help-0

[twin nimbus]

yes

[gleaming jacinth]

nope i think im good for now

tysm

.close

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[raven void]

!help

[lone heart]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[next stratus]

does it go on forever

[tardy stag]

$\sqrt{11\s{11\s{11...}}} = x$ then square both sides

[ocean seal]

hayley (no cheese)

[next stratus]

if so i got 11 and 0, maybe options are wrong?

[raven void]

i got the smae

[next stratus]

also i think 0 is rejected

[raven void]

the text book says its d

[tardy stag]

i'm not sure where those numbers would have even come from

i also get 11 and 0 as fixed points of f(x) = √(11x)

[next stratus]

it also depends on what the question means

if its like what does it approach if we started with a random value then its 11

but if we take 0 specefically then we will get 0

[raven void]

the text book include a hints section let me pass te hint

what does it means idk

[lost badger]

The book used (a^(n-1))^n/2

[raven void]

is the question worng or very badly worded?

[raven void]

oh

[lost badger]

And if you use 11 as a and 16 as n, then option d) comes out

[next stratus]

I think the second part of this video helps to understand what the solutions mean: https://www.youtube.com/watch?v=CfW845LNObM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr&index=12

[raven void]

yay

[lost badger]

It’s the generalised formula for nested radicals

[raven void]

im solving grade 9 question

[raven void]

i did not know

[next stratus]

oh nvm but its still interesting to know what it means

[raven void]

i thought a is i multiplay

[raven void]

im going to watch the full series im on ep 2 rn

i have another question

[next stratus]

yes

[raven void]

solve it please i am literally demotivated that im not able to do that simple of a question

[next stratus]

use laws of exponents to find the value of n

did you do that?

[raven void]

i used law of indices got m=4 n=2 which is worng

[next stratus]

m can still be any value it need not be 4

but n=2 is correct

[raven void]

please solve it 🥲

[next stratus]

yeah the qs is wrong

but if you interchange m and n in the first part

then its solvable

answer comes out as 2

[raven void]

it becomes

right

ok

last question

i do not even know where to start

[next stratus]

prime factorisation

[raven void]

oh i get it

[next stratus]

and think of the radicals as powers

yeah

also what is this for? olympiad, I dont think i ever saw Qs like these in 9th

[raven void]

yeah obv

this way out of school territory

thnx to the server im able to study

[next stratus]

yeah i barely studied before my finals and still got neary full in 9th, school exams are pretty easy

[raven void]

yeah

i have a last one

[next stratus]

ok

[raven void]

it requires no solving

but i cant figure out the right option

[next stratus]

ok um whats the Qs

[raven void]

im getting (81/64)*x

[next stratus]

that's wrong

[raven void]

i know thats why im here

[next stratus]

you have to use the approach in the begonnong

beginning

take it as x

and square both side

you'll get sqrt(81/64*x)=x

then just solve

[raven void]

is it b?

[next stratus]

no its 81/64

srry mb

one sec

[raven void]

please solve

[next stratus]

yeah its 81/64 i'll send sol give me a min

[raven void]

ok

[next stratus]

do you get this?

[raven void]

yeah i got this too

but it is not in the options

[next stratus]

yeah now both are equivalent

so sqrt(81/64 x)=x

squaring both sides

81/64 x=x^2

=>x^2-81/64 x=0

factorise and fin sol

[raven void]

oh x=81/64

[next stratus]

yesss

[raven void]

you are the goat

[next stratus]

this method is called recursion

[raven void]

ok

[next stratus]

anything else?

[raven void]

yeah

i see a question

[next stratus]

hmm it doesnt seem to fit the case a=b=c=p=q=r=1, so there must be some mistake

[raven void]

let me screenshot the hint

[next stratus]

they're basically doing some random steps to get p=q=r=3, so yeah the qs is wrong from the counter example i provided

[raven void]

so its basically a^1/3 b^1/3 c 1/3??

[next stratus]

yess each term a b and c is equal to that acc to qs

i mean hint

[raven void]

solve it please

[next stratus]

i mean its wrong so there isnt any point in solving it

but their powers are same

that p=q=r=k

pqr is k^3

a^k=b^k=c^k implies a=b=c

so abc=a^3

k=3

pqr=27

[raven void]

the question is worng??

[next stratus]

take all the values as 1

you wont get pqr=27

pqr=1

[raven void]

see options

[next stratus]

none of the options will give one

[raven void]

ohh

[next stratus]

you'll get 2 3 9 2

[raven void]

ok

iunderstand thnx

thnx

im going to play clash royale bye bye

[next stratus]

bye lol

[raven void]

.close

[lone heart]

Channel closed

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[raven void]

.reopen

[lone heart]

✅

[raven void]

insane pull rn

.close

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[plush echo]

Guys

[plush echo]

I need help

[undone cedar]

You should probably post your question so a helper knows what exactly you need help on

[plush echo]

How can I do that

Alr

Is it ok if it's in spanish?

[undone cedar]

Type it out, post an image

The rules say it’s ok, but just know it might increase the time it takes for you to get help

[plush echo]

basically I need to calculate the "net force"

Or smth like that 😭

[raven void]

i can help

[plush echo]

YES

PLEASE

[raven void]

send the photo of the question

i ill google translate do not worry if its in spanish

[plush echo]

I used google translate 😃

[raven void]

5 or 4?

[next stratus]

you know how to resolve vectors and add them?

[plush echo]

I don't

😭

[hexed beacon]

thats going to take some time to explain 💀

[raven void]

yeah

[plush echo]

https://tenor.com/view/maymun-mordeus-gif-3446599367391932953

[next stratus]

uhh well have heard about stuff like cos theta component

sin theta component?

no?

[plush echo]

yes

[next stratus]

alright resolution is basically that

[plush echo]

wth 😭

[next stratus]

bro removes spaces that shi is impossible to read

[raven void]

its chatgpt

wait lemme screenshot the solution

i know how to solve this but im kinda sleepy its 11 pm here

[next stratus]

!nogpt

[lone heart]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[raven void]

ok

[plush echo]

but

[whole wasp]

which arena or league

[next stratus]

here is an example for resolution

s(sorry for terrible handwriting)

[raven void]

im kinda noob not playing regurlarly im arena 15

[plush echo]

HAHAHA I LOVE IT

[whole wasp]

uss

[next stratus]

now free body diagram is basically resolving all the forces on the body in two directions

[next stratus]

which are perpendicular to each other

butterfly

[plush echo]

:O

[next stratus]

so think of the forces as vectors and try drawing one

if u don't get it i'll help

[plush echo]

Thank you so much!

[raven void]

which arena are u?

[limpid turret]

Seriously. Don't use gpt. It's a bannable offense

[raven void]

im sorry

😭

[lone heart]

@plush echo Has your question been resolved?

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[warm quarry]

4, A is not invertible and B is?

[warm quarry]

Like I dont really know what approach your supposed to do for this normally

mb it is invertible ;-;

det A = 2 and det B = 0 so not similar but is there like a better/faster way?

[vale wigeon]

not really

like, you could establish an eigenvalue for one matrix that the other one "obviously" lacks or whatever

if said obviousness can even be pulled off

not much else you can do

[warm quarry]

aah okay

thanks ann :)

[vale wigeon]

you can look at trace

[warm quarry]

trace?

aah is that uhm

the sum thingy?

[vale wigeon]

sum of entries down the diagonal

aka the sum of all the eigenvalues

[warm quarry]

aaah alright

[vale wigeon]

this matches for similar matrices and isnt hard to calculate

[warm quarry]

true

alright thanks

I know enough for now thank you Ann have a good day/night

.close

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[warm quarry]

.reopen

[lone heart]

✅

[warm quarry]

I made a mistake they indeed both have det (A) = det (B) = 0

[vale wigeon]

their traces are different

[warm quarry]

ye imma do that now

[vale wigeon]

3 vs 4

it's near instant

[warm quarry]

how did u notice that so fast?

[vale wigeon]

trace is the sum of all the diagonal entries

[warm quarry]

u cant just read the diagnals right?

[vale wigeon]

yes you can lol

[warm quarry]

huh is that not only allowed with a triangle matrix?

[vale wigeon]

you misunderstand

a triangular matrix has the property that the eigenvalues themselves appear on the diagonal.

but even if your matrix isn't triangular, the sum of the eigenvalues is invariant under similarity.

[sly mantle]

$\tr A=\sum_i a_{ii}$

[ocean seal]

ロケットジャンプ

[sly mantle]

this formula sums diagonal entries and ignores all others

[warm quarry]

aaaah alright thanks guys :)

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[pliant hill]

i solved this integral

but it was a multiple choice answer question

a) x+tan(x) + C
b) tan(x)-cot(x) + C
c) x+cot(x) + C
d) tan(x)+cot(x) + C
e) 1/cos^2(x) + C
f) 1/sin^2(x) + C

[pliant hill]

is this straight up wrong or is it equal to one of the answers above?

[serene scarab]

write cot as 1/tan and then expand it

what you've done is correct

[pliant hill]

ah good idea

initially i tried expanding as cot(x+x)

[serene scarab]

i think that should work as well

[pliant hill]

but i got tanx-cotx doing this

[serene scarab]

yeah thats correct

[pliant hill]

yeah thanks

silly question by me

[serene scarab]

its a pain to remember cot(a+b) if you already know tan(a+b)

[pliant hill]

exactly

had to google it ))

.close

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[honest harness]

Is my induction correct?

[undone cedar]

what is the original function?

[honest harness]

Fibonacci numbers

<@&286206848099549185>

[winter light]

Yep, it's correct

[lone heart]

@honest harness Has your question been resolved?

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[honest harness]

thank you!

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[wise holly]

i want help with this partial fractions problem

[vale wigeon]

ok lets just retype that so i dont have to squint my eyes to read it

[wise holly]

sorry

[vale wigeon]

$\frac{2x^2 - 5x + 4}{x(x-1)^2} = \frac{A}{x} + \frac{B}{x-1} + \frac{C}{(x-1)^2}$

[ocean seal]

Ann

[vale wigeon]

ok, current progress?

[wise holly]

hold on im uploading a screenshot to discord

literally havent done anything past this and idwk if its the right way

in the lecturen he told us to set x as some value that maes the others 0

basically singling out a b or c so u can easily find the value

[forest marsh]

<@&268886789983436800>

Uuh

[wise holly]

but obs that wont work here

or i dont think it would idk

[vale wigeon]

ok heres the thing

when you choose which x-values to plug in you are not actually constrained by any rule that says you HAVE TO plug in any specific ones

it's CONVENIENT to pick ones that kill as much as you can except one term so you can get the value of one of the letters directly ish

here, you can set x=1 and get C, and also set x=0 and get A

once you know these, you can proceed by one of two routes:

• plug in your A and C into the equation 2x^2 - 5x + 4 = A(x-1)^2 + Bx(x-1) + Cx and simplify as much as you can, then find B that way
• plug in whatever other random value of x you want, and get an equation involving A, B and C --- but that'll be OK anyway as you know A and B already.

[wise holly]

ok i think i got it

just wanna make sure this is right (idk if its legible...)

thanks so much btw

[lone heart]

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[mighty kelp]

.

[latent cosmos]

So you're supposed to start at a and going right in a loop for the top box right?

My notes dont really show any examples for this....honestly starting to becoming a reoccuring thing and getting frustrating xP

[proud tree]

Did you find the current in the top loop?

*middle wire

[latent cosmos]

think thats what im doing now.

[proud tree]

Ok tell me if youre stuck on smth

[latent cosmos]

I found a sorta similar example so going off that now:

[proud tree]

Yes and here you will only need the top loop since the only unkown is the Voltage

[latent cosmos]

so just going similar to the loop in the example...

Wouold the 4ohms be postive?

[proud tree]

If you go counter clockwise then no

If you do KCL on the point connecting the 3 wires theres 1A entering and 2 exiting so the 3rd wire has to be 1A entering this point

[latent cosmos]

KCL?

[proud tree]

Did you take kirchoff circuital law?

[latent cosmos]

It says Kirchhoff's loop rule for me

so guess things what you mean

I_1 = I_2+I_3

[proud tree]

Yeah maybe

Yeah all the I entering = all I exiting basically

So you will get that the current in the middle is going from b to a

And its value is 1A

[latent cosmos]

Oh wait, ok so everything left of emf_1 is negative cuz it goes through the voltage if im remember correctly

ok, so think I can form the formula from there.....hopefully lmao

so 6ohm and 1 ohm at the top are positive?

[proud tree]

Yeah if youre going with the direction of current anti clockwise

[latent cosmos]

how do you know, cuz clearly i dont

cuz I thought it was based on the voltage point

[proud tree]

If you find trouble withthe direction extend the arrow of the current

If youre going with the arrow its positive if opposite then negative

But make sure not to extend it into other wires without checking if the current in them is the same

[ocean whale]

It's based on convention, if you "enter" through the positive side, following the direction of the loop, then it's positive. If you "enter" through the negative side, it's minus, but the +/- should be consistent for the loops

[latent cosmos]

theres only the 2 down arrows though

4 and 1 go through emf 1 which goes into negative

but that doesnt matter for the top one?

they are just based on the 20v

[ocean whale]

Are you drawing your loops ccw like that?

[latent cosmos]

yes

counter clockwise

oh do loops start at the a,b points or the voltage points?

[ocean whale]

It doesn't really matter

[latent cosmos]

I dont have an example with 2 voltage points is the thing

like the way to looks youre starting at positive 20v

so 1, 4, & 1, are positive and just 6 is negative

(based on my understanding)

[ocean whale]

You can start anywhere, it's just an equation you are forming

You start at any point

You just have to be consistent

[latent cosmos]

so is that correct?

[proud tree]

Basically if you go one direction for example with the current the values will be positive if you go the other direction they will be negative but the battery will also bi negative so they cancel out

[latent cosmos]

but idk when theyre switching.....

[ocean whale]

So for example, if you went ccw and when you "entered" the resistor and said that's the positive end, then it would look like this

You just have to be consistent with signs, you cannot swap midway

[latent cosmos]

ok so think I gotcha.

20V is negative into positive, wich makes 1 negative, which then goes into +4 and comes out negative...ect.

[ocean whale]

Like E1, notice for the 4 ohm, I drew it entering the resistor as positive and exiting as negative, you do the same with the 6 ohm

[ocean whale]

Signs for voltage source is the same, ie the 20v, going ccw, it enters the + end, so it's positive

Oh wait

Sorry, I just realized they grouped two components, resistor and voltage source into a tiny area

So into the 20V source, it's negative, then the 1 ohm resistor is +, then the 4 ohm is +, then 1 ohm is +. E1 is + and 6 ohm is +

[latent cosmos]

so its all positive?

cuz thats the other thing, I dont have an example with a double voltage in a single loop

and ive barely been scrapping by as it is 😂

im so lost honestly

[ocean whale]

As I mentioned, consistency. If you are entering a resistor, you denote that as positive, so for the top loop, going ccw, when you are entering the resistor it's +

[latent cosmos]

but isnt 6 entering from a negative?

[ocean whale]

No

It enters on the right side

Because we are going ccw

Having two voltage sources doesn't impact anything as long as you are consistent with the signs

[proud tree]

Heres the method I use if you find it easier when youre making your loop when you reach a resistor if the direction of your loop is the same as the arrow then + if not then - and for the batteries if you meet the battery at the negative pole then - and if its positive pole then +

[ocean whale]

Loop 2 is when there are some that are negative, because going ccw, current enters the 1 ohm and the 4 ohm from the - side since we denoted those signs from loop 1 already

[latent cosmos]

why are the middle arrows going left?

[latent cosmos]

Ok so wait, anytime I go through an EMF its positive on both sides?

[ocean whale]

My guess is loop 1 is the bigger loop, loop 2 is the bottom half

[ocean whale]

No it's based on the side you enter from

[latent cosmos]

6 enters the right though which is the negative sign???

[ocean whale]

That's my point, consistency. Yes it enters on the right side of the 6 ohm, but if you recall that I said, if you enter a resistor, we denote the side as the positive end

[lone heart]

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[waxen turtle]

Idk how to do C

[lone heart]

@waxen turtle Has your question been resolved?

[pseudo ice]

Do you know how to identify the type of critical point you have for F, based on what happens to its derivative F'?

[lone heart]

@waxen turtle Has your question been resolved?

[waxen turtle]

umm no

OMG HI CHARTBIT

[marsh hamlet]

Note that here, $F''(x)=f'(x)$, and that if (at least, in this context) $F''(x)<0$, it is a maximum, and if $F''(x)>0$, it is a minimum.

[ocean seal]

mathisfun

[honest nacelle]

just look at the sign change of the derivative of F(x) at each critical point. if it changes from - to + it is a local min and if it changes from + to - it is a local max

[waxen turtle]

idk

wat do u mean sign change at each

[honest nacelle]

you found the derivative of F(x) with respect to x, yes?

[waxen turtle]

no idk wat u guys r talking Abt

[honest nacelle]

how did you find the critical points then

[marsh hamlet]

Did you, just by random guessing, choose the roots of f instead of actualyl analyzing the question?

[waxen turtle]

i just looked at the x axis fr

[honest nacelle]

💀

the critical points are where the derivative of F(x) with respect to x is 0 or defined

[waxen turtle]

Idk my teacher just said like "it's when it hits the x axis"

[honest nacelle]

well, in this problem yes, but think about why that is

[waxen turtle]

Or like the x intercepts I think

[honest nacelle]

it's because d/dx F(x) = f(x)

[waxen turtle]

ohhhh

omg bcuz liek derivative liek undoes the integral right

Fr

[honest nacelle]

yeah i think it's called the fundamental theorem of calculus or something

[waxen turtle]

Fr

so liek how do I know if it scortepsends to a min or max

and how to justify

[honest nacelle]

well, since you know that d/dx F(x) = f(x), simply look at the sign change of f(x) at each critical point

ill do the first one (x=0) for you

[waxen turtle]

wat does sign change do

[honest nacelle]

at x=0, d/dx F(x)=f(x) changes signs from - to +, so x=0 is a local min of F(x)

[waxen turtle]

ohh

[honest nacelle]

it tells you what is happening to the derivative at that point

[waxen turtle]

Soo at 4 it's neother

Bcuz it stays + to +

Fr

[honest nacelle]

yes

[waxen turtle]

OK TY

[waxen turtle]

How do I do D.

[honest nacelle]

the candidate's test states that the absolute max and min of f(x) on [a,b] must occur at a critical point of f(x), at x=a, or at x=b

[waxen turtle]

idk

[honest nacelle]

this basically means that the absolute maximum and minimum values of f(x) must occur at a critical point or on the boundary

does that make sense?

[waxen turtle]

Ohhh

how do I know if it's the absolute extreme

or just a local one

[honest nacelle]

evaluate f(x) at all candidate points

the largest f(x) will be the absolute max

the smallest f(x) will be the absolute min

[waxen turtle]

Don't the local extrema = 0 bcuz they are at the x axis

[honest nacelle]

oh, im sorry

you're trying to find the absolute max and min of F(x)

so evaluate F(x) at all critical points of F(x) and on the boundary

the largest value of F(x) will be the absolute max, and the smallest will be the absolute min

[waxen turtle]

oh F(0)= -2

F(4)=π

Do I check F(2) bcuz it is like the lower bound

How do I check F(x)

[honest nacelle]

well, remember what i said earlier

the absolute max and min can only occur at a critical point or on the boundary

you've evaluated F(x) at all critical points, so where else should you evaluate F(x)?

[waxen turtle]

The boundaries

[honest nacelle]

yes

so do that

[waxen turtle]

wat r the boundaries

[honest nacelle]

well, think about the interval of x-values that F(x) is defined

note that F(x) is defined only when f(t) is defined

[waxen turtle]

I thought it was the bounds of the integral

[honest nacelle]

so what do you think the boundaries are?

[waxen turtle]

2

And infinity

Idk

[sly current]

yeh

[honest nacelle]

no, look at the graph of f(x)

what values of x will give a result for f(x)?

[waxen turtle]

-2 and 6

[honest nacelle]

yes, f(x) is defined only when -2<=x<=6

[sly current]

0 -1

[honest nacelle]

which means F(x) is defined only when -2<=x<=6

[waxen turtle]

WAIT so is this talking Abt like the y value

On the graph

[honest nacelle]

yes

[waxen turtle]

So cool

[honest nacelle]

y=f(x) is graphed

[waxen turtle]

Is F(2)=0

[sly current]

yeh

[honest nacelle]

yes, but x=2 is not on the boundary

[waxen turtle]

Oh I mean -2

[sly current]

no 2

[waxen turtle]

And is F(6) = π+4

[honest nacelle]

yes

so now list all your candidate points in a table: x-values in one column and the corresponding F(x) values in another

[waxen turtle]

Soo (0,-2) and (6, π+4) are my extremes

[honest nacelle]

i cant remember what all the candidates were

oh, yeah -2, 0, pi, pi+4

so yeah pi+4 is highest and -2 is lowest

good job

[honest nacelle]

hopefully it makes sense that there really is nowhere else the absolute max and min can be

[waxen turtle]

ft

Tr

Fr

[honest nacelle]

you know how to find inflection points and concavity?

[waxen turtle]

I have never heard of them

well I've heard or concavity

of

but idk how to find

[honest nacelle]

say we have a function y=g(x)
if g''(x)>0 at a point then g(x) is concave up at that point
if g''(x)<0 at a point, then g(x) is concave down at that point

the inflection points of g(x) will occur when g''(x) changes signs

[waxen turtle]

wat Abt g''(x)=0

[honest nacelle]

g(x) is neither concave up nor concave down

[waxen turtle]

So cool

[honest nacelle]

so, any ideas how to do E?

[honest nacelle]

oh, and by the way. if a function is concave up it will look like a smiley, and if a function is concave down it will look like a frowny

so, a straight line is neither concave up nor concave down anywhere

[waxen turtle]

umm do I prime F

and then do it again

idk

[honest nacelle]

excellent idea

[waxen turtle]

F prime

Equals f

Right

[honest nacelle]

yes

[waxen turtle]

Bcuz liek the prime undoes the intgeral

YAYAYAYA

[honest nacelle]

well, dont stop there

[waxen turtle]

so then I get f'(x)

Or t

[honest nacelle]

you get f'(x)

d/dx F(x) = f(x)

d/dx f(x) = f'(x)

so, remember what i said earlier, inflection points will occur when F''(x) changes signs

[waxen turtle]

OK

So

like

It changes signs at like

WAIT NO

At 2

And 4

Right

Fr

[honest nacelle]

yep

and the justification is simply that you can see on the graph that F''(x)=f'(x) changes signs at those points

now try to do F by yourself

[waxen turtle]

(2,4)

[honest nacelle]

easy

congrats

[waxen turtle]

YAYAYAYA

TY

[honest nacelle]

no problem

[waxen turtle]

wait so a is the like the one at the bottom of the integral right

[honest nacelle]

?

[waxen turtle]

liek on a normal integral

i didn't pay attention in class

plz

[honest nacelle]

i dont understand the question

[waxen turtle]

also how I justify

do I say I you subtract area when it goes below the x axis

is that a reasonable justification

Idrk

[waxen turtle]

liek on bottom and top of the S integral sign

[honest nacelle]

if you're trying to find the area under f(x) on the interval a<=x<=b, then you would find integral from a to b of f(x) dx

where a goes at the bottom and b at the top

[honest nacelle]

it's decent and valid, but mathematically you want to show that G'(x)>0

since G'(x)=f(x)>0 on (0,4) U (8,12), G(x) is increasing on (0,4) U (8,12)

[waxen turtle]

Okii

Ty

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[waxen turtle]

.reopen

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✅

[waxen turtle]

Is 0 and 12 critical points

[honest nacelle]

yeah, critical points of G(x) occur wherever G'(x)=0 or G'(x) is undefined.
since G'(x)=f(x) here, and f(0)=0, 0 is a critical x-value
since G'(x)=f(x) and f(12)=0, 12 is a critical x-value

[waxen turtle]

Okii

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[gleaming jacinth]

<@&268886789983436800> im sorta knew, is this channel not supposed to close?

[clever folio]

It says you closed it?

[gleaming jacinth]

yeah but it still says occupied

so im just confused

[clever folio]

Oh it just takes the bot some time to shuffle it thru

[gleaming jacinth]

oh alr thx

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[tame pebble]

25 - 7 * root 64 / 4 + 32
25 - 7 * 8/4 + 32
25 - 7 *2 + 32
25 - 14 + 32
43

[grizzled stump]

Idk anything about algebra I don't retain information well and I'm in pre algebra my finals are Tomorrow and it's 852pm I've been studying all tri but still fail even ask for help

[vague swan]

me too gang my things due tmr 😭

[vague swan]

thnx for the help!

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[tame pebble]

b o divison m addition s

divison comes first

[vague swan]

oh whoops i meant sub

my brain is dead

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[warped topaz]

Part (b)

y(t) = 0

t^2 = 4

t = +-2

[solid sinew]

hmm i'll give you a hint

[warped topaz]

We dont know whether A is on +2 or -2, but I can see from subbing in x(2) we will get a negative number

So (-2)^2 - 2(-2) - 3

[solid sinew]

1. compute the derivatives

[warped topaz]

4 + 4 - 3 = 5

So A is at (5, 0)

y'(t)/x'(t)

-2(5)/2(5)-2

-10/8 = -5/4

So the answer should be
(1, -5/4)t + (0, 5)

But thats not what they wanted 🤔

I was close, but what did I do wrong?

<@&286206848099549185>

[slim kite]

You should substitute t here, not x

t is -2

[warped topaz]

Ohhhhhhhhhh

-2(-2)/2(-2)-2

4/-6 = -2/3

[warped topaz]

So it should be (1, -2/3)t + (0, 5)?

[slim kite]

Yes

No

Not t, but any constant

[warped topaz]

Ohhhhhh

Wait

But t is any constant

[slim kite]

No, t is time here

The vector shouldn't depend on time

[warped topaz]

I thought thats how you make a vector

[slim kite]

That's the position vector given the point has a velocity

[warped topaz]

Oh

[slim kite]

Here, they just asked a vector tangent to the path. It shouldn't depend on time

[warped topaz]

Ok I see

[warped topaz]

But how come I got different numbers

[slim kite]

And, the y coordinate is not negative, the x one is

[warped topaz]

To the answer they wanted?

[slim kite]

Since the lambda is any constant, it doesn't really matter

They got -4 times your answer

[warped topaz]

-2/3 * -4 = 8/3

[slim kite]

The point moves in this direction, so x should be -ve and y should be +ve

Sorry, -4/3 not -4

[warped topaz]

-2/3 * -4/3 = 8/9 😭

[slim kite]

Bruh

Wtf is wrong with me

Just a sec

[warped topaz]

Its early no worries 😝

[slim kite]

You do the math, their answer / ur answer

That's what it is

[warped topaz]

okok 😇

[slim kite]

Yeah, they did 2 times

*6 times

[warped topaz]

Yeyeye

I see now

Alright, thank you so much!!

❤️

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[hollow scaffold]

help please, so i did a question and i got an answer but my answer was incorrect, and i know how the correct answer was gotten and also how the method works but i dont understand how my answer was incorrect and how i can avoid making that mistake in an exam, i added the question and the correct answer i rubbed out my incorrect answer but i can explain how i got it

[vale wigeon]

well, yeah, do explain your incorrect answer and the method that yielded it.

in as much detail as you possibly can.

[hollow scaffold]

okay so

i started with the isosceles triangle has 2 equal angles

and got 68

then i did angle abg = 68 because vertically opposite angles are equal

and then bgh = 68 because alternate angles are equal

and then i thought the one opposite must also be 68

so 68x2=136

and then 180-136=44

and then i split 44 into 2 for both sides

[vale wigeon]

ok let's see hold on

[hollow scaffold]

and got 22

[vale wigeon]

so, ok, you got angle BGH = 68 and everything up to and including that is correct

and then i thought the one opposite must also be 68
which one's that...?

[hollow scaffold]

lemme show u

[pale lodge]

What was the correct answer?

[vale wigeon]

FGJ then

vertically opposite

[vale wigeon]

see pic 2 in OP

[hollow scaffold]

112

[vale wigeon]

and then 180-136=44
so then how/why did this happen?

did you... think that the 4 angles around G all added up to 180° ?

[hollow scaffold]

...Ohh yeah i did-

now i see where i went wrong

so they add up to 360

[vale wigeon]

a full circle is 360° of course.

[hollow scaffold]

lemme redo it uhh

[pale lodge]

Well you can see the line adds up to 180°

[hollow scaffold]

360-136=224

[pale lodge]

So just 180 - 68 is enough

[hollow scaffold]

and that halved = 112

[pale lodge]

Yep that works too

[hollow scaffold]

yeah i didnt notice that part at first-

i just wanted to understand where i made the mistake

thanks guys<3

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[modern pagoda]

Can someone please explain what it means to derive something and how you typically do it? I need to derive the gompertz differential equation for my big assignment and I am stuck. Maybe just some tips for getting unstuck? srsly my sister won't help me it sucks.

[modern pagoda]

https://cdn.hackaday.io/files/8586367343424/From the Mendelsohn model to the Gompertz and logistic growth law.pdf

This is the paper I am trying to understand.

[north rover]

In general, you want to take something known, and either compress (generalize) or shrink (make it specific).

[modern pagoda]

ok

Would that include approximation?

[north rover]

What kind?

[modern pagoda]

maclaurin series

I've never learnt anything about series before

[north rover]

Sure.

You start with what you know.

[modern pagoda]

but this derivation approximates a value with the maclaurin series

[north rover]

And use your tools (formulae) to get a result.

[north rover]

(I can’t view the document, could you screenshot the portions please?)

[modern pagoda]

fomulae

yes

just showing everything in case you need background info

[north rover]

Ok.

[modern pagoda]

this guy MathIsGreatFun on yt did a video on it

screenshot from video

So he basically starts explaining Volume^2/3 is proportional to area which the paper states

and then that leads to the mendelsohn model

[north rover]

I feel like this goes from general->specific.

[modern pagoda]

oh just tell me something general then

I am soo stuck

just some kind of tips and knowledge might go a long way

like i have never done a derivation

so i use my tools( formulae)

[north rover]

I’m trying to comprehend it.

[modern pagoda]

which in this case is Volume and area

which gets compressed to the mendelsohn equation

bc V^2/3 really isnt the Area just proportional to it

could you call that compressed?

[north rover]

Yes.

[modern pagoda]

ok the next step is appromating the mendelsohn equation to get the gompertz equation

typo

anyway that's generalising again i suppose

it's not shrinking

[north rover]

Eh, not really.

More of a transformation.

[modern pagoda]

okay how so

[north rover]

Like, there are lots of different things to do.

[modern pagoda]

I feel like the approximation is so random.

why do that

i mean it turns out to work is that the only reason??

[north rover]

Hmm.

[modern pagoda]

ok what kind of different things are there

to do

[north rover]

Well, in general.

[modern pagoda]

I will just watch more videos and read maybe it'll make sense before I have to turn in my assignment :/ or my sister decides to help haha

have a great one

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[bright crypt]

hey i need some help with divisions. i know it sounds stupid but it's complicated. anyway i need some help with dividing numbers with decimal points, like 11,3 by 8,4 for example, and some kind of explanation of the algorithm used to do it, thanks

[next stratus]

you can make them whole by multiplying both sides by 10

113 by 84

and then do division normally

[alpine sable]

Don't you have to devide them by 10 once your done

[next stratus]

no

[bright crypt]

got to that point, but i get stuck after one or two decimal points since it becomes 29/84, which is roughly 1/3~ for the 2nd, but i need three digits after the whole

so i have 3/84

[next stratus]

you take a zero from 113.0000

and take as many zeroes for as many decimals

the decimal point in Quotient should have same position as in dividend

[bright crypt]

i completely forgot about the 0 part

thank you so much

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[vale wigeon]

$\int \cos^3(7x) \sin^3(7x) \dd{x}$

[naive ridge]

I don't know hot to solve this. Tried with U-substitution but I really just know the basics about it

[ocean seal]

Ann

[vale wigeon]

is this your integral?

[naive ridge]

yep

[vale wigeon]

what did you take as your u?

[naive ridge]

7x

is it correct?

[vale wigeon]

hm well that kinda doesn't do much at all

[next stratus]

try taking trig funtions

[vale wigeon]

i have a different suggestion

simplify the stuff inside the integral first using sin(2t) = 2sin(t)cos(t)

[naive ridge]

i tried to put it in symbolab but I just didn't understand

[vale wigeon]

you'll get $\frac{1}{8} \int \sin^3(14x) \dd{x}$

[ocean seal]

Ann

[vale wigeon]

which is amenable to a different substitution

[naive ridge]

wait, im processing it in my head lol

ok, think i got it

then i can use u-substitution?

[next stratus]

yes

after a step tho

[vale wigeon]

yes but you have to be smart in what you take as u.

u=14x is a somewhat inconsequential substitution.

[naive ridge]

what would you say i have to take as u then?

[next stratus]

think of cos

[vale wigeon]

u := cos(14x) if you want a spoiler

[naive ridge]

alr, i'll try it

thank you guys so much

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[wispy salmon]

eres gay

[wispy salmon]

no se cuanto es 10t [phone]t

[sly mantle]

no tú

[lone heart]

@wispy salmon Has your question been resolved?

[sly mantle]

.close

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[raw quartz]

Is this right or am I cooked for tomorrow's exam?

[keen idol]

seems correct

[raw quartz]

Thx 🙏

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[prime patio]

can someone double check my work?

[tight pier]

looks correct

[prime patio]

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[prime patio]

tyy

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[heady finch]

What am I doing wrong here?

[marsh hamlet]

You forgot to multiply the 1 by (1+t^2)

[heady finch]

Ohh

Tysm

[marsh hamlet]

On the second step

You're welcome

[heady finch]

Right yeah

.closee

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[real hemlock]

if i have a linear function y=2x evaluated on an open domain (a,b) and i want to find an absolute max, is that the point (limx->b, 2limx->b) or does no absolute maximum exist?

[pulsar kernel]

It's an increasing function so the absolute maximum is simply the ending point.

[real hemlock]

but the endpoint isn't in the domain as it's an open interval

[marsh hamlet]

You could technically say the supremum, but with the formula definition of a maximum, no.

[real hemlock]

okay thank you !

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[blazing brook]

Help solve this for advanced functions trigonometry please 🙏

[buoyant saddle]

quadratic

[pulsar kernel]

2tan^2x - 5tan(x) - 3 = 0
2tan^2x - 6tan(x) + tan(x) - 3 = 0
2tan(x){tan(x) - 3} + {tan(x) - 3} = 0
(2tan(x) + 1)(tan(x) - 3) = 0

2tan(x) + 1 = 0 --- (1)
tan(x) = -1/2
x = arctan(-1/2)

tan(x) - 3 = 0  --- (2)
tan(x) = 3
x = arctan(3)

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[lilac jolt]

i need someone to check if my item 9 and 10 is correcr

[light jetty]

go ahead

[lilac jolt]

wait

[lilac jolt]

while solving for item 10, for the right side

i get a 0/0

do i need to evaluate it in such a way it doesnt go 0/0

[light jetty]

yes

also

for 10

you need to evaluate it from 2 functions of gx

same with 9

[lilac jolt]

wdym, like from left side and right side?

[light jetty]

yes

since it's spilt between 2 different equations

the left and right

[lilac jolt]

@light jetty

here is my workk

[light jetty]

yeppers

good job

looks good

[lilac jolt]

thank you!!

for C though

idk how to do it

[light jetty]

if the limit exists, that means the left side= the right side

so for both respective limits, set the left equation = to the right equation

for 11

[lilac jolt]

2x - a = ax + 2b?

[light jetty]

yeah

wait

[lone heart]

@lilac jolt Has your question been resolved?

[light jetty]

this is the way

but gaddamn

i feel like im missing something

it might be a system of equations thing also, to solve for a and b

[lilac jolt]

is chatgpt reliable with this xD

[light jetty]

might be

[lilac jolt]

my a is 3 + b

[light jetty]

it tends to be wrong when i ask it stuff

[lilac jolt]

i subbed -3

and i got a = 3 + b

[light jetty]

so what did you get for the individual values

[lilac jolt]

what

[light jetty]

of a

and b

a= b=

[lilac jolt]

a = 3 + b
and b = a - 3?

do i sub a and b

[light jetty]

yeah

[lilac jolt]

i just get a = a and b = b 😭

[light jetty]

where are you subbing it into

did you also do the equations for lim approaching 3 ?

[lilac jolt]

oh do i sub it into g(x)

😭😭

[light jetty]

you need to do that find a and b

[lilac jolt]

not yet

[light jetty]

because from lim -3 you got b = a-3

you get another equation from lim 3

and then do system of equations from there

to find both a and b

[lilac jolt]

i got x = 3

a = (-b - 15)/ 3

and b = -3a - 15

[alpine nacelle]

yep

[light jetty]

good job

[alpine nacelle]

if you look at x = -3 you have another eq

so now it's a system

[lilac jolt]

now what

[alpine nacelle]

what are your two linear eq ?

one is b = -3a-15

[light jetty]

you can do elimination or substitution

set them up and find a and b

ex
x+y=3
-2x+y=4

and then you cancel them to find each variable

[lilac jolt]

i wanna do sub

but where do i sub them to

[alpine nacelle]

one into the other
you have a = b+3
and b = -3a-15
so for example you can replace the b in the first eq

or you could replace the a in the 2nd

[lilac jolt]

i got a = - 3

[alpine nacelle]

yup

so b = ?

[lilac jolt]

-21?

[alpine nacelle]

no, careful with the signs

[lilac jolt]

-6

[alpine nacelle]

yes

[lilac jolt]

😭

now what

[light jetty]

those are your value

s

plug them into the gx equations

and find the limit

[alpine nacelle]

the question asked what were a and b such that the limits exist, you have them
then it asks for the limits, which are g(-3) and g(3)

[lilac jolt]

erm theyre both dne

@alpine nacelle @light jetty how did i do

[light jetty]

hold on

where is the absolute value

oh

lhopitals

[lilac jolt]

absolute value?? 😭😭😭😭

[light jetty]

oh my bad wrong question

[alpine nacelle]

there's no dne, you chose a and b such that the limits exist

[light jetty]

i was looking at the ones for 9 and 10

[alpine nacelle]

I think you're confused

[light jetty]

whatd you get for a and b again ?

[lilac jolt]

-3 and -6

[light jetty]

a =-3 and b=-6

?

[alpine nacelle]

yes

at x = -3 and x = 3, g(x) = ax+2b = -3x-12, so you only need to give g(-3) and g(3) (you chose a and b such the limits exist so you can take the def of g at these points)

[light jetty]

dont the limits need to be equal from the left and right

for there to be a limit

[alpine nacelle]

if you define a function at x0, then for the limit to exist means continuity, f(x0) = lim f(x) when x -> x0

g is defined on -3 and 3

[light jetty]

you did the lim from -3 right wrong

well you missed a 2b

[lilac jolt]

oh silly

[light jetty]

yeah

but the limits need to be equal from the left and the right for there to be a definite limit at point c

[lilac jolt]

omg they do exist

is it done now

[alpine nacelle]

that's already what is forced, since the question asked for a and b such that the limit exist

it has to be continuous, you chose a and b such that it is

[light jetty]

but theres no hurt in doing that

im assuming this is for an ap exam

[alpine nacelle]

I mean, indeed

[light jetty]

theyll want to see the work for both sides

[alpine nacelle]

but you're calculating the same thing by the very definition

twice

[light jetty]

yeah i get that

im just saying