help-23

[visual swift]

@raven vessel

[safe radish]

@visual swift Has your question been resolved?

[safe radish]

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[steep magnet]

-3x - 3 = x/3 - 29/3

x = 2

(2)/3 - 29/3

y = -9

[visual swift]

Isn’t it -x/3

[steep magnet]

But I need to get the perpendicular line no?

[visual swift]

Oh yea mb

[steep magnet]

sqrt((3 - 2)^2 + (0 + 9)^2)

[visual swift]

What are the two points of intersections

[steep magnet]

=sqrt(82)

Which is also wrong

🤔

[steep magnet]

(2, -9) and (3, 0)

Oh wait its supposed to be -3

which gives sqrt(106), which is also wrong 💀

[thin bridge]

still wrong

show how you're getting that second pount

[steep magnet]

Ohhhhh

Its supposed to be (0, -3)

[steep magnet]

y intercept of line l

[thin bridge]

yeh, you mixed up you're x and y coords

[steep magnet]

Finally hahaha

[steep magnet]

Yep sooo many silly mistakes

But thanks guys!

❤️

.close

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[celest dune]

hi i need some help, I think the answer for a is 0 since we're seemingly not moving in the z direction but im not sure since z isnt provided anyway
for b im lost!

[light shoal]

are these 2-dimensional vectors or 3-dimensional? if 2, then there is no z direction

[celest dune]

yea thats why im not sure the answer is 0, but i dont know how to tell if its pos/neg if thats the case

its an xy plane so im under the assumption z exists but is not provided

[light shoal]

well it appears that at any point (x,y), the vector field is horizontal and its magnitude doesn't change as you move horizontally

so $\frac{\partial}{\partial x} F_x = 0$

[flat frigate]

Bungo

[light shoal]

and there is no y or z component, so those partials are also zero

so the divergence is zero

[celest dune]

makes sense

i was thinking the curl was clockwise but thats more of a guess

[light shoal]

probably a good idea to reason from the formula:

F_y and F_z are zero, so the i component is zero

F_x doesn't vary in the z direction (as far as we know) so the j component is zero

so that just leaves the k component

F_y is zero so you're just left with :

$-\frac{\partial}{\partial y}F_x \textbf{k}$

[flat frigate]

Bungo

[light shoal]

so examine how F_x varies as you change y

you can also argue intuitively, imagine that the vector field represents the flow of some stream of water, and you take a small stick and put it in the water at some point, which direction will the stick rotate?

[celest dune]

wouldn't it not rotate and just follow the stream

[celest dune]

I asked for clarification and this is a 2d vector field, so z is simply not there

that does mean that our previous answer of 0 was correct right

[safe radish]

@celest dune Has your question been resolved?

[celest dune]

this would mean Fx is increasing with y in the upper half plane and decreasing with y in the lower half plane, so ∂F_x/∂y would be positive right

and since in that message, -∂F_x/dy k = the curl, a positive ∂F_x/dy means the curl is negative which is clockwise?

[celest dune]

<@&286206848099549185> hi! would love if someone could double check my answer before I submit! I have about 15mins until this hw is due

[white umbra]

Don't troll

Yea sure I can look

[white umbra]

Yup

As Bungo said, imagine the vector field is the flow of some water. You can think of divergence as "water sources" or "water sinks". If there's no sources or sinks where water is magically appearing or disappearing, then the vector field has zero divergence.

And curl is how much the water causes something to rotate if it got stuck there, like a whirlpool.

[celest dune]

great, thanks! i put down those same explanations with 0 and clockwise as answers

[safe radish]

@celest dune Has your question been resolved?

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[jovial sentinel]

need an explanation on why +c is needed in integration

[jovial sentinel]

or link a video that explains it well

[devout shale]

What is the derivative of 5x?

This will help explain why the +C is needed

[jovial sentinel]

still not sure

its 5

using power rule

[devout shale]

and what is the derivative of 5x+11?

[jovial sentinel]

16 im guesisng

only started learning this today

[devout shale]

No, the derivative of a constant is 0

so the derivative of 5x+11 is still just 5

[dull sequoia]

The (indefinite) integral of a function returns a family of functions

[devout shale]

bro

overboard

[fathom jewel]

bro

[devout shale]

read the room

[white vale]

C'mon man

😔

[jovial sentinel]

oh right

[fathom jewel]

Sam just learnt it

[devout shale]

so if I ask you, what is the derivative of 5x+C, where C is just any constant

what is it?

[jovial sentinel]

0

[fathom adder]

A function has infinite antiderivative since the derivative of a constant is 0 so we add that +C to cover up all possibilities

[jovial sentinel]

or like

[devout shale]

not the derivative of C, of 5x+C

[devout shale]

bro

[jovial sentinel]

yeah 5

[devout shale]

exactly

so if we integrate 5

we want to know

taking the derivative of what function gives uf 5

but as you've just seen

possible answers are 5x, 5x+11, 5x+89

or really just 5x+C

where C is any constant

so this is why we add the +C

because there is more than one function that after differentiating will give you the function you are taking the integral of

[fathom jewel]

what about 6x

[devout shale]

its derivative would be 6

[fathom jewel]

you only proved it for 5x

[devout shale]

@stable estuary

[jovial sentinel]

ok yeah i get it

[frank horizon]

yeah austin

incomplete proof 😔

[jovial sentinel]

thanks

[devout shale]

np

[jovial sentinel]

.close

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[dull sequoia]

When you do an indefinite integral you’re asking “what functions is there, when i differentiate, gives the integrand?”

[fathom jewel]

i dont have a family

[dull sequoia]

So it gives you all the functions that are offset by some constant as well

[fathom jewel]

offset is a rapper

[dull sequoia]

Since their tangent slopes are the same at every point

[devout shale]

The procedure of indefinite integration encompasses the identification of an equivalence class of antiderivative functions, each member of which, under the differentiation operator, yields the specified integrand. This equivalence class is distinguished by the presence of an indeterminate constant of integration, a consequence of the derivative operation's inherent insensitivity to constant terms. Thus, the resulting family of functions, each differing by an additive constant, possess isomorphic tangent vectors at every locus along their respective manifolds, signifying homologous first-order differential properties. This invariance in their derivative spectra underscores a uniformity in their infinitesimal displacement vectors, in strict accordance with the tenets prescribed by the fundamental theorem of calculus, thereby elucidating the intrinsic structure of the antiderivative's solution space.

[empty gyro]

[rustic goblet]

[white vale]

I like your pfp

[safe radish]

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[twin prawn]

how tf do u find angle b

[quartz egret]

just 180-angle a-angle c

[twin prawn]

why 180?

[quartz egret]

cause it is a straight line

[twin prawn]

ah

[quartz egret]

the angles are all on a straight line

[twin prawn]

angle b isnt

its two rays technically

oh wait nvm

holy god

[twin prawn]

so essentially a + b + c = 180

cause of the straight line behind angle b

[quartz egret]

yesss

[twin prawn]

24 i feel like has something more deeper than that fsr

[quartz egret]

nah I don't think so

[twin prawn]

so it is what it is

[quartz egret]

yup

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[mortal rock]

Can someone look over my work and tell me if i did it right?

[hard crest]

answer 1 doesn't make sense (and you never said which one was bigger)
answer 2 is almost right but your imprecise handwriting has made you lose a factor of 1/3
the rest are right

answer 4 would benefit from writing out log7 + log2 + log2

[terse lichen]

question 1 is actually quite easy to approximate which one is bigger

[mortal rock]

its log3 30 right?

Cuz both values are bigger

[hard crest]

log2(2) is the same as log5(5)

[mortal rock]

wait sorry what did i mess up on 2?

[terse lichen]

nope

[mortal rock]

wait how do i figure that out then?

[terse lichen]

(hold on lemme check so im not talking out of my ass)

[visual swift]

yea it's not

[hard crest]

i can't quite tell where your error is because of your handwriting so consider how to make that more legible. it seems like you dropped a factor of 1/3 somewhere

[hard crest]

use estimates, log2(17) is close to a whole number

[terse lichen]

yes log_3 (30) is smaller

17 is greater than 16

log_2(16) is 4, thus log_2(17) is greater than 4

for log_3(30), break 30 into 3 * 10

then use the same logic

[hard crest]

or just see that 3^4 is 81 which is way bigger than 30, so log3(30) has to be less than 4

[terse lichen]

||10 is greater than 9 and less than 27, log_3(9) is 2 and log_3(27) is 3, thus 2 < log_3(30) < 3, then 3 < 1 + log_3(30) < 4 ||

[mortal rock]

how does this look?

[hard crest]

fine

[terse lichen]

add the logs though

log_2(2⁴+1) ≈ 4

[mortal rock]

k i added it

I have a few more pages if you guys dont mind checking them over? Im near the end of my course and every mark counts

[hard crest]

did you fix answer 2?

[mortal rock]

oh right i need to fix that one up

wait i dont see the issue? I used the 3 in the root to get the 1/3

where is the problem?

[hard crest]

where'd the 2 go?

[mortal rock]

oh yeah

I have no clue lol

[hard crest]

mmk well then it sounds like you need to rewrite it so you can keep better track of your things

[mortal rock]

OH ok i remember where it went

i take the +2 out making log_2(2)

and log_2(2) = 1

[hard crest]

how did you do that?

[mortal rock]

isnt that the sum rule of logs

[hard crest]

,tex .log rules

[flat frigate]

hayley 🥥 🌴

[mortal rock]

the first one

log2(A^4 ^3root( 3x + 2))

Becomes Log2(A^4 ^3root3x) + log_2(2)

[hard crest]

how?

like

you just pulled the 2 out from several levels

log2( a^4 cbrt(3x+2) )
= log2(a^4) + log2( cbrt(3x+2) )

[mortal rock]

log2(A^4 cbrt(3x) + 2) - log2Q

log2(a^4 cbrt(3x)) + log_2(2) - log2Q

[safe radish]

@mortal rock Has your question been resolved?

[white yoke]

How log2(A^4 * cbrt(3x+2)) can be equal to log2(A^4 * cbrt(3x)) + log2(2)?

It is not true

[mortal rock]

ohhhhhh i thought it was log2(A^4 cbrt(3x) + 2)

shoot

[mortal rock]

ok i fixed it

jsut added the 2 back in

[white yoke]

What do you have like answer then?

[mortal rock]

I typed it cuz my writing sucks

[white yoke]

Yep, that's it

I think you said you needed help for other pages right?

[mortal rock]

yeah im just finishing it

[white yoke]

Everything is good

Just, the answer at 3) can be simplified further

Also, while the answer for the x-intercept is good, I don't understand well the step before the answer. Is it supposed to be -1 - 1/9?

[safe radish]

@mortal rock Has your question been resolved?

[mortal rock]

its x = -3^-2 - 1

[white yoke]

Okay, then it's good

[mortal rock]

cool now just one page left

sorry 3 left

Im not sure how 4 works

[safe radish]

@mortal rock Has your question been resolved?

[safe radish]

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[safe radish]

@versed ermine Has your question been resolved?

[versed ermine]

<@&286206848099549185>

[safe radish]

@versed ermine Has your question been resolved?

[versed ermine]

<@&286206848099549185>

[safe radish]

@versed ermine Has your question been resolved?

[velvet nebula]

do you understand the question

[versed ermine]

No

[velvet nebula]

okay firstly they use the notation $K_{k=1}^n[a_k:b_k]$ for that continued fraction thing

[flat frigate]

Element118

[velvet nebula]

I think the trick to the last question is showing that one side is bigger

then proving by induction

okay not just bigger, but bounded in some sense

[versed ermine]

He wants us to prove him wrong

[velvet nebula]

and then proving this bound by induction

do you see how it is clearly true for n=2?

[versed ermine]

Yes

Show that the bottom equality cannot be satisfied for any value that the numbers b_1,b_2...b_n R^+ can take.

[velvet nebula]

my guess is we have to show this
$$K_{k=1}^n[1:b_k]<K_{k=1}^n[a:ab_k]<aK_{k=1}^n[1:b_k]$$

[flat frigate]

Element118

[versed ermine]

You figure it out, how do you understand? I don't know English, I'm looking at the translation, it's a waste of time.

[versed ermine]

b_1 b_2... b_n will not provide for any value

In the equation below

[velvet nebula]

you have to show for all positive $b_1,\dots,b_n$

[flat frigate]

Element118

[versed ermine]

Yes

None of them were provided

[velvet nebula]

you need your argument to work no matter what positive $b_1,\dots,b_n$ you get

[flat frigate]

Element118

[velvet nebula]

do you know how to do mathematical induction?

[versed ermine]

No I want help

[velvet nebula]

okay so the main idea of mathematical induction is you show for some n, and you show if it works for m, then it works for m+1

so you get to climb up to any number you want

it works for 10
since it works for 10, it works for 11
since it works for 11, it works for 12
since it works for 12, it works for 13
... and so on

the aim is to induct on n

[versed ermine]

I understand

So, can you solve this question with this method?

[velvet nebula]

yeah you can

but I'm not going to solve for you, the point of asking here is for you to learn

[versed ermine]

It is important that you need to solve

We are on summer vacation, I am spending my time on these.

Don't worry, I will learn

[velvet nebula]

on this server, it is important for you to learn

[versed ermine]

Yes, I just came here and found it very useful.

[velvet nebula]

firstly, i kinda dislike the notation because the definition is not easily recursive

so I would propose using a different definition, since it would make it easier to do the proof

I propose this definition
$${K'}{k=1}^1[a_k:b_k]=\frac{a_1}{b_1}$$
$${K'}{k=1}^n[a_k:b_k]=\frac{a_n}{b_n+{K'}_{k=1}^{n-1}[a_k:b_k]}$$

You should be able to see how to translate between that definition and this definition

[flat frigate]

Element118

[velvet nebula]

i simply reversed the order of the indices

[versed ermine]

Okey

[velvet nebula]

this makes it much easier to induct

because you can see how the n case is built from the n-1 case

what is the base case where you start mathematical induction?

[versed ermine]

One min

K' Why did you take the derivative?

[velvet nebula]

that is not derivative

that is just saying "something else other than K"

you can notate it differently if you want

[versed ermine]

Oh i understand

Okey

[velvet nebula]

this is the main idea of the proof

it's mildly challenging if you haven't spotted this idea

[versed ermine]

I notice on paper

OK, how can we find evidence of b_1.. b_n from here?

[velvet nebula]

mathematical induction is different from inductive inference

mathematical induction relies on solving the base case, and showing you can go upwards

[versed ermine]

Will mathematical induction be used in this question?

[velvet nebula]

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

[velvet nebula]

It's a relatively easy way to write out the argument

[versed ermine]

Oky

How do I do it next?

[velvet nebula]

you said you could do for n=2

[versed ermine]

I didn't say anything, I know as much as you say.

If n=2 is provided, b_2 is also provided

b_2 should not be provided

[velvet nebula]

what do you mean by "b_2 should not be provided"?

[versed ermine]

should not be provided for any value

The question wants us to show this

b_1 , b_2 ... b_n Should not be provided for any value

[velvet nebula]

if you are doing it for arbitrary b_2, it should be fine

[versed ermine]

Not just b_2

b_1 , b_2 ... b_n

[velvet nebula]

yeah, you shouldn't be assuming anything about those values while you write the proof

besides that they are positive reals

[versed ermine]

I don't know induction 😦 skip this question and ask another short question

Function

The set of non-negative real numbers R≥0 ;

f(f(x)) = |x-1|

A f:R≥0 →R≥0 that satisfies the equation Does it have a function?

[velvet nebula]

these look somewhat olympiad-level

[versed ermine]

Yes

Olympian who prepared the questions

[velvet nebula]

try evaluating some things

1 -> ? -> 0 -> ? -> 1
1-eps -> ? -> eps -> ? -> 1-eps (for 0<eps<1)

3 -> ? -> 2 -> ? -> 1 -> ? -> 0 -> ? -> 1

-2.5 -> ? -> 1.5 -> ? -> 0.5 -> ? -> 0.5

we need to fit these chains together somehow

[versed ermine]

can you do it

[velvet nebula]

i think I might need axiom of choice

[versed ermine]

What is that

[velvet nebula]

it's a funny thing that allows you to make infinitely many decisions at once

[versed ermine]

Sht

The question seemed easy

[velvet nebula]

easy enough

just fit those chains together

there's one chain for each number from 0 to 1

[versed ermine]

There are also negative numbers in the chains

[velvet nebula]

yeah but chances are nothing should map to a negative number

especially since there are no negative outputs

[versed ermine]

Is there f:R≥0→R≥0 or not?

he asks this

[velvet nebula]

oh wait

same idea works tbh

3 4/6 -> 2 5/6 -> 2 4/6 -> 1 5/6 -> 1 4/6 -> 5/6 -> 4/6 -> 1/6 -> 2/6 -> 5/6 ->...

an example of how a chain can look like

when you match it up

oh wait I'm not allowed to fit the 0.5 chain with itself

aha

so there might really not be

and there seems to be nothing to fit with the 0.5 chain

[versed ermine]

Forget the 0.5 chain, try integers

[velvet nebula]

that's the second part?

[versed ermine]

Z+ , 0

[versed ermine]

What

[velvet nebula]

what's that

[versed ermine]

İ forgot translate

[velvet nebula]

hmm, but then there might be nothing to fit with the integer chain

because all nonnegative integers are part of the chain

[versed ermine]

Do we have to create a chain

[velvet nebula]

the chain visualises what happens when you apply f

when you apply f, you step forwards

[versed ermine]

Can you solve it?

[velvet nebula]

likely

[versed ermine]

Okay I'm waiting

Thank you in advance

[safe radish]

@versed ermine Has your question been resolved?

[versed ermine]

How's it going

[versed ermine]

.close

[safe radish]

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[keen furnace]

I can find a basis for the matrix A but I can't find a basis for S, any hints or guidance here?

[peak estuary]

what do you mean when you say you can find a basis for a matrix

T(v)=1*v is a very special type of equation. what kind

[keen furnace]

isn't it just the identity matrix

e1, e2, etc?

[peak estuary]

an equation is not a matrix, no

[keen furnace]

it's a linear transformation

[peak estuary]

what do you mean with it

[keen furnace]

Tv = v?

[peak estuary]

its not used here to define what T does

its an equation describing what v does to vectors in S

T(v)=lambda v

what is that kind of thing related to

[keen furnace]

i am extremely lost in what the second sentence is describing in the original question

are v and n just completely arbitary vectors that have nothing to do with each other?

so is the v in T(v) the same as the x in Tx = Ax

If so this is just stating that Tx = x normally but T(x) = -x if x is perpendicular to S?

[peak estuary]

if by "normally" you mean that x in S, yes

Tx=x if x in S, Tx=-x if x is normal to S

normal being another word for perpendicular and being the reason they called it n

[keen furnace]

I presume the question then wants me to put this information together to find subspace S then find the basis for S but I'm not sure how to do that first part

[peak estuary]

equivalently, Tx-x=0 for all x in S

[keen furnace]

👀

[peak estuary]

(T-id)x=0 where id is the identity matrix

aka, some matrix * x = 0

[keen furnace]

this is true because x is a multiple of both?

[peak estuary]

Tx-x = Tx-id x = (T-id)x by distributive law, yes

[keen furnace]

ok, i need to get in the habit of manipulating vectors around more like a normal equation

thank you, that helps a lot

[peak estuary]

yw

[keen furnace]

.close

[safe radish]

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[lean otter]

Find... in terms of ... and ...

[lean otter]

I have no idea how I could solve this

FUCK

[lean otter]

?

<@&286206848099549185>

[wind laurel]

!15mins

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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.

[lean otter]

I did it bc of the previous comment

[wind laurel]

sorry i would help but i was just about to go to bed cause its pretty late here...

[wind laurel]

oh ok

[lean otter]

yep, it's fine, I understand

[raven pike]

is there an explaination on how 2+2=5?

[safe radish]

@lean otter Has your question been resolved?

[granite flower]

What absen mean ? @lean otter

Just the sin value or arcsin or what

Oh just realized it

It is a * b * sin^2(theta)

You may use the sin law

[lean otter]

yepp

that is what is asking me to solve

[lean otter]

I can't

this is not that topic

[granite flower]

You didn't study it yet?

Or what

[lean otter]

I know about it, but I am catching up on the

topics I should have studied

before

bc I joined this academy two months later

in may

instead of march

[granite flower]

Hmm it would be much easier than this though

[lean otter]

I don't know

[granite flower]

What topic is that about ?

[lean otter]

Just trigonometric ratios

I

[granite flower]

Angle identities?

[granite flower]

Which is the sin law I think

[lean otter]

No

[lean otter]

If you are talking about the law of sines, no

I'll give examples

[granite flower]

I understood from the image

[lean otter]

I need to solve it like this

[granite flower]

There are some error in the bottom left corner here if you consider to fix it

[lean otter]

ok, I'll check

[granite flower]

Yeah in the triangle it should be theta - B
Not 90 - B + theta

Are you allowed to use trig identities @lean otter

[lean otter]

mm just the simple ones

but I think no

Just by definition

like csc = 1/sen

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[cedar hemlock]

do you speak spanish_

?

it's easy

you just know law of sines and this problem will die

[safe radish]

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[cedar hemlock]

that's all

[safe radish]

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[gusty vault]

hi, i need help with the following. not really sure how to go about it. thanks

[safe radish]

@gusty vault Has your question been resolved?

[gusty vault]

<@&286206848099549185> please help

[white umbra]

What rules of logic have you learned so far?

[gusty vault]

commutative, associative, distribute

and i think the complements as well

[white umbra]

Alright

[gusty vault]

so far i've applied associative rule to RHS where I get (A - B) U (A - C)

[white umbra]

Wait what

How did you get that

[gusty vault]

am i right?

[white umbra]

Well first I think you should simplify the minus signs

It tells you the formula for the minus signs

What do you get if you plug that formula into the equation?

[gusty vault]

i can't see how I can plug it into the original question

or am i missing something?

[white umbra]

For example

B - C = B intersect (complement C)

So I can plug that in:

[A \cup (B \cap \overline C) = (A \cup B) - (\overline A \cap C)]

[flat frigate]

pasooERIC

[white umbra]

You'll want to do something similar to simplify the - in the right-hand side of the equation

[gusty vault]

so would it be easier for me to simplify both sides until equal or to manipulate LHS so that it looks like RHS

[white umbra]

it'll probably be easier to simplify both sides until equal

[gusty vault]

ok let me try it now

[gusty vault]

this might sound stupid but based on this, is it fair for me to write the RHS as:

[(A \cup B) \cap \overline (\overline A \cap C)]

i was hoping it would come out on texit

$$ [(A \cup B) \cap \overline (\overline A \cap C)] $$

[flat frigate]

Epoch

[gusty vault]

but the second bracket would have an overline for all of it

[white umbra]

it's not stupid don't worry :)

[white umbra]

what you have to do is do curly braces around what you want to be overlined if it's more than one character

(and also if you do the [...] notation, you have to add slashes before the brackets so like \[...\])

[(A \cup B) \cap \overline{(\overline A \cap C)}]

[flat frigate]

pasooERIC

[gusty vault]

yes that's what i wanted

[white umbra]

Yup perfect :)

That's correct

[gusty vault]

ok let me try again

so now if i simplify that, can it be:

$$ [(A \cup B) \cap ( A \cup \overline C)]$$

[flat frigate]

Epoch

[gusty vault]

which then looks like my LHS

[white umbra]

yes! perfect :)

so let's see what rules have you used here

[white umbra]

You used De Morgan's Law to simplify this

[white umbra]

And then you used distributivity to simplify the LHS of this

And then you got that they're equal, so you're done :)

[gusty vault]

thank you so much

.close

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[gusty vault]

I'm trying to answer this question. I've written my solution but not totally confident. can someone please verify for me? thank you

[safe radish]

@gusty vault Has your question been resolved?

[gusty vault]

<@&286206848099549185>

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[lean otter]

from a pedagogical standpoint, something like "f(x) = 1/x^2 as mapping from f:R -> R" is a wrong statement right?

[lean otter]

unless we have a one point compactification of sorts?

[light shoal]

the domain is not R, since f cannot be evaluated at x=0

[lean otter]

yeah but that issue is solved with a one point compactification right?

wait i would also have to push this to the extended reals?

i think this is true

sure thanks

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[modest drift]

Ive attempted thsi question and have not gotten the answer multiple times

[leaden glade]

ok so

you wanna write it in general form frist

yes?

[modest drift]

yea

[leaden glade]

then u need to find out the coefficient of x^8 and x^10

so u wanna

write it out using

the combinatorics formula

do u know it?

[modest drift]

yup

so its nC8 * 3^8

[leaden glade]

nono

[modest drift]

and nC10 * 3^10

[leaden glade]

do u know the actual ncr formula?

[modest drift]

?

[leaden glade]

ok i think thats why

do u know how ncr even works

[modest drift]

oh the n!/(n-r)!r!

[leaden glade]

yeahhh

that one

[modest drift]

oh ok

[leaden glade]

so u wanna

put the coeff of

x^8

over

x^10

which equals

1/2

[modest drift]

yea

[leaden glade]

cos ur ratios are in

1:2

and then

i tihnk u should be good

try to solve it from there

[modest drift]

ok

i have tried with that and its still not working

[leaden glade]

it definitley works

ur probably doing a calculation error somewhere?

keep trying

[ebon yacht]

no

it doesn't work

[modest drift]

bruh

[ebon yacht]

2nC8 / 9nC10 = 1/2

[leaden glade]

it works

once u get to there

open it

[ebon yacht]

nvm it's nC8 / 9nC10

it works

[leaden glade]

yes

i know

then u open it

@modest drift keep trying

[modest drift]

ok

[ebon yacht]

no

it doesn't work

[safe radish]

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[chrome perch]

What are the domain and ranges for this thing

Function

[lean otter]

What can you put in a square root

[chrome perch]

R x R

[lean otter]

What

[chrome perch]

All real numbers

[lean otter]

Yes

No

It’s only defined for positive real numbers

If you put -5 in there you’ll get problems

Unless you consider complex plane

[chrome perch]

That’s what we’re supposed to find right

The domain and range

Well

[lean otter]

Assuming we’re in only the real plane

[chrome perch]

Domain is [0,inf)
Range is [-inf,0]

I’m confused about the range

[lean otter]

You can only put non negative real numbers in

Range is (-inf, 0]

[chrome perch]

Yeh how

[lean otter]

Basically the graph of sqrt(x) has been reflected in the x axis because of that minus sign infront l

[chrome perch]

I got [0,inf)

[lean otter]

Yes and then reflect that

Because of the - sign

[chrome perch]

Why tho

[lean otter]

This would be true if it was y = sqrt(x)

If you multiply the right hand side by -1 then all the values swap which side of the x axis they’re ok

It’s a reflection in the line y = 0

[chrome perch]

Is it not?

[lean otter]

Do not do this

When you consider the square root of something

Its likes a quadratic but you ignore half

Because otherwise it’s a many to one mapping which is not defined as a function

[chrome perch]

Because Y is negative so I can’t ^2?

I do understand the graph

But I want to know how to calculate without using graphs

[lean otter]

If you consider y^2 = x

It includes both red and blue

[chrome perch]

Uhhuh

[lean otter]

See

Whereas you only want the blue graph

[chrome perch]

Yes

But do u know how to calculate it

It just doesn’t make sense to me

Like this

This is if there is no negative in front of sqrt x

But what I found is that if there is

The range would be

The workbook I have only has answers so I came to the conclusion on my own

I don’t know if I just got the right answer accidentally or this is the correct way.

I still don’t understand how to get there

Hey

Never mind

I got it

I have it

Thank you

[safe radish]

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[steep magnet]

!status

[safe radish]

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

[steep magnet]

4

What would you rate my proof

Out of 10

.close

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[safe radish]

Please don't occupy multiple help channels.

[brazen parrot]

Is the second one inelastic because eK is not conserved?

this is what i got for after

[flat frigate]

°Jason Parker°

[brazen parrot]

um..

what..

omg is it ok for u to help me with matrices later!?

[craggy geode]

Did you take this channel already?

Sorry, Let me move to another one

[brazen parrot]

yes :P

[craggy geode]

it depends, I'm not an expert

I will help if I see your problem and I know how to do it

[brazen parrot]

its only transformations i dont get 🙁

is it ok if i Dm u later?

[craggy geode]

sure

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[hollow vector]

can anyone help me with maths

[hollow vector]

plss

[fathom adder]

Ask your question

[hollow vector]

i need help with like 2345 *23

like stuff like that

[fathom adder]

Ok

You want to multiply it ?

[hollow vector]

times it

[fathom adder]

Ye

Without calculator ?

So you take 2345 *20 and 2345 *3

And add them

For the first one you take 2345 times 2 = 4690

And 4690 times 10 is 46900

So 2345*20 = 46900

[hollow vector]

ok thnks

[fathom adder]

Then for 2345*3 its 4690 + 2345 = 7035

So 46900+7035=53395

2345*23= 53395

[hollow vector]

thnak

[safe radish]

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[next shuttle]

why is zero to the pow zero undefined and not one?

[peak estuary]

why should it be 1

why shouldnt it be 0

[fathom adder]

Well it depends in which domain of math you are

In algebra its 1

In analysis its undefined

¯_(ツ)_/¯

[next shuttle]

wdym by analysis here

like applied math?

[cunning pasture]

https://tenor.com/view/genius-smart-analyze-math-gif-13397499

[rich harness]

wha

its still undefined

[cunning pasture]

I have known it to be controversial

[rich harness]

atleast i learnt it to be undefined

[fathom adder]

Well

Ima give example

[cunning pasture]

I think we need real life examples to define its value.

For example 0!.

[fathom adder]

The newton binomial is defined in x=0 if 0^0 = 1, or the définition in series of e^x exist only if 0^0 = 1

So

[fathom adder]

It is a debate

Indeed

But by convention its mostly 0^0 = 1

[rich harness]

well you could say it is 1

[cunning pasture]

0/0 is indeterminate.

[next shuttle]

huh

[rich harness]

i mean it is

nvm my english bad

its like lim(x->0) x^x = 1

thats what i want to say

get it?

[brave wolf]

but limit of 0^x as x->0 is 0 (right sided)

[rich harness]

no it isnt?

what

[brave wolf]

for all x > 0, 0^x = 0. So the limit is indeed 0

,w lim x->0 0^x

[flat frigate]

Results provided by WolframAlpha

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

Requested by methisalwaysright

[rich harness]

i see

[fathom adder]

Well there is no consensus but 0^0 = 1 is acceptable as undefined is acceptable

[rich harness]

yes

you are right

apologies for my mistake

[fathom adder]

But if you need it for a calculation, taking 0^0 = 1 is the most common way to deal

[next shuttle]

.close

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[round canopy]

where do i even start

[safe radish]

@round canopy Has your question been resolved?

[round canopy]

<@&286206848099549185>

[rich harness]

there are 4 hemispheres

[safe radish]

@round canopy Has your question been resolved?

[safe radish]

@round canopy Has your question been resolved?

[round canopy]

btw i dont really understand this
surely a sphere being symmetrical can be split in half from infinite angles

(keep in mind im dumb)

[buoyant shadow]

It's always true

OK, I've no clue

[round canopy]

😭

[buoyant shadow]

i guessed right by accident

you draw a plane through all 3, and then there's a plane parallel to it that goes through the center

[round canopy]

wait why does this mean they always fit into a hemisphere?
sorry im not good at this stuff

[buoyant shadow]

hard to explain

the planes are parallel, so each one is entirely on one side of another

so the points are also all on one side of the second plane, so that's what we wanted

[round canopy]

so the first plane is the triangle you get when you connect each of the points?

[buoyant shadow]

yes

[round canopy]

and the second plane is the same triangle but moved in a direction

[buoyant shadow]

exactly

of the center

it's just like with a circle and 2 points

even if the points can be inside, that still works

[round canopy]

sorry so the second plane's centre is the centre of the sphere but its at the same angle and stuff
i know im kinda dragging this out but im really tired and want to understand completely

[buoyant shadow]

that's correct yes

[round canopy]

what if the first plane is already like that then

[buoyant shadow]

that's totally fine

[round canopy]

oh right ok

[buoyant shadow]

i would say that the points are in both hemispheres at the same time

[round canopy]

ahh

yeah

i think i get it now

thank you!

.close

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[visual mica]

can someone explain how they went from -24^2 - 4264 - a = 0 to 8a + 64 = 0

[rigid inlet]

the typesetting on this question makes my teeth itch

[rigid inlet]

so whoever wrote this is allergic to things like parentheses

I'm assuming what they meant to write was $(-24)^2 - 4 \cdot 2 \cdot (64-a)$

[flat frigate]

Steakanator

[rigid inlet]

this thing hopefully simplifies to 8a+64

,calc 24^2 - 64*8

[flat frigate]

Result:

64

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[whole rivet]

Im not sure how to do this

I mean, the calculations are right there but, what am I supposed to look for?

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[whole rivet]

<@&286206848099549185>

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[ionic isle]

I need help on a question however due to my school policies i am not allowed to send it so it more of a discussion, I have a 3d plane with incoming sunlight which hits a mirror located at the origin however it is then rotated to hit an object at a different point

[ionic isle]

I am given this formula the position vector of the incoming sunlight and the position vector the object it is supposed to hit

I need to find the unit normal vector of the light ray in the new position

How should I go about handling this?

[safe radish]

@ionic isle Has your question been resolved?

[ionic isle]

<@&286206848099549185>

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[solid mountain]

help probability

[safe radish]

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[tame violet]

What this supposed to be?

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[brazen parrot]

how come for 7a my textbook says the asnwer is negative

[bronze gust]

Well speed can't be negative so

[brazen parrot]

What if ur going backwards

Or is that velocity

[bronze gust]

That's velocity

Since that makes it a vector quantity

Speed is scalar

[cedar void]

going backwards is scary af

[bronze gust]

So it only represents the magnitude

[brazen parrot]

oh

[brazen parrot]

oh

ita m to the b

m to the b

m m m m m to the b

hey! im starting calculus next week

is it fun

tomorrow*

[cedar void]

it will probably be your most favourite thing

after you've studied it

[brazen parrot]

plz no probability

[cedar void]

damn, I suck at probability

[brazen parrot]

SAME!!!

[cedar void]

I think most of the humans does

[bronze gust]

I probably suck at probability too

[brazen parrot]

i almost got 100% in my test but ended up getting 77% BECAUSE OF PROBABILITY

[bronze gust]

After you learn calculus you should be able to do your kinematic physics question easily hopefully

[brazen parrot]

wow why dont they just teach calculus before this!

wow so useless

isaac newton bad

[bronze gust]

Isaac newton did calculus too😭

[brazen parrot]

oh

i hate whoever madde prbaiblity

[cedar void]

and Leibnitz too

no one gives credits to him😭

[bronze gust]

Nuh uh I like physik man more

Newtons method 🔥

[cedar void]

I am more into physics than maths too

[bronze gust]

Newtons notation looks ass though

[brazen parrot]

guys

do i need this

if i want to do electrical engineering

[bronze gust]

Idk I'm still in secondary school 😭

[brazen parrot]

hey same :P

[bronze gust]

Calculus is pretty useful in kinematics though

Speed is the first derivative of position

[cedar void]

engineering😶

[bronze gust]

Acceleration is the second derivative of position

[cedar void]

it's change in position btw

[bronze gust]

Yea

Displacement

Ig is a better term

[winged flare]

its according to cartesian conventions; your idea of "going backwards" isnt entirely wrong - left and down are considered negative; whereas right and up are considered positive

even the equations of motion are built on the cartesian convention

so if you get negative while substituting it means "in the direction which is considered negative"

here it means downwards

[winged flare]

they do

the notation dy/dx is LITERALLY CALLED leibnitz notation

but thats for another day

[cedar void]

not all of them, only some do

[winged flare]

no idea how youll feel; can say its extremely powerful though

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[west hedge]

guys

[west hedge]

furry animal

aaaaaaaaaaaaaa

aaaaaaaaaaaaaaaa

okay

I have a question about trig

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

but it is written in chinese

.close

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[daring forge]

why can we just pretend that the less than sign in an equal to sign

[thin bridge]

that isn't the full work

[bronze gust]

We solve for the x intercepts and then the expression is less than 0 between those two intercepts

If you finish the video they should address that

[desert swallow]

We aren't pretending. For a, quadratic $ax^2 + bx + c$ where $a > 0$, the range of values $x$ where it is less than zero, lies between the roots

[flat frigate]

StrangeQuarkAL

[bronze gust]

So basically -5<x<-1

[daring forge]

ok thanks

.close

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[idle hearth]

where did i do wrong?

[safe radish]

@idle hearth Has your question been resolved?

[safe radish]

@idle hearth Has your question been resolved?

[idle hearth]

i saw an approach by differentiating from the reflection formula itself, but i dont quite understand what happened in the 2nd line here

do i need to also differentiate the arg in the gamma function itself or what?

[long oracle]

Yeah its called the chain rule

so for clarity, im guessing youre confused about the ln(Gamma(1-z)) term after differentiating?

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@idle hearth Has your question been resolved?

[idle hearth]

yeahh

[idle hearth]

but actually im still confused on why mine doesnt get the same thing

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[main mica]

hi just wanted to make sure im doing this correctly, havent done parametrizing in a while. i approached this by setting x = t first, then y = 25 - t^2, then z = 1/pi arctan(t/(25-t^2)). i then said that t =! 5

[arctic locust]

You'd have less trouble writing x and y in polar form

If you take x/5 and y/5 they parametrize a circle of radius one

so why not x(t) = 5sin(t), y(t)= 5cos(t)

And it will be much easier to find z

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@main mica Has your question been resolved?

[main mica]

ohh i didnt even think about putting it in polar form

tysm

[arctic locust]

You're welcome

[main mica]

so i could just get z = t/pi

[arctic locust]

Yes

[main mica]

then the range is 0 to 2pi ?

bc the functions would cycle around that

[arctic locust]

Yes

[main mica]

youre a lifesaver ty

<3

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[brazen parrot]

what does area of a displacement time graph give?

[pliant hill]

Velocity

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@brazen parrot Has your question been resolved?

[thin bridge]

don't think it gives anything meaningful

[brazen parrot]

ahh ok

thx :P

area of a force/time graph

gives

uh

oh shiza i forgot alr

change in momentum?

.close

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[steep magnet]

https://cdn.discordapp.com/attachments/846459264162988066/1267155648722894951/image.png?ex=66a7c229&is=66a670a9&hm=a7a9e037c59b358c4c7bc812cef16a547fc15429947799743b4f4ee41906a1f3&

[steep magnet]

I thought I could solve it but I couldnt
From the previous part of this question O is at the origin, A is at (0,1), B is at (1, 1) and C is at (1, 0)

I dont see what I did wrong tho

C1 = (1/n, 0)

The slope of the line AC1:

0 - 1 = m(1/n - 0)

• 1 = m/n