help-19

[timid solar]

that wasnt that hard, pretty fun actually

thanks!

.close

[odd edge]

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[silk crescent]

need help answering this question thats kinda it 💔 💔

[silk crescent]

not sure how im supposed to get the amount of seconds

so far i figured out that the period is 60s

and ive gotten 15.7s through plugging in 40

to the equation given

just not sure if its correct

cuz i also need the other periods of time

to add up

[indigo dirge]

wait, what do you mean "plugging in 40?"

[silk crescent]

they gave an equation

i plugged 40 into h(t)

and solved for t

[indigo dirge]

ok

one sec i dont have a calculator on me

[odd edge]

@silk crescent Has your question been resolved?

[silk crescent]

<@&286206848099549185>

[lean yew]

this seems to be asking you to find the range(s) at which h(x) > 40m, then find the total width of those ranges with the constraint of 0 <= t <= 60

[silk crescent]

yeah

not sure how i would do that tho

[lean yew]

step 1 would be finding the range(s) at which h(t) > 40, which should give you 2+ ranges of t

[silk crescent]

uhh

was plugging it in the right course of action

[lean yew]

there's no plugging anything here except the value of 40 substituting h(t)

ok let's make it simple. if i asked you to find when h(t) = 40m, can you do it?

[silk crescent]

yeah

i thought “plug in” just meant “substitute in”

so just replace h(t) with 40

[lean yew]

oh sorry, i didn't know what you were plgging in

[silk crescent]

then solve for t

[lean yew]

yeah correct

mhm

but instead of an equal sign

you now use a > sign

[silk crescent]

i got t > 15.7s

[lean yew]

just to double check, do you have the working?

[lean yew]

think that inequality sign is the wrong way around

wait nvm

[silk crescent]

i used equal sign for the work

but u can just substitute it with the < sign anyway

since im not dividing wny negatives

any

[lean yew]

actually you got that sine value right

you should find the other angle that has that sine value in a different quadrant

(hint: pi - angle)

this gives you another angle value to work off of, and thus another t

[silk crescent]

angle?

[lean yew]

you got sin(the entire stuff in there) = 0.56 right?

there are two values for which this is possible

you've found one of them

[silk crescent]

what other way can i solve it tho

[lean yew]

this would most likely be the intended solution

or to make it easier right

you know sin(x) = 0.56 gives you a height of 40 meters

find x

two values of x possible

hint: once you found the base value of x, do pi - that angle to get the other one

once done, let x be equal to the expression inside the sine

solve for t in the two equations you get (1 for each x)

oh and since the question tells you to use the graph, once you've gotten your two t values, spot them on your graph and see where the graph is above the points you spotted

[silk crescent]

alrighty

[lean yew]

sorry for the confusion earlier :<

[silk crescent]

its mainly the fact that u use the word angle

[lean yew]

ah yeah i see why it can be confusing cuz it's a height hahah

but trigonometry functions usually work with angles so that's my go-to term
my bad

[silk crescent]

x is 15.7

so then

pi-15.7=12.558

negative

ill see what i can do

.close

[odd edge]

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[lean yew]

that's t btw

[silk crescent]

ya

[lean yew]

sin(x) = 0.56

x shouldn't be 15.7

it should be a number under 1 rad

[silk crescent]

.reopen

[lean yew]

gl from here though!

[odd edge]

✅

[lean yew]

oh

[silk crescent]

oh nvm

[lean yew]

sure

i'm down to continue

but you should get an angle under 1 rad

now, why an angle, you might ask

think of this angle as how far the wheel has rotated

to get the rider above 40m

[silk crescent]

okok

[lean yew]

then you should get x = {something in radians}

but sine is positive in quadrant 2 as well (between pi/2 and pi radians)

so you need to find the Q2 angle that gives the same sine value by doing pi - the answer you got

those are the two x you need

[silk crescent]

this is a bit hard to process uhh

but i did

[lean yew]

okok one step at a time

find the initial x first

reminder, we are looking for x in sin(x) = 0.56

[silk crescent]

0.59

[lean yew]

correct

now find the Q2 value of x (pi - this value)

you can quote it to 3 digits

[silk crescent]

2.55

[lean yew]

good

so you used arcsin or sin^-1 to find the answers right?

now originally, the sine function was being applied to (pi/30)(t-10)

and you solved for x in
sin(x) = 0.56

so you know that (pi/30)(t-10) is actually the x we are looking for

but since we have two values of x, we have two values of t

(pi/30)(t-10) = 0.59
(pi/30)(t-10) = 2.55

solve for t in both

separately*

[silk crescent]

i dont understand where the second answer came from exactly

[lean yew]

the second answer came from the sine graph

[silk crescent]

is it because we inversed sine?

[lean yew]

not exactly

so you know sine is positive from 0 to pi/2 radians, right?

at pi/2 radians, sine is 1

precisely speaking, you found the intersection point here

but if you look a little more to the right

you see another intersection point

that's the second answer

[silk crescent]

yeah

ok i got

t1 as 34.35s

t2 as 15.634s

[lean yew]

good!

now mark both points on your graph

and draw a line at y = 0.56 (just sketch, don't have to be accurate)

those two points should be on the line

hint: since you're sketching, just draw a line about halfway up the sine graph, then dot the two intersection points

[silk crescent]

alright

so im guessing now

just find the difference

[lean yew]

yup, now just draw a line through the two dots

no need! no more calculation necessary

[lean yew]

draw a horizontal line through the two dots

then, you are asked to find the time at which the rider is above 40 meters

that's easy - it's just the time that the sine graph is above the line you drew

to find the amount of time

oh yea you need to do one difference

i need coffee

[silk crescent]

35.35-15.634

[lean yew]

yep

eh 34.35

not 35.35

[silk crescent]

ah yeah

got the answer

[lean yew]

then you should get the answer (+/- some rounding difference)

[silk crescent]

now my only problem left

is how will i solve this again if it comes up on my test

do u have maybe a set of steps i should follow for questions like these?

[lean yew]

if you are given a distance and told that it varies by a trigonometric function

and you are given a value to work off of

solve for the trig function

then find all possible angles (within the given range) that satisfies the trig function

then solve for the expression inside the trig function

but questions can vary, so pay attention to what the question is asking for

[silk crescent]

alright ill try to remember this

[lean yew]

but for sine and cosine, remember that in a full rotation, every sine/cosine value has 2 possible angles

you can play around with a graph to see why

just go to geogebra and type
y = sin x
or
y = cos x

then draw as many horizontal lines as you want to with
y = {constant value between -1 and 1}
you should always find two intersection points within one repetition

[silk crescent]

okok

thanks for the help and clarification

[lean yew]

nps, sorry for the confusion earlier :<

[silk crescent]

its alright!

ill try to remember this for my test

[lean yew]

aye, good luck!

[silk crescent]

anyways time to close this channel

.close

[odd edge]

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[noble dome]

\begin{center}
\textbf{Prove that no natural interval ( [1, n]_{\mathbb{N}} ), with ( n \in \mathbb{N} \setminus {0} ), is equipotent to the empty set ( \emptyset ).}
\end{center}

[noble dome]

my idea was to show that f: A -> \emptyset is not injective, but I'm unsure if that's right

[clever fjord]

licentia

[odd edge]

@noble dome Has your question been resolved?

[noble dome]

<@&286206848099549185>

[left matrix]

[lean yew]

from my understanding it seems like any relation that maps a natural interval to the empty set will have to be the empty relation
but the codomain of such a relation is the empty set, so basically no image exists

maybe this could help, but not sure how this would be formally worded

whatever relation between these two sets cannot be injective (image is empty set) and cannot be surjective (for every y in the empty set, which makes no sense)

[tidal matrix]

if it helps, there is a definition of injectivity related to the kernel of said mapping

[lean yew]

could we possibly talk about the cardinality of the two sets though?

since the empty set has no elements, it has a cardinality of 0
the interval [1, n] must have at least one element because n != 0 (meaning n must be 1 or greater) -> the cardinality of the interval is >= 1
0 != n, therefore the two sets cannot be equipotent

[odd edge]

@noble dome Has your question been resolved?

[tidal matrix]

i assumed there was a reason for using f, but this does work, so long as an ordering is defined on N

[lean yew]

i see

[odd edge]

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[slender locust]

⊤ ⊢ (((p ∙ q) ∨ p) ≡ p)
How would i go about proving this tautalogy? ive tried setting up a proof by targetting (p/\q)/p->p and p->(p ∙ q) ∨ p) to form a biconditional introduction but I cant figure out how to get to the two conditionals

[mystic saffron]

what are your rules

[slender locust]

ig js regular deduction rules but it has to be formated like premise number, schema, citation, rule

this is a different question i did

i have to fill out questions like that

[mystic saffron]

how would you prove things of the form AvB -> C, and A->AvB

[slender locust]

i prove conditonals using discharge of premise which is the D but idk how to form that in this question

normally i premise introducte the antecedent of the conditional and then find the conclusion through a few other lines of proof and then use discharge of premise which later cancels the introduced antecedent out

[mystic saffron]

tbh i dont know all rules you are using, but anyways, do you have any rule that let you convert a proof of A ⊢ B<-->C into A ⊢ B -> C and A ⊢ C -> B?

[slender locust]

thats a list of the rules i think your reffering to BE?

[mystic saffron]

tbh i dont know how to get a disjunction elimination with those rules

[slender locust]

that ones DE

[mystic saffron]

another DE

to prove AvB->C, show A->C and B->C

anyways, not sure how to translate that to your system but my strat would be prove (A^B)vA -> A and A -> (A^B)vA

for (A^B)vA -> A split into (A^B)-> A and A -> A

[slender locust]

thats what i want to do as well but idk how 😭

[mystic saffron]

ok maybe i cant help but lemme try something

how would you prove this weaker statement first

ok maybe this one

idk there are various similar ways

[slender locust]

[1] (a->c)^(b->c) P
[1] (a->c) (1)CE
[2] c P
[1,2] a (2)(3)MT
idek 😭

i think thats similiar to this?

idrk tbh we js started this unit n im so lost

[mystic saffron]

do you have any example where there is a <-> in the conclusion?

i wanna see how they split it

[mystic saffron]

mmm

do you have an example for tautologies?

[slender locust]

i couldnt figure out how to do this either the prof helped another person do this one

[mystic saffron]

where is step 6 used?

sorry, im just trying to understand how this system works

[slender locust]

not sure tbh, the prof said something about how this shows contradiction

maybe proof by contradiction?

[slender locust]

we do row number [premise number] schema (citation) rule

[odd edge]

@slender locust Has your question been resolved?

[slender locust]

<@&286206848099549185>

[mystic saffron]

i think maybe (and just maybe i understand your system now)

genually, i would prove it like this instead

anyways

im not sure though

tbh its the hardest system of natural deduction ive seen

first check if it makes sense to you

i may be wrong cuz im not familiar with this very system

[mystic saffron]

the red ~q is a typo, i meant ~p

[mystic saffron]

another typo in line 8, it would be D 6,7

[slender locust]

just tried it

im not sure if im missing a line

oh it didnt show in screen shot but the top right warning sign says the proof does not establish conclusion, perhaps an unwarranted assumption being used?

its cuz line 9 our premise number is 2 which comes from -p P

which is an assumption

idk how 2 fix that tho

[slender locust]

i think it should be sumwhat similiar to this, i had the same error on this question but then the prof fixed it for another student

[mystic saffron]

thats how you have it wait

uh idk then

ok i see what you mean now

alr wait

dont you have any example when you have to assume more than 2 things simultaneously?

extra assumptions

not assumptions of the LHS

[mystic saffron]

besides this

[slender locust]

i assumed 4 and 8 here

[slender locust]

but i think that ones better example cuz its like the same concept i think?

[mystic saffron]

welp tbh thats all i can help

i dunno, ping helpers or talk with student / professor idk

[slender locust]

if u free u wanna try another q it should be easier im js hella lost 😭

its cool if u got smth to do

[odd edge]

@slender locust Has your question been resolved?

[slender locust]

.close

[odd edge]

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[odd edge]

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[tired estuary]

help :(

[tired estuary]

i have no idea how to start

[red perch]

try to find f^-1

[wanton bison]

The inverse is the mirror image of the function at y=x

[tired estuary]

yeah i was thinking just draw y=x then see if any points overlap but wouldnt that be 2?

[wanton bison]

You basically have 4 possible inverse functions

[tired estuary]

then do i graph it? or what do i do with it 😭

[red perch]

uh let $f^-1(x)=a$

[clever fjord]

Bleach_Enjoyer

[red perch]

crap im so bad at those commands

then $f (a)=x$

[wanton bison]

f < 0 which means x < 0 so it's either the inverse in the second or third quadrant

[clever fjord]

Bleach_Enjoyer

[red perch]

put function as a

and put a as the main

[wanton bison]

f keeps decreasing so it's likely the long part

[tired estuary]

i do not understand 😔

[tired estuary]

whats the green bit?

[wanton bison]

f(x)

[tired estuary]

oh

wait howd u know it was there i dont get itt arhiwuiwlbt

[wanton bison]

First you cut the graph into four subgraphs that are bijective

[tired estuary]

whats bijective

[wanton bison]

Then look at f(x) you realize it's negative

[wanton bison]

1 2 1

i meant one to one function

[tired estuary]

ooh i see

[copper quarry]

australian?

[wanton bison]

Since f(x) is negative (f is the inverse of f^-1) it must be in the second or third quadrant

[tired estuary]

yes!

[copper quarry]

hsc?

[tired estuary]

yep

[copper quarry]

haha knew it

[tired estuary]

okaayy

[wanton bison]

Now f also behaves montonically decreasing it fits the leftest part of f^-1

[wanton bison]

You end up with that then

[tired estuary]

i seeee

[copper quarry]

is this 3u

[tired estuary]

ues im gonna cry its yr 11 work

[copper quarry]

oh lmao

thought yr12

[tired estuary]

nau im in yr 12 but this is yr 11 assumed knowledge it might get tested in trials and hsc

[copper quarry]

oh right

trials are soon right

[tired estuary]

yeah in 3 weeks

[copper quarry]

GL

4u as well?

[tired estuary]

thanks i need it 💔

[tired estuary]

nooo

[copper quarry]

haha

[tired estuary]

wait no i still dont get what you do with this info

worked solutions

[wanton bison]

You can now figure out how many intersections there are, which is one (at local left minimum)

[tired estuary]

i seeeee kinda

[wanton bison]

They intersect right at y=x

[tired estuary]

yeah i just dont understand lwhat u meant by 4 subgraphs

[wanton bison]

The red marks

These 4

[tired estuary]

OH i see

[wanton bison]

They are all 1to1 which have an inverse

Because a quartic equation can have four solutions

[tired estuary]

ohh soitll depend on the question how many subgraphs

soz the equation

or graph

[wanton bison]

But you are given a specific inverse you figure then out where that would be

[tired estuary]

and tthis is a bit confusing did u find the decreasing because f(x) is negative?

[wanton bison]

Yes

[tired estuary]

bc i thought the graph drawn was f-1(x)

[wanton bison]

sqrt is always positive or 0 so -sqrt is always negative or 0

Oh wait

Decreasing because we have a sqrt function

and yes since it goes to -inf i concluded decreasing

[tired estuary]

huhh

[wanton bison]

sqrt(x+1) is typically increasing
sqrt(1+sqrt(x+1)) too
So
-sqrt(1+sqrt(x+1)) decreases

,w plot sqrt(x)

[clever fjord]

Results provided by WolframAlpha

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Requested by adoniszgks

[tired estuary]

wdym typically increasing

[wanton bison]

it is known sqrt(x) is increasing, so a translation like sqrt(x+1)+1 doesnt change that

[tired estuary]

oh yes okok

isnt that like the same as what u said before like because the original f(x) is a negative the inverse the decreasing or is that not always the case

but it is in this question bc its a squareroot

[wanton bison]

I know it's in the 2nd or 3rd quadrant, then I only got 2 choices. Since f is decreasing, it must be the inverse of the purple because if you drew the mirrored function at y=x you would get a decreasing inverse, unlike if you look at the blue

[tired estuary]

oooh

sucha hsrd question thanks for explaining

[odd edge]

@tired estuary Has your question been resolved?

[odd edge]

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[odd edge]

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[mystic saffron]

,,y=\cos^{2} x + \cos x^{2} + \cos^{2} x^{2} + \cos (x^{x}), find \frac{dy}{dx}

[clever fjord]

!

[narrow crypt]

c h a i n r u l e

also

[ x^x = e^{x\ln x}]

[clever fjord]

k

[mystic saffron]

,,\frac{dy}{dx}=-[2x\sin x^2 + \sin2x + 2x\sin^{2} x^{2} + (x^x + x^x\log x + \sin x^x]

Is this right?

[wooden python]

that last term looks wrong

[clever fjord]

!

[mystic saffron]

Typo

[wooden python]

still looks sus

[mystic saffron]

Oh afk brb

[wooden python]

why have you got sin(x^x) plus stuff

[late sinew]

should be multiplied, whatever it is

your diff is correct tho for the last term

just wrote in addition instead of multi

[mystic saffron]

Ye mb typo

Thanks

.close

[odd edge]

Channel closed

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[frigid isle]

[mystic saffron]

Imagine this is the question asked in latest maths class 12 compartment

[frigid isle]

Which

[mystic saffron]

The one i asked

[mystic saffron]

This

[frigid isle]

Ye what abt it

[mystic saffron]

Nothing

I heard compartments were so hard

[narrow crypt]

yes

[late sinew]

what is a compartment in this context

[narrow crypt]

math compartments are very very hard

competition, i think?

[late sinew]

O

[mystic saffron]

No

[narrow crypt]

? 👀

[mystic saffron]

Compartments in india refer to re exam (those who have failed)

[late sinew]

wut

hsc?

[mystic saffron]

What

[late sinew]

which board

[mystic saffron]

Cbse

[late sinew]

o

[solar peak]

every board has i think

[late sinew]

i didnt know re exam was called that

[frigid isle]

[late sinew]

yeah

but ive not heard anyone call it compartments

or maybe i just dont talk to enough people

[solar peak]

oh lol

[zenith tartan]

when was it?

[mystic saffron]

Today

[zenith tartan]

oh

[mystic saffron]

My maths teacher sent the question paper

[zenith tartan]

huh?? 💀

[late sinew]

💀

[zenith tartan]

like after it was conducted right? 💀

[late sinew]

Bhai kya hai ye

[zenith tartan]

lmaoo

[frigid isle]

💀🗣️

[late sinew]

bharat aage badh raha hai

[zenith tartan]

nah this can't guy can't be serious

[vivid wyvern]

I think he means he isnt a hsc candidate
Rather js a student who got it from his maths teacher after the exam was done

[late sinew]

bro just dropped a bomb like it was nothing and went afk

[late sinew]

hopefully

[odd edge]

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[mystic saffron]

Ye idk whats a hsc, ye i got i from my teacher after the exam was over, im just an ordinary cbse class 12 student

[mystic saffron]

.close

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[vivid wyvern]

Yeah that's similar to cbse
A 12 grade would give hsc js like u will give cbse

[vivid wyvern]

.close

[odd edge]

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Closed by @vivid wyvern

Use .reopen if this was a mistake.

[desert jolt]

Stop closing and opening channels over topics which should be discussed in other channels.

[vivid wyvern]

It was a mistake(will this open a channel

Yeah ,was js trying to reply to a text

[desert jolt]

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[somber remnant]

Can i just cancel out (x-1) and |x-1| like i did in the picture?

[quasi sparrow]

what's the sign of (x-1) when x < 1?

[somber remnant]

minus?

[sand horizon]

So what does abs value becomes

[somber remnant]

can u elaborate a bit?

[sand horizon]

Thats actually what you did

|x-1| = ? If x - 1 < 0

[somber remnant]

This?

[sand horizon]

Use the definition of abs value

[quasi sparrow]

,tex .abs def

[clever fjord]

riemann

[sand horizon]

Wunderbar

[somber remnant]

gimme a sec

[somber remnant]

-(x-1) ?

[hasty dome]

Yes, that's correct.

[somber remnant]

ohhh alr thx

i might actually have to go back and read absolute value again

[hasty dome]

You're dealing with x < 1 (see where you wrote "; x < 1").

So, you can just replace |x - 1| with -(x - 1).

[somber remnant]

ohh

ye i think i understand

thx guys

.close

[odd edge]

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[hasty dome]

No problem.

[odd edge]

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[devout vessel]

Hello humans so there was this question that I couldn't solve (5c) and I tried to solve it but my answer is comming wrong (ans is supposed to be -1,2) can anyone tell me what I did wrong? Thank youuu

[wooden python]

5c? do you mean 5d?

also x^2 + 1 is supposed to be equal to x + 3 not x + 2*3.

idk what you even did and tried to frame it as another "insertion of arithmetic means" problem or something

[devout vessel]

Oh yea 5d my bad

[devout vessel]

Wait what

[wooden python]

x, x^2+1 and x+6 are in AP

x and x+6 are two positions apart (1st and 3rd term respectively) and their difference is 6

that difference must be 2 times the common difference of the AP

thus the common difference is 6/2 = 3

as you yourself found

do you understand this? yes/no

[late sinew]

"Hello humans"

[devout vessel]

Yea I understand till that part

[wooden python]

ok

but the 2nd term is only supposed to be ONE common difference away from the first

$a_2 = a_1 + d$

[clever fjord]

Ann

[wooden python]

here $a_2=x^2+1$ and $a_1=x$, yes?

[clever fjord]

Ann

[devout vessel]

What

Oh yea wait

It is

But isn't it n2

Instead of a2

[wooden python]

idk what you mean when you say n2.

[red perch]

We can get (X+X+6)/2 if is the middle x^2+1 right?

[wooden python]

brackets.

[red perch]

Idk I might be wrong

Srry

[wooden python]

also overcomp but leads to the same thing anyway.

[devout vessel]

I'll try once agian

Thank you mermaid human

[red perch]

Mb let me fix it

[devout vessel]

( or I assume that's a mermaid in ur picture

[wooden python]

eh, been mistaken for worse

close enough

[red perch]

I think X is like 2

Since d would be 3

Each terms

[devout vessel]

Wait I got x square is equal to 5 now

[wooden python]

show work.

i think you're at risk of overcomplicating it all and getting lost in a million formulas and trying to apply them where they don't fit

[desert jolt]

[devout vessel]

Wait sorry

My charge finished

[wooden python]

what's m1. what is that supposed to mean.

you kind of didnt follow my lead at all

[odd edge]

@devout vessel Has your question been resolved?

[odd edge]

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[royal frost]

Hi

[royal frost]

Can anyone help me to understand this question? Why can't I apply kcl directly?

[odd edge]

@royal frost Has your question been resolved?

[narrow crypt]

kirkchoff's law

?

[late sinew]

Kirkchoff

[narrow crypt]

oh nvm

is the circle thing the battery

or?

[late sinew]

Prolly an ammeter

[narrow crypt]

where is electricity coming from

im not familar with this notation

[late sinew]

No idea

[late sinew]

Same

Idk what that diamond box is

Go to physics server #old-network

[narrow crypt]

maybe theres a changing magnetic field outside

at which point, i wouldnt know what to do next

OHH

[late sinew]

That's the notation for a resistance

Not a battery

[narrow crypt]

why would a resistor have a + and -

[late sinew]

To show current flow

[royal frost]

yes Kirchhoff's current law

[shell rivet]

Do you know kvl?

[royal frost]

Yes

But why can't we use kcl directly?

[shell rivet]

Which nodes will you write the equations at?

[royal frost]

I noted it as green dot

[royal frost]

it is just for polarity

[royal frost]

ok

[sturdy wolf]

I think the circle with an arrow is a fixed Constant Current Source

And the square with an arrow is a current controlled current source

[royal frost]

yes you are correct

in controlled source the overall value depends on another factor that is i_0 here

the thing is I dont understand what is wrong with applying kcl here?? what did I miss ?

I got the result as 7.2 while the book got it as 6 A

[sturdy wolf]

Can you elaborate on your solution? I used kcl and got the book's answer

[shell rivet]

Why would none of the current go through the resistor?

[royal frost]

do u see that green dot here? I chose that node and figured the current getting in and out from that node

9 A entering node
i_0 , i_0/4 leaving the node

so 9=i_0+i_0/4

i_0=7.2 A

[sturdy wolf]

Apoorv is right, there is also current going thru the 8 ohm resistor

[royal frost]

there is definitely current going to the resistor

[sturdy wolf]

So let current thru the 8 ohm resistor be i_1, say

[shell rivet]

So how is 9-i0 = i0/4

?

[sturdy wolf]

Then equation should be 9 = i_0 + i_0 / 4 + i_1

[royal frost]

I mean i_0 is the amount of the current going to the resistor

[shell rivet]

The 8 ohm resistor

[shell rivet]

Yup

[royal frost]

as far I understand we generally look for the current entering and leaving this node exclusively.. so how come the 8 ohm is interfered with this ?

[sturdy wolf]

Good question. The current leaving the green node to the right will be used to go thru both the cccs and the 8 ohm resistor

[shell rivet]

How is this circled current i0/4?

Let the circled current be some i1

[sturdy wolf]

Yes the current that Apoorv circled does not just go to the cccs

[royal frost]

I followed the direction of i_0/4 which lead the node

[royal frost]

I see..

[shell rivet]

Ig you'll have to pick another node for another equation

Not sure

[sturdy wolf]

I think you will get the answer you want now

[royal frost]

lemme try to do it

[sturdy wolf]

OK let us know how it goes!

[royal frost]

I got the answer finally !!

[sturdy wolf]

Great job

[royal frost]

nah no need for 2 equations cuz all elements are in parallel so they will all have the same voltage v_0. So the 2 ohm resitor has also v_0 so v_0=2*i_0 so we can insert this in place of v_0

[royal frost]

you helped me alot on this thanks

[shell rivet]

Yes figured that out

[royal frost]

i thought we just focus on the node and see the current and stop when we see another node. But turns out we should consider the current of other elements

[royal frost]

yeah, thanks alot for your help

[sturdy wolf]

Np glad to help

[royal frost]

imma close this now

bye!

.close

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[remote axle]

i dont really understand this. what is M_y and N_x? where does the second partial derivative come in? how is it proving exactness if the supposition at the start is that its already exact?

[tidal matrix]

\begin{itemize}
\item $M_y = \pdv{M}{y}$ and $N_x = \pdv{N}{x},$ these are just shorthands. You may also see $D_1 M \coloneqq \pdv{M}{x}$, but this is more of a physics definition.
\item Since $M = \pdv{f}{x}$, for example, then $$M_y = \pdv{M}{y} = \pdv{y} \left( \pdv{f}{x} \right) = \pdv{f}{y}{x}.$$ It's just subbing in $M = \pdv{f}{x}$, basically.
\item Because the equation is manipulated, we get an "equivalent definition" for exactness. Exdactness isn't proven again, it's just restated, then it's used to prove $M_y = N_x.$
\end{itemize}

[clever fjord]

haseeb

[tidal matrix]

Exdactness

[remote axle]

ok i think im getting closer to understanding. Thank you

[brisk stag]

ok

[tidal matrix]

np :) anything else i can maybe clarify? or do you just need to stare at it

[remote axle]

i need to work through it. I can see where they are going but the middle is kind of fuzzy, probably because my multivariable is weak.

[tidal matrix]

thats fair :) you can close and reopen later if you have more questions

[remote axle]

.close

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[runic drum]

x = 7pi/4 can also be expressed as x = -pi/4. when do we know which one should be used

[faint knot]

either one works

here you’d pick the answer that has 7pi/4 because there isnt one for -pi/4

[runic drum]

yes that is true

but im thinking that in large domains [-pi, 2pi]

you can miss out on some values

when solving for the equation

wait maybe not

7pi/4 + -2pi is -pi/4

okay im dumb

thank u for ur help

.close

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[signal copper]

Good afternoon guys, can anyone help me solve this question

[faint knot]

you’ll need to post this in a new help channel instead of someone else’s

[odd edge]

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[tiny pendant]

question

[tiny pendant]

solution

i do not understand the underlined step

can anyone explain?

[wooden python]

9C2 counts the ways to pick which two nonzero digits your number is made of,

4C1+4C2+4C3 counts the ways to place copies of the lower digit in the number

[tiny pendant]

wdym by "copies of the lower digit"

[tepid pelican]

say that 9C2 chooses e.g. 3 and 5, then 4C1 counts numbers which have digit 3 once and digit 5 three times, 4C2 counts numbers which have digit 3 two times and digit 5 also two times ...

[tiny pendant]

how does 4c1 count numbers which have digit 3 once and digit 5 thrice

[wooden python]

3555, 5355, 5535, 5553

(i think there was a more transparent way to write this btw)

(why not 2^4 - 2)

(that way we could all numbers made up of 3's and 5's and then take away 3333 and 5555)

[tepid pelican]

that's far easier actually

[wooden python]

that it is

[tiny pendant]

so the 2 numbers we picked by 9c2 will have 2x2x2x2 ways to occupy 4 spaces?

[wooden python]

the 2 digits picked by 9C2

but yes

[tiny pendant]

digits?

[wooden python]

and then you have to subtract 2 to remove the ones where it's all the same digit like 3333 or 5555 or 9999

[wooden python]

yes, digits. can you remind me what your native language is so that i can translate it into yours?

[tiny pendant]

i understand what is a digit but arent we counting the possible pairs {x,y} which can be arranged in 4 spaces?

[wooden python]

no

look

okay let's imagine we JUST want to count the numbers that we can make with 1's and 2's such that there's at least one of each

like just make it concrete for a moment

are you OK or not OK with this

[tiny pendant]

ok

[wooden python]

alright

i should also mention they're four-digit numbers

which is about to be important

just looking at the options we have for each place within the number, we get 2 * 2 * 2 * 2 = 16 different numbers

and here they are:

1111 1112 1121 1122 1211 1212 1221 1222 2111 2112 2121 2122 2211 2212 2221 2222

however, since we want at least one of each digit (i.e. at least one 1 and at least one 2), we have to throw away the two numbers that don't look that way (1111 and 2222)

thus our count is 2^4 - 2

(or 14 if you want)

[tiny pendant]

yes

[wooden python]

ok

but nobody said that our numbers had to be made of ones and twos specifically

we could play the same game with any pair of digits

(except ones with 0. because 0 is special, and that's handled in the last term in your pic)

there are 9C2 ways to pick two different nonzero digits

[tiny pendant]

ohh so 9c2(2^4 -2)

[wooden python]

yes

[tiny pendant]

so its equal to 4c1 + 4c2 + 4c3

[wooden python]

yes

[tiny pendant]

then for the last term

we will handle zero

so every pair will always have zero along with some other number 1-9

so there are 9 possible pairs

[wooden python]

yes

digit not number

but yes there are 9 possible pairs: {0,1}, {0,2}, ..., {0,9}

and the other digit always has to occupy the first place in the number bc numbers can't begin with 0

[tiny pendant]

so its 2^3 - 2?

6x9 54

[wooden python]

2^3 - 1 this time.

again imagine like 0 and 1

1000 1001 1010 1011 1100 1101 1110 1111

only 1111 needs to be thrown out

[tiny pendant]

oh cuz 0 can never be in the thousands

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[elder vault]

Hello

[elder vault]

That’s a system of equations involving 2 variables

Let’s discuss about the corresponding determinant value when it has infinite, only one of no solutions

Am I fighting my own battles

Can someone speak to me, I feel lonely

[solar peak]

3 equations involving 2 variables 🤔

[tepid pelican]

determinant of what matrix?

[elder vault]

Coefficients

[tepid pelican]

a1 b1 c1
a2 b2 c2
a3 b3 c3
?

[elder vault]

Yes

[solar peak]

isnt that for 3 variables

u sure its not c1 z?

[elder vault]

Yes

It

Cs is just the constant term of line equations

Let’s say the system has only 1 solution, what the determinant of the coefficient will be

[low locust]

determinants should not be used to think about solvability of systems

[elder vault]

Why

I do not agree

Think about Cramer

[low locust]

just fundamentally, determinants can only decide between two options, zero determinant or nonzero determinant. but there are three options for the solvability, no solutions, one solution, infinitely many solutions

just do fucking gauss

[elder vault]

I do not agree with you

[solar peak]

what is there to not agree with

[elder vault]

Zero or nonzero the determinant implies the numbers of solutions

If 3 different lines intersect, the determinant will be zero

[elder vault]

And thats a statement from my textbook

I’m trying to figure out why

I get dismissed again

Is not it a meaningful question

[tepid pelican]

this seems more likely to be true

but that doesnt mean you can determine the n.o. sols just based on the determinant

if the lines are parallel, im pretty sure the determinant would be 0 as well

[wooden python]

det=0 cannot distinguish between "one solution" and "infinitely many solutions"

[tepid pelican]

oh

[elder vault]

Why

[tepid pelican]

so then it cant distinguish between anything at all actually
1 1 1
2 2 1
3 3 2

this also has 0 determinant, but the lines are parallel (i.e. no sols)

[elder vault]

Ann the smartest animal in this world, could you explain why det=0 then lines intersect

[tepid pelican]

thats not right, the opposite implication is

if all 3 lines intersect, then det = 0

[elder vault]

Why would it be this case. And why det=0 doesn’t necessarily means lines intersect

[wooden python]

consider the following two systems:

(system A)
x+2y=3
x+2y=3
2x+4y=6

(system B)
x+y=10
x-y=4
3x+7y=42

[tepid pelican]

x + y + 1 = 0
x + y + 1 = 0
x + y + 1 = 0
This has determinant 0 and infinitely many sols (3 same lines)

[wooden python]

A has infinitely many solutions, B has only one, but determinants are 0 for both!

[tepid pelican]

x + y + 1 = 0
2x + 2y + 4 = 0
3x + 3y + 5 = 0
(3 lines with same slope -> parallel, but unequal)
and this also has determinant 0 and no solutions

[wooden python]

actually yeah for det=0 you can even think up a system with NO solutions.

[tepid pelican]

oh I missed this smh

[wooden python]

so it is absolutely useless!

[woeful vine]

the number of solutions is given by comparing the ranks of the full matrix and of the matrix without the last column
det = 0 just tells you this rank is not 3

you could have

x + 1 = 0
x + 2 = 0
x + 1 = 0

for no solutions

[wooden python]

(system C)
x+y=1
x+y=1
x+y=2

[woeful vine]

As you can see from these examples you were given, the determinant alone just doesn't give you enough information, you need to know the full rank of your matrices to distinguish all cases

[tepid pelican]

and as for the implication
3 lines intersect -> det = 0:

If it has a solution (x, y), then (x, y, 1) must be in the nullspace and its non-zero, hence it has det=0

[odd edge]

@elder vault Has your question been resolved?

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[shut remnant]

Hey guys i need help understanding this graph, we need to make a same one in our files but i feel that this wrong cause the intervals seem to be pi/12

[opaque eagle]

why is there string

[shut remnant]

but if it was pi/12 wouldnt it be wrong cause it would cause there to be more than one zeroes on the x axis?

[opaque eagle]

yeah it doesn't seem right

[shut remnant]

its like a short project instead of drawing the graph with pencil we need to use string

[opaque eagle]

okay lol

those points aren't supposed to be equidistant though

[shut remnant]

Graduate the axes approximately as shown in Fig. 5.1 by taking unit on
X-axis = 1.25 times the unit of Y-axis.
5. Mark approximately the points
,sin , ,sin , ... , ,sin
6 6 4 4 2 2

p p 
p p 
p p 
     
      in the coordinate plane and at each
point fix a nail.
6. Repeat the above process on the other side of the x-axis, marking the points
– – – – – –
,sin , ,sin , ... , ,sin
6 6 4 4 2 2

p p 
p p 
p p 
     
      approximately and fix nails
on these points as N1
¢, N2
¢, N3
¢, N4
¢. Also fix a nail at O.
7. Join the nails with the help of a tight wire on both sides of x-axis to get the
graph of sin x from
–
to
2 2
p p
.
8. Draw the graph of the line y = x (by plotting the points (1,1), (2, 2), (3, 3), ...
etc. and fixing a wire on these points).
9. From the nails N1, N2, N3, N4, draw perpendicular on the line y = x and produce
these lines such that length of perpendicular on both sides of the line y = x
are equal. At these points fix nails, I1,I2,I3,I4.
10. Repeat the above activity on the other side of X- axis and fix nails at I1
¢,I2
¢,I3
¢,I4
¢.
11. Join the nails on both sides of the line y = x by a tight wire that will show the
graph of 1 y sin x − = .

these were the instructions, we are trying to draw arcsin using sin

[opaque eagle]

take a screenshot instead

[shut remnant]

lemme resend it, looks like i cant copy paste direclt

[opaque eagle]

but im not interested in the procedure

your graduations are off

[shut remnant]

i didnt do the graduations this is the sample sent to use by the teacher

[opaque eagle]

oh its one of those fucking ncert math lab "activities"

[shut remnant]

this is the graph in the doc

[shut remnant]

yeppppppppp

"activities"

veryyy useful in the learning process

[opaque eagle]

this is just wrong lmao

even despite the typos

1/2, 1/3, 1/4, and 1/6 are not equidistant

[shut remnant]

do you mean pi/2,pi/3,pi/4?

[opaque eagle]

yeah

whatever

you can scale your graph anyways

[shut remnant]

i got them to be equidistant if you take the unit to be pi/12

[opaque eagle]

sure you can do that

[shut remnant]

but i still dont get that extra interval on the x axis

[shut remnant]

this one, either i am forgetting soemthing or its blatantly wrong

[opaque eagle]

pi/12, pi/6, pi/4, pi/3, 5pi/12, pi/2

you need to have another thing in between

5pi/12

[shut remnant]

oh yeah

ah nvm ig i will just ask my teacher tom , the activity is pretty badly wirtten and explaained though

.close

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[shrewd trellis]

I got b wrong

for some reason

this was the answer apparently

[copper quarry]

,w (-1/3)^3 + (-1/3)^2 +1/3

[mystic nova]

$-(-\frac{1}{3})=\frac{1}{3}$

[clever fjord]

Alexis_Fx

[mystic nova]

You messed up this part

[clever fjord]

Results provided by WolframAlpha

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

Requested by waterrbeam

[wooden python]

show your work for calculating (-1/3)^3 + (-1/3)^2 - 1/3

it looks like you may have fumbled a sign somewhere

[distant surge]

hi

im new here

[glass vault]

Yeah idk when i do it i get 7

[wooden python]

oh wait right the last term should be -(-1/3)

-x with x=-1/3

[wooden python]

hi. this is a help channel currently occupied by somebody else.
go to #discussion or #chill if you just wanna chat; if you have your own question, please open your own channel

see #❓how-to-get-help for how to do that

[glass vault]

Yeah thats right nvm

[shrewd trellis]

what did i mess up?

i used a calculator

[glass vault]

You got minus sign mixed up

[wooden python]

right here

where i circled in red

do you understand

[distant surge]

whats this maybe i can help

[shrewd trellis]

oh right

i get it

[mystic saffron]

if a completes a work in 15days and b completes in 20 days in how much days they would together complete the work

[mystic nova]

!help

[odd edge]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[shrewd trellis]

why are npcs stealing my ticket D:

[glass vault]

Lol

[distant surge]

take their reciprocals to find how much they can do in a day

[wooden python]

!occupied

[odd edge]

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).

[glass vault]

Thats crazy that 2 people tried to get help in an occupied channel in the same channel for one problem

[manic grail]

Its +1/3 ay the end

You forgot that there is already a minus

[wooden python]

late to the punch

[manic grail]

Oh my fault

I just saw he corrected

[odd edge]

@shrewd trellis Has your question been resolved?

Channel closed

Closed by @shrewd trellis

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[marble ibex]

How to i proof √2 is irrational

[ivory grove]

We do proof by contradiction

[marble ibex]

Whats a contradiction

[narrow crypt]

there are many proofs on the internet

[sand horizon]

Say p/q = sqrt2 with p,q coprime

[ivory grove]

it means, we suppose √2 is irrational

[narrow crypt]

assume that sqrt(2) is rational and show that it leads to nonsense

[ivory grove]

and then prove that that can't happen

[marble ibex]

Whats coprime

[sand horizon]

Might be a typo

[marble ibex]

Okay

[narrow crypt]

😭

[stuck coyote]

Hii

[narrow crypt]

gcd(p,q) = 1

[sand horizon]

No common divisor except 1

[copper quarry]

👋 jet dau yaku

[ivory grove]

?

[sand horizon]

eau

[marble ibex]

LCM HFC?

[stuck coyote]

I hate math

[wooden python]

#chill

[marble ibex]

@mod

[sand horizon]

You don't suppose sqrt2 to be irrational and show it never happen

[marble ibex]

<@&268886789983436800>

[stuck coyote]

Integration going on here

[wooden python]

this doesnt call for a modping just redirection

[stuck coyote]

[narrow crypt]

what is this mess

[wooden python]

but @stuck coyote this channel's occupied and you're not helping, go to #chill for chatter

[marble ibex]

Are you guys helping me or fighting each other replys

[stuck coyote]

Oh

Mb

Shit

[sand horizon]

Well the greatest common divisor is 1

[stuck coyote]

Didn't see channel name

[tropic remnant]

It's OK but please save modpings for more serious things in the future

[marble ibex]

Okay

[wooden python]

well ppl have already told you most of the ideas you need in order to come up with a proof for the irrationality of sqrt(2)

[marble ibex]

Ok

[marble ibex]

Ok

[narrow crypt]

so hfc is 1 in other words

[wooden python]

you need to know some number theory

[marble ibex]

Yes

[wooden python]

and also proof by contradiction is a very common proof strategy in math

where to prove a statement you suppose it's false and then try to run yourself into the ground to show it can't possibly happen

[marble ibex]

Youre making a false statement then debunking it

Icic

[wooden python]

that's kind of the idea yes

[marble ibex]

Yes

[narrow crypt]

u can see some other proofs on this wikipedia page https://en.wikipedia.org/wiki/Square_root_of_2

[wooden python]

maybe wouldnt say debunking it

more like saying "If this were true, then things would break outright and here's how"

mb that's also a debunk

[marble ibex]

...

????

[wooden python]

im trying to explain how the logic behind proofs by contradiction usually works

[marble ibex]

Im gonna watch a 1h tutorial

[marble ibex]

What other proofs use contra

Contra

Dictionary

Thats autocorrect not me

[wooden python]

hmmmm

[marble ibex]

Contradiction

Yws

Very long short word

Bro wtf my hamster escape his cage again

Guys I gtg I do NOT wanr my dog to chew it

Want*

[wooden python]

here's one result i thought of just now that can be proved by contradiction in a straightforward-ish manner

[marble ibex]

How do I close this

[wooden python]

oh uh

[narrow crypt]

suppose R is countable is a very famous proof of contradiction

[wooden python]

you close with .close

[marble ibex]

Straightforwardnesses is a word

Bai

.close

[odd edge]

Channel closed

Closed by @marble ibex

Use .reopen if this was a mistake.

[wooden python]

if two polynomials of degree ≤ n coincide at n+1 points then they're the same polynomial

this is what i was gonna mention

[marble ibex]

Last time my hamster died by not eating

[narrow crypt]

sorry to hear that..

[marble ibex]

Thats b!tch deserved it, IT WAS A BORN WITH RAGE IT, it kept attacking my hamster and made it escape

Wait no

The hamster which left was the one who died by my dog

The other hamster died by not eating

[marble ibex]

I hated this one

Never recommend hamsters as a pet

[odd edge]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[pulsar tiger]

I already turned in my homework. I just wanted to konw what the proper way was to prove that h is continuous on [a,c].

[low locust]

lhl = rhl at b

obvious everywhere else

[pulsar tiger]

Yeah, but I wanted to know what are formal answers to this problem.

[low locust]

what I wrote, except writing out the limits

[pulsar tiger]

...

[woeful vine]

do you know how to check if a function is continuous at a point?

[pulsar tiger]

Yeah

I just wanted to know what other formal answers there are to this problem.

[woeful vine]

“other” to what alternative?

[pulsar tiger]

Checking the limits

[low locust]

you are free to do eps delta if you want

[woeful vine]

if you know other ways to characterise continuity you can check with those

[pulsar tiger]

Nevermind then.

Hey Teacher, can you demonstrate a formal proof of one of the alternative methods?

"Yeah, sure. You can do x. That is it!"

But... can you demonstrate it?

"Nah, I am just going to say it"

[woeful vine]

I don't know what you're trying to say here
you want Denascite to prove it in the ε-δ way for you?

[pulsar tiger]

Sure. I want to see these alternative ways.

[low locust]

take epsilon arbitrary

because f is cont you get a delta_1 that works for all x<b

because g is cont you get a delta_2 that works for x>b

take delta=min(delta1,delta2)

I will not write it out in more details

you are free to try and then we can adjust

but I will not write out proper solutions

[sinful grove]

This is good; the point is to be guided not spoon-fed unless you’re struggling with a very specific thing

Take this with a good heart Lennerd

That’s how you’ll learn, but I understand your perspective

It could be frustrating

An alternative approach would be to do it by limits. We know that b is a limit point to [a, c] so it suffices to check that the limit of h(x), x -> b is h(b).

[woeful vine]

He mentioned that he wanted approaches different from taking limits

[sinful grove]

Oh, missed that my bad

[pulsar radish]

how to find the modulus of inequalities?

[sinful grove]

#❓how-to-get-help

[odd edge]

@pulsar tiger Has your question been resolved?

[pulsar tiger]

I am figuring out this delta and epsilon definition f for this proof

[quasi sparrow]

learn to be more specific with your questions

[quasi sparrow]

such as this

[quasi sparrow]

instead of being vague

[pulsar tiger]

Yeah, I am being intentional vague. I don't want to pigeonholed into another channel proof

[quasi sparrow]

the fuck are you complaining for then

[amber veldt]

this is a clear application of the pasting lemma, QED

[quasi sparrow]

you should figure out what you want before opening a channel spewing complaints when you get exactly what you've asked for

Hey here's a vague question

"Yeah, sure vague answer"

But... can you give a specific answer to a question i didn't ask at all?

"??????"

also no one here claims to be a teacher

!vol

[odd edge]

Helpers are just people volunteering their time to help you. Be polite and patient.

[pulsar tiger]

I wanted a formal proof for the epsilon-delta proof instead of using the functional limits from the left and right.

[quasi sparrow]

should also learn to stop contradicting yourself while also learning how to ask questions

[pulsar tiger]

Where is the contradiction?

[quasi sparrow]

maybe you don't know the meaning of the words you're using

[pulsar tiger]

Yeah, I don't want to go through an entire proof of me doing it. I just wanted what the alternative was.

A furnished and finished one.

[quasi sparrow]

^

[pulsar tiger]

SO, if I just want a walkthrough of a method, I have to learn it?

[quasi sparrow]

yes because there are plenty of examples online and textbooks already

[pulsar tiger]

WHere can I find examples of tis?