help-0

[wheat prawn]

great

get it xd

corny joke lol

[alpine sable]

what is wrong here

[vale wigeon]

what are the drop-down options for point A?

and most importantly, why does it have two contour lines passing through?

[alpine sable]

I dont know...

[vale wigeon]

hm.

there's honestly no telling what's going on at A

[alpine sable]

what really?

[vale wigeon]

i would put 'not a critical point' but im honestly not sure

[alpine sable]

ok

so B,C,D are correct?

[whole maple]

Can anybody tell me the formula to find the truing point (linear equations)

[vale wigeon]

as far as i can tell, yes

[vale wigeon]

the turning point of... what?

[whole maple]

Oh idk

[vale wigeon]

??

[whole maple]

I just needed like a formula

[vale wigeon]

a formula for what

[whole maple]

Like this for example

[vale wigeon]

do you know calculus?

[whole maple]

No I’m in year 8

[vale wigeon]

okay then you'll need the special case for parabolas

for y = Ax^2 + Bx + C, the turning point occurs at x = -B/(2A)

[whole maple]

Oh ok

Ty

[sullen pagoda]

Does anybody know how to make a graph from this?

im very lost

[paper maple]

is the turning point the lowest or highest point?
then it should be -b/4a

[wild leaf]

im sure its the first option

[vale wigeon]

why would it be -b/(4a)

[paper maple]

((-b + d )/ 2a + (-b - d) / 2a )/2 right? @vale wigeon d = sqrt(b^2-4ac)

[vale wigeon]

yes...

this simplifies to -b/(2a).

(-b + d) + (-b - d) = -2b, after all.

[paper maple]

ahh, I realise my mistake

[pallid ferry]

can i get some help with this problem im not sure if im doing it right

so far i have csc(2θ)=-2 and csc(2θ)=-3 but im not sure if its right or what to do next

[stable pecan]

Do you know the general solution for the equation sin(theta)=sin(alpha)?

[last dome]

not really math but do anyone know these 2?

[stable pecan]

This channel is occupied

@last dome post somewhere else

[pallid ferry]

no i dont think i know about sin(theta)=sin(alpha)

[stable pecan]

It's alright, try to convert this csc(2θ)=-2 into this form sinx=siny, then we will proceed from there

[pallid ferry]

alright give me a second to figure it out

[alpine sable]

this was the answer btw

got it after a few guesses

[wild stump]

what is $$d^3x/d^3y$$

[ocean seal]

toadmilk

[wild stump]

what does it represent

[ionic jewel]

you typed this wrong?

[stable pecan]

this channel is occupied

[ionic jewel]

looks like it was meant to be third derivative

[wild stump]

oh sorry I thought it was done

[ionic jewel]

ah sorry alacris

[pallid ferry]

is this right?

[stable pecan]

this one is for csc(2θ)=-2?

[pallid ferry]

yes

[vale wigeon]

looks a little sus to me

do you have work to show?

[stable pecan]

My answer is npi/2+ (-1)^n pi/12

How did you reach your answer @pallid ferry ?

[pallid ferry]

i wasnt quite sure what to do with the 2 and then i was looking at a similar problem in my text book and i tried to do the same thing so im not really sure

[stable pecan]

Can you show your steps please?

You need to treat the 2theta as you normally treat a single theta. Then divide by 2 at the very last step

[stable pecan]

How's sin(2theta) = -2?

[pallid ferry]

i meant to put csc(2theta)

[stable pecan]

Try again then

[pallid ferry]

alright give me a second

[vale wigeon]

uh

sin(2pi) is not 2???

[pallid ferry]

yeah i wrote it wrong

i got this now

[stable pecan]

The original question was cosec(2theta)=-2

I told them to convert it to sine form

[vale wigeon]

sin(2pi) is still not 2

[stable pecan]

I know

It's out of range

[stable pecan]

Please show all your steps

[pallid ferry]

that sin is meant to be csc

i keep mis writing

[stable pecan]

You need to convert the cosec into sine

It's 1/sin(2theta)

Now try again

[pallid ferry]

i dont know what to do with that my text book doesnt have any examples like that

[stable pecan]

Convert the cosec into sine, then proceed

You know that cosecx=1/sinx, right?

[pallid ferry]

yes i just dont know what to do with 1/sinx

[snow roost]

@stable pecan can you help me

[stable pecan]

If 1/sinx = -2, then what is sinx=?

[pallid ferry]

ohh i see now

let me try it again real quick

[stable pecan]

Post it in another (free) channel, I will be there

[stable pecan]

If sin x= sin y, then you can write x = nπ + (-1)^n y, If y ∈ [-π/2, π/2]

7π/6 doesn't belong in the interval [-π/2, π/2]

rewrite sin(7π/6) so that the angle inside sine belongs to the above interval

Otherwise correct

[pallid ferry]

should it be pi/6 then?

[stable pecan]

yes

[pallid ferry]

what is the part about the y

[knotty sleet]

If you already have sin2theta =-1/2 you can just immediately find values for 2theta

[stable pecan]

yes

[knotty sleet]

Writing it as -sin(pi/6) complicates things😅

[stable pecan]

But we need to find the general solution

[pallid ferry]

oh so the pi/6 is equal to y?

[stable pecan]

which part

[pallid ferry]

at the beginning

[stable pecan]

It will be -pi/6

Sorry, I missed the lack of negative sign there

[stable pecan]

Do you mean this - If sin x= sin y, then you can write x = nπ + (-1)^n y, If y ∈ [-π/2, π/2] ?

[pallid ferry]

yes

[stable pecan]

Which part do you not understand?

[snow roost]

@stable pecan #help-2

[stable pecan]

Do you want to know why y has to belong in the interval [-π/2, π/2]?

[tired geyser]

Sketch the triangle with corners in (1, 1), (2, 1) and (1, 3) and parameterize its edge so that the points
are completed in the specified order.

can someone give the solution to this

would help a brother out

[pallid ferry]

im confused about when you said sinx=siny and im also a little confused about the y in the interval

[craggy dirge]

how would i do this?

[jagged imp]

wow 3 different questions in the space of a minute in one channel

im impressed

maybe use another one

[tired geyser]

need help man xD

?

[stable pecan]

This channel is occupied

Post somewhere else

[stable pecan]

If sinx = siny, then we know that x = nπ + (-1)^n y, right? That's what you did in the last step of your solution as well

[tired geyser]

can u help me

[stable pecan]

Please post in another channe;

[pallid ferry]

ok i think i get it

do i have to do this again for the other part of the equation?

[stable pecan]

you will need to rewrite sin(7π/6) so that the angle inside sine belongs to the interval [-pi/2,pi/2]

[honest umbra]

how can I find x so that 2x, 3x+1 and (x^2)+2 r the first 3 terms of an arithmetic sequence

[boreal prawn]

how many three digit numbers in base 9 have the property that each digit increases by 1 when the number is converted to base 8?

[jagged imp]

wow is that 4 different questions ontop of the already ongoing one in like 10 minutes?

I'm impressed

[pallid ferry]

is this better

[jagged imp]

use another channel, please

[jagged imp]

you too

[boreal prawn]

sorry

[stable pecan]

yes

It's correct

I hope you can do csc(2θ)=-3 on your own now?

It's similar

[pallid ferry]

yeah i think i can do that

[stable pecan]

wait

there should be a - sign in front of pi/12

[pallid ferry]

oh yeah

so the other problem should be the same thing then right

[stable pecan]

yes

[pallid ferry]

alright thanks

[alpine sable]

wdym solve

theres nothing to solve for

[vale wigeon]

it says "simplify", polla

@alpine sable this is a matter of careful exponent manipulation

perhaps it'll help to rewrite all roots as fractional exponents

maybe even make a temporary substitution like x := sqrt(a) to make your own life a little easier

[alpine sable]

just do what Ann says rewrite them

so it's just makes your life easier

[pastel jasper]

Instead of = wouldn't it be more correct if it was an arrow ->

[vale wigeon]

no

you are already writing "lim"

[pastel jasper]

oh

but it means f(x)->1 right

[vale wigeon]

if you want, you can write ``$f(x) \to 1$ as $x \to 2$''

[ocean seal]

Ann

[pastel jasper]

oh

thanks!

[hot osprey]

how do i find the exact value of cos (-19pi/6)

[heady helm]

Student desmos scientific calculator on google

[hot osprey]

yeah i meant showing work and stuff

[vale wigeon]

add a suitable integer multiple of 2pi to the angle so that it falls between 0 and 2pi

[hot osprey]

yes done that, got 5pi/6

[vale wigeon]

then look at the unit circle

[hot osprey]

but i am not sure

if like

the quadrant i picked is right

[vale wigeon]

that is correct, 5pi/6 is exactly what you should be getting.

[hot osprey]

does converting it to degree help?

[vale wigeon]

if it helps you then yes

[hot osprey]

so that's 210 degrees

[vale wigeon]

no

5pi/6 is not 210°

[hot osprey]

wait whoos

150

2nd quadrant right

[vale wigeon]

yes

[hot osprey]

then since cos of pi/6 is

radical 3/2

it would be 5 rad 3/2?

[vale wigeon]

you meant sqrt(3)/2

and no, cos(5x) is not 5cos(x)

[hot osprey]

oh yeah, sorry about my english

oh wait

uni circle chart

[vale wigeon]

unit

[hot osprey]

t

sorry lol did it bother ya xD

[ocean seal]

Πολλά άτομα είναι

Πολλά άτομα είναι

[jagged imp]

good so far

although equals suffices over the implies arrow here

[ocean seal]

Πολλά άτομα είναι

[jagged imp]

whatever

equals is best anyways imo

[alpine sable]

up to you ¯_(ツ)_/¯

I use arrows

So what do I do

now

[jagged imp]

you want the sqrt to have an 18 under it instead of a 2

[alpine sable]

yeah

[jagged imp]

so find that sqrt(9) in 36 that makes the sqrt into sqrt(18)

[sacred vigil]

It's easy, just multiply them

[ocean seal]

Πολλά άτομα είναι

[jagged imp]

well thats 6, not 36.

[alpine sable]

Well that's root 36

[sacred vigil]

Wait

May I give the exact answer

[jagged imp]

36=12*3=12*sqrt(9)

was the point i was getting at

[alpine sable]

oh right ok I didn't get it at first

alright

[jagged imp]

yeah no worries i was having trouble wording it in an easily parsable way in the first place

[ocean seal]

Πολλά άτομα είναι

[jagged imp]

ye

[ocean seal]

Πολλά άτομα είναι

[jagged imp]

yes.

[ocean seal]

Akhandanand Tripathi

[alpine sable]

k cool cheers

[jagged imp]

nw mate

[sacred vigil]

It was easy, why were you stuck?

??

[jagged imp]

easy is relative

[sacred vigil]

[cyan saddle]

What happens to the slope if you take the reciprocal of a function?

Assuming, it isn't 0

[alpine sable]

I knew what I wanted but didn't know how to do it

[sacred vigil]

Okay

[jagged imp]

wym by the slope, as in for straight lines? If so, the recirpocal of a straight line isn't necessarily a straight line

if you're talking about the derivative of the reciprocal, you'd have to consult the chain rule

[cyan saddle]

No, not a straight line necessarily

Any function

[cyan saddle]

Yeah derivative

[jagged imp]

Well if the derivative of f(x) is f'(x), chain rule tells us that the derivative of 1/f(x) is -f'(x)/(f(x))^2

so its not really very clean

[cyan saddle]

You used the division rule, right?

I wanted to prove it

[jagged imp]

Uh you can use the quotient rule for this but I used the chain rule

with the "outside" function being g(u)=1/u and the "inside" function being f(x)

[cyan saddle]

Oh pretty smart.

Thanks

@jagged imp any way to prove the multiplication rule, using chain rule?

[jagged imp]

by multiplication rule you mean product rule(this)?

[cyan saddle]

yep

[jagged imp]

might be a language barrier thing but i've never heard it called multiplication rule

anyway, its not proved with the chain rule

you have to do it from the definition of the derivative/first principles

[cyan saddle]

Oh

[jagged imp]

there's another method too i just found, i can link you to a site with both methods if you like

[cyan saddle]

Sure!

[jagged imp]

the other method than the limit definition is implicit/logarithmic differentiation if you wanted to try it yourself

https://tutorial.math.lamar.edu/classes/calci/DerivativeProofs.aspx#:~:text=Product Rule %3A (fg),be proved using Logarithmic Differentiation.

if you scroll down its listed under product rule

there's also khan academy or something along those lines if you'd prefer a video

[cyan saddle]

That's alright, I think I got it

Thanks a bunch

[jagged imp]

nw mate

[spare marsh]

can someone help me make the venn diagram? I'm also confused on how to measure the percentage in part b for example, am I taking 36% of 43?

I think this is it?

[sinful sail]

any other ways to get the area of a circle than r x r x pi ?

[jaunty plover]

$A=\pi \left(\frac d2\right)^2$ ?

[ocean seal]

PristineWolf

[sinful sail]

so A=Circumference x R:2 is not ok ?

[jaunty plover]

what's R?

[sinful sail]

radius

[jaunty plover]

no it's not okay

[sinful sail]

does it work ?

[jaunty plover]

no.

what you said is basically $A=C\cdot \frac R2$

[ocean seal]

PristineWolf

[jaunty plover]

wait

wait

my bad my bad

@sinful sail your thing works as well

[sinful sail]

cool

[jaunty plover]

i misunderstood

[vale wigeon]

no

-3/2 cos(2x),

but also, if all you wanted is an answer, you could've gone to wolfram alpha

try taking the derivative of $-\frac32 \cos(2x)$ and you'll see.

[ocean seal]

Ann

[vale wigeon]

hopefully you will have enough sense not to claim that the derivative of cos(2x) is -sin(2).

the derivative of a composition is not the composition of the derivatives.

[subtle mantle]

If you want to know how you’d do it, you use a u substitution u=2x, du = 2dx so 3sin(2x)dx
-> 3/2sin(u)du and then you just integrate sin(u)du normally

[vale wigeon]

+C, but yes

you're trying to see a pattern where there isn't one

[crisp grail]

Some stuff js harder, if you do the y=2x substitution, it should be more clear

[fading zephyr]

set the two functions equal to each other

that is, 6x - x^2 = x + 4

this is a quadratic and has 2 solutions, which are the values of x at which the curves intersect

you then evaluate either of the two functions at these 2 values of x to get the y coordinate (it doesn't matter which function, since the two are equal at these values of x)

this will yield 2 points of the form (x,y)

is this a calculus course?

ok

the area is an integral

you can integrate the difference of the two functions

and the integration limits are the x coordinates you just found

the y values are the functions

[unkempt stream]

integrate top-bottom

[fading zephyr]

due to the linearity of integration, yes

it is rather integral (f2 - f1), but as you said, you can split this into two integrals

[marble seal]

hi guys

i'm solving this equation

2x + 2  -5 = 4x + 3
    ---          ---
     6            6```

x = 31
-----
12
right?

[manic quail]

$$2x+\frac26-5=4x+\frac36$$

[ocean seal]

heuwuernwufntmkiearsetnuyyyf

[manic quail]

Do you mean this @marble seal ?

[alpine sable]

Still need help with this?

[sharp sparrow]

yes please

[alpine sable]

Lets move to another channel

[marble seal]

yes

[alpine sable]

let @manic quail and @marble seal use this

[sharp sparrow]

okay what channel?

[marble seal]

my answer is $$x=\frac3136

[manic quail]

Could you please first tell me if the equation I wrote is the equation you meant?

[marble seal]

yes

[manic quail]

Okay, nice

,w solve 2x+\frac26-5=4x+\frac36

[ocean seal]

Results provided by WolframAlpha

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

Requested by veryhappyperson#1152

[marble seal]

my answer is
x = 30
---
12

[marble seal]

noiiiiiiiiice

[manic quail]

That isn't your answer though 0.0

[manic quail]

$$2x+\frac26-5=4x+\frac36 \ | \ -2x$$
$$\frac26-5=2x+\frac36 \ | \ - \frac36$$
$$-\frac16-5=2x \ | \ \times \frac12$$
$$x=\frac{-\frac{1}{6}-5}{2}$$

[ocean seal]

heuwuernwufntmkiearsetnuyyyf

[manic quail]

and $$x=\frac{-\frac{1}{6}-5}{2} \Longleftrightarrow x=\frac{-1-30}{12}=\frac{-31}{12}$$

[marble seal]

https://tenor.com/view/kevin-hart-dafuq-blinking-stunned-surprised-gif-8345056

[ocean seal]

heuwuernwufntmkiearsetnuyyyf

[marble seal]

why like this 😄

[manic quail]

I solved the equation, what do you mean?

[marble seal]

i solve it in easier way

[manic quail]

Your solution was wrong though?

[manic quail]

,rotate

[marble seal]

oh my bad

[manic quail]

,rotate

[marble seal]

hahahhaha

[manic quail]

,rotate

[manic quail]

Okay, great, that's fine too.

[marble seal]

ty 🙂

[pliant roost]

Hello, I got a question regarding a 3d world. I have 2 points. The point YOU are at, and the point you WANT to go to.
I get the distance in between these 2 points and I'll substitute it as D.
I would like to get the time it'd take to travel from point A to point B accounting for not only the X but also the Y
Right now I have
time = D / speed but I wanna also include the Y axis which this does not, how could I do such a thing?

[subtle mantle]

that's the correct formula for constant speed

[pliant roost]

but it doesn't count for the Y axis, only X

[subtle mantle]

what? yes it does

that's what D is for

[pliant roost]

fuckkk

my brain is broken

[subtle mantle]

it's the distance between the two points, i.e. for two points (x1, y1, z1), (x2, y2, z2) D = sqrt((x1-x2)^2+(y1-y2)^2+(z1-z2)^2)

so it takes all of the coordinates into account

[pliant roost]

yeah I see that now

okay thx lmao

[subtle mantle]

np

[rotund osprey]

can someone help me
(int from -inf to 230 (1/(sqrt(2pi)10)(e^((x-g)²/(210)))))=0.034
how can i get the average (g) out of this
its the gauss function

[lean gust]

no

z^3 not equal 3sqrt(z)

[subtle mantle]

no, that's $z^{\frac{3}{2}}-a^{\frac{3}{2}} = \sqrt{z^3}-\sqrt{a^3}$$

[ocean seal]

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

[subtle mantle]

third try's the charm

[ornate peak]

@subtle mantle @lean gust thank you

[lean gust]

somenone have a exemple test of math in english level (terminale or prepa ) last years of high school or first year of university in maths or physique

[marble seal]

can i know the solution of this plz

[subtle mantle]

just write / for fractions

it's so much more readable

[lean gust]

write in paper it's not clear

[marble seal]

x +10 15 - x 12 2x - 12
------ - ( --------- - ------- ) = -----------
6 3 2 18

[lean gust]

ah

[marble seal]

better?

[lean gust]

yes

[subtle mantle]

(x+10)/6-((15-x)/3-6) = (2x-12)/18

[marble seal]

my answer

x = 156
-----
-5

,solve (x+10)/6-((15-x)/3-6) = (2x-12)/18

[alpine sable]

,calculate (x+10)/6-((15-x)/3-6) = (2x-12)/18

[ocean seal]

The following error occured while calculating:
Error: Invalid left hand side of assignment operator = (char 29)

[marble seal]

😦

[lean gust]

3x/18 -2x/18 -6x/18 = -12/18 +90/18 -108/18

-5x/18 = -30/18

5x=30

[marble seal]

why - 108?

[lean gust]

x=6

[marble seal]

i did it + 108

[lean gust]

• • 12/2

+12/2=.....

[marble seal]

wait

[lean gust]

108/18=....

...=-108/18

[marble seal]

yes

no

wait what

[lean gust]

i haven'ta good computer

[marble seal]

why i did it + 108

lol

i just did
3x + 30 - 90 - 6x - 108 = 2x - 12

[marble seal]

r u sure?

[lean gust]

x +10 15 - x 12 2x - 12
------ - ( --------- - ------- ) = -----------
6 3 2 18

x +10 15 - x 12 2x - 12
------ - --------- + ------- = -----------
6 3 2 18

x +10 15 - x - 12 2x - 12
------ - --------- = ------- + -----------
6 3 2 18

[marble seal]

why + ???

in the middle

[lean gust]

where

[marble seal]

oh u removed the bracket so the sign changed

[marble seal]

continue plz

[lean gust]

3x 3*(10) 3* (15) -3x - 3* ( 12 ) 2x 12
--- + --- - ----- ---- = ------- + ------ - ----- 36 3 6 3 3 2 18 18

[marble seal]

https://tenor.com/view/baby-crying-baby-crying-gif-5943733

[glass lichen]

tf is that formatting?

[marble seal]

lol

[lean gust]

3x 3*(10) 3* (15) -3x - 3* ( 12 ) 2x 12
--- + --- - ----- ---- = ------- + ------ - ----- 36 3 6 3 3 2 18 18

[marble seal]

wait wait lemme stay more simple 😄

[lean gust]

Okok

[alpine sable]

is anyone good here with science

like cell cycles

[dusk gazelle]

yoo

give me a hard one

[rotund osprey]

find x

[dusk gazelle]

of what ?

the equation ?

[dusk gazelle]

want me to solve it ?

[marble seal]

hi guys , can i just know how to solve this in a simple and step by step way? (please be simple)

2x - z = 4
3y + z = 2```

[dusk gazelle]

hmm

I forgot it lmao

[glass lichen]

dont suggest breaking rules..

[dusk gazelle]

lol

[dusk gazelle]

sorry my bad

[glass lichen]

do you know linear algebra?

ie augmented matrices

[dusk gazelle]

I forgot it

[glass lichen]

wasnt asking you

[dusk gazelle]

I know

I trying to solve it

[marble seal]

nah

[glass lichen]

ok so from eqn 1, what's z?

[dusk gazelle]

we dont know

we need to find z first maybe ?

[knotty sleet]

Why wouldn't you just use elimination?

Sorry for interrupting

[dusk gazelle]

np

I tried but forgot how

[knotty sleet]

Oh are they required to use matrices

[glass lichen]

again... im not asking you these questions

[dusk gazelle]

bruuh

okay am out

😕

[glass lichen]

they said they didn't know Lin Al, so I'm just walking through subs

[knotty sleet]

Ah right kk👍

[glass lichen]

From equation 1, $$z=5-x-y$$ this means that 1a into 2 and 3 gives $$2x-(5-x-y)=4$$ and $$3y+(5-x-y)=2$$

[ocean seal]

Mosh

[alpine sable]

https://gyazo.com/ea6ec2c55f25ee73abd72c345a098677

can someone explain me whats here?=

[drifting jacinth]

what do you mean ?

[plucky crow]

find x in terms of z and y in terms of z and plug them into the first equation

from the two equations below

[scarlet spire]

yo sorry if im interrupting something but is a horizontal compression by a factor of 1/2 the same as a horizontal stretch by a factor of 2

[alpine sable]

Can anyone help undestrand how should I work out the x-coordinate of G?

For the y-coordinate it's just a triangle but I cant figure out the relation between s and xG

[marble seal]

tooooooooooooooo long

[sour echo]

help?

<@&286206848099549185>

[plucky crow]

oo thsi is fun

ill try

dms

[sour echo]

ooo ok thanks

[shut elk]

what's up @lost moss ?

are you asking what the solution is?

[lost moss]

yes

[shut elk]

have you tried?

[lost moss]

yes im just to stupid

[shut elk]

not possible, explain how you've tried

[alpine sable]

can someone explain how to do this?

it says 4+i ; 4-i ; -2 by the way

[jagged trout]

https://www.youtube.com/watch?v=eDb6iugi6Uk

[marble seal]

ty i need it

[marble seal]

@dusk gazelle

[alpine sable]

let me know if u can help

[silk terrace]

I need to find the taylor series for the function and show that it converges. Could someone help with the approach?

I have found the taylor series of exp(t^3) but am unsure on how to continue from here.

Does integrating from 0 to t yield the desired taylor series?

I thought it was open. My bad. Thanks

[viscid junco]

is it resolved now

[silk terrace]

Oh so it is still me

[viscid junco]

ok

[silk terrace]

Okay; I have seen the example but I am still unsure since i integrate from 0 to x

and not 0 to 1

Isn't that the same as taking the indefinite integral and have c=0?

So just integrate each term of the taylor series of exp(t^3)

[hollow pelican]

guys does anyone know how to do this?

[rigid smelt]

what have you tried?

[hollow pelican]

i solved it

but im not sure if need to put brackets anot

[viscid junco]

with or without are both fine

[lean gust]

I solide it ×=6 but he didn't undrestand

[coral pagoda]

Not quite. Here you want to integrate $\sum_{n=0}^\infty \frac{t^{3n}}{n!}$ from 0 to x with respect to $t$.

[ocean seal]

dackid (jump king +)

[silk terrace]

So I am essentially integrating each term in the series

[coral pagoda]

Exactly

And this is something you can do in the radius of convergence

[silk terrace]

So I found to be the taylor series of exp(t^3).

[coral pagoda]

Look at my series. They are the same thing

[silk terrace]

I see that now! So I can integrate directly in a sum?

[alpine sable]

@coral pagoda

[coral pagoda]

Yep, mainly because the Maclaurin series for e^u is convergent for all u. So when u=t^3, the taylor series also converges.

[alpine sable]

is there anyway you can help me if i dm you something

[coral pagoda]

No, this is the only problem I am helping with. I have other things to do today

[alpine sable]

k

[coral pagoda]

That's why I found the Taylor Series in 0.5 seconds

[silk terrace]

Okay so the whole problem is essentially this. The taylor series is given by the integral from 0 to t wrt x of the sum that you linked. Then I have to give an argument that the taylor series must converge to my function for all x

[coral pagoda]

That's super easy to do. Just use the ratio test

[silk terrace]

To show that the taylor series must converge to my function for all x is the same as finding the radius of my taylor series to be infinity?

[coral pagoda]

Indeed

[silk terrace]

got it. the only thing left to do is integrating then

Thanks!

[coral pagoda]

Sure is! Happy to help mate

[silk terrace]

wait it is from 0 to x wrt t right?

not the other way around

[coral pagoda]

Correct

[sour echo]

Do you still need the solution?

@lost moss

[random crypt]

Is the channel in use ?...

[alpine sable]

Can anyone help undestrand how should I work out the x-coordinate of G?

Can anyone help me understand how should I work out the x-coordinate of G?
For the y-coordinate it's just a triangle but I cant figure out the relation between s and xG.
It's a rotating half disk
does not really say anything apart from this

G is the barycenter of the disk
i can find it's y-coordinate just by tackign l-lsin\theta where l is the height of the line with A
but i cant seem do find anything for the x-coordinate

[dense snow]

Anyone can do this?

[fluid ember]

@dense snow Is that a SAT mathlevel2 question?

[dense snow]

I don't think so

[wraith phoenix]

@here

can anyone help out?

[wet fulcrum]

oh my bad channel in use

[wraith phoenix]

any body?!1

[random crypt]

Which channel can I use to ask questions ?....

[fluid ember]

@random crypt any that is free

this aint btw

[fluid ember]

36 I think
8²/100 is 64/100 that leaves remainder 36
N is 8 I believe

how about this

[dense snow]

uh.. y 8^2?

[fluid ember]

wdym?

it says N^2/100

[dense snow]

no like why is it 8?

oh

wait

stupid me, sorry XD

[fluid ember]

np lol

[fresh parcel]

no thats just gauss 8

[jagged trout]

why 8?

[fresh parcel]

N is 41 because 129^2 mod 100 is 41

[fluid ember]

it says positive integer

the 2 lines can only be 8 no?

[jagged trout]

When I understand this right, then we have a 6x6 square in the middle to build the rectangles

[fervent holly]

Is the minimum relation of an equation the vertex?

[calm grove]

Reflexive and Transitive
Not symmetric

[autumn apex]

@random crypt do you know what it's asking?

[random crypt]

Uhh kinda

[autumn apex]

you're given the derivative factorized. critical numbers are when the derivative is zero, right?

[random crypt]

Yeah

[autumn apex]

if you have a factorized polynomial of a single variable, how do you read off the roots?

[random crypt]

But why would they give me factorixed. It makes things harder

Right..?

[autumn apex]

nope, easier

[random crypt]

Obv

Oh *

[random crypt]

I dont know.

[distant bay]

Hi

Could someone help me with an exponential problem

[autumn apex]

this channel is taken

[distant bay]

🥺my bad

[autumn apex]

@random crypt so if you have an expression like f(x) = (x+2)(x-3), if either of the terms in parenthesis is 0, the whole expression is zero, so you have a root

how would you make one of the terms in parenthesis equal to zero?

[random crypt]

X+2= 0 ; x=-2

Like that?

[autumn apex]

how do you pick x such that it sends (x+2) to zero

and how do you pick x such that it sends (x-3) to zero

both of those selections of x are roots

[random crypt]

Factor

Then find x?...

[autumn apex]

you're already given the factored expression

so the roots of f(x) = (x+2)(x-3) would be x=-2, x=3

make sense?

[random crypt]

Yes

So

[autumn apex]

what are the roots of f(x) = (x+2)^4

[random crypt]

5,-2,0

[autumn apex]

where'd you get that from

[random crypt]

From the whole equation

[autumn apex]

oh that's your whole answer

[random crypt]

Yeah

[autumn apex]

yep you got it

[random crypt]

So what’s next

I found the x

What do I do now

To find the critical #

[autumn apex]

as easy as checking the definition of critical number

they're the roots of a derivative of a function, and you have the derivative of a function

so you have the answer

[random crypt]

Ohhh that’s it ?...

[autumn apex]

yep 🙂

[random crypt]

Then how do I find if the intervals of increase or decrease of F

@autumn apex

[autumn apex]

so when is a function increasing, given its derivative?

[random crypt]

F>0

[autumn apex]

yep

[random crypt]

Ok

[autumn apex]

from roots of the derivative, you know the endpoints of the intervals

[random crypt]

You mean the critical points right ?

X=0,-5,-2

[autumn apex]

the critical points of f are the roots of the derivative of f, same thing

[random crypt]

Ok

Then what

[autumn apex]

check if the derivative is positive or negative between each interval -- it has to be only one of these, since for the answer to change it must cross zero

[random crypt]

So do I plug in the critical numbers in the function

[autumn apex]

you can check the value between them

[random crypt]

Like between 0 and -5?...

[thorn sky]

Help

[autumn apex]

channel is taken

so your intervals are [-inf, -2], [-2, 0], [0, 5], [5, inf] (don't forget the 5 is positive)

[random crypt]

Why is the flag positive

5

I thought we said the five was a negative

[autumn apex]

this was correct

[random crypt]

Ohh

[autumn apex]

you swapped it a few minutes later

[random crypt]

Ohh

Sorry

Do I plug in a number between negative infinity and -2 into the function?...

[autumn apex]

yep

any will do

[random crypt]

So ex: -1?

[autumn apex]

yep, I'd do -3, -1, 1, 6

channel is taken

[random crypt]

Give me one second I’m plugging everything in and I’ll show you what I did

[dense snow]

Wai twai wati…

How do we even get these numbers? I understand @fluid ember ‘s because 8 is a side length and 8^2 mod 100 is 36

The if n is 41,41^2 mod 100 is 81, which isn’t ananswer

[thorn sky]

As

As

A

As

[random crypt]

@autumn apex

[autumn apex]

looks right

[random crypt]

So then what do I do

[autumn apex]

just remember what you were after, i.e. ^

[random crypt]

We were trying to find the interval of increase or decrease of f

[autumn apex]

if a function's derivative is positive in a given interval, you know that function is increasing in that interval

use the sign of the derivative at each value you checked to decide for that interval

[barren furnace]

🤷

[autumn apex]

channel is taken.

[random crypt]

OK I know if f’>0 then it’s increasing and vide versa

Vise

After I figure it out and plugged all these numbers in

I don’t know how to tell which one is increasing or decreasing

@autumn apex

[random crypt]

Here

[autumn apex]

you calculated values where f'>0 and f'<0, so you know where f is increasing and decreasing, right?

[random crypt]

They all came out negative except f’(1)

[autumn apex]

yep

[random crypt]

Is this right ?...

[autumn apex]

so if you want a local maximum, and you know two adjacent intervals (shared critical point) have negative derivatives...

yep

channel is taken

[random crypt]

So what does it mean to find the location of the local maximum and the local minimum

[autumn apex]

if a function's derivative is 0 at a point you know, and the interval on either side is negative, what does that imply for the original function at that point you know?

[random crypt]

So I know that the derivative is X=0

It’s one of the derivatives

**

It implies that it’s interval decreases

[autumn apex]

on both sides, yep

[autumn apex]

channel taken.

[halcyon leaf]

Can someone please help me?

[autumn apex]

please ask in an open channel instead

[halcyon leaf]

so which channel?

generla?

[autumn apex]

check for one where the last question asked has been answered

[halcyon leaf]

k

[autumn apex]

so @random crypt if you know the function decreases on either side of this value, what does that imply (in terms of local minima and maxima) for that function?

[random crypt]

The point where it most decreases is the local minimum?...

I’m not sure to be honest

[autumn apex]

think about it like this -- is f decreasing or increasing or neither when f' = 0 (remember, f'(-2) = 0)

[random crypt]

Increasing

Because I plugged it into a function

[autumn apex]

so f' > 0 means f is increasing, right?

[random crypt]

Yes

[autumn apex]

what about when f' = 0

[naive dock]

hi

[random crypt]

It’s the same

Neither

[autumn apex]

channel is taken @naive dock

[naive dock]

am soory

[random crypt]

But it’s not decreasing or increasing

[autumn apex]

right, you might want to plot a parabola on a sheet of paper and think about it for a moment

[random crypt]

Ok

I just sketched a parabola on paper

[quartz sage]

If anyone can help me, I’m in #help-4

[autumn apex]

so if the parabola opens upward, where is the minimum

[random crypt]

0

Like zero is the lowest part

[autumn apex]

for f(x) = x^2 yes

[random crypt]

Is that what you’re asking

[autumn apex]

yes, just trying to get you to understand the local minima/maxima are able to be understood in terms of the derivative

so what is the derivative at that point?

and is f increasing or decreasing on either side?

[random crypt]

I have a function already graft in front of me

[autumn apex]

local minima and maxima are also referred to as stationary points, i.e. derivative is zero

[autumn apex]

yeah unfortunately the scale makes it a bit hard to tell

[random crypt]

Is it like this

[autumn apex]

plot from -4 to 0 to see

[random crypt]

Nothing At -4,0

[autumn apex]

that's looking like -4.5 to -3

[random crypt]

I think it says the maximum is negative to zero but I don’t know how they got there

-2,0 *^

[autumn apex]

it should look like this

[random crypt]

Oh

Can I see that graph

[autumn apex]

https://www.wolframalpha.com/input/?i=f(x)%3Dx(5-x)(x%2B2)^4+from+-3+to+1

[random crypt]

Ok

How am I supposed to use the answer for part B to find the locations of the local maximum local minimum

Because I’m not allowed to use it from a graph

[autumn apex]

you know what local minima and maxima are, right?

what happens to a function on either side of a local maximum? Decrease or increase?

[random crypt]

Increase

Like it’s the height pint in a graph

And local min is the lowest point on graph

Highest *^

Point *^

[autumn apex]

you've got it reversed

[random crypt]

Oh

[autumn apex]

a parabola opening upwards has a minimum but no maximum

[random crypt]

And vice Versa ??

[autumn apex]

a parabola opening downwards has a maximum but no minimum, and you know the function on either side of a downward opening parabola is doing what, increasing or decreasing?

[alpine sable]

the first derivative

[random crypt]

Decreasing?... because it’s going downwards ?...

[autumn apex]

right

so local maximum means 'the function is decreasing on either side'

[random crypt]

So does that mean the local minimum means the function is increasing on either side

[autumn apex]

yep

[random crypt]

Ohhh

So I already found at the interval increases from 0 to 5

Does that mean I already found my local minimum????

[autumn apex]

you know things about f' which tell you whether f is increasing or decreasing

you know f'(-2) = 0, so f can't be increasing or decreasing at that value

kinda like the symmetry point of the parabola, right?

[random crypt]

Yaha

[autumn apex]

and you know on either side f'<0, which means f is doing what on either side, increasing or decreasing?

[random crypt]

Decreasing

Right?...

[autumn apex]

yep

so if you know f(-2) is a stationary point, you have two options for what happens on either side of f(-2), both increasing or both decreasing

[autumn apex]

^

[autumn apex]

^

[random crypt]

Yeha

So f(-2) is increasing

Bc it’s less than 0

And f’(x) > 0 is increasing

[autumn apex]

f(-2) increasing would mean f'(-2) > 0

is that the case?

[random crypt]

Uhh

But I thought we said if F(-2) = 0

So it’s neither

[autumn apex]

correct

[random crypt]

Ok ok

So when the question as to find a location

Does that mean we have to give a certain exact point

Or not

[autumn apex]

yes

so "where is the local maximum of f given F" is the same as "around what point is f decreasing on both sides"

[random crypt]

But we really got where it decreases

So where in decreases is what it means to say the local maximum ?

I’m so dumb. I’m sorry

[autumn apex]

the derivative of f will be zero at a maximum or minimum

you know where those points are

[random crypt]

-2

[autumn apex]

you have a set of possibilities: f is increasing AND decreasing around a point == NOT a stationary point == NOT a maximum or minimum; f is decreasing on either side of a point == local maximum; f is increasing on either side of a point == local minimum

you only need to evaluate this around the critical points, and use your answer from b that had info about f decreasing and increasing in the various intervals

the answer must be a critical point, f' = 0

[random crypt]

Can you please show me on paper what you’re talking about because I think I understand what you’re saying but ...

How am I supposed to know that this point can be increasing or decreasing

[autumn apex]

the derivative carries that information

you know everywhere f is increasing or decreasing already -- you did that bit

[random crypt]

On

Ok

[autumn apex]

when I said 'f is increasing AND decreasing == NOT a stationary point' that means that value won't be one of the ones you found (-2, 0, 5), so that isn't a case you're worried about

[random crypt]

So if it’s the most negative then it’s the local maximum which means it’s 5, infinity ?....

[autumn apex]

make sure you understand the conditions I listed

you're looking for local minima and maxima, and there's one of each in this case. Knowing what happens around the critical points tells you which of the exactly 3 possibilities is true for that point: local maximum (a stationary point), local minimum (a stationary point), neither (not a stationary point)

channel is taken

[fluid ember]

Mb

[random crypt]

I apologize. This is my third time retaking this class

I’m failing it for a reason

I Understand what you’re saying but it’s just not clicking

[autumn apex]

you're clear on what a local maximum and minimum are though, right?

and that when I say stationary point, I mean one of those two possibilities

[random crypt]

That if F is decreasing on either side and it is local max

F is increasing on either side it has a local minimum

[autumn apex]

and you know 'increasing on either side' means, if I move left OR right from this point, I get a higher value

[random crypt]

Yes

[autumn apex]

and that if a function is increasing on either side, it must 'level off' at that point?

i.e. derivative of the function is zero there

[random crypt]

Yes

[autumn apex]

so you have a set of information which is necessary to find the answer of 'where are the stationary points'

what information do you use?

[random crypt]

The critical points?...

[autumn apex]

you use whether or not the function increases/decreases on both sides of the critical points

[random crypt]

How do I do that

Like I already chose for numbers that’s in between the critical points

And I already sent that to you

[autumn apex]

the critical points tell you where the function's derivative is zero

and "function's derivative is zero" means "stationary point"

[random crypt]

I already plugged in the critical points and none of them came out zero

[autumn apex]

the critical points are exactly the ones where f'=0

don't lose track of what you're trying to find out

what would it mean for f(-2) to be a stationary point?

could it be increasing on one side and decreasing on the other?

[random crypt]

So if F is any of the critical points that means zero

[autumn apex]

yep, "critical point" is just a term that lets you talk about the "critical points of f" which is information about F

namely, F=0

[random crypt]

What do I plug in and what do I do to know exactly which one is that local l maximum/min

Like I’m understanding everything you’re saying it’s just I don’t know which one is a local Max on which one is the local minimum

[autumn apex]

also just to be clear, you're using F to mean derivative of f, right?

[random crypt]

Yes

[autumn apex]

a local maximum, in terms of critical points, is "to the left AND right of this critical point of f (F=0), f is decreasing (F<0)"

a local minimum, in terms of critical points, is "to the left AND right of this critical point of f (F=0), f is increasing (F>0)"

f(-2) is a local maximum because f decreases on either side, and you know this from your previous answer

[random crypt]

I thought -2 was one of the critical numbers

[autumn apex]

it is

in order to be a local maximum or minimum it must be a critical number

a function can't decrease on both sides or increase on both sides of a point unless it's a critical number

barring the case of a singularity, but not relevant here

[random crypt]

Can you show me a piece of paper how you found that -2 Decreased on both sides

[autumn apex]

the graph I linked shows it

this is f' or F

it's a bit hard to tell but at -2, the curve touches y=0

you already know this though, F(-2) = 0 from part a

and YOU found out that f decreases on either side by checking a value inside each interval

the signs of the values you found by plugging in values -3, -1, 1, 6 tell you whether f is increasing or decreasing, because they told you whether F>0 or F<0 at those points

so you know f(-2) is decreasing on either side because you checked at -3 and -1 and determined F<0 for both

^^^

[random crypt]

Is is f(6) is the local min

F(5)

I’m literally the most stupidest human you’ll ever meet

There’s a reason I failed this class twice

[autumn apex]

it's important to take breaks if you've been working too long

brain doesn't work great without breaks

[random crypt]

Im wrong aren’t I ..

I’m sorry if I wasted your time

I’m just trying my best to learn

[autumn apex]

it's ok I just had to make sure I wasn't giving a wrong answer

the places where the derivative of f equals 0, i.e. -2, 0, 5, are the places where f changes direction

so critical points are where local minima and maxima are

I may have inadvertently confused you by using increasing and decreasing the way I did

[random crypt]

No no. Trust me. The amount of ppl that tried to explain calculus to me is insane.

You’re the best person of explaining it to me.

I understood from you the most

[autumn apex]

a good way to develop the intuition would be to plot the derivative you were given (F) and its integral (f)

you'll see what the function does relative to its derivative, and how the values of the derivative associate to minima and maxima of f

[random crypt]

I appreciate your patience

W me

[autumn apex]

np

[random crypt]

And helping me step by step

[autumn apex]

I can't stress enough, you should take a break if you haven't

brain drain will take you from perfectly competent at calculus to 'how does algebra work'

[random crypt]

I’ll try. I kinda can’t Bc I work 3 jobs supporting my family. And right now is the only time I can finish my school work

[autumn apex]

oh you only need to take a few minutes for a break

trust me, working a problem straight through without breaks while you're brain drained will take longer than doing the problem with breaks

[random crypt]

I appreciate it.

Will do

[native temple]

Can x^2 = 4py be converted to ax^2 + bx + c = y?

[calm grove]

yes why not
(x² + 0.x + 0)/4p = y

[obtuse cove]

Can I receive help on these two questions? 🤣

Or is this channel closed?

[sharp flare]

In

9 51 15/17
— = —————
17 98

15/17 Put Into A Decimal Is 0.882......

And 9 x 98 is 882

Is this just a coincidence?

[quartz sage]

I THINK NOT

[sharp flare]

Lol

But seriously tho does anyone know

[native temple]

how to find vertex of parabola in x^2 = 4py

[calm grove]

Vertex will be (0,0)

The formula is -b/2a for x coordinate of the vertex and if you put x=-b/2a in eqn you shall get y coordinate
Of the vertex too

[alpine sable]

The marks obtained by four students in a math test are displayed in the table shown here.

Which of the following ranges is most appropriate to represent the numerical data on the vertical axis of a Bar Chart?

A.    10 to 50
B.    0 to 100
C.    0 to 50
D.    10 to 100

[sharp flare]

I suck at charts but I’m pretty sure it has to be B or D as A and C don’t go to 100

[alpine sable]

maybe its d because the lowest score is 45% so it isnt necessary to go to 0

[sharp flare]

yeah

Rawrbin said D

That should be right

[alpine sable]

thank you

[sharp flare]

Lol thank rawrbin

Hey rawrbin

In

9 51 15/17
— = —————
17 98

15/17 Put Into A Decimal Is 0.882......

And 9 x 98 is 882

Is this just a coincidence?

[autumn apex]

it's a coincidence.

[sharp flare]

Lol

I’ve been looking over this for an hour

Trying to find a formula that gets something like this

[alpine sable]

This Bar Chart shows the weight in kilograms of fruits sold in one day.

Why is the Bar Chart misleading?

A.    The heights of the bars do not represent the correct numbers.
B.    The vertical axis shows unequal intervals.
C.    The horizontal axis is missing one type of fruit.
D.    The width of the bar representing Jackfruit is more than the width of other bars.

i got another

[autumn apex]

9*98 / 1000 = (3^2)(7^2)/(2^2)(5^3) ~= (3)(5)/(17)

[quartz sage]

can someone help?

[autumn apex]

I think this channel is taken

[quartz sage]

damn

[sharp flare]

Lol I’m in middle school i don’t know any of that stuff so queque

DONQUEQOR

[autumn apex]

you can factorize ratios of integers into prime numbers and compare them more directly

[sharp flare]

Oh WAIT

[alpine sable]

thank you again rawrbin

[sharp flare]

nvm I know that I just didn’t know what the arrow sign meant

[alpine sable]

why is 8th grade math so hard

[autumn apex]

if you mean ~= yeah that's a bad font, just means approximately

[sharp flare]

oh I mean like the ^

is that just multiplication

[autumn apex]

exponent

[sharp flare]

Oh ok

Thx

[autumn apex]

np

[sharp flare]

So the exponent here would be what?

[autumn apex]

there are several exponents in what I posted

[sharp flare]

oh duh

Si the first exponent would be 98*9

[autumn apex]

nope that's multiplication

[sharp flare]

I’m smooth brain

[autumn apex]

so if you have 2^3 that means 2 times 2 times 2

[sharp flare]

OH

That’s what you mean

[autumn apex]

just count how many multiplicative 2's you throw together

[sharp flare]

I thought u meant like ^ as a place holder

Like x or y

Thx

[versed osprey]

A particle is moving in a circle of diameter 20m. What is its displacement in 1 round, 1.5 rounds, 2 rounds, and 2.5 rounds

could someone explain this

[autumn apex]

you're missing a part of your problem

[versed osprey]

oh crap

[autumn apex]

what is a 'round' in terms of the movement of the particle

[versed osprey]

the problem asks for distance

aahhaha

nvmnvm

thanks

[autumn apex]

np

[versed osprey]

wait shit it gave a table too

ill just send a pic

[alpine sable]

This Bar Graph shows the percent increase in the prices from the year 1981 to 1999.

What is a problem with the way this graph has been drawn?

A.    The scale along the vertical axis is divided into unequal intervals.
B.    The widths of the bars are not equal.
C.    The vertical scale used is too large for this data.
D.    The heights of the bars do not represent the correct percent increase.

[alpine sable]

thank you again rawrbin :)

[surreal delta]

Eh, is this math?

[versed osprey]

its technically physics but i think it comes here

[autumn apex]

part of this question still seems to be missing

[surreal delta]

Okay hang on, I know how to solve it😄

[versed osprey]

this is what it says online, still dont get it

[autumn apex]

oh wait by 'rounds' do they mean full orbits?

[versed osprey]

oh ok

[versed osprey]

ye

[autumn apex]

agh what a horrible use of terminology

[versed osprey]

sorry i shoulve menitoned

[autumn apex]

np

[versed osprey]

*mentioned

[autumn apex]

so what's the displacement of a particle if it goes around the circle once?

[versed osprey]

yeah, they do that a lot in the powerpoints they give in my class

[versed osprey]

according to the answer i sent it says 0, i still don't get htis

*this

[autumn apex]

displacement being distance [accumulated] between start point and end point

and presumably 'distance' here means how long was its path

[native temple]

IDK how to complete square outside of this form ax^2 + bx + c = y

[autumn apex]

so you accumulate perimeter as you travel (distance), but if you travel an integer multiple of a round the displacement must remain zero

[native temple]

How to solve this?

[surreal delta]

@versed osprey

circumference = diameterpi
= 203.14
1 circle = 1circumference
1.5 circles = 1.5circumference
This is how to solve distance😄

[surreal delta]

Sorry I can't read it😔

[gloomy lintel]

Yeah I can’t read it either

Could you send a clearer pic please?

[native temple]

sure

[versed osprey]

ok one sec brb\

[versed osprey]

oh ok, im clear with the distance part now, i don't get the displacement part, ill brb

[autumn apex]

displacement is at most one diameter, it's the distance between the start point and end point ignoring the path you took