help-17

[wind belfry]

if all the binary operation result give me results that are in the group it is on then it means the group is closed (if thats what its called)
I think

[silk kindle]

the result is x

[wind belfry]

okay so the definition in my book is
a binary operation on group A is a match that matches every oredered pair of data from the group A, one and only result

then I have another defintion where if every match on A is also from A then it is closed a closed binary operation

[wind belfry]

but you are saying that this defintion is part of the defintion of a binary operation?

i am looking online and you seem to be right which is against what my uni taught me lol

[silk kindle]

yeah it's weird

I mean I remember it like that

anyway, follow what your book says o what you were taught, maybe they use different words (?

[wind belfry]

literally pretty much direct translate what i wrote above

straight from the book

[wind belfry]

so by this defintion of a binary operation, would you say the first question is true and the second is false?

[silk kindle]

oh I meant that maybe their terminology is different (my english is not that good either)

[silk kindle]

yes

[wind belfry]

yea and like after this i have question where i need to say if a operation is closed(as in a*b is always in A) so idk haha

thank you for the help, the wording for some reason got me really confused on that question

!close

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[faint harbor]

Guys im stuck in this problem. Can u pls help me
Problem:
Giving ABC a right triangle in B and AB=2 and BC= 9 we have H the perpendiculaire foot of ABC .using cevas theorem what is the value of HC/HA

[vocal sleet]

@faint harbor Has your question been resolved?

[faint harbor]

No

[dreamy viper]

then click the x

[glad python]

where are you having trouble?

[faint harbor]

@glad python I didnt find the equation that i need

Cevas need 3 points but i only have 1 so how can i apply it

[vocal sleet]

@faint harbor Has your question been resolved?

[vocal sleet]

@faint harbor Has your question been resolved?

[final zephyr]

What do you mean by this

[faint harbor]

Is that we only have H in BC thats all there are two points in AB and AC

To fulfill the conditions of cevas

[final zephyr]

Well, if you don't have enough points then maybe draw some points

[faint harbor]

But where and what is thier relation

[vocal sleet]

@faint harbor Has your question been resolved?

[heavy talon]

Why do you have to use cevas theorem?

[faint harbor]

U dont

[vocal sleet]

@faint harbor Has your question been resolved?

[calm fox]

@faint harbor

nvm

[vast shale]

you can try express HC/HA as some other proportion

[faint harbor]

How

Pythagore theorem

[vast shale]

yes, that's part of it

and also consider similar triangles

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[urban obsidian]

Hi, what would the answer to this be?

is it 480?

[vast shale]

how did you reach 480

[urban obsidian]

it doesn't match your answer?

i just did 10 * 1 * 8 * 1 * 6 * 1

10 choices for first student

1 choice for second student

and so on

oh wait

these "groups" can also be in any order right?

so 480 * 3!

[vast shale]

yeah you gotta do the permutations too

[urban obsidian]

and then each element in the "group" can be permuted as well?

so 480 * 3! * 3(2!)?

[vast shale]

that seems right

wait

can all students receive the same kind of gift?

because it does not state that each "group" must have a different type

[urban obsidian]

idk

maybe

but isn't that included in our analysis?

[vast shale]

you did 10 * 1 * 8 * 1 * 6 * 1 which is not quite right to me

[urban obsidian]

you mean 10^3 instead?

[vast shale]

ye ye

[urban obsidian]

but that doesn't make sense?

oh

10 types of gifts

but what if these 10 types of gifts are 10 gifts itself

[vast shale]

then the instructions would have to clarify how many of those 10 gifts are of the same type

or else the 8 and 6 in your original calculation would be out of nowhere

[urban obsidian]

hmm makes sense

the question is weird then lol

would the answer just be

[vast shale]

it is

[urban obsidian]

10^3 * 3! * 2! then?

yk when i write it out in this way it's kinda weird because

10 1 10 1 10 1

but the "groups" i can create with this case can be different?

1 and 2 don't have to be together?

like 2 and 3 can be together instead?

[vast shale]

yeah A and B, C and D, and E and F does not necessarily have to stay together

so maybe turn 3! * 2! into 6! is better

[urban obsidian]

i think

it's just 10^3

😭

we're both wrong

lol

[vast shale]

no permutations?

aww

😭

[urban obsidian]

yeah i asked a math tutor

he said it's 10^3 lol

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[alpine mist]

After factorization(s), solve in ℝ the following equations

[alpine mist]

i did that but i dont know what to do with the rest

,rotate

[harsh canopy]

simplifly the inner bracket

[alpine mist]

wait i can just develop the 2(7x+2) ?

[harsh canopy]

yeah

multiply it

[alpine mist]

thats so easy then

idk

sometimes its illegal to do things like that

so its (5x-1)-(14x+4)

[harsh canopy]

yep and then you can simplify that further

[alpine mist]

-9x-5

[harsh canopy]

yep

[alpine mist]

i have a question

it was illegal here cause it was squared

?

[harsh canopy]

yes

[alpine mist]

i understand now thats why i didnt do it instantly

i just remembered i couldnt do it like that once

so its (2x-3)(-9-5x)

[harsh canopy]

yeah

[alpine mist]

the solutions are then 1.5 and -1.8

[harsh canopy]

sounds right

[alpine mist]

alright thanks

😄

[harsh canopy]

np

[alpine mist]

u here ? @harsh canopy

[harsh canopy]

yeah, you need something?

[alpine mist]

yeah please let me show u

[alpine mist]

i thought of doing that

but it looks so wrong with the signs

,rotate

[harsh canopy]

(x^2 - 1) is not the same as (x - 1)^2

[alpine mist]

hmmm ye

ik

i was trying to find a way to have same

between both sides

[harsh canopy]

the other bracket is (x + 1) so how does that even make it the same

[alpine mist]

ik ik

thats why i said it looks so wrong with the signs

[harsh canopy]

but you can rewrite that (x^2 - 1) correctly and it will work pretty well

[alpine mist]

but x²-1 wont be same as x+1

its not a problem?

[harsh canopy]

do you know what (x^2 - 1) factorises to?

[alpine mist]

omg but ye

x²-(1)²

(x-1)(x+1)

[harsh canopy]

yeah, and now you can do something with that

[alpine mist]

ik those things but i always miss something

cause i was focusing on something which was wrong but i tried so hard to make it work

idk

[harsh canopy]

well you now have terms that are equal on both parts, so what can you factor out?

[alpine mist]

(x+1)

common factor

[harsh canopy]

and

[alpine mist]

i should apply the minus sign on all right side no?

[harsh canopy]

oh wait, you got the (9x^2 - 4) term wrong as well

[alpine mist]

yeah

[harsh canopy]

you realise what it should be?

[alpine mist]

9x²-(2)²

[harsh canopy]

not - in from of the 9

[alpine mist]

(9x-2)(9x+2) ??

ik its not right

[harsh canopy]

9x * 9x wouldnt give you 9x^2

[alpine mist]

yeah

but isnt it a²-b² --> (a-b)(a+b)

here a is 9 no?

[harsh canopy]

a^2 is 9

[alpine mist]

ah cause there is the x

if it was 4² already written for example

it would stay as 4?

[harsh canopy]

yeah

[alpine mist]

ok i see

when there is a x after it means the number is already squared

calculated as squared i mean

idk if that sounds good lol

but i think i understand

[harsh canopy]

??

[alpine mist]

OMG

im stupod

[harsh canopy]

its just that you want (9x - 4) in the form a^2 - b^2

equate the terms

[alpine mist]

if i have 2²-4² it will become (2-4)(2+4) ?

[harsh canopy]

yes

[alpine mist]

anywyayyyyy

so its (3x-2)(3x+2)

[harsh canopy]

yeah

[alpine mist]

good ?

[harsh canopy]

i think the 0.5 should be positive but other than that it looks good

[alpine mist]

yep mb

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[solid mist]

Checking my two answers!

[vocal sleet]

@solid mist Has your question been resolved?

[solid mist]

<@&286206848099549185>

I do not want to occupy another chat, but I also came across another question on my assignment

[mild flower]

I think you're dividing by 0 slightly because of your bounds

[solid mist]

for f_X or f_Y?

[mild flower]

both of them

just needs ≤ to change to < and it's not even that big of a deal

[solid mist]

Oh for the supports! That makes sense! I think I did it with ≤ since that is how it was given to me in the original question. But, it makes since since 0 can't be in the denominator.

Why does it need to be < fir f_Y though?

[mild flower]

what's the domain of ln?

[solid mist]

*0 to +inf

OH

but since it is negative doesn't turn into -inf , inf?

But I am also bounded by my given inequality...🥲

[mild flower]

no, you're concerned about domain here not range

if we were taking ln(-y) then it'd be a bit of an issue but we have -ln(y) and all values > 0 are valid inputs for that

[solid mist]

So even with my given problem and bounds, the f_Y (y) support would still need to be 0<y ?

[mild flower]

it doesn't hugely matter since it's just one point

thinking about it some more, why are you going from y to 1 and not from 0 to y in that integral?

[solid mist]

Since y<=x<=1

It was a note I took from class and following a somewhat similar example.

[mild flower]

oh right it's triangular not rectangular

right okay because ln(y) will always be negative in that interval

[solid mist]

I will be sure to add that note as well.
Thank you Hayley!!!

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[thin root]

Let S  be the surface obtained by revolving the plane curve $2x = \sqrt{9-y^2}$ about the y-axis. Obtain a vector equation for S.

[twin meteor]

LeGM

[thin root]

I have no idea how to start this

is it like

parametrizing the surface?

<@&286206848099549185>

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@thin root Has your question been resolved?

[thin root]

<@&286206848099549185>

[supple basin]

is there more context

like what plane curve

[thin root]

huh

it's literally given

so when you revolve a curve about the y axis

it needs to be a function of y

so we have x = sqrt(9-y^2)/2

so what I'm asking is

Can I just parametrize the surface then turn those parametric equations into a vector equation?

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@thin root Has your question been resolved?

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[silk kindle]

Mmm think of it like circled with radius x 🤔. When you rotate a point around y axis, the radius of rotation is the x component of that point. Basically you have circles parallel to z plane, with centers in y axis, and radius = x. Let y be the parameter and you can work it out from there I think

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[real gale]

What is the maximum area of rectangle than can be inscribed in an ellipse of the equation x²/2 + y² = 1?

[real gale]

I tried using the Lagrange multiplier method

A(x,y) = xy has to be maximized given x²/2 + y² = 1

[icy spear]

4xy. but yes

[real gale]

4xy, how?

[icy spear]

the ellipse is centered at the origin

positive and negative values of x and y are valid

[real gale]

[icy spear]

so the horizontal component of the rectangle will be 2x, and likewise for the vertical component being 2y
2x = x - (-x)

[real gale]

Right

I get it

That was my mistake

[icy spear]

anyways it's just a constant factor so assuming the rest of your work was correct you should be good

[real gale]

I'm still getting a wrong answer

[real gale]

considering f(x,y) = x²/2 + y²

So, (4y, 4x) = λ (x,2y)

4y = λx and 4x = 2λy

[real gale]

Substituting x² = 2y² in f(x,y) = 1,
y = ± 1/√2

x² = 2y² implies x = ±1

To maximize A(x,y), the suitable points are (1, 1/√2) and (-1, -1/√2)

And the maximum value of the function A(x,y) hence will be 1/√2 which is approximately 0.707 units squared

[woeful cloak]

those aren't the only candiates, you forgot about (1, -1/sqrt(2)) and (-1,1/sqrt(2))

[real gale]

Yeah I know

But those yield negative values when plugged in A(x,y), so we can ignore them?

[woeful cloak]

right, yes

[real gale]

Oh wait

I have forgot that A(x,y) =4xy

,calc 4*0.707

[twin meteor]

Result:

2.828

[real gale]

Good

.close

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[icy spear]

these are your minima

[real gale]

Yes

[vocal sleet]

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[crimson pumice]

I feel like I know how to do this but the problem is that I dont know how to plot these coordinates

[vocal sleet]

@crimson pumice Has your question been resolved?

[crimson pumice]

<@&286206848099549185>

huh, guess vectors isn't it today

[soft mango]

yes

[crimson pumice]

😔

[soft mango]

u want help?

[crimson pumice]

yea

[soft mango]

question?

[crimson pumice]

its above

the picture?

[soft mango]

ok let me see

To find the unit vector direction from location A to location B, we need to calculate the displacement vector between the two points and then normalize it to get the unit vector.

The displacement vector can be calculated as follows:

Displacement vector = (B_longitude - A_longitude, B_latitude - A_latitude)

Now, we need to normalize this displacement vector to get the unit vector:

Unit vector = Displacement vector / Magnitude of Displacement vector

Let's calculate the unit vector step by step:

Location A: Latitude = 129.625° N, Longitude = 32.324° E
Location B: Latitude = 129.637° N, Longitude = 32.371° E

Step 1: Calculate the displacement vector
Displacement vector = (32.371° E - 32.324° E, 129.637° N - 129.625° N)
Displacement vector = (0.047° E, 0.012° N)

Step 2: Calculate the magnitude of the displacement vector
Magnitude = √((0.047)^2 + (0.012)^2)
Magnitude ≈ 0.0474

Step 3: Calculate the unit vector
Unit vector = (0.047° E / 0.0474, 0.012° N / 0.0474)
Unit vector ≈ (0.992, 0.253)

The unit vector should be specified as (0.992, 0.253) relative to North East. This means the drone should fly approximately 0.992 units in the East direction and 0.253 units in the North direction for the delivery. Note that the unit vector specifies the direction only and does not consider the actual distance or scale of the locations.

let me know if it is wrong

[crimson pumice]

holy

[soft mango]

mother of potato

[patent nymph]

did you use gpt?

[crimson pumice]

I have a hunch he did

[soft mango]

no other ai

[crimson pumice]

my guy

the ai is dumb

it cannot do maths

unless its wolframe, that ones designed to do it

[soft mango]

is it let me try gpt then

sorry

[crimson pumice]

gpt is even worse

[patent nymph]

north and east are like x and y coordinates

[crimson pumice]

it can't do maths for crap

[crimson pumice]

ah I see

[patent nymph]

wolfram isn’t even ai

[crimson pumice]

huh though it is, its a machine then?

were getting off track

[patent nymph]

you do know what a unit vector is?

[crimson pumice]

somewhat

[patent nymph]

knowing that north and east are like x and y, can you continue on the question?

[crimson pumice]

yes but I confused myself now because I realised I don't actually know what a unit vector means

I understand what a vector is

its just coordinates

but then you have a magnitude of a vecotr

[patent nymph]

can you solve the question if it said “vector” instead of “unit vector”?

[crimson pumice]

how do you measure the distance of a point

yea probably

its just a to b

which is y=rise/run but the vector version for that

too long to type out hence why i shortened it

[patent nymph]

a unit vector is a vector with a length of 1, they arise when you scale a vector down by its magnitude

[crimson pumice]

I see

[patent nymph]

so can you send your work so it can be checked?

[crimson pumice]

oh I didn't do any work because I was so dazed by the coordinates

the picture here is all i've done

[crimson pumice]

this

[patent nymph]

have you asked your teacher for clarification on what they mean?

[crimson pumice]

no this is a homework question

[patent nymph]

I realized this is probably wrong, sorry about that

[crimson pumice]

I never got a chance to ask them

if i gave you the answer could that help>

[patent nymph]

Has your book defined these coordinates?

[patent nymph]

Yes

[crimson pumice]

0.2474 N, 0.9689 E

[patent nymph]

they didn’t give a worked solution?

[crimson pumice]

oh they did

oh... they did....

oh well

they used the unit vector thing twice

[patent nymph]

what a weird question

what does it mean

what does 129.637deg N, 32.371deg E mean

has your book defined it?

or teacher

[crimson pumice]

its longitude and latitude I think

because thats the only real life application of something like this

[patent nymph]

Ohhh

[crimson pumice]

for.. planes I think?

like the bearings where it starts at north

so dumb

so N is longitude which is y? and latitude is x?

[patent nymph]

It would help to draw a diagram

[crimson pumice]

it doesn't matter for this question because its unit vector

[patent nymph]

<@&268886789983436800> ai generated content

[patent nymph]

drawing a diagram always helps

[crimson pumice]

its just a line

ok so I understand the unit vector thing

but a unit vector is defined as 1

[patent nymph]

the positions of A and B aren’t just a line

[patent nymph]

no, 1 is not a unit vector, 1 is a scalar

[crimson pumice]

I see

so to correct myself, if I said a unit vector has a magnitude of 1?

because the answers do not show that they are 1

[patent nymph]

a unit vector does have a magnitude of 1

[patent nymph]

because they divided the vector by its magnitude

[crimson pumice]

oh, so were finding the x and y magnitude to find the unit vector

ahhh that makes sense

[patent nymph]

do you mean the x and y components, or the magnitudes of the components?

[crimson pumice]

magnitudes of the component

[patent nymph]

y and x work on the plane, but longitude and latitude are of the sphere

[crimson pumice]

well the worked solution treats it as a plane

I think they just threw this in to be different

it actually just serves as x and y

[patent nymph]

So you’re supposed to pretend they’re x and y instead of longitude and latitude?

[crimson pumice]

yea

[patent nymph]

they’re different things, because the sphere is curved

if you want, you can ask your teacher if it was intended for you to consider the curvature of the sphere when you made your answer

[crimson pumice]

well who am I to argue this to? they treat it as x and y

also the points have a difference of 0.012 so I don't think the curvative becomes a problem

[patent nymph]

If it’s just this one problem that uses latitude and longitude, then I guess you can move on

[crimson pumice]

alr

but what i don't get is what does "What unit vector should be specified?

because lets just use an example

v=2i +3j

find the unit vector

how do you find the unit vector of this, its just a point

or is it call coming from 0?

[patent nymph]

It isn’t just a point

[patent nymph]

you find the unit vector of a vector by dividing by the magnitude

[crimson pumice]

wait

does the vector thing literally mean this

[patent nymph]

a vector is an arrow

[crimson pumice]

I see

[patent nymph]

this is v

[crimson pumice]

I get it now

alright I think I can do this now

thanks for the help

.close

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[paper depot]

gptfo

[paper depot]

oh ffs i didnt notice this was open

whatever.

[viscid ore]

LOL

Ok lemme use this then

[paper depot]

weh oh ok whatever ig

i mean

[viscid ore]

Where was I? Oh yeah

We still need to put 0

[paper depot]

you were proving $\bigcap_{n=1}^{\infty} (-1/n, 1/n) = {0}$ yes?

[twin meteor]

Ann

[viscid ore]

Yes

[paper depot]

which inclusion specifically are you stuck at

$\subseteq$ or $\supseteq$

[twin meteor]

Ann

[viscid ore]

Oh wait I wasn't using inclusion, i just excluded positive numbers usibg contradiction

[paper depot]

weh

slippery

$\supseteq$ is obvious as clearly 0 belongs to every single one of those intervals

[twin meteor]

Ann

[paper depot]

$\subseteq$ is the interesting one

[twin meteor]

Ann

[paper depot]

you need to prove that (∀n ∈ N)(-1/n < x < 1/n) => x = 0

you've already proved x can't be positive yes?

[thin vale]

@paper depot reference

[paper depot]

??

[thin vale]

oh nvm lmao the channel is literally owned by you

I thought there was an imposter

[viscid ore]

Done

[nimble elm]

do not use AI to generate content here, especially not to try and help others.

[paper depot]

lmao

[viscid ore]

Actually i'm done

[paper depot]

you do seem to be

[viscid ore]

Even for the negative numbers

[paper depot]

coose time?

[viscid ore]

coose for now, I have other stuff i might get stuck in

[paper depot]

.coose

[viscid ore]

Haven't done these for so long 😭

[paper depot]

.close

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[vast shale]

Hi

[vast shale]

John has 2 identical english books, 2 identical math books and 4 identical science books and a shelf that fits only 5 books. In how many different ways can he arrange these 8 books into that self

Is there a better way to do this question?

[sudden compass]

what is your current method?

[hasty pulsar]

^

[vast shale]

Cases

Like is there a formula for these type of question?

[pastel ruin]

learning pnc might help

[vast shale]

Ik pnc

[twin meteor]

.fire007

[vast shale]

Into that 5 rommed self

[sudden compass]

u can do this only when the objects are distinct

[vast shale]

So, cases is the only way?

[sudden compass]

it is the safest

do 8!/(2! * 2! * 4!), that gives u all possible permutations

[vast shale]

Yes

So PIE

Then?

[sudden compass]

oh shit

the shelf is only 5 books

[vast shale]

Yes

That's why 8 choose 5

[sudden compass]

hmm lemme think...

[vast shale]

So, the question is basically

how many 5 word letter can be formed using the letter

EE, MM, SSSS

I was thinking in this way

Can't I apply distribution of alike obj ( beggars method) concept here?

[sudden compass]

I havent learnt that yet, so idk abt it (i am learning combinatrics too)

[vast shale]

Alr

[pastel ruin]

looking at it this way, cases seems better option

[vast shale]

Ye but what if I've 5 E's, 15 M's, 25 S's, 8 k's, 98 Q's ....

And more letter

Cases don't look fun on that

[pastel ruin]

i have a pretty similar prob here, i used it back then

[vast shale]

In ur case R,S,G are distinct

[pastel ruin]

i used this

[vast shale]

This is what I was talking about before

[pastel ruin]

shelves can be treated same

[vast shale]

.

[pastel ruin]

yea y not?

[vast shale]

Or perhaps

[pastel ruin]

solve individually for each sub ig?

then add em up

[vast shale]

x1+x2+x3+x4+x5=8

Probability

Whyd delete

I was reading

Alr kul ill do it with cases

.close

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[pastel ruin]

wuts the ans tho?

[pastel ruin]

eh wut? i didnt mean to sry mb

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[vast shale]

for e), i am wondering what i am doing wrong? everything kind of simplifies to [
(1-x^2)^{-1}(1-x^4)^{-1}(1-x^6)^{-1}
]

[vast shale]

but the coefficient of all of those just ends up being k choose k

no wait, there is something weird here

[vast shale]

this ends up transforming to [
\bracks{\sum_{k=0}^\infty \binom k k (x^2)^k}\cdot \bracks{\sum_{k=0}^\infty \binom k k (x^4)^k} \cdot \bracks{\sum_{k=0}^\infty \binom k k (x^6)^k}
]

[vast shale]

what are u meant to be doing here

[sudden compass]

factorize ig?

[sudden compass]

oh u have to find x^10. i was wondering what to find

[sudden compass]

well just find all possible ways to obtain ten from factors of 2,4 and 6

[river minnow]

Probably not the approach you want to do, but this problem can be interpreted as a Diophantine equation one;
How many solutions does 2a + 4b + 6c = 10 have where a, b and c are natural?

Oh, which is the same as what Kraken said

[sudden compass]

lol same approach same time

[vast shale]

i dont follow. Why should it be similar to that?

[sudden compass]

I said the same thing bean said, but I said it in a casual way, bean said it in a formal way

[river minnow]

First brackets contain terms of the form x^2a, the second brackets - x^4b and the third - x^6c
So, when you multiply them, each term will have an exponent of the form 2a + 4b + 6c

And the coefficient of x^k would be the amount of possibilities when 2a + 4b + 6c = k

[vast shale]

ohhhhhh i see

we can solve that using generating functions

okay one last question guys

how did they go from the first line to the second?

like, the sum of x^(n-1) is just not 1/(1-x)

how the hell did they get that

[river minnow]

Isn't that just the geometric series formula?

[vast shale]

yes it is

but i get 1/(1-x)x

like how is it 1/(1-x) lol

[river minnow]

Probably a typo yeah

[vast shale]

phew i am not going mental

too much combinations

i have been studying for the past 10 hours or osmethnig

[sudden compass]

[vocal sleet]

@vast shale Has your question been resolved?

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[hushed tree]

If there are 23 seats, which 4 seats are in the middle?

[hushed tree]

I wanna go to the cinema

And i want the 4 seats that are in the middle

Is it 10,11,12,13?

[obtuse sierra]

there are no middle 4 seats

[hushed tree]

11,12 and 13 are

Right

And the i can choose between 10 and 14

For the 4th seat

?

[obtuse sierra]

11 12 13 are middle 3 seats

if you choose either 10 or 14 as the fourth, the four seats wont be in the middle

[hushed tree]

Then which should i choose

I want 4 seats

[obtuse sierra]

you want perfectly middle or just middle?

[hushed tree]

Perfectly

[obtuse sierra]

not possible

[hushed tree]

Tell me the seat names

Other people will get them first

If i cant decide

[hushed tree]

These, right?

Or 11, 12, 13, 14

These are as close to perfect as i can get, right?

@obtuse sierra

[obtuse sierra]

yup

10, 11, 12, 13 also works

[hushed tree]

Ok

[dire plover]

why do those tickets look so disorganized

[hushed tree]

Which ones would you take

[dire plover]

amc has better ui

ohh is this a math problem

[hushed tree]

There are stairs on the left

[hushed tree]

Nah i wanna go watch a movie tomorrow and i have to book seats

[opal folio]

gm

[vocal sleet]

@hushed tree Has your question been resolved?

[hushed tree]

Whats gm

[faint hill]

Oppenheimer?

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[viscid ore]

Oh shit

I mean C((\bR))

[paper depot]

you mean what

$C(\bR)$?

[twin meteor]

Ann

[paper depot]

as in the set of all cts functions from R to R?

[viscid ore]

Yes

Damn i'm sleepy as hell my baf

[paper depot]

hunch: a function is a zero divisor iff it vanishes on an interval of nonzero length.

[viscid ore]

I did characterize the zero divisors and units of (\mathcal{F}(\bR))

[twin meteor]

Riku

[viscid ore]

In this particular case, the zero divisors are functions with atleast one vanishing point on it

If no vanishing points, it's just the unit

[paper depot]

what's F(R)

[viscid ore]

Set of all functions from R to itself

In case of this, all non zero elements are either units or zero divisors

But the problem is, C(R) has also non zero elements which are neither zero divisors nor units

So I have no clue how to start

[paper depot]

hunch: a function is a zero divisor iff it vanishes on an interval of nonzero length.

[vocal sleet]

@viscid ore Has your question been resolved?

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[opal obsidian]

To verify S= {1,-1,i,-i} forms a group under complex multiplication

[opal obsidian]

I verified that they are closed under complex multiplication

1 is the identity element for all x in S

but couldn’t find a single inverse

[wraith venture]

Try harder

Is 1's inverse in S ?

[opal obsidian]

Can a group have more than one inverse?

[wraith venture]

-1's ?

[opal obsidian]

1 is it’s own inverse

[wraith venture]

So that's already 1 inverse out of 4

[opal obsidian]

but for each element inverse seems to be different

[wraith venture]

As expected ?

[opal obsidian]

ohh right

inverse or i is -i

I thought when there exist some element b such that for all x, x dot e = 1

It’s written for each element, I misinterpreted as for every

mb

[paper depot]

⚠️

[opal obsidian]

yes, i understand that’s extremely false

[paper depot]

it's poorly written too

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@opal obsidian Has your question been resolved?

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[desert lagoon]

How do I solve this? It seems so basic, but I can't figure it out

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@desert lagoon Has your question been resolved?

[hard atlas]

what loubere method are you talking about

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[steady pewter]

pls help

[mild flower]

since the smaller rectangles don't overlap you can just add them up

[steady pewter]

i did

i got 192

[mild flower]

yep that's what i got as well

[steady pewter]

and it not right

[mild flower]

,calc 16*12

[twin meteor]

Result:

192

[mild flower]

do you need to include the units?

[steady pewter]

i don't know

it didn't say

also i did

and it wasn't right

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[steady pewter]

.reopen

[vocal sleet]

✅

[steady pewter]

.close

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[vague root]

does the squared, cancel out the square root ?$(\frac{\sqrt{17}{4})$

[mild flower]

$\lp\frac{\sqrt{17}}{4}\rp^2 = \frac{\lp\sqrt{17}\rp^2}{4^2} = \frac{17}{16}$

[vague root]

o

[paper depot]

typo in the first part

[mild flower]

ty

[twin meteor]

Hayley

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

[vague root]

.close

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[alpine mist]

After a possible factorization establish the sign table of
the expression and solve in ℝ the following inequalities:

[alpine mist]

factored form= (x-3)^2

so its never <0

since its squared

right?

[dull maple]

Yes

[alpine mist]

3°) ]-∞;3[ [U] ]3;+∞[
4°) ]-∞;3] [U] [3;+∞[

[alpine mist]

what do i write for 5 and 6 then?

nothing ?

[dull maple]

What's that? Makes no sense to me.

[alpine mist]

this is the interval in which its >0

its positive between -infinity and 3

3 = 0

and its positive again between 3 and + infinity

[dull maple]

Yeah. Maybe write a $\phi$ since that denotes null set.

[twin meteor]

Enemagneto

[dull maple]

Alright. I think i'm just unfamiliar with ][ notation.

[alpine mist]

idk thats how we write the intervals in france

when its 3[ it means 3 excluded

when its 3] it means 3 included

[dull maple]

We'll write that(first one) as (-∞, 3) U (3, ∞).

( is for when you wanna exclude. To include, we use [

Regardless, doesn't your question only want sign of expression ?

[alpine mist]

nah then resolve them it says

[dull maple]

Oh. Solve as well.

[alpine mist]

its like everyone does ?

good to know lol

we might be the only one doing that in france

[dull maple]

Maybe. I took french classes for 3 months. Surely didn't learn much. Lol

Anyway, for the 6th one, it won't be $\phi$ as 3 is a solution.

[twin meteor]

Enemagneto

[alpine mist]

yeah thats what everyone learns here lol

After a possible factorization establish the sign table of
the expression and solve in ℝ the following inequalities:

i only needed to do what i did right ?

for the 3/4

[dull maple]

Yeah. Seems so.

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@alpine mist Has your question been resolved?

[alpine mist]

alright thx

[vocal sleet]

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[misty violet]

im unsure how to do this

[misty violet]

can anyone assist?

[flat whale]

Ratio test

Or root test

[misty violet]

hmm

that doesnt sound too familiar to me

shoot

[worthy citrus]

Alternating series test?

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[leaden jackal]

Trying to factor this

[calm light]

x^2-x = x(x-1)

[fringe lynx]

What are we trying to find?

Just factorising this?

[leaden jackal]

I’m

[fringe lynx]

Since I got 'w' = -2

[leaden jackal]

What do you mean w=-2

I was just trying to factor it

[fringe lynx]

Oh

[leaden jackal]

But what do you mean w=-2

[fringe lynx]

So I got (2w + 3) = 1

[leaden jackal]

How did you get equals sign

[fringe lynx]

Idk

Added (2w +3) to both sides

[leaden jackal]

What do you mean both sides there’s no equal sign?

[fringe lynx]

Then I would have gotten (2w + 3)(1 X 1 - 1) which makes no sense

[leaden jackal]

I thought this is just 2 terms minus another term

I didn’t know u can solve for w? Without any = sign

[wraith imp]

If you treat (2w+3) as a single unit k, then the expression becomes k^2 - k

You can then factor out k to get k(k-1)

[leaden jackal]

Umm

[tawny nacelle]

Remember what I said yesterday?

Factoring is the inverse of distributive property

[leaden jackal]

HI!!

Yeah I do remember that but

So it’s 1b^2 - (1b-1)squared

[wraith imp]

Um

How did you get that?

[leaden jackal]

Umm so

1b^2-1b is the question and 1b-1b is 0 so then it’s 1b-1

Wait

[wraith imp]

I’m assuming that you turned (2w+3) into b right?

[leaden jackal]

Yea but not for real

Just to say something

[wraith imp]

Yes that’s fine

We’ll unpack the term afterwards

So (b^2 - b) has a greatest common factor of b

When you factor something out, you divide the terms by that factor

So for this case, divide b^2/b = b and b/b = 1

[leaden jackal]

Im up to here first

Is this okay

[wraith imp]

Is this (2w+3)(2w+3-1)

[leaden jackal]

Noo..

[wraith imp]

The last two lines are correct, but they need to be multiplied together

[leaden jackal]

Ummm

[wraith imp]

That’s correct

[leaden jackal]

I feel like im just skimming through..

[wraith imp]

Okay let’s think about it differently

[leaden jackal]

Hey also

Can I ask you something

[wraith imp]

Sure

[leaden jackal]

Um so before someone said that w= something . Is that true that they can find out how it equaled something without any equals sign

[wraith imp]

Uh

I mean this is an expression not an equation correct?

If there is no = sign then you cannot find the values of the variable

[leaden jackal]

Okay good

He confused me

Okay so what were you saying

[wraith imp]

You know that factoring is the opposite of distributing

[leaden jackal]

He ing told me that

[wraith imp]

So that would mean we’re trying to two expressions that multiply to make x^2 - x

Note that x(x-1) satisfies this

[leaden jackal]

Yep

It’s just you guys always seem to know like x(x-1) you can make them into your Own term but I always think there’s a lot more numbers

So 2w+2

I couldn’t think . About making it into your set of rules

Like well known rules

You guys seem to be able to understand how to translate a big term into

Those small rules

If that makes sense

It’s hard to explain

[wraith imp]

Mm

It’s not always possible to do that either

[leaden jackal]

And I almost distributed

The -1 into the bubble

Because i have done that before in other problems

B*b-b | and this

That’s how

I got it wrong and thought it was just 2w+3-1

Sorry I’m just trying to change the way I’m thinking to your thinking it’s hard

ING showed me a lot of stuff aswell I just get confused

[pure bramble]

Would you mind elaborating on what the line brackets mean?

[leaden jackal]

Just seperating

[pure bramble]

Okay so are the B and b different or are they the same term

Does B = b to simplify further

[leaden jackal]

Yea

[pure bramble]

Okay so when you did B*b -b

It is not exactly correct

As it is really (b*b) -b

[leaden jackal]

What the difference

[pure bramble]

You must perform the multiplication in the bubble first

So it is b^2 - b

[leaden jackal]

Isn’t that the same thing

[pure bramble]

The issue is that when you have an exponent

You can not subtract is by the one without an exponent

They are different terms

[leaden jackal]

Okay yeah I remember that rule

So

[pure bramble]

Exactly

So now going back to your problem

Can you please elaborate on what was the main issue

[leaden jackal]

Umm

So your saying I can’t

Do that because I have to multiply the bracket first

[pure bramble]

Exactly

[leaden jackal]

Hmm okay

That makes sense

[pure bramble]

But let’s say we wanted to factor b(b) - b

We know that b is common between all the terms

[leaden jackal]

So b(1)-1

[pure bramble]

Close

It is rather b *(b-1)

[leaden jackal]

Oh yea I ment that

Hmmmm

[pure bramble]

Excellent just make sure to use the correct notation to make your response a bit more clear

[leaden jackal]

Hmmm

So this is how it works

[pure bramble]

Exactly

[leaden jackal]

Hmm now I understand

Okay I feel good now! 😁

Thank you 🙏

[pure bramble]

Happy to help

[leaden jackal]

.close

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[vast shale]

it’s -6, -1, right?

[mild flower]

yeah

[vocal sleet]

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[vast shale]

thanks hayley

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[sharp swallow]

@gritty sage hi

[gritty sage]

Hello.

[sharp swallow]

can u help me with this problem

these are the questions

[gritty sage]

What are the steps they mention?

Just the questions?

[sharp swallow]

i went ahead and graphed this

[sharp swallow]

just the questions

this is tricky because this time i only have two curves instead of one

[gritty sage]

What do you mean by two curves?

[sharp swallow]

106 + 67 = 173
173/2 = 86.5
d = 86.5

[sharp swallow]

like u know the last problem they gave us the two points

this time they gave us more but we dont know if its the min or the max

i decided to take the min and max points provided and tried to find the verticle shift

[gritty sage]

OK, that looks good for the midline.

So, what is the amplitude?

[gritty sage]

Oh, I see. It's a year-long cycle.

Like that's what it does every year, so to speak.

[sharp swallow]

19.5?

[gritty sage]

Yes, that looks good.

So, because it repeats every year, you can't get lower (as a monthly average) than the lowest point you're given.

OK, what's the period?

[sharp swallow]

i think its - 10

[gritty sage]

Why do you think it's 10?

[sharp swallow]

7 - 12 = -5
-5 * 2 = -10
Period = -10

[gritty sage]

Oh, OK. That's a good way of thinking about it, but it only works with perfect sinusoids.

For this one, you want to look at how often the wave as a whole repeats.

[sharp swallow]

oh so how do i do that then

[gritty sage]

OK, so this is repeated every year, right?

Like you have all 12 months of the year.

And then it repeats next year and the year after that and so forth.

Does that make sense so far?

[sharp swallow]

yes

[gritty sage]

OK, and it only shows one minimum and one maximum.

And those happens once a year.

So, the distance between repeats of the sinusoid wave is 12 months.

Do you see why?

[sharp swallow]

yes

[gritty sage]

OK, so the period is 12 months since that's how often it repeats everything.

That's what period means.

[sharp swallow]

i understand but what is the math behind that though

[gritty sage]

Oh, it's just that the definition of period is how often the sinusoid repeats itself.

Like sin(x) repeats itself every 2pi.

So, the period of sin(x) is 2pi.

So, here, there's not really math calculations exactly.

You just notice that this is a yearly schedule.

[sharp swallow]

okay

[gritty sage]

And so it repeats every year.

And so since the repeating period is 12 months, the period is 12 months.

[sharp swallow]

unfortunately i have to go right now will u be available in like 20ish mins?

[gritty sage]

If it made a nice sinusoid wave every 3 months (like it went to minimum and then maximum four times a year), then it would be three months, but it's not that fast.

I might be. If you can't find me, you can ping @Helpers, but only once per question.

[sharp swallow]

ok should i ping u too?

[gritty sage]

Oh, and at least 15 minutes after you post the question, but that'll be met here.

Sure, ping me first and then if I don't show up, try @Helpers.

[sharp swallow]

okay thank you! ill see u soon

[gritty sage]

No problem.

[vocal sleet]

@sharp swallow Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[sharp swallow]

.reopen

[vocal sleet]

✅

[sharp swallow]

@gritty sage

<@&286206848099549185>

[gritty sage]

Hello.

OK, what's the frequency factor?

@sharp swallow

[sharp swallow]

hiii welcome back :)

b=pi/6

[gritty sage]

OK, what's the phase shift?

[sharp swallow]

i have no idea how to calculate phase shift

[gritty sage]

OK, where does sine start out (sin(0))?

[sharp swallow]

0?

[gritty sage]

Right, which is the midline.

Cosine starts out at 1, which is the maximum.

So, what is the midline here?

[sharp swallow]

Hmm 🤔

12

[gritty sage]

I think that was for the previous problem.

[sharp swallow]

oh

86.5

[gritty sage]

Right.

Now, starting from 1 and going right, when do you first come very close to the midline?

[sharp swallow]

isnt the midline above 1

[gritty sage]

No, I mean starting from month 1.

[sharp swallow]

Ohhh

4

at least 4 according to the table

[gritty sage]

OK, so what do you need to do to 4 to get it to be 0 like in sin(0)?

[sharp swallow]

hmm not sure

[gritty sage]

Well, think back to the beginning of algebra.

You have to do something to 4 to get it to turn into zero.

What can you do?

[sharp swallow]

multiply by 0

[gritty sage]

Good, but phase shift is adding or subtracting.

[sharp swallow]

subtract 4

[gritty sage]

Right, so to undo the phase shift, you subtract 4.

[sharp swallow]

ohhh so the phase shift is -4

Oh thank you!!!!!

[gritty sage]

No problem.

What do you think the function is?

[sharp swallow]

19.5 sin (pi/6-pi/2)+86.5?

[gritty sage]

Don't forget x.

[sharp swallow]

im not sure where that would go 😓

[gritty sage]

Well, what's the general formula for a sinusoid?

[sharp swallow]

a sin (b(x)) + d

[gritty sage]

It's something like f(x) = a sin(b(x + s)) + d

I used s for the phase shift because I don't know what you use.

[sharp swallow]

i think thats the same here

[gritty sage]

Oh, looks like people use c for phase shift.

It's sort of like a, b, c, d.

[sharp swallow]

that would be f(x)= 19.5 sin (pi/6 (x - 4)) + 86.5

[sharp swallow]

oh yeah when i started doing this assignment i found that formula on google since ididnt have it memorized

[sharp swallow]

but the teacher used this one with the s

[gritty sage]

OK, good. Now to check it, either do all 12 inputs and see if the temperatures are close to the ones you were given or pick like three at random.

Oh, OK.

Or if you're allowed to graph it, graph it with your blue points from earlier.

See if the blue points are near the curve.

(For tests, checking several points is good, unless they let you use a graphing calculator)

[sharp swallow]

i graphed it