help-0

[alpine sable]

2sin(2x)=2sinxcosc

x

this is where im at now

[tacit arch]

this is wrong

$\frac{2}{2} = 1$

[ocean seal]

riemann

[alpine sable]

2cot(x)=2cos(x)/sin(x)

[lone heart]

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[coarse rampart]

brains not working

[keen pasture]

What did you try?

[coarse rampart]

i havent attempted it but im guessing you have to work backward using the mean

[keen pasture]

Yes

[coarse rampart]

how do i do that

?

[keen pasture]

How is the mean calculated?

[coarse rampart]

add all values then divide by number of values?

[keen pasture]

Yes

So what is the age of all boys/girls combined?

Seperately

[coarse rampart]

2 seconds

would it be for the boys 18x16.2=291.6 and for the girls 27x16.7=450.9

[keen pasture]

Very good 👍

[coarse rampart]

thank you!

[keen pasture]

Now how old all people combined? (Or did you already figure out how to do it from here?)

[coarse rampart]

I believe I've figured it out

[keen pasture]

OK, what was your endresult?

[coarse rampart]

16.5

[keen pasture]

Got the same answer 🙂

[coarse rampart]

perfect

[keen pasture]

You can close the channel if you no longer need it?

[coarse rampart]

how do i do that?

.close#

.close

[lone heart]

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[unique salmon]

Hello, I wrote

3 • 2½ 3½
(-------- + ------- ) •
2 1

2½. 3½
(----- - ------
2 1

I only need a small hint to know how to continue from here

Can I use aⁿ + a^m = aⁿ+^m

Wouldn't this only work when both numbers are the same

Like 2⅓ and 2⅘

Or should I do 2½ = 1/2-²?

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[unique salmon]

.close

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[warm hazel]

where did i go wrong?

[tacit arch]

what's 1 * 4 ?

[warm hazel]

ok i see

[tacit arch]

how'd you go from (2-t, (2-t)^2) to (-1, -4 +2t) ?

Oh I think T's definition is missing

[warm hazel]

the second vector is the derivative of the first

T is the derivative of what's inside F1

[tacit arch]

you're missing this evaluated at 0

,calc (-4 * 2 + 4) - (-2^4 / 4)

[ocean seal]

Result:

0

[tacit arch]

oh what

nevermind. you just have a sign error here

[tacit arch]

,w integral -(2-t)^3

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[tacit arch]

stop trolling

<@&268886789983436800>

[warm hazel]

im getting the same answer

[tacit arch]

same answer as what?

[warm hazel]

before

its still 0

[tacit arch]

show

[tacit arch]

your -8 should turn into +8 here

[warm hazel]

why

[tacit arch]

what's a^4 for a=-2

[warm hazel]

positive 16

i switched the signs there but -8+4+4 is 0

[tacit arch]

evaluate this for t=0

[warm hazel]

16/4 = 4

[tacit arch]

how did you get 0

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[hallow dust]

i have no idea waht to do 🙏

[alpine sable]

Might be asking you to draw a vertical line (undefined slope.)

Or any line at all passing through that pointl

Really isn't clear.

[hallow dust]

yeah and there isnt a undefined mbutton

there is these

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[upper thistle]

Bro how do I do this

Been working on it for like 2 weeks and I still don’t get it

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[twin phoenix]

to solve for h could you rearrange A=(Ao)(1/2)^t/h to h=(t)(ln)(2)/ln(a/ao)

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[pulsar kindle]

i don’t think so

i think if you’ve got a ln(2) in there, there must be a negative sign somewhere

just try and break it down into steps

[twin phoenix]

darn

ok ty

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[harsh shadow]

hello

[harsh shadow]

So basically my question for today is

about a square

its geometry

if you want to prove a square

what do you demonstrate

equal measure

uh

perpendicular edges

adjacent sides

how do I figure it out

[plain flame]

equal sides is not enough

you need right angles

[harsh shadow]

oh

thease are the options

which is most right

or at least

correct for a square

[harsh shadow]

I personally think its all sides are of equal measure

I don't know if im corredct

[plain flame]

its option 1

[prime badge]

only 1

[plain flame]

this shape has sides of equal measure

but its certainly not a square

[harsh shadow]

oh

what is this

Dont mind the slope

I can do that easily

this is what I have done so far

I have attempted it but

what is this asking

actually

am I correct

sorry for the multiple pings

@tacit arch Ive seen you helping in other channels

do you have any idea?

Sorry for the bother

<@&286206848099549185> sorry for the ping but

im in a rush

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[rocky swift]

hi, do you have a book on integrals?

[rocky swift]

exercises, maybe

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[tacit arch]

Go to #book-recommendations for this type of question

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[lunar lintel]

could someone explain this to me

[lunar lintel]

please

[misty dome]

How to solve tan tan a + cot cot a/ sec sec a ?

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[lunar lintel]

s

[lunar lintel]

yo

this my channe;l

Was wanting an explanation on this

no worries

[tacit arch]

this is the full solution. what explanation is missing to you?

[lunar lintel]

i dont understand it

[tacit arch]

which part first don't you understand?

A'(r) ?

[lunar lintel]

ye why did they take the dervative

[tacit arch]

error of radius tells you error of area

[lunar lintel]

i also dont get this part

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[analog umbra]

Hi

[analog umbra]

My question is LaTeX Related so it might be off topic but
Im trying to turn a .tex file into a .pdf file using cloudconvert but i got a package in my tex file and it cant convert it because of it. is there a way to bypass that while still using the package?

[merry depot]

are you trying to just output some tex code?

[lone heart]

@analog umbra Has your question been resolved?

[analog umbra]

wdym

like

i got my .tex file and i tried converting it in .pdf on cloudconvert

it didnt work cuz of the themepackage that i using

this the .tex file im talking about

and the package im using that cloudconvert cant read is "beamerkuleuven2"

so this one

and im just trying to get a pdf file of the first .tex file with the theme being used in it

[merry depot]

is cloudconvert a tex compiler?

[analog umbra]

what is a compiler

its mostly a converter from what i know

[merry depot]

typically when typing in tex you need a tex compiler like MikTex or TexWorks to compile the code into a pdf, or beamer presentation

[analog umbra]

i tried downloading MikTex but didnt understand how to use it at all

[merry depot]

when you have miktex installed, go to the file, you should see a subfile that's executable called TexWorks

open TexWorks and paste the code you have into that and press the green compile button.

it'll probably have to download some packages, but it should spit out the presentation pretty quickly

[analog umbra]

and where do i put the package?

[analog umbra]

this

[merry depot]

it'll ask if you want to downlaod the packages you called in the code and then automatically download and install them once you approve it

[analog umbra]

does it take alot of time installing every single package?

[merry depot]

not usually

[analog umbra]

uh

oh

i think i did something wrong

[merry depot]

a few minutes, depending on how many non-standard packages you called

[analog umbra]

it said that i didnt have a local repository

and that i could make one

so i did by copypasting a command on their site

https://miktex.org/howto/local-repository

[merry depot]

you might just try a fresh install of miktek, i'm not sure what would cause that error
follow the instructions when starting it up to get all the packages installed and necessary things set up

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[candid tree]

I’m doing test corrections and don’t understand how to solve this problem, could someone help?

[subtle horizon]

y = -0.5x-10 into Ax+By+C=0

[candid tree]

Sorry what?

[limpid turret]

@subtle horizon is new to the server and has not learned how to use the help channels

@subtle horizon, delete your messages and read the FAQs.

[limpid turret]

Are you familiar with implicit differentiation?

[candid tree]

Yes, but I am confused about the natural log parts

[limpid turret]

Well have you worked the problem out at all? What answer did you get?

[candid tree]

i got 2x ln^3 for my answer

I combined x —> x^2

And factored out ln^3

[little drum]

do you know logarithmic functions?

[candid tree]

Yeah

Not sure how comfortable im with them though

[little drum]

then do you know what y = log x means?

[candid tree]

I am unsure

[little drum]

Alright no worries. You might've heard of exponential functions, like e^x, a simpler example is 3^2 where 3 to the power 2 is 3 x 3 = 9, 4^5 = 4 x 4 x4 x 4 x 4
Logarithmic functions are inverse of exponential functions. Here's a graph of how they look like:

,w plot y = log x

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[candid tree]

I see

[little drum]

so when it's written $y = x \ln^3 x$, it's meant $y = x(\ln x)^3$ and $\ln x$ is a function so you cannot just take out the argument and treat "ln" as a variable

[ocean seal]

Arya

[limpid turret]

Ah I see the confusion. fyi, ln³x= (ln(x))³

It's just a shorthand

[candid tree]

oh i see

[limpid turret]

Oh, I see someone else is already explaining this

[little drum]

anyways, as for how to differentiate that: \ \ $\frac{d}{dx} (x \ln^3 x) = \ln^3 x \cdot \frac{d}{dx} (x) + x \cdot \frac{d}{dx} (\ln^3 x)$

you use product rule ^^

[ocean seal]

Arya

[candid tree]

d/dx (x) = 1 correct?

Heres what I did

[limpid turret]

you forgot chain rule

and your hand writing is very neat

[candid tree]

Thanks lol

where did I forget chain rule?

Here?

[limpid turret]

Wait I am silly. I read your 3ln(x^2) part

I think you mean 3ln²x

[candid tree]

oh yeah

What would i have to do next?

[limpid turret]

you're done

you got the answer

oh wait jk

Sorry I'm in like 5 servers right now.

[candid tree]

Lol

[limpid turret]

Okay, I was right the first time.

You have you're answer.

You're done

[candid tree]

I put that answer on my test but it got marked wrong @limpid turret

[limpid turret]

read it again, carefully

[candid tree]

You sure I did everything neededb

Ok

[candid tree]

wait sorry would the answer be “none of these” then 😅

[limpid turret]

mhm

[candid tree]

tysm for ur help

[limpid turret]

Yeah that tripped me up too

It's why I thought you weren't done

I was like "Where'd that extra x come from??"

[candid tree]

haha

.close

[lone heart]

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[astral osprey]

I tried :

Valid strings
String of length n-1 followed by : 0 , 2
String of length n-2 followed by : 11, 21
String of length n-3 followed by : 001, 101

but eqn An = 2An-1 + 2An-2 + 2An-3 doesnt seem to work

what am i missing? o.0

[lone heart]

@astral osprey Has your question been resolved?

[noble sinew]

Don’t really understand your answer. Why is 0001 not allowed? It isn’t according to what you wrote as valid strings

[astral osprey]

wouldnt 0001 go into n-4 tho?

was only checking up to n-3 cuz 201 is 3 characters

[noble sinew]

What?

String of length n-4=4-4=0

What is that supposed to mean

This isn’t really a good way to attempt to do the problem - instead I would suggest trying to use the fact that you know there are 3^n ternary strings

(If you aren’t using all information given there is likely a problem in your method)

[lone heart]

@astral osprey Has your question been resolved?

[astral osprey]

hmm ok

.close

[lone heart]

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[slate egret]

I honestly don't even know where to start

[fathom mantle]

what is the topic on?

[slate egret]

find area between two functions

using integrals

[fathom mantle]

have you thought of creating a graph?
you can do one for f(x)=x^2 and g(x)=-x^2

[slate egret]

I try to tackle these problems without graphing

as on test I would be unable to do that

[fathom mantle]

draw a graph on paper? you can't do that on the test?

[slate egret]

I'd be able to do that on a test

I'd just like to learn how to solve this problem theoretically

[merry depot]

can you determine which one is the top and which one is the bottom function?

[slate egret]

well x^2 is a concave up parabola

with - y intercept

so it'd be at the bottom

[merry depot]

yep

[slate egret]

and vice versa

for g(x)\

[merry depot]

so, you have a top and bottom function. How do you find the area between two functions?

[slate egret]

is it upper function - bottom function?

[merry depot]

yep

[fathom mantle]

yeah

[slate egret]

so would it be g(x)-f(x) = 8

[merry depot]

no

you need to integrate it

[slate egret]

Oh ok

[merry depot]

the bounds of integration are either given (none are given here) or where g(x) - f(x) = 0
So you can find those values to bound your integration

[slate egret]

I find bound from f(x) = g(x)

[merry depot]

yep, same thing

[slate egret]

2c^2=2x^2

How'd I find the bound though?

[merry depot]

solve for x

[slate egret]

x=+-c

[merry depot]

so you integrate from -c to c

[slate egret]

Oh i see

-c to c for (g(x)-f(x))

[merry depot]

yes

[slate egret]

and it equals to 8

[merry depot]

and set whatever you get equal to 8 and solve for c

[slate egret]

but hold on

I'd need to find the antiderivative

[merry depot]

yes

[slate egret]

which should give me

$2c^2x-(2/3)x^3$

[ocean seal]

Sateral

[slate egret]

because c is a constant right?

but I'm not sure how to proceed

would I need to find the F(c)-F(-c)

[merry depot]

yes

[slate egret]

wait I think I got it

assuming the antiderivative

is right

[merry depot]

it is

[slate egret]

I got c=3^(1/3)

[merry depot]

,w integrate from (-3^1/3) to (3^1/3) of (3^(2/3)-x^2) -(x^2-3^(2/3)) dx

[ocean seal]

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[slate egret]

LETS GO

I have another question about bounds however

if a graph looks like this

would the lower bound be equal the left green point?

@merry depot

[merry depot]

you'd want to integrate with respect to y
and the lower bound would be the lowest y-value, which is the right-most green dot (it has a negative y-value, the other is positive)

[slate egret]

this is what I had done

so I interpreted a and b incorrectly?

[merry depot]

no, a is -7, b is 2

you'd integrate with respect to y
y will go from -7 to 2

[slate egret]

If I were to integrate with respect to x

would a and b be -4 and 41?

cause technically if I isolated for y and solved

I still shouldve got -4 and 41

[merry depot]

no, with respect to x it would be a cluster f*ck
x=-4 to 41 would get you from the left green dot to the right green dot and leave out the left most part of the parabola

[slate egret]

Ah man

the question asks me a) find the bounds in respect to x and b) bounds in respect to y

[merry depot]

i guess maybe that's what they want for that question, because those are the x's where the functions intersect... but in terms of actually finding the area between the curves you'd be leaving something out

[merry depot]

ah. ok

gross

you can compute it with respect to x by splitting it up into two different integrals

you'd find the area between a and b by solving for y and getting a +/- square root, finding the area between those.
and then between b and c you'd do the (red line) - (blue line) integral

[slate egret]

where would I even start

for a-b

[merry depot]

^^

take the blue line equation, solve for y

you'll get +/- a square root

[slate egret]

of x+8

[merry depot]

that's your top and bottom function

[merry depot]

y^2 = x+8

[slate egret]

y = +-sqrt(x+8)

[merry depot]

yes

so you have two functions, a positive root and negative root

find the area between those curves between a and b

[slate egret]

and a would have to be when x = -8

[merry depot]

yes

[slate egret]

how would I find b

[merry depot]

same as before, where do the red and blue line intersect?

[slate egret]

oh when the other function intersects

so -4

a = -8, b = -4

and then for the next integral, it'd be -4 to 41

but then again I am stumped

on how to determine what f(x) would be and g(x)

[lone heart]

@slate egret Has your question been resolved?

[lone heart]

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[winged otter]

Help pls

[gilded vessel]

what are you stuck on

[gilded vessel]

find an open channel

[winged otter]

I ddint got to follow our lesson

So im fucking left behind

[gilded vessel]

#❓how-to-get-help

[winged otter]

Man

[gilded vessel]

just go to a new channel

It's not that hard

[lone heart]

@magic mantle Has your question been resolved?

[lone heart]

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[lone heart]

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[strong schooner]

Trying to change the summation into a form where I can plug in n > inf, but currently stuck

[alpine sable]

c is true

i think

[strong schooner]

[alpine sable]

can you check answer??c is true or not???

[strong schooner]

Unfortunately there is no answer (yet)

[alpine sable]

ok

[strong schooner]

And would be nice if I can get hints/tips on whether I'm going on the right direction or not

[night sigil]

umm have u tried dividing numerator and denominator by root n for all those terms

[strong schooner]

If I divide the numerator by root n won't that just make it into 0/something

[night sigil]

0/something = 0 (as long as the something isnt 0 or infinity)

constant/infinity = 0

[strong schooner]

According to the mc answers I am quite certain the answer is not 0

And even if I did multiply it by 1/sqrt(n) / 1/sqrt(n)

it still won't make sense

you will get something like 0 / sqrt(n+3)

= 0

[rigid smelt]

are you familiar with riemann sum?

[strong schooner]

Yes, it is the only summation I have been taught

I did think of turning it back to an integral, no clue how thou

[rigid smelt]

good, you will want to apply riemann sum here

more specifically the right hand rule

here, you can factor out an n^2 from the square root, and since n is approaching infty, this means we dont need to worry about n being negative, so sqrt(n^2)=n

so now your limit is in the form $\lim_{n\to \infty} \sum_{k=1}^n \frac{1}{n} \cdot \frac{1}{\sqrt{1+\frac{3k}{n}}}$

[ocean seal]

waler

[rigid smelt]

can you see what function we should be integrating here as well as what our bounds should be?

[strong schooner]

Processing please wait

From what I am seeing, delta x should be 1/n?

[rigid smelt]

yes

so what should our bounds be?

[strong schooner]

ok slightly confused

Because to find delta x it would be something like Upper Bound - Lower Bound / n

[rigid smelt]

ok, lets just do it step by step

so now with what you found, we have $\lim_{n\to \infty} \sum_{k=1}^n\frac{1}{\sqrt{1+3k\Delta x}}\Delta x$

[ocean seal]

waler

[strong schooner]

yup

[rigid smelt]

right, now lets not worry about the bounds then, since it might be easier for you to find it by figuring out what our function should be first

now note that here our function is definitely of the form 1/sqrt(something here)

so from what you might have learnt, our partitions for x_i has the form x_i=a+(i-1)dx

however, we dont have a k-1 in our expression above

but that's okay too, since we can also rewrite the partitions as x_(i+1), this is basically the right hand rule (evaluating our rectangles at the right endpoint)

are you following with this?

[strong schooner]

Loading

ok

[rigid smelt]

great, so this means that the "1" in 1+3kdx is a constant in the function

so f(x)=1/sqrt(1+something)

which also leads us to setting x_(i+1)=3kdx (probably)

now we just have to make sure if 3kdx is actually our partition

so from what I said, we can use the right hand rule for riemann sum, meaning our x_i=a+idx. But from the expression, we have an extra 3 here

so now that implies 3 is a coefficient, and is not a part of the partitions

so that means x_k=kdx

and our function f(x) is 1/sqrt(1+3x)

do you agree with this?

[strong schooner]

yup, got the same solution

[rigid smelt]

great

so what should our bounds be then?

note that we set x_k=0 + kdx

[strong schooner]

Lower should be 1?
Upper should be 2

[rigid smelt]

no

[strong schooner]

wait

I feel like something is wrong

[rigid smelt]

our lower bound has to match the one in the partition

our partition has the form x_k=a+kdx where a is the lower bound

[strong schooner]

wait

Lower 0
Upper 1

$\int_0^1\frac{1}{\sqrt{1+3x}}$

[ocean seal]

ṼØῳ

[strong schooner]

and if I integrate it I get 2/3

[rigid smelt]

yes

that's correct

[strong schooner]

yay

guess I'll have to revise more Riemann sums, thank you for your help @rigid smelt

.close

[lone heart]

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[rigid smelt]

np

[strong schooner]

.close

[lone heart]

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[pliant kayak]

How to simplify this polynomial? Who can give the step to me, please?
(-2a^3+a^2+8a-6)+(5a^3-3a)

[lone heart]

Please don't occupy multiple help channels.

[echo socket]

Perhaps add similar terms?

[pliant kayak]

Make it to the shortest

But I don't know how to slove

My homework will expire soon...

[echo socket]

Yes, so first add similar terms, 5a^3 to -2a^3 and -3a to 8a

[pliant kayak]

How the ^3 disappeared?

5a^3 to -2a^3 this part, I forgot how to do

[gray isle]

if you had 5 apples and I stole 2 from you, how many apples would you have?

[pliant kayak]

3 apple.

[gray isle]

same idea here

[pliant kayak]

Is it 5a"^3" - 2a"^3",
so the solution will be 3a here?

🧐

[solid gust]

$5a^3 - 2a^3 = 3a$ ?

[ocean seal]

Potet

[gray isle]

no

[pliant kayak]

$5a^3 - 2a^3 = 2a$ ?

[ocean seal]

[代理服主] 玩球呢

$5a^3 - 2a^3 = 2a$ ?

[gray isle]

no

[stiff surge]

no

[pliant kayak]

Hmmmm

[gray isle]

if you had 5 apples and I stole 2 from you, how many apples would you have?
you didn't say that you be left with 3 apples with multiple bites in them did you?

[stiff surge]

Simple subtraction

[pliant kayak]

So .w.

$5a^3 - 2a^3 = 3$?

[ocean seal]

[代理服主] 玩球呢

[gray isle]

earlier you didn't say that you have 3 ,just the number 3 non apples did you?

[stiff surge]

Dude

You missed something

@gray isle Should I tell the answer

[gray isle]

maybe

[pliant kayak]

3a?

[gray isle]

no

[stiff surge]

$5a^3-2a^3=3a^3$

[ocean seal]

realhuman

[pliant kayak]

also 3a^3?

[stiff surge]

YES

[gray isle]

wdym by also

[pliant kayak]

Costant term?

[stiff surge]

cancelling out only works in multiplications and divisions whereas in addition and subtraction you just got add or subtract the same terms

[pliant kayak]

Oh

[gray isle]

5a^3 - 2a^3=3a^3
and NOT 3*(anything that isn't a^3)

[stiff surge]

yea

[pliant kayak]

$5a^3-5a^2$ = ?

[ocean seal]

[代理服主] 玩球呢

[gray isle]

just like what happened here

if you had 5 apples and I stole 2 from you, how many apples would you have?
3 apple
you are left with 3 * the object you had
(and not something else)

[stiff surge]

No answer

[pliant kayak]

I think 1 hours

....

[solid gust]

你这两个不是相同的值

[pliant kayak]

My time!!!!!

[stiff surge]

You can't solve that question

but you can factorise it

[pliant kayak]

完了, 功課要做不完了

[stiff surge]

The powers are different

[solid gust]

这种题是要你找相同的值，把它们缩减就可以了

[gray isle]

I would recommend looking up like terms

[pliant kayak]

Am I right?

[gray isle]

no

[stiff surge]

No

[gray isle]

adding 1 red apple with 1 green apple doesn't get you 2 green apples or 2 red apples

[stiff surge]

Only like terms can be added or subtracted

You gotta understand the concept

[pliant kayak]

a^3 and a^2 are unlike term?

[solid gust]

前面没有什么的话，括号可以去掉

[stiff surge]

Yes

the powers are different

[pliant kayak]

2ab^4 and b^4 is a unlike term or like term?

[stiff surge]

unlike terms

[pliant kayak]

thx

[stiff surge]

[pliant kayak]

I am the secondary school form 1

[stiff surge]

Nice

[pliant kayak]

Thanks for your(all helper) help~

Skill: Dead line fighter!!

.close

[lone heart]

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[steep flax]

the differential equation is https://gyazo.com/85414c328184bf8c89ce9727f96bff1a

calculate the slope mark in P(0,1)

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[vestal storm]

hi

[vestal storm]

what would the PI be for this

so the guess?

the CF gives roots -4,1

so would it be

Axe^(-4x) + Bxsinx + Cxcosx + Dx^2

<@&286206848099549185> ?

help plz

@ me if ur gonna help

thanks

[lone heart]

@vestal storm Has your question been resolved?

[lone heart]

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[vestal storm]

<@&286206848099549185>

[lone heart]

@vestal storm Has your question been resolved?

[vestal storm]

someone??????/

[lone heart]

@vestal storm Has your question been resolved?

[vestal storm]

ffs

[little drum]

First you figure a homogeneous solution:

,w y'' + 3y' - 4y = 0

[ocean seal]

Results provided by WolframAlpha

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

Requested by Ansh_#3502

[vestal storm]

yeah

but then what would the CF be

[little drum]

hmm, with that you'll have managed the 10e^{-4x} term on the right as well I believe.

for the particular solution, you can see a trigonometric function and a linear function

[vestal storm]

yeah

but one of the roots is 1 which is repeated?

or does the 1 not matter

[little drum]

so a good guess could be:

M sin x + N cos x + (px^3 + qx^2 + rx + d)

[vestal storm]

https://cdn.discordapp.com/attachments/490557019623915520/1047136868526993418/image.png

tf

fine ok

thanks

[little drum]

there's no repeated root though. it's just -4 and 1.

[little drum]

why the Bxsin x, and Cx cos x?

there's no xsin x or xcos x term in the ode though

[vestal storm]

idk thats just the way ive been taught

the ones not needed would cancel out i think

[little drum]

repeated roots mean you'll have an ODE that goes something like: \ $y'' - 2y' + y = 0$ where r = 1 is repeated

[ocean seal]

Arya

[vestal storm]

oh

okay

[little drum]

You can get the rest ig

[vestal storm]

bruh wow

u did all of that

nicee tysm!!!!

[runic perch]

Hello, I have a question

Can you determine a function if you were given the limit of x and the y?

[lone heart]

@vestal storm Has your question been resolved?

[lone heart]

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[brisk heath]

I'm trying to find y = mx + c
i put it (-x + 2) because (x-2) when x approaches -infty is negative

HELP

[little drum]

? what's the question?

can you send a ss or a pic?

[brisk heath]

it's in arabic

[plain flame]

google lens me baby

[little drum]

no worries, the expression would be comprehensible probably

[brisk heath]

i need to find y = mx + c
where m is not 0 you know
next to -infty

i'm trying

anyway i want lim of the final line to be 0

2. complete to square root

can i just
(x-2)²+1-(-x+2)² = 1 ?

in the numerator

^calc (x-2)²+1-(-x+2)²

.calc (x-2)²+1-(-x+2)²

[little drum]

yes it's 1.

for 1) you have to evaluate $\lim_{x \to -\inf } f(x)$?

right?

[brisk heath]

yes

[ocean seal]

Arya

[little drum]

alright, for 2) you have to complete the perfect square of x² - 4x + 5?

what does it translate to in English

[brisk heath]

complete to square

[little drum]

then it's (x - 2)² + 1, okay?

[brisk heath]

yes

[little drum]

then, what does 3) translate to?

[brisk heath]

you know what is y = mx + b

idk what it's called

find y that lim f(x) - y =0

that tilted long line

[little drum]

Ah okay

right?

[ocean seal]

Arya

[brisk heath]

yes

[ocean seal]

Arya

Arya

[little drum]

you get it?

because you see, 2m + b will be finite and is not dependent on "t"

[brisk heath]

that's brutal

where did the 2m come from

[little drum]

btw, that should be t \to -\inf

[little drum]

since x - 2 = t, x = t + 2, mx + b = m(t + 2) + b = mt + (2m + b)

[brisk heath]

the way i was told is after completing the square (x-2)²+1
ignore 1 and find the absolute of x-2 = -x+2
y = -x +2

[little drum]

hmm

[little drum]

that does work but idk if its fine to do that without understanding how it works

[brisk heath]

honestly was only stuck at that part
but when you asked for pic and started to help i thought i may learn something new or an easier way

[brisk heath]

because x to -infty right?

[little drum]

yeah ig

[little drum]

welp, yeah that's about right

[brisk heath]

appreciate this 🙏🏻

.close

[lone heart]

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[midnight void]

hello guys

what does it mean when it says the difference quotient ?

does it have anything to do with the definition ?

[lone heart]

@midnight void Has your question been resolved?

[alpine sable]

$\frac{f(x)-f(1)}{x-1}$

[ocean seal]

Buraian

[alpine sable]

@midnight void .close

.close

[midnight void]

@alpine sable thank you, i had an idea but just wanted to make sure

[lone heart]

@midnight void Has your question been resolved?

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[royal plank]

well, since 70 is like the low middle of 81 and 64, try to get 8.5^2 next, then look if its more or less than 70 and go down/up by decimal steps

you can round such small numbers like X,Y like X^2 + 2X*Y

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[slate egret]

I need to find delta x right

so wouldn't that be the upper function, 6x be subtracted by x^2

which then is squared because the area is pi*r^2

making the inner function (6x-x^2)^2

<@&286206848099549185>

[alpine sable]

.close

[slate egret]

relax bro

<@&286206848099549185>

?

[alpine sable]

<@&286206848099549185>

[slate egret]

.close

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[median siren]

how do i solve

[median siren]

8 = 2(y - 3)

Equation

$8 = 2(y - 3)$

[ocean seal]

MR. Lorém

$8 = 2(y - 3)$

[vague marten]

8/2 = 2(y - 3)/2
4 = y - 3
y = 4-3
Y = 1

8/2 = 2(y - 3)/2
4 = y - 3
y = 4+3
Y = 7

[worn fox]

Don't give out answers

[median siren]

why not?

[vague marten]

My bad.

[median siren]

i needed that

[worn fox]

Because that's not whay the server is for

[median siren]

well he did step by step

[vague marten]

I devided it up in steps thought

[median siren]

yeah

[vague marten]

So he can understand the thought process

[median siren]

that's what i am doing

[vague marten]

Great, sorry if i broke any rules! Wont happen again

[median siren]

i sorry too

thanks for the help i understood the method :D.

[worn fox]

You guys are good dw just try and walk it through as u go

[vague marten]

Good to hear!

[median siren]

.close

[lone heart]

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[vague marten]

Btw i see i rushed the answer, can you spot my error?

[median siren]

omg these equations are annoying

[median siren]

no

there is no error right?

[vague marten]

You are right 😁

[median siren]

Y = 7

😮

there is an error

[lone heart]

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[median siren]

help

[median siren]

$8 = 2(y - 3)$

[ocean seal]

MR. Lorém

$8 = 2(y - 3)$

[heady pollen]

you want to find y?

you distributive rule

[median siren]

its an equation

it just says solve the equations

[median siren]

the point of an equation is to find the value of the variable

[heady pollen]

yes

use distributive rule

[median siren]

i'm not familiar with this distributive rule

[vague marten]

Yep!

[median siren]

i'm from sweden

[vague marten]

Sorry if i misslead you

[heady pollen]

a(b+c)=ab+ac

[vague marten]

Can you spot the error ?

[median siren]

the answer is wrong and no i cannot spot the error

[cold jasper]

Just do exactly the same @median siren as last question you asked

[median siren]

i cant its not the same

[vague marten]

Look at this step 4 = y - 3

How can you get y alone?

[cold jasper]

You just want to find y right? then it's the exact same as we did with x before 🙂

[pearl cape]

can anyone solve this for me?
Replace the ? inside the Solution of the Following:
line ( 1 , 2 ) , ( 3 , 1 ) = -?/?x +?/?

[median siren]

4 + 3 = y - 3 + 3

right?

[cold jasper]

yes

[vague marten]

Right.

[median siren]

but why dont i replace the 4 with the Y

so it becomes

Y = 4 - 3

[vague marten]

because then its not equal anymore

[median siren]

@cold jasper you said i can move everything where i want it

[median siren]

oh...

[cold jasper]

Yes within the laws XD

[vague marten]

In equations you must keep the equality on both sides, hence the word equation! Think of it as a balance weight

[cold jasper]

If you remove a -3 you do it by adding 3

And you have to do that on both sides

[median siren]

yup so this is right 4 + 3 = y - 3 + 3

[cold jasper]

Yep

[median siren]

because the answer will be 7 = y

[cold jasper]

Yep

[median siren]

do i need to change the 7 with the y

[cold jasper]

Nah it

It means the same

[median siren]

like Y = 7

okay okay

[cold jasper]

You can if you want to, but it means the same

Just practice what you use to isolate different things

If you have a -1 to move it you have to add +1 each side

If you have multiply, you have to devide

If you have devide you have to multiply

[median siren]

i will note that down thank you whtwl and notzaj for the help 😄 truly amazing people

[cold jasper]

Same as with a +1 to move it you have to -1

[median siren]

i understood :D.

[cold jasper]

But always remember you have to do both sides

[median siren]

yup both sides have to be equal

[vague marten]

great to hear! To test that, what would 2x = 6 be then?

[cold jasper]

And also, it doesn't matter what the value is

It can also be 2g=6

It would be the same steps you have to take

[vague marten]

yes, this is also important. The letter can be anything, heck it can be an emoji if you want. They are just placeholders for values.

[median siren]

2x/2 = 6/2

[cold jasper]

Or a text even, you will run into that in physics

Correct

[median siren]

lol thanks for now ill call for help later :D.

.close

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[cold jasper]

np

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[arctic pebble]

Consider an interest rate that is quoted as 24% per year with compounding frequency m=4. The equivalent rate with compounding frequency m = 365 is: anyone know?

18.8528%.

20.2289%.

25.1986%.

28.9981%.

[arctic pebble]

hey gang, anyone have an idea how to solve this?

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@arctic pebble Has your question been resolved?

[arctic pebble]

<@&286206848099549185>

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@arctic pebble Has your question been resolved?

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@arctic pebble Has your question been resolved?

[kindred fog]

y varies directly as the square of x and when x=4 y=80

what is the equation

hey guys

anyone knows about variations ?

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[keen elk]

how do i solve for x 3x^2-4=2x^2

[wanton tusk]

Move everything to lhs

And use a^2-b^2 formula

[keen elk]

whats ihs

[wanton tusk]

Left hand side heheh

sry

[keen elk]

oh

lmao

[wanton tusk]

it’s a common abbreviation thing

[keen elk]

i got this and it says its wrong

[wanton tusk]

why are there complex numbers o-O

did you move everything to the left

[keen elk]

discriminant is -80

[wanton tusk]

roots are real here

[keen elk]

yes

[wanton tusk]

what did you get

[keen elk]

^

[wanton tusk]

no I mean

after you shifted to the left

you got x^2 -4 yes?

[keen elk]

-5x^2-4

[wanton tusk]

how

3-2 is 1

[keen elk]

if you move a tern doesnt it change signs

over the equals sign

[wanton tusk]

uhhh

it does

also if it doesn’t

how did your 5 become -5

but it shouldn’t be a 5, it should be 1

[keen elk]

oh wait its suposed to be -3x^2

i accidently typed it wrong

[wanton tusk]

Ah

okie makes more sense HAHAHA

yeah roots are complex

do you have your working?

[keen elk]

yeah

but i think i got it

thx

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[true tide]

are these right

[true tide]

proofs

and if so

how do i minimise steps

[limpid turret]

what about proofs?

[minor needle]

factored form of a polynomial

then sub y - intercept to find leading coeff

[limpid turret]

@stuck roost get your own help channel

[true tide]

?

proving the first statement in each like

thing

paragraph

[limpid turret]

what do you mean by just "proofs"?

[true tide]

.

using trig identities

[limpid turret]

They're not "proofs" they're just identities

[true tide]

?

well sure

[limpid turret]

No "proof" is given on whether they are true

[true tide]

but it's like proving those identities given the basic ones

[limpid turret]

So they're just identities

oh heck it's all one proof

the word "these" really was confusing in "are these right"

[true tide]

oh

i see

yeah

it's 3 different ones

[limpid turret]

You got me thinking this was a list of separate identities

Oh I see now

[true tide]

yeah

[limpid turret]

first one is fine

second one is right

they're all correct

[true tide]

ok cool

can i make them smaller

[limpid turret]

they're perfectly fine as is

[true tide]

ok

thanks

.close

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[quiet hare]

Can anyone help me with this? I'm confused on how to find out if its directly proportional.

[limpid turret]

It's proportional if Area=k*length for some constant k

[quiet hare]

ah, ok! but i'm confused on what "k" means

oh wait nvm

i figured it out

thx for helping!

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[quiet vector]

pi(20.7/2)^2 inch squared

[fast garden]

it says its wrong

[lost jungle]

what was your exact answer?

[gray isle]

how are you getting 20.7pi

[lost jungle]

@fast garden what is (20.7/2)^2

[fast garden]

somone said it was the anwer

[gray isle]

who

[fast garden]

them

[quiet vector]

no one here i presume

[gray isle]

no?

[quiet vector]

[lost jungle]

this is not the same as 20.7pi

[gray isle]

$a^b \redneq a\times b$

[ocean seal]

ℝamonov

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@fast garden Has your question been resolved?

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[night path]

How can I make f(x)=250-25x and solve it for f(0)

[fierce prairie]

plug in 0 for x

[winter tangle]

so replace every x by a 0