help-36

[rigid parrot]

year 12

AS level

grasde 11?

[shadow cosmos]

it gets easier for me toexplain then

[shadow cosmos]

I don't understand it

what age?

[rigid parrot]

17

[shadow cosmos]

oh

I am 17 too

nice

[rigid parrot]

W

idk what this mean ngl

i have been sketching graphs in a book for 9 hours straight

[shadow cosmos]

great! you must have practiced it well now

[rigid parrot]

yes

Half of my course in 2 days

[shadow cosmos]

whoa

btw, do graphs cover half of your course?

[rigid parrot]

basically hahaha

[shadow cosmos]

lol

the syllabus is kinda simple then

[rigid parrot]

yeah

just transformations of graphs

alot of diffgerentiation

polymoniaslsd

il; send it to u

one sec

[shadow cosmos]

ohh nice

this is your school syllabus, right?

[rigid parrot]

no

my whole as lervel syllabus

so llike

we do AS level

then A level

which is harder

im doing both

but Alevel next year

@shadow cosmos

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[normal hill]

Ik this is a maths discord, but anyone familiar with biot savart law?

[normal hill]

Ive been asked to plot the flux density as a function of lateral distance

a set up like this https://gyazo.com/e967ed8d4c4dfb6a418226f366749f9a

where we adjuct the distance from the center of the coil fowards and backwards

but i cant figure out what the function will be

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Please don't occupy multiple help channels.

[silent scroll]

just divide it up in triangles and rectangles

get the areas of those

and add them

yessss

[naive pumice]

for the right triangle 25 x 10

[silent scroll]

yes divided by 2

so you get 125

[naive pumice]

yes\

14 x 11 for the left triangle

[silent scroll]

yes

[naive pumice]

77

[silent scroll]

yes

[naive pumice]

left rectangle 32

2nd rectangle 14 x 5

is that correct

@silent scroll

[silent scroll]

yess

I got 304 I think

[naive pumice]

77 + 32 + 70 + 125

yes

304

[silent scroll]

yay

[naive pumice]

thanks

[silent scroll]

np

[mossy knoll]

nice email address

[naive pumice]

crap

[mossy knoll]

lol

i mean it shouldnt really matter

[naive pumice]

yeah like you can mail me no passwords

[mossy knoll]

ye

[manic herald]

also leaked his school lol

location matches with the timezone in the pic

[naive pumice]

burn it

the school

[manic herald]

your pic is still up dude 💀

however deleting it will close the channel

so maybe just remove the image

[naive pumice]

yes

[final saddle]

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[naive pumice]

thats alr

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[stray stump]

does this work?

I should also show g(0,0) = 1 = limit

[dusty harbor]

$\forall \in \mathbb{R}$ has no meaning

[soft zealot]

heavy

[dusty harbor]

and why define w = xy if you are not going to use it?

also it doesnt make sense to define

$\delta = \sqrt{\delta}$

[soft zealot]

heavy

[dusty harbor]

youll want to write delta as a function of epsilon

such that for epsilon >0 its easy to find a delta > 0 by using that function

[stray stump]

i meant to define $\delta = \sqrt{\delta_1}$

[soft zealot]

KN

[stray stump]

so i can turn this into the single variable case

[dusty harbor]

it doesnt quite look right

just try again

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[hushed merlin]

How do you calculate probability?

[manic herald]

inference

need to be more specific

do you have a specific question?

[hushed merlin]

I have this Question but i'm not sure how to get around it.

[final saddle]

@hushed merlin Has your question been resolved?

[fluid sky]

so probability that both counters taken out are blue = all possible pairs of blue counters that can be taken out / all possible pairs of counters that can be taken out

[hushed merlin]

Thank you

[bold hinge]

Hi is anyone here be able to help me with this math problem?

[hushed merlin]

https://discord.com/channels/268882317391429632/907022703230345237

ask there

[bold hinge]

Ok sorry about that

[hushed merlin]

np

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[blazing hollow]

how do i approach this problem?

[dusty harbor]

educated guess

you know what $27^{\frac{1}{3}}$ is

[soft zealot]

heavy

[blazing hollow]

yes

cube root of 27

[crystal nimbus]

729 = 27^2

[blazing hollow]

not the answer, i just want to know how to solve these kinds of peoblems

problems*

[crystal nimbus]

its not an answer

its how you solve it

you notice 729 is 27^2 and solve from there

[blazing hollow]

how do i solve for the missign exponent

[crystal nimbus]

a^b = a^c means b=c

[dusty harbor]

depends on a🤓

[blazing hollow]

yes ik that

[crystal nimbus]

so use 729 = 27^2 to solve for x

[blazing hollow]

ok thx!

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[worthy cipher]

can someone do this for me please?

[onyx peak]

Do you know formula for volume of prism?

And also volume of pyramid?

[worthy cipher]

nope

i forgot

[onyx peak]

Ok, nvm. Do you know what prism is?

[worthy cipher]

yes i do

[onyx peak]

great. The formula for volume of prism is V=B*H, where B is area of base, and H is height

[worthy cipher]

yes

[onyx peak]

And formula for volume of pyramid is V=B*H/3.

[worthy cipher]

alright

[onyx peak]

Now you know the volume of prism. And since you also know the formula, you can substitute for V and get 330=B*H

330=B*H Do you understand this?

[worthy cipher]

yes so i have to find the b and h

[onyx peak]

Well... you don't have to and you also can't. But look at the formula for volume of pyramid. V=B*H/3

Is there anything you could do?

[worthy cipher]

idrk..

[onyx peak]

You have these 2 equations: 330=B*H, and V=(B*H)/3

[worthy cipher]

so i do have to find the b and h because i cant solve

[onyx peak]

actually - you don't have enough info to find B and H

[worthy cipher]

ohh

[onyx peak]

But you don't need to find both B and H to find volume of pyramid. You just need their product. B*H, and you already know what B*H is, right?

330=B*H, and V=(B*H)/3 Again look at this ;)

[worthy cipher]

yes

[onyx peak]

okay, so what is B*H?

[worthy cipher]

base and height

[onyx peak]

Do you know what star symbol means?

It's multiplication :)

[worthy cipher]

yeah i took it

[onyx peak]

330=B*H, and V=(B*H)/3 Okay, Once more what's the numerical value of B*H?

Take a look at this

[worthy cipher]

330

[onyx peak]

Correct

[worthy cipher]

yes

[onyx peak]

V=(B*H)/3 Now can you substitute it here?

You know what B*H is, so it shouldn't be problem finding (B*H)/3

[worthy cipher]

hmm

so we divide them

with 3

[onyx peak]

Yes!

[worthy cipher]

okayy

[onyx peak]

So what is the result?

[worthy cipher]

idk

oh wait

i divide 330 with 3

[onyx peak]

the result is 110

and that's also the volume of the pyramid

[worthy cipher]

oh okayy

[onyx peak]

so a) is solved

[worthy cipher]

whats the full answer the i have to write

also thanks!

[onyx peak]

The volume of pyramid is 110 cm^3

[worthy cipher]

okay

done

now lets do b!

its not hard i have to make a flow chart..

[onyx peak]

And I would also describe how did you get to the solution

[worthy cipher]

okay

[onyx peak]

To be honest I have no idea how to make flowcharts in math, so I probably can't help you with b)

[worthy cipher]

its okay

its like showing steps

[onyx peak]

You can resend the question

and someone else would answer

[worthy cipher]

no its fine i think i can do it!

[onyx peak]

okay, great :)

[worthy cipher]

thank you so much :)

[onyx peak]

you are welcome :)

[worthy cipher]

.close

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[rocky birch]

i got this answer right but my teacher wanted me to substitute so my teacher marked it wrong. x= 5/2

[rocky birch]

how do i do it by subst?

i did it by isolating the radical, squaring, and solving from there

but i only got half credit for doing it that way

[fierce orchid]

Let u=(x-1)^2

[rocky birch]

wait sorry im dumb and uploaded the wrong problem

give me a second...

i meant this one!

[proper flicker]

u=2x-1

Substitute

[rocky birch]

what exactly is u though? i should definitely know this by now but ive been practicly asleep during math class

[oblique portal]

another constant so it makes things easier to see

well jot constant

variable

[rocky birch]

in which form?

.close

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[potent yacht]

How do you integrate this

[high beacon]

feels like trig sub

with uhh

x = 4sin^2(u)

or just sin^2(u) if you move your coefficients out

[potent yacht]

I don't think I am too familiar with that

[high beacon]

okay

[potent yacht]

Not sure how or why we would want that

[high beacon]

trig sub uses a few trig identities to simplify integrals like this

recall sin²x + cos²x = 1

ur pythagorean trig identity

in this case also, you can factor 16 from that nasty thing and remove it entirely

to the outside of the integral

4*int(sqrt(1-x^2))

if you rearrange that trig identity, it can look a lot like what you now have in the root

it is maybe worth noting trig sub is a calc 2 concept

[potent yacht]

I have no idea

Like this?

[high beacon]

yea exactly

and you can integrate that

[potent yacht]

But it's dx shouldn't we make it dz

[high beacon]

yes

[potent yacht]

How

arcsin?

[high beacon]

if x = sin(z), then dx = cos(z)dz

[potent yacht]

Oh

[high beacon]

so its like u sub where you end up cancelling something, but you don't have to rearrange for dx because its already done

Oh

the bounds as well

need to be updated

this is crazy btw for a non uni question

[potent yacht]

Huh they do??

[high beacon]

yea so

[potent yacht]

Why

[high beacon]

because theyre still with respect to x

[potent yacht]

Never learnt about that ok

[high beacon]

so when x = 1, then sinx = 1

[potent yacht]

Ig it's not the same curve we are trying to find the area under anymore?

[high beacon]

i would honestly be amazed if you had

[high beacon]

I'm not 100% sure

I assume its a different curve because the bounds are different

[potent yacht]

Alright how do we change them then

[high beacon]

right so take your bound value and set it = x

where x is also sin(z)

so sin(z) = 1

that one is easy but if it's not a happy number then arcsin both sides

new bound should be value of z

[final saddle]

@potent yacht Has your question been resolved?

[high beacon]

.close

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[near frost]

how to prove these two have the same countability?

i guess i have to find bijective function between Power set of X and set of functions that go from X to {0,1}

but idk how to start

[hearty zephyr]

do you know anything about X?

[near frost]

only that its not empty

[hearty zephyr]

nothing else? like countable? finite?

[near frost]

nothing

[desert mantle]

pick a subset of X. you can describe this uniquely by saying which elements of X are in the subset and which are not

that's a binary choice for each element in X

[near frost]

i dont understand..

[near frost]

u mean in P(X) ?

hmmm

like that?

but its function for elements of X, its should be for subsets

hmm can i do just the same thing with subset?

like

swich small x to big X and it will mean subset

[final saddle]

@near frost Has your question been resolved?

[desert mantle]

f(x) as you have written is a function from X to {0,1}

so you associated an element of P(X) to an element in {0,1}^X

show that this association is a bijective map

[near frost]

okaay i already got it thank u

.close

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[tranquil pine]

2nd derivative to find local minimum

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[gentle spear]

I have plenty of resources for the USA math curriculum but none for my province, what course in the USA corresponds to what course in British Columbia, Canada?

[dry light]

That's something for to ask your school board

And that's not what help channels are for

Read the rules

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[noble lotus]

On 30-60-90 triangles to find the longer leg I understand it is the shorter leg square root of 3. What do I do if the length is the fraction 1/2?

[robust ledge]

I guess its easier to remember by sin a = opposite side/ hypotenuse

Where a is the opposite angle

Then sin30 = 1/2x

Sin60 = y/x

[noble lotus]

Im sorry😂 Im gonna be honest I don’t know how to do that at all im in Geometry 1 in secondary school and Im just now learning this thank you though. How would I put it in square root form?

[robust ledge]

Ok, no problem

[grim badger]

Fractions are numbers too

[noble lotus]

I know I just mean how do I format it

[grim badger]

It's the shorter leg times by sqrt(3)

Multiply the two

[noble lotus]

Because I can’t do 1/2 square root 3

[grim badger]

Do you know what $\frac{1}{2} \cdot \sqrt{3}$ equals?

[noble lotus]

No

[soft zealot]

dldh06

[grim badger]

Do you know what $\frac{1}{2} \cdot 3$ would be?

[soft zealot]

dldh06

[noble lotus]

Yes

[grim badger]

And that is?

[noble lotus]

1.5

[grim badger]

What is it in fraction form?

[noble lotus]

Or 1 and 1/2

[grim badger]

Do you know how to multiply with fractions?

[noble lotus]

Like I know how to cross multiply and stuff yeah

[grim badger]

If you have $\frac{1}{2} \cdot \frac{5}{6}$, do you know how to multiply those?

[soft zealot]

dldh06

[noble lotus]

But the question just wants me to put it like x square root 3

[grim badger]

I'm getting there, it's just applying the concept of multiplying fractions

[noble lotus]

5/12 right?

Bc it’s not asking to cross multiply

[grim badger]

Yes, how did you do that?

[noble lotus]

1 times 5 and 2 times 6

[grim badger]

Same process with $\frac{1}{2} \cdot \sqrt{3}$

[soft zealot]

dldh06

[grim badger]

Recall that $\sqrt{3} = \frac{\sqrt{3}}{1}$

[noble lotus]

1 times sqaure root of 3 and 2 times sqaure root of 3?

[soft zealot]

dldh06

[grim badger]

Not quite

[noble lotus]

Wait so

Well yeah because any number divided by 1 is itself

So that makes sense

So I would do

1 times sqaure root of 3 and 2 times 1?

[grim badger]

Yes

So that equals?

[noble lotus]

So square root of 3 over 2

[grim badger]

And so y equals?

[noble lotus]

Just did that on calculator 0.87

[grim badger]

You don't need a calculator

[noble lotus]

I was never taught how to do that without a calculator im sorry

[grim badger]

Doesn't this look like one of the existing answers?

[noble lotus]

Yeah it is

Oh wait so that can be the answer ohh

[grim badger]

I was saying y = $\frac{1}{2} \cdot \sqrt{3}$

[soft zealot]

dldh06

[noble lotus]

Oh right right yes that makes so much more sense you explained it much better than my teacher😂 thank you!

.close

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[unkempt canyon]

Hey could someone please tell me if I have done this correctly?

[fresh star]

yh that looks fine

[unkempt canyon]

Thanks

[silk saddle]

pro tip: use wolframalpha to check

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@unkempt canyon Has your question been resolved?

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[raven bridge]

we have such a function and set A
what is f(A)?

[final saddle]

Please don't occupy multiple help channels.

[raven bridge]

i would say it is equal to R\Q

but i'm not sure

[silk saddle]

also what is i A

[raven bridge]

A is any set

[tulip coyote]

[in particular, the difference between two irrational numbers need not be irrational]

[silk saddle]

err...

[raven bridge]

with following properties

[silk saddle]

A = (R\Q)^2 here

[silk saddle]

adding on, here's a concrete example. let x = sqrt(2) - 1, y = sqrt(2) - 2

[raven bridge]

oh, i think i see it

[silk saddle]

the irrational numbers aren't closed under +

[raven bridge]

so it is a set of real numbers, am i right?

[silk saddle]

in fact it is all of R

[raven bridge]

well, actually it is all of C

[silk saddle]

oh x-yi?

like i was the imaginary unit?

if not then no

[tulip coyote]

[silk saddle]

and if i was the imaginary unit then it's completely different now

and the question would be flawed

[raven bridge]

a + bi, where b = 0 B))

[silk saddle]

um

I'm so confused

so that's just R

[raven bridge]

nah, i'm just talking non sens right now

[silk saddle]

all good

[raven bridge]

i know it is R lol

[silk saddle]

if you know some analysis

closure of I is all of R

which might be convincing

[raven bridge]

.close

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[raven bridge]

when is this implication false?

[silk saddle]

what is ~

[raven bridge]

implikuje means implies

~ means that sets have the same number of elements

[tulip coyote]

Like you can create a bijection between them yea?

[raven bridge]

yes

i see that the (A / B) ~ (B / A) implies A ~ B

but i cannot find an example for why it doesn't work the other way around

[tulip coyote]

For an infinite counterexample, take $\bN$ and $2\bN$ I would think

[soft zealot]

chartbit

[silk saddle]

N x N perhaps

[raven bridge]

oh, i think i can see it now

thanks

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[stoic venture]

I have a word problem I need help with

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[fleet pelican]

how to do 6A?

[fossil geyser]

It's a rectangle, so A=(length)(width)

Can you express the length and width in terms of x?

[fleet pelican]

but the

factoered form is

-2x(x-20)

like the vertices are at (0,0) and (20,0)

[fleet pelican]

wdym

[fossil geyser]

this is the completely factored form, but there are other forms

[fleet pelican]

like what forms

[fossil geyser]

I mean, from the picture, what's the width of the rectangle

[fleet pelican]

x

[fossil geyser]

and what's the length?

[fleet pelican]

unkown

we just know he has 40m of fencing

[fossil geyser]

that's enough to figure out the height

[fleet pelican]

how

wait heres my thought

since the parabola is at

0, 0 and 20,0

then the width would be 20 cm

and since the max is 40 m* of fencing

and theres a brick wall

there would be 20 cm left

and from the image, the height of boths ides are qual

meaning the height of each side is 10 m

so the area is 200m^2????

[fossil geyser]

The area is variable, because the width is variable: x

Don't worry about the parabola, just look at the geometry

[fleet pelican]

u mean the heigh

ok

[fossil geyser]

If there's 40m of fencing

You use x meters for the north side, and x meters for the south side

The west side requires no fencing because it's just the wall

So how much fencing is left for the east side?

[fleet pelican]

x???

[fossil geyser]

Hmm

let's try this:

Let's call the height y

Then, since there's 40m of fencing

2x + y = 40

Does that make sense?

[fleet pelican]

yes

ty

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[wispy pulsar]

how do i solve this?

[wispy pulsar]

do i have to put in the value of 1 to x?

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[crystal creek]

this is the work I have so far on this problem, I know the answer is 1/6 but I’m not sure how to make the numerator 1

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[viral shoal]

How many ways are there to distribute 6 different toys to 3 children so that each child receives at least 1 toy?

[viral shoal]

I have no clue how to proceed

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[pale hatch]

So I've been trying to understand what a determinant is and have come across the
following:

1. Defining the determinant explicitly using the formula in the image
   It looks pretty unintuitive imo are there any merits to this?

2. Defining the determinant as the general signed volume of vectors (general in the sense whatever volume could mean in higher dimensions) / a multilinear form acting on vectors
   It makes more sense than the first definition but I still can't understand the signed part using this. What exactly does the sign represent?

3. Defining the determinant as the scaling factor in a linear transformation
   Again makes more sense the first definition and the sign can be interpreted as telling if the linear transformation flipped the orientation.

4. Just remembered there's also the recursive definition using cofactors and then defining the determinant of a 1x1 matrix to be its only component. It works out well but again doesn't make any intuitive sense to me

Is any definition here more preferable than the rest? And for what reason?

[neon slate]

maybe watch this, his videos usually aim for gaining some kind of intuition beyond just the definition and it sounds that's what you're looking for
https://www.youtube.com/watch?v=Ip3X9LOh2dk&ab_channel=3Blue1Brown
(i think this is part of a whole series you might find interesting btw)

[pale hatch]

I have watched this
that's where I got num 3 from

[neon slate]

😂

[tranquil pine]

its also possible to define the determinant using axioms

[night lotus]

Exactly, and it can also be shown that an image which satisfies those axioms is unique, and it is not too hard to show that that "difficult formula" satisfies those axioms, hence it is the determinant

So in practice, it's not too useful, but it helps when first defining the determinant

[tranquil pine]

i think its hard to define the determinant as the scaling factor, like, how do you define the scaling factor then?

[pale hatch]

like this?
https://math.stackexchange.com/questions/668/whats-an-intuitive-way-to-think-about-the-determinant

[neon slate]

i don't know that there's any "this is what the determinant is and now it's 100% clear" or if there is please share with me as well. My answer would be that it's great that you are already looking at different interpretations of it and trying to tie them together and that intuition of where it's relevant comes from doing problems that involve determinant to kind of get an idea of various other concepts it ties into

[silk saddle]

I'd love to see it too

[tranquil pine]

yes

[silk saddle]

wow that is cursed

the MSE user is talking to themselves

[neon slate]

this is a pretty good one

[pale hatch]

If I interpret the determinant as the signed volume then this should represent the volume made by the basis vectors
So this identity determinant = 1 would only really be true in specific cases (for example an orthonormal basis) so the 2nd and 3rd interpretations wouldn't exactly work with what the determinant is actually defined as right

[pale hatch]

yeah thinking of the determinant like this
what would its sign represent?

[pale hatch]

actually by this definition a change of basis would change the determinant

which seems kinda weird

for something that represents volume / something geometric?

[neon slate]

hm best i can think of it is almost like every quadrant \ octant (depending on the dimensions youre considering) etc belongs to a certain one of two parities

[tranquil pine]

a positive sign could represent an even number of flips and a negative sign an odd number of flips

[neon slate]

so if you're in the + + + octant, your determinant is +

and every time you cross a plane you flip the sign

[pale hatch]

ah that makes sense

[neon slate]

so how many flips of the sign does it take to reach that quadrant \ octant whatever from the + + + one?

but extended up to n dimensions

i dunno if that makes sense lol, not sure how to interpret that for a 1x1 matrix where the value of the determinant is just the value of the single entry itself 🤔

i guess it's just rhe + or - part of the number line actually

[pale hatch]

yeah in the 1D case + and - octant equivalent would just be what side of the line you're on

[neon slate]

hm i have an idea...

in 2d would it work to interpret the sign of the determinant as whether the sum of the column as vectors has a positive slope or not?

or is that complete gibberish

😄

[pale hatch]

which vector's slope?
aren't there multiple vectors as input?

[tranquil pine]

i think .. but im not sure, if the determinant is positive, you can represent the transformation just by using composition of scaling (with positive scalings) and rotation transformations alone, but if the determinant is negative you also need one reflection transformation, is that true?

[neon slate]

yeah hrm it's just some intuition im getting but dont think im expressing that properly \ correctly, wish there was ssome online tool where i could draw two 2d vectors and it would spit out the determinant for a matrix using the vectors as rows \ columns

[neon slate]

interesting

if youre looking at transforming a matrix step by step through row operations, would a reflection operation involve multiplying a row by -1 ?

and scaling = multiplying a row by a positive number?

and rotation = switching rows?

because then you could think about how you need to go about step by step through row operations to obtain a certain transformation from the identity matrix \ transformation

and yeah if you don't need to multiply any row by a negative number, then the determinant would remain positive since it's linear in each row

[pale hatch]

do elementary row transformation even have an intuition?
I can see why they work because from definition of matrix multiplication
$AB = C \implies \sum_k A^i_k B^k_j = C^i_j$
since the row index corresponds to A doing row transformation on A does it on C as well
I never thought if it had any meaning

[soft zealot]

Frisk17

[neon slate]

yeah i think they correspond to exactly what @tranquil pine said

scaling \ rotation \ reflection

now my next question is how do you visually interpret the rows that make up a matrix as vectors

because it's pretty clear what happens to vectors when you scale \ rotate \ reflect them but not sure about how that affects the matrix as a whole when you are doing it to an individual row

[pale hatch]

not completely sure but since each column represents what the basis vector of a vector space gets transformed into
each row represents what each basis covector of the dual space gets transformed into

on applying the linear transformation

the matrix represents

[neon slate]

basis covector of the dual space
can you clarify this a little bit

its been a while since ive taken linear algebra

a lot of cobwebs in my brain

but i like where you are going

😄

[pale hatch]

The vector space of all linear functions that map vectors to scalars (aka covectors / 1-form / linear form) on a vector space is called the dual space of that particular vector space
The basis vectors of this vector space are called the 'dual basis' defined by $\epsilon^i(\vec{e_j}) = \delta_{ij}$ where e is the basis vector of the original vector space and epsilon is the dual basis vector

Now since linear maps are just (1,1) tensors they can take in a vector or a covector and transform it into a vector or a covector
That's why I think you should be able to interpret the row as transformed covector components buuuut I don't know if it helps here at all

Disclaimer: I don't understand this topic well myself and have just heard some stuff from this video series https://www.youtube.com/watch?v=LNoQ_Q5JQMY&list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG&index=6

[soft zealot]

Frisk17

[neon slate]

hm yeah i semi understand that \ semi dont

anyway i do need to get going but good discussion, always loved to think about linear algebra, i did forget a lot of it 😛

[pale hatch]

well thanks a lot everyone
I think I understand determinants a little better now

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[pine citrus]

When you use L'Hôpital's rule I noticed that in this example the result ended up being the highest exponents fraction... Is this always true? In which case I don't need to do like 4 derivatives to find that out?

[hybrid heath]

If you're unsure, you can try proving it

As a hint, consider induction proof

[pine citrus]

Got it ty

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[vital crag]

just fyi

https://www.storyofmathematics.com/limits-of-rational-functions/

[fathom walrus]

Good thinking, Stephen

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[tough raft]

Which statistical test would we use to compare our algorithms?

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[heavy laurel]

I’m confused on a problem. I need to know which of these graphs represent y as a function of x

[high beacon]

The easiest way to visually verify that something is a valid function is with the vertical line test

If you can draw a vertical line ANYWHERE on the graph and have it only intersect once, then it's a valid function

This works because you're basically checking that every x only has one corresponding y

[heavy laurel]

So the vertical line test works in checking if these graphs represent y as a function of x?

[high beacon]

exactly

and be careful on the first one with that dot

i almost didnt even see it

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[rocky wind]

Can I have a hint of where I would go from here

[tranquil pine]

divide both sides by A^(-2)

[rocky wind]

Hello mate back at it

Ok let me try that

[soft zealot]

Toby

[tranquil pine]

use power laws

[rocky wind]

Very solid idea, was too tired to spot that

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[rocky wind]

Could I just sqrt 50 by 8/5 from here? @tranquil pine

Wrong as

Ss

Don’t mind the bottom line

[tranquil pine]

what's this math?

[rocky wind]

It’s some logarithm homework I’m doing that doesn’t seem to involve logarithms

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[tidal stratus]

<@&286206848099549185>

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[harsh citrus]

Hello!

[reef bolt]

you beat me to it lol

[harsh citrus]

Can anyone give a hint on how to solve this? I know the fraction it is getting smaller.

I can't find the pattern

[desert mantle]

1,3,6,10,15,21,...

what are the differences

[harsh citrus]

2 3 4 5 6

OHH

how you do that so quick omg

[desert mantle]

well the numbers are pretty easily recognizable

called triangular numbers btw

[harsh citrus]

ok thank you very much

how do I end chat?

[desert mantle]

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[feral siren]

Can someone explain ii to me please

[nocturne elbow]

What part of it

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[stray stump]

SHow that if $(a_n)$ is not bounded, then it has a monotone subsequence

[soft zealot]

KN

[stray stump]

To prove this, can I come up with an algorithm to generate the subsequence?

[sturdy cypress]

what's it even about

[stray stump]

This question

[vital crag]

yea a construction is sufficient

[stray stump]

okok

So wlog assume the sequence is unbounded from above.

[silk saddle]

that follows incredibly fast

[silk saddle]

the WLOG here needs to be justified a bit more

I can follow your argument though

[stray stump]

Choose the first term of the subsequence as $a_{n1}$ to be the first term in the orginal sequence $a_n$ such that it is greater than 1. Then choose $a_{n_2}$ to be greater than $a_{n1}$, etc

[soft zealot]

KN

[stray stump]

why's that?

i thought wlog is just there to take care of similar cases?

[silk saddle]

depends on what your prof wants really

The case IS similar

I completely agree with you

[stray stump]

okok, im just asking bc i never really learned how to use wlog. I just dont wanna say the wrong thing lol

[silk saddle]

I agree the other case is similar but

can you provide it as well

(esp if your prof wants it)

[stray stump]

sure

lol im sus now, is there something that might go wrong??

ill write the other case out as well

lol

tyty

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[reef frost]

this is the problem that I'm stuck on

it should be a pretty simple mixing equation, but for some reason my answer is incorrect

I even tried putting it in wolfram, so it has to be something wrong with my setup

that's the diffeq that I solved, and got an answer of 1.79 minutes with

so basically what I'm asking is is there something wrong with the equation I used to set up this problem?

never mind im extremely silly. should be 50 + t in that denominator

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[reef frost]

1,2,3,6,8 are all wrong

if you're reflecting a point across an axis but its already on the axis, then it's just in the same spot

like in 8, C gets reflected to the same spot

as for 10, it's the exact same process for all of your other ones. Reflect each point across the x axis. you're just going to have more overlap

easiest way to check if you reflected a point correctly is to make sure that the old point and new point are both the same distance from the axis you reflected it across

(so for 8, your old C is 0 units away from the x axis, but your new point C' is 1 unit away when it should be 0)

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[reef frost]

@tranquil pine so for 8, your point C is already on the x axis

so its reflection is also on the x axis

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[placid rapids]

which regular N-gons can be decomposed into a finite set of non-overlapping parallelograms? solutions for the square and hexagon are trivial, obviously there is no solution for the triangle, and I think I've found a solution for the octagon

wondering if there is a systematic way to construct a solution where one exists... I am particularly interested in the pentagon and heptagon

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[dreamy hinge]

Hi,
I have $$ f: A->B $$ a surjective mapping between to sets. I have $$ f^{}: P(B) -> P(A) $$ with M gets mapped to $$ M^{-1} $$
It should follow that $$ f^{} $$ is injective.

In general, the function f* maps a coset from the powerset B to its preimage, right?

Now if f* where not injective there would exist a $$ f^{} (M) = f^{}(B) $$ with $$ M =/= B $$.
So I have $$ f^{-1}(M)=f^{-1}(B)=X \in A $$ and I have that M and B are not equal and I have that f is surjective, so I know that every $$ b \in B $$ has a non empty pre-image.

[soft zealot]

aabb

[dreamy hinge]

Is the Problem now that there would have be some element from x that would map to too different objects?

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<@&286206848099549185>

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[dreamy hinge]

.reopen

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✅

[silk saddle]

"coset"

,tex \factoid original

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@dreamy hinge Has your question been resolved?

[dreamy hinge]

sorry, subset. Translation error

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[polar juniper]

Hello my name is Jumger and I need some help in these two problems. I was able to solve them, however I felt like the answer for number 3 felt arbitrary and number 4 too simple to be true (considering the points). Maybe its a mind trick or I am just doing it wrong.

[polar juniper]

Heres my solution and answer for number 3

and as for number 4. The measurement of angle A is 35 degrees. Because 180 = <A + 85 + 60

[warm frigate]

both seems right

[polar juniper]

Ohh so as far as anything, there isnt any alternative answer/way to solve this?

[warm frigate]

there's plenty of alternative ways

but your solution seems to be the quickest

[polar juniper]

I see... Thank you very much for the help sir @warm frigate :)))

.close

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[granite grove]

My name is Arka and I need help for question no. 2 and 3. I really appreciate any kind of help 🙏

[neon slate]

well if you try to multiply the I_(2k+1) and I_2k using the definitions on the top

youll notice that the first has all even factors on top and odd factors on the bottom, and the second one vice verse, so which of those factors can you cancel out and which remain?

[granite grove]

I see.... thank you so much for the reply 🙂

[neon slate]

kind of a pain to write it all out in chat but you can see these ones all correspond

if you think of those two expressions being multiplied together, the green cancels with the green etc.

and everything in between since its every odd \ even number down to 3/2

so all you're left with on the first one i guess is 1 / (2k+1) * pi/2

[granite grove]

what about the 3rd question, I_2k-1 ?

[neon slate]

well youll have to use the pattern given and figure what that big product would look like

I_2k starts with 2k on the bottom and 2k - 1 on top right (so matches the subscript of I on the bottom and subtract 1 from it on top)

I_(2k+1) starts with 2k+1 on the bottom and subtract one from that on top, so what would I_2k-1 start with?

[granite grove]

2k-1 on the bottom and 2k on the top ?

[neon slate]

remember top first numerator is 1 LOWER than the first denominator for all others

so just think (2k-1) - 1 = ?

[granite grove]

so 2k-1 bottom and 2k-2 top ?

[neon slate]

$I_{2k-1}=\frac{2k-2}{2k-1}\times\frac{2k-4}{2k-3}\times\dots\times\frac{4}{5}\times\frac{2}{3}$

[soft zealot]

Sooshon

[neon slate]

right and then has every even number thats lower on top as a factor and every odd number thats lower on the bottom

so now compare that with I_2k and see which factors don't cancel out and which do

[granite grove]

so its 1/2k

[neon slate]

yep

[granite grove]

Thank you so much for the help. Been struggling since yesterday and i can figure it out now. Thanks again mate :))

[neon slate]

welcome

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[stone cedar]

hello, how can I solve this problem?

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@stone cedar Has your question been resolved?

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[vocal atlas]

my textbook says this but i dont understand

i put in calculator 0.5 and it works too

[fluid sky]

the domain must be from -0.8 to infty

[vocal atlas]

oh wtf

i misread

yo

the way to test this is only with calculator?

or im expected to know logaritms?

is there more efficient way than just typing in calculator?

[fluid sky]

u must know that u cannot find the logarithm of a negative number

[vocal atlas]

oh

[fluid sky]

so whatever u have inside a log( ) must be +ve

[vocal atlas]

so 5 * 0.8 = 4

[manic herald]

and that you can find the logarithm of all positive numbers

[vocal atlas]

but wait

if 0.8 is 4 that would mean log 5 (0)

which is possible

would that mean 0.8 is [0.8, infinity>

[fluid sky]

log 5 (0) is not possible

[vocal atlas]

oh

[fluid sky]

what is a number that you can raise 5 to the power of, to get 0?

[fluid sky]

there is no such number

[vocal atlas]

fr

[fluid sky]

so there is no log5(0)

[vocal atlas]

very nice!

but wit

wait

the domain is from - 0.8

but wouldnt then 0.8 positive be also imposible?

oh no

[fluid sky]

+0.8 is possible

5 * (0.8) + 4 = 8 and 8 is +ve so yeah

[vocal atlas]

@fluid sky can i apply lhospital here?

oh it works

.close

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[severe abyss]

help

[severe abyss]

cmon

anyone\

dm me if you can help me with graphs and gradient

[amber holly]

How can anyone help you if you don't post a question

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@severe abyss Has your question been resolved?

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[tranquil pine]

well for c f(x)=1

f(0)=1

[onyx peak]

He can speak

Example?

Oh right, wonderful proof by counterexample

Oh, yea ofc

[neon slate]

this guy is trolling in multiple channels

someone needs to ban him =\

[onyx peak]

Damn that's awesome :0

I need help plz, could you be my teacher?

[tranquil pine]

okay okay

[onyx peak]

Pre-university maths tutor?

[tranquil pine]

how will c to a give me estimate of 5

[worldly vale]

I feel bad for the people you tutor

[tranquil pine]

how

f(1)=3

f(0)=1

[onyx peak]

lol

I just needed help with some trig

[tranquil pine]

dude

[worldly vale]

<@&268886789983436800> troll

[onyx peak]

Could you pls tell me what's value of this at s=2?

I am really bad at this stuff

pls

[tranquil pine]

<@&268886789983436800> ^

[worldly vale]

you've just come in and spouted nonsense and been insulting to people, do it elsewhere

[vital crag]

it's just chatgpt trained on 4chan

[opaque ember]

ty

[neon slate]

really it's a bot?

[onyx peak]

He seemed really good. He could earn good money by solving millenium prize problems :( I was just going to introduce him to riemann hypothesis

[tranquil pine]

so how will i find f(-1)

[onyx peak]

Estimate

You can't find it exactly

[tranquil pine]

ill go with -.25

i thought it was supposed to be exact

[onyx peak]

Reasonable estimate

For c) there are 2 solutions btw

you should list both of them, did you?

[tranquil pine]

yes

thank you easier than i thought

i can't believe that was a chatgpt bot

"math is not always right"

mayb it was just a joke

4chan troll

[onyx peak]

I can't believe it too, I've never seen so toxic community as was that guy

[tranquil pine]

bizarre

well thanks

.close

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[ocean linden]

I'm not sure how to go about this probability problem:

In a bookstore, the "Mathematics" section contains six equal books on
statistics, seven equals on analysis, four equals on geometry and three
equal on trigonometry, filed on one bookshelf. The copies
are arranged according to the arrangement "analysis," "statistics," "geometry" and
"trigonometry." A job student is tasked with taking all the books from the shelves,
take them, dust them off and then, after polishing the bookshelf, put them back
However, he randomly places the books back. In how many
ways can the person in charge of the science department from the
bookstore recover the math books?

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@ocean linden Has your question been resolved?

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[vocal atlas]

Df = R / {1} right?

[versed crater]

what is Df and what is R and what is {1}

[vocal atlas]

Domain is all real numbers except 1?

[echo mason]

Yes.

[versed crater]

i've never seen it be written like that but yes

[vocal atlas]

but on graph it show like this?

[versed crater]

it's just missing a point

desmos doesn't show it

[vocal atlas]

I calculate that vertical asymptote is -2

but on my online homework they say 1

[versed crater]

share the desmos

[versed crater]

show your working for this

[vocal atlas]

they say vertical asymptote must be 1

but I calculate with limx-->1^+ = -2.001....

[versed crater]

why do you think the vertical asymptote is at -2?

[vocal atlas]

lim x-->1^- = -1.9999

because i calculate domain is cant be 1 right

and i test for approaching of domain from right and left side

is this the method?

[versed crater]

hold up

the domain doesn't include 1

right?

[vocal atlas]

yes

[versed crater]

that's because -2x + 2 cant be 0

let's have a look at this part

when x is very close to 1 but less than 1, you have -1.9999999 + 2

which is 0.000000001 ish

very small positive number yeah?

[vocal atlas]

yes

[versed crater]

so the function is the top divided by a very small positive number

so it's massive

[vocal atlas]

hmm wait

[versed crater]

f(0.99999999999) is very very positive and big

[vocal atlas]

i mean it was result of whole function

not just the numerator

when i put value of 0.99999 or 1.000001

as x

[versed crater]

show me this

,w f(x) = (2x^2+2)/(-2x+2), solve f(0.99999)

[soft zealot]

Results provided by WolframAlpha

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

Requested by Frosst#1111

[chrome cove]

Isn't the numerator supposed to be 2x² - 2?

[final saddle]

@vocal atlas Has your question been resolved?

[chrome cove]

[vocal atlas]

im back i was mke coffee

[vocal atlas]

I get result -1

you put wrong

numerator is -2

.close

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[flat nebula]

Hey there, I'm stuck on this one question that is asking about quadratics and graphs and I just have no idea what I'm doing, I tried my hardest to figure it out but I just cant

[flat nebula]

The smoothie chain makes multiple $0.15 increases to the average prices of their smoothies. The table shows the average profit of the chain compared to the number of price increases. The data models a quadratic function.

Oh I did this wrong didnt I

Ope, yep I definitely read the how to get help chat wrong

I think it should be fine

Use the data in the table to answer questions 3-5.
3. Use technology or hand calculations to determine the equation for the quadratic function modeled by the data in the table. Show an image of your final answer. (10 points)

4. Using the equation from question 3, determine the maximum profit. (5 points)
5. Using the equation from question 34, determine how many price increases will cause the smoothie chain to have zero profit. (7 points)

Really its number 3

Increases (x) Profit (y)
25 204
60 285
105 368
132 384
155 376
172 356
200 318
254 185
290 70

Im gonna start over...

.close

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[sonic crystal]

How would I do this ?

[normal hill]

hm

maybe make 3sqrt(3) into sqrt(27)

so a is 27

and b is 3

[sonic crystal]

Is there a specific reason we choose 27

[normal hill]

yEa

We have $3\sqrt3$

[soft zealot]

Mortta

[normal hill]

to put the 3 outside back into the square root

we times by 3^2

so we get $\sqrt{3\times 3^{2}}$

[soft zealot]

Mortta

[normal hill]

which is sqrt (27)

[sonic crystal]

Ohh

Okay

[sonic crystal]

So we don’t do anything to the B?

Just leave is as 3?

[normal hill]

well yea

because