help-13

[flint plinth]

other than that, looks ok

33/11 is of course also known as 3 😁

[prime island]

ooh yeah

would this be x?

[flint plinth]

well that holds true, but it's not really useful since you have x on both sides

[prime island]

oh wait is it all divided by x^2 instead?

[flint plinth]

instead you could rearrange as 2x^3 - 27x^6 / 1331 = 0

factor out x^2

see what's left

[prime island]

ooh okay

Is this right?

[flint plinth]

yea it looks right, unless there's a calculation error somewhere that i overlooked

eyeballing the graph, that value of x looks plausible

cube root of 2662/27 is about 4.6

[prime island]

aah okay ill solve for y now

🤔

oh wrong question

lol

[flint plinth]

haha oops

[prime island]

It actually worked

woaaa

thank you!!!

[flint plinth]

nice!

wd

[prime island]

/close

.close

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[quick glade]

Hi

[quick glade]

I need help with number one i

[dire geode]

!noclopen

[cedar kiln]

Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.

[dire geode]

#help-17 message

[quick glade]

Oh okay

[cedar kiln]

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[maiden sorrel]

So basically I need to do a linear regression in matlab using two pieces of data called death and total, I need to put it into an equation of death(i)=(approximatly) mtotal(i)+b and I'm basically trying to find m (the slope) and b (y intercept) the equation I came up for this is m=inverse(transpose(total)*total)*transpose(x)*death the only problem is that the values I get are infinite which makes me think I'm doing something wrong here

[maiden sorrel]

This is the data

[frigid osprey]

Hey, lemme look over this rq and I may be able to help you

[maiden sorrel]

Sounds good I'll send the full question as well underlined my printing is abit messy

[frigid osprey]

Can you send a picture of the question you are working on so that I can fully understand what you are working on?

[frigid osprey]

So this is a y=mx+b problem.

[maiden sorrel]

Pretty much just with vectors

[frigid osprey]

Oh lovely.

[maiden sorrel]

I have to specifically put it through matlab which is the hardest part because when I did so I got infinite values

[frigid osprey]

Can I see that?

I may be able to see if you made any errors putting that in.

I mean it looks like you have everything right

[maiden sorrel]

Yea I'm not sure what I'm missing here

From the way my proff explained it has to have a sort of set up with (x1,x2,x3,.....xn)*(m, b)=(b1,b2...bn)

But he dident explain to deeper then that

Also let me know if u can see the pic of the screen u may need to do close up on it

[cedar kiln]

@maiden sorrel Has your question been resolved?

[cedar kiln]

@maiden sorrel Has your question been resolved?

[cedar kiln]

@maiden sorrel Has your question been resolved?

[cedar kiln]

@maiden sorrel Has your question been resolved?

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[ionic finch]

An example of a function whose derivative doesn't satisfy intermediate value theorem

[ionic finch]

does f(x)= { x^2sin(1/x), x!= 0
0, x=0

Works?

or is it darboux theorem?

<@&286206848099549185>

[cedar kiln]

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[solid sage]

Hi

[solid sage]

How can i show thar

[sharp lotus]

can you elaborate?

[cedar kiln]

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[hidden hound]

$\frac{366!}{2!*(366-2)!}$

why doesnt this work in calculator

[wraith dagger]

pixel

[livid hound]

requires the calc to compute 366! which its not capable of

[hidden hound]

,calc 366!/2!*(366-2)!

[wraith dagger]

Result:

Infinity

[hidden hound]

bot unable to do so either?

[subtle harbor]

366! is too large

[hidden hound]

this is the same as 366C2

which gives 66795

[livid hound]

,calc 366!/(2!*(366-2)!)

[wraith dagger]

Result:

NaN

[subtle harbor]

but you can simplify this

[livid hound]

,w 366!/(2!*(366-2)!)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by ramonov

[subtle harbor]

which WA seems to do

[livid hound]

use a more powerful calc

[subtle harbor]

lmao

[hidden hound]

ok ty

[subtle harbor]

or ye

[livid hound]

or factorial rules and do it by hand

[subtle harbor]

or just..simplify it first then do the calc

yea

[hidden hound]

I know how to do it, i was just wondering why the calculator was acting up

thank you guys

.close

[cedar kiln]

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[cedar kiln]

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[cedar kiln]

@gloomy totem Has your question been resolved?

[crimson sedge]

@gloomy totem nothing is given about the like apn ?

cause i think something more is needed

what you think ?

[cedar kiln]

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[gloomy totem]

.reopen

[cedar kiln]

✅

[gloomy totem]

maybe

im not really sure where to begin

<@&286206848099549185>

[opaque pivot]

i would begin by writing OM in terms of a and b

can you think of a way to do this

[gloomy totem]

OM would be 1/2(a-b)

wait no

1/2(a-b)+b

[opaque pivot]

yeah

now OP is 3/5 of OM

try and work from that

[gloomy totem]

sure

[crimson sedge]

yeah do that

[crimson sedge]

atleast get p in terms of a and b

then think of on:nb

[wicked mantle]

nvm, you’re working on it

@crimson sedge Have you gotten the answer?

[gloomy totem]

ive found OP as (3a+3b)/10

what next

[wicked mantle]

[crimson sedge]

nope just need one more info then its done

[wicked mantle]

Sure

@gloomy totem Do you have the answer?

[gloomy totem]

no

[wicked mantle]

okay

[gloomy totem]

i found OP but idk what to do next

[wicked mantle]

What is OP

Could you state it?

[gloomy totem]

.

[wicked mantle]

yeah, it’s good

You’re only one step far from the answer

[crimson sedge]

||triangle law at opn ?||

[wicked mantle]

Nope

[gloomy totem]

whats the next step

[wicked mantle]

Actually, if I were the one who do this question, I would abandon a and b XD

They’re kinda annoying

[gloomy totem]

so what do i do

[crimson sedge]

you got answer ?

[wicked mantle]

3:4

[crimson sedge]

fuck i am just too dumb

[wicked mantle]

Nah

Try not to use a and b

It would be easier

Those are just rubbish

[gloomy totem]

how am i supposed to use this

[wicked mantle]

State OP with AO and AB

[gloomy totem]

idk

youve got me confused

[crimson sedge]

nothing is given about AN ?

[gloomy totem]

@wicked mantle can i see your solution

[wicked mantle]

Is this homework?

[gloomy totem]

yeah

[wicked mantle]

Sorry, I can’t

The server rule has the say

[crimson sedge]

can you send it to me on my dm ?

[wicked mantle]

Sure

[crimson sedge]

yeah please :)

[gloomy totem]

aww cmon this is the only one i dont understand

[wicked mantle]

You can explain to him later

[wicked mantle]

Nah, no way

[gloomy totem]

:(

[wicked mantle]

But you can still add me

🙂

!done

[cedar kiln]

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[normal shore]

what does it mean for small values of x^2

[mighty shuttle]

for x<<<<<1, I think

[normal shore]

whaa

i juz binomial expansion that right

[wicked mantle]

[normal shore]

wouldnt binomial expansion directly give me the coef for x^4

[mighty shuttle]

use the binomial approximation IMO

I could be wrong though

[normal shore]

eh i will try ty

.close

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[silk hound]

@normal shore chill out. If you're not getting anything, let us help you.

[normal shore]

i think ik,, juz expanding those two bracket and then find the ccoef of x^4

[wooden frigate]

what're you gonna do with the x^4/3 term?

[cedar kiln]

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[normal shore]

Is it not?

But I have no idea why question states for small values of x²

Is it suppose to be smtg important?

.reopen

[wooden frigate]

i thought you wanted to use binomial approximation like physics people

[normal shore]

Uh idk, the binomial approximation ik is about statistics

[wooden frigate]

binomial for any index is only valid for small value of x^2 or whatever variable is there

[normal shore]

But why did the question mention for smaller values of x as if it's smtg

[normal shore]

Sooo for my question what does it want lmao

The thing that satisfy both is abs(x²)<1/6

Wait x² is already positive , no need abs

[wooden frigate]

and 1/6 is less than 1

[normal shore]

Which works right

[wooden frigate]

yeah

[normal shore]

Lol so the question juz type it out for fun

[wooden frigate]

your x^2 must be less than 1 that is what is mentioned and since 6x^2 might be greater than 1 for some numbers its written for small values of x^2

[normal shore]

So the term "small values" indicate <1

[wooden frigate]

much less than 1

[normal shore]

Ty kind human

.close

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[stray nest]

you can send x as 1/x in the denominator and substitute 1/x to t and try at it again

[tawdry dagger]

eli5

explain like i'm 5lol

[stray nest]

are you aware of how substitutions work?

[tawdry dagger]

yeah

but where do i plug in 1/x i mean where's the denominator?

its x(a raised to 1 over x subtracted by 1)

[stray nest]

$x/1$ can be written as $1/(1/x)$

[wraith dagger]

frostman

[tawdry dagger]

oh okay, then do i've differentiate it?

[stray nest]

then as x tends to infinity 1/x tends to zero

[stray nest]

do you remember a standard result?

[tawdry dagger]

uhmm no ig
which one though?

lim x-> infiinity(a raised to 1 over x -1)/x ? this one?

[stray nest]

yeah

[tawdry dagger]

is it log of a?

[stray nest]

it just goes to loga

yeah

for x tending to zero

[tawdry dagger]

then ? what's the answer i mean we're left with just lim x-> infity (log a) right?

[stray nest]

yeah

which can ve written as option d

[tawdry dagger]

ohh youre great thanks buddy

[stray nest]

@tawdry dagger thanks and please close this channel

[tawdry dagger]

uhh how?

[stray nest]

.close

[tawdry dagger]

.close

[cedar kiln]

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[cedar kiln]

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[vagrant mist]

In the plane, point P is inside a rectangle ABCD and the points Q and R are on the sides of this rectangle such that PQDR is also a rectangle, as shows the figure.

[vagrant mist]

Knowing that the area of ​​rectangle ABCD is 60 cm2 and the area of ​​triangle BPC is 15 cm2, the perimeter of the rectangle PQDR is equal to...?

[wicked mantle]

!status

[cedar kiln]

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

[long arrow]

Start from finding BC

Using area of BPC

[wicked mantle]

Start from showing your progress

[vagrant mist]

1

[wicked mantle]

Sure

Do you know where to set x?

@vagrant mist

You know a side of the triangle and you know its area

[vagrant mist]

I used the BPC's triangle area to find BC then used the area of ABCD rectangle to find the right side

but I missed by 1 cm

My answer was 21 cm

but the correct it's 20 cm

[silk hound]

Dude you calculated area. Question asked perimeter.

[wicked mantle]

Problem solved XD

[vagrant mist]

You right!

Haha

[wicked mantle]

!done

[cedar kiln]

If you are done with this channel, please mark your problem as solved by typing .close

[vagrant mist]

thank you!

.close

[cedar kiln]

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[tepid grail]

i dont think this is the correct route to take

[mental trail]

do you have the maclaurin expansion for cos?

[tepid grail]

in my formula book, there is a mac series for special function, cos x = 1 - (x^2)/2! + (x^4)/4! -...

but ion know how to apply it

[mental trail]

so when x is close to 0, cos(x) = this expansion

but let A = x-x^2

[mental trail]

this does approach 0 too right?

so what is cos(A) ?

[tepid grail]

A is x-x^2?

[mental trail]

yeah

so cos(A) would be what?

according to your formula

[tepid grail]

1 - (x-x^2)^2/2!...?

[mental trail]

exactly

[tepid grail]

but like i need to find a^5

so its coefficient of x^5

[mental trail]

yep

[tepid grail]

but cos x expension doesnt have that

it only has pos nums

[mental trail]

pos nums?

[tepid grail]

i mean pos power

x power 2 4 6 etc

[mental trail]

you mean even

ok

[tepid grail]

oh sht yeaj

mbmb

[mental trail]

but what happens when you expand?

is it still true that cos(A) is only in terms of even powers of x?

[tepid grail]

that would take a lot of time i suppose

cuz this q allows calculator

[mental trail]

yeah it is about expanding a bit

but i'll help to see what's useless to consider

for example

cos(A) = 1 - A^2/2 + A^4/4! - A^6/6! + ...

if we only want a_5

from which point do we need to stop adding terms?
*

like is A^8 useful for a_5?

[tepid grail]

nah

prob a6

[mental trail]

A^6 is (x-x^2)^6

[tepid grail]

oh

[mental trail]

what is the smallest power of x you get from expanding this?

[tepid grail]

do you use binominal expansion now?

[mental trail]

that's kinda it

[tepid grail]

to find the combinations that gets x^5?

[mental trail]

yep

[tepid grail]

oh

oh waot

[mental trail]

will expanding this give us some terms in x^5?

[tepid grail]

lemme try

[mental trail]

yeah sure

[tepid grail]

the x^5 is in the power 4

man its late here i give up

imma try again tmr

haiz

.close

[cedar kiln]

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[cedar kiln]

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[brisk lance]

If I have a general ”symbolic” system of 3 linear equations in 3D.
How would I ”find the conditions for the different types of solutionspaces” to that system?

[cedar kiln]

Please don't occupy multiple help channels.

[crimson sedge]

You must first solve your system with its parameters by working on its associated matrix

[brisk lance]

So if i have this system

[crimson sedge]

Oh du talar svenska !

[brisk lance]

Haha aa

[crimson sedge]

Jag lär mig svenska men jag talar inte jättebra än

anyway, do you know how to find the matrix of this system?

[brisk lance]

The augmented matrix or the echelon matrix?

[crimson sedge]

any of them will do the job

In either case you will want to end up with the row-echelon form

[brisk lance]

Right

[crimson sedge]

beware when dividing by the coefficients though, as they should not be zero

[brisk lance]

Okey I’ll give it a go one sec

Hm

[brisk lance]

Is that what I should work with or

[cedar kiln]

@brisk lance Has your question been resolved?

[crimson sedge]

exactly. Don't forget that, because you divided by A1, you should treat the case A1=0 separately

As you can see you're on for pretty long calculations

That's the reason why we never use a general formula for these systems

[brisk lance]

Seems unreasonable for me to do it so I’m guessing they expect something less

They want conditions for the coefficients for the different scenarios

Aka conditions on the coefficients that lead to different amounts of pivots I guess?

Would it be enough to just give the basic matrices of 1’s and 0’s that give the different scenarios?

[crimson sedge]

I am not sure tbh

maybe you can try to discuss it geometrically

solutions to your system are the points of intersection between 3 planes

so their number is:

• 0 (3 parallele planes)
• 1 (only 1 point in common)
• an infinity with 1 parameter (a line)
• an infinity with 2 parameters (at least two planes are the same)

[cedar kiln]

@brisk lance Has your question been resolved?

[cedar kiln]

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[crimson echo]

I have probability mass
X = -2, -1, 0, 3.5
P(x) = .1, .2, .4, .3

I calculated the kurtosis as 3.154 can someone help me verify?

[crimson echo]

this was my thought process if i am wrong

ping me if you answer

[cedar kiln]

@crimson echo Has your question been resolved?

[cedar kiln]

@crimson echo Has your question been resolved?

[cedar kiln]

@crimson echo Has your question been resolved?

[cedar kiln]

@crimson echo Has your question been resolved?

[crimson echo]

.close

[cedar kiln]

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[crimson sedge]

Any help is appreciated, please ping me when anyone responds

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

[nimble veldt]

what is your question?

[crimson sedge]

a b c

[crimson sedge]

a
b
c
in the photo

Im so confused

please help me im begging 😭

[nimble veldt]

i have read it, but what is your question?

[crimson sedge]

I don't know what each line does on Desmos

or what b even means

[nimble veldt]

open desmos, type every line and look what happens.

[crimson sedge]

Ive done that I have it open rn

i see it moves lines but idk how to put that into words

[nimble veldt]

what happens if you type just the first line?

[crimson sedge]

Its the red line that goes up and down and up

without the straight red or blue line

[nimble veldt]

its drawing the graph for the function you have typed.

[crimson sedge]

Okay

Do you know what the (cf(c)) does

I know it made the c slider that then changes the red and blue lines location

[nimble veldt]

type it and you will see it.

it does not make the slider the slider comes form the line c = ...

[crimson sedge]

Well it didnt make

I thought it was associated

when I get rid of and add it I dont notice any change

[crimson sedge]

both sliders work without it too

im so confused

[nimble veldt]

what do they do "without it"?

[crimson sedge]

The c slider moves the intersected point of the red and blue line along the red graph from the function

the h slider changes the tilt of the blue line

Is the blue line the tangent line?

Can you help me get the correct vocabulary for what to call them please

[nimble veldt]

so you have the description what they do. (thats what a) wants you to do).

[crimson sedge]

Okay

But what does

[crimson sedge]

(cf(c)) do

and f'(c)

when i remove / add f'(c) also nothing happens

[crimson sedge]

What

how do I get that

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

.close

[cedar kiln]

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[cedar kiln]

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[glacial summit]

id like to do this via integration by parts

[sharp lotus]

you don't need IBP, you can just distribute the x^3 and then use power rule on the terms

[glacial summit]

less so i need to but im a bit new to the method and i want to learn how to apply it correctly

i keep getting 1/5 when the answer should be 3/10

[sharp lotus]

did you end up applying integration by parts 3 times until you got rid of the x^3 or what?

[vagrant elbow]

even if you are integrating by parts you should differentiate (2 - x) tbh

[sharp lotus]

true

[glacial summit]

i split it into (2-x)((x^4)/4)-integral(((x^4)/4)(-1)dx

[open yew]

yes

[sharp lotus]

when you did your u\v whatever substitutions, did you either later convert everythng back to x's or recalculate the limits of the integral? that's a common mistake

[glacial summit]

im not sure

let me just relay what i did

[sharp lotus]

looks ok so far

[glacial summit]

it went 2(x^4)/4 - (x^5)/4-(x^5)/20

[sharp lotus]

+x^5/20 because you have that (-1) factor in there

[glacial summit]

oh ok

thats where i goofed

thanks for the help

.close

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[sharp lotus]

L'hopitals?

[honest torrent]

whas that for

[short blade]

i think they want you to treat this as a derivative

unless this is finding the derivative via the limit defn

[sharp lotus]

useful for lots of limits that give you indeterminate forms like 0/0

or infty / infty

[honest torrent]

i dont get how it becomes 1/sqrt(9+x^2)+3

then plug in 0

[sharp lotus]

is that what your book's solution shows or something?

[honest torrent]

yeah so i assume they rationalized or conkjugated

[sharp lotus]

i don't know, but it's easy with lhopitals

[dire geode]

did you try multiplying the rational conjugate

[honest torrent]

i tried

[sharp lotus]

yeah what riemann said, multiply by $\frac{\sqrt{9+x^2}+3}{\sqrt{9+x^2}+3}$, seems like it would cancel

[dire geode]

!show

[cedar kiln]

Show your work, and if possible, explain where you are stuck.

[wraith dagger]

Soosh

[sharp lotus]

you should get 9 + x^2 - 9in the numerator

[honest torrent]

oh -9

[sharp lotus]

now 9's go poof and left with x^2 in numerator

[honest torrent]

oh wow

then x divide

[sharp lotus]

yeah and you just have the denominator of conjugate thingy you multiplied with

[honest torrent]

got it ty clearing it up

[sharp lotus]

thanks to riemann, i alone would have shoved learning lhopitals down your throat 😛

[honest torrent]

do i learn that?

[sharp lotus]

im sure you will

[honest torrent]

is it viable for every limit or smt

nah im alr on to derivattives

idk if we go back to lim

[sharp lotus]

basically if you have a fraction where if you take limit of top and its 0 and also the bottom is 0

you can take derivative of numerator and denominator individually then evaluate the limit of that, if that is then a limit it also gives you the limit of the original f(x) / g(x)

[honest torrent]

seems more ez

[sharp lotus]

like for example: lim x-> 0 (sin x / x)

dunno if you did proof of that using just squeeze theorem or whatever in your class at some point, it's a decently long proof with that method

[honest torrent]

i forgot squeeze proof for that

[sharp lotus]

but with lhopitals, you see ok its 0 / 0 so take derivative of top and bottom and it's:
lim x-> 0 (cos x / 1) = 1 bam done

[honest torrent]

wooow

seems very useful then

[sharp lotus]

good tool to have in your toolbox

[honest torrent]

noted

[sharp lotus]

also can be applied with you have infinity / infinity type stuff or -infinity / infinity etc.

but youll probably learn it in your class eventually, usually comes later than other limit stuff

probably when learning stuff like improper integrals and whatnot

[honest torrent]

ty for the info

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[twin wave]

Can soemone show me the working out for 3a iii)

[twin wave]

ping me if you do

[distant wyvern]

i: each digit has 6 possibilities

[twin wave]

yes

[distant wyvern]

ii is simply 6P4

since permutations are different numbers

[twin wave]

ii is 360

i is 1296

[distant wyvern]

iii try complimentary counting

ooh wait no more than twice

so it'll be

total no. possible numbers - no repetitions - 3 repetitions - 4 repetitions

[twin wave]

so 4 reps would be 6 and 3 reps 18?

[distant wyvern]

for 3 reps you can have aaab and its permutations

so uhh

[twin wave]

i got 1296-360-24-6=906 but answer is 810

[distant wyvern]

i got 1296 - 360 - 6 - 120

[twin wave]

yeah thats correct

[distant wyvern]

yeah so for 3 reps it'll be

[twin wave]

how do i get the 3 repetition?

[distant wyvern]

aaab and its permutations

you can put the b anywhere. the other 3 will be a

so 4 permutations

so 4 * 6p2

[twin wave]

why is it 6^2

[distant wyvern]

its 6p2

6*5 not 6^2

a has 6 possibilities, and since a and b cant be the same b has 5 possibilities

6*5

and its permutations 4 x 6 x 5

[twin wave]

oh alright

thanks

[distant wyvern]

np

[twin wave]

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[magic solar]

for some reason I can't do this. Could someone walk me through it?

[magic solar]

a) is +-(1+3i)

[wicked mantle]

!status

[cedar kiln]

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

[magic solar]

I've done the question, but i keep getting the wrong answer

[wicked mantle]

May I see your progress?

[silk hound]

For the a option, have a habit of observing the answer directly rather than finding the square root.

[magic solar]

ok, ill rewrite it though because my writing is little illegible here

[wicked mantle]

Sure

[wicked mantle]

Agree

Intuition sometimes works on such questions

[crimson sedge]

for a, it's a good idea to write it in polar form

[silk hound]

Nope even better, try to see -8 + 6i = 1-9 + 6i = 1 + (3i)^2 + 6i

[crimson sedge]

sure that works as well

[magic solar]

I didn’t write the last few steps I did because I’m kind of confused at what I even wrote

[crimson sedge]

you can also just directly use the quadratic formula for the second one

z =[ (7-i) +/- \sqrt{(7-i)^2 - 4(14-5i)}]/2

simplifies to (7-i +/- \sqrt{-8+6i})/2 and now use answer from part a

which is 1+3i

so [7-i +/- (1+3i)]/2

u can simplify

[magic solar]

I think they were trying to get me to use this method

[crimson sedge]

oh ok yeah you can do complete the square too since its one of the ways the formula for roots of quad. is derived

[magic solar]

the sqrroot of (-8+6i) i get to be +-(2+6i)

and then i do $z-(\frac{7-i}{2})^2=+-(2+6i)$ which is wrong

[wraith dagger]

annyeong

[crimson sedge]

sorry i got something else for the RHS

i'm getting (-8+6i)/4

instead of times 4

So we're at $$(z- (7-i))^2 = (-8 + 6i)/4$$

[wraith dagger]

swimmingland

[magic solar]

oh yeah i factorised it wrong

[crimson sedge]

So you get z-7+i = \pm (1+3i)/2

and then you simplify

[magic solar]

i see

thnks for spotting my mistake

ty for help

.close

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[crimson sedge]

sure thing

[cedar kiln]

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[ocean tide]

https://wikimedia.org/api/rest_v1/media/math/render/svg/f457958c973773cdc8881b7e6d22efaab6c70518 going through bellman’s equation and i don’t understand why we need a max here. This is a summation it will just give me 1 number, max of 1 number is that number

[cedar kiln]

@ocean tide Has your question been resolved?

[short blade]

[\max_{x\in [0,1]} x]

[wraith dagger]

maximo

[short blade]

this notation is saying "take the maximum value of x in the interval [0,1]"

x will always give you a number, and the max of a number is that number
but we are interested in saying "the max of this function of x over some domain"

in the same way, your notation is saying
"give me the maximum value of this sum when i change the sequence a_t"

if you put some sequence a_t, the summation may be 0

but if you put some other sequence you may get 1

etc.

@ocean tide let me know if that is unclear

[ocean tide]

So basically its saying give me the summation of that multiplication based on t, where each summation is different for each t and then find the max of those summations?

[short blade]

i wouldnt use that language

its saying

compare all of the possible summations for all the possible sequences a_t

and take the largest value out of all of them

as a simpler example, consider
[C = \max_{{a_t}^\infty_{t=0}}\sum_{t=0}^\infty a_t]

[wraith dagger]

maximo

[short blade]

this is saying
"give me the maximum value out of all series"

the idea is that we get to try out every sequence of values for the series

for example, we could do a_t = t

or a_t = 1/t^2

or a_t = e^-t * t

and so on

and we want the maximum value after we try all the sequences

[short blade]

this C is undefined though since if you just take a_t = 1, the sum diverges

so there is no maximum

[ocean tide]

Thinking one sec

Something like this

? Graphed out

Basically we pick the max of the summations we get based on our action At, where At iterates based on t. So in this case we test all the actions and get the value of the best

I see

Whats tripping me hard is what metric i could use to get the value from F

[short blade]

what do you mean

[short blade]

but this is the idea yes

you theoretically go through all sequences a_t

and take the one that gives you the maximum value for the summation

[cedar kiln]

@ocean tide Has your question been resolved?

[cedar kiln]

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[crimson sedge]

how can natural numbers and integers map together? as natural numbers actually have a beginning ( start with 1 or 0) while integers can start from either side (negative or positive -1 or 0 or 1). I say map cause thats how you prove that they are countable cause you can map them so im just confused with integers..they dont have a strict beginning like natural numbers

[short blade]

why would that be relevant to having a map between them

you are probably expecting this function to hold on to some of the structure

in particular, what you are imagining is probably a map which keeps the idea of "<" intact

but functions in general dont need to do such a thing

[crimson sedge]

how else would you prove integers to be countable

[short blade]

im not saying a map between them is irrelevant

what i was asking is why having a strict beggining is relevant

let me use some stronger language to explain why there can be such a map

what you are describing as a "strict beginning" is due to a relation on the set of natural numbers

in particular, it could be the partially ordered set (N, <)

where a<b in the standard way

[crimson sedge]

how else would u map them like idk wouldnt it get confusing? like for eg, for natural numbers we pick 0 and for integers...uh..what do we pick? do we pick -1 or 0 or 1 yk

[short blade]

the set (N, <) is ordered like you said

but N

without the "<" added on

has no such structure

it is just a collection of symbols

[crimson sedge]

a is N?

[short blade]

let me go back

we have N

[crimson sedge]

ye

[short blade]

N = {0, 1, 2, 3, 4, ...}

[crimson sedge]

ye

[short blade]

now you would tell me that 0 is the smallest number in that set

[crimson sedge]

yes

[short blade]

but that is under a specific relation on the numbers

what if i defined 1 to be smaller than 0

as in

what if i swapped 0 and 1

so now they go
1 < 0 < 2 < 3 < ...

remember that these are symbols

not strictly numbers

[crimson sedge]

but you cant do that

[short blade]

remember that they are symbols

i can do that if i want

the idea that N has a smallest element is actually
"N has a smallest element with respect to some ordering"

Z also has a smallest element

if you order it the right way

[crimson sedge]

yea

[short blade]

for example, we could order it as
0 < -1 < 1 < -2 < 2 < -3 < 3 < ...

remember

these are symbols

and < doesn't mean "less than" in the numeric sense

it is just some arbitrary order i am giving them

[crimson sedge]

oh

so youre syaing

when youre mapping

you can be random?

[short blade]

yes

[crimson sedge]

like order doesnt matter

[short blade]

yes

because

we want to mak N and Z

[crimson sedge]

as long as they map

[short blade]

not (N, <) and (Z, <)

[short blade]

these here are distinct

and that is what you had in mind

you have good intuition for that

but N and Z are less structured

[crimson sedge]

mapping wise? or do u mean in general?

[short blade]

without even considering maps

N and Z are just the sets

when you add that order that you are talking about

they become different

but as sets

they are basically the same

because they are both countably infinite

[crimson sedge]

so basically we shouldnt stucturize them

[short blade]

not right away

if the question asks about their cardinalities

there is no immediate reason you should add structure

all you need is a bijection

between sets

which is different from the ordered sets you were thinking of

as a quick example

think about the set {1}

and the set {2}

they are different sets

[crimson sedge]

TRUEE

[short blade]

they are different in their contents

but they are very similar in that both have a single element

so they are more alike than they look

same goes for Z and N

as sets they have different contents

and you can structure them differently

but as sets they are very alike

to summarize, Z and N are alike, but (Z, <) and (N, <) are not

[crimson sedge]

hence structrizing them doesnt matter cause they are alike and hence can be mapped unlike w irrationals, like u have 1(as a natural number) and for irrational u got (0.001), CANT MAP COZ AINT ALIKE

so focus should just be on mapping em instead of

on em elements

like

[short blade]

yes sort of
we care about the size of the sets

not the actual content

at the end of the day, whether we have
{a,b,c} or {1,2,3}

we just want them to have the same number of elements

we dont care what theyre called

[crimson sedge]

yeee

[crimson sedge]

mhm so they just tryna prove that natural numbers and integers, both are alike hence can be mapped hence both are countable..and my mistake was just being too specific AQHAHASO8YDGQF

ok

thank

yOOOOU

😄

SO MUCH

ok

byee

.close

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[quartz salmon]

I've been working on some series problems and I could really use some assistance in understanding how to determine whether these series are convergent or divergent, as well as possibly calculating them. Here are the series in question:

a) (\sum_{k=0}^{\infty} \frac{1}{2^{k}})

b) (\sum_{k=2}^{\infty} \frac{1}{2^{k}})

c) (\sum_{j=1}^{\infty} e^{-j})

I'm a bit stuck on how to approach these. Could someone walk me through the steps or provide some hints on what methods or tests to use?

[wraith dagger]

dgh

[quartz salmon]

From what I gather, if k -> infinity means the term goes to zero, then that means the series converge?

Whereas, if when k -> inf and the term goes to a non-zero number, then the series diverge?

So why is it that we say a), b) and c) converges?

[short blade]

they are all of the same form

[short blade]

this is not true in general

just because the terms go to 0, the series wont necessarily converge

the condition is that if the series converges, the terms must go to zero

not necessarily the other way

[quartz salmon]

What does this mean, "to be of the same form"? As in being a rational number?

[short blade]

no

they are all a specific kind of series

what kind of series have you seen before

[quartz salmon]

What's the difference here between the two, 1/small number + ... + 1/large number ?

[short blade]

i dont understand your question

[quartz salmon]

Explain with an example what you mean

just because the terms go to 0, the series wont necessarily converge
the condition is that if the series converges, the terms must go to zero
not necessarily the other way

[short blade]

this diverges even though (\frac{1}{n}\to 0)
[\sum_{n=0}^\infty \frac{1}{n}]

[wraith dagger]

maximo

[quartz salmon]

What's "this"

[short blade]

the series

below

the terms go to 0

but the series diverges

the condition is

if (\sum_{n=0}^\infty a_n) converges, then (\lim_{n\to\infty} a_n = 0)

[wraith dagger]

maximo

[quartz salmon]

By "the terms go to 0", do you mean that the last terms are 0?

If we take this example

$\sum_{k=0}^{\infty} \frac{1}{2^{k}}$

[wraith dagger]

dgh

[short blade]

there are no last terms

there are infinitely many terms

[quartz salmon]

Ok, so the terms go to 0

Here

But how do we know if the series converge or diverge

Because the answer says it converges

[short blade]

you have to use various tests

divergence test, ratio test, root test, limit comparison test, direct comparison

[quartz salmon]

Do I need to have them remembered

Or is there a way to "intuit" the answer

[short blade]

depends on the series

but typically you need to memorize them yes

[quartz salmon]

Man

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[full forum]

Im keep getting wrong answer for part c

I used sine rule insteead of cosine rule

(sin(35)/5.76) x 10 =

0.99579

sin^-1 (0.99578) =

84.74

Why am I getting different value?

[livid hound]

limitations of sine

[full forum]

can you tell me more about it??

[livid hound]

there are two solutions to
sin(B) = 0.99579
for 0 < B < 180°
taking the inverse only gives the solution between 0 and 90°
this is related to ambiguity of the sine law

[full forum]

Ohhhhh

So since the drawing makes it hard to determine if its accute or obtuse, so i should use cosine rule

right?

[livid hound]

yes

[full forum]

ahhh okok

Thank you very much

.Close

[livid hound]

think you need to use a lowercase c

[full forum]

.close

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[small rock]

11 iv

[real tree]

Do u have the answers to it

just the solution

I dont think I know how to solve but I have found some solutions which I would like to check

if its right I can explain

[astral steppe]

you could set an equation system

[small rock]

I tried this

[small rock]

Book has given the answers

A 2 b 3

[real tree]

ok I got it right

its easy

u want the explanation?

wait u already did half of it

[real tree]

u can further take i vector common and put in bracker 4a-2b

then j vector common 2a+6b

then separately equate the i vector terms on lhs and rhs

and then the j vector temrs

u will get 2 simultaneous equations

solve them oto get a and b

[small rock]

Lemme try

Thanks

I got the ans

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[remote owl]

If P is any point on the hyperbola whose axis are equal , prove that $SP\cdot S'P=(CP)^2$

[wraith dagger]

Intecules ∮

[remote owl]

S and S' are the foci and c is the center

I proved it using the distance formula already but I want to know if there is a better way

[cedar kiln]

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[remote owl]

<@&286206848099549185>

wait I got it

using similar triangles

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[sharp cargo]

hey i have question -
At a dance club party, 4 boys and 3 girls arrived. The club's rules dictate that each girl randomly chooses, independently of the others, a boy to invite to dance. Let X be the number of boys who receive exactly one invitation. Find the probability function of X.

[cedar kiln]

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

[sharp cargo]

3

[cedar kiln]

Show your work, and if possible, explain where you are stuck.

[sharp cargo]

The sum of P(x=0) + p(x=1)+p(x=2)+p(x=3) need to be 1.

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[sharp cargo]

no

[quasi abyss]

<@&286206848099549185>

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[frigid sinew]

how do i do thisproblem

[dire geode]

https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/05%3A_Integration/5.03%3A_Riemann_Sums

[frigid sinew]

ty

but

what do they mean by evaluate

[unique valley]

calculate

[dire geode]

find the number the expression equals to

[frigid sinew]

But n goes to infinity

Ah

Do I have to convert this i^3 into n

[dire geode]

i is an index that ranges from 1 to n

[frigid sinew]

Yes

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[vernal gulch]

ABC is a right-angled triangle of hypotenuse BC circumscribed to the circumference C. Knowing that AB is congruent to the 4/3 of CA and the perimeter Is 24 cm, determine the radius of C.

I solved for x and found that x=6
Following the theorem leg1+leg2-hypotenuse/2=radius the result is 1 but the book says 2

[crimson sedge]

Did you make a diagram or something?

[vernal gulch]

You mean if I drew the triangle?

[crimson sedge]

Yeah

[vernal gulch]

Yeah

[crimson sedge]

Send that

hypotenuse BC circumscribed to the circumference C
What does that mean?

[vernal gulch]

BC is the hypotenuse of the triangle and the triangle is circumscribed to the circumference

BRUH

[crimson sedge]

What

[vernal gulch]

how did I miss that

[crimson sedge]

Lmao

[vernal gulch]

😞

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[brisk lance]

I have the following problem

””
Consider the following sets in R3:
(b) What is the solution set to (i.e., what type of object)
{
A1x + B1y + C1z + D1 = 0
A2x + B2y + C2z + D2 = 0
A3x + B3y + C3z + D3 = 0.

Again, there are various options. Try to give conditions on the coefficients for the different cases to occur. Some cases are difficult to give any simple conditions on, but do your best.
””

[brisk lance]

I tried starting to reduce it to RREF but with it being general that just gave me something very very complicated

I was advised to use pivots but I don’t get it :/ :(

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[hearty sand]

What am I doing wrong?

[dire geode]

how did you get r_in = 2 - y?

and this r_out = 2-sqrt(x)

[hearty sand]

I’m not sure, I followed my note

[dire geode]

yes that works because they're all in terms of x

but you have one radius in terms of x, and another in terms of y

[hearty sand]

I forgot to change it on my graph, I’ll fix that

All my work is in terms of y

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[crimson sedge]

Hey, need some help with this guys

[crimson sedge]

I started off by finding a parametric expression of x^2 = 2y

But can't figure it out for 3z = xy

The equations are wrong in the SS by the way, x^2 = 2y and 3z = xy are correct

This is what I did

[cedar kiln]

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[carmine bronze]

Here's a bit of a hint.

[carmine bronze]

.

[cedar kiln]

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[vernal shell]

Hello. This is correct so far, now find z in terms of t now that you have x and y in terms of t

[carmine bronze]

That approach is more complicated than it needs to be. 00 should use a level curve to make finding a parametric equation easier.

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[fringe ocean]

Given the truth table below. Is the following correct?

Q: To appreciate using ROM to implement truth tables, estimate how many gates are needed in the following cases (gates can take a lot of inputs):
1- AND-OR implementation:
Does this also equal decoder's gates because eventually it's the same❓

2- Using a decoder (including the gates inside the decoder):
Decoder will need 4 NOT gates (for each input) and 16 AND gates (for each output term). To implement the functions, Z3 will need 7 minterms in 1 OR gate, Z2 will need 8 minterms in 1 OR gate, Z1 will need 8 minterms in 1 OR gate, and Z0 will need 8 minterms in 1 OR gate yielding a total of 24 gates.

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[fringe ocean]

😞 last time

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[lone jay]

Hello! I have to find angle alpha between normal vector and axis ox. The vetor is normal to a curve that is described by three know points A, B and C. How can I do that?

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[hoary vessel]

can someone help with (d)?

[hoary vessel]

the answer makes a discriminant from the derived quadratic, but what's to say that quadratic has to have 2 solutions?

[cedar kiln]

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[dire geode]

but what's to say that quadratic has to have 2 solution
fundamental theorem of algebra

[cedar kiln]

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[hoary vessel]

what if the vertex is above y=0, or on it, on this concaving up parabola?

[dire geode]

oh my bad. should say at most* 2 solutions

[hoary vessel]

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[crimson sedge]

Hi, so ik theres like a order from greatest to smallest of the different functions but dont remember them.

[surreal cave]

think about 10^10 compared to 10!

[short blade]

n! = n * (n-1) * (n-2) * ...
n^n = n * n * n * ...
which one is greater?

[crimson sedge]

10! would be bigger right?

[valid bolt]

Is penaldo not finished?

[crimson sedge]

wait

[surreal cave]

10 copies of itself of 10*9...

[crimson sedge]

oh i thought of it as

10^2

mb

yes

n^n is bigger

[crimson sedge]

huh

[valid bolt]

Answer is no

[crimson sedge]

😭

so the answer would be 0 right

cuz the bottom is getting bigger faster than the top

[surreal cave]

👍

[crimson sedge]

thank youuuuu

[surreal cave]