help-0

[raw shard]

yeah

[subtle cedar]

Then divide and distribute and that jazz and make it 24

[snow nest]

then just expand the brackets and that shit

[subtle cedar]

This is a sweet discord server tysm

[raw shard]

well actually add everything together on the left side

then subtract constants

but i’m sure you knew that

[subtle cedar]

Yes

[snow nest]

the scary thing of maths is you don't know what others know

[raw shard]

lol

[snow nest]

so i'm always scared to assume that say, you know how to do the navier stokes equation

you don't but like

[raw shard]

what field is that in

like what kind of math specifically

[subtle cedar]

Algebra is where I’m at

[raw shard]

makes me think of vectors

[snow nest]

lol no

it's one of the 'great math problems'

[raw shard]

oh

[snow nest]

the Millennium Prize Problems

if you knew how to do it you'd quite literally win a million USD

"To date, the only Millennium Prize problem to have been solved is the Poincaré conjecture, which was solved in 2003 by the Russian mathematician Grigori Perelman. He declined the prize money."

why the heck did he decline a million

[old hemlock]

Is x^(2/6) equal to x^(1/3)? If you do legal math and simplify the exponents, it is the same. However, if you graph them, they are not the same. X^(2/6) will never be negative since you square it. X^(1/3) however can be negative. Therefore they are technically not equal.

Take x=-1 for example, they both give different answers

If they are equal, they should give the same answers

[raw shard]

they are equal for positive x

actually wait

the 2/6 one has even exponents

so it turns negatives positive

the 1/3 one leaves it as positive or negative

[snow nest]

i'm getting the same answers for both?

[old hemlock]

For x=-1?

-1^2 is 1

[raw shard]

are you doing the root first or power first

[violet surge]

whats h can anyone help me really quick

[old hemlock]

Doesn't matter, you square the negative either way

[raw shard]

law of sines

[tight venture]

What’s 34.5 • 2?

[raw shard]

you square root the negative

not square

basically this is confusing

[old hemlock]

Can we move to another channel?

If you dont mind

I got more questions about this

[raw shard]

ok

what channel

#discussion

[old hemlock]

Idk what topic of math this is

[raw shard]

@violet surge do you know law of sines?

[violet surge]

no

[raw shard]

do you know some trig?

[violet surge]

a little

not that much

im in grade 9

[old hemlock]

@raw shard #serious-discussion pls

[raw shard]

so law of sines is A/sin(a) = B/sin(b) = C/sin(c)

the capital letters are the side lengths

the lowercase letters are the angles opposite to the side lengths

you know i might be overcomplicating this

when you split the triangle, is the base 6000 for both triangles?

aka is it split directly down the center

[violet surge]

hm i get what you're saying

but if you split it straight down

i dont think its 6k for each

[raw shard]

then law of sines is all i can think of

there could be another way but i don’t know one

wait is this from like, an assignment

actually no that won’t help, i can already see the base won’t be 6000

@violet surge do you want to try law of sines?

[violet surge]

yeah sure

[devout summit]

Turns out this particular triangle is isosceles

[violet surge]

yes

70-70-40

[raw shard]

wow i over complicated it

[raw shard]

not surprised

[violet surge]

ohhhh i solved it

lets go

[raw shard]

i can do advanced stuff but not basic stuff without overcomplicating it lol

[violet surge]

lol

hopefully one day i can be good at trig

[cyan willow]

Part a is 12 and b is 14, why?

I cant figure it out

[snow nest]

okay so

@cyan willow

[cyan willow]

hello

Wait

[snow nest]

if there are four options for each question

oh okay

waiting

[cyan willow]

This might help u ?

[snow nest]

what is that

[cyan willow]

Binomial cd function

[snow nest]

like what do those values signify

[cyan willow]

it's the table

[snow nest]

i am big dumb never heard of that

[cyan willow]

Actually nvm, show me your way

[alpine sable]

hi does this tree have a depth of 3 or 4?

[snow nest]

hang on wait i've forgotten my combinations

[alpine sable]

I got points taken off because my program said it was 3

[snow nest]

gimme a second

[cyan willow]

Oki

[frank nacelle]

hey

[cyan willow]

Ye

Hi

[late parcel]

This isn’t specifically a math question but is a thinking question

Can I ask it

[cyan willow]

Ok

[raw shard]

if it’s related to math yes

[frank nacelle]

what is the purpose of \e

[frank nacelle]

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[late parcel]

I’m confused between C and D

Would you consider D a density I depended?

[raw shard]

c

[frank nacelle]

ur right

its c

[raw shard]

c has nothing to do with population

[late parcel]

?

[frank nacelle]

habitat decreases as population increasise

floods are natural disasters and happen even if population is low or high

habitat can be reduced due to high population

[late parcel]

Ok thanks

[frank nacelle]

,tex e

[ocean seal]

sainallani

[frank nacelle]

what is the purpose of euler's constant

[raw shard]

it’s basically the face of calculus

[frank nacelle]

sorry im in alg 2 rn

[raw shard]

other than that i really don’t know, i just know it’s really important

[frank nacelle]

oh ok

[raw shard]

do you know e^(pi*i)?

[frank nacelle]

no clue man

[raw shard]

never mind then

[late parcel]

Thank you so much

Really appreciate the help

That was AP environmental by the way

[frank nacelle]

no problem

[late parcel]

But it uses a lot of math

[frank nacelle]

oh should i take it?

im in 9th grade

should i take it next year?

is it ez and useful if im not gonna go into science major?

[late parcel]

I’m a senior. From what I have heard it is one of the easiest APs but for me it’s hard

[frank nacelle]

oh

[late parcel]

I love science so it’s intersecting to me but it’s all on the teacher when it comes to difficulty

[dense lotus]

how would i solve this

[late parcel]

My teacher spend 9 years at Virginia Tech and has like 2 masters and a bachelors degree so it is an intense class at my school

[rapid nova]

e^(ix) = cos x + i sin x
is better

e^(pi i) is just its special case

[raw shard]

that’s the one everyone knows

if they don’t know e^(ix) they don’t know e^(pi*i)

[bleak ridge]

,rotate

[raw shard]

do you know if the angle opposite to 100 degrees is also 100 degrees?

probably not actually

[bleak ridge]

Ye itd only be that if you extended the left line down

Thatd prob be a way of finding it out

Idk if itd be the best

[raw shard]

i have something

[dense lotus]

The bottom right? Doesnt seem like it

[raw shard]

now that i think about it i can’t think of anything

i thought of something but it was incomplete

so it wouldn’t help

[dense lotus]

i dont know where to start in the problem

[raw shard]

neither do i

everything i’m thinking of is 1 step short

[bleak ridge]

I mean

Just start writing formulas

[raw shard]

i did

[devout summit]

(5x+y)+(5x-y)=180 - 100

[bleak ridge]

100 + 2x + y + 5x + y = 180

Ye

Then you can uhh

[raw shard]

not sure how you got that

you mean 5x+y+2x+y

[bleak ridge]

Since the angles add up to 180 in the triangle

[dense lotus]

7x + 2y = 80 tight

right

[bleak ridge]

I think focusing on the bottom left corner

Would be a very good idea

[raw shard]

it’s not a rectangle

[devout summit]

This is even better you directly get x

[raw shard]

i don’t know how you got that

[short night]

need help

[raw shard]

occupied

i can’t think of any way those things are connected in this situation

[dense lotus]

why would you subtract 100

[rapid nova]

do right arrows mean they are parallel?

[dense lotus]

yes

[devout summit]

Sum of co-interior angles is 180°

(100)+(5x+y+5x-y)=180

[raw shard]

i guess i forgot what that meant

because apparently that makes sense

[dense lotus]

Can you highlight the co interior angle lines for representation?

[devout summit]

The red ones

[dense lotus]

Got it

How would you solve for Y in this situation?

[devout summit]

5x-y=2x+y

[dense lotus]

100 = 7x + 2y, where 7x would be 56?

[cedar slate]

?

[devout summit]

That's fine too. (It's 7x+2y=80 though)

[dense lotus]

That’d be in the top right, right?

And how would i get the value of Y from the equation 5x-y=2x+y

[snow nest]

5x - y = 2x + y
5x - 2y = 2x
-2y = -3x
2y = 3x
y = 3x/2

[dense lotus]

Thank you

Got it

[wise stump]

Isn't sin3pi/4 = sqrt2/2

but cos3pi/4 = -sqrt2/2?

doesn't that mean they're not equal at x = 3pi/4

[limber urchin]

Yeap 3pi/4 is not an answe

7pi/4 as well

[white blaze]

is there a function that i can use to produce a landscape similar to this but with more bumps to it? rn im using the following:
sin(x) * (abs(square(x ** 2 + y ** 2)))) / sin(x)

[bleak ridge]

You could use that as a base function and use perlin noise or smthn to add that randomness

Idk if thats applicable to your problem but

[white blaze]

ah thats such a good idea

thank you :) my mind is so beat rn i really appreciate it!

[bleak ridge]

Np

[paper saddle]

does anyone know how to solve for p, focus, and directrix for this parabola equation?

[sweet dove]

Need some help :/

[paper saddle]

scale factor is just the new rectangle over the old one

but u shouldnt have skipped me

cause no one helped me yet

[glass wren]

can anyone tell me why i cant do ths

apparently its because the individual limits does not exist but i dont understand why ;-;

[charred flint]

@glass wren it's fine to think it works like that

it's just that you shouldn't have an equals sign for something that's not a number that exists

[glass wren]

oh i see

thanks for the insight

[formal bane]

do u guys know any app good for math? like photomath

[quiet finch]

I quite enjoy this website

https://www.symbolab.com/

It's not as convenient as simply taking pictures of problems but it can do more

[formal bane]

ok ty i will try, i have calculus assignment 😭

[gloomy hazel]

can someone help me to do this

"the given limit represents the derivative of a function y=f(x) at x=a. Find f(x) and a."

[solar jetty]

hi
can someone suggest some projects to be done with newton raphson method
a unique one infact
where you explain the project objective
methodology
problem statement
and algorithm

[inner sequoia]

why is it like this

i thought distributive property made (a+b)^2 = a^2 + b^2???

[loud cedar]

think about it

(a+b)^2=

(a+b)(a+b)

which means

there are:

a times a
a times b
b times a
b times b

[lapis valley]

what part

[loud cedar]

a times a and b times b can be expressed as a^2 and b^2

then there are two abs so 2ab

@inner sequoia

[lapis valley]

You let $u = t^3+4$ so $du = 3t^2 \ dt \rightarrow dt= \frac{du}{3t^2}$ and then if u substitute dt it just becomes the 2nd line.

[inner sequoia]

oh shit wait

thanks

[ocean seal]

hduxueiwkwnxudi

[scarlet heart]

never mind i figured it out

[lapis valley]

nice

[wheat prawn]

for this calculation what am i doing wrong

i get the wrong answer

[sacred orchid]

is dis channel busy or no?

[slow wraith]

what postulate is this?

[sweet dove]

Ah ok thanks

[paper saddle]

there are 2 sets of correlating sides and 1 set of correlating angles

do you know all the different postulates

@slow wraith

[slow wraith]

We're only studying about SAS, AA, SSS

this is for an exercise btw

[paper saddle]

ok well is there are 2 sets of correlating sides and 1 set of correlating angles

so if you had to take a guess which postulate would you think it is

[slow wraith]

SAS?

[paper saddle]

yea

[slow wraith]

ohhh i see

thanks

i didnt get it at first

[paper saddle]

np

its the same thing with all the other postulates too

[slow wraith]

this one is AA right?

[paper saddle]

aa is angle angle

but it isnt giving you any angles

[slow wraith]

its SSS then?

bc theyre both triangles???

[paper saddle]

its sss

but wdym they are both triangles

[slow wraith]

yeah i thought so

[paper saddle]

all postulates are gonna be only triangles

[slow wraith]

no its like SSS bc both of them are congruent triangles right

[paper saddle]

the postulates prove if two triangles are congruent

but congruency isnt supposed to be used as proof of a postulate

because the main reason for them is to find whether triangles are congruent

[slow wraith]

ohhhhh

[paper saddle]

so the reason its sss is because there are 3 sides that are congruent

it only gives you 2 sides but you can find the 3rd side to be congruent because of how the triangles connect

[slow wraith]

i see

thanks a lot

[paper saddle]

np

[light kestrel]

Can someone walk me through how to do number 2

,rotate

[light kestrel]

first i take the derative of r right

i mean isolate the r

so r = sqrt(15/pi)

no

fkkk

relate rates make my brain hurt

[spice path]

seems like the right track

[shadow widget]

https://cdn.discordapp.com/attachments/719796293899386893/902420157341761536/76BA6A68-08D3-48B1-99F4-4295199761F4.jpg

anyone know how to do this

[spice path]

Awww yeah bruz

Spesh maths

[shadow widget]

you australia?

[spice path]

Hell yeah

[shadow widget]

awesome lol

[spice path]

I did that last year

So good luck on your exam

[light kestrel]

Dame

[shadow widget]

if u know how to do the question pls help out

[shadow widget]

tyty

[spice path]

Well I'm also doing calc study atm

I'll have a lil peak

[shadow widget]

thankss

[scarlet agate]

can i ask a question

[spice path]

bruh, why are they all asking in the one chat

[wanton spoke]

I see. Yeah idk either It's just that I am used to have only 1 equation for a worded problem. May I ask if I can solve the problem using one equation only? Like, formulate a different equation and solve that to find n, the number of students?

[ashen blade]

gonna assume this channel is free since there hasn't been a comment in 10 mins

https://i.imgur.com/XsEggRW.png
from the 3rd to 4th step
why do they divide x+y by z
as opposed to the entire thing?
it's (x+y)(dx/dt + dy/dt) = z(dz/dt)
so shouldn't z divide the entire thing?
dz/dt = [(x+y)(dx/dt + dy/dt)] / z

[solar jetty]

hey

can someone suggest applications of newton raphson method

an equation

or smthing like that

like for eg: manning equation

[mellow tinsel]

For a two by two matrix:
If A^3*A^3=I, A^3≠I, and A^2≠I, how do I figure out what A is?

[chrome patrol]

Can anyone tell this

please can anyone share the written solution for this? will really help, thanks :p

[thorn kindle]

No.

[pulsar lance]

Differentiate numerators and denominators to find limits and then equate both of those limits to find p

[ashen blade]

sorry, does anybody have an idea about this?

https://i.imgur.com/XsEggRW.png
from the 3rd to 4th step
why do they divide x+y by z
as opposed to the entire thing?
it's (x+y)(dx/dt + dy/dt) = z(dz/dt)
so shouldn't z divide the entire thing?
dz/dt = [(x+y)(dx/dt + dy/dt)] / z

[chrome patrol]

can you please solve this? and share?

[ashen blade]

bro go solve it yourself
people here aren't going to do your homework for you

[chrome patrol]

ok rude but its okay understood

[ashen blade]

im literally stating facts

[chrome patrol]

ok

[ashen blade]

at least make an attempt at the problem before asking

[chrome patrol]

ok

[alpine sable]

How do i write an equation using the point-slope form?

[alpine sable]

Thanks

[lapis goblet]

how do i find the surface(s) of intersection of 2 ellipsoids

[jaunty crane]

There English below and answer at the side

Pls help

[lapis goblet]

<@&286206848099549185>

[lapis goblet]

.

what about the volume

[plush wagon]

please help me understand the given solution of problem

i am confused

[pulsar yarrow]

What part do you not get?

[rich basin]

for (d), why can you simply just find the derivative and then you can calculate for when it equals 0 you can find the time for which it will be empty

like if you have something like v = u +at, how can you differentiate in respects to t, and get "a" to find when v = 0?

you can't because a is a constant, but why in (d), you can calculate t, and find the equation equalling to 0

[jaunty crane]

omg thank you so much

[opaque totem]

can anyone help me

with this

[gray reef]

Can't sorry

[opaque totem]

issfine

[raw nexus]

Hello this channel free?

[opaque totem]

yeaa kinda

[opaque totem]

i mean can u help me with this

[raw nexus]

I've worked out, the total weight of the empty ferry to be correct 30.4367 MN

I'm just stuck on this question below?

The answer is 3505 m^3 but not sure how to get this answer

The distance D is 0.4m

Please can someone help me?

<@&286206848099549185>

[light oyster]

If i choose x and y from the interval [a,b], its obviously (x,y) always in [a,b], but how can i denote it?
its $(x,y)\subseteq[a,b]$ or $(x,y)\in[a,b]$?

[ocean seal]

小馬

[light oyster]

For a function f defined on the interval [a,b], for some c$\in$[a,b], is it always true that f(c)$\in$[f(a),f(b)]?

[ocean seal]

小馬

[light oyster]

OK

solved my problem lol

[alpine sable]

Given the expression $\sqrt{ T^2 + 4T\sin\alpha + 4w^2 }$, with everything but $w$ being positive real numbers, how do I get it to the form $Cw$ where $C$ is a real number?

[ocean seal]

leadersheir

[alpine sable]

<@&286206848099549185>

pls help me i have no idea to do question :Want to write three types of mark on a stick that is not one long, which is a line that divides the stick into 10 equal parts. A mark that divides the wood into 15 equal parts. and the line that divides the wood into 18 equal parts When cutting the sticks as written here How many sticks will you get in all?

[alpine sable]

i would start by defining $\beta$ as $T^2 + 4T\sin\alpha$

[ocean seal]

bertaunth

[alpine sable]

since everything other than $w$ is a positive real number (a constant)

[ocean seal]

bertaunth

[keen basalt]

Can anyone help me solve this problem?? Thanks in advance 💗

[wary iron]

@keen basalt I hope this helps https://socratic.org/questions/d-dx-cosx-cos2x-1-cosx

[pulsar yarrow]

You can use either quotient rule or product rule(for which you have to break it into two parts ig and it'd be more tedious)

[keen basalt]

Yeah I tried to solve it in that way.
I also at first tried to simplify the equation using cos2x formula then tried to differentiate but then the answer doesn’t match with the other. Now I don’t know what to do

[pulsar yarrow]

you don't need the cos(2x) formula for derivatives only for integrals

d/dx (cos(2x)) = -sin(2x) * 2 using chain rule

[keen basalt]

So does that mean this process is wrong?

[pulsar yarrow]

the algebraic process involved doesn't look wrong i guess other than the fact that you missed a negative sign(?)

But this doesn't work because you're enlarging the domain of the function

[alpine sable]

can i ask a question about a direct investigation i currently have, its on 'loopy polygons' and the main part is finding a formula that links the number of shapes and the perimeter so you can estimate the perimeter by only having the shape

and the the formula section is what i am struggling on the most, please dm me if you feel like you can help 🙂

thank you in advance

[pulsar yarrow]

you'd probably be better off just asking where you're struggling here rather than wait for somene to help you in dms

just a suggestion

[alpine sable]

ok ok i'll get a screenshot of the task sheet and the section im confused on

so that is part a of the direct investigation, i have created the six shapes asked and found the inner/outer perimeter

this is the graph plus a few patterns+notes i've noticed, but i'm really struggling to find a pattern linking the number of squares in the loop, to the inner/outer perimeter

[rapid nova]

can you link the number of squares in the loop to the inner perimeter if we assume that the loop is always rectangular?

[alpine sable]

well in my case i have to make sure the pattern works for at least 3 of my shapes

[rapid nova]

i understand but for a start answer my question

[alpine sable]

well i'm not completly sure since this whole time i've been trying to find a pattern with my shapes, not by assuming they are always rectangular.

[rapid nova]

also try considering different shapes of loops with the same amount of squares

you will see their perimeters match

that's because you can always rearrange squares in such a way that it becomes rectangular, and on each step the perimeters do not change

(if you move square by square)

[alpine sable]

yeah but for some reason i can't think to find a pattern that links the number of squares to the perimeter. like i'm not sure how i'm supposed to know the perimeter with just the number of squares. i'm listening to your advice and i understand rearranging the shape to a rectangular way to keep the same perimeter but to me changing the shape of the shape, i'm not show how that would help me

[rapid nova]

if you know how to calculate perimeters for a rectangular loop, then you also know how to calculate it for every loop with the same number of squares

[rapid nova]

so try finding an answer to this question

[harsh belfry]

I wasnt too sure on how they got to this step.

Did they just divide by 10?

then toss over the dh/dt?

[light oyster]

yeah

[alpine sable]

by the looks of it

[harsh belfry]

Alright, then I'm not sure why its not working with my numbers

I was given

Which gave me

[light oyster]

you want the details of the step?

$10 = 324\pi\frac{dh}{dt}$

[harsh belfry]

Sure

[ocean seal]

小馬

[light oyster]

$1 = 32.4\pi\frac{dh}{dt}$

[alpine sable]

Do I ask questions here? Like I'm extremely new to the group

[ocean seal]

小馬

[light oyster]

yeah

[alpine sable]

if there are currently no questions

[harsh belfry]

My ROC is 8 (Theirs is 10)

[light oyster]

$\implies dt = 32.4\pi dh$

[ocean seal]

小馬

[harsh belfry]

They have 324pi I have 9pi

So my equation is

I would just divide by 8

for

right?

For some reason I keep getting marked wrong

[alpine sable]

Ouuu, so I don't ask now...

[light oyster]

maybe expand it?

multiply by 3.14

or is the problem of unit?

[harsh belfry]

this is my last attempt on trying to get the correct answer 😅

[light oyster]

like ms^-1

[harsh belfry]

Perhaps I could post the original question.

Maybe I got a step wrong?

I'll outline my process

is the formula for volume

my r, as stated in the question is 3 times my height

therefore r:

[light oyster]

calculate dV/dt first

[harsh belfry]

I don't think thats the move here

maybe

[vapid oak]

that is the move yes, becuase you need to find dr/dt

[harsh belfry]

Only once i insert r I can find my derivative right?

[light oyster]

yeah

[harsh belfry]

So now I think i find the deriv

Am I incorrect?

[harsh belfry]

Because v=1/3pir^2h would give a very different derivative than

[harsh belfry]

this equation

[harsh belfry]

Does this make sense?

Not sure if I did that part correctly

[light oyster]

then it becomes finding dh/dt

since you replaced r

[alpine sable]

Do we ask calculus related questions here?

[light oyster]

yes

[harsh belfry]

Channel in use

[harsh belfry]

So did I do this correctly?

Im a little bit confused.

[alpine sable]

Oh as I said I'm extremely new so sorry

[light oyster]

$\frac{dV}{dt} = \frac{d}{dt} \frac{1}{3}\pi(\frac{3h}{2})^22h$

[ocean seal]

小馬

[light oyster]

yeah

thats right

[harsh belfry]

After that point I then just plugged in 2 for r

and got 9pi

[vapid oak]

you cannot just do that

[light oyster]

but the question told you to calculate the rate of change

[harsh belfry]

then theres the mistake I guess

what should I do

[vapid oak]

yes, but you just plugged something into the idea of rate of change for Volume to try and work out height

[harsh belfry]

I was just following this if it helps make sense

[harsh belfry]

What should I start by doing then?

I'm very new to ROC calculus questions

[vapid oak]

i dont have much paper with me but ill try my best to explain

yeah they are very hard so no worries

basically you want to differentiate the Volume function

so you want to differentiate V= 1/3 * pi * (3h/2)^2 * h

[harsh belfry]

OH

Sorry I skipped a step

I actually meant i plugged in r into this equations

second

writing it

[light oyster]

I thought its my mistake lol

[harsh belfry]

Nah nah, I had forgotten to mention that I found the derivative already

[vapid oak]

well what did you get for the derivative

[vapid oak]

you're forgetting quite a few variables there

[harsh belfry]

huh

[vapid oak]

expanding the brackets first, the expression is $\frac{\pi \cdot 9h^3}{12}$

[ocean seal]

Omfish

[vapid oak]

do you undertstand where I got that from just from simplifying this expression

[harsh belfry]

I dont...

[vapid oak]

so we have 1/3 and pi, and then the (3h/2)^2 becomes 9h^2/4 and theres an extra h

so Ive combined it all

$\frac{1}{3} \cdot \pi \cdot \frac{9h^2}{4} \cdot h$

[ocean seal]

Omfish

[harsh belfry]

yeah I did that part

I just simplified it

I think this guy did the same thing as me

[vapid oak]

however you got this which is incorrect

[harsh belfry]

Is this explanation wrong?

[vapid oak]

ok thats perfect then if you understand that

no the explanation is correct

[harsh belfry]

Whats wrong with mine?

[warm brook]

This is right. The only thing missing is $\frac{dh}{dt}$

[ocean seal]

kirby

[harsh belfry]

ah I see

ok

[vapid oak]

and then you equate it to 8, to find dh/dt

[harsh belfry]

Would that be correct?

Also thanks @warm brook

[warm brook]

Yes, I think so

[harsh belfry]

This is where I get stuck.

I have no Idea what to do next

[vapid oak]

you want to find dh/dt

does knowing that help?

[harsh belfry]

I don't think so

could I perhaps do this

[vapid oak]

wait

[vapid oak]

wait you have subsituted 2 in for the height too early

[harsh belfry]

oh really?

ok

[vapid oak]

that is looking good

and remember, you know that equals 8

so, still using r as a variable, try and find out what dh/dt is

[harsh belfry]

once I simplify this it should work out

[vapid oak]

well im not sure why you've decided to use b as dh/dt but yes

[harsh belfry]

ah because Its easier to type

😂

[vapid oak]

that is your formula for the rate of change of the height

and so now you may plug in your value of r

[harsh belfry]

8/9pi

I think thats it isnt it

[warm brook]

Yes

[harsh belfry]

I'll go check if its right

[warm brook]

That's just dividing both sides by 9pi in this one

[harsh belfry]

oh that would have been easier

haha

i havent slept in over 24 hours so I'm a bit out of it

will write that in my notes

Thanks.

[warm brook]

Yeah I presumed you knew that you were trying to solve for dh/dt

yeah ofc

[harsh belfry]

Thanks a bunch you guys

[vapid oak]

hope you learnt something or that this helped you figure somethings out 🙂

[harsh belfry]

Knowing the steps certainly helps

haha

[raw nexus]

This channel free?

[harsh belfry]

Yes'

[grave saddle]

Im to assume my end dates are october 2021.
How would I calculate how many months there are to this date from any date (month and year)

so like if I have march 2020, ill get 19

[raw nexus]

I have worked out the up thrust acting on the spar bouy to be 6.5749MN

It's asking "what is the tension"

Which I'm not sure how to work out?

[alpine sable]

can someone help me with this guy? I've currently done it like this so far but I don't really know how to continue or if I'm even on the right track. Thanks in advance!

[alpine sable]

Any ideas on how to solve

thanks, you can tag me

[alpine sable]

Brackets
Exponent
Division
Multiplication
Addition
Subtraction

Solve in this order.

Exponent means square, squareroot stuff.

[cyan willow]

Guys are these two thingy true

Or is one of them wrong

[alpine sable]

I guess it is.

I mean both correct.

[alpine sable]

Thank you! ❤️

[harsh belfry]

No idea what occurred in this step

[harsh belfry]

In this problem I am given the speed of 600

I am solving for the rate in radians that the elevation

My angle is 45 deg

I keep getting the answer incorrect

[visual bolt]

ok

[harsh belfry]

I think I would be using tangent at 45 degrees 5/x

Would I start by finding the derivative?

[visual bolt]

yes yes do that for tan 60 and 70

[harsh belfry]

ah so the derivative without the angle

then i input 45?

[visual bolt]

wait I am doing sth in that question

just a sec

[thorn wasp]

If I have to "vertically shrink [a function] by a factor of 2", I multiply the original function with 1/2 right?

the function in hand is, sqrt(x). so shrinking by a factor of 2 will make y = 1/2sqrt(x). right?

or is it the opposite?

[harsh belfry]

😅

[visual bolt]

can you try pi rad in that?

[spare vale]

I mayve labelled wrong

[tender anchor]

Are vectors in the domain of multivariable functions? E.g If we have a multivariable function f(x,y) defined everywhere, can we write f(<1,1>) = f(1,1)? I would assume not but I'm just checking

[oak chasm]

@tender anchor If the vector is in the domain, yes. For example, if the function is ℝ² → ℝ, then you can use any vector in ℝ² as input.

[tender anchor]

oh cool. Thanks for helping!

[oak chasm]

No problem.

[glacial hawk]

can someone help me with this?

i literally cant get the answer for this

[tender anchor]

PU = -UP

so it becomes EU + UP - EP

which is EP - EP

[glacial hawk]

ohhhhh

so its -UP?

[oak chasm]

You can also see it this way: EU - (EP + PU).

EU - EU.

[glacial hawk]

wait so EU-EP-PU=-UP?

[visual bolt]

0?

[oak chasm]

Nope.

[glacial hawk]

oh wait its 0

cause it cancels

[tender anchor]

yep

[glacial hawk]

thank you so much

[glacial hawk]

this statement would be true right?

[spare vale]

Ignore the jaffas 😤😤😤

[glacial hawk]

.

[grim pelican]

need help

for part a I went ahead and computed for the standard equation of the sphere

idk if thats what they want tho

[grim pelican]

i did the first part idk the 2nd part

[waxen cypress]

Hi! Just wanna ask how I can antidifferentiate this equation. The it’s dydx for the sequence of integrating but i’m not sure how I can integrate this trig with polynomial inside

[rigid kiln]

my gut says integration by substitution but I'm not sure

[novel kettle]

Plss help me 💀

How do I do that

[rigid kiln]

you can find this angle

[novel kettle]

Ok but it should be 360° right

[rigid kiln]

the interior angles of that shape will sum to 360 yeah

[novel kettle]

Ohhh so the out side one doesn't matter? Then do I find a° or the other one that you did

[rigid kiln]

the other one will help you find a

here's a hint

[novel kettle]

Oh ok thank you

[rigid kiln]

no prob, hope that makes sense

[novel kettle]

So that will be 60° so now I do 180°-125°=a° which will be 55°

[tulip swallow]

what is pronumeral

[novel kettle]

I don't even know

[unkempt umbra]

Quick question:
if the sum of 4 vectors is the 0 vector, does it mean that they form a parallelogram? or does it just mean that they form any regular quadrilateral ?

[tulip swallow]

if u move in 4 straight lines and end up back where u started

what would that be (yes a quadrilateral)

but if the vectors are not connected end to end like that, they don't form anything

take (1,1),(1,-1),(-1,-1),(-1,1) vectors going away from origin. they don't form anything

[stark plover]

By what does the function y = 4^x need to be stretched to "end up" with 7^x? Express your answer in the form log(a)b.

[tawny fable]

Hi

Can a linear equation with more variables than equations have one unique solution?

[raw shard]

@stark plover start with 4^(n*x) = 7^x

take ln of both sides

if you know logarithms well and you look at it for a second, it’s obvious what n should be

[stark plover]

@raw shard isn’t this the starting equation though?

[raw shard]

if a and b are constants i don’t think it’s possible for those two to always be equal

actually it’s definitely not possible

7^x grows much faster

[stark plover]

So the best we'd be able to do is define a and b in terms of x and b/a?

[raw shard]

define a or b in terms of x

if it need to be in that format, pick a few x values, maybe 1 2 and 3 and try stuff

i still don’t think this will work

can’t think of a reason why it would, even if it’s defined in terms of x

[arctic gust]

i guess multiply by (7/4)^x?

then both eqs would be the same

[raw shard]

they need it in terms of a log

[arctic gust]

oh

[raw shard]

technically something stupid like log2(2^((7/4)^x)) will work

but i hate this

that’s a test

[rose plaza]

and whats the problem?

[dull ocean]

how do i work with n

[raw shard]

@rose plaza you aren’t allowed to ask for help on tests

[rose plaza]

i wont do

[raw shard]

there’s a timer in the top right, and stuff is blacked out

there’s a time limit on a study guide

[dull ocean]

bruh

[rose plaza]

he tried

._.

[raw shard]

lol

better than some other people

some people post the whole uncropped thing

[rose plaza]

:DDD

[raw shard]

sometimes you can literally see people post stuff that obviously says test

no

[rose plaza]

no dude

[rose plaza]

xD

[raw shard]

as soon as i saw that you blacked stuff out i was suspicious

still doesn’t explain why there’s a time limit on a study guide

and i know that’s a time limit and not a timer

there’s a progress bar under it

well, beside it

[fading zephyr]

is this a graded evaluation

[raw shard]

they literally said it was a study guide, but you can see a time limit

doesn’t check out

[tall wing]

band

[fading zephyr]

someone else confirmed it's an exam, so banned

[eager pebble]

lmaooo

hey guys can u help with question pls

[raw shard]

yeah

i can try to help

[eager pebble]

I tried looking up the formula for linear approximation and it's f(a)+f'(a)(x-a)
but idk what to do with that

[raw shard]

yes that’s it

you pick a value close to x

basically pick a value a that is close to x, that you know the value of f(a)

[eager pebble]

But you have to x's here right? 6.05 and 6

so something in between?

[raw shard]

yeah x would be 6.05 and 6

so something close to there that you know the value of 1/a

do you know what 1/6 is?

[eager pebble]

yeah

[raw shard]

so you can probably just skip that part

and just do 6.05

so use 6 as a

[eager pebble]

so what would x be? 6.05?

[raw shard]

yes

[eager pebble]

hmm ok

@raw shard I plugged that in and got 0.16528 but it says its wrong

then it gave me this as a hint

[raw shard]

you didn’t subtract 1/6

i guess that works too

[eager pebble]

hmm let me try again

[raw shard]

@verbal marsh what’s after that 2 on the end?

[verbal marsh]

x

[raw shard]

had a feeling it was

ok

[rose plaza]

same

[raw shard]

so they took out a (1-x^2)^(-7/3)

[rose plaza]

if u factor it out you have to adjust the terms in the inside of the bracket

[raw shard]

multiply the coefficient by (1-x^2)^(-7/3) and the stuff after the coefficient by (1-x^2)^(7/3)

[verbal marsh]

i see it as the factor*A=(1/1-x^2)^4/3, then just isolate A

[verbal marsh]

What coefficient?

[raw shard]

the number in the front

the 2/3

i knew i shouldn’t have said coefficient lol

probably to get ride of the negative exponents in the parentheses

i guess whatever to get rid of the negative exponents

[verbal marsh]

For better context

[raw shard]

i was about to say you can simplify it a bit more lol

[verbal marsh]

Is this for formality? Because can’t you tell the expression is > 0 at x = 0 from the first line of the second derivative?

Oh wait

There’s a dividing by zero moment

[raw shard]

oof

no way to prevent that

also idk i don’t remember much about second derivatives

[verbal marsh]

It’s cool, my question has been answered

[fresh quail]

can someone guide me through this double integral problem

[lapis goblet]

sinx/x doesn’t have an elementary solution I though

Integral of sinc x is like Si(x)

[fresh quail]

it does if u change

the order of integration

it would give an elementary solution

just trying to figure out

[lapis goblet]

If x =2, x = sqrt(y)

Then you have to solve for y

Same for y = 4, y=0

I’d recommend graphing it

Easier to visualize

[fresh quail]

ok

so y = x^2

[lapis goblet]

Yeah so graph the function along with the boundaries

Then find which lines are used when going vertically

[alpine sable]

Is that right so far and need help filling rest out

I don’t understand the rest of it

[lapis goblet]

yeah

looks right so far

the other 2 boxes for the sqrt is asking what happens when a is bigger than 1

lets say

y = 3sqrtx

try graphing it on desmos seeing what happens

then try y = -3sqrtx

and finally when a is between -1 and 1, which would be a fraction or 0. y = .5sqrtx , y = -.5sqrtx

i think you should be able to draw some conclusions from these graphs

[alpine sable]

Ok I’ll give it a go. Thanks @lapis goblet

[lapis goblet]

np

[glacial cave]

TRADING TW ION FOR FENNEC

oh worng server

my bad

[brave remnant]

Hello

Can someone explain to me

What value (I should) use to represent a value approaching negative infinity

[jagged trout]

big negative numbers

[brave remnant]

Just any?

What should the constraints be

[arctic gust]

whats the whole q

[brave remnant]

?

[arctic gust]

the entire question?

[brave remnant]

Not important…

[arctic gust]

oh

so its just the most negative negative numbers

[brave remnant]

Which are

[arctic gust]

like -10000000

[brave remnant]

Anything it should be > or < ?

What should the constraints be

[arctic gust]

tbh thats not how you solve limits

[brave remnant]

Probably not

[arctic gust]

i think you use a few rules

[brave remnant]

Yes I know

You can use a rule for this

However

It should be possible without of course

[lapis goblet]

just keep plugging in large negative numbers and see what happens if you dod

[jagged trout]

https://www.youtube.com/watch?v=NmLljBAg82o

[arctic gust]

even if you approx using this method you still wont get the answer unless you simplify/factorize

[brave remnant]

That’s true

But usually you only want the approx value

On tests etc

[lapis goblet]

just plug in larger and larger negative numbers

like -10, -100, -1000

[brave remnant]

Great

[lapis goblet]

see what happensa nd see if it converges at 0 or diverges to infintiy/ negative infinty what have you

[arctic gust]

lol its easier to factorize than squaring/adding/subtracting those huge negative values

[brave remnant]

Well I would probably do both

[lapis goblet]

i mean for lim -> inf , of 1/x

you can't simplify further

[brave remnant]

^

[lapis goblet]

just plug in and see what happens

in this case itll just get closer to 0

so lim at inf is 0

[arctic gust]

anyway if you get 1/x anywhere, if it approaches negative infinity it becomes 0

[lapis goblet]

yes

[arctic gust]

but thats only if you are lucky

[lapis goblet]

basically if the x is in the denominator then it'll prob appraoch 0

[arctic gust]

if you get x in the numerator theres a very low chance you'll get it right

[brave remnant]

!thank @arctic gust @lapis goblet @jagged trout

[arctic gust]

yw

[cinder sorrel]

what about this

[arctic gust]

lol

its a nice trick to use on your friends tbh

[cinder sorrel]

yeah

is it true that sq rt i = 1

??

[raw shard]

i think the problem is that on one side they did i^5 first and on the other they did sqrti first

actually that’s definitely the problem

[cinder sorrel]

i thought it doesnt affect

[arctic gust]

the trick is in the 5th step RHS

[cinder sorrel]

(whats rhs )

[arctic gust]

right side

it should be plus minus 1 not just -1

[raw shard]

stuff like this confuses me

[cinder sorrel]

it should be -1 ^4

not ^2

[cinder sorrel]

but thats the same tho?

[arctic gust]

yeah

[lapis goblet]

they didn't put +- sqrti for step 6

[arctic gust]

i^4 ig

[cinder sorrel]

but its the same

[arctic gust]

yeah

[raw shard]

@lapis goblet i^2 is -1

[lapis goblet]

no im saying because the sqrt

[arctic gust]

same on the right side

it should be minus or plus

[cinder sorrel]

thezy dont have to put +/-

[lapis goblet]

technically you do

[cinder sorrel]

its just more explanatory

well not exactly

you are demanded to give one right equation

not all the correct ones

[raw shard]

i don’t get this so i’m just gonna say something is obviously wrong lol

[cinder sorrel]

if i say sqrt9 is 3 im not wrong

[lapis goblet]

there is no "one right equatoin"

it's a set of 2 solutions

-1 = -1, 1= 1

this is what happens when you take sqrts

ppl usually omit the negative because they have no use for it

[cinder sorrel]

but its not wrong if we disregard either of them

[lapis goblet]

or the asnewr is only defined when y>= 0

[arctic gust]

you have to check if the square root gives a positive or negative value

if positive, both should be

[cinder sorrel]

when we say a = b, we dont necessarily mean that a equals nothing but b

[raw shard]

step 3 is definitely the problem

[cinder sorrel]

how come?

[raw shard]

(sqrt(i))^5 = -sqrt(i), sqrt(i^5) = sqrt(i)

actually i guess step 2 and 3 are the problems

because step 2 implies step 3

[lapis goblet]

even then

they dind't put +- in front of sqr

[alpine sable]

Guys, emergency : I need to use Math to figure out who roped me into this.

[mild yacht]

hey, can someone figure out what n equals to? totally lost herw

[glass lichen]

is the e, and?

and what have you tried?

[mild yacht]

yes sir

[mild yacht]

equation system

but i always get lost

[glass lichen]

$(n+2)!=(n+2)(n+1)!$

[ocean seal]

Mosh

[mild yacht]

yesh

that i know

these are the options btw

[glass lichen]

Yeah... so apply what I gave you

then it's simple algebra

[mild yacht]

that's my problem lol but ye ty

nvm got it

<3 ty

[raw shard]

@thorn wasp possibly do both sides do the power of 10

so you have 10^ln(x+1) / x = 10000

and maybe rewrite 10 as e^ln(10)

actually that doesn’t really help

are you three aware that only one person can use a channel at a time

[elfin wasp]

sorry, didn't see.

[vernal fog]

$\sum_{x=1}^{\infty} \frac{1}{x}$

im not sure if this results in 2 or infinity, and im not sure how to look for it online
i am stuck with the little math i learned at school and im trying to learn some things rn
how would i put this equation to words?

$\sum_{x=1}^{\infty} \frac{1}{x}$

[ocean seal]

Java³

[glass lichen]

the harmonic series diverges

[vernal fog]

actually i meant

$\sum_{x=1}^{\infty} \frac{1}{x²}$

[ocean seal]

Java³

[glass lichen]

converges to pi^2/6

[vernal fog]

in find infinity confusing

thanks

[glass lichen]

https://math.wikia.org/wiki/Basel_problem

[vernal fog]

thx

[limpid flower]

Hi, is there a simple explanation why any algebraic number has a multiplicative inverse that is also an algebraic number?
I googled it and found only explanations that uses properties of rings, which is a concept I'm not familiar with, and I once saw a very simple proof that didn't include any ring related stuff.

[lucid imp]

I just need help with this 1 question and I should be able to do the rest myself

I just completly forgot how to figure this out

[warm brook]

@lucid imp
Go down from the top, what’s the limit as x->1 from the left and from the right?

If they’re the same, then the limit exists

[lucid imp]

from the right is it 1 and from the left is it 2?

or is it not 2 since its a open circel

circle

[warm brook]

Holes don't matter for limits, you just look at the value it approaches

[warm brook]

but yes

[lucid imp]

oh

okay

Preciate it

[lucid imp]

wait after I find that out

what do i do after

[alpine sable]

HA

[warm brook]

?

[alpine sable]

Think about it for 0.5 seconds. 😬

[lucid imp]

since the numbers are not the same is it DNE

[warm brook]

Yes

[warm brook]

My definition is not precise, I know

[lucid imp]

okay thanks

[alpine sable]

Well no I was referring to-. . .Nevermind.

grumble grumble

[warm brook]

In general if
[\lim_{x\to c+} f(x) = \lim_{x\to c-} f(x)]
then $\lim_{x\to c} f(x)$ exists and is the result above.

[ocean seal]

kirby

[lucid imp]

wait if it has a + next to it

does it mean

it comes from the right

[warm brook]

Yes

[lucid imp]

and - means from the left

oka

thanks

just want to make sure this is correct

[warm brook]

Yes