help-27

[maiden bridge]

how do i implement this in python? do i just slice off the string at the 10th digit in each line and them sum all of them up?

[mortal vale]

didnt u already find a solution

idk if this new approach is going to be faster in python

[kind tiger]

just realised that just because our digits are length m our sum may be way bigger

hm ig not all too much you can do to worry about that

just makes the chance of this even lower

[maiden bridge]

yes i did, i was just interested if its possible to get faster speeds in python

[kind tiger]

i would say any additional overhead you add is gonna end up slower

if you were working with like thousands of thousand digit numbers then you might see the gains

but at this scale probably just slower

[maiden bridge]

yes makes sense

still glad to know this approach

thankyou everyone

.close

[devout snow]

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[devout snow]

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[radiant breach]

When I used conservation of momentum, I got u1 - u2 = v2 + v1 - A Wrong

[radiant breach]

Correct answer is D?

Answer used coefficient of restitution, but I don't understand why conservation of momentum is wrong?

[jaunty mantle]

I think you’ve assumed equal mass in your use of conservation of momentum

[rare kernel]

How do u know if mass of spheres is same

[radiant breach]

Yep I see it now ty

Just out of curiousity tho, if they did have the same mass, why would only coefficient of restituion not work

[wicked turtle]

none of the answers make sense unless you assume the masses are the same

[lilac moat]

why are they spheres, that's so abstract. they should be balls

[wicked turtle]

they should be ideal point particles, cmon this is physics 😆

[jaunty mantle]

Oh the arrows are just being tricky

[wicked turtle]

ah wait i take that back

still i think there's something dubious here

[devout snow]

@radiant breach Has your question been resolved?

[radiant breach]

Well if both are true, and we add them together, then we'd get u1 = v2, which doesn't sound completely unbelievable

Ik this aint a solution, but im just trying anything atp

Ok I think that works acc

u1 = v2
u2 = v1

So the balls just bounce in the opposite directions, with eachers inital speeds

As shown in the simulation

@devout snow question resolved

.close

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[alpine mist]

find the parent equation
I feel like im doing this wrong. i don’t think i was suppose to square root to find t? cuz now i have two solutions😭

[alpine mist]

would square rooting kill off solutions? (that’s what my teacher said I think)

[drifting sinew]

Keep going, you're doing fine so far.

[sharp kayak]

no unless you miss the +- which you got

[drifting sinew]

This looks good, but I recommend simplifying this.

[drifting sinew]

Finally, consider the $-2 \le t \le 2$ to restrict the domain of your Cartesian function.

[woven radish]

@drifting sinew

[alpine mist]

idk how I can simplify it further other than writing square root of x/3 as (x/3)^1/2 😭

[alpine mist]

nor do i know how to implement this :/

[drifting sinew]

Actually, now that I take a closer look at your answer, it seems like that's the simplest form.

[drifting sinew]

You might be overthinking it.

• What is the minimum possible value of 3t^2?
• What is the maximum possible value of 3t^2?

[alpine mist]

min: when t = 0, so 0
max: when t= 2, so 12

[drifting sinew]

✅

[drifting sinew]

Now you can restrict the domain with an interval of x.

[alpine mist]

[0,12]

do I have to do the range too

[drifting sinew]

I don't think so, unless it was explicitly asked.

[alpine mist]

it didnt

so I would just write the final answer like this?

tyy

.clos

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[wispy geyser]

am i right with B here

[wispy geyser]

<@&286206848099549185>

@misty crest reactin but aint contributing

😭

[misty crest]

you’re the guy that cheated right?

"am i right with __ here"

[kind tiger]

just submit it and find out 😭

you dont need someone here to check every answer

not gonna have that luxury in an exam

and if you dont learn how to check your own work youll be screwed when that does come along

[misty crest]

my guess is it’s a graded quiz

[kind tiger]

yeah i assumed but just use wolfram alpha lmao

or like ... a calculator

[misty crest]

some people aren’t that bright..

like dawg why go here to cheat

just go to some llm or google or whatever

this isn’t something that’s hard to generate an answer for

[wicked rover]

pls show work

[devout snow]

@wispy geyser Has your question been resolved?

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[royal laurel]

Is there any formula that relates to joules

[royal laurel]

Work?

E=mc^2

How about watt?

[knotty sage]

any type of energy get the units joules... not sure what is your question here

[royal laurel]

How about watt?

[knotty sage]

J/s

(in SI units)

[royal laurel]

How do I know and memorize?

Is there any formula relates to it

[knotty sage]

P=W/t
P=Fv
P=mgd/t
P=E/t

power has the unit watt (joules per second)

[royal laurel]

What about volt

[knotty sage]

J/C (from W/q)

joule/coloumb

[devout snow]

@royal laurel Has your question been resolved?

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[onyx fog]

hi

[brave cipher]

hey

[onyx fog]

i need help with math

[brave cipher]

whao

[onyx fog]

yes

[brave cipher]

what is it my gngie

[onyx fog]

gngie

[brave cipher]

alrt my fault dawg

[tall knoll]

!da2a

[devout snow]

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/

[onyx fog]

what is gngie

[brave cipher]

just gang but w ie

its pronounced gang-ee

[onyx fog]

i need help with math

[brave cipher]

whoa

[onyx fog]

linear programming

[brave cipher]

ok what is it

[onyx fog]

linear programming

[brave cipher]

🤓

[onyx fog]

chapter

[brave cipher]

dawg idk what problem you need help with 😭

[tall knoll]

you need to ask a question if you want someone to help you

[onyx fog]

two tailors a and b earn 150 and 200 per day , a can stich 6 shirts and 4 pants while b stich 10 shirts and 4 pants per day how many days shall each work if it is desired to produce 60 shirts and 32 pants at a minimum labour cost also calculatae the least cost

[devout snow]

@onyx fog Has your question been resolved?

[fossil locust]

first step is to set up the inequalities, as in convert the words to maths

if A works for x days and B works for y days, how many shirts will they make all together?

then they must produce 60 shirts or more

[devout snow]

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[last pebble]

the digits of a 2 digit number differ by 3, if the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?

[last pebble]

need help

[last pebble]

idk how to get the number so if anybody knows abt it help me.

[junior chasm]

let the numbers a and b

[last pebble]

k

now what?

[junior chasm]

the digit at unit place is b, and tens place is a

and the question says difference between the number at tens place and the number at ones place is 3

so a = b+3

[last pebble]

ok

[fossil locust]

also, the 2 digit number is 10a + b

[junior chasm]

you can write the two digit number has 10a + b

a is b+3

so 10(b+3) + b

[fossil locust]

yeah that's enough information to set up a 2nd equation (the digits are interchanged....)

okay I should shut up I guess

[fossil locust]

I feel like I'm stepping on you

[junior chasm]

nah

[last pebble]

so how to do the 2nd equation?

[junior chasm]

digits are interchanged

[last pebble]

ok

[junior chasm]

first is 10a + b

so if u interchange digits

what do u get

[fossil locust]

yeah so the reverse number isn't 10a + b but...

[last pebble]

um 10b + a?

[junior chasm]

yes

now what?

[last pebble]

add it?

[junior chasm]

yes

[fossil locust]

yep

[last pebble]

bro how do i add it?

it just a and b

[junior chasm]

.

[last pebble]

but we dont know b right?

[fossil locust]

the digits are a and b

but your numbers are 10a + b and 10b + a

[fossil locust]

that's the whole point

[last pebble]

so how can we get it?

[junior chasm]

solve the equation

[fossil locust]

as you said you add the numbers

[last pebble]

idk how to

[junior chasm]

10(b+3) + b + 10(b) + b + 3 = 143

solve for b

[last pebble]

uh 10a + b + 10b + a = 143?

[fossil locust]

yep

and then you can sub in a = b + 3

multiple ways exist

[last pebble]

what if we dont need 2 variables?

just stick with x

[junior chasm]

x is a variable too

[last pebble]

but it aint 2

just 1 variable

[junior chasm]

u can

the second number will be written as x+3

just as b+3 here

[fossil locust]

the issue is that x can be anything, but we know x is a two digit number with digits a, b

[junior chasm]

i just took a for a more bottom up approach

[fossil locust]

it's hard to encode this specific info into x

[junior chasm]

oh like that

nah

[last pebble]

10x + x+3 = 11x + 3

for the ffirst one

and for the 2nd

10(x+3) + x =10x + 30 + x

11x+30

[junior chasm]

yeah

its the same thing

[last pebble]

so 2nd is 11x + 30

now we add them both?

[fossil locust]

yeah

[junior chasm]

yes

[last pebble]

11x + 3 + 11x + 30 =143

22x + 33 =143

22x = 143 - 33

22x = 110

x = 110/22

5

x = 5

x + 3 = 8

so 58!!!

58 + 85 = 143!!!

[fossil locust]

yeah, and we actually made a important assumption at the very start

[wispy geyser]

could anyone help with my question here

[junior chasm]

!occupied

[devout snow]

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

[fossil locust]

we actually assumed that a > b here

so like 58 is fine

[wispy geyser]

my bad

[fossil locust]

but if you start off with 85, that also works

58 + 85 = 85 + 58

[last pebble]

ye ik that

so someone close this?

[junior chasm]

its .close

[last pebble]

.close

[devout snow]

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[devout snow]

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[fathom bough]

"The train tracks must turn 45 degrees.

The train tracks are 1.5 units apart.

The train will turn 45 degrees over 6 units horizontally, and 12 units vertically."

The Train must turn 45 degrees and the train is in the exact middle of the tracks. therefore the tracks on one side will be X degrees less than 45 degrees, and the other one will be X degrees more than 45 degrees

I am modelling a set of train tracks in Unity3D

<@&286206848099549185>

forgot to say I am trying to find out how to manipulate the track's angles in order to like

make the train tracks accurate

[devout snow]

@fathom bough Has your question been resolved?

[devout snow]

@fathom bough Has your question been resolved?

[devout snow]

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[viral rapids]

a long time after the switch has been closed to position X, the 4C capacitor has a charge Q. then the switch is closed to position Y. find the energy stored in the 4C capacitor after a long time

[thick ledge]

Where are you stuck on

[viral rapids]

idk how to start

actually

ik that after a long time the voltage across the capacitors are equal

[thick ledge]

After a long time(while switch is still jn position X)

What is the charge on it?

[viral rapids]

Q

[thick ledge]

I.e write Q in termsof C and E

[viral rapids]

4CE

[thick ledge]

Yeah okay so when it is switched to Y and left for a long time, what will happen

[viral rapids]

the 4C capacitor will discharge and the C capacitor will charge

[thick ledge]

Until?

[viral rapids]

they have equal voltage

[thick ledge]

Yes

So assume some charge q that has flown through the circuit.

Then charge on 4C will be Q - q and charge on C will be q

Equate the pd of both the capacitors

As as steady state, no current flows through the resistor

[viral rapids]

why Q-q

[thick ledge]

Cuz net charge on the circuit should remain constant

[viral rapids]

oh

so (Q-q)/(4C)=q/C?

[thick ledge]

Yeah

[viral rapids]

Q-q=4q

[thick ledge]

Wait no

Negative

Sign should appear

Apply KVL on the circuit

You'll understand

[viral rapids]

isn’t it Vc-V4c=0

[thick ledge]

Depends on the direction as well

[thick ledge]

Instead of writing this, write the polarity of plates of C and 4C and then conveniently do KVL

[viral rapids]

polarity means positive and negative right

[thick ledge]

Yes

[viral rapids]

how do you figure that out

[thick ledge]

Just observe in which plate the charge q is flowing into for C

The lower one right?

So that plate becomes negatively charged

And since same charge q is coming out from the upper plate, that plate becomes positively charged

[devout snow]

@viral rapids Has your question been resolved?

[viral rapids]

oh

[devout snow]

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[thick ledge]

What's an "aleks" ?

Uh could you show a question (a specific one)

If y9u had a doubt in it

[autumn girder]

That is prolly not a good idea to do that on internet and to a person who you don't knw

<@&268886789983436800>

[thick ledge]

Sigh

[autumn girder]

I feel bad for her brother and hope he recovers soon

[thick ledge]

Yeah

[modest dagger]

I don't think that justifies trying to cheat.

[autumn girder]

Well I personally am of the opinion that health is more important than academics

[thick ledge]

Nothing wrong with praying for his health though

[ember palm]

damn wtf was that

[modest dagger]

Me too, that doesn't make it okay to cheat.

[ember palm]

tf is goin on is someone sick?

[modest dagger]

Somebody was trying to get folks to cheat for their sick brother.

[thick ledge]

It's true i was the folks

[modest dagger]

Usually the bot closes channels after the original q gets deleted.

[autumn girder]

Welp, whatever, I hope she realises the danger she was gonna put her brother in by trying to publically share his ID

[autumn girder]

That's what I was thinking too

[modest dagger]

Ah yeah that is no good.

[autumn girder]

That is what I was gonna reprimand her about when the mods got to her

Well whatever

@modest dagger would you like to do the honors or should I do them?

[modest dagger]

You got this

[autumn girder]

Alr

.close

[devout snow]

Channel closed

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[autumn girder]

IDK why this was required but whatevs

[devout snow]

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[restive river]

So I know an algorithm to construct a propositional formula A s.t every boolean formula can be expressed as the truth assignments of A. My question is, how does one prove that construction indeed work?

[faint zinc]

@restive river I'm not quite sure I understand the question.

Can you give a simple example of your algorithm in action?

[restive river]

Alr let me find it. Basically taking disjunctions of (conjunctions for every row). For example, if one row has T,T,F and output T, and other row has T,F,F and output T, then A = (p1 and p2 and ~p3) or (p1 and ~p2 and ~p3)

Ok what Id like to know is how to elaborate the last paragraph of the proof

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[shell heron]

Can someone help with a proof? I'm not sure how I can start?
I'm given a Tree T with a root r and a collection of nodes N
I have to proof that the relation "..is a ancestor of ..." is a partial order on K
I know that in order to prove partial order you have to confirm reflexivity, asymmetry and transitivity but I how do I even begin? Do I just use induction?

[devout snow]

@shell heron Has your question been resolved?

[gleaming niche]

I don't think you need induction. Define the "is ancestor of" relation, and go from there.

[devout snow]

@shell heron Has your question been resolved?

[devout snow]

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[heavy quail]

Hi how would I go about solving this integral

I tried using power reduction formulas and u-subbing Cos[2x] but it's getting me no where

Im thinking of splitting the Cos^4(x) into Cos^2(x)*Cos^2(x) but im not sure which formula I can use

[timber pebble]

maybe 2sinxcosx hmm

[runic grove]

nah

sinx = k

[timber pebble]

think this works out

[runic grove]

@timber pebble

[timber pebble]

right

[heavy quail]

i'll have a lash rq

[runic grove]

a what

[timber pebble]

now (1-cos2 x)

[heavy quail]

i'll have a go thanks

[runic grove]

no wait i have another idea

[timber pebble]

and ur fine

i think

[devout snow]

@heavy quail Has your question been resolved?

[devout snow]

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[cinder plover]

This is the formula to find an area under the parametric curve

[cinder plover]

Problem 36

How do i know which function to declare the derivative? and which one shouldnt need it

Like should I make x the derivative function

or y the derivative function

How would I know

[timber pebble]

yea

you can kind of remember it like

normal "little area slice" of a function is y * dx

just multiply by dt/dt

$y \dv{x}{t} \dd t$

[woven radish]

jan Niku

[timber pebble]

if thats helpful

[cinder plover]

how would i know when to make y the derivative function instead

[timber pebble]

hmm well you know it makes sense to pretend y is a function of x here because otherwise its not a function

x cant be a function of y in the graphs you showed

it fails the horizontal line test (the vertical line test but for x(y) )

[cinder plover]

in that case

y would always be normal?

like you wouldnt need to take

the derivative of it

am i understanding that

[timber pebble]

i dont understand what youre attempting to extrapolate out to generale rule here, i guess

it doesnt really matter which one you take the derivative of as far as the formula is concerned, no

but #1 the problem asks for area between the curve and the x-axis

and #2 these functions arent functions if y is the indepedent variable

these 2 things clue you in that you should not be taking the derivative of y(t)

does that help?

if they arent true, if you want the area between the curve and the y-axis, then yea maybe in that case

[cinder plover]

it does

tyahib7\

tf

thak u

[timber pebble]

tyahib7\

[cinder plover]

.close

[devout snow]

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[devout snow]

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[tall sand]

im not sure where to go from here

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[restive river]

So for any who knows, i am the same person solving this problem again but with a different approach

Because i believe that the shape cut has to be a constant shape that can only be enlarged

And can be constructed by forcing a rectangle into a circle (wont work but the base of the rectangle will become a circle while the outermost will just be a arc)

Imagine rolling a book into a cylindrical shape, the pages will form this special shape

Im outside but i could if you want

Jkjk

Here is what i was thinking about

[lilac tulip]

theoretically it is made of N number of circles, each with a radius of r + (n * delta(r)), where delta(r) is the thickness of the paper

[thick ledge]

Are you only talking about the shape formed by the pages?

[restive river]

New info idk if its useful ornot, this shape can be resized and cut based on the values of s

[restive river]

More or less yes

[restive river]

Yess

[lilac tulip]

are you trying to find the amount of printing space you would get?

[restive river]

No not really

Im finding a way to cut a roll of sheets such that when unrolled have equal dimensions

[lilac tulip]

if you are okay with loss of paper, then an inverted triangle would do the trick

[restive river]

Yes im ok with the loss

Whats a inverted triangle gonna do to help

[lilac tulip]

something like this

would get you equal sheets

to find the angle

[restive river]

Wow thats kinda boring but a great solution though

What would the dimensions of this triangle be

[lilac tulip]

$$ 2 \pi r_1 = \frac{\theta}{360} 2 \pi r_2$$

[woven radish]

Edward kenwey

[lilac tulip]

here r1 would be the inner radius and r2 would be outer radius

so the angle would be

$$\theta = 360 \frac{r_1}{r_2}$$

[woven radish]

Edward kenwey

[restive river]

Wait what angle is this

Angle for arc length?

[lilac tulip]

so the triangle would be an isoceles triangle with angle being theta

[thick ledge]

interesting

[lilac tulip]

no the above angle

the angle between the lines of the triangle

not a triangle really, but an arc

[restive river]

Ohhh that

[lilac tulip]

yea

the above one

[restive river]

Is it so?

[lilac tulip]

this angle

[restive river]

Oh

Wouldnt that be hard to measure

[lilac tulip]

if you are doing this practically

draw a straight line from the base to the tip

find theta

find theta/2

then mark that angle on either sides

and make your cut

but the smaller the inner radius, higher the paper loss

[restive river]

I see

[restive river]

Well its ok because its just a puzzle i want to solve

But thanks anyway

[lilac tulip]

alr alr

good luck

[restive river]

Wait

But what if

I want to reduce paper loss

[lilac tulip]

im not sure i know any way

[restive river]

What should i do to the inner circle after the cut

Lets say the paper roll i have isnt hollow

[lilac tulip]

inner circle is hollow

[lilac tulip]

well then you would have 100% paper loss

and you have to figure out another way

its too smart for me to figure out

[restive river]

Hmmm i see

Dont worry i will try my best to find another approach

Tq for your help

.close

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[fiery briar]

what does the n sign in the middle mean?

[stable flare]

That would be the intersection

[lyric hornet]

the intersection symbol, but in probability I've seen it be used as "and"

so this is said in English as "the probability of event R and Q"

[fiery briar]

ohh ok that makes sense thanks

[stable flare]

Isn’t that union tho

[fiery briar]

what would the one with the line down the middle mean then?

[lyric hornet]

that's or

[stable flare]

I think you might have it mixed up

[lyric hornet]

that is said in English as "the probability of R such that Q"

that is, given that event Q has occured, what is the probability that R occurs?

[lyric hornet]

happens, I just think of the venn diagram

usually helps

[stable flare]

Wait…

You might be right

I was looking at this originally

But most other sources suggest the opposite basically

[lyric hornet]

Yeah cause that wouldn't make sense, the intersection is where both A and B are true, which only makes sense for and

and the union is where either A or B are true, which only makes sense for or

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[crisp mason]

hi i have a question regarding limits, this part is for one asking about a population model (first order ODE things)

i need to prove that
$\lim_{p to 0^+}f(p) = 0$
where
$f(p) = -k p \log(\frac{p}{a})$
i don't think i can just plug it in because there is a condition that $p > 0$, so i thought to use the sandwich theorem, i know the upper bound could be just $lim_{p to 0^+}0$, but i don't know what the lower bound would be

[woven radish]

dis_da_mør

[devout snow]

@crisp mason Has your question been resolved?

[devout snow]

@crisp mason Has your question been resolved?

[thick ledge]

Have you tried doing l'hospital

[crisp mason]

would the fraction be $\frac{f(p)}{1}$ ?

[woven radish]

dis_da_mør

[thick ledge]

Fraction?

[crisp mason]

because that's what l'hopital's rule requires?

[thick ledge]

Idk what y9ure saying but write p as 1/(1/p)

And then use the rule

[crisp mason]

i tried and it didn't work

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[devout snow]

@humble siren Has your question been resolved?

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@humble siren Has your question been resolved?

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@humble siren Has your question been resolved?

[brave plaza]

I suggest you make a substitution write $p = \frac{x+y}{2}$ and $q = \frac{x-y}{2}$, so now using sum of cosines and sum of sines $a = \cos{x} + \cos{y} = 2\cos{p}\cos{q}$ and similarly $b = \sin{x} + \sin{y} = 2\sin{p}\cos{q}$

[woven radish]

yuka

[brave plaza]

and we wish to find $\cos(2p)$

[woven radish]

yuka

[brave plaza]

we want to keep using p and q from here

note that $\frac{b}{a} = \tan{p}$

[woven radish]

yuka

[humble siren]

ok. how to use tan p?

[brave plaza]

theres a formula for cos2p in terms of tanp there is also $\tan^2{p} + 1 = \frac{1}{\cos^2{p}}$

[woven radish]

yuka

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[round tendon]

I know how to solve this if only one of the numbers are x but not when there is two

[peak needle]

use the chord chord intersection theorem. you will get a linear

[wind mason]

Do you know the chord-chord power theorem?

[wind mason]

Pretty sure it'll be linear

[round tendon]

im not sure

[round tendon]

doubt it will be quadratic because theres only one solution to x

[peak needle]

yes, i misread the chords

it is a simple application of this theorem

[round tendon]

so (x+3)(15)= (2x)(12)

[peak needle]

indeed

[round tendon]

so first minus two?

i mean three

and you get (x)(15)= (2x)(9)

or am i just being a lil stupid rn

[peak needle]

i hope you can solve linear equations. just multiply out the stuff and simplify the equation

you will get x=5

[wind mason]

!noans

[devout snow]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[peak needle]

i think the main meat of the answer was in applying the chord theorem, for which i did not give out the answer directly

[wind mason]

Yeah, you need to distribute first though

[wind mason]

It's still an answer though, its not like it is trivial for OP lol

[round tendon]

ok so (15x+45)=(24x)

[peak needle]

continue

[round tendon]

-15x from both sides'

45 divided by 9

so x=5

thx guys

.close

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[peak needle]

glad to help 😄

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[north roost]

did i do anything wrong?

the book says all questions in the section requires CR (rightside contraction)

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@north roost Has your question been resolved?

[rose verge]

I

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[cinder bay]

step by step please I’m dumb

[rare kernel]

first multiply both sides by 2k

[cinder bay]

2k times it self then multiply 2k by 4?

[rare kernel]

do u know how to cross multiply?

[cinder bay]

yeah multiply across numbers

@rare kernel I realize I can cross multiply, just that there’s still the H sooo

because both of them are fractions

Wait when I cross multiply them normally, I get -6k/12k??? I have no idea on what to do here, especially with the H in the way

<@&286206848099549185> yo?

I can’t be this dumb where ion get any help💔

[full rampart]

We got (h-3k)/2k = -3/4.

Divide numerator and denominator on left hand side by "k" to get

(h/k-3)/2 = -3/4

Now solve it simply to get h/k on one side and a number of other side then solve for k.

Try this method and solve it

@cinder bay

[cinder bay]

why is the k in front of the negative?

and why are we diving h by k

dividing

[full rampart]

It is (h/k) - 3 and not h/(k-3)

You can do with the normal method of multiplying both sides by 2k

[cinder bay]

wait can u use the texit bot

[full rampart]

Aah ok let me try

[cinder bay]

so it shows what it looks like

alr ty

[full rampart]

$$(h-3k)/2k = -3/4$$

[woven radish]

Shubham1029

Shubham1029

Shubham1029

[full rampart]

You see? You can solve for h/k from here

Then get k in terms of h

[cinder bay]

I don’t think I wrote this correctly

[full rampart]

Or do it by normal method like
(h-3k)/2k = -3/4
h-3k = -3k/2
...

[full rampart]

Oh

Sorry my bad

[cinder bay]

nah it okay

[full rampart]

Do you understand what I just did here?

Dividing numerator and denominator by k?

[cinder bay]

u just divided by 2 on the other side

[full rampart]

Actual equation

[full rampart]

Dividing numerator and denominator by k

[cinder bay]

yeah but I don’t understand why the k is being divided now

[full rampart]

Multiplying by 2 on both sides

[full rampart]

It is a trick so that all variables (in this case h and k) come in a single term

So that we can seperate variables on one side and numbers on other

Is it going over the head?

I mean if you get it, you are ok to do it like normal. I did not mean to confuse you.

[cinder bay]

so it’s used to get rid of the h variable?

[cinder bay]

nah ur good

[full rampart]

Basically it makes calculation easier.
You once do it like normal then do it with this method and compare.

[cinder bay]

If multiply by both sides by 2, why is it -3/2 and not -3/8?

[full rampart]

Maybe in not this question but in many others it works better

[cinder bay]

alr what’s the next step

[full rampart]

$$-3/4 * 2 = -3/2$$

[woven radish]

Shubham1029

[full rampart]

Multiply by 2 gives -3/2, not -3/8

[cinder bay]

oh mb

I understand that now

[full rampart]

$$h/k-3=-3/2$$

[woven radish]

Shubham1029

[full rampart]

$$h/k=3-3/2$$

[woven radish]

Shubham1029

[cinder bay]

added 3 to other side

[full rampart]

$$h/k=(6-3)/2$$

[woven radish]

Shubham1029

[full rampart]

$$h/k=3/2$$

[woven radish]

Shubham1029

[full rampart]

$$2h/3=k$$

[woven radish]

Shubham1029

[cinder bay]

where the 6 come from

[full rampart]

How do you calculate 3 - 3/2?

[cinder bay]

well u put 3 as a fraction

3/1 - 3/2

[cinder bay]

that’s not even a answer choice

[full rampart]

This is option B

[cinder bay]

cuz that’s saying 2h is numerator

wait

[full rampart]

Is Option A mentioned as Correct answer?

[cinder bay]

ye nvm

[cinder bay]

no that was my guess after spending 10 hours

[full rampart]

Oh

[cinder bay]

I got no clue what the answer was

[full rampart]

How do you solve it further

[cinder bay]

and it doesn’t tell u

[full rampart]

Oh, option B is actually the correct answer

[cinder bay]

would just be 3/1 or idk

[full rampart]

Oh you haven't learnt how to add two fractions

[cinder bay]

alr thanks

[full rampart]

3/1 - 3/2

You have to make denominator same to subtract or add two fractions so you multiply "3/1" by 2 on numerator and denominator to get

$$32/12 - 3/2$$

[woven radish]

Shubham1029

Shubham1029

[cinder bay]

ohhh I see

[full rampart]

Now denominator is same so you can subtract

$$(6-3)/2$$

[woven radish]

Shubham1029

[full rampart]

$$3/2$$

[woven radish]

Shubham1029

[full rampart]

You understand?

[cinder bay]

yeah I do

[full rampart]

That's how you get the 6 there

After that any problem?

[cinder bay]

.close

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[vestal jacinth]

Genuinely forgot how to do this

[full rampart]

Area = (1/2) (sum of lengths of parallel sides) (height)

[tawny pewter]

you can also split it into 2 triangle and one rectangle

and sum the areas

[vestal jacinth]

idk sounds easier the first way

on top of that my brain is fried

but thanks for the help tho

.close

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[wind mason]

??

[potent tusk]

its over he knows ahh channel

[faint gorge]

tonights not the night

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[thorn oriole]

So, I'm looking to get help with defining Jacobi Elliptic functions WITH a complex value for k

Currently using this function:

void sncndn(float u, float k2,
            out float sn, out float cn, out float dn) {
  float emc = 1.0-k2;
  float a,b,c;
  const int N = 4;
  float em[N],en[N];
  a = 1.0;
  dn = 1.0;
  for (int i = 0; i < N; i++) {
    em[i] = a;
    emc = sqrt(emc);
    en[i] = emc;
    c = 0.5*(a+emc);
    emc = a*emc;
    a = c;
  }
  u = c*u; sn = sin(u); cn = cos(u);
  if (sn != 0.0) {
    a = cn/sn; c = a*c;
    for(int i = N-1; i >= 0; i--) {
      b = em[i];
      a = c*a;
      c = dn*c;
      dn = (en[i]+a)/(b+a);
      a = c/b;
    }
    a = 1.0/sqrt(c*c + 1.0);
    if (sn < 0.0) sn = -a;
    else sn = a;
    cn = c*sn;
  }
}```

I've tried usng real parts, imaginary parts and lengths squared where the function is expecting a float but the variable is complex, but haven't gotten it to work.

[devout snow]

@thorn oriole Has your question been resolved?

[supple knot]

Try #computing-software

[thorn oriole]

Will definitely do, but also gonna leave this up for a bit in case someone wants to help me tackle it. 🙂

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[spring gulch]

The definition in the image looks to me like it say for one real number:

[spring gulch]

Shouldn't the author have said "for all"?

or maybe leave it out all together.

[tender cobalt]

for all could be used in {alpha v1 | for all alpha in R}, but you mean to say {alpha v1 | alpha in R}, which is slightly different set builder notation than what they are using

they are saying that its {v in V | fulfilling a condition} instead of {all the possible v1 | by varying this number}

they both give you the same space, so youll have to be used to seeing the set built up either way

the condition theyre giving has its uses, its making clear its only the v in V which can be reached by an alpha v1

[spring gulch]

I dont know. I'm not happy about it.

I guess I'll accept it.

thank you

[tender cobalt]

np

personally I dont use this, Id rather "for all"

[spring gulch]

It's kinda hard for me to acknowledge that math notation can be ambiguous.

[faint gorge]

another issue would be that for alpha = 0 it would be wrong if v wasnt the null vector (or rather even more restrictive, changing the nature of that set)

[misty crest]

for all here is blatantly wrong

[spring gulch]

Maybe like {v in V | v = a v1, a in R}

Why is zero wrong?

That would just give the zero vector.

[faint gorge]

yea and v doesnt have to be necessarily the zero vector

[spring gulch]

I'm still confused. The span is all the vectors, including zero.

[misty crest]

it’s the set of all such vectors that are scalar multiples of v_1, it is certainly not the case that a vector is a scalar multiple of another vector if it’s equal to every possible scalar multiple of that vector

[spring gulch]

If v1 is zero vector, then forall a would be zero vectors.

[misty crest]

and?

it makes no mention of v_1 = 0

this is a general definition

[spring gulch]

I'm sorry, I don't understand this sentence.

[tender cobalt]

thats not what I mean by "two different ways"

there are two different approaches to writing down the same set

one of them considers the vectors as "you have to satisfy this condition to proceed"

[spring gulch]

I wasn't talking about what you said.

I'm saying, in general.

There's interpretation needed in some notation.

[misty crest]

here’s an example, v_1 = (1, 1) then the span(v_1) = (alpha, alpha) for some alpha in R

for example, v = (69, 69) is in the span of v_1 since there exists alpha such that v = alpha v_1, namely alpha = 69

but obviously (69, 69) isn’t alpha(1, 1) for every single choice of alpha

alpha = 420 doesn’t work

it just has to be some scalar multiple of it

[tender cobalt]

the benefit here is that different interpretations allow for different approaches, I wouldnt consider this an example of ambiguity but of different perspectives
(even though I would never want to see span written this way since it provides no benefits)
once you see it here, you have to gain the skill of seeing its different kind of intuition (its part of a broader set of intuitions of which this is an example), then hopefully you never need to see them writing the span of a single vector this way again

[misty crest]

what other way is there to write this?

it’s a set of vectors not a set of scalars

[misty crest]

it isn’t for all alpha in R

[tender cobalt]

I had to put in the "for all" for the guy somehow

[misty crest]

you can say {alpha v_1 : alpha in R}

[tender cobalt]

its not grammatically correct

but it gets the point across

alright thats fixed

[faint gorge]

Say $V = \R^2$ and $\vec{v}_1 = (1,0)$ then $$V_1 = {\vec{v} \in V \mid \vec{v} = \alpha (1,0), : \alpha \in \R}$$
is not the same as
$$V_1' = { \vec{v} \in V \mid \vec{v} = \alpha (1,0), : \forall \alpha \in \R } = {,}$$
because there doesn't exist a vector that satisfies this, for a vector unequal $(0,0)$ it doesn't work especially because of $\alpha = 0$.

[spring gulch]

reading...

[tender cobalt]

I will say part of this may be other people misinterpreting how you intend to use for all

[tender cobalt]

also Ive edited this post

[spring gulch]

I'm sure I'm reading it wrong, but I don't agree with your V'_1

[tender cobalt]

thats good at least

[misty crest]

he purposely made it wrong because that’s what you said earlier

[spring gulch]

I don't see that being an empty set.

[tender cobalt]

oh dear

[spring gulch]

who are you talking about here? me?

[misty crest]

because if v_1 is nonzero then there do not exist any vectors that are equal to alpha v_1 for every choice of alpha

[tender cobalt]

how about we resolve making sure we understand the original "for some" definition before getting into what this specific variant of "for all" is being used for?

[misty crest]

you

[faint gorge]

If we take an arbitrary vector say (x,0) then x(1,0) = alpha(1,0) implies x = alpha only one solution, which should already tell you that there exists one solution of alpha, not infinite many

[spring gulch]

I'm not sure what you're refereing to, but I can assure you I haven't "purposely" made anything wrong. I already make lots of mistakes, I don't need to add to them on purpose.

[tender cobalt]

to be clear, do you understand the reasoning behind the original for some definition

[misty crest]

no adonis purposely gave the wrong interpretation which was yours

[misty crest]

^

he explained why this was wrong

[spring gulch]

no, that's why I'm asking.

[tender cobalt]

we can focus on that first

this first picks out a vector out of the vector space V

then checks if it satisfies a certain condition

if you can write the vector as a real number * v1, then its considered to be in the span

if not, it gets left out for not following the condition

if you want for all, youre more or less thinking of:

,,{\alpha\vec v_1\mid\alpha\in\mathbb R}

[woven radish]

mtt

[tender cobalt]

theres a few things to note here

first is that it goes through all the vectors using alpha
second is that it does not use the for all symbol, its a convention

[tender cobalt]

now youll notice that this definition is equivalent to the one they gave

[spring gulch]

oh, I think I undestand the bigger picture of the difference,

[misty crest]

for all has a completely different logical function than saying "where alpha is in R" or "for alpha in R"

[tender cobalt]

a slight difference between for and for all then

oh right thats the key

[tender cobalt]

"for all alpha in R" has a very specific definition that means "this condition should hold for every real number which we will call alpha"

[spring gulch]

You guys mean this?:
It's like, in a programming language loop:
a) each loop uses the singular A for the selection, vs
b) each loop uses all A's at the same time

[tender cobalt]

programming language is not necessarily the correct way to go about this

its a bit more declarative than that

[misty crest]

sounds like you get the idea

[spring gulch]

I mean, if it's an analogy

[tender cobalt]

for, here

here, the general pattern being used is
for each v in V,
if these conditions hold,
it is in the set

so the conditions "for some" is an OR gate for any number in R, the condition "for all" is an AND gate for all numbers in R

[spring gulch]

So then, this would work too, no?: {v in V | v = a v1, a in R}

[tender cobalt]

yep

[spring gulch]

that "for some" did a number on me.

[tender cobalt]

this one is more direct and goes,
for each alpha in R,
include alpha * v1 in the set

this is called a "parameterization" for going through each element directly instead of requiring conditions

[faint gorge]

geometrically, you can't scale a vector with two non zero factors and expect the same outcome logically

[tender cobalt]

there might be some ambiguity there because when I read that, I automatically assumed the a was a "for some"

[spring gulch]

I'm interpreting you saying that: a * v1 != a * v2 when v1 != v2

[tender cobalt]

usually mentioning a variable without a corresponding "for all" or "for some" defaults to "for all"

so by default it can be read as ${v\in V\mid v=av_1\text{ for all }a\in\mathbb R}$

[misty crest]

he’s saying that if you have some fixed vector v and multiply it by two different scalars then clearly you should expect two different vectors

[woven radish]

mtt

[tender cobalt]

which is not your intention

[spring gulch]

Yeah?

What does that relate to?

[tender cobalt]

this relates to writing the set notation this way

[misty crest]

ok you still don’t understand then

[faint gorge]

to you saying for all alpha meaning no matter how you scale (1,0) you always get the same v

which is clearly not the case, cause each alpha returns a different multiple of (1,0)

[tender cobalt]

the idea here is that "for all" is being used as an AND gate which strictly means that v can be written as av1 for every choice of a in R, which you didnt intend

"for all" is for ANDs, not for fors

for example 0 * any number = 0, which is written as:

[spring gulch]

oh, ok. Yeah, I get it now. That would be like saying {v in V | v = 1*v1, v = 2v1, v = 3v1} in each condition.

[tender cobalt]

yep

[spring gulch]

I mean, I got it before.

[tender cobalt]

since you had that string replacement when you asked the question, it seemed to be what you wanted to go for

be careful with that sort of replacement

mostly only substitutions and particular laws are allowed

just like with ANDs and ORs and NOTs

[spring gulch]

It's kind of not super easy to read some set definitions.

I really have to stretch my brain to understand what the author means.

[tender cobalt]

it like anything requires practice, but it lets you be set-theory-specific with how you want things to be defined

[spring gulch]

I mean, I know it's a me problem, but still.

[tender cobalt]

its an everyone problem

[misty crest]

have you read an intro to proofs/logic book before

[spring gulch]

Yeah, I have a few. I started to read a very good one, but had to pause because there's only so much free time, so I'm prioritizing linear algebra, at the moment.

[misty crest]

which one?

[spring gulch]

The proof one? let me see

"How to Read and do Proofs", 6ed

[misty crest]

never heard of it

[spring gulch]

I really like it. Additionally, the author has an accompaning lecture series on the publisher's website.

If I only had more time.

[misty crest]

are you a college student?

[spring gulch]

no, I'm not. I'm learning for fun, kindof.

[misty crest]

ahh

nice

[spring gulch]

I expect that, in about 2-3 years, I'll have the level of knowledge that I'm hoping to achieve.

Though, I'll never stop learning,

[misty crest]

where are you hoping to get to

any particular subject?

[spring gulch]

Are you familiar with programs like Autodesk Maya, or 3DS Max?

[misty crest]

nope

[spring gulch]

It's like a 3d visualization package. For 3d graphics.

I'm building a small one, for myself.

As a hobby

[misty crest]

oh nice

linear algebra makes sense then

[spring gulch]

Yeah, can't be scaped. At first, I was hesitant, but now I like it.

It's just, there's alot of concepts to learn that are inter-related.

[misty crest]

i didn’t enjoy computational linear algebra but proof based was nice

[spring gulch]

Proofs make my head hurt.

I do understand that they are very important, and teaches you how to think like a mathematician, but they are hard.

[misty crest]

mhm

it’s an adjustment

[spring gulch]

I consider it like "eating your vegetables", when you were a kid.

[misty crest]

i had to relearn how to read basically

reading proofs requires your full attention

[spring gulch]

totally

[misty crest]

you can’t just skim or read it passively

it is expected that you take a lot of time on a single page sometimes

that’s how you digest it

[spring gulch]

That's how I'm going with the linear algebra stuff, too; to be honest.

I might be a slow learner, because I have to go over some sections a bunch of times to make them sink in.

Even then, I have to go back and re-study them and connect them to new stuff I just learned.

[misty crest]

better to be a slower learner than someone who doesn’t learn at all

🤷🏼‍♂️

[spring gulch]

The one good thing is that it's forcing me to take good notes, which I'm really starting to appreciate.

[misty crest]

but you’re also only comparing against yourself

[spring gulch]

I'm starting to see what people talk about when they say "beautiful maths" and stuff.

Check this out:

I finished this one page today

I mean, more that just that. But that's one of them.

[misty crest]

writing notes like this is a good habit

[spring gulch]

I know it's like a child that only a father can love and what not, but I'm kinda proud of taking notes

[misty crest]

try to do it without just looking back and forth at the book

helps you remember it and really tests if you understood what you read

[spring gulch]

impossible

[misty crest]

nope

[spring gulch]

my brain doesn't have that kind of development, at this point.

[misty crest]

never said you had to just read it once then write notes

read it a few times and play around with it

[spring gulch]

but, I do notice that I'm starting to understand the diff notations easier.

[misty crest]

then try to put it in your own words

[spring gulch]

oh, I see what you mean.

Well, I have taking enough of your guys/gals time. I really appreciate the help.

See you around.

[misty crest]

have a nice night

[spring gulch]

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[jade kelp]

Can anyone do smth like a visual diagram explaining this question the answer is B but idk how you get it

[jade kelp]

thx

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[upbeat elbow]

anyone know how to do this

[wise scarab]

hint: try to factor this expression

the top and bottom separately

[tawny pewter]

first do you know factorials?

[wise scarab]

hint 2:

[upbeat elbow]

yuh

[wise scarab]

oh wait oops I did that wrong. ignore hint 2

[upbeat elbow]

oh ok

did i go too far on the numerator

should i just have done (n+1)n!

[wise scarab]

updated hint 2:

[wise scarab]

maybe try to pull out an entire factorial instead

[tawny pewter]

i would say you should try to factor as much as you can numerator and denom

[wise scarab]

notice that you could've also written the top here as $(n+1)n!-n!$

[woven radish]

00100000

[upbeat elbow]

yes

[wise scarab]

then, it looks awfully close to the form $ab+ac=a(b+c)$, right?

[upbeat elbow]

i dont get the denominator for this one

[woven radish]

00100000

[upbeat elbow]

yuh

[wise scarab]

oh did i make another mistake 💀

[upbeat elbow]

i dunno i just dont know how u got that

[wise scarab]

I think mine looks right

[upbeat elbow]

wait nvm

gimme a sec

[wise scarab]

I'm just checking it over to make sure that I didn't make a mistake lol

[upbeat elbow]

i got it

i forgot n! can be n(n-1)!

[wise scarab]

yup

that's the key observation

and once you've cancelled the factorials out from the expression, it becomes easy to observe what n must be

[upbeat elbow]

uh i think i did something wrong

[wise scarab]

yes there's a mistake somewhere

[upbeat elbow]

i have made the second numerator

a factorial for some reason

[wise scarab]

it's hard to label, but the mistake is uhhhhh... on the second line on the right

the numerator is not $n!(n!)$

[woven radish]

00100000

[upbeat elbow]

yeah

so n can be 6 or 6/5

[wise scarab]

no, n is 6

[upbeat elbow]

wha

[wise scarab]

wait a second

I mean

I'm not aware of how factorial is defined for numbers outside of non-negative integers

[upbeat elbow]

so could 6/5 be rejected

[wise scarab]

oh I see https://en.wikipedia.org/wiki/Gamma_function

[upbeat elbow]

what the hell😭😭😭

[wise scarab]

well, no, but it's this very fancy extension of a factorial lol

I mean, I don't know what level of math you're studying

[upbeat elbow]

like yr 11

aus

[wise scarab]

but I would assume from the context of the level of this question, you're probably meant to just implicitly assume that n is an integer

but your teacher is not being super clear about this

so......

[upbeat elbow]

yh i dunno either

im gonna say rejected

cuz i aint ever heard of a gamme extension factorial thingy

[wise scarab]

yes, I think considering you're an 11th grader, that's likely the idea

but the concerning thing is, many times in grade school math, we use theorems that we don't prove but accept to be as facts

i dunno. I'd say n=6

[upbeat elbow]

pythagoras

[wise scarab]

there's no debate if the question said "find some positive integer n such that"

[upbeat elbow]

it says find value

[wise scarab]

no we definitely prove pythagorean theorem

[upbeat elbow]

so i duno

prove pi

anyway thx for ur help

ppreciate it

[wise scarab]

source:

glad to be able to help!

[upbeat elbow]

.close

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[devout snow]

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Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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

[torn jackal]

i feel a bit dumb asking but here 1/2 only applied to the 10 and not the rest of the RHS? then when they div both sides by 5 how come x and sin93 are unaffected?