help-0

[dapper hound]

idk how to solve that

since idk what two numbers would multiply to -0.25 and add up to 2

@alpine sable

wait

would I just use the quadratic formula

[alpine sable]

do you use delata formola

[dapper hound]

deleta formula?

whats that

[alpine sable]

?

means quadratic formola
b^2 -4ac

[dapper hound]

this is what my teacher did

I dont understand it

like why

[alpine sable]

a x^2 + bx +c

delta = b^2 - 4ac

[dapper hound]

oh yeah no duh I know that

isnt that jus the sqrt() part of the quadratic function

thing

formula

[alpine sable]

i cant undestand your problem

where?

[dapper hound]

ok basically

what do I do to solve for the h(x)=0

for the x

[alpine sable]

first find delta

[dapper hound]

what is delta

[alpine sable]

b^2 - 4ac

[dapper hound]

the sqrt() inside quadratic formula?

why would I do that though

[alpine sable]

yes

[dapper hound]

shouldnt I just use the whole quadratic formula

thats what my teacher did

[alpine sable]

it's public formula that is easy way to solve quadratic formula
there are an other way but it is easyer

[alpine sable]

you can use other formula that you like it

[dapper hound]

.close

[lone heart]

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[rugged pebble]

where did

ohhhhhhhhhhhhhhh

.close

[lone heart]

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[rugged pebble]

\

[nova saffron]

this should be easy but idk how to do it

how do u do it though

oh

its ok lol

[viral pagoda]

Just substitute

[nova saffron]

i just dont know how to solve it

subsitute zero?

[viral pagoda]

No

The options

And see if u get 0 for f(x)

[nova saffron]

ohhhh okay

thx

would it be -3

[lone heart]

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[nova saffron]

would y<4 be correct?

[nova saffron]

or would it be y≤ 6

[cursive wharf]

this

[nova saffron]

oh

because y≤ 6 would be the highest point right

would a25= 95

[cursive wharf]

looks like

[nova saffron]

huh

[cursive wharf]

yes it's correct

[lone heart]

@nova saffron Has your question been resolved?

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[nova saffron]

is this correct

[alpine sable]

how is there more gas after driving 240 miles

Holy shit I thought this was recurrence relations for a second and got PTSD

[nova saffron]

oh lmao how did i not notice that

[boreal verge]

bro created fossil fuel

broke the economy istg

hate when that happends the 5739th time

🙄🙄

[nova saffron]

LMAOOO

[rose sigil]

shouldn't it be like a_n = 24 - (something involving n)?

[autumn valley]

no idea

have not read the question yet

😅

[alpine sable]

You got this Natalia

[autumn valley]

Thank youuu😀

@autumn valley i'm new here just started 😅

but i think i got it

[lone heart]

@nova saffron Has your question been resolved?

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[native nebula]

help

[native nebula]

what should I do next?

[surreal meadow]

i would multiply by x^2, make the substitution u = x^2, then solve the quadratic in terms of u

[tribal haven]

square both sides again seems to get you somewhere

[native nebula]

can you explain

[surreal meadow]

eh it looks ugly anyways, i don’t think it’s the right way to go about it

[surreal meadow]

maybe cubing it here?

[lone heart]

@native nebula Has your question been resolved?

[noble smelt]

Are you sure you did the equation right..?

I can't find any possible solutions

[native nebula]

how is this true?

[noble smelt]

cubed

not sure how to explain

[native nebula]

how it is a^3-3a?

[surreal meadow]

cube both sides

[noble smelt]

^

[surreal meadow]

you should get x^3 + 3x + 3/x + 1/x^3 = a^3
and the 3x + 3/x = 3a

[jovial sandal]

i think if we can figure what x^6 is numerically, you can solve it.

its essentially asking for (x^6)^12 + (x^6)^11 + x^6

[surreal meadow]

i think x^6 is complex though

[jovial sandal]

yea, can't find the roots of x^4-x^2+1=0

[tribal haven]

doing this, then again, then again .. gets you a bunch of nonsense that you might be able to reduce high powers of x with

[jovial sandal]

no roots

[tribal haven]

ye you can quickly figure out x is not real

[tribal haven]

nice

[native nebula]

thx 😄

.close

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[native berry]

Did all the math and got 13824 and put in the link but says I got it wrong anyone know what I did wrong?

[plucky torrent]

It seems like a PEMDAS issue to me. Do you know PEMDAS?

[native berry]

yes?

yes

[plucky torrent]

I

I'm sorry I was looking at the first problem. Is your issue on the second problem?

[native berry]

no im supposed to solve all of the problems then raise the sum of all of them to the power of 3

first picture is the questions

[hot marsh]

+.+ @native berry

U did first task?

[native berry]

what?

[hot marsh]

Is that result for first task

[native berry]

for 1 i got -16

[plucky torrent]

I believe 2c is wrong

[hot marsh]

With which do u have problems

[native berry]

idk i cant tell which one is wrong

[plucky torrent]

Look at 2c

[native berry]

is it not 18?

[plucky torrent]

No, try redoing your work and if you get 18 again I'll talk you through it

[fringe sleet]

$-z=-(-1)=1$

[ocean seal]

Duh Hello

[native berry]

i did (4+2)(4-1)

and got 18

[hot marsh]

See above

[native berry]

omg

[plucky torrent]

What Duh Hello typed is correct and it's where you are running into your problem

[native berry]

im so dumb XD

ok yeah i got thanks yall

[plucky torrent]

No problem

[native berry]

.close

[lone heart]

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[queen raven]

What would be the most efficient way to do these (e.g part c)

Would it just be to use the derivative to find the turning points and find y and x normally?

Or is there some simpler thing that I'm missing

[pseudo ice]

Graph transformations

[queen raven]

Ohhhhh, I see

[pseudo ice]

Let $f(x)=9 x^2 - x^4$ and relate the ones they’ve written to that

[ocean seal]

chartbit

[queen raven]

for c x is just shifted one unit to the left with a dilation factor of 2

I see...

Thank you!

Have a good day

.close

[lone heart]

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[pseudo ice]

You too!

[lone heart]

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[lime parrot]

i need help for reviewing for my math test tommorrow

[alpine sable]

do you want like, someone to teach u all of that or something?

[lime parrot]

someone to teach me all of it cause its pretty challenging for me

[hot marsh]

Maybe see video tutorials

[lime parrot]

ok so can someone helpme with laws of radicals

[true sandal]

here

[lime parrot]

i need to copy that formula"? or someethin

[true sandal]

those are laws of radicals

you can use them for simplifying or manipulation

[lone heart]

@lime parrot Has your question been resolved?

[lime parrot]

wait can u explain some of it? im still a little confuse

[noble smelt]

Basically you're simplifying and expanding

Not necessarily expanding

[lone heart]

@lime parrot Has your question been resolved?

[lone heart]

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[sonic mauve]

hey

[sonic mauve]

In the following expression, combine the terms. What is the coefficient?

9b + 8 + 5b + 9

In the following expression, combine the terms. What is the constant?

1b + 3 + 3b + 9

[jagged cobalt]

the coefficient is the number in front of the b, the constant is the standalone value (non variable)

[sonic mauve]

so it would be

9

and

1

?

oh wait oops i thought both were coefficient

so the first one is 9

[surreal meadow]

join the like terms first

[sonic mauve]

found it!

also another question

[alpine sable]

some one knows nmpd

numerical method and partial difference

[lone heart]

@sonic mauve Has your question been resolved?

[lone heart]

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[lone heart]

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[alpine sable]

The center of the surface relative to the x and y axes

[wanton valley]

center of mass?

[alpine sable]

The point where the x- and y-axis intersect is called the origin.

[alpine sable]

answered

[alpine sable]

please dont massage

i am not massaging i am messaging

@ help

lol

@alpine sable please

ok

sorry

??

[wanton valley]

is your question what the center of mass is?

[alpine sable]

center of area

@crisp iron

.close

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[surreal meteor]

Is it true that it's a reflexive relationsship

[lone heart]

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[lone heart]

@glass bay Has your question been resolved?

[lone heart]

@glass bay Has your question been resolved?

[ocean seal]

Mehdi_Moulati

Mehdi_Moulati

[hollow sparrow]

@glass bay

[lone heart]

@glass bay Has your question been resolved?

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[alpine sable]

Convert that decimal into a fraction and make your life easier

But yet again, I don't know what your question wants. An exact or simplified answer?

[tacit arch]

fraction = a/b where a and b are integers

[alpine sable]

What language are you most comfortable with?

[lone heart]

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[strange forum]

hey guys

[strange forum]

can someone please help me with a slope question?

[pliant cedar]

what is ur question

[strange forum]

this is it

[pliant cedar]

and what is the slope-intercept form of a line?

[strange forum]

im not sure lol

[pliant cedar]

u must have learnt a formula

[strange forum]

do u know the formula?

[pliant cedar]

i do but

[strange forum]

i dont know it

[pliant cedar]

what do u learn when u learn abt lines

[strange forum]

we dont really have classes lmao 💀

im in college

well i know basically everything about grpahing excpet this

[pliant cedar]

do u know the equation of a straight line

[strange forum]

and trigonemetric functions

yea its

y= b and c

[pliant cedar]

y=b and c?

[strange forum]

mx+b

[pliant cedar]

exactly

this is what i was referring to as formula

[strange forum]

is that right

[pliant cedar]

and this is the slope-intercept form of a straight line

what does m stand for here?

[strange forum]

sheesh wild guess 😅

is it -6/5?

[pliant cedar]

whyd u turn it around

[strange forum]

oh yea sorry

-5/6 i mean

[pliant cedar]

yeah thats the gradient of the line aka slope of the line

then u can just substitute in the coordinates given and find b

[strange forum]

so the coordinates are

5,-7

so i do -5/6(5)?

[pliant cedar]

yeah so in (5, -7), x is 5, y is -7

[strange forum]

mhm

[pliant cedar]

and because u also have y = mx + b with m=-5/6

when x = 5 and y = -7

can u find b?

[strange forum]

yes i think i can

it would be -7 + 5/6(5) = b

is that right?

[pliant cedar]

yeah

[strange forum]

so in that case

b is equal . -2.83

[pliant cedar]

yeah ig, its -17/6

[strange forum]

how did u do that

how did u keep it as afraction

oh

nvm im dumb

[pliant cedar]

lol

[strange forum]

so the answer is that?

idk what it means when it asks for line in point slope form

[pliant cedar]

so then y = -5/6x - 17/6

is the line in slope-intercept form

[pliant cedar]

so if u know the coordinates $\left(x_0,y_0\right)$ of a point that a line having slope $m$ passes through

the point-slope form of its equation is

$y-y_0=m\left(x-x_0\right)$

[ocean seal]

SilverSoldier

SilverSoldier

[strange forum]

ok

[pliant cedar]

so i guess u can figure out the answer?

[strange forum]

yea i got it

ty

hey @pliant cedar

are u still there

[pliant cedar]

yeah

[strange forum]

can u help me figure this out

i got the first one now its asking for slope intercept form

[pliant cedar]

this is the slope-intercept form

u just have to do the same thing u already did

[strange forum]

so it would be -1/2(2)+5

or is it -5

[pliant cedar]

so m = -1/2

and u want y = mx + b
so -5 = (-1/2) * 2 + b

find b

[strange forum]

ok

i just got -6

b=-6

[pliant cedar]

so -5 = -1 + b

so b is not -6

[strange forum]

oh

-4

[pliant cedar]

yeah

r u sure u understand how to come up with this equation for b?

[strange forum]

yea

u just isolate b on the right side after solving

i just dont know how to format the answer in slope form

like ok b is -4 now what LMAO

it would be

y=-1/2x-4?

is that the answer

[pliant cedar]

yeah

[strange forum]

oh okay

I get it 😄

BUT

what if theres a number here

[pliant cedar]

where

[strange forum]

look at this

how is the y -3 and not -2

[pliant cedar]

u r mixing up the slope-intercept form and slope-point form

[strange forum]

this is a diff question

[pliant cedar]

something that looks like y=mx+b is the slope intercept form

[strange forum]

yea ik ik im not mixing it up

[pliant cedar]

something that looks like y-(some number) = another number * (x - a diff number)

is the slope point form

[strange forum]

but look at the ss

[pliant cedar]

oh wait

lol sirry

[strange forum]

its okay

i was just confused cause this is the answer

but its supposed to be y+6=2/3(x-2)

right?

[pliant cedar]

well (-2, 6) is not the only point it passes thru

u can use the coords of any other point it passes thru also

[strange forum]

so this would also be a correct answer?

[pliant cedar]

so here y - 3 = 3/4(x+7) is also the equation of the line coz it also passes thru (-7, 3)

[pliant cedar]

yeah and u must have 3/5 there not 2/3

[strange forum]

oh yea oops

[pliant cedar]

wait

[strange forum]

theres a number there -67799

[pliant cedar]

and also y-6 and x+2

[strange forum]

but would that number not do anything to the equation

the -67799

[pliant cedar]

so y-6 = 3/5(x+2) is also a correct answer

[strange forum]

NO its -2 +6

right?

ur confusing me 😭

[pliant cedar]

can u send the entire quetsion

theres something on top

that uve cut out

[strange forum]

this is the whole question

[pliant cedar]

okay so we have a line y = 3/5x - 6799

[strange forum]

mhm

[pliant cedar]

and we have ANOTHER line, that is parallel to this one

and passes thru -2, 6

[strange forum]

yes

wait

it doesnt say theres another line

it just says it passes thru those points

[pliant cedar]

that line must have slope 3/5

[strange forum]

oh

nvm

yes

[pliant cedar]

and they ask u for the equation of that OTHER line

they arent asking u anything about the 6799 line

[strange forum]

so that number doesnt change anything

[pliant cedar]

yeah

it doesnt

[strange forum]

ok good

also

is it always y-y1

or what if the y point is positive

it would still be y-y1

[pliant cedar]

yeah

[strange forum]

BUT UR LYING

[pliant cedar]

so if a line shud have slope 3 and pass thru (2, 3)

then its eqn would be y - 3 = 3(x - 2)

[strange forum]

here the y is positive

HOW

[pliant cedar]

because y - (-5)

[strange forum]

i think its flipped

OH

so if its negative its positive

if its positive its negative

got it 👍

[pliant cedar]

yeah u always subtract the y coord of the point it passes thru

[strange forum]

ok

mhm

mh

i had one more question

are u good with trigonemetric funtions

and period shifting

[pliant cedar]

yeah..

[strange forum]

can u just explain this for me silversoldier

ik the first one is 4 but i dont understand the other stuff

[pliant cedar]

so reflected over x axis means u see like the same function upside down

its like looking in a mirror

do u get it

here for example the blue parabola is a reflection of the red one about the x axis

[strange forum]

yea

how would u know if it does without desmos tho lol

[pliant cedar]

u dont need desmos, can u think what command u must use in desmos to make this graph?

not command maybe like what must u input

so if u had y = sin(blah blah blah), its reflection about the x axis is what function

[strange forum]

the period?

shift

idk 😭

[pliant cedar]

okay lets think the red parabola there is ur trig function

[strange forum]

ok

[pliant cedar]

so at x = 0, what do u get as y

[pliant cedar]

look at the graph u can see some numbers

[strange forum]

4

[pliant cedar]

yeah, but in the blue function, which is the reflection of ur function, what do u get for y, at x = 0

[strange forum]

6

[pliant cedar]

actually ok

ah sorry the numbers are not right here

[strange forum]

lol whats wrong

💀

[pliant cedar]

i thot the orange line was the x axis

[strange forum]

no its 5

y

[pliant cedar]

yeah so if this were the x axis

then what must the value be

[strange forum]

1

[pliant cedar]

so thats for the red parabola

[strange forum]

mhm

[pliant cedar]

for the blue one?

[strange forum]

-1

[pliant cedar]

yeah

how abt at x=1

red one's y coord = ?
blue one's y coord = ?

[strange forum]

2

[pliant cedar]

do u see a pattern

[strange forum]

wait

yea its the same

[pliant cedar]

not the same same

[strange forum]

wdym whats the differnce

the negative?

[pliant cedar]

is this

[pliant cedar]

yeah

[strange forum]

ok so that means it doesnt reflect

[pliant cedar]

blue ones y coord = - red ones y coord

blue one = red one's reflection

[strange forum]

ok i get it

[pliant cedar]

so red ones reflection y coord = - red ones y coord

so if y = sin (blah), what is its reflection?

do u get it

[strange forum]

yea

[pliant cedar]

so what is it

i dont think u got it

[strange forum]

i got it

well basically it doesnt reflect because

the reflection is a -

and the actual function is a positive

[pliant cedar]

yeah

so its not exactlyyy that but i gues u got the idea

so it will be a reflection if its reflection is equal to itself

but that does not happen

[strange forum]

ok

[pliant cedar]

its not that the actual function is positive; it may still be negative its just that in such a case the reflection would be positive

so whenever the function is +ve, the reflection is -ve, whenevre the function is -ve, the reflection is +ve

anywya

so ig that answers 2

[strange forum]

yea i get it dw

what about calculating period

its 32pi in that question

[pliant cedar]

so

the period is like everytime the function resets

so if u draw this, the graph looks like a certain part repeating itself over and over again right

[strange forum]

yea i know what the period is and all

[pliant cedar]

oh

[strange forum]

we learned about that but its dumb ash cause they dont actually show u how to calculate it

they just show u what it is lmao

[pliant cedar]

wait im thinking of a way to tell u

[strange forum]

isnt there a formula for finding period?

bruh all this math hurting my brain i have a test on graphing in like 2 hours lol

[pliant cedar]

well i cud tell u i guess

okay then

[strange forum]

sure

[pliant cedar]

so if u have $A\cdot\sin\left[Cx+D\right]+E$

[ocean seal]

SilverSoldier

[strange forum]

is b sin

[pliant cedar]

A is the amplitude, -D/C = phase shift, E is maybe called the vertical shift, and the period is 2pi/C

[strange forum]

but how is 2pi/1/16 = 32 lol

[pliant cedar]

$2\pi\div\dfrac{1}{16}$

[ocean seal]

SilverSoldier

[strange forum]

yea

i get it

i think

[pliant cedar]

u multiply by the reciporcal

so 2pi * 16 = 32pi

[strange forum]

yea

what about the phase shift

[pliant cedar]

-D/C

[strange forum]

yea that makes sense too

[pliant cedar]

in ur thing C = 1/16. D = 1/16 * 2pi/3

[strange forum]

so u just disregard x and turn into 1

[strange forum]

yea

no its just c = 1/16

D is x + 2pi/3

[pliant cedar]

no d is the constant term

[strange forum]

wym

[pliant cedar]

ur thing is 1/16(x+ 2pi/3) = 1/16x + 1/16* 2pi/3

right?

the rhs is what is in the form cx + d

[strange forum]

yea pretty much

[pliant cedar]

if u have like a(x+b), then this is ax + ab

the constant term wud be ab

[strange forum]

yea

[pliant cedar]

hope u get it

[strange forum]

i do

so in a trig function B is sin or cos?

[pliant cedar]

b?

[strange forum]

yea cause u know

the ampititude is A

[pliant cedar]

if u had a cos u can turn it into a sin

[strange forum]

i cant spell

[pliant cedar]

and just work with the sin

[pliant cedar]

i only put C after A coz i forgot abt B lol

[strange forum]

oh ok

lol i was like uhh

[pliant cedar]

lol

its just the number in front of the x, the constant term, and teh number multiplying the entire sine that matter

[strange forum]

i think im ready for this math test 💪

[pliant cedar]

call them whatever u want

A, B, C or P, Q, R

[pliant cedar]

great

[strange forum]

ima just study a bit more

[pliant cedar]

what do u get in ur test

trig and graphs?

[strange forum]

wym

its basically that yea

[pliant cedar]

oh

hope i cud be of help

[strange forum]

u were bruh dw

lol

[pliant cedar]

😄

so ig imma go sleep now

👋

[strange forum]

ok bye

[lone heart]

@strange forum Has your question been resolved?

[lone heart]

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[formal hornet]

how do i use simultaneous equations to solve this???

[formal hornet]

do i get the equation for the second line and the distance formula for point A to rotation and then solve it?

if so, how do i solve the distance formula thing

[lone heart]

@formal hornet Has your question been resolved?

[formal hornet]

wrll

well

i figured it out

.close

[lone heart]

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[night dagger]

A person named Barten was killed. Who killed him?
Here is a statement from each of the suspects, 3 are lying but one is telling the truth.

1. Snuslæstn: Næpsilda killed Barten
2. Læmselars: Karsk-Kjetil was not the killer this time.
3. Næpsilda: Karsk-Kjetil was playing Yatzy with Snuslæstn when Barten was killed
4. Karsk-Kjetil: Næpsilda is not the killer.

[royal plank]

the formal way to do this is to write it as implikations

[night dagger]

how can I do that

[royal plank]

well, if Snuslaestn tells the truth that implies that Naepsilda killed Barten

[vale wigeon]

to throw away all the fluff, the 4 suspects say this:

S: it was N
L: it wasn't K
N: it wasn't K nor S
K: it wasn't N

try analyzing 4 cases based on who the one truth-teller is

[vale sluice]

2. Læmselars: Karsk-Kjetil was not the killer this time.

[night dagger]

Well the only thing that makes sense in my head is that Karsk-Kjetil is the killer, but im not sure if im taking the right approach or if I just got lucky

[alpine sable]

i have math homework that i need help with can someone help?🧍‍♀️

[night dagger]

#❓how-to-get-help

[alpine sable]

it told me come here tho

[vale sluice]

if N is truly saying K wasn't the killer, then K would be the killer because L and N cannot both be telling the truth

[vale wigeon]

no, it told you to use an available channel, not channel zero.

[night dagger]

take #help-17 that one is free

[alpine sable]

ohh alr thanks

[night dagger]

yeah thats what Im thinking as well. for every other case there is contracdictory information, telling us that its wrong

[vale wigeon]

one of S and K has to be the truth teller, otherwise they can't both be lying

if S is telling the truth then so is L, so that won't do. thus K is telling the truth and everybody else is lying

[night dagger]

Yeah it makes sense now thx

[vale sluice]

also K apparently has a reputation for murder beforehand so

[night dagger]

yeah thats true, but not relevant to solve the problem (although it would be irl)

.close

[lone heart]

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[west girder]

Is there a clean way to solve this?

I made an ugly system of 4 equations but I’m sure there is a better way

(btw this is all of the info in the question)

[earnest raptor]

plz help me

[maiden urchin]

what 4 equations were you using?

[west girder]

Use pythag, also wrong channel

[west girder]

Ed, ae, cd, bd

And then some pythag

[maiden urchin]

so like two pythags on those lower triangles?

[west girder]

3 pythags

The lower 2

And acd

The fourth equation was Stewart’s I think on acd

[maiden urchin]

honestly if there's a better way I'm not seeing it either

i tried a system of equations to find some of those internal angles but it got ugly fast

[west girder]

I was supposed to solve this is 3 minutes with a calc

So there has to be a good way

[lone heart]

@west girder Has your question been resolved?

[lone heart]

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[gaunt harness]

Alr solving for t and like I already asked Google but that didn't work out

[high rapids]

You could substitute sin t with another variable and find quadratic solutions

[gaunt harness]

Alrr

Ohhh

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[lone heart]

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[grave roost]

I've been exploring Pisano Periods, but am having a hard time finding the words to describe the phenomena that I've been observing. The mathematics I've observed on the wikipedia article is far beyond my depth, unfortunately, but I feel confident that what I'm describing should have some terminology already in existence

[grave roost]

This feels like a naive use of this channel, to be honest. Sorry in advance

Sorry

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[lone heart]

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[coarse oasis]

i already did part a

[coarse oasis]

calc question

im stuck on

wait nvm im stupid

.close

[lone heart]

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[primal horizon]

I’ve tried subtracting the numbers below. Then take the number in the middle of the triangle to subtract the result to find the above one , but it didn’t work for the last one

[lone heart]

@primal horizon Has your question been resolved?

[primal horizon]

<@&286206848099549185>

[lone heart]

@primal horizon Has your question been resolved?

[lone heart]

@primal horizon Has your question been resolved?

[silver iron]

what is the question related to the triangles?

[pliant cedar]

i think its like a number pattern thing

[silver iron]

yea, are they looking for a certain pattern though? I see different patterns for some

[pliant cedar]

i dont see a consistent pattern anywhere lol

[pliant cedar]

u r supposed to fill in the missing number according to the pattern

ig

[silver iron]

first 2 are consistent for me

[pliant cedar]

oh right thhe numbers at the top are just 2 less the previous number

what else is consistent?

[silver iron]

9+7-3=13 and 7+6-4=9

[primal horizon]

Ive tried this but didnt work for the last one

[pliant cedar]

but 3+10 - 20

[silver iron]

right

[pliant cedar]

is not 10

[silver iron]

the last one is 3x10-20=10

weird but thats how i see it

[pliant cedar]

but then the first ones are not like that

[primal horizon]

They all should be the same pattern

[pliant cedar]

yeah

[silver iron]

oh ok

[pliant cedar]

thats what i meant by consistent

[silver iron]

ahh i see

what subject is this? @primal horizon

[primal horizon]

Math I couldnt think of any other subject haha

[silver iron]

lol

[primal horizon]

Can it be something like this ?

Im not sure

[pliant cedar]

what is the +3, +2, +1 thing

ah okay

[silver iron]

i dont see it

nvm

[pliant cedar]

so in each triangle u subtract the one in the middle and the left bottom one

then u get 0 in the last one, 1 in the one before the last, then 3 and in the first one 6

so the third one = 1 + fourth one

2nd one = 2 + third one

1st one = 3 + 2nd one

[silver iron]

idk it only relates the middle and the bottom left corner

is there like an answer sheet in the back of your book or something?

[primal horizon]

Unfortunately there isnt one lol

[lone heart]

@primal horizon Has your question been resolved?

[lone heart]

@primal horizon Has your question been resolved?

[gray pier]

Help pls

[woeful pulsar]

I have centre = largest corner plus left corner minus right corner

@primal horizon

hence the answer can be 4

[gray pier]

@woeful pulsar

[woeful pulsar]

#❓how-to-get-help

[gray pier]

@lone heart

[lone heart]

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[alpine sable]

do the exponent 3's cancel out?

[alpine sable]

is that why we get -3 as the answer

[woeful pulsar]

cube root is inverse function of cube

[stark plinth]

its bc indices

[alpine sable]

i see thx you

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[lone heart]

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[stark plinth]

you understand my explanation?

[lone heart]

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[alpine sable]

does conditional statements exist in Mathematics?

[waxen flame]

Yes. There are piece-wise functions.

[alpine sable]

so that means can i do something like x = 1 if y == 1 else 0?

[waxen flame]

Yes.

[alpine sable]

and how can i write it in math?

like how should it look like, i suppose it would be some operator, not if

[noble sinew]

For example abs value of x is that

$$|x|=\begin{cases} x & \text{if } x\geq 0 \
-x & \text{if } x<0\end{cases}$$

[ocean seal]

ScapeProf

[alpine sable]

aha! ok thx:)

.close

[lone heart]

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[solid coral]

help

[alpine sable]

sending help

(ask your question)

[solid coral]

what is the square root of 672

[alpine sable]

definitely...not any nice number

use a calculator or approximate it

[solid coral]

hmmm wait

[keen pasture]

Is it 672 or 676?

[solid coral]

672

[keen pasture]

,calc sqrt(672)

[ocean seal]

Result:

25.922962793631

[solid coral]

square root of 66

[gray isle]

all these can be obtained from a calculator

[solid coral]

uhmm oki

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[lone heart]

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[deft sparrow]

What should I do?

[deft sparrow]

a &b& c are Natural

[spring scarab]

Jacobi's iteration

[deft sparrow]

Thanks

[spring scarab]

@lone heartJacobi's iteration

[deft sparrow]

.close

[lone heart]

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[brittle sun]

Calculus - Trigonometry and limits
Hey folks, I started learning about the aforementioned subject this week and a few things confuse me. I'll explain with an example:
lim x->0: [ (cosx * (1 - cosx)) / (x^2 * (cosx + sqrt(cosx)) ]
I figured I could simply do the following:
lim x-> 0: cosx = 1
lim x -> 0: (1 - cosx) = (lim x-> 0: 1) - (lim x->0: cosx) = 1 - 1 = 0
So the limit up the left side of the expression is 0, and the right part is positive, hence the limit is 0.

I understand that this technique is wrong, but I'm sure sure why - and I'd really appreciate some advice on this.

Trying to edit this for the sake of readability:
for lim := lim x -> 0:
lim ((cosx * (1 - cosx)) / (x^2 * (cosx + sqrt(cosx))
so
lim cosx = 1
lim (1 - cosx) = (lim 1) - (lim cosx) = 1 - 1 = 0

[alpine sable]

are you saying that you have
[
\lim_{x \to 0} \frac{\cos(x)(1-\cos(x))}{x^2(\cos(x) +\sqrt{\cos(x)}}
] and from that you evaluated the numerator to be equal to 0, thus concluded that the entire limit needs to be equal to 0, as well?

[ocean seal]

♡LexQa♡

[brittle sun]

Correct, through a few counterexamples I can tell that this is clearly not true

[boreal verge]

and youre asking why that isnt the case?

[keen plinth]

x^2/2/(2x^2)

[brittle sun]

Well, amongst other things.

I don't understand what I don't understand in all honesty

[boreal verge]

the lower half of the limit can be infinity for instance

[brittle sun]

Ah, fair enough.

[boreal verge]

and just generally it isnt great to assume that just because part of a limit is something the whole limit it

[brittle sun]

I think I might be mixing up sequences arithmetic with function arithmetic

[boreal verge]

check the lower limit to see if its also 0

[brittle sun]

I've already plugged in the entire thing into WA, I was kind of surprised to see that the answer is 1/4.

Meaning, its nore minus infinity or 0

[boreal verge]

well then it most likely is 0 so wolfram did l'hopitals or somethin

it can be 0 which is indeterminate

so you do l'hopital

[wooden jewel]

facts

[brittle sun]

I'm not sure what that means

[boreal verge]

you dont know l'hopitals rule?

[brittle sun]

I might, could just be language differences. Lemme check

[boreal verge]

this?

[alpine sable]

wait is it [
\lim_{x \to 0} \frac{\cos(x)(1-\cos(x))}{x^2(\cos(x) +\sqrt{\cos(x)})}
]

[brittle sun]

Oh, we haven't gotten around to derivatives.

[boreal verge]

oh

yeah makes sense

[ocean seal]

♡LexQa♡

[brittle sun]

Yeah that'd be the exercise

[alpine sable]

oh okay you dont have to use l'hopital

[brittle sun]

I figured, otherwise that'd be kind of unfair haha

I'm wondering how I should go about this exercise though

Since my current understanding on how to calculate limits is clearly flawed

Apparently I can't just separate expressions and calculate their limits to just add them all up

[boreal verge]

not always

especially not if you might get indeterminates like here

you might

especially since its a fraction

it really depends

[brittle sun]

When can you do it?

[boreal verge]

honestly id just think through both sides of the limit and see if its indeterminate

if it is

dont do that

otherwise go ahead

[brittle sun]

There's no clever arithmetics I can do with the function?

[boreal verge]

thats what i was thinking about

[wooden jewel]

is there any way you can simplify this function?

[boreal verge]

the bottom half looks too weird to do anything arithmetically

[brittle sun]

Errr
(-cosx / x^2) * ((cosx - 1) / (cosx + sqrt(cosx))
?
Not sure what the hell to do with the right hand side though.

Just trying to make these into "edible" expressions.

[boreal verge]

do you know how to use latex?

[brittle sun]

I wish

Would make explaining things a lot easier

[boreal verge]

ill try and write it out in latex

[brittle sun]

Cheers

[wooden jewel]

wait lemme try to figure this out it should take a minute

[boreal verge]

$\frac{-cos(x)}{x^2}\frac{cos(x)-1}{cos(x)-\sqrt{cos(x)}}$

[brittle sun]

[
\lim_{x \to 0} \frac{-\cos(x) * (\cos(x) - 1)}{x^2 * (\cos(x) +\sqrt{\cos(x)})}
]

Well, was worth a shot lol

[boreal verge]

why tf is it putting it in the top

[wooden jewel]

alright I found out how it's pretty simple

[brittle sun]

Yeah?

[wooden jewel]

multiply the numerator and denominator by the conjugate 1+cosx

[boreal verge]

there

jesus christ

[ocean seal]

Kel.plush

[brittle sun]

Haha

Yeah that's it

[brittle sun]

Pardon?

Christ studying math in anything other than English is such a handicap

[wooden jewel]

Wait you know the identity lim x->0 sinx/x = 1 right

[brittle sun]

Right

[wooden jewel]

Try it out and let me know if you have any problems

you should be able to find the answer >:)

[brittle sun]

It's just that I'm not sure what conjugate means

[wooden jewel]

Oh basically the conjugate of 1-cosx is 1+cosx

thats what i meant

by muliplying your expression by this you can use other trig identities to simplify

[brittle sun]

Oh

I'll give it a shot

[brittle sun]

Uh, I don't really know what to do with the denominator

Becomes kind of crazy

[wooden jewel]

Thats fine you don't need to touch that

[brittle sun]

Oh?

[wooden jewel]

Do you see something you can simplify on the numerator?

[brittle sun]

Uhh yeah it looks familiar
I don't yet know the identities by heart, gotta open the right page real quick

Closest thing I'm finding is 2cos^2(a) - 1 = sin(2a)

perhaps there are more identities I don't yet know
That or I'm blind, which is also possible

[wooden jewel]

how did you get this

[brittle sun]

Hm?

What do you mean

This is one of the identities we have in the book, I didn't really do anything

[wooden jewel]

on the numerator

[brittle sun]

I mean, it's just 1 - cos^2(x) innit?

[wooden jewel]

correct

[brittle sun]

Beyond that, it's just identities

No?

[wooden jewel]

what identity is that

[swift terrace]

i believe its cos2a

sin2a=2sinacosa

[brittle sun]

Oh?

[alpine sable]

$\cos^{2}x + \sin^{2}x = 1$

[wooden jewel]

yep!

[brittle sun]

Oh right

Blind indeed

[ocean seal]

♡LexQa♡

[wooden jewel]

now do you see how you can solve the limit?

[odd fern]

I don’t really get it

[brittle sun]

I mean this is great, I still don't know what to do with the denominator though

What did you mean by "I'm not supposed to touch it"?

[brittle sun]

What?

[wooden jewel]

I meant that you don't need to simplify it in anyway

[brittle sun]

Maybe divide it into small chunks

[wooden jewel]

Now do you see how you can use your sinx/x identity

[brittle sun]

And then figure out the limit?

Yeah I can look at sin(2x) / x * x individually now, but I still don't know what to do with the rest of the denominator

[wooden jewel]

sinx^2/x^2 simplifies to 1

So you can remove that from your limit

[brittle sun]

ah yeah sorry, wrote it wrong

[wooden jewel]

and after it is no longer 0/0 and you can just plug and find the answer

[brittle sun]

Yeah that one I managed, what about sqrt(cosx) and stuff?

Ohh

Let's see..

[odd fern]

I just need some help

[brittle sun]

Okay, but why in my channel though'

That's pretty rude

[odd fern]

I’m sorry I’m new here

[odd fern]

I’m sorry I just don’t know where to go

I’m lost

Where would I go for help

[brittle sun]

#info

[brittle sun]

I'm kind of amazed that this worked

ngl

[wooden jewel]

honestly lowkey satisfying to solve

[brittle sun]

How'd you see that?

Just practice?

Or like, certified genius moment

[wooden jewel]

i took calc 1 last semester and its something the prof said to do

before we learned l'hopital

[brittle sun]

The answer that was offered to me is so much harder, incredible

[brittle sun]

Just think whether one can multiply by expressions in order to simplify them?

What is it they said exactly? Genuinely curious

I want to adopt whatever you did

[wooden jewel]

Well tbh when you see something like this, you can try multiplying by the conjugate when nothing else seems to simplify

[brittle sun]

Because seeing cos(x) * (1 - cos(x)) and thinking ah I can obviously make this sin^2(x) is not obvious to say the least, at least not to me

[brittle sun]

Oh, the conjugate you say?

I'll write that down

Oh actually this is funny

The expression I displayed here is already uh... multiplied by the conjugate I think

[wooden jewel]

what do you mean haha

[brittle sun]

It was oroginally (sqrt(cosx) - cosx) / x^2

Then I multiplied the nominator by this "conjugate" I think?

[wooden jewel]

ohhh yeah you did lmao

[brittle sun]

sqrt(cosx) + cosx / sqrt(cosx) + cosx

[wooden jewel]

thats crazy lol

[brittle sun]

Ah!

Incredible

Would've never thought about doing it twice, that's funny

anyway tysm for the help

[wooden jewel]

np

[brittle sun]

Thank you* everybody who helped, if you read this by any chance

~

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[royal marsh]

Hello, can someone help me write this equation in Latex please?

[surreal meadow]

$$\cos x \sin(\frac{2}{3}\pi + x) - \sqrt{3}\cos^2 x = \sin x \cos(x-\frac{\pi}{6})$$

[ocean seal]

maximo

[royal marsh]

Thank you

[pseudo ice]

Depending on your setup, you may need \left( and \right) for the brackets to size themselves

[pseudo ice]

As per the sin here

[royal marsh]

It looks fine dw 🙂

Thanks everyone

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[flat zealot]

What is the formula of area of sector

[green folio]

$$area~of~sector = \frac{\theta}{360} πr^2~square~unit$$

[flat zealot]

Thanks

[green folio]

Wlcm

[flat zealot]

How can I close this channel

[ocean seal]

anand

[green folio]

.close

Both theta and 360 will be in degrees ofc

[flat zealot]

Yess I got it

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[void canyon]

is this correct?

[green folio]

Yep

[void canyon]

what about this one

[green folio]

1/2 ryt?

Scale as in perimeter or area?

[void canyon]

what does ryt mean

[green folio]

Ryt = right

[void canyon]

oh so it was 1/2 not 1/4

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[alpine sable]

Kathy and Cheryl are walking in a fundraiser. Kathy completes the course in 4.8 hours and Cheryl completes the course in 8 hours. Kathy walks two miles per hour faster than Cheryl. Find Kathy’s speed.

[alpine sable]

How do I solve this, any resources videos or anything would be appreciated

[steel olive]

@alpine sable let the total distance be 'x' kms

what will be the speed of kathy and cheryl now

[pseudo ice]

(units)

[steel olive]

my bad

*mile

s

[alpine sable]

What?

I dont understand