help-39

[sullen lion]

the homework website says its wrong over and over again
but i feel its right cuz ive reworked this like at least 5 times now...

alr alr ty

imma have to talk to my teacher then

.close

[pearl pond]

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[tulip leaf]

Hay everyone!

I need help with question g please

My answer for this question was 2p - 4

.

I got 2p - 4 because I did 5 - 3 first which = 2

.

So 2 ( p - 2) = 2p -4 when expanded

[fluid knoll]

You can't do that, order of operations

idk if y'all use PEMDAS or BEDMAS

[tulip leaf]

oh yeah bidmas

[fluid knoll]

But you must distribute the 3 into the brackets first

[tulip leaf]

brackets first

in bidmas

[quiet goblet]

What is i stand for

[tulip leaf]

indices

[quiet goblet]

Ok

[tulip leaf]

but there are no indices in question g

[quiet goblet]

Yeah

[tulip leaf]

sorry i confused lol been a long time havent study maths

hmm so -3 (p - 2) = -3p + 6 is the first step.

oh wait i think i done it wrong

[quiet goblet]

You omitted 5

You can do first step but 5 is part of expression so there must be 5 in it

[pearl pond]

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[rapid flame]

hi

[tulip leaf]

But I dont know how to get p.

5- 3 (p - 2)

5 - 3 = 2

[sullen leaf]

.

[rapid flame]

I need help on this q:

I'm getting that its 1/n^p * 1 * 2 * 3 ... * n-1 * n

[quiet goblet]

Bracket should come first

[rapid flame]

but as n tends to infinity, 1 / n^p tends to zero but n! tends to infinity

[tulip leaf]

Yeah Im really not sure how to get p though Calamity.

I very confused

Ill think about it moroe

more

[quiet goblet]

You can't substract before multiplication

3 is multiplied to (p-2), you have to solve that first

[tulip leaf]

I mean I cant do brackets first because I dont know what is (p-2).

oh ok

[quiet goblet]

P-2 is an expression

You can not substract a lion from a stone

Let that be

P and 2 are unlike terms

So bracket part is there to show that the whole stuff is multiplied to 3

[tulip leaf]

ok so I need to do -3 (p -2) and expand the bracket.

[quiet goblet]

Yes

[tulip leaf]

oh alright thank you

[quiet goblet]

Np

[tulip leaf]

-3p + 6

[quiet goblet]

Yes

[tulip leaf]

is the answer when expanded

thanks

[quiet goblet]

5-3p+6

Don't omit 5

[tulip leaf]

so now I have to collect like terms.

5 + 6 = 11

11 - 3p

[quiet goblet]

Thats the simplified ans

Well done

👍

[tulip leaf]

Calamity you genius thank you so much for being patient with me🙂

[quiet goblet]

No problem, we were destined to pass so I landed my help

[rapid flame]

.close

[pearl pond]

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[tulip leaf]

Yay.

Have a great night Calamity my friend

.close

[quiet goblet]

Same to you

[pearl pond]

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[true island]

https://media.discordapp.net/attachments/1165726276330471575/1165726276582117436/image.png?ex=6547e632&is=65357132&hm=c2b7b534fdfe979dd1f94ae6c035568e7dbf832a79702626da73784ade9a53f7&=

[true island]

I'm stuck on how I can drive a state space model.

Here's what I've tried so far

I'm not sure if what I did is even in the right direction

I tried to define my state variables in this case X1 and x2 and solve Fnet = ma

[pearl pond]

@true island Has your question been resolved?

[true island]

I actually did it and solved my self

/end

or whatever

[plush bramble]

.close

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[polar steppe]

Did I use the log/exponential rules properly ?

[unborn swallow]

Nope

ln(x+y) is not lnx + lny

ln(xy) is lnx + lny

you can simplify it further a bit though

[polar steppe]

wait

where did I make that error?

[unborn swallow]

when you did $\ln{(\frac{2}{3}x^{\frac{3}{2}}+C)}=\ln{(\frac{2}{3}x^{\frac{3}{2}})}+\ln{(C)}$

[jolly parrot]

Astral

[unborn swallow]

you can do $\ln{(\frac{2}{3}x^{\frac{3}{2}}+C)}=\ln{(\frac{2}{3}x^{\frac{3}{2}}+\frac{2}{3}K)}=\ln{(x^{\frac{3}{2}}+K)}+\ln{\frac{2}{3}}$ though, not much of a simplification

[jolly parrot]

Astral

[polar steppe]

are you distrubuting the 2/3 to the k?

[unborn swallow]

I'm saying C=2K/3

both C and K are just constants of integration

I just scaled it differently, it doesn't matter since C and K have the same range (both are just in R)

[polar steppe]

I follow that part

[unborn swallow]

that way I can factor out a 2/3 from every part being ln'd, which I can then move out into +ln(2/3)

[polar steppe]

I see

hmm

can you explain where it comes from though?

the 2/3k

[unborn swallow]

yes, C is a real number

[polar steppe]

like why is c = 2/3k

indeed

[unborn swallow]

C=2K/3 because C is arbitrary and ranges from (-∞,∞), so 2K/3 does as well, and we can determine that K also has range (-∞,∞) therefore we can simply declare K a replacement constant of integration

C=2K/3 because I said so, because it would simplify best

I could've said C=K^3, but that's unhelpful, doesn't help me simplify

[polar steppe]

so

can we only do this because c is a constant?

[unborn swallow]

C is an arbitrary constant of integration, if you differentiate it it becomes 0

[unborn swallow]

if you plug in this answer into your original dfq

you will find K does not matter, ie K is any real number

[polar steppe]

gotcha

[unborn swallow]

same goes for the raw unsimplified answer, C does not matter, it'll cancel out upon plugging into the dfq

you use the constants to solve for specific conditions

[polar steppe]

gotcha

in this case though

they didn't give me a condition right?

usually they'd right like y(0) = 5

or something like that that

or are you talking about something else?

[unborn swallow]

so you leave it in its general form

with its constants of integration located somewhere in your answer

like how y'=y is solved by Ae^t, any real A will solve y'=y for y=Ae^t, hence it's the general equation

but only one A solves y=Ae^t for a given input condition

[polar steppe]

gotcha gotcha

ty ty

.close

[pearl pond]

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[late jolt]

hi

[late jolt]

so I completed all the questions except #5

how would I do question 5.

[nimble osprey]

i had a dejuvu

[late jolt]

what

[nimble osprey]

that page

[rigid mist]

what😂

[late jolt]

whats wrong with the page?

[nimble osprey]

i already see it

[late jolt]

where

[nimble osprey]

in this discord

[late jolt]

when

[nimble osprey]

maybe yesterday ..idk

you known!

[late jolt]

so what do I do for 5.

@nimble osprey u trolling or smth?

[nimble osprey]

no nvm

i am too tired to even read point 5

I prefer to eat a nice pizza

[late jolt]

then stop talking here?

if you ain't gonna help

[plush bramble]

#discussion or #chill for general chat.

[toxic lichen]

!redir

[pearl pond]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

@late jolt Has your question been resolved?

[pearl pond]

@late jolt Has your question been resolved?

[pearl pond]

@late jolt Has your question been resolved?

[late jolt]

<@&286206848099549185>

[ocean basalt]

How would you do 5?

In the directions, it gave you City names and coordinate points, I would start off by just plotting those on the graph first.

[late jolt]

the cities have the same number

[ocean basalt]

The three cities have three different coordinate points (x,y). That is what they want you to plot first

[late jolt]

okay I'm finished

sorry for the late reply

and please ping me once you reply!

[ocean basalt]

No worries!

[late jolt]

so what do I do after?

I plotted the different coordinates

do I do the central station now?

they do have the same distances

[ocean basalt]

I just reread, I would use that coordinate they gave you

[late jolt]

so that would be (-3.5, 1.5)

or the ones I solved for?

[ocean basalt]

bc then you need to label the boosters and where those would be if they are needed based off the distances
Central Station would be your (-3.5, 1.5)

[late jolt]

okay brb

[late jolt]

does that seem correct so far

[nocturne plover]

for breeze and cedar i think you flipped x and y

[late jolt]

wdym

[nocturne plover]

breeze is -8, 1 yes?

[late jolt]

yes

[nocturne plover]

is that not flipped from what you drew?

actually all of them seem flipped

unless your x is vertical

the first number is that vertical or horizontal?

[late jolt]

so like that?

[nocturne plover]

yeah where the blue dot is

for breeze

that would make sense to me

with it being (-8, 1)

[late jolt]

like this?

[nocturne plover]

yeah

[late jolt]

<@&286206848099549185> what would I do after

[nocturne plover]

draw the shortest path to the highway from central station

that's one of the things

[late jolt]

.close

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[pearl pond]

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[kind solar]

hello

[kind solar]

i am trying to graph this

in my graph calculator

but when press graph nothing pops up

i pressed y= first and put that in

then graph

[feral leaf]

Then you need to adjust the window scaling

[kind solar]

uh

to waht

i just put random numbers in the winddow now i have error

😭

i think i messed my calc up

[pearl pond]

@kind solar Has your question been resolved?

[pearl pond]

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[wind lantern]

Question 6th.

[wind lantern]

I do not understand the problem.

What are we supposed to find.

[unique ibex]

The question is unclear

[unique ibex]

have you tried solving the differential equation?

[wind lantern]

Yes. The solution comes as
ln y = ((1/x-3) + C ) where C is any arbitrary constant.

[woven topaz]

I suspect the question is asking you to identify the domain of definition for the solution to the differential equation. In doing so, they want to know which of those intervals is contained in the larger domain of definition for your solution

[lean flicker]

Black book?

[wind lantern]

Yes.

[wind lantern]

I do not quite understand.

[woven topaz]

So, you've found a solution:

$$y = \exp\left(\frac{1}{x-3} + C\right)$$

[jolly parrot]

Ammardian

[woven topaz]

This solution will have a domain of definition

I suspect what they are asking is for you to find which of those 4 intervals would be contained within this domain

[woven topaz]

This function for example, may have some divide by 0 issues at a certain x-value, so your goal is to work out where that issue is

and so what the domain of this function is

At the end of the day, the question is, "Which of these 4 intervals does not contain the x-value for which the solution to your differential equation above is undefined"

[wind lantern]

Ok. I think I get it.

.close

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[midnight haven]

\def\P{\mathrm P}
A pair of fair dice is tossed. Find the probability of getting at most a total of 10.

\vs{5 mm}
\textbf{My attempt:} For this, let $B$ be the event of getting at most a total of 10. Then, $\comp B$ is the event that you get at least 10. So: [
\comp B = \set{55,56,65,66} \implies \abs{\comp B} = 4
]
Then: [
\map \P B = 1 - \map \P{\comp B} = 1 - \f4{36} = \f89
]

[midnight haven]

How did I fuck up in the above?

[muted locust]

well is says atmost so how did you include 66

[muted locust]

and 56

[brisk scarab]

complement of B

[muted locust]

atmost is maximum

[rustic gate]

at most 10 complement is more than 10

[muted locust]

oh fk mb

[brisk scarab]

have you been given the 'right' answer

[midnight haven]

no its just that teh system is rejecting my answer

[midnight haven]

this is probably it tho

i have to exclude 55

[rustic gate]

[midnight haven]

[brisk scarab]

^ yeah the q is inconsistent about the 10 case

[rustic gate]

[ \lnot(x \le 10) = x > 10 ]

[midnight haven]

man my logic game is fucking weak

wtf

[rustic gate]

weak logic

you missed logic day

[midnight haven]

thanks tearfox and Edward II

[rustic gate]

what about edward the first

[midnight haven]

we dont talk about him

.close

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[azure bay]

For function notation that’s written as f: A -> B, A is the domain and B is the codomain right? And the range would be the “actual” values that A maps to with the function right?

[azure bay]

Just need some clarification to make sure I’ve understood this part of my lecture correctly

[tropic saddle]

yes

[pearl pond]

@azure bay Has your question been resolved?

[pearl pond]

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[pearl pond]

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[proud finch]

can i do this this way?

[warm current]

no

$(a+b)^n\ne a^n+b^n$

[jolly parrot]

SWR

[proud finch]

thx

[proud finch]

what can i do

[warm current]

binomial expansion

[proud finch]

i’ve never learned that formula

[warm current]

short version
$(a+b)^4=4a^4+4a^3 b+6a^2 b^2 + 4ab^3 + b^4$

[jolly parrot]

SWR

[proud finch]

yes are you sure that is the only way to resolve this problem bc i’m not sure my teacher would give us an assignment where we need to use a formula that wasn’t taught yet

[warm current]

If you're doing integral calculus, you should have learned binomial expansion three years ago in an Algebra class.

You could do u substitution too, I suppose

[proud finch]

im in canada so idk if its the same but no i haven’t learned that formula

[warm current]

Look it up then, you should def know it by know if you're in a calculus class.

[proud finch]

yes i am

i did calc 1

im doing calc 2

[warm current]

Then you should absolutely know it by know.

But if you want to skip it for now, do u substitution

[pearl pond]

@proud finch Has your question been resolved?

[pearl pond]

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[slim turtle]

Let a_n and u_n be real sequences.

[slim turtle]

Suppose that we have a borel set A with positive lebesgue measure such that $\sum_1^\infty |a_n cos (nx + u_n)|$ is finite

[jolly parrot]

dreamalice

[slim turtle]

Show that $\sum |a_n|$ is finite

[jolly parrot]

dreamalice

[slim turtle]

This is for all x in the borel set A

I don’t even know where to begin looking at fejer right now but I feel dumb cause it feels easy

Trying to show it on an interval first

[pearl pond]

@slim turtle Has your question been resolved?

[slim turtle]

Ok fejers theorem got me nowhere

<@&286206848099549185> if any of you know where to start with plz send help this is obviously false for an arbitrary interval but idk where to go, positive lebesgue measure so I can work this on an interval

Ok I have [a,b] where it holds for x in it, then wat

nvm il ask this in the topic chanel

.clos

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[midnight haven]

An Airbus is a wide-body, twin-engine commercial jet aircraft that weighs 560 tons and flies at 0.85 Mach (1 Mach is equivalent to 340 m/s) at an altitude of 10 km. Determines its kinetic, potential and mechanical energy.

Kinetic energy: E_C= 1/2 m ∙ v^2
Potential energy: E_P= m ∙ g∙h
Mechanical energy: E_(M ) = E_C+ E_P
Where: m = mass, h = height, v = speed and g = gravity = 10 m/s2

This is from my math class, and I swear I have never had a physics class in my school, so I don't know how I should express those values.

For example, they say that it weights 560 tons, but it doesn't say the mass, how can I find it? do I need to use the formula for the force?
For the mass, what unit should I use?

I know:
Velocity = 289 m/s
Height = 10 km = 10 000 m

[feral leaf]

Given that you have m and km, you would have to convert 560 tons to kg

As m and km are metric

[midnight haven]

so mass = weight??

[feral leaf]

No

[midnight haven]

at least in this case

[midnight haven]

why

(I want to learn about this)

I know they are not equal, but maybe I can assume that mass through its weight

[feral leaf]

Mass is the amount of matter an object contains, weight is the force of gravity on that mass

[midnight haven]

I know

that

[feral leaf]

You cannot say mass equals weight as they are two different concepts

[midnight haven]

I know that

[midnight haven]

so you aren't using the weight as mass

[feral leaf]

No because tons is a unit of mass

Not weight

[midnight haven]

which one do I choose? I suppose m

[feral leaf]

When I said m and km, it's the units in m/s and km, so m is meters and km is kilometers, metric units

[midnight haven]

mm oh okay, so when they said "An Airbus is a wide-body, twin-engine commercial jet aircraft that weighs 560 tons", they should have said mass?

[feral leaf]

Tons is not metric so you have to convert to metric

[midnight haven]

I use these units, I am from Perú

[midnight haven]

I get it

[midnight haven]

they are also part of the SI I think

[midnight haven]

Mass = 560 000 kg

[feral leaf]

I think you are getting them confused with ton and tonne, ton is imperial, tonne or metric ton is metric

[midnight haven]

mm I don't know that difference, english is not my first language

toneladas is in spanish

[feral leaf]

1 ton does not equal 1 metric ton

1 ton, is imperial is equal to 2000 pounds or 907.18 kg. 1 metric ton is 1000 kg

[feral leaf]

That says "tonne"

Not ton

Like the problem

[midnight haven]

I put the prolem on the translator

[midnight haven]

oh okay, thanks, I didn't know that

so it's tonne then

[feral leaf]

It's the spelling, in English tons and tonnes are different because one is imperial, the other is metric. In other languages, you don't mess with imperial units so it defaults to metric, most of the time, so when you translated ton, and converted, it defaulted to tonnes (metric tons) because spanish uses metric

Was that problem originally in spanish or english?

[midnight haven]

mm I get it, I do use metric units

[midnight haven]

spanish

so...

E_C = 1/2 (560 000 kg) ∙ (289 m/s)^2 ?

[feral leaf]

If it was originally in spanish then the 560 is metric tons

[midnight haven]

mm yes

[feral leaf]

Yes

[midnight haven]

does it have any special units? or it's just a number

[feral leaf]

It has units

E_C = 1/2 (560 000 kg) ∙ (289 m/s)^2
If you expanded that out, you'll get (1/2 * 560 000 * 289^2) kg * (m^2/s^2)

Because (289 m/s)^2 = 289^2 m^2/s^2

And then I just moved things around

[midnight haven]

so, it would be $2,338588 x 10^{10} kg * m^2/s^2$ ?

[jolly parrot]

ale.r

[feral leaf]

Yes

Note that $1 \text{kg } \cdot \frac{m^2}{s^2} = 1 \text{J}$

[jolly parrot]

CaptainNova22

[feral leaf]

J is Joules

Unit for energy

[midnight haven]

ohh okay, thanks
so: $2,338588 x 10^{10}J$ ?

[jolly parrot]

ale.r

[feral leaf]

Yes

[midnight haven]

and EP = (560 000 kg) ∙ (10 m/s2) ∙ (10 000 m)

[feral leaf]

Are you using the acceleration due to gravity as 10 m/s^2?

[midnight haven]

yes, I think it should be 9,8 ???
but they told me that

[feral leaf]

It's 9.81 m/s^2 but it told you to use 10, that's fine

[feral leaf]

So yes

[midnight haven]

ohokay

[midnight haven]

$5,6 x 10^{10} J$?

[jolly parrot]

ale.r

[feral leaf]

Yes

And as a suggestion, don't use x when you're showing scientific notation, use \times

$5,6 \times 10^{10} J$

[jolly parrot]

CaptainNova22

[midnight haven]

and

E(M ) = $2,338588 \times 10^{10} J + 5,6 \times 10^{10} J = 7,938588 \times 10^{10} J$

[jolly parrot]

ale.r

[midnight haven]

oh okay, thanks

[feral leaf]

Yes

[midnight haven]

that was all, thanks a lot for the help (:

.close

[pearl pond]

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[jaunty wigeon]

I'd like to know how to generally approach these problems

[jaunty wigeon]

And is it possible for me to ever get good at this?

I tried like 5 times to come up with a solution and gave up

They have a whole ass explanation but I just can't logically grasp the intuition in a way that makes me confidently say that I get what happened

[vestal tapir]

the problem is much easier that the explanation implies

after 1st step, we definitely have 3 closed doors
with probability 3/4 we have two after step 2
after step 3 it's (3/4)(1/2) to have 3, and (3/4)(1/2) to have 1
with probability 1/4 we have 4 closed doors after step 2, and then it's defintiely 3 in the end
3(3/4)(1/2) + 1(3/4)(1/2) + 3(1/4) = 9/4

but I guess the problem doesn't matter, you're asking if you will ever understand the smart explanation

[jaunty wigeon]

Oh, this does make more sense

Thank you so much

[jaunty wigeon]

I didn't even know there was a different approach to this

I just wanna get good at probability and stats

I love the subject but I feel so dumb

[vestal tapir]

the hard approach wolud still work if there's like 7 doors and 9 steps, examining all states like i did would become too slow

[jaunty wigeon]

Makes sense

So the hard approach is choosing to focus on a single door

It finds the E(X) of that single door

[vestal tapir]

yep

[jaunty wigeon]

But my brain fails to understand it because the probabilities change depending on each iteration

Though I think I see it now

At least I feel like I do

Will I get better with more practice lol

[vestal tapir]

they noticed that there's 2 cases where a door is closed, either no one touched it, or 2 people did

[jaunty wigeon]

This class has made me dumber than any class ever

feel dumber*

[jaunty wigeon]

yeah, I wouldn't have figured that out in a million years probably

Either way, thank you so much for the help

I'm gonna keep practicing

.close

[pearl pond]

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[full pawn]

hey guys

[full pawn]

help

E(x) is a floor function

whats E(x) if x ∈ ]-∞, 1[

[warped shuttle]

are those brackets flipped?

[full pawn]

no

[warped shuttle]

cause im assuming its supposed to be [-∞, 1]

oh whar

[full pawn]

-inf cant be [

[warped shuttle]

you spittin

[tropic saddle]

its different notation for (-inf,1)

[full pawn]

or can it 😳

[midnight haven]

Wtf

[warped shuttle]

makes sense ive just never seen it represented that way

[midnight haven]

Something like that exists?

Flipped closed brackets

[full pawn]

i just got it in a test exam

[midnight haven]

....

[full pawn]

wtf

yall triping me

[midnight haven]

Oh wait ] = ( ?

Wtf

[full pawn]

i always used ]-inf wtf

[midnight haven]

.

[midnight haven]

Bruh

[full pawn]

wait yall dont uuse []?

[midnight haven]

I do use [] and ()

But not ][

[tropic saddle]

it just differs between some countries

[midnight haven]

Ohh

[full pawn]

huh??

how the f

[ and ] are way way diff

[warped shuttle]

1 is upper bound and if E(x) is a floor function then it should be E(x) = 0 as x = 1 and the greatest integer <= 1 is 0

[midnight haven]

][ = ? () or []

[full pawn]

no

[tropic saddle]

][ is known as french notation

[midnight haven]

So u use [] this as Greatest integer function and ][ as closed interval

?

[full pawn]

for example ]-inf cuz inf cant just be one const value

[brisk scarab]

no [a,b] is closed interval and ]a,b[ is open interval

[midnight haven]

What do u use [] for

[midnight haven]

💀

[full pawn]

[a,b] means that in the interval both a and b can be used

[midnight haven]

Dude that makes alot more sense than ()

How is () this open lol

[full pawn]

]a,b[ means that a, b cant be used

[full pawn]

fr

[midnight haven]

I'll start using][

[full pawn]

anyways back to my problem plz

[warped shuttle]

@full pawn iirc this is how floor functions work

[midnight haven]

Floor function

And roof function

Is also known as greatest integer function and smallest integer function

I forgot which is which

[warped shuttle]

floor is greatest integer

[midnight haven]

Oh ok

So

[warped shuttle]

cause they return greatest integer <= the input

[full pawn]

didnt quite get it

[midnight haven]

[•] = f(x) = floor function

[midnight haven]

I'll tell ya

Lemme draw something

[full pawn]

ik how floor functions work, what would E(x) if x ∈ ]-∞, 1[ return tho

[tropic saddle]

well depends on x

[brisk scarab]

well for numbers between 0 and 1, it returns precisely 0

[tropic saddle]

!original

[pearl pond]

Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.

If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.

[brisk scarab]

and it can obviously return any negative integer

[full pawn]

what would E(x) if x ∈ [1, 2] return

[full pawn]

yes

[tropic saddle]

if x=2 then it returns 2. otherwise it returns 1

[full pawn]

yes corect

mb meant to say [1,2[

anyways let me show u what im supposed to do in this test

sec

is "the definition set" a valid mathematical word?

cuz i study this shit in french

[tropic saddle]

is this a test you are currently writing?

[full pawn]

no im doing the test

its 1am

[tropic saddle]

you are probably looking for the word domain

[full pawn]

yes yes

so im given
f {
f(x) = E(x) + sqrt(2 + E(x-1)) if x ∈ ]-∞, 1[
f(x) = x^3 + sqrt(x-1) if x ∈ [1, +∞[
}

im asked to get the "domain"? is it called domain

yes domain

domain for f

[rare yarrow]

7

[brisk scarab]

ensemble de définition?

[full pawn]

yes!

[brisk scarab]

yes domain

[full pawn]

ok how would i get it in this case

[brisk scarab]

so you want the x where f makes sense

so E makes sense for any x

[full pawn]

yes

its prtty easy i just cant find the E(x) for an interval that has inf ?

first time seeing that

[brisk scarab]

can you send the original question? in french

[full pawn]

soit f la fonction definie par:```
f {
f(x) = E(x) + sqrt(2 + E(x-1)) if x ∈ ]-∞, 1[
f(x) = x^3 + sqrt(x-1) if x ∈ [1, +∞[
}

1)a) determiner l'ensemble de definition de f

[brisk scarab]

ok so not every x in ]-∞, 1[ allows f to make sense, I'll give that

and the issue isn't in E(x)

because any x in

so the issue is in the square root

what can you not take the square root of

[full pawn]

yeah i tried that

the E() is always there

it has to return a value right?

or does it return an interval

[brisk scarab]

it returns a value

[full pawn]

whats the value tho

[brisk scarab]

E(x)

the question is asking: I'm picking an x < 1. However, f may not always work because we're not allowing something inside it. Which x less than 1 does it actually work for?

[full pawn]

wait..

2 + E(x-1) cant be negative

[brisk scarab]

for the square root to make sense, exactly

[full pawn]

E(x-1) >= -2

hm

so basically

what's the interval that if we were to floor woud give a value included in [-2, -1[?

which returns -2 ?

[brisk scarab]

well, a priori in [-2, ∞[

rather than [-2,-1[

[full pawn]

huh why

[brisk scarab]

oh wait

yeah you're right

[full pawn]

isnt that part of the function difined in that interval

yeah

[brisk scarab]

I forgot that we initially have x<1

[full pawn]

ok anyways

is my thinking right?

[brisk scarab]

yes

[full pawn]

E(x-1) = -2

fuck my head hurts

imma go sleep thanks for the help rlly appreciate it

[pearl pond]

@full pawn Has your question been resolved?

[pearl pond]

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[wet gull]

I don’t know how do this problem

[verbal gate]

What is the question asking you to do

Do you know?

[pearl pond]

@wet gull Has your question been resolved?

[pearl pond]

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[blazing rover]

can someone walk me through how to derive x^sinx

[rigid mist]

derive x^sinx as such its derivative right?

[blazing rover]

i'm not sure what you mean by that

[snow sail]

what do you mean derive

do you mean differentiate?

[blazing rover]

yes sorry

i'm solving

which means that i need to differentiate x^sinx

[snow sail]

don't you need to rewrite this?

[feral cedar]

Okay, so lim(x—>0) x^(sinx) becomes 0^0, so you’ll need to rewrite this first so that it becomes either 0/0 or inf/inf

[snow sail]

yes

[blazing rover]

oh i see

i'm not sure what to do in order to rewrite this

[snow sail]

maybe a log property could be helpful here?

[blazing rover]

i know i can use ln, but i'm not sure how to do it with the lim(x->0) in there

i'm getting tripped up by the lim

[feral cedar]

Just pretend it’s not there

[blazing rover]

can i just make it lnx^sinx?

then sinx(lnx)

[feral cedar]

That’s a thing yes, and then what is the reciprocal of sinx?

[blazing rover]

1/cscx

?

[feral cedar]

Mhm

So then you could write maybe… lnx/cscx?

[blazing rover]

oh i see

[feral cedar]

Then what happens as those two approach 0?

[blazing rover]

both are undefined

ok then i can differenciate both

[feral cedar]

You get inf/inf

And then you’re good from there

[blazing rover]

i didn't know i was able to multiple the x^sinx by ln without another side of the equation

like when its y=x^sinx you have to do the same to the y to keep it equivilant

does it not change the value of the function?

[tame monolith]

Think of it as
$$ \lim_{x \to 0^+} x^{\sin x} = \lim_{x \to 0^+} e^{\ln\left(x^{\sin x}\right)} = \lim_{x \to 0^+} e^{\frac{\ln(x)}{\csc(x)}} = e^{\lim_{x \to 0^+} \frac{\ln(x)}{\csc(x)}}$$

So you're going to need to take the answer you get from lhopital and apply exp to it.

[jolly parrot]

Morrow

[blazing rover]

Ok

.close

[pearl pond]

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[muted night]

A statement asks to prove that if P(n) is true for all n∈N, then Q(n) is also true for all n∈N. How can we prove this?
There are multiple answers.

1. Proving that P(n)⇒Q(n) for all n∈N
2. Assuming that there exists a number n such that Q(n) is false and showing that P(m) is false for a certain m∈N
3. By proving that Q(0) is true and proving that (P(n) and Q(n))⇒Q(n+1) for all n∈N
4. Assuming that P(n) is true for all n∈N and Q(n) is false for all n∈N and finding a contradiction
5. By proving that Q(0) is true, then assuming that there exists n∈N such that P(n) is true but Q(n) and Q(n+1) are false and finding a contradiction

[muted night]

I think 1 makes sense, I could be wrong tho

[pearl pond]

@muted night Has your question been resolved?

[pearl pond]

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[rustic cargo]

i have the rate of change for the radius

how can I change it to the diameter?

i got 0.009 by multiplying 0.0043 ( then rounding it to 3 decimal places)

[pearl pond]

@rustic cargo Has your question been resolved?

[pearl pond]

@rustic cargo Has your question been resolved?

[rustic cargo]

.close

[pearl pond]

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[naive dirge]

why ppl use a "die" instead of a "dice"?

[naive dirge]

I mean die is an old use to mention this gambling gadget

why ppl, especially when it relates to topics of math, use die? im so confused

[echo iris]

die is like simpler probability

ig dice is more complex

maybe

[naive dirge]

I suppose they are all refer to the 6-sided gambling tube?

[echo iris]

yeah

[dense goblet]

most sources support my impression that die is the singular and dice is the plural
dice is generally also accepted as a singular form

one website said that dice outdates die in the english vocabulary but idk

[pearl pond]

@naive dirge Has your question been resolved?

[pearl pond]

@naive dirge Has your question been resolved?

[dense goblet]

what do you want lmao

[pearl pond]

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[warped ocean]

im stuck and cant figure out how to calculate for time when i dont have v_f

[worldly glacier]

omg hi bestie

[warped ocean]

and im not sure how to calculate for it

[worldly glacier]

to do this question bestie

you can use the equation

$\triangle x = 1/2at^2 + v_i(t)$

[warped ocean]

OH RIGHT I FORGOT ABOUT THAT

THANK YOU

[worldly glacier]

slay queen

you can close it now if you don't have any qs

[warped ocean]

im solving through it rn

ill just keep this open in case i get stuck again but if not ill close it

[toxic lichen]

\Delta x

[worldly glacier]

ty bestie

[toxic lichen]

with all due respect, i am not your bestie.

[worldly glacier]

sorry

[warped ocean]

wait

i thought it was

$\Delta x = v_it + \frac{at^2}{2}$

[jolly parrot]

Kaiyan

nosqldb

[worldly glacier]

ur right lmao

[warped ocean]

does "vertically upward from the ground" mean that i can infer that $\Delta x = 0$?

[jolly parrot]

Kaiyan

[worldly glacier]

$x_i = 0$

[jolly parrot]

nosqldb

[worldly glacier]

but what about x_f???

[midnight haven]

Work out the displacement when it reaches the top and use that minus the other displacement to solve for time

you change it into 2 equations. The first one you're calculating displacement from the ground to the top, the second one you're calculating the time it takes to get from that displacement to 1.27m

[warped ocean]

im struggling with that part

i know i have to solve for the vertex

but the only equations i know for tthat are -b/2a and (r+s)/2 in which r and s are roots

[midnight haven]

Are you allowed to use any of these? (s is displacement, u is initial velocity)

[warped ocean]

i havent learned these specific equations yet but i think it should be fine

there are the ones my teacher gave

[midnight haven]

Ohh yeah those are the same as the first 3

So you're given that Vi is 5.89m/s, when it reaches the top what is its velocity?

[warped ocean]

the stuiff in the question is the only given

i inferred everything else from it

[midnight haven]

Yeah you have to split it

One sec I can draw it out

The key idea is that when you throw a ball up, at its maximum height its velocity is 0

And then it turns back down again

And when it's going up, gravity is working against it so the acceleration is negative. When going down, gravity supports it so acceleration is positive

[warped ocean]

yeah that makes sense

the part i dont get is how to find v_f

since thats what im missing for time

[midnight haven]

Vf is 0 for the first part

At maximum height the velocity is 0, that's your Vf

Then the ball falls down and is stopped at 1.27m, you don't need velocity to work out time there

You can use the first equation

Imagine they asked it in 2 questions. The first question they asked you to work out time and displacement when it goes from the ground to its maximum height. Then they asked you to work out the time it takes for it to go from maximum height down to 1.27m

Your values for v, t, a and d are different for both questions

[warped ocean]

ok heres what i got for the first one

[midnight haven]

Yeah that's right

[warped ocean]

now from max to 1.27m

im a bit confused still

i know i have to use gravity

[midnight haven]

So your acceleration was -9.8m/s^2 going up, what will it be going down?

[warped ocean]

speeding up

[midnight haven]

Yeah

So it becomes +9.8

Your ball reached maximum height, it's final velocity was 0m/s, what would it's initial velocity be now then?

[warped ocean]

oh

0

[midnight haven]

Yes

Wait you needed to calculate d going up I think

[worldly glacier]

bestie

[midnight haven]

That's the distance from the ground to max height. Then you take the distance from max height to 1.27m above the ground

[worldly glacier]

are you guys still working on the q?

[warped ocean]

yes

[warped ocean]

makes sense

[worldly glacier]

why didn't you just say 1.27 m = 1/2 (-g)t^2 + 5.89t

[warped ocean]

let me check the displacement equations again

[warped ocean]

because 1.27 is displacement and not velocity

[worldly glacier]

yes

I got 0.94 s

is that correct @warped ocean

[warped ocean]

wait

[warped ocean]

this still doesnt work

because 1.27 is not the change in y

[worldly glacier]

doesn't it say height?

[midnight haven]

He's got it

Let him do it

[warped ocean]

it goes up

and gets caught at 1.27

[worldly glacier]

mhm

so x_i = 0m

x_f = 1.27 m

$\Delta x = 1.27 m$

[midnight haven]

xf isn't 1.27

[jolly parrot]

nosqldb

[midnight haven]

It goes up and falls back down to 1.27

[worldly glacier]

I mean y_f

[midnight haven]

So the first displacement is higher, then it falls from there to 1.27

[worldly glacier]

mhm but screw the first displacement

just consider y_i = 0

and y_f = 1.27 m

[warped ocean]

you cant

[worldly glacier]

this is a good idea of the projectile motion

[warped ocean]

ok wait this one makes more sense

[worldly glacier]

slayyyy

[warped ocean]

but something is off

[midnight haven]

I don't think the acceleration stays negative the whole time

[worldly glacier]

it's gravity

[worldly glacier]

bestie do you have the answer

numerical answer to check with

[warped ocean]

oh

[warped ocean]

where did 5.98 come from

oh wait

nvm

[worldly glacier]

bestie

it's good

the answer is good

[midnight haven]

It is 0.92s

He needs to know how to get there tho lol

[warped ocean]

ill try to derive it on my own

lets see

[worldly glacier]

ofc bestie

[midnight haven]

You just did 1.27 = 1/2 (-9.8)x^2 + 5.98(x) and solve for x?

[worldly glacier]

ye

[warped ocean]

i brute forced it

[worldly glacier]

good shit queen

🙏

[midnight haven]

I mean if you can just factorise like that in your head then ur good

[warped ocean]

i used quad formula

[midnight haven]

Ohh yeah

Mb

[warped ocean]

its ight

thanks for the help guys

my teacher said we're gonna discuss this question in class anyway so if theres a diff method then he'll teach it to me soon

[worldly glacier]

gn bestie

you can ".close"

[warped ocean]

ight

farewell

.close

[pearl pond]

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[midnight haven]

is 1 < x <=3 and 3 <= y <=5 an open or closed set

[midnight haven]

(x,y) in R^2

[copper umbra]

it's not open since at $(x,y) = (3,5)$, any open ball you draw would exceed this region

[jolly parrot]

Dee3Cay

[midnight haven]

can i also say it has its boundary poitns

3 is a boundary point right

iin this case

[copper umbra]

3 as in

[midnight haven]

(-1,3]

[copper umbra]

it's R^2? 🧐

[midnight haven]

yes

[copper umbra]

this is an interval not a point

3 is a point in R^1 not R^2

[midnight haven]

it includes all points from -1 (excluding -1) to 3 (including 3),

dont you say that by (1,-3]

[copper umbra]

well sure but

again this is just a set of points in R^1

[midnight haven]

oh ok

[copper umbra]

for example, if you want to say points on this line are boundary points, I would say it's points on ${3} \times [3,5]$

[jolly parrot]

Dee3Cay

[copper umbra]

that would be R^2

[midnight haven]

yeah but im looking at one at a time

first at x then and y

[copper umbra]

well you can't really do that?:/

[midnight haven]

ok

[copper umbra]

coz if you look at a particular x it's not a well-formed point in R^2

back to your question

it's also not closed

this can be shown in 2 ways:

1. the complement is not open
2. there exists a sequence of points, converging to a point outside of the region

[midnight haven]

what is this

then

not open but not closed

im confused

[copper umbra]

at point (x,y) = (3,5), draw an open ball, it goes outside of your region

ok back to square one
what's the definition of open and closed

[midnight haven]

open is that

i can find something in the set

• epison

or - epsilon

and still be in the set

[copper umbra]

em

not entirely accurate

open is that for every point in the set, you take a "small neighbourhood", this small nbhd is still "within" the set

[midnight haven]

that is what i said

small neighbourhood = episolon

[copper umbra]

yes

but you said "i can find something in the set, +/- epsilon"

[midnight haven]

yh you give me a point

i find +/- epsilon

open set

[copper umbra]

ok so to be accurate, what points may I give?

[midnight haven]

a point within the set?

[copper umbra]

is there restrictions on what points in the set can I give?

[midnight haven]

well it shouldnt be outside the set

but if you're in the set it should be fine

no matter which point you give me

[copper umbra]

ok so to be more accurate (especially in writing proofs)

[midnight haven]

i picture it as a number line

[copper umbra]

you want to say for every point, ...

[midnight haven]

(0-3)

[copper umbra]

your idea is correct

[midnight haven]

any number you can think of between these two

i can give you a +/- epsilon

since there are infinitely meaning nubmers between any two numbers (if they arent the same i suppose)

[copper umbra]

ok so back to your question

how can we show it's not an open set?

[midnight haven]

well either i can show it has all its boundary points

or do the complement thing

not quite sure how though

[copper umbra]

let's try to show by definition

you've stated the definition of "open sets"

can you negate that definition to become "not open sets"

[midnight haven]

yes

the point 5,3

and 3,0?

[copper umbra]

(5,3) and (3,0) are not in 1<x<=3 and 3<=y<=5?

[midnight haven]

[5,3] is a point in the set

right

but not that + epison

[copper umbra]

ok you're going to quick

[midnight haven]

ok

[copper umbra]

<--

let's not go to naming points first

[midnight haven]

itsn that just that i cant give you a +/- epsilon

[copper umbra]

such that?

[midnight haven]

then its closed?

[copper umbra]

no?

[midnight haven]

didnt we just say if i could its open

[copper umbra]

ok 1) not open does NOT mean closed

[midnight haven]

so if it contains all its boundary points

then its closed

surely

[copper umbra]

how about this
could you write it down in symbols form?
like epsilon, B(x, \epsilon)?

[copper umbra]

yes

but does this contain all its boundary points?

and 1 step back, what's the definition of boundary points?

[midnight haven]

a point where

every neighborhood of that point

will contain a point outside and inside the set

[copper umbra]

ok great

so are all boundary points contained in (1,3]x[3,5]?

aka this rectangular region

[midnight haven]

(1

does this fail it?

[copper umbra]

(1,?)

[midnight haven]

that this is a half open interval

[copper umbra]

you'll need a point in R^2 as example

ok question

what is the course you're taking?

[midnight haven]

its just called intro math

linear algebra and calculus

[copper umbra]

ok

[midnight haven]

mixed into one

[copper umbra]

so does calculus allows anything over 1 variable

[midnight haven]

yes

[copper umbra]

ok

[midnight haven]

the book this question is from is called functions of mutiple variables

[copper umbra]

all of your ideas are correct if you're playing in R^1

in R^2 or above you can't think of "open neighbourhoods" as "open intervals"

at least it has to be "open circles" or "open balls"

[midnight haven]

ok, ill try to not do that

so you cant look at them separetely

[copper umbra]

for example, x = 1 is getting there, but you need to pick an actual (x,y) point, say (1,4)

now I draw an open circle (of radius epsilon) at it, some part of it outside, some part of it inside

just like definition of a boundary point

but the point (x,y)=(1,4) is not in the set, since 1 < x <= 3

so boundary points are not contained, thus not closed

[midnight haven]

but not closed doesnt mean open

[copper umbra]

yes it's not closed and also not open

[midnight haven]

what is it then

[copper umbra]

it is neither :]

[midnight haven]

oh

[copper umbra]

A set can be both not open and not closed

[midnight haven]

i read the question wrong

[copper umbra]

ok so

[midnight haven]

is that set we jsut talked about

determine if the set is restricted or not

[copper umbra]

wdym

[midnight haven]

that is the question

im translating to english

to get the correct term, one second

maybe finite set?

the definition of it will be easier

if you can contain the set in a cirkel, that has center in origo it is restricted

or a ball structed thing

[copper umbra]

what language was it in?

[midnight haven]

danish

[copper umbra]

could you take a pic of the question?

there's gotta be some sort of image language translator or sth

[midnight haven]

we dont need one if you know the definition of this

lets say x^2 + 1/4*y^2 >= 1

then i can incapsulate this in a circle or ball, then it is restricted

remind you of anything concept?

[copper umbra]

it is bounded maybe?

[midnight haven]

||a|| < R

mby this definition

[copper umbra]

ok bounded it is

wait so what's the question 👀

[midnight haven]

is it bounded or not

[copper umbra]

this?

[midnight haven]

it says "if you can incapsulate it, in a circle or ball, then it is bounded"

yes

[copper umbra]

well this is not

we prove this by contradiction, assume it is in a ball of radius r

can we choose a point outside this ball?

[midnight haven]

in the set

or just if we can ever?

[copper umbra]

yes a point in the set that's outside the ball

[midnight haven]

not if everything is in the ball

[copper umbra]

x^2 + 1/4*y^2 >= 1 <-- you're talking about this right?

[midnight haven]

no

still the other one

[copper umbra]

<-- this?

[midnight haven]

yes

[copper umbra]

well then it is bounded

[midnight haven]

okay

but what if i just make my ball infinitely big

[copper umbra]

you can just take balls like radius 100?:]

[midnight haven]

what sets does a infinitely big infinitely many dimensional object

[jolly parrot]

Dee3Cay

[midnight haven]

i meant not contain

not contain

[copper umbra]

I don't understand?

[midnight haven]

i think i have missunderstood the definition

because well

if i can choose a ball in inft many dimension and that is inft large

how does it not contain y=x^2

my circle is exactly as big as x^2

[copper umbra]

y = x^2 is a parabola?

[midnight haven]

yes

but my circle is infinitely big

[copper umbra]

well you can't exactly define an "infinitely big circle"

and also the idea of bounded means you have to fix your circle size

you can't have circle size depend on some variable x

[midnight haven]

but didnt we just chose it to be 100 last time

[copper umbra]

yes but I fix this 100

I will not make it larger or smaller

[midnight haven]

okay i fix mine at infinite then

[copper umbra]

you can't fix a circle radius at infinity because infinity is not a "value"