help-33

[tender mantle]

AB, BC, AC then sum check

[stoic saddle]

"sum check"?

[tender mantle]

I meant if the sum of two vectors

Equal to third one or not

[stoic saddle]

$\overrightarrow{AB} + \overrightarrow{BC} = \overrightarrow{AC}$ is \textbf{always} true. so checking that won't tell you anything.

[elfin berry]

Ann

[stoic saddle]

you will want to take two of these three vectors (any two) and check whether they are parallel.

[tender mantle]

We will check if they have any scaler quantity in common

AB = x Bc

Like this

Bc= x CA

[stoic saddle]

yes

[tender mantle]

I have a good question for you now

B is incorrect by my knowledge

[stoic saddle]

B is indeterminable

it may be true or it may be false, but we do not know

we cannot say either way

[tender mantle]

False how

[stoic saddle]

well it can so happen that a = 2b

then a won't be b and won't be -b

so (B) will end up false

(for the sake of my example i am assuming here that a and b are both nonzero)

[tender mantle]

If a =2b then it's clearly collinear no?

[stoic saddle]

yes

that's my point

the premise (a and b are collinear) is true, but statement B (a = ±b) is false

you ask how B can be false i give you example where B is false

simple things

[tender mantle]

but I don't think your example is correct.

example should be false

[stoic saddle]

but B is false.

[tender mantle]

a=2b is not false

[stoic saddle]

and it isn't supposed to be!

IF a and b are two collinear vectors,

this means we are ONLY considering pairs of vectors that ARE collinear

and we DON'T CARE when the vectors AREN'T collinear

[tender mantle]

yes

[stoic saddle]

i've known you enough not to ascribe malice to this but please see the clear logic here

[willow owl]

but B isnt false because a and b are collinear if and only if $ \exists \lambda \in \mathbb{R}$ s.t. $a=\lambda b$

[elfin berry]

calculus is fun

[stoic saddle]

you are sowing more confusion

[tender mantle]

suppose we took lemda = 1

[stoic saddle]

let me repeat my original point

[tender mantle]

then b is correct

[stoic saddle]

WE CANNOT CONCLUDE EITHER WAY whether B is true or false with ONLY the premise that a and b are collinear.

[tender mantle]

we can say it is correct

[stoic saddle]

no, we cannot

look

[tender mantle]

a= 1(b)

a=(-1)b

[stoic saddle]

can i say something

that uses the same logic

[tender mantle]

which is clearly not collineary?

[stoic saddle]

because i think you are failing to see my logic

[tender mantle]

I think yes

[stoic saddle]

ok

so let's first agree on some premises:

• every human on earth is either married (to someone, but that's not important) or not married.
• children cannot be married, but adults can.

do you agree or disagree with these premises? @tender mantle

[willow owl]

ah yes i see your point

we can say that it is wrong

because what this statement says is that $\vec{a}$ and $\vec{b}$ are collinear $\implies \vec{a}=\pm{\vec{b}}$ $\forall \vec{a} \vec{b}$ which satisfy this

[elfin berry]

calculus is fun

[willow owl]

and this is wrong because you can find infinitely many counter examples one of them is the one you gave

[tender mantle]

agree

[tender mantle]

but how?

[stoic saddle]

ok then in this case

let's say there is a room with some people in it

[tender mantle]

okay yes

[stoic saddle]

if we choose a person in the room and they turn out to be an adult man, then the statement "the chosen adult man is married" is?

(A) definitely true
(B) indeterminable
(C) definitely false

[tender mantle]

What do you mean turn out to be?

A few years later?

[stoic saddle]

no

let me reword this

[tender mantle]

A

[stoic saddle]

if we choose a person in the room and we find out that they are an adult man, then the statement "the chosen adult man is married" is?

(A) definitely true
(B) indeterminable
(C) definitely false

answer again

[tender mantle]

A

[stoic saddle]

wrong

you don't know that all adult men in the room are married

[tender mantle]

So you meant in the statement that adults can be married cannot be married?

But if we choose and find out it is children then it is definitely not married right?

[stoic saddle]

yes, adults can be married but can also not be.

but a child is never married.

[tender mantle]

Yes that's what I said

If we find out this is children

[stoic saddle]

don't care

[tender mantle]

Then we can say a definitely statement

[stoic saddle]

not what i asked

[tender mantle]

Okay got it

So now back to our question?

A and b are collinear

[stoic saddle]

back to our question

instead of people we now have pairs of vectors a and b

instead of adults we have pairs where a and b are collinear

instead of married people we have pairs where a = ±b

[tender mantle]

Hmm so?

[stoic saddle]

statement B here is indeterminable

[tender mantle]

Ahhhh

I am sorry i still didn't get it with your example. I meant I couldn't connect it

@undone bane can you help me in Hindi?

a= +-(b) is clearly visible that it is co linear

How can we not determinate it?

My answer to the question is C

They should be proportional

The rest of all are correct to me.

What is your answer to the question Ann B and C?

[ancient slate]

I think you can say that only option A is absolutely true statement here. That immediately makes option C incorrect. Option B and D can be true in some cases, but not generally true.

I'm assuming lambda in A is nonzero here

[stoic saddle]

Option B and D can be true in some cases, but not generally true.

i tried saying this for the last hour or so, but language hard.

[undone bane]

sorry, vectors nahi pda hai abhi

[tender mantle]

What is your answer to this question generally or not generally?

If a and b are co linear and non zero then a b d co linear 1000000%

[tender mantle]

I would like to know how they will fail to be co linear option B and D

[ancient slate]

I'm not saying they're not collinear. I'm saying that collinearity doesn't imply anything about their magnitude

Option B implies they have the same magnitude, which is not necessarily true

[tender mantle]

Co linearity just means parallel

[ancient slate]

Yes

[tender mantle]

No direction and magnitude affect it

They can be same or not same in direction and magnitude

[ancient slate]

Key words "can be"

Option B is saying that they necessarily have the same magnitude

[tender mantle]

What? They are vectors not megnitude

[tender mantle]

Ohh wait

[ancient slate]

I'm not sure if this is language barrier or not (I hope it is) but all I can say is that options B and D are making unnecessary assumptions about the magnitude of the vectors

[tender mantle]

But they are satisfying the statement so we can't be discarded

[ancient slate]

They satisfy the statement in some cases

Not always

A is ALWAYS true, provided lambda is nonzero

C is ALWAYS false since A is true

[tender mantle]

Is it not always true?

[ancient slate]

In that particular case it is always true

but the question never said that vectors a and b are those particular ones, didn't it

[tender mantle]

What is your example like this to be fails

[ancient slate]

This is a problem with the generality of the statement

I'm not saying it's not true in certain cases

I'm saying it's not ALWAYS true

[tender mantle]

I just want to know one single example to feel it can be wrong too

[ancient slate]

In fact, you can choose b = 2a

[tender mantle]

Can you make it one example no??

[ancient slate]

b=2a is collinear with a

but $\vec{a}$ \neq \pm\vec{b}$

wait how do you do parallel again

[tender mantle]

How can you multiply it with random numbers?

🤔

[elfin berry]

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

[tender mantle]

Ohh now i got it

Bingo

[ancient slate]

The plus minus guarantees they have the same magnitude

[tender mantle]

Yoooo

I got it yeeeeeeeee

[ancient slate]

GOOOOOD

nice one bruh

[tender mantle]

You meant that if a and b are co linear so we will have many vectors in a=lembda forms

But some of them will be a=b

[ancient slate]

yes

some

[tender mantle]

Others will not be equal

Fuck this little statement

[ancient slate]

Hahaha it do be like that

[tender mantle]

Now i can understand what was she saying

It is true only for a=b

Not for all a,b pairs

Okay now option D

[ancient slate]

Option D is saying they MUST have the same direction

sorry typo

[tender mantle]

Looool this is harassing the statement

Where did they say must?

[ancient slate]

by saying that a and b have the same direction

they don't have to have the same direction to be collinear

[tender mantle]

They are just picking some random vectors which is satisfying

[ancient slate]

exactly

you can't be picking specific vectors and make general statements

[tender mantle]

Set X : A,B are collinear
Set y: same direction and different megnitude

Y is subset of X so how can we it is false

[ancient slate]

they're talking about subsets of X

[tender mantle]

Subset will be always true

[ancient slate]

true, but what about the rest of X

the problem is asking about X, not its subset

[tender mantle]

We are only talking about Y only ...there always be a case for each subset to make it false in some terms

Is this why you guys were saying either or either not?

[ancient slate]

The only premise they gave is that a and b are collinear

D is immediately saying they have the same direction, which need not be the case

[tender mantle]

Then we are just comparing X and Y subsets

If this is the case then the full definition case option A will be correct

B,C,D all are incorrect

C is totally incorrect

B,D will be incorrect in some cases

Say YES for my statement @stoic saddle @ancient slate

[stoic saddle]

i don't want to continue this sorry

[ancient slate]

For nonzero lambda, only A is true always

C is always incorrect, B and D are sometimes correct, sometimes incorrect

[tender mantle]

No problem

[tender mantle]

That's it

Thank you all of you

.close

[marsh citrus]

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[marsh citrus]

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[ancient slate]

What do you think is the answer?

[tender mantle]

|lembda| |a|=1

[stark trail]

lambda*

[stark trail]

yes but this isn't one of the options above as currently written

see if you can rearrange it to be so

[tender mantle]

got it

4

[stark trail]

(D)

yes

[tender mantle]

YOOOOO

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[hazy lion]

does $\frac{-y}{2} \lim _{\varepsilon \to 0} \qty( \varepsilon ^{\alpha + 1} ) = 1$ imply necessarily $\alpha = -1$

[elfin berry]

jan Niku

[hazy lion]

I know this is probably a dumb question

[plain stump]

y is fixed?

[hazy lion]

yea

[plain stump]

also long time no see jan Niku

[hazy lion]

sup

i do not remember your name

[plain stump]

Was Neko

[hazy lion]

OH

sup neko

[plain stump]

before the dark ages happened

[hazy lion]

lol

its been a long time neko

[plain stump]

you're doing your masters now?

[hazy lion]

https://tenor.com/view/cat-fall-cute-gif-19509162

i am

you?

[plain stump]

nice!!

undergrad still

[hazy lion]

brutal

pure math?

i dont remember at all

[plain stump]

Not so pure anymore

I took some stats class and some ml classes

[hazy lion]

how much longer do you have?

[plain stump]

1 year

[hazy lion]

you gonna do grad?

[plain stump]

yea

[hazy lion]

where at

if u can say

we should pomo again

im getting back into it

[plain stump]

im @ nyu rn for undergrad

theres no way in hell im doing a ms here

cause my scholarship wouldn't carry over

also yea

i do need to pomo cause i stay at home to study a lot now

[hazy lion]

is there some study server were both in

[plain stump]

possiblly for a bit? pomodoro server or something

was mostly on here before they removed the voice channels

[hazy lion]

im about to be running the heck around

friday is a busy day for me

[tender mantle]

what is happening here?

[hazy lion]

sup arjunn

[ancient slate]

[warped wind]

inf arjunn

[hazy lion]

were talking abuot limits

sup toomany cooks

can you solve my problem lol

[tender mantle]

I can try it

[hazy lion]

@plain stump we can find a spot

[ancient slate]

what's the point of -y/2

[hazy lion]

how about just the study server

[warped wind]

I would say it both implies the value of alpha and y

[plain stump]

yea sure

[hazy lion]

youre on it?

[warped wind]

I think

[hazy lion]

i usually go to 6

[plain stump]

not anymore

[hazy lion]

ah

[plain stump]

you could link me later

[hazy lion]

okay

[hazy lion]

y doesnt have a value

its a variable

but for sure theres no other way for this to happen right

alpha has to be -1

[tender mantle]

I don't think it has to be -1

[hazy lion]

yea im confused

but i guess the goal is only to find a candidate

@ancient slate it comes from a perturbation problem

the thought was to assume that $\epsilon ^{2 \alpha + 1} y^2 \sim -2 \epsilon ^\alpha y$

[elfin berry]

jan Niku

[hazy lion]

the limit results from this

im not really certain if the process is supposed to determine alpha, or just candidate alpha

or if multiple values of alpha can even come from this

this specific limit i mean

but if you assume its fixed then it must come out as -1?

[stoic saddle]

tfw wrong epsilon

[ancient slate]

varepsilon or riot

[hazy lion]

either way

[ancient slate]

Is there more context about that expression that you can provide?

[warped wind]

Well, the limit only exists for $\alpha \in \mathbb{N}_{0} \cup {-1}$, right? And it's 1 iff $\alpha = -1$ and 0 otherwise? Or am I missing something \thonk

[hazy lion]

it comes from trying to find roots of $\epsilon x^2 -2x+1=0$

[elfin berry]

Mikkel

jan Niku

[hazy lion]

singular perturbation

so we took $x = \epsilon ^{\alpha} y$ for finite $y$

[elfin berry]

jan Niku

[hazy lion]

re sub to the problem

then use dominant balance

does that help @ancient slate

[hazy lion]

ye

[ancient slate]

[hazy lion]

im not sure how the rest of the solutions are getting tossed

[ancient slate]

mm... yes... dominant balance.. mhmm

[hazy lion]

clearly epsilon = 0 is trash

[hazy lion]

lol idk i just "learned" this today

i guess you just assume that one of the terms is asymptotically not important

[ancient slate]

I have no idea what it is either 💀

[hazy lion]

along epsilon

I guess this implies that the other two terms are asymptotically equivalent

so if you have A + B + C = 0 and C vanishes

then A ~ B

i guess ONLY C vanishes is maybe more correct

[warped wind]

And then y is forces to be -2, no?

[hazy lion]

y is a variable

oh, i see what you mean

yea this whole process doesnt make any sense to me

[ancient slate]

Ah I get it now

You said the epsilon is a tiny perturbation right?

[hazy lion]

yes

[ancient slate]

Tell me if I get this right

$\varepsilon^{2\alpha +1} y^2 - 2 \varepsilon^\alpha y + 1 = 0$

[elfin berry]

TooManyCooks

[ancient slate]

Then you said take limit as epsilon goes to 0

which means the leading perturbative term is $-2\varepsilon^\alpha y$

[elfin berry]

TooManyCooks

[ancient slate]

did I get that right?

[hazy lion]

well, no

the thought is that you assume that one of the terms is insignificant

so then the other two will be significant

then they should be asymptotically equivalent

one wont dominate the other

[hazy lion]

so i dont think this makes sense

[ancient slate]

I just wrote what you gave me

So to clarify

You want the first term to vanish?

[hazy lion]

its more like we assume that a term will vanish, and then check them one by one, to see if the assumption makes sense

i just happen to know that the term 1 will vanish asymptotically

[plain stump]

if you're solving for this, can't you try like ex^2-2x\approx 0

for dominant balance

[hazy lion]

well, if you check the other two, you'll see they fail

so if one works, it will be 1 vanishing

[hazy lion]

ultimately this is basically what happens

i think?

the substitution with alpha results in $y^2 - 2y + \epsilon = 0$

[elfin berry]

jan Niku

[hazy lion]

assuming that limit makes sense and provides alpha = -1

which is the part i dont get

[plain stump]

[hazy lion]

why sad?

[plain stump]

i did not nearly pay enough attention in my numerics class

[ancient slate]

[hazy lion]

@ancient slate the balance is gonna imply asymptotic equivalence right

or am i crazy in jumping to this

my prof just sorta skirted over everything

it makes sense that in A+B+C=0 if only C vanishes then A~B must be true right

otherwise either A or B would vanish, too

[ancient slate]

I got promoted

[hazy lion]

heyy welcome to helpful

ohhh

@warped wind i get what you meant now

about -1

but then this also has implications for the value of y

so thats a problem

maybe

[warped wind]

Yes

[hazy lion]

yea im not sure how to resolve that

[warped wind]

Unless something monkey funky happens for the whole expression for the cases where the limit is going to infinity

[hazy lion]

my prof just matched powers

[warped wind]

But I would assume not

[hazy lion]

but this seems dumb to me

ill ask him about the ~

i must be making some mistake in moving from the assumption into ~

i dont see how anything else pops out

thanks for the help, crew

.close

[marsh citrus]

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[hazy lion]

.reopen

[marsh citrus]

✅

[hazy lion]

sorry u were typin

👀

.close

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[gray shale]

how can i show that:

[odd dove]

Oh shit sorry didn't notice you had already posted here

[gray shale]

$1-cos(x \pi) =2sin^2(\frac{\pi x}{2})$

[elfin berry]

Max.cc

[willow owl]

Use the fact that $\cos(2x)=\cos²(x)-\sin²(x)=1-2\sin²(x)$

[elfin berry]

calculus is fun

[marsh citrus]

@gray shale Has your question been resolved?

[gray shale]

ye but it's 2x not pi*x

[unborn condor]

$\cos(2K)=cos^2(K)-sin^2(K)=1-2sin^2(K)$

let's see if renaming the variables here help you

[elfin berry]

LordFelix

[gray shale]

K = x*pi/2 then

ok thx

.close

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[jolly sigil]

So I set up the integral but I feel like the smaller radius might be wrong

how about this, someone correct my reasonining. I don't care what the integral is rn.

I chose 27x^3 as the larger raidus because it was the furthers way from x= 2

and x = 1 to be the smaller radius because it was closer to x=2

[sacred kestrel]

look at it geometrically, is the inner radius changing at all?

[jolly sigil]

ummm

hmm

Is the inner radius changing

no?

hmm wait

you've stumped me. Cause I wanted to say that I don't think the radius would change but then how do I explain the larger radius

that will change depending on x

[sacred kestrel]

its been a minute since ive done this let me look at my old notes

[jolly sigil]

okay

[sacred kestrel]

okay so this should be shell method, with respect to x ( same axis of rotation ) if memory serves.

[jolly sigil]

to help this is the washer/disk method

[sacred kestrel]

you are using washer method, which would be a y integration i believe

[jolly sigil]

I was told you can use them both

I thought dx because the width was determined by the x axis

[sacred kestrel]

in this case, x axis radius, not width.

width of the washer would be dy

draw it out

its a horizontal washer

[jolly sigil]

horizontal washer meaning like it's laying flat

[sacred kestrel]

right

[jolly sigil]

instead of say, on it's side

[jolly sigil]

so dy is the width

okay

[sacred kestrel]

right, but i would 100% use shell method here

if you've already covered that, that is.

[jolly sigil]

Sure

[sacred kestrel]

shell method allows you to use the same axis of rotation if rearranging the function in terms of the other var gives you something ugly.

[jolly sigil]

so that's 2pi times height times radius

[jolly sigil]

I feel like that's going over my head

idk why

when we talk about axis of rotation I start to gloss over

[sacred kestrel]

good rule of thumb is disc/washer method uses the other axis that didn't rotate.

don't stress, there's only two ways to rotate, by x or by y.

in this case, its rotated "around" an x value, so we use the other axis for disc/washer, since we integrate by width.

[jolly sigil]

the other axis being the y axis?

[sacred kestrel]

yes

if we rotated around a y value, then x would be used, since our width would be in the x axis.

dx/dy is shorthand way of saying how we slice things

you wouldn't slice the volume with dx here, because you'd be cutting straight through the volume, instead of getting only a uniform slice.

with shell method it allows us to use the same axis and makes it way easier to deal with something like this when the washer method will give us an ugly cube root.

[jolly sigil]

what do you mean use the same axis

[sacred kestrel]

axis of rotation

[jolly sigil]

like you can use either or

or that you're using both

[sacred kestrel]

with washer/disc you are forced to use the axis that didn't rotate.

shell i think can be either/or

[jolly sigil]

ughh

[sacred kestrel]

listen, shell is easy here

so you know the formula?

[jolly sigil]

yes

It's just I'm not getting some of this stuff. I have the main idea, computing the volume using integration. Boom, got that down.

But some of these smaller details I'm lost

[sacred kestrel]

i struggled a bit too on this stuff.

just takes practice

[jolly sigil]

yeah

[sacred kestrel]

the key is drawing it out

it helps a ton

and remembering that when we slice, we must get the shape we need. otherwise its the wrong axis.

so if you draw out the cylinder we will integrate

i marked the inner and outer radii

[jolly sigil]

I see that

[sacred kestrel]

so when x = 1, we need the radius of 1 from x = 2

but

if we take x at 0.5

radius will need to be 1.5

[jolly sigil]

what's the relationship of those points?

[sacred kestrel]

if we just rotated at x = 0

we could just use 2pi x * height

but since we are rotating at a specific x, we need to modify that x

2pi ( circumference ) * height

what formula would give us the proper radius at every x from x = 2

sorry my book says circumference for the formula, but technically we are replacing that with the distance from the point of rotation

[jolly sigil]

it's fine I recognize that from my own reading

I don't know

but now I think the height would be y = 27x^3

[sacred kestrel]

hold up we aren't at height yet

but yeah that would be the height

lets say i give you x = 0.5

whats the formula for finding the distance from x = 2, to that 0.5

its very simple, dont overthink it

just look at the graph and tell me the distance from 2 to 0.5

[jolly sigil]

would you just take the difference between 2 and 0.5 ?

[sacred kestrel]

right

0.5 was the x we chose

BUT

that relation will hold for ALL x on the axis

[jolly sigil]

ohhhhhhh

[sacred kestrel]

so we get (2 - x) for our radius of the shell

[jolly sigil]

so 2 - x would work for every x

[sacred kestrel]

right

[jolly sigil]

ahhhh

[sacred kestrel]

so thats our circumference for the formula

[jolly sigil]

I see

[sacred kestrel]

so then put it all together and integrate

[jolly sigil]

I think I've seen that before

I just didn't follow it very well

[sacred kestrel]

that will be a key concept moving forward

[jolly sigil]

good

that's not very difficult

I see why it works now

[sacred kestrel]

you'll need to be able to visualize distances along the axis for later stuff like hydrostatic pressure

[jolly sigil]

oh man

is that calc 2?

or calc 3

[sacred kestrel]

yes

calc 2

[jolly sigil]

okie

I'm in calc 2

can't wait

[sacred kestrel]

calc 2 is fun because it has so much variety, but also terrible because of it haha

[jolly sigil]

variety with what? Applications?

[sacred kestrel]

just so many new things

differential equations, integration with respect to force/work done, series,

logistic growth, etc.

[jolly sigil]

I'm sure I'll like it. I get in a real bad mood when I don't get something so I just sit in a hole for a bit unfortunatly and it becomes harder to learn. But now I feel like I'm getting this better.

[jolly sigil]

ah!

nice

[sacred kestrel]

series is where shit gets real

[jolly sigil]

I got a workbook on differential equations I haven't used yet.

stoked

[jolly sigil]

oh boi

[sacred kestrel]

you find out there are approximations for everything lol

[jolly sigil]

oh man

idk what you even mean by that

[sacred kestrel]

you'll know when you get there lol

[jolly sigil]

does it have any applications to stats

I usually try finding examples to get me exicted if it has a translation to stats

[sacred kestrel]

stats relies on approximation... so yes 😛

[jolly sigil]

or probability

I meant series specifically

[sacred kestrel]

oh yeah. the meat of calculus is in series imo

you've touched the surface

[jolly sigil]

hellll yeah

well thank you for walking me through that

[sacred kestrel]

series allow curve fitting and all that

[jolly sigil]

ah

okie okie

I'd love to go over a disk/washer method but I don't want to take up your time

[sacred kestrel]

good luck! glad i could help even though my memory was a bit fuzzy

[jolly sigil]

Na you've been great

[sacred kestrel]

key is drawing it out. the more you draw it out, the easier it gets, eventually you wont need to draw.

[jolly sigil]

Sometimes your professors forget what it was like to learn the material so they gloss over some stuff

gotcha

will do

have a good one

[sacred kestrel]

you too 🙂

[jolly sigil]

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[modest python]

I want to know what's the best way to decide how to check if a system of linear equations is inconsistent?

[modest python]

for example here, I need to find a value of p so that the system is inconsistent

[marsh citrus]

@modest python Has your question been resolved?

[modest python]

<@&286206848099549185>

[marsh citrus]

@modest python Has your question been resolved?

[bright jay]

Do you know what an inconsistent system is?

[modest python]

yes, but I don't know if I should check every existing number for p to know if it give an inconsistency

or if there's a way to know what numbers to check

[bright jay]

What does an inconsistent system mean?

[modest python]

when the rank of the augmented matrix is greater than the rank of thematrix

[bright jay]

In other words, there's no solution correct?

Like one line is parallel to another

[modest python]

yeah

but I still don't get it

[bright jay]

Do you know how to reduce that into REF?

Because having it in that form would help out

[modest python]

like, with Gauss-Jordan?

[bright jay]

Yeah

It's two more steps you can do

[modest python]

okay yeah, I have it

Excuse my handwriting

[bright jay]

Solve the last row, you'll see that you'll end up with two values of p

[modest python]

with the augmented matrix?

[bright jay]

Yeah, you can just focus on the last row

[modest python]

okay, thanks

I got 7 and 11, I just need to test those out?

[bright jay]

Yes

[bright jay]

If you recall, no solution is when the left side of the bar is all 0s and the right is still some number

[modest python]

okay, thank you so much!

.close

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[bright jay]

I'm assuming you got it?

[modest python]

hahah yes

[bright jay]

And you got?

[modest python]

11

[marsh citrus]

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[feral summit]

how would i do this one

ive never done it in like fraction percents

[marsh citrus]

@feral summit Has your question been resolved?

[quick moth]

7 1/4 percent is just 7.25 percent

7 5/8 percent is 7.625 percent

@feral summit

Here’s your equations

[feral summit]

Oh

[quick moth]

It’s either 32 or 31 dollars depending on where you round

[feral summit]

[quick moth]

its like 108 or 109 dollars

i would just assume they want you to round after each person

so i would put 109

@feral summit

[feral summit]

[quick moth]

what did u put on the last question

did u put 31 or 32

@feral summit

i guess its 108 then

[feral summit]

32

[quick moth]

one sec

ok they dont want u to round until the end

so its gotta be 108

[feral summit]

Bro is a life saver

[quick moth]

haha

do understand it now tho

if its fraction just put 7/8 in your calc

you get .875

so its 6.875 percent which just turns into a rate of .06875

[feral summit]

ohh

[marsh citrus]

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[exotic magnet]

Could someone please check my work I have a feeling I messed up somewhere

[brave spire]

Can u provide the question

[exotic magnet]

Calculate the shortest distance from point C to any point along point along AB

And the points are A(3,5) B(-1,7) C(-7,-3) and D(5,-7)

[willow bison]

i would recommend graphing the points on desmos

essentially what you want to do is the following:

1. find the equation line connecting A and B

2. find the line that is perpendicular to line segment AB such that it passes through C

3. find where these lines intersect

4. find the distance between the point of intersection and point C -- this will be the answer

[exotic magnet]

Our teacher doesn’t let us use Desmos she wants us to do it by hand

That’s why is so complicated

This is what I get in desmos

I think I messed up one of the equations

@willow bison

[willow bison]

sorry i'm a bit busy

you don't need desmos

you can easily graph this by hand

do you know how to find a linear equation using two points?

[exotic magnet]

Ya

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[thorny jungle]

@wet holly Sorry to pin, i do have a follow up qeuestion

[thorny jungle]

I am not sure how to argue from -sup(A) = inf(-A) to sup(-A) = -inf(A)

[marsh citrus]

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[torpid owl]

help.

[torpid owl]

!status

[marsh citrus]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[torpid owl]

1

<@&286206848099549185>

[velvet vine]

Line EF is the perpendicular bisector of segment BD and the bisector of angle BAC

[still temple]

Only the last option is correct..
BD is a curve hence EF does not form a 90 degrees with it

[velvet vine]

It says segment BD, which means that it is the line segment between points B and D

[marsh citrus]

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[marsh citrus]

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.reopen

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✅

[torpid owl]

@velvet vine @still temple so what's the answer?

there's probably only two correct options.

(if that helps)

[velvet vine]

Line EF is the perpendicular bisector of segment BD and line EF is the bisector of angle BAC

[marsh citrus]

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[worthy spindle]

Can anyone numerically confirm my answer is correct?

[worthy spindle]

i've attached work

[marsh citrus]

@worthy spindle Has your question been resolved?

[worthy spindle]

<@&286206848099549185>

[marsh citrus]

@worthy spindle Has your question been resolved?

[marsh citrus]

@worthy spindle Has your question been resolved?

[worthy spindle]

<@&286206848099549185> please 🙏

[marsh citrus]

@worthy spindle Has your question been resolved?

[strong jewel]

It looks like you don’t even need the fact that the staircase is helical, since gravity only works downwards

[marsh citrus]

@worthy spindle Has your question been resolved?

[open relic]

Hello. Yes I agree that the staircase being helical is not really important in this case 🤔. Anyway you should get the correct value as all the components are defined correctly

,w integral from 0 to 120 of (230-2/120 h) dh

[elfin berry]

Results provided by WolframAlpha

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

Requested by eleonardo

[open relic]

Yes it's correct 👍🏽

[marsh citrus]

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[fallow jolt]

f(x+h) = 5/(6-x+h) - f(x)= 5/(6-x)
Common denominators:
f(x+h)= 30-5x/(6-x)(6-x+h) -f(x) = 30-5x+5h/(6-x)(6-x+h)
Subtract:
5h/(6-x)(6-x+h)
Divide by H from the denominator of the function:
Get's the answer : 5/(6-x)(6-x+h)

[marsh peak]

f(x + h) is not equal to that

$f(x + h) = \frac5{6 - (x + h)} = \frac5{6 - x - h}$

[elfin berry]

A Lonely Bean

[fallow jolt]

ohhhhhh

okay

let me try that

After doing that, I get -5 / (6-x-h)(6-x) and it's wrong
f(x+h) = 5/6-x-h - f(x) = 5/6-x
Common Denominators:
30-5x/(6-x-h)(6-x) - f(x)= 30-5x-5h/ (6-x-h)(6-x)
Subtract:
-5h/(6-x-h)(6-x)
Cancel out the h from denominator in the function
-5/(6-x-h)(6-x)

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[gilded pivot]

I must calculate those for n>=1

What do I need to do exactly to calculate them ?

[brave spire]

Separate the sum for 1st one

[gilded pivot]

Then ?

[wind beacon]

you can use the formulas after seperating

[worthy spindle]

THANK YOU LOL, i already got it but thanks for the response still

[gilded pivot]

Do you have a screen of all the formulas please ?

Or somewhere I can have them

[brave spire]

For first one use sum of finite GP, sum of AP I think, then for n-3 it will just n-3 n times so it becomes n^2 - 3n

[gilded pivot]

What does GP mean and AP

Im not familiar with English writings

[brave spire]

GP = Geometric Progression
AP = Arithmetic Progression

[gilded pivot]

Ah yeah ok

Thx

Im not sure I really understood

Is that about it ? @brave spire

@wind beacon

[brave spire]

Ur doing the sums wrong

[gilded pivot]

Wdym

N-3 should stick together ?

[brave spire]

Yes

[gilded pivot]

How do I know that

[brave spire]

Also the sum of the GP 2^k is not 2^m

[brave spire]

Actually not necessary

It's fine that way

[gilded pivot]

2^n is only the gp

Not the sum

It’s that ?

[brave spire]

The terms of our GP are 2, 4, 8
...
Observe that they are all of the form 1 * 2^k. Comparing with a*r^n, we observe that a=1,r=2,n=k

By sum of GP formula

S_n = a(r^n - 1)/(r-1) = 1(2^n - 1)/(2-1) = 2^n - 1

[gilded pivot]

Good?

I saw that

[brave spire]

https://images.app.goo.gl/qAguNTAvubNSqJVR9

[gilded pivot]

I don’t need n+1 in thzt ?

It’s good like that ?

Are they good ? @brave spire

[marsh citrus]

@gilded pivot Has your question been resolved?

[marsh citrus]

@gilded pivot Has your question been resolved?

[wet holly]

hm

[marsh citrus]

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[stark field]

Helper Rieman ask me this but i was making food

i am surprised to how he is surprised that this cant be

Does anyone think this is OK?

[main idol]

I never said it was wrong

[stark field]

Its derivation

[main idol]

I asked for justification

[stark field]

So the question is to find y(w,p) , but we do that from problem of profit maximisation with y (production) as variable

[main idol]

I also asked for a starting equation

[stark field]

y(w,p) is function of production of a firm in the short run which means r*K is ignored

so first order condition FOC: derivation of profit function by variable (y) in this case must be 0

and from there i start with derivation

[main idol]

Yea you didn't give any of that information earlier

[stark field]

Sorry i thought like just the math part of it i don't know if i got it correct I think it is?

also Pi is profit function

y - Function of supply of producer, w - price of Labour (L) , p - Price of product, Pi - Profit function

😢

i fail to prevail

[marsh citrus]

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[marsh citrus]

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[tardy idol]

i cant understand how to expand this

[tardy idol]

i dont know how they did that

[still vortex]

First they did polynomial division, then they factored the denominator

[tardy idol]

oh well my bad i shouldve mentioned i factored the denominator fine

its just the top i couldnt figure out what they did

one sec i forget what polynomial division is

ok yeah how do you use polynomial division here?

[still vortex]

Example:

[tardy idol]

i see.. but

what would you be dividing?

like the denominator by (x^3 + 3)?

[still vortex]

So you mean what would be the divisor?

[tardy idol]

yes

sorry

[still vortex]

x^2+3x+2, because that's the denominator

[tardy idol]

ok

could you give me like 2min so i can try to do it to see if i understand

[still vortex]

Ok

[tardy idol]

ok could you possibly show me how to start the polynomial division

[still vortex]

I'll try to typeset it because I'm not on a phone and I can't take pictures

[tardy idol]

ok 👍

[still vortex]

This looks weird but it's the best I can do

[hollow sparrow]

yep exactly! The remainder you can do as (7x + 9)/(x^2 + 3x + 2) and then they factored the denominator to (x + 2)(x + 1)

nice work 🙂

[marsh citrus]

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[tardy idol]

this was a fantastic example thank you

.close

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[sacred kestrel]

Need help on highlighted parts a, d

[sacred kestrel]

the book doesn't directly explain these points

this is all i could find on a

[scarlet hinge]

I would say both are true.

[sacred kestrel]

so a linear transformation is the same as a linear function then?

linear would be special for functions i suppose

[scarlet hinge]

A linear transformation / linear function is just a function that is linear.

[scarlet hinge]

yes generally

Transformation might highlight that it is multidimensional or geoemtrically significant

[sacred kestrel]

the word "special" threw me off honestly

[scarlet hinge]

I think they just mean that not every function is a linear function

so they are just a special kind of function

[proper zodiac]

d is a bit vague imo

[scarlet hinge]

same with a imo lol

[proper zodiac]

if all your spaces are finite then you can represent a linear transformation between them as a matrix transformation

[sacred kestrel]

for part D this is all that is said

[proper zodiac]

whether you interpet that as saying they are matrix transformations is ehh

[scarlet hinge]

ehhh, you can do infinite matrices kinda.

[proper zodiac]

you wouldnt really call it a matrix at that point

[scarlet hinge]

Depends on your definitions.

I have definitely seen people call them matrices.

Either way it seems pendatic.

[sacred kestrel]

oh i found it

[scarlet hinge]

💀

Well thery could mean different hthings by this.

[sacred kestrel]

so every matrix transformation is a linear one, but its not always true in reverse?

thats confusing as hell

[proper zodiac]

id be interested in those examples

[scarlet hinge]

Either they do exclude infinite matrices or perhaps they want specifically a representation.

You can definitiely write a mapping that does not look like a matrix representation at all.

Today I alrady helped one that wanted the matrix representation of the polynomial mapping phi(P) = P(X + a).

[sacred kestrel]

alright, settle down boys this is chapter 1 of my LA book lol

[scarlet hinge]

One can argue that without a basis that it is not yet a matrix transformation.

[sacred kestrel]

im trying to find those examples for you though

[proper zodiac]

yeah it'll likely just be an abstract linear map on two vec spaces

[sacred kestrel]

so idk if the terminology went over my head but i went through the examples in chapt 4 and 5 and none specifically said it was an example of a linear transformation that wasnt a matrix transformation.

[proper zodiac]

whats the book?

[scarlet hinge]

lol

[sacred kestrel]

David Lay - Linear Algebra and its Applications

[scarlet hinge]

The thing I can tell you for sure though is, that if you do fix a basis, then you always REWRITE any linear mapping as a matrix mutliplication.

[sacred kestrel]

ISBN 10: 0-321-38517-9```

[scarlet hinge]

If you have infinite dimensional vector spaces in your mapping then the matrix will of course also be infinite.

[sacred kestrel]

at this point we haven't covered basis, determinants, subspaces, or any of that yet

[scarlet hinge]

ah...

[sacred kestrel]

this is still chapter 1

[scarlet hinge]

short outlook then.

[scarlet hinge]

In the more general sense, people call anything a vector space that has linearity properties.

[sacred kestrel]

are there spaces where linearity is impossible?

[scarlet hinge]

In some cases you might not be able to have a natural vector representation.

A basis is just you choose some predfined vectors and use them as your stating point to put together any other vector with them.

[sacred kestrel]

so would
[ 1 0 ]
[ 0 1 ]
be the basis for the cartesian coordinates?

[scarlet hinge]

Like you can put together any vector in 2d real space with the standard basis (1, 0) and (0, 1).

[scarlet hinge]

yeah exactly.

You could also use (0, 1) and (128738, 123873137812387) though

[scarlet hinge]

this is an example of an extremely high dimensional vector space

[sacred kestrel]

so, the book doesn't really justify the statement that every matrix transformation is a linear transformation, but states it anyway. what would i put as a justification?

[scarlet hinge]

If I was feeling snarky I would say "I think so yes because... but the book says no on page X"

Yeah I would probably just point at the page.

[sacred kestrel]

yeah because it really doesn't back up that statement at all lol

final answers

[scarlet hinge]

wait

[scarlet hinge]

um

Am I dumb or does it literally claim the opposite?

[sacred kestrel]

LOL

yeah

[scarlet hinge]

I am reading there will be counter examples in chapters 4 and 5

[sacred kestrel]

so every matrix transformation is a linear transformation, but not every linear transformation is a matrix transformation

but again, it doesn't really explain why that is besides a "trust us, or read chapter 4 and 5"

[scarlet hinge]

yeah

It's probably either the basis thing or the dimension thing.

It's really just terminology.

I can guatantee you that later on if you do more advanced mathematics people are not going to obsess over this distinction.

[sacred kestrel]

honestly the terminology is already confusing in chapter 1, theres like 5 different ways to say things already

[scarlet hinge]

[sacred kestrel]

thanks for the help though guys, time to move onto the next problem.

[scarlet hinge]

no problem and good luck

[sacred kestrel]

.close

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[narrow mural]

I need help please

[narrow mural]

I don’t know how to do this cause my teacher didn’t specify, if anyone is familiar with the topic please help me :,))

<@&286206848099549185>

Excuse the handwriting

😭

[marsh citrus]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[marsh citrus]

@narrow mural Has your question been resolved?

[trim quest]

@narrow mural Would you be comfortable describing the volume of those two boxes?

the space that needs to be filled with styrofoam is (volume of big box) - (volume of small box)

[narrow mural]

1728 - x^3

??

@trim quest

[trim quest]

yep

that describes the extra space in the big box that has to be filled in

[narrow mural]

I need the whole solution

😭

[trim quest]

well that is the whole thing for the first question

[narrow mural]

How do I factor polynomials??

Or what method do I use etc

[trim quest]

hm, this is a difference of cubes

I mean literally, it's two boxes that are cubes

and also mathematically, those are both perfect cubes

I bet you have a formula for sum/difference of cubes

[narrow mural]

I do

I need to answer what the a= and b= how do I solve this or what should I put

[trim quest]

well

your a^3 is 1728

so what is a?

like, what did you cube to get 1728 in the first place?

[narrow mural]

12^3

[trim quest]

yeah, a is 12

and how about b? since your b^3 is x^3

[narrow mural]

x

[trim quest]

yep, a = 12, b = x

[narrow mural]

THANK YPU SO MUCH

WAIT

[trim quest]

waiting

[narrow mural]

Wait that’s all

Thanks so much

Like a lot

This is 100% my grade

[trim quest]

no problem 👍 glad it helped

[marsh citrus]

@narrow mural Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[zinc smelt]

I don’t know how to continue the problem

[marsh peak]

From -12 < x - 6 < -10 you can imply that |x - 6| < 12

So you have |x - 6||x + 5| < 12|x + 5|

And with correct delta you can make 12|x + 5| < epsilon

[zinc smelt]

so would on the left side would i choose |x+5| <12eplison?

[marsh peak]

epsilon/12 perhaps?

[zinc smelt]

oh yea im dumb

ok, i think i got it from there

Thanks!

.close

[marsh citrus]

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Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[humble river]

hello

[humble river]

I am having some trouble here

Like i know cube root for these numbers

is 3 and 5

[wooden citrus]

What is the question

[humble river]

Factor formula

[undone bane]

is this a test?

[wooden citrus]

Ok so you know that 3^3=27 and 5^3=125

[humble river]

No is my home work

Yes i do

A test wouldnt have the options of ask your teach and need help etc i guess

[wooden citrus]

then what is (3^3)*s^3

[humble river]

i get

27s^3 again

[elfin berry]

Dyssrupt

[humble river]

Ah this formula

[undone bane]

exponent rules are not required here

[wooden citrus]

But to get 3s^3

[undone bane]

the op forgot the identity

which is required for the problem

[humble river]

Oh

[marsh citrus]

@humble river Has your question been resolved?

[marsh citrus]

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