help-36

[ruby jungle]

help please

[ruby jungle]

so i got the bounds for x and y

0 <= x <= 5

3-x <= y <= 5-x

and i want to substitute u for y-x and v for y+x

this is the step im stuck on

i kind of forgot how to do substitutions

[final saddle]

@ruby jungle Has your question been resolved?

[ruby jungle]

<@&286206848099549185>

[final saddle]

@ruby jungle Has your question been resolved?

[ruby jungle]

please ping me if you decide to help

[final saddle]

@ruby jungle Has your question been resolved?

[ruby jungle]

.close

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[indigo plover]

.close

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[tranquil pine]

What's the mathematical symbol for the representation of modulus

[tranquil pine]

so say for instance, I want to represent the remainder of 16/4 mathematicallly, how would it work?

[tired walrus]

you make up your own notation or steal it from a programming language who has one

[tranquil pine]

wait really?

[tired walrus]

yes really. there's no Commonly Accepted™️ notation for the modulo operation

(modulo, not modulus. english is dumb)

in C/C++ the symbol for it is %

[tranquil pine]

Well I can't make up stuff in a mathematics exam

[tranquil pine]

ahh gotcha

thank you so much

[tired walrus]

what problem are you looking to solve anyway

[tranquil pine]

nothing

I was just doing a task on inductive proofs

and this really random thought came in my head

[tranquil pine]

gotcha

[tired walrus]

i think you don't need a notation for remainder here

Since 4 MOD 4 = 0,
replace this with
Since 4 is divisible by 4,
or
Since 4 is divisible by itself,

[tranquil pine]

gotcha

thank you so much

I guess it's application specific

have a great day

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[hidden kiln]

can someone help me with this pls?

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@hidden kiln Has your question been resolved?

[hidden kiln]

<@&286206848099549185>

[trim crown]

let x be number of people in favour and y be number of people against.

then you should be able to write 2 equations from the question

[final saddle]

@hidden kiln Has your question been resolved?

[hidden kiln]

let's assume that the total no. of people are 'x'.
no, of people in favour of the resolution = (x/2)+7
no. of people against the resolution = (x/2)-7
no. of people holding up both their hands = (0.06)(x/2)+7

but idk what to do after this

can someone pls help

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[cold basin]

Hey so I pretty much got the answer to this but I had a question

in most cases when you foil and end up with something like

(x + 5)(3x - 4)

the answer will be the opposite so

x = -5, 4/3

but in this case the answer is the same or
x = 5, -4/3

why is that?

[tired walrus]

because you fucked up actually

[barren hound]

isn't it 3x²-11x

[tired walrus]

$\vmqty{3x & x \ 11 & x}$ is $3x^2 - 11x$ and not $3x^2 + 11x$

[soft zealot]

AnnGhost

[cold basin]

ahh

thats true

det is minus

alrighty ty for ur help

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[tranquil pine]

Another notation question, is [
\set{(x,y) \where x^2 + y^2 = 9; x \ge 0, y \ge 0}
]
fine to write?

are there better ways of writing this maybe?

[tranquil pine]

a

[grim nebula]

yes

, instead of ; is also fine

[tranquil pine]

can you do some stupid shit like

(x,y) \ge (0,0)

[grim nebula]

please dont

[tranquil pine]

[barren hound]

i wouldn't do that

[grim nebula]

[ \set {(x, y) \in \R_{\ge 0}^2 \where x^2 + y^2 = 9} ]

[grim nebula]

[ \set {(x, y) \in \R_{\ge 0} \by \R_{\ge 0} \where x^2 + y^2 = 9} ]

[barren hound]

${(x,y)\geq^2(0,0)}$ clearly

[soft zealot]

hayley

[grim nebula]

[tranquil pine]

lmfao

okay ty

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[desert mantle]

in some contexts (a,b) >= (c,d) is used

but please not here

[tranquil pine]

what's the issue though

[grim nebula]

[tranquil pine]

[desert mantle]

well probably >= in this way hasnt been defined for you

[tranquil pine]

probably not..

.reopen

[final saddle]

✅

[tranquil pine]

also can you be quirky and say

[grim nebula]

can you be quirky
no

[tranquil pine]

[
\set{(x,y) \where x = 3\map \cos \theta \wedge y = 3 \map \sin \theta, 0 \le \theta < \f \pi 2}
]
or is that fucked notationally

[grim nebula]

just write commas

[tranquil pine]

bruh is ; not a mathpunt

[grim nebula]

it is

[grim nebula]

[ \set {(x, y) \mid x = 3\cos\theta, y = 3\sin\theta, 0 \le \theta < \tf\pi2} ]

[desert mantle]

but also comma instead of the \wedge

[tranquil pine]

wait why not

[desert mantle]

and if you write x and y that way you could also just write {(3cos theta, 3 sin theta): 0<= theta < pi/2}

the wedge just kinda looks like shit. no one uses it except logicians

[tranquil pine]

[grim nebula]

yeah thats the true reason

[tranquil pine]

#foundations seething

[tranquil pine]

oh right this makes sense ok

Ty boys and gals

. close

. close

. close

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[tranquil pine]

[grim nebula]

quadruple close

[tranquil pine]

I'm on phone ok campus WiFi ded

[modest stag]

average campus wifi

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[frank thicket]

How do I go about solving this?

[random rampart]

um

Pythagoras theorem lookin handy here

[random forge]

area of circle minus area of rectangle

[random rampart]

yep ^

try drawing lines to see if u can find a diameter that's findable

after that, calculate the area of circle, then area of rectangle

circle - rectangle

ans

[frank thicket]

Area of rectangle is 12

And then

Wait no

Okay wait I got it

!close

[modest stag]

.

[frank thicket]

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[hearty badge]

I don't know what I need to do for this type of question, I've done the long division part but I don't know what the product of two factors means.

[random rampart]

let f(n) = (10n^4+ ... +18)

f(2)

if f(2) = 0 the (n-2) is factor

if no then the remainder will be given

u get me?

[hearty badge]

Not really

[random rampart]

oh wait it ask for long division

if there is no remainder from your long division

the (n-2) is factor

remainder is located in bottom right of your long division

seeing your rough work

there's 0 in remainder

therefore it's a factor

[hearty badge]

Yes it's a factor but what is the factor?

Oh wait

[random rampart]

(n-2) is factir

[hearty badge]

So the (n-2) is what I'd put in the second box for the question?

[random rampart]

10n^2 +n -9 is quotient

[random rampart]

nope

if there is no remainder

no need to put

the question ask you to put remainder

not the factor

literally the factor is given

teacher wouldn't ask you to copy it down 🤣

[hearty badge]

"If it is, write the polynomial as a product of two factors."

That's where I'm confused

[random rampart]

oh

my bad

it's the quotient in your rough work

the 10n^2 one

[hearty badge]

It says incorrect

[random rampart]

it should be +9

[hearty badge]

Did I mess up my long division?

[random rampart]

at the end

[hearty badge]

Oh

[random rampart]

try

[hearty badge]

Still incorrect

[random rampart]

it must be +9

u f up the second term

[hearty badge]

So I just need to redo my long division?

[random rampart]

is 10n^2 + 5n + 9

your final answer?

[hearty badge]

Yeah, I tried that but it didn't work

[random rampart]

try (n-2)(10n^2+5n-9)

[hearty badge]

Multiplying the polynomial?

[random rampart]

no

the answer

[hearty badge]

Oh it worked

[random rampart]

ye

[hearty badge]

How did you figure that out?

[random rampart]

u were right but 9 was wrong

[hearty badge]

9 was wrong?

[random rampart]

-9

is +9

check ur rough work

[hearty badge]

-9 worked for the problem

As part of the answer

[random rampart]

oh dam

me dum

but cuz the answer said two factors

so that's why the 2 5hings to multiply with

[hearty badge]

Oh

Alright thank you

[random rampart]

usually for rough work I write -) 9n+18

then put - later that's why me confuse

but np

good luck

[hearty badge]

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[real juniper]

Determine for all n a formula for the Taylor polynomial of nth order
for the function g(x) = sin(x^2).

[real juniper]

how do i prove this?

you can use that T_2ng(x)=T_nf(x^2)

[desert mantle]

whatever that notation is supposed to mean

[final saddle]

@real juniper Has your question been resolved?

[real juniper]

ill send a picture

Iill translate:

Let f: R->R be a function that satisfies f^(n) exsit for all n. It is around the point a =0

Consider following function g(x)=f(x^2). Show that T_4g(x)=T_2f(x^2)

I've solved the first one. However question b)

[desert mantle]

also dont ignore the bot

[real juniper]

For all n, determine a formula for the Taylor polynomial of nth order
for the function g(x) = sin(x^2)

[desert mantle]

what is the text in the middle

[real juniper]

betwee a and b?

[desert mantle]

yes

[real juniper]

it means you can use the equation

but not in equation a, only in b

"in can be shown that T2ng(x) = T_nf(x^2) for all n"

[desert mantle]

well then just do it? surely you know the taylor polynomials of sin(x)

[real juniper]

sin(x^2)=x^2-(x^2)^3/6 + (x^2)^5/120....

but im not quite sure how this will show that

[desert mantle]

show what

this is it

[real juniper]

yh but ill need a generel formula for it

[desert mantle]

well do you have a general formula for sin(x) ?

[real juniper]

this right?

[desert mantle]

yes

[real juniper]

but i cant see a way to write it like so

for sin(x^2)

[desert mantle]

plug x^2 in

and then simplify (x^2)^(2n+1)

[real juniper]

are u sure one can simply this

[desert mantle]

(a^b)^c = a^(bc)

[real juniper]

so

2 *(2n+1)

so 4n+2?

[desert mantle]

yes

[real juniper]

so this would be for sin(x^2)?

@desert mantle

[desert mantle]

yes

well, you are asked for just the polynomials and not the whole series

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@real juniper Has your question been resolved?

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[past oxide]

I know the answer is B but why is it B?

[past oxide]

I was doing some testing practice and was unable to find an answer for this

I wasn't sure what to do so any help is appreciated

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[strong condor]

Hello, I'm in Algebra 2, and hoping to skip Precalc next year. What resources can you recommend for a comprehensive pre-cal test?

[strong condor]

I know the basics of matrices, logs, and inverse functions

i am weak with trigonometry

[sleek token]

Khan academy

[frigid hawk]

yea

for trig, khan is definitely the best

make sure to cover parametric, polar, vectors, and complex numbers

[strong condor]

ok

is there anything else?

[sleek token]

try posting in the pre calc channel

this is for more specific math problems

[strong condor]

ok, thank you!

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[scenic rapids]

i dont understand this

[final saddle]

@scenic rapids Has your question been resolved?

[ashen tree]

Use the geometric definition of the dot product

@scenic rapids

[scenic rapids]

the product of their magnitudes and the angles betwen them

ahhh so their angle is 90

[ashen tree]

Alrigt, you got it

[scenic rapids]

so the set of points on a and r form an angle of 90 betwn them

THANK U!! ❤️

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[spare cave]

Hello I am sorry I did already ask this question and I got an answer but I am still confused, in a question like this where it asks you to reflect in the y-axis and then translate by the vector, why do you end up with "y = f( -(x-2) ) -1" rather than "y = f( (-x) -2 ) -1"

[spare cave]

its just hard to get my head round it cause shouldnt you do the negative first or not?

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@spare cave Has your question been resolved?

[spare cave]

<@&286206848099549185>

sorry Im just struggling to get my head around why you do that order as in why wouldn't you just apply the reflection first and then translate

because if you started with graph of "y= f(-x)" then when you apply translation 2 in x and -1 in y shouldnt you just get "y=f(-x-2) -1"

[spare cave]

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[jolly rune]

I'm quite confused on rewriting for variable n. Im stuck at 3n = 4pm - 5nm. I would appreciate some help

[iron mist]

Isolate p

[jolly rune]

I did isolate p and I got p = (3n + 5nm)/4m

The one highlighted in yellow

[iron mist]

Yes

Ok

[jolly rune]

Im more confused on isolating n

[iron mist]

But you can try solving for n also

It’s the same, put all the terms with n on one side

[jolly rune]

hm

something like 3n + 5nm = 4pm?

How can I isolate n in that equation?

[iron mist]

ok

Do you know how to factor?

[jolly rune]

Ohh

n(3 + 5m) = 4pm?

[iron mist]

Yes

Should be academic now

[jolly rune]

I completely forgot about factoring n out

thank you so much

I appreciate it

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[atomic spindle]

90% sure its c?

[atomic spindle]

ping me if u reply

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[tranquil pine]

I plan to start community college in America in a few months, and I am around algebra intermediate and will take Math 97. I want to study math in my own free time and see if I can get ahead or improve my understandings of what I already know

[tranquil pine]

but I am kind of lost on where to start

I did this website called wamap for the placement testing and went off of categories on where i need to study but after looking into it I am not sure where to continue afterwards

[tiny gorge]

have you looked at khan academy?

[tranquil pine]

no not yet

[tiny gorge]

that would be my generic recommendation for learning or reviewing material at that level

[tranquil pine]

is it free?

[tiny gorge]

yep

[tranquil pine]

also I kinda get overwhelmed on all the subjects and am not sure what level i am on

would i just start from the easiest level and just go up from there?

[tiny gorge]

if you have enough time you could do that, like quickly skim topics until you get to material that you don't know so well

[tranquil pine]

ah i see

alright ill try that thanks

[tiny gorge]

sure, gl

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[rugged yoke]

is this allowed for induction?

p(n-2) => p(n)???

they skipped p(n-1)

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[tranquil pine]

Use the chain rule to find dz/dy for the implicit surface yz+xln(y) = z^2

[tranquil pine]

I took the derivative and got

z + y(dz/dy) + x/y = 2z(dz/dy)

which simplified to

dz/dy = (z+(x/y))/(2z-y)

but the notes say the solution is

1/[y(2z-y)]

[final saddle]

@tranquil pine Has your question been resolved?

[royal gust]

Random x got generated

Derivative of zln(y) needs to be product ruled. It is:
dz/dy ln(y) + z/y

[tranquil pine]

oh sorry

its

[royal gust]

Kind of sus the solution doesn't have a ln(y) in it

[tranquil pine]

xln(y)

[royal gust]

Okay that's a bit better. But I imagine x is still a function of y?

[tranquil pine]

wdym?

[royal gust]

Product ruling that, I get:
dx/dy ln(y) + x/y

[tranquil pine]

i dont get why u do that

[royal gust]

Or, sorry x and y are independent axis. Okay. Then x/y makes sense.

[tranquil pine]

i still dont see what i did wrong @royal gust

[royal gust]

I don't either. It looks good.

[tranquil pine]

thats what I thought

maybe question is wrong

.close

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[thick estuary]

I have this question and I need to find the derivative

[thick estuary]

im assuming that z, A and B are variables. So I did A * y^-10 + Be^y but im not sure what to do after that

[tiny gorge]

derivative with respect to what variable?

[thick estuary]

it just tells me to "Differentiate the function"

[tiny gorge]

i guess you should interpret it as z(y) = ...

[thick estuary]

if it was with respect to z I assume it would be 0 but the answer is z' = -10A/y^11 +Be^y

[thick estuary]

ok

[tiny gorge]

yea that would be the derivative wrt y

[thick estuary]

but I still dont get how I wouild do that

does that make it so that A is a constant? and not a variable?

[tiny gorge]

A and B are constants

[thick estuary]

ok

[tiny gorge]

only y is a variable

[thick estuary]

would I use the quotient rule on the fraction?

[tiny gorge]

you could but it's easier to just use the power rule or whatever it's called

[thick estuary]

or can I just make it A y^-10

[tiny gorge]

yea do that

[thick estuary]

so then do I have to do the product rule? or whatever the one is for multiplication

alr I figured it out thanks for help

.close

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[shut ibex]

statments and reason

help

<@&286206848099549185>

[final saddle]

@shut ibex Has your question been resolved?

[shut ibex]

.close

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[gaunt silo]

Hello

[gaunt silo]

I have a few questions on AP Stats

[final saddle]

@gaunt silo Has your question been resolved?

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[supple jolt]

For condominiums in a city, the prices shown in the table are charged depending on the living space.

a) By how much does the purchase price per square meter increase on average between 40m² and 80 m²?

b) What is the purchase price for an apartment with 87m² of living space if you expect a uniform increase in the purchase price between 80m² and 100 m²?

[tired walrus]

do you know how to find avg rate of change

this feels like something you've come here with before

[supple jolt]

for a) i need to do 222k-135k / 80-40

right?

[tired walrus]

missing parentheses.

[supple jolt]

right

[tired walrus]

what?

[supple jolt]

what about for b

oh

you forgot what i said?

or what

[tired walrus]

no, i fully remember it.

[supple jolt]

ok then

[tired walrus]

and i still think it was incredibly disgusting of you to say that.

anyway for b you will need a similar calculation and also some reasoning

[supple jolt]

i was thinking maybe draw a straight segment between the 2 points

[tired walrus]

sure.

[supple jolt]

i found m

[tired walrus]

you're gonna need the calculations either way.

[supple jolt]

its 2

but how do i find b

[tired walrus]

between 80 and 100 m^2, the price increases at a rate of ____ euro/m^2.

[supple jolt]

it doesnt cut the y axis

[tired walrus]

you don't need it to cut the y-axis.

you could extend it that far if you wanted, but it's unnecessary.

[supple jolt]

y=mx+ b

and b is the cut with y axis

but the function is uniform only between 80 and 100

so i cant extend the line

[tired walrus]

think about what you actually want

you want the value of this function at x=87

[supple jolt]

yes

so we need a function

[tired walrus]

you can find this by adding 7 times m to its value at 80.

unless you are such a square that failure to follow Universally Applicable Rules sends you into a panic attack.

[ember jay]

can u send photo here?

[supple jolt]

whats that supposed to mean (ann)

[ember jay]

if u need help is photos allowed

[supple jolt]

yes

[versed crater]

This isn’t your channel though

If you need help go to #❓how-to-get-help

[supple jolt]

how did you get to that

[ember jay]

sorry i didnt know

[tired walrus]

P(87) - P(80) = m * (87 - 80)

P(x) is the price of a flat with area x square meters

whether you measure price in euros or kiloeuros is up to you but you have to pick one and stick with that choice.

[supple jolt]

P(87)=m*something?

[tired walrus]

...

no?

[supple jolt]

then how did the m get there

[tired walrus]

m is that slope which you just found

[supple jolt]

m* something - m* something else= m(something-somethign else)

[tired walrus]

or which you said you found

[supple jolt]

yeah m is 2

[tired walrus]

2 k€/m^2?

[supple jolt]

wait

[tired walrus]

congrats on the worst statement of the distributive law ever lol

[supple jolt]

m is 2000 not 2

euros/m^2

[tired walrus]

2 euros/m^2?

[supple jolt]

2000

[tired walrus]

ok sure

so the price goes by 2000 euro for every square meter added between 80 and 100

an 80 m^2 flat costs 222,000 euro

we add 7 m^2 of area to it

how much does the price increaese

increase*

[supple jolt]

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

2000*7

btw what would be the equation of the line

y=2000x?

on the interval [80, 100]

?

[tired walrus]

y = 222000 + 2000(x - 80) if you wish.

you can put that in y = mx + b form if that puts you at ease or calms the demons in your brain.

[supple jolt]

ok

thanks

.close

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[torpid birch]

can anyone help with binary numbers?

[torpid birch]

especially 1’s and 2’s complement numbers

[final saddle]

@torpid birch Has your question been resolved?

[final saddle]

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[night vigil]

I have a matrix A = 3×3 (0 1 2 0 0 3 0 0 0). How can i easily calculate A+A²+A³+...+A²⁰?

I don't want solution, only formula to apply

[night vigil]

<@&286206848099549185>

[candid hull]

so $A = \begin{bmatrix} 0 &1&2\0&0&3\0&0&0\end{bmatrix}$

[soft zealot]

aPlatypus

[candid hull]

just making sure @night vigil

[night vigil]

Okk

[candid hull]

yeah just compute A^2 and A^3

you'll see something nice happening

[night vigil]

Alright

[candid hull]

@night vigil got it ?

[night vigil]

@candid hull got ( 0 0 3 0 0 0 0 0 0)

[candid hull]

yeah that's A^2

what about A^3

[night vigil]

That's A³

[candid hull]

nope

it is A^2

[night vigil]

A photo is sending

[candid hull]

alright

[night vigil]

@candid hull

[candid hull]

yes you computed A^2 not A^3 here

you even wrote A^2

[night vigil]

(0 1 3 0 0 0 0 0 0) is the result of A²

Then i multiply with A

[candid hull]

nah the 1 shouldn't be there

[night vigil]

Can you circle where i got wrong?

@candid hull

Nvm i found the problem

@candid hull THE A³ IS ONLY 0

[candid hull]

yeah

[night vigil]

TYSM

[final saddle]

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[tranquil pine]

a walker covers 12 km in one hour show that there is at least one 30 min interval during which he covers exactly 6 km

[tranquil pine]

someone to help I never did this type of problem

[wheat igloo]

Are you sure about the exactly ? He could travel 6.1km in 30min and 5.9km in the 30 other

[tranquil pine]

Yeah this the question

It’s in French and I did the translation and it’s correct since I know both french and English

I think we will use the ivt but idk how

I have to find a function here

[wheat igloo]

Ho i get it now

Yes

[tranquil pine]

Idk what is the function

[wheat igloo]

You should use two functions

The first one is the lenght of the path he covered in t time

Such that f(0)=0

and f(60) = 12 (In minutes)

The second is the distance he covers in 30 min

[tranquil pine]

Oh I see noa

Now

[wheat igloo]

g(t) = f(t+30)-f(t)

Which is the distance covered in 30min

[tranquil pine]

Oh thank u so much to use the ivt I have to find an f(alpha)xf(beta) =0?

[wheat igloo]

No you actually have two options

You have to do a bijection

Either g(0)=f(30)<6

then g(30) =f(60)-f(30)>6

[tranquil pine]

Why 6?

[wheat igloo]

f is the distance in km

f(60)=12km

and f(0)=0km

Also f is continuous since the movement is continuous

[wheat igloo]

We're doing a bijection where we look at three cases :
g(0)<6
g(0)>6
g(0)=6

Since we want to show that there exists a 30min interval in which he travels exactly 6km

[tranquil pine]

Why we can’t use the ivt ?

[wheat igloo]

And g is the function that gives us the distance traveled in 30min from a point t

[wheat igloo]

You have to fulfil the conditions of the ivt to use it

You have to show that there exists two values of g such that 6 is in [g(alpha);g(beta)]

[tranquil pine]

Oh cuz we don’t work like that in school wait

[wheat igloo]

La fonction f doit être continue sur l'intervalle [a;b] + le réel k doit être compris entre f(a) et f(b) (from the web)

[tranquil pine]

YEs I see now haha I think since I study maths in French it’s confusing sometimes

[wheat igloo]

Ok 👍🏻

[tranquil pine]

Here k is 6

[wheat igloo]

Indeed

and you have to show that you can "encadrée" 6 by two values of g

[tranquil pine]

G(0)=6?

[wheat igloo]

We'll do a "Disjonction des cas"

All the cases are covered by the three relations :
-g(0)<6
-g(0)>6
-g(0)=6

[tranquil pine]

G(0)=f(30)-f(0)

12?

[wheat igloo]

If g(0)=6 the answer is a given

[wheat igloo]

Yes

Let's take the case g(0)<6 so that you can vizualise better

[tranquil pine]

Well sorry I’m dumb

[wheat igloo]

No dw

[tranquil pine]

Haha okay

[wheat igloo]

if g(0)<6

f(30)<6

Now we will compute g(30)

its f(60)-f(30)

we know that f(60) = 12

[tranquil pine]

Yeah

[wheat igloo]

And f(30) is smaller than 6

Meaning f(60)-f(30) is bigger than 6

[tranquil pine]

Yeah I see now

[wheat igloo]

So you found your two values

And now you can apply the ivt

For g(0)>6 you do the same reasoning

[tranquil pine]

Here u just suppos that g(0)<6 right ?

[wheat igloo]

yes

[tranquil pine]

Okay so basically we have to find the k that verify the condition ?

[wheat igloo]

Since g(0)<6, g(30)>6 and g continuous on 0, 30, by the ivt there exists at least one value "a" for which g(a)=6

[tranquil pine]

Oh okay thank u so much

[wheat igloo]

np

[final saddle]

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[quaint forge]

can I get some help with b pls?

[quaint forge]

here is my sketch and (a) part

[wet warren]

!status

[final saddle]

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

[wet warren]

So you are at 4?

[quaint forge]

no like I know how to do a and I've done it

but idk how to start for b

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@quaint forge Has your question been resolved?

[final saddle]

@quaint forge Has your question been resolved?

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[distant spindle]

Idk Part b

[distant spindle]

<@&286206848099549185>

.close

[final saddle]

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[vagrant wraith]

Need some help for rules of inference, if x is not an element of A, then x is not an element of AintersectB

[vagrant wraith]

what am i suppose to use for this?

[robust mulch]

A intersect B is a subset of A

[tranquil pine]

do you just want to show that this statement is true?

[vagrant wraith]

yes, im suppose to use one of the rules of inference to show this

[tranquil pine]

can you use a proof by contradiction ?

[vagrant wraith]

oh yes i think im allowed to

is there no more direct way though

[tranquil pine]

i think contrapositive or the contradiction methods are the fastes not sure about a direct way

[vagrant wraith]

hmm okay i will try to think about it a bit more, thanks for this

.close

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[tranquil pine]

Hey so, I do not necessarily want a proof, I would simply be happy if somebody could help me with some of the notation of specifically 3.:

[pearl plinth]

How fast do you usually receive help if it all @tranquil pine

[tranquil pine]

As far as I have understood, \pi(a) = [a] and Sec(\pi) is just the set of all s: \pi(s([a])) = 1 right? Specifically, is $1_{R // ~}$ the identity element of $R / ~$?

Oh wow, this does this right here, sorry I'm new to this

[tranquil pine]

This is my first time here after a long time

[pearl plinth]

I feel people only really go to channels about hs math and quadratics I don’t think anybody will be coming any time soon 💀

[soft zealot]

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

[tranquil pine]

Hahah okay I mean I tried

I'm just a poor CS grad taking math courses and being a lil confused

[pearl plinth]

I wish I could help but this looks like it’s passed what I’ve learned

[tranquil pine]

Thank you a lot anyhow

[pearl plinth]

What class tho

I’m the opposite I’m a math undergrad taking cs courses

[tranquil pine]

It's about Computer Algebra and we are just setting up definitions

Essentially, generalising the Euclidian algorithm for division

[pearl plinth]

Oh yeah makes sense why I wouldn’t know

[tranquil pine]

And later doing some symbolic math stuff. The people have taking a few abstract algebra classes and I'm a little lost, but it is starting to make some sense

Just 3. is tripping me up a little

[pearl plinth]

I’m taking it soon I know some stuff about like groups and stuff but that’s about it

[tranquil pine]

I mean that's already quite a lot then

[pearl plinth]

Have u done any topology

[tranquil pine]

No not really

[pearl plinth]

Dang well worth a shot

Yeah just thought I’d say I doubt anyone will come to save us

😅 it’s just people helping with quadratics and hs math for the most part. At least from what I’ve seen

[tranquil pine]

The "advanced mathematics" section has some pretty wild stuff

[pearl plinth]

There are separate channels based on topics though maybe you’ll have more luck there

[final saddle]

@tranquil pine Has your question been resolved?

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[tawny ivy]

Dont know if h can see it

But what am I doing wrong

I set up the hessian matrix

To figure out if it’s a saddle paddle, local min, local max

[final saddle]

@tawny ivy Has your question been resolved?

[tawny ivy]

No lol

[vital crag]

!original

[final saddle]

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

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

[vital crag]

why do you say your work is wrong?

[tawny ivy]

Because I get both eigenvalues are positive

Which means it's a local min

But when I look at the facit

He gets that A=(1,1) should be a saddle point

Which I would've also gotten if the eigenvalues were mixed signs

[vital crag]

i see

you shouldn't be finding the eigenvalues of the Hessian

you should follow the second derivative test

[vital crag]

like it says here. see p 1010. should look something like https://mathworld.wolfram.com/SecondDerivativeTest.html

[tawny ivy]

Wtf?

page 1010?

What is even that?

That's the coolest thing ever

[tawny ivy]

p. 1010?

[vital crag]

it's your book, so maybe?

[tawny ivy]

We don't have a book

hahaha

It's from 2021

So maybe they had

[vital crag]

yea just use this link i guess

[tawny ivy]

But thanks for this https://mathworld.wolfram.com/

this is very useful

But, this is also sort of what I had done

I also had it in this cheat sheet i had

but i just thought

I still had to do the hessian matrix

Which i technically also do actually

And then it's the determinant of that

@vital crag what's the point of the hessian matrix and eigenvalues then?

If you don't even need all the eigenvalues stuff

[vital crag]

see https://en.wikipedia.org/wiki/Hessian_matrix#Second-derivative_test

depends on the problem you're trying to solve

[tawny ivy]

But it looks like it says the same?

test whether a critical point x is a local maxiumum or minimum

[tawny ivy]

It annoys me a bit i can't use hessian matrix because I feel like that's the point

"Minima/Maxima for Functions with more Variables"

like wut

[tawny ivy]

But i still don't get the right answer i get D=108

Oh.. I see I have done a mistake with 6 instead of -6 as well.

[tawny ivy]

But still.. ^>:(

okay i guess it was above as well

weird..

But I’m guessing this is right

[final saddle]

@tawny ivy Has your question been resolved?

[final saddle]

@tawny ivy Has your question been resolved?

[final saddle]

@tawny ivy Has your question been resolved?

[final saddle]

@tawny ivy Has your question been resolved?

[final saddle]

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[severe pier]

Can someone help me?

[severe pier]

I need the sum of roots of 6x^3-30x^2+7

[tired walrus]

do you know vieta's formulas

[final saddle]

@severe pier Has your question been resolved?

[severe pier]

When I did it myself I got 5

Using the vieta

Does is sound right?

[outer hamlet]

yup

[severe pier]

Thanks

[final saddle]

@severe pier Has your question been resolved?

[final saddle]

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[rugged yoke]

any tips on this?

I am so confused

what is it even asking me

[final saddle]

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[wicked wolf]

is option d true?

[wicked wolf]

the options says it should be but I didn't get relation

solved

Q.32. For a constant vector $\vec{a}$, which of the following relations is/are CORRECT?
(a) $\vec{\nabla}(\vec{a} \cdot \vec{r})=\vec{a}$
(b) $\vec{\nabla} \cdot(\vec{a} \times \vec{r})=0$
(c) $\vec{\nabla} \times(\vec{a} \times \vec{r})=2 \vec{a}$
(d) $\vec{\nabla} \cdot[(\vec{a} \cdot \vec{r}) \vec{r}]=4(\vec{a} \cdot \vec{r})$

[soft zealot]

emergency_math

[wicked wolf]

I had doone a calculation mistake

.close

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[tranquil pine]

I am asked to state following set enumerated form: H = {x ∈ N| x < 0}

My question is: How is it possible that x is less than 0 if x is a natural number?

[candid hull]

How is it possible that x is less than 0 if x is a natural number?

you're right it's impossible

@tranquil pine

[frozen hull]

Assuming there isn't an error, that set is the empty set.

[candid hull]

that's maybe a bit too much of a hint lol

[tranquil pine]

So just H = {}?

[candid hull]

yes

[tranquil pine]

Ok

solved

.close

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[upper folio]

i've been try to solve this but i just can't find the right answer

[rustic wedge]

send the full problem

[upper folio]

i think its related to this but we already answered this question

[cosmic warren]

What's T_k

[upper folio]

what's T_k?

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[hardy parrot]

Can anyone help me with this please? Idk if what i did is correct. The question is "is the subspace W = P2(x)?

[hardy parrot]

I did the matrix thing and resulted in one of the equations being 2=0 so i just discarded that base, but idk if i can do that

I forgot a minus o: but still, the question remains the same, idk if i can just discard a base like that

I think the proof might be incomplete

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[deep dome]

I need help with this angles exercise. Calculate x

[junior radish]

Orange = 180°

[little python]

!status

[final saddle]

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

[deep dome]

1

[little python]

do you know this

[deep dome]

yes

although they told us that we should not complete it

that's why I sent it that way

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[spice field]

Anyone knows how to solve the following question ?

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[coral basin]

need help setting this up

4x + 1/x?

[rotund citrus]

missing the equality, it has to be positive.

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[digital scroll]

Help why did it round off

[digital scroll]

Idk

[rotund citrus]

I wanna say it's because that although 0.16 is not something you usually round up, in the context, the rabbits are definitely more than 1986788, but you can't have a fraction of a rabbit, so they round up.

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[peak zinc]

am I doing either of these right?

[rotund citrus]

1. you forgot the negative when using power rule. (-1/2)

[peak zinc]

ah i see

that shouldn't effect my final answer since im looking for x = 0 right

[rotund citrus]

also when moving dx over to the rhs for 2, it should be for the whole thing

dy/dx = 6x + 5
dy = (6x + 5)dx

[peak zinc]

ok got that

so my number 2 should be 11.6 and 23.2?

[rotund citrus]

yesd

[peak zinc]

what about my number 1? do i do anything else after solving for x=0?

[rotund citrus]

well they are asking you for the linear approximation, since you missed the (-1/2) when finding the derivative, you're missing the -1 factor for your slope. other than that it should be good.

y = (-1/54)x + 1/3

[peak zinc]

any idea how they got the number on the right here?

these are the answers btw

[rotund citrus]

dy/y maybe for the relative error?

not sure what that is

[peak zinc]

hmmm, ok it could be a mistake so ill ask about it later

anyways thanks for the help!

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[peak zinc]

I am getting a super large number, am I doing this right?

[severe hawk]

it's correct up until y=3125x-12500; it isnt onwards

m=3125, not 3125x

[peak zinc]

ah ok, just accidently wrote x in there

what about the right side?

[severe hawk]

on the right, "y" would be your result, 4.9^5; however, your "x" is 4.9, not 4.9^5

also, you cannot use the equality, since you're not calculating 4.9^5 exactly. You're approximating it.

[peak zinc]

so i would use 4.9 instead of 4.9^5?

[severe hawk]

so you'd have that (4.9^5) is approximately equal to 3125*4.9 -12500

[severe hawk]

because you're now working on the line

[peak zinc]

i dont know what you mean by working on the line

[severe hawk]

okay, gimme a second to graph it

This is your function x^5 (scaled in y to 1/600 so it doesnt go to bullshit high)

now, computing the 5th power of a number is hard

because you gotta multiply the number by itself 5 times and that sucks

so you wanna work less

[peak zinc]

ok im following

[severe hawk]

so you want an "approximate" value that is close, but easier to calculate.
So you're gonna draw that same function, but approximately. At least, close to 5

since straight lines are easier to draw and calculate, you're gonna get a straight line that is "kind of" the same as the function.
That's your tangent line, y=3125x-12500

[peak zinc]

ok i got it

[severe hawk]

now, that line is a good approximation close to x=5 (again, scaled so it doesnt go to bullshit values)

[peak zinc]

ok i think i understand

[severe hawk]

since you calculated the tangent at x=5, the line AND the finction are equal at exactly x=5. They are also close when you're near x=5

since computing values on the line are only one multiplication and one addition, and that's easier than 5 multiplications, you're gonna calculate "where am i in the line, if x=4.9"

[peak zinc]

ah ok

thanks for explaning!

[severe hawk]

so if you're in x=4.9 on the line, you got that approx(y) = 3125*4.9 - 12500

[peak zinc]

thanks for the help!

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[severe hawk]

.scaled better, B would be your tangency point, and A your approximate point on the line

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[plucky spoke]

The result of applying a 50° clockwise rotation followed by a 50° counterclockwise rotation with the same center is

[random forge]

what do you think it is

[plucky spoke]

I think it's the same rotation

Like it cancels eachother out so it lands in the same spot

But im not sure out of the answers given whatd i click

[random forge]

identity kinda means "no change"

[plucky spoke]

So it would the identity motion?

I didn't know that thanks

[random forge]

well identity in things like that means "the thing you have to do to have no effect

you could say an identity function could be like f(x) = x

so an identity motion is the motion where you start and end at the same spot

its like not quite right, but the idea is the same

yeah E seems like the best answer

[plucky spoke]

Ok thanks!!

I have one more question

I am completely lost

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[random forge]

any thoughts?

vector v is <1, 2> where it goes across one and up two

[plucky spoke]

i got it

it was caeb

[random forge]

good work

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[sonic crystal]

Not sure how to begin with this

[eternal granite]

I’d say to use the dot product formula to find the angle

[sonic crystal]

What’s the dot product?

[eternal granite]

So turn EA into a vector and EM to a vector

[sonic crystal]

Oh I know nothing about vectors

[eternal granite]

Oh is this not a vector question?

[sonic crystal]

nope

It’s just geometry/trigonometry

[eternal granite]

Well turning it into vectors could solve it

If you want another way to solve it

[sonic crystal]

Well I haven’t learnt vectors so yeah lol

Surely there’s another way that’s much more simpler

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[abstract imp]

i dont understand the question and the answer

can someone explain please

[tranquil pine]

Does that make sense

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[abstract imp]

why isnt only run number 5 +1 because isnt the other runs all /2 since it says all the other games they score twice as many?

so like why does run 1 3 7 9 also have +1 instead of /2

[tranquil pine]

In 5 games they won with double points and in other 5 games they lost by one