[dense jolt]

can someone explain why

[nimble blaze]

by definition

what property do points on the x-axis have?

[dense jolt]

not sure

[nimble blaze]

can you list a few points that are on the x-axis

(any)

(forget about the equations you have for now)

[dense jolt]

oh, 2?

[nimble blaze]

no

[dense jolt]

oh x

[nimble blaze]

no

[dense jolt]

looks like 3?

[nimble blaze]

no

[dense jolt]

damn it

[nimble blaze]

I'm asking for points

[dense jolt]

(0, 3) ?

[nimble blaze]

that doesn't lie on the x-axis

that lies on the y-axis

[dense jolt]

oh so (3, 0) ?

[nimble blaze]

can you identify others?

[dense jolt]

(2, 0) ?

no

(0, 2) ?

(2, 1) ?

now it just looks like iam saying anything

[nimble blaze]

only one of those lie on the x-axis

[dense jolt]

knew i should have studied before, rather than cramming in 3 hours before a test

[nimble blaze]

do you know the equation of the x - axis?

[dense jolt]

4 - 2y ?

[nimble blaze]

no

not an equation either

do you know what I'm referring to when I say x-axis

[dense jolt]

the horizantal axis in the graph

[nimble blaze]

yes

and can you tell me the equation of that line

or plot a few points on that line and tell me what they all have in common

[dense jolt]

equation maybe x + 2y = 4 ?

[nimble blaze]

no

(forget about the equations you have for now)

[dense jolt]

how is y intercept 2?

[nimble blaze]

what I'm asking is purely about the property of the x and y axis

you'd need to know this to be able to identify intercepts in general

on some piece of graph paper can you
highlight the x-axis
plot a few points on the x-axis
tell me the coordinates of those points

or if you know it, tell me the equation of the x-axis

and I'm repeating this

(forget about the equations you have for now)

[dense jolt]

wait

x = 0?

[nimble blaze]

no

[dense jolt]

am i close atleast?

[nimble blaze]

sorta,

[dense jolt]

y =0?

[nimble blaze]

yes

the equation of the x-axis is y = 0

thus to determine the x-intercept, you'd sub in y = 0

[dense jolt]

ahhhh

[nimble blaze]

same idea for the y-intercept

[dense jolt]

gotchaaa

thanks alot!

.close

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[mystic saffron]

can someone help me find the vertex of the parabola 4x = y^2 - 4y?

[viscid flint]

complete the square in y

[mystic saffron]

i got 4 + 4x = (y - 2)^2

[viscid flint]

ok solve for x

[mystic saffron]

x = (y - 2)^2 -4 /4?

nah

[mystic saffron]

on lhs take 4 common

[gusty pulsar]

Only 4 is divided by 4?

[mystic saffron]

oh no the whole thing

[mystic saffron]

GCF of 4?

[gusty pulsar]

Then that is right, yes

[mystic saffron]

wait so now what

[mystic saffron]

compare
standard form of a parabola: ((y - h)^2 = 4p(x - k))

take 4 common

so p = 1

[gusty pulsar]

Actually I don't think that's needed. The parabola's vertex will be at y=2

[mystic saffron]

vertex at k = -1 and h =2

cuz when vertex is at origin h,k = 0,0

[gusty pulsar]

Yeah actually it will be at y=2. You don't need to divide the right side by 4. x = (y - 2)^2, x = (y - 2)^2 + 5 and 6x = (y - 2)^2 + 24 will all have the same vertex y

[mystic saffron]

when I take out 4 i got 4(x +1) = (y - 2)^2

and then would the vertex be (-1,2)?

yup

you got it.

ohhh thank u!

thank you for your effort too fix error!

.close

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[wise sonnet]

could i get help finding a quick ratio?

[indigo crater]

!da2a

[odd edge]

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/

[wise sonnet]

.

[indigo crater]

do you know what is quick ratio?

[wise sonnet]

I found the current ration and working capital but havent founf the quick ratio,

As far i know its all cash, accounts receivable and short term accounts / total current liabilities

[indigo crater]

yeah... basically the total current assets without inventory

divide by current liabilities

[wise sonnet]

i got 2.33

without inventory?

[indigo crater]

I got 1.55

Yeah

[tender bloom]

I got Lincoln

Wtf

[indigo crater]

inventory is not quick

well, quick assets is things that you can easily liquidate to cash without inventory

[wise sonnet]

I was confused because i googled inventory and it said it was considered quick

[indigo crater]

yeah... but in most case, we don't consider that

depends on your business

if it is easy to liquidate, then sure

[wise sonnet]

Thank you. I will probably have more questions later. Should i close the room for now?

[indigo crater]

and by the way, <@&268886789983436800>

yeah you can close it

[wise sonnet]

.close

[odd edge]

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[warped grove]

I'm not really sure what you meant by this, but please don't interrupt other people's help channels

[odd edge]

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[modest void]

do you guy know how to solve this parallel vector problem

i filled in the values and it was simplified to

-20i -8j simplified

but idk how to solve for parrell

parallel

i thought to find parallel you have to divide by the square root of both the numbers squared added

[indigo crater]

think about it for a second: what does a parallel vector mean?

[modest void]

a vector in the same direction

[indigo crater]

yes.

so for some scalar k and if A is parallel to B, I can say A = kB (why?)

[modest void]

what is scalar?

[buoyant hinge]

something you multiply your variable by

[modest void]

isnt scalar different from vector

oh so i can just pick a random number?

[buoyant hinge]

yeah

and you use a scalar to multiply to vectors because multiplying vectors gives something else

[modest void]

so is the vector is -20i-8j

i can just multiple both numbers by 2

and that works?

[buoyant hinge]

ummm

[modest void]

so what kind of numbers would i multiply that cna work

[mystic saffron]

69

[buoyant hinge]

first you want to find the direction to z

[mystic saffron]

[buoyant hinge]

by finding the components in i and j

i think its -12i - 8j

[modest void]

bro 💀

[modest void]

wait so how you find the direction?

[modest void]

its -20i -8j

[buoyant hinge]

oh damn

well

more or less that is the direction

[modest void]

oh its the 3rd quad right

[buoyant hinge]

but if you want a unit vector you divide by its magnitude

z divide by |z|

[modest void]

that what i though like (-20i-8j)/sqrt( (-20)^2 + (-8)^2)

that wahts i thoguth u do

but when i did that same thing for the previous version of that question i did

i got it wrong

cause when u add both direction and sqrt it it gives the magnitude right

[buoyant hinge]

maybe (-20)i/sqrt464 + (-8)j/sqrt464

because that is the direction but you could also simplify by take out a factor 4 from 20 and 8

making to 4(-5i -2j)/sqrt464

even more take out the negative from the components

because it did ask for a simplified version and also simplify the surd

and rationalise

[modest void]

oh okay so make sure to rationalize and try that

i get 3 tried to get it correct

so i should ratonilize first

[modest void]

and the try this next ig

wait do if i take out the ngative woulnt that change the direction

[mystic saffron]

Hehe

[mystic saffron]

Take - as common?