help-0

[barren notch]

h e l p im blanking out on a simple question

[placid zinc]

Same as |x| = 2 + 1/x (for x ≠ 0, which is a solution)

Worth trying to graph both

[sage violet]

yeah

hmmmmmmm

actually

try considering two cases: x < 0, x ≥ 0

then see what happens

[placid zinc]

That's a good idea too

[barren notch]

i tried testing some values, but that got me nowhere

[placid zinc]

Yeah, let's back up and do that instead. Pretend x is negative, then how can we rewrite the original equation to not include ||?

[barren notch]

well we could first rearrange the equation like you said lxl = 2 + 1/x

and if x is negative

[placid zinc]

Ignore I said that haha it was dumb.

[barren notch]

then the absolute value would make it positive right?

[placid zinc]

So if x is negative, then |x| = -x

That way, -x becomes positive

[barren notch]

hmm

wait nvm

I was doing mathcounts trainer on aops

and as I was entering the answer the problem changed

:/

thanks anyway

.close

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[placid zinc]

🤔

[barren notch]

its a bug on aops

i think its because aops was timed out for such a long time the problem changed

idk its weird

[barren notch]

also, i figured it out

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[barren notch]

its -1

[barren notch]

.close

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[hybrid moon]

(probability that the total after rolling 4 fair dice is 21) > (probability that the total after rolling 4 fair dice is 22)

Can someone explain to me why its not equal

Im using joseph blitzen statistics 110 course

[rose sigil]

why would you expect it to be equal?

if you roll two 5 sided dice, is the probably of getting rolls that sum to 2 the same as getting rolls that sum to 7?

[slow hound]

the way i think about it is like a bell ish shaped curve centered at the mean (3.5 * 4) that tapers off on both sides

since 21 is closer to the mean than 22

P(21) > P(22)

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[small cypress]

for m of AB i did (b-2)/(3-a) = 2

for distance i did

root (a+3)^2 + (2 + b)^2 = root 125

after epxanding

i got a^2 + 6a + 9 + 4 + 4b + b^2 = 125

idk what to do from here

a^2 + 6a - 112 + 4b + b^2 = 0

[gray isle]

you have a system of equations \
$$\begin{cases}
\frac{b-2}{3-a} = 2 \ \
a^2 + 6a - 112 + 4b + b^2 = 0
\end{cases}$$ \
solve using something like substitution

[ocean seal]

ℝamonov

[lone heart]

@small cypress Has your question been resolved?

[small cypress]

so like a is 1

then b is 1

smth like that

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[quartz tusk]

Hello

[quartz tusk]

So i was going through examples of set.

and there was this example.

"the collection of all boys in your class" and was mentioned that it is not a SET.

WHY?

oh pardon me guys.

i read it incorrectly.

sorry.

/close

.close

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[tender dew]

Is there a way to "tilt oscilations"?

so that normal lines to a tangent in points k*pi would also be line of symmetry of 1 cosine mountain?

[tacit arch]

Just tilt your coordinates. Doing what you're suggesting doesn't give a function

[tender dew]

but if I tilt coordinates, space won't be uniform

I know that what I can naturally picture doesn't come as easily in algebraic form

hence my question

guess there will be no symmetry since it's decreasing, unless I make oscilations to dampen in a step

Idea of them tilting remains

I think cosine must arise from a tangent, but not sure how to create it

[lone heart]

@tender dew Has your question been resolved?

[tacit arch]

I think the main problem is your tilt is different for every point. So it's not really useful to think of how to map g to h. Instead just decide how to map f to h directly. This can be done by finding the perpendicular line at every point, then calculate the amplitude in direction using the cosine and exponential, or maybe that's just g. This will probably have to be done using parametric form

[tacit arch]

What does this mean mathematically

[tender dew]

first statement from what you said further on

[tacit arch]

?

[tender dew]

"I think the main problem is your tilt is different for every point."

that part

I wonder how to create perpendiculars for every point, whether I can rewrite mathematically, this thing will require to solve linears for every point with a = -1/f'(x). In program everything would be possible, but can 1 equation express desired function at the end?

[tacit arch]

Yea that's the right direction. You just need to find amplitude. Again, gotta do it parametrically

Also, once you have the normal vectors using -1/f', you have to move it to the curve f

[tender dew]

so is it confirmed that there is no 1 equation?

[tacit arch]

I never said that

You should try

[tender dew]

yeah, so solving for every point

linears

[tacit arch]

Oh. Then yes. Your normal vector will be different at every point

The only thing that has a constant normal vector is a line

[tender dew]

different A and different B

maybe finding patterns in them changing will help

[tacit arch]

It's just calculating -1/f' for a couple periods

[tender dew]

hmmm, seems like tampered hiperbolic function

how B changes

bit ridiculous

[tacit arch]

That only gets you the directions

[tender dew]

What desmos did is probably draw infinitely many perpendiculars that would take up an entire plane, but all are calculated on a line of original function

[tacit arch]

I told you to find the amplitude and do parametrization. I already said you won't be able to find a function

[tender dew]

I knew he won't be able to draw h(x) but that was worth a try

[tender dew]

hmmm yeah, I think I see my error in y(x) deffinition

altough for every point it probably turned out that bad

I try solve discretely now

[tender dew]

it may seem like it, but they don't pass by the same point

[tender dew]

was wondering whether this spot makes some finite are but I guess with every new normal it increases in size faster than argument arise

[paper ridge]

This took way too long, but I got something

[lone heart]

@tender dew Has your question been resolved?

[tender dew]

you did it that way?

looks like you used desmos too

I mean I wonder how you got an amplitude

I had one idea to calculate cos times f(x) being sqrt(deltax^2 + deltay^2)

but doing so many calculations for 1 point is nuts

[paper ridge]

depends what "that way" is, I was trying to do something with rotations but it got ugly, then I found a simpler way to do it by accident

https://www.desmos.com/calculator/tjmgf6bja4

here it is all cleaned up

square wave on exp 🙂

[tender dew]

What gave an idea to calculate derivative to it's module twice?

[paper ridge]

I'm assuming your talking about this part?

[tender dew]

correct

I think I understand why calculate derivative to it's module since I wanted do it as well to get the length of normal vectors along parent function f(x) but why twice?

[paper ridge]

Are you good with the first part to get the unit tangent?

[tender dew]

I guess

[paper ridge]

The normal vector to a curve is usually defined using the arclength parameter (as far as I've seen), but using chain rule and FTC I think it should be the same in the standard parameterization, hence why I do it again

[tender dew]

It's a bit for me to take in, I still need to fiddle with the system, very much appreciate the effort, equations are quite compact

.close

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[tender dew]

welp, x^n is not a signal but generaliation of such

I can use matlab for it

[tender dew]

OK, I recalled a bit of this and that

I knew that this peak at x = 0 is in effect of spectral leakage

https://en.wikipedia.org/wiki/Spectral_leakage

unfortunately I no longer have access to program that rid that

[lone heart]

@alpine sable Has your question been resolved?

[tender dew]

it's about removing offset from signal

signal = signal-mean(signal);

that still gives back peak at 0

welp, no signal closer to harmonic so maybe it should be this way

[alpine sable]

What is mat lab

[lone heart]

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[plucky geyser]

I just wanna say that's a good question you know

I'm just kidding

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@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

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[alpine sable]

no clue what to do with this integral

[rose olive]

How do i move farword

[alpine sable]

im using this channel sorry

[lone heart]

@alpine sable Has your question been resolved?

[fallen venture]

Oh this is one of the integrals where it cycles

[alpine sable]

<@&286206848099549185>

[fallen venture]

So essentially

[alpine sable]

im all ears

one sec im gonna get some water

[fallen venture]

You get the integral itself

When you do integration by parts

And you let I = to the integral

Substitute

And solve for I

So if you let I = to the integral

You get

I = (e^2x sin(x/2))/2 - 1/4 I

Then solve

Oh wait

Nvm

You need to do integration by parts again

And then you can do that

So the cosine turns into sine

[alpine sable]

wtf is this evil ass integral

[fallen venture]

Do integration by parts

Then do the method above

[alpine sable]

what

im confused

if i do integration by parts i cant get any further

i just get stuck at this

[fallen venture]

do IBP on the cos e^x integral

[alpine sable]

whats IBP

oh

integration by parts

okay

one second

[fallen venture]

And then you can substitute I for the integral

And solve

[alpine sable]

so i create a double integral?

im kinda confused

[fallen venture]

Anyways i gotta go

Cya and gl

[alpine sable]

ok

cya

ty

<@&286206848099549185>

[alpine sable]

.close

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[worn fox]

Do you know any graphs that are continuous at a point but not differentiable there? Not asking for at x=1 yet

[tidal zealot]

no

what does it mean by non differetiable

how is something not able to be diffrentiated

[worn fox]

That the derivative does not exist at that point

[tidal zealot]

so how would that happen

[worn fox]

Well what's your definition of the derivative at a point?

[tidal zealot]

gradiant

[worn fox]

Just gradient?

[tidal zealot]

yeah?

[worn fox]

Alright

,w plot |x|

[ocean seal]

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[worn fox]

What do you think the gradient is at x=0 of this function

[tidal zealot]

0

[mellow tusk]

@worn fox would this work ?

[mortal trellis]

that's not continuous

[tidal zealot]

discontinuos

[mellow tusk]

oh

[mellow tusk]

is there any name for a graph like this?

[karmic rapids]

discontinuous graph at point X

[mellow tusk]

okay

[worn fox]

Why do you think this?

[tidal zealot]

then wht else would it be

or would it be underfined?

[worn fox]

Yes there is our issue

There's no sensible value to assign to the derivative at that point

[tidal zealot]

okay?

[worn fox]

1 and -1 seem like good choices from certain perspectives

But there is no agreement

So it's not differentiable at that point

[tidal zealot]

oh

[worn fox]

(Lots of maths rigour is hidden behind my words)

[tidal zealot]

okay

[mellow tusk]

i have another doubt, is there any name for this graphs like these, or are these function not defined

[worn fox]

But you would agree its continuous at that point

[tidal zealot]

yes

[karmic rapids]

piecewise function?

[tidal zealot]

so how would i make one for my question at x=1

[mellow tusk]

but there's nothing in the inteval x1,x2

[worn fox]

Well if |x| satisfies the condition at x=0, how can we transform this graph to make kt satisfy it at x=1?

[karmic rapids]

okay and?

[karmic rapids]

open your own help channel btw

[tidal zealot]

@worn fox can we do this

[mellow tusk]

alright

[mellow tusk]

i meant like wouldve piece wise function been those which are defined in that x1,x2

nvm i got it ig

[worn fox]

Yep

What's the equation of that graph

[tidal zealot]

|x-1|

[worn fox]

Very good

And you agree that it's continuous at x=1 but not differentiable there

[tidal zealot]

yes

[worn fox]

Awesome

Good job

[tidal zealot]

ok thank you, i have learnedd something today

.close

[lone heart]

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[alpine sable]

first make sure that the first function's limit as x approaches 0 is 0

make sure that $e^{\frac{-1}{x^2}}\sin\frac{1}{x}$ approaches 0 as x approaches 0

[ocean seal]

Legolas

[mellow tusk]

x->0+ , e^-inf * sin 1/h=0, x->0- ,e^-inf * -sin 1/h=0, thats why its continuous
was my first step right?

[alpine sable]

Yeah

[mellow tusk]

i cant solve the lhd and rhd (left and right hand derivatives )

[alpine sable]

so now we know the derivative exists

[mellow tusk]

they're basically lim h , f(h)/h

[mellow tusk]

no, we cant be sure until we check their lhd or rhd

[alpine sable]

Oh yeah

mb

[mellow tusk]

im unable to calculate it

[lone heart]

@mellow tusk Has your question been resolved?

[mellow tusk]

<@&286206848099549185>

[lone heart]

@mellow tusk Has your question been resolved?

[mellow tusk]

.close

[lone heart]

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[hallow vessel]

was looking for help with matlab

[hallow vessel]

is this smth that anyone could help w?

[worn fox]

post your Q, if someone sees it and can help they will

[hallow vessel]

ok cool

Im trying to make a monte carlo integration sim

and am new to matlab

how do i pick random points in a set domain

[worn fox]

MATLAB has a random function i imagine

https://www.mathworks.com/help/matlab/ref/rand.html

[hallow vessel]

i tried using it and it doesnt work how i want it to

[worn fox]

explain how you want it to work

[hallow vessel]

1 sec

im looking to make it pick a random coordinate in between the bounds of [-2 2 -2 2]

[hallow vessel]

that was in the matlab help??

bruh i must be blind

[worn fox]

yes lol

like one scroll down

[hallow vessel]

ohhhh

i think i typed it wrong earlier

i was using the inbuilt matlab guide

ill give it a try

ok so

i get returned a 2xn

but i neeed to then check if these pairs lie within an area

does anyone have any help?

[lone heart]

@hallow vessel Has your question been resolved?

[lone heart]

@hallow vessel Has your question been resolved?

[lone heart]

@hallow vessel Has your question been resolved?

[lone heart]

@hallow vessel Has your question been resolved?

[lone heart]

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[vital steeple]

Hi

[vital steeple]

Is the following proof correct?

$\begin{align*}
&M_3 = {(a_1, b_1), (a_2, b_2), ..., (a_k, b_k)} \subseteq A = \mathbb{N} \times \mathbb{N}
\
&\text{Let poset } \leq \text{ be defined as } (a,b) \leq (c,d) \Leftrightarrow a \leq c \land b \leq d.
\
&\text{Show that Supremum exists.}
\\
&\text{My try at this:}
\
&\underline{\text{1st case:}}\text{ Let } a \in M_3 \text{ with } a = (a_s, b_s), a' \in M_3 \text{ with } a' = (a_i, b_i), s.t.
\
&a_i \leq a_s \land b_i \leq a_s. a \text{ is per definition maximum and thus supremum of } M_3.
\\
&\underline{\text{2nd case:}} \text{ Assume there is no maximum in } M_3.
\&\text{Then there's no supremum being element of } M_3.
\
&\text{Yet there could be a supremum of } M_3 \text{ in A as a superset.}
\
&\text{Let } b=(a_s, b_s) \in A, \text{ arbitrary } b'=(a_i, b_i) \in M_3:
\&b \notin M_3 \land a_i \leq a_s \land b_i \leq b_s
\Rightarrow b \text{ upper bound of } M_3.
\
&\text{Yet to show is that b is lowest upper bound of } M_3 \text{ and so supremum. So let be...}
\
&b''=(a_j, b_j) \text{ is arbitrary upper bound of } M_3 \text{ s.t. }
\
&a_i \leq a_s \leq a_j \land b_i \leq b_s \leq b_j \Rightarrow \text{b is supremum of } M_3.
\
\end{align*}$

[ocean seal]

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

[vital steeple]

Small addition: To be shown is that Supremum exists for M_3

[wanton nova]

Tarik Barletti

[alpine sable]

Tarik Barletti

[vital steeple]

first time hearing that game figure

Tarık's my name, 'B' the initial of my surname

[wanton nova]

Nice

[gloomy wolf]

i am not sure about your proof

this seems like it wants to be argued inductively

try induction on k

[vital steeple]

What doesn't seem to work in my proof? And how would I do induction on k?

[gloomy wolf]

eh actually i think i misunderstood your argument

this should do it

[lone heart]

@vital steeple Has your question been resolved?

[vital steeple]

thanks James

[lone heart]

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[pseudo spear]

How can I prove the following:

[pseudo spear]

$e^x+ e^{-x} \leq 2 \cdot e^{x^2}$

[ocean seal]

gnomechomsky

[pseudo spear]

Seems right to me but im not sure if I can make it simlper

[tacit arch]

,w plot 2 e^(x^2) - e^x - e^(-x)

[ocean seal]

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[pseudo spear]

oh I guess not

Oh no wait, that is right

It never goes negative, meaning it is right

But how would I show it more simply?

[tacit arch]

,w plot e^(x^2) - e^(-x) for -1 < x <1

[ocean seal]

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[pseudo spear]

Oh right

[worn fox]

man of many words

[tacit arch]

i imagine it's grouping 2e^(x^2) the right way to bound each term on the left individually

[pseudo spear]

Im not sure what you mean

After playing around with it a bit I think it is right, but im not sure how to show it

[molten pivot]

Hello

Combine the fraction on lhs

[paper ridge]

Are you familiar with the hyperbolic trig functions @pseudo spear ?

[pseudo spear]

not really

[paper ridge]

This one is most useful here. It's an even function and strictly increasing for $x>0$, so $\cosh(x)\leq\cosh(x^2)$ for all $x$

[ocean seal]

Tymelord14

[ancient moss]

that’s not right

[worn fox]

not for |x| < 1 😦

[paper ridge]

ah, good point

[worn fox]

i personally don't care much for (-1,1) lets just be gone with it

[pseudo spear]

Thanks for the help anyway guys but I'd best sleep now

.close

[lone heart]

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[still storm]

I have done part a, but how do I construct this right-handed orthonormal frame along the curve? can someone please help

[naive valley]

well you showed in part (a) that the acceleration is orthogonal to the velocity, and in part (b) you're given that these are both nonzero, so you have two out of the three components you need for an orthogonal frame

given two orthogonal vectors in R3, do you know how to construct a third that is orthogonal to the first two?

[still storm]

can I use gram-schmidt?

[naive valley]

no it's simpler than that

an operation on the first two vectors that produces a third

[still storm]

cross product?

but how do I make sure it is along the curve?

[naive valley]

well the velocity is tangent to the curve right?

[still storm]

yes 🙂

[naive valley]

so doesn't that automatically make the frame "along the curve"? (not sure exactly what you mean by that)

[still storm]

because in question it ask for the frame along the curve(

[naive valley]

the only remaining steps: you probably want to normalize the vectors to make them unit vectors, and you should check that it is in fact a right-hand frame as requested

for the right-hand part: only one of (vel x acc) or (acc x vel) will satisfy the requirement, so make sure you know which one you need

[still storm]

ok, that make sense alot

can I ask you another question?

[naive valley]

sure

[still storm]

is that one

for a

I'm not sure about derivative of r(f(t))

[naive valley]

ok, well as in part (a) of the previous question, the speed will be constant if and only if $|\frac{d}{dt}r(f(t))|$ is constant, or equivalently if and only if $|\frac{d}{dt}r(f(t))|^2$ is constant

probably easiest to work with the squared version

so you won't have a square root to deal with

[still storm]

please wait for a min, I'm taking pic of my work

[ocean seal]

Bungo

[still storm]

sorry, the picture is not working. so my question is if I have r(t)=(1,t^2), f(t)= 2t, then is r'(f(t))=(0,8t) or (0,4t)?

like do I substitute f(t) into r' directly or I have to substitute into r and take the derivative of r(f(t))

[naive valley]

well, r'(t) = (0, 2t), so r'(f(t)) = (0, 2(2t)) = (0, 4t)

however

you don't want r'(f(t)), you want d/dt r(f(t)), which involves the chain rule

[still storm]

so d/dt r(f(t)) = r'(f(t)) * f'(t)

[naive valley]

yes

[still storm]

that's where I stuck

[naive valley]

well as above, r'(f(t)) = (0, 4t)

what's f'(t) ?

[still storm]

2

[naive valley]

right

so d/dt r(f(t)) = r'(f(t))f'(t) = (0, 4t)2 = (0, 8t)

[still storm]

yep, I get to here, but I don't know how to find a general f(t) s.t. every speed is constant

[naive valley]

well they're asking for a differntial equation, not a solution to the equation

[still storm]

emm, what's the difference?

[naive valley]

so depending on how much you want to simplify, it's just $|r'(f(t))f'(t)| = c$ right?

[ocean seal]

Bungo

[still storm]

yes

[naive valley]

a differential equation is an equation involving derivatives of functions, a solution is a function or functions that satisfy that equation

in parts (a) and (b) they're just asking for equations, in part (c) they want a solution (I think)

[still storm]

ok... so if I have f'(t)^2=c/|r'(f(t))|, is that correct

$f'(t)^2 = c/|r'(f(t))|$

[ocean seal]

Acrab

[naive valley]

no, either everything should be squared or nothing should be squared, depending on whether you're working with speed or speed squared

[still storm]

$f'(t) = c/|r'(f(t))|$ ?

[ocean seal]

Acrab

[still storm]

Do I need to keep going

[naive valley]

LHS should be |f'(t)|

RHS should technically be ||r'(f(t))|| in the denominator since r' is a vector

[still storm]

right, I get it, do you think that's everything for part a?

should I go ∫

[naive valley]

I'm not sure that's really any more simplified than the original form $|r'(f(t))f'(t)| = c$ or maybe (pulling out $f(t)$ since it's a scalar), $|r'(f(t))||f'(t)| = c$, but in any case you can't really simplify much beyond that without knowing the specific $r$

[still storm]

or I can leave this as the answer

[ocean seal]

Bungo

[naive valley]

no if it's asking for a differential equation then definitely don't integrate it

[still storm]

ok, I get it. thanks a lot!

.close

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[craggy summit]

Can you give an example of a set $S$ with $|S| > 1$ and a formula $\varphi$ such that $(\exists x \in S)\varphi(x) \rightarrow (\forall x \in S)\varphi(x)$?

[ocean seal]

q5

[lone heart]

@craggy summit Has your question been resolved?

[tacit arch]

What. Why not just identity phi=x

[lone heart]

@craggy summit Has your question been resolved?

[craggy summit]

yeah I guess that would work. That's not a very interesting example though

[lone heart]

@craggy summit Has your question been resolved?

[swift shore]

@craggy summit by “formula” do you mean a predicate function?

Like it takes an argument and returns true/false

[tacit arch]

What are you looking for exactly

Show the original question if it's from homework or text book

[swift shore]

@craggy summit hmm after thinking about this for a bit

I think phi has to relate to the other elements of S somehow

Because if phi is just some random quality of x, who says it dictates anything about the rest of S?

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[keen sinew]

Hello,

I derived to get the answer and the interpretation is to get the instataneous rate of change wrt concentration of a substrate

[keen sinew]

I guess what im trying to rap around my head is when do I know when i should just find the an answer without the derivative

[swift shore]

Wdym “when to find the answer without the derivative”

Like, generally speaking? Not this problem?

[keen sinew]

yes

I guess what im trying to resolve is that a biologist would use it to find the rate rate of the reaction

But they would react to find the rate of change on the reaction through deriving?

[swift shore]

Well it depends on the problem of course

Hmm

[keen sinew]

i guess what im trying to say is that we just derive to find the instant change of a function?

like if im driving, i know im going at x amount of miles per hour

but if i derive one time i get velocity

derive twice acceleration

derive thrice I get the jerk?

[swift shore]

Yeah

Well this is a little hard

[keen sinew]

yea sorry about that

[swift shore]

Basically you’re seeing how a small change in S, the concentration, will affect the speed of the reaction

[keen sinew]

right as h -> 0

[swift shore]

No it’s not your fault lol

Yep

I mean it’s all a little abstract, I’m not sure how you’d apply it exactly lol

[keen sinew]

ive always been bad at math so im trying to get better at it

thank you!

[swift shore]

Np don’t worry bout it

[keen sinew]

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[swift shore]

you definitely know what’s going on 🙂

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[thin urchin]

I am thinking 3^3 or 3!

but I could be way off

this is one of those challenge questions that is not like the other questions

[tight locust]

'derangement'

[oak perch]

Use inclusion-exclusion principle, we have

$\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}(n-k)!$

[ocean seal]

Cogwheels of the mind

[oak perch]

Now plug in n=4

[thin urchin]

hmmm

they didnt teach the inclusion-exclusion principle to us in sum form

[oak perch]

You can prove it yourself, it’s easy

[thin urchin]

ok so a sum of 0 to n in negatives multiplied by n choose k multiplied by the factorial of n-k?

[oak perch]

Also (-1)^k

[thin urchin]

oh

that looks pretty general, is it just the -1 that is specific to this problem or is that just the general formula for these kind of problems?

[oak perch]

At least Two ways. Direct counting or using the fact that inverse of matrix (C(i,j))_i,j is ((-1)^(i-j)C(i,j))_i,j

Don’t know what you are talking about.

Inclusion-exclusion principle is a general result

[thin urchin]

oh

they tought us like (A U B U C) = A + B + C - (A n B) etc

we certainly did not learn matricies yet

[oak perch]

Then direct counting

[thin urchin]

ok

I just need a little help setting it up for direct counting

[oak perch]

|A_1 union …. union A_n|=|A_1|+…+|A_n|-|A_1 intersection A_2|-….+|A_1 intersection A_2 intersection A_3|*…

To prove this

Compare both sides

Any x from A_1 union … union A_n

Say x belongs to m many sets amount A_1,…,A_n

For LHS, x is counted exactly one time

For RHS

x is counted

$\sum_{k=1}^{m}(-1)^{k-1}\binom{m}{k}=1$

[ocean seal]

Cogwheels of the mind

[oak perch]

Times

Therefore x is counted for exactly one time both sides

QED

[lone heart]

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[thin urchin]

hmm ok

thanks

.close

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[crimson solstice]

for this

on the left

would i apply the product rule to cos(xy) * y and then apply the chain rule to cosine then apply the product rule to xy?

[tacit arch]

sounds right

share your work here if you want to check it

[crimson solstice]

yeah doing it rn

bout to send it cuz i think im stuck just a sec

[crimson solstice]

not sure what to do past here

also not sure if i found the dy/dx of cos(xy) correctly here

[tacit arch]

all looks right

just use algebra and solve for dy/dx

if it helps, set z = dy/dx and solve for z

[crimson solstice]

is it possible for my answer to have dy/dx?

[tacit arch]

no

[crimson solstice]

hmm

but if there is dy/dx on both sides how would i get rid of one of them

[tacit arch]

z + 2z * cos(x) = 3z * log(x). how do you solve for z?

[crimson solstice]

divide 3z by both sides

wait

i dunno

[tacit arch]

bah bad example. i'll fix it

z + 2z * cos(x) + tan(x) = 3z * log(x). how do you solve for z?

[crimson solstice]

hmm

would you move all z to left side and factor a z out?

[tacit arch]

do the same for dy/dx

[crimson solstice]

ok let me distribute

then going to try that

worked!

tysm

incredibly helpful man ty

[tacit arch]

[crimson solstice]

just have one more question

i think i messed up on this one

so im here

wait

ok i think i messed up here cuz the answer isnt correct but im not sure where

[tacit arch]

Can't read the initial equation

It's that a y?

[crimson solstice]

yeah'

sorry

y = 2cos(x+y)

[lone heart]

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[tacit arch]

i don't know how y' became 2

[lone heart]

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[atomic comet]

I am getting D but answer given is A and B,how? What is the mistake in my process?

[tacit arch]

,w plot x + sqrt(x) - 6

[ocean seal]

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[tacit arch]

(A) is definitely wrong

[oak perch]

a+sqrt(a)-2<4

By the way Riemann that problem is solved, f(f(x)+f(y)) thing, I proved it can only be constant 0

[atomic comet]

How?

[oak perch]

Not this problem you asked, another problem we were discussing

[atomic comet]

That's what I think too,a can never be negative as it is inside the square root

[atomic comet]

Ohh sorry!

[oak perch]

So I got -3<sqrt(a)<2, since a>0, I got 0<a<4

[atomic comet]

Yeah same here

So the answer given is wrong,i suppose

[oak perch]

Probably

[atomic comet]

Okay I see

Thanks for confirming

[oak perch]

Np

[atomic comet]

.close

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[thin urchin]

am i way off?

for part a

<@&286206848099549185>

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[tidal lantern]

First you chose one ace from the four in the deck : C(4,1) ways to choose, then you choose 4 others cards which aren’t aces C(48,4) possibility

The probability of taking a card is equal for all cards, so the probability is given by the number of hands which contains one ace and the total of hands possible

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[west dirge]

Hi

[west dirge]

Trying to do this question

what ive tried so far is

subbing in z = x + yi

then using the Cauchy Riemann equation to see where it is differentiable

these are what i get

but not too sure how to express where it is differentiable nicely

and how to format the derivative

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[lone heart]

@west dirge Has your question been resolved?

[lone heart]

@west dirge Has your question been resolved?

[lone heart]

@west dirge Has your question been resolved?

[elfin snow]

maybe ask in #real-complex-analysis @west dirge, you will probably get a better answer there

[tidal lantern]

You made a sign mistake for the cosinus formula, not sure if it will solve your problem though

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[alpine sable]

pls help

[alpine sable]

i don't even know where to start on this one lol

[placid zinc]

https://tutorial.math.lamar.edu/classes/calci/volumewithrings.aspx

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[kindred crater]

I'm having trouble with u substitution. Where does the du go in this step?

[tacit arch]

they did the integral?

[kindred crater]

oh so when you do the integral the du disappears with it?

[tacit arch]

yes. same for any integrating variable

$\int x^n dx = \frac{x^{n+1}}{n+1} + C$

[ocean seal]

riemann

[tacit arch]

etc. https://www.integral-table.com/

[kindred crater]

Another question, in this step (pic attached), how does the 4x^5 dx disappear when plugging it back into the original integral?

it turns into this

-1/12du = 4x^5dx. So does it just simply replace the original variables there?

[worn fox]

Yes 4x⁵ dx is being replaced with -1/12 du

[kindred crater]

alright, I think I understand it now then. thanks guys

.close

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[ebon prawn]

Im not sure on how to progress from there but can I add both of the logarithms on the left to make it 1/2 log x

[placid zinc]

What was the original question?

[ebon prawn]

Its in there

Below the x=1 x=-1

[abstract badge]

whenever you have a+b and a-b try to reach a place where those 2 terms multiply

use the product rule

@ebon prawn

[placid zinc]

You cannot add logarithms like that, no. Worth keeping a list of log identities nearby.

Hint, the left can be written as:
log(√[x+2]) + log(√[x-2])

Once that happens, you can combine the logs using the log product rule

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[abstract badge]

he can also factor out the 1/2

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[ebon prawn]

Sorry for not replying, i solved the problem but I was eating

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@mossy talon Has your question been resolved?

[mossy talon]

<@&286206848099549185>

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@mossy talon Has your question been resolved?

[elfin snow]

maybe ask in #linear-algebra @mossy talon

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[unreal kiln]

Claimed

[unreal kiln]

How do I create one that satisfies both

[wary stream]

Is this assignment, a test?

[unreal kiln]

Assignment

It’s worth marks tho

[wary stream]

So like a homework, where you can get outside help?

[unreal kiln]

Yeah

Completion marks

@wary stream can you help?

[tacit arch]

Non permissible means you can't define the function at those points

No idea about x=y though

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[unreal kiln]

I need an example

[glass tree]

(sorry read the wrong message)

[unreal kiln]

Ok

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[old sentinel]

I've got the question "The value of p^q - (digit sum of p)^2, where p and q are integers and q>=3 and the number is 5 digits long, is there any way to work out all the possible options easily?

[lone heart]

@old sentinel Has your question been resolved?

[old sentinel]

<@&286206848099549185>

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[obsidian plover]

Are you familiar with domain and range? Have you tried these problems?

[sharp jolt]

I am familiar but I would need a review for this

[obsidian plover]

So domain is all possible values of x

[sharp jolt]

(-inf,2]

?

[obsidian plover]

But the second part of the line continues doesn’t it?

If you go to x=3 you can still get a value

[sharp jolt]

It continues down wards

[obsidian plover]

Well diagonally

[sharp jolt]

Yeah that

[obsidian plover]

And that’s still increasing X

[sharp jolt]

Ooooh yeah your right

(-inf, +inf)

[obsidian plover]

Yep

Try range

[sharp jolt]

With the ()?

[obsidian plover]

Yea

[sharp jolt]

(-3,-inf]

[obsidian plover]

That’s not proper interval notation, (lowest first, then highest)

[sharp jolt]

(-inf,-3]

?

[sharp jolt]

That’s that ally to everything?

[obsidian plover]

Yes

[obsidian plover]

Wdym

[sharp jolt]

Apply

Like does that apply to domain and range ?

Or just range

[obsidian plover]

Domain and range

[sharp jolt]

Alrighty I’ll remember that by heart

How about c

I know for sure there is an x intercept for problem C

[obsidian plover]

X intercept is where the line touches the x axis

[obsidian plover]

How do u know?

[sharp jolt]

Idk 🥲

Wait so there isn’t one

Because it’s on the y axis

[obsidian plover]

Nothing hits x except the y axis which is an arbitrary line that is just a marker

[sharp jolt]

Wait but there is tho

So -3,1

Wait so if it hits the y axis what do I put?

[obsidian plover]

thats a y intercept

theres no x intercept

[sharp jolt]

Pretty sure this answer key is wrong

[obsidian plover]

it seems so

[sharp jolt]

Yeah so I was right

There is no x intercept

[lone heart]

@sharp jolt Has your question been resolved?

[sharp jolt]

Actually yes

.close

[lone heart]

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[river remnant]

Points P, Q, R and S in that order divides the line segment joining points A(2, 5) and B(7, - 5) in five equal parts. Find the coordinates of P, Q,

[river remnant]

Could anyone help me

[desert tendon]

u know section formula

[lone heart]

@river remnant Has your question been resolved?

[river remnant]

Wanna check if my solution is right

[oak chasm]

Draw a picture of it first.

Or, what is your answer?

[river remnant]

1.8, 3. I know it's wrong

[oak chasm]

Yes, that's wrong.

Do you have a picture of what's going on drawn on paper?

[wanton pebble]

try to find ratio at which P and Q divide line segment

do you want ans? or want to know how to solve it

[oak chasm]

One of the rules is to not just give the answer.

It's OK to explain how to get it, though.

@river remnant How did you get 1.8? How did you get 3?

[river remnant]

Uhh, i putted section formula

[oak chasm]

OK, there's a little bit of a simpler method.

You take the x coordinates of A and B, and you do (Bₓ - Aₓ)/5 (the 5 is the number of sections).

That's how much each section will increase its x by.

So, like here, you have (7 - 2)/5 = 5/5 = 1.

So, A has 2 for its x.

P will have 3 for its x.

Q will have 4 for its x.

Because it's going up by 1 each time.

You can do the same thing with the ys.

(By - Ay)/5 will be how much to increase it by each time.

What do you get for that?

[river remnant]

Oooo

The average method?

[oak chasm]

Kind of. The change in x of a section if all the sections are the same length.

@river remnant

You get the total change in x and divide it into 5 parts.

Because there are 5 sections.

[river remnant]

Did not get it but thanks

[oak chasm]

It's like if you have a string that's 150 cm long.

[river remnant]

Yes

[oak chasm]

If you cut it into 5 equal pieces, that's 150 cm/5 for each piece.

So, 30 cm for each piece.

[river remnant]

Yes

Oh

[oak chasm]

Same thing here.

[river remnant]

Right

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[modest lava]

how do I find the first 4 terms of the sequence a_n = 3n^2 - 5

[alpine sable]

substitute n=0,1,2,3 into the expression for a_n

[modest lava]

to be honest, these things still confuse me, can you show me what to do afterwards?

[alpine sable]

$a_{\color{red}0}=3\cdot\mathbf{\color{red}0}^2-5=3\cdot0-5=-5$

[ocean seal]

Toby

[modest lava]

-2, 7, 22, 43

is this correct??
I dont know if this is right

[alpine sable]

yeah looks fine

[modest lava]

ohh nice

thanks

.close

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[vast bobcat]

does anyone know how to prove part 2 and 3?

Especially the very last bullet point

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[alpine sable]

thats correct

[tidal zealot]

good

bcs this has no solutionsa

im sad

idk if im right ornot

.close

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[hallow vessel]

need help with an epsilon delta proof

[oak perch]

Answered before

[hallow vessel]

i need some more help

i didnt really get it

[oak perch]

Any ε>0, there exists δ>0 such that any |h|<δ, we have |T(h)|<ε. So any |t|<δ/|v|, |T(tv)|<ε

I literally don’t know what else you need

[hallow vessel]

ohh i didnt see this i think

i mustve been v sleepy

but the part i dont know is getting to the delta value

[oak perch]

Really, two people asked the same question.

[hallow vessel]

delta/|v|

lmao

must be same course

[oak perch]

Check your definition

Your textbook

[hallow vessel]

of epsilon delta?

[oak perch]

Yeah. I already gave all details, the full proof

If you don’t get it check your textbook

Nothing more can be done

[hallow vessel]

bruh this icy cold

ok imma come back in 10 minutes, ill see if i can get it

.close

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[vital root]

What formula or function can one use to get the following output (Y) with the given input (X)?

 x  | y 
1.00| 0
0.10| 1
0.01| 2

So on and so forth, where every 1/10th step increases Y by 1.

[vital root]

I'm thinking it's a logarithmic scale but I can't for the life of me figure out what specifically

It's like reverse logarithmic

Doh, I got it: log0.1(x)

.close

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[keen lance]

How do I make a pair of simultaneous equations with whats given for (a)?

[alpine sable]

choose any two pairs of the three equal expressions as your pair of simultaneous equations

eg, 4x+4=5x and 5x=60y-100

[keen lance]

i see

thanks

.close

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[vestal pilot]

Linear algebra
What does doing this mean?

[alpine sable]

weird

it means "T is a map from the kernel of T to the image of T"

which makes no sense at all lol

[vestal pilot]

I had to find the Ker(T) and Im(T) of the transformation I got, and then they ask me to find the transformation matrix of T after the reduction with respect to the basis that I found in the beginning

Wouldn't doing Ker to anything give me a 0 vector

[alpine sable]

yeah

[vestal pilot]

Oh wait maybe because Im(T) is the image, then it equals to W in V->W

[alpine sable]

if T is only defined on its kernel, then its the zero map

[vestal pilot]

And that would mean that Ker(T)={0}

[alpine sable]

I dont understand whats going on in your picture, sorry

[vestal pilot]

I was just finding the Ker and Im

[alpine sable]

that part looks fine

[vestal pilot]

Oh, you mean the first picture

I mean doing Ker(T)->Im(T) is not wrong

I've seen it done a ton of times

I just don't remember what it means

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[strange fractal]

hi!

[strange fractal]

i need help

nvm

[hollow vapor]

if you're finished please type .close

[strange fractal]

i need more hel

[hollow vapor]

ok

?

[strange fractal]

nvm!

[hollow vapor]

ok-

[lone heart]

@strange fractal Has your question been resolved?

[strange fractal]

question

why is it 1/16

i gotthis

<@&286206848099549185>

[alpine sable]

2/32=1/16

[strange fractal]

but if i bring the 2 over from other side

it's -2

?

@alpine sable

[alpine sable]

divide both sides by 32

[strange fractal]

why?

OH

TYMSM

[alpine sable]

yw

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[sage violet]

wdym\

y = x ?

[alpine sable]

Try x log x

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[ashen copper]

This is a question about Monte Carlo Algorithm
I just read about this algorithm recently
I would like to know how I may apply this
In a game of 5 our side units and 1 opponent enemy unit
Each units create damage on enemy
In the contrary, the enemy also create damage to our units.
The Total Damage is the accumulate damage where our units made to the enemy unit.
Each units has a CriticalRate.
Normally the CriticalDamageRate is 2; but based on buff and debuff this could changed.
Also each game could have different seed.
Now the question is that how do I apply Monte Carlo Algorithm so I can get the Expected Accumulated Damage that is trustful

[inland oriole]

What is a Cartesian product?

[worn fox]

Sorry you got beat to this channel, grab another one

[lone heart]

@ashen copper Has your question been resolved?

[lone heart]

@ashen copper Has your question been resolved?

[noble sinew]

just do it a bunch of times and take mean?

[ashen copper]

I am actually trying to ask the math of this

As like I don’t quite understand how to use this algorithm

[elfin snow]

perhaps try asking in #computing-software @ashen copper

[ashen copper]

Okay

[noble sinew]

Your monte carlo algorithm isn’t actually an algorithm

Its just a class of algorithms which use simulation

And what I said is how you use that

[ashen copper]

So for each hit of an attack I will be able to get a damageData with the following information
NonCriticalDamage
CriticalDamage
CriticalRate

I think I should use the formula
NonCrit*(1-critrate)+crit*critrate?

[noble sinew]

Sure if u want to

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[still lynx]

Hello, i would like to get a bit of help on this one I try to multiplicateur by sinx-cosx but doesn’t work

[dusk moth]

Which one

1 or 2

[marsh rapids]

That is a good idea

It does simplify nicely. Just go a bit deeper with that idea

[dusk moth]

The first one

[lone heart]

@still lynx Has your question been resolved?

[still lynx]

Yes 1

I am now stuck with (sin(2x)-1)/cos(2x) < 0

How am I suppose to solve this ?

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@still lynx Has your question been resolved?