help-23

[peak siren]

nice nice

[dense sphinx]

@peak siren

I get it now

FUCK

IT WA SO EASY AND I WAS SO DUMB

[peak siren]

lmfao

all good

[dense sphinx]

IM NOT WORTH

xD

[peak siren]

i would’ve made a sign chart probably

[dense sphinx]

okay

NO NONO

Wait

look

this is what I figured out

[peak siren]

still gotta see which is max and which is min

[dense sphinx]

that's how I am going to do it from now on, fuck

[peak siren]

oki

[dense sphinx]

so

look @peak siren

we can do this

divide 360/4

so

we get 90, right?

so

[peak siren]

cosx - sin2x = 0
cosx - 2sinxcosx = 0
1 - 2sinx = 0
sinx = 1/2
so like when????
pi/6, 5pi/6, find which is min which is max, yay

[dense sphinx]

we call each 90 a side or a square

[peak siren]

okay

[dense sphinx]

now, in order to find when it repeats we do the following

so

consider that the sin and cos depend on the angle

all we need is get that angle again

and how do we do that?

pretty simple

we do 180, 270 or 360

-the angle we want

so, do we want cos 60?

we do 180 - 60, 270-60 an 360-60

this will give us the same sin

of course, the sign will depend on the cuadrant we are

but it's also a piece of cake

why?

we do the following rule

sin is positive for the first two sides

and negative for the rest

cos is positive at first, then negative, then negative then positive

look @peak siren

180 - 120 = 60

[peak siren]

okay

this just feels very convoluted

but if it works it works

[dense sphinx]

hmm

I see a problem here.

why

look

rule applies

[peak siren]

uh okay

[dense sphinx]

rule applies

but not here

why?

270-60 is not 240

hmm

I think I get it now

perhaps.

SO

HAHAHA

YEAH I GET IT

HAHAH YES

YES YES IT WAS EASIER THAN I THOUGHT

okay

so,

for the thirs side

ie from 180 to 270

the rule doesn't apply. Instead we do 180 + the angle we want

so do we want sin 30? we do 180 + 30

do we want cos 30? we do 180 + 30

yes, it works.

so that's the rule I am gonna use until I die.

[peak siren]

sounds good

[dense sphinx]

So, yeah

[peak siren]

so what was your final answer?

[dense sphinx]

So, this is how the rule looks like

in this way, it is easy to tell when sin and cos repeat

[dense sphinx]

I'm gonna solve it now xd

I was busy doing this rule thing

[peak siren]

😭😭

[dense sphinx]

that will come handy

during my test.

[peak siren]

alright

[safe radish]

@dense sphinx Has your question been resolved?

[dense sphinx]

done

@peak siren

thank you

.close

[safe radish]

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[lean otter]

I can not figure out how to do this to save my life

I got 96 but it’s wrong

The square yard and square foot conversion is messing me up

.close

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[olive vault]

so i have the polynomial x^2 - 2x + 2 (in Z[x]), why doesnt the rational root theorem work for it?

[austere cypress]

,w solve x^2 - 2x + 3 = 0

[flat frigate]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by wkaue

[austere cypress]

no rational roots

[olive vault]

yeah so why is that

[austere cypress]

the rational root theorem is about roots that are rational

it doesn't say anything about roots that are not rational

[olive vault]

oh sorry + 2 not + 3

[olive vault]

so it doesnt say that there must exist a rational root?

[peak siren]

,w solve x^2 - 2x + 2

[flat frigate]

Results provided by WolframAlpha

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

Requested by climb.

[peak siren]

still no real roots

[olive vault]

ohh

so the theorem says that if a rational root exists, its one of these

[austere cypress]

there are many polynomials with no rational roots

[olive vault]

yeah that makes sense

thanks

.close

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[timber orbit]

Hi

[timber orbit]

.close

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[rain bear]

instead of saying that you need to just post the question

[blazing olive]

ok thanks, here is the question

[safe radish]

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[slate flint]

A mathematican determines the amount of pocket mone yto give his son each week by getting him to play the game on Monday morning. if the son spns and the product is greater than 10 then he boy gets 10 dollars. Otherwise, he gets 5. Find how much in total should the boy expect to get after 10 weeks of playing the game. The game involves spinning two spinners. The expected value is 7.5.

The game involves spinning two sinners. One is numbered 1, 2, 3, 4,. The other is numbered 2, 2, 4, 4. Each spinner is spun once and the number is recorded.

[safe radish]

Show your work, and if possible, explain where you are stuck.

@slate flint Has your question been resolved?

[slate flint]

e

[slate flint]

I solved it. Sorry

[safe radish]

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[dense sphinx]

Does

X*ln(x) have a max min?

[dense sphinx]

I differentiated it and got

Ln(x)+1

And because I cannot get a negative number through logarithms, yeah.

[peak siren]

lnx + 1 = 0
lnx = -1
x = e^-1
x = 1/e

minimum

[dense sphinx]

What??

e^-1?

how?

[peak siren]

uh

cause lots?

logs

[dense sphinx]

Logs?

[peak siren]

logarithms

[dense sphinx]

Yeah, I don't get it, you see.

Lnx = -1

[peak siren]

yes

[dense sphinx]

But then it becomes x =e^-1

[peak siren]

now convert into exponential form

[dense sphinx]

How?

[peak siren]

yes

[dense sphinx]

Why?

I don't get it...

[peak siren]

convert to exponential or raise both sides to the power of e

[austere cypress]

$e^{\ln(x)} = x$

[flat frigate]

kaue

[peak siren]

thank you i was dreading doing latex on my phone

[bronze gust]

ln(x) is the inverse function of e^x

[dense sphinx]

So, if I get ln(x)

wait, lemme get this...

[austere cypress]

$\begin{aligned}
\ln(x) = -1 \
e^{\ln(x)} = e^{-1} \
x = e^{-1}
\end{aligned}$

[flat frigate]

kaue

[dense sphinx]

Okay, but

1/e

Wait...

[bronze gust]

Yea $a^{-1} =\frac{1}{a}$

[dense sphinx]

How do I solve equations when I get logarithms?

[flat frigate]

denzio321

[bronze gust]

These is one of the indice laws

Generally
$a^{-n} =\frac{1}{a^n}$

[flat frigate]

denzio321

[austere cypress]

naturally, when you have square roots, you might want to do the squaring operation. Similarly, when you have logs, you might want to exponentiate both sides

because they are inverse* operations

[dense sphinx]

How?

Could you do a brief example?

[bronze gust]

Graphing ln(e^x) we get the line y=x

[austere cypress]

by the very definition, $\log_7(2)$ is the number you raise 7 by to get 2$, so $7^{\log_7(2)} = 2$

[flat frigate]

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

[austere cypress]

idk why the 'so' next to the 7

[bronze gust]

Basically the function
$\ln(x)$ gives us a value such that $e^{\ln(x)} =x$

[flat frigate]

denzio321

[austere cypress]

ln(5) = 1.609...

e^(1.609...) = 5

[bronze gust]

How did you guys learn logs in school without this definition anyway

[austere cypress]

if i remember well, sam learned about logs directly here on a help channel

[bronze gust]

Oh

Fun

[dense sphinx]

Okay but does ln (1/e)-1=0?

[peak siren]

yes

[bronze gust]

No but ln(1/e)+1=0

[peak siren]

oh wait

[peak siren]

yes

this

i tired

[dense sphinx]

Ah, yes.

Thank you.

[bronze gust]

That was what he wrote initially

[dense sphinx]

But wait

How is that possible.

[bronze gust]

Wdym

[dense sphinx]

Does that mean ln 1/e is a negative number?

[bronze gust]

No that just means 1/e is a negative power of e

Which it is

e^-1

[dense sphinx]

Yeah, but how is ln 1/e + 1 = 0 then

[bronze gust]

ln(1/e) is negative

Because it is - 1

1/e however is positive

[dense sphinx]

Wait

can logarithms give us negative values?

[bronze gust]

Yes

Because negative powers exist

As seen in this graph of ln(x)

[dense sphinx]

What is logarithm again?

the number we need to ^ in order to get the number?

[bronze gust]

Alright let's do this once again

[peak siren]

$a^x = y \ \log_a y = x$

[dense sphinx]

Thank you.

[bronze gust]

$\log_n$ is a log with base n

[flat frigate]

denzio321

Climb

[bronze gust]

When we use a log and give it a value

We are asking for the power we need to raise the base to

To get that value

Take $\log_2(8)$

[flat frigate]

denzio321

[dense sphinx]

The power we need is 3.

[bronze gust]

Mhm

[austere cypress]

no way you can just \, i've been using \begin{aligned} all this time for nothing

[bronze gust]

So $\log_2(8)=3$

[flat frigate]

denzio321

[peak siren]

😭😭😭

gg

[dense sphinx]

Let's do some equations now, shall we?

Let's say we have, I don't know

log2(x) = 8

I could convert that to 2^x= 8, right?

[bronze gust]

Uh

Nuh uh

[bronze gust]

Alright maybe let's look at what this equation is saying

It's that

[dense sphinx]

Yeah.

[bronze gust]

The power we need to raise 2 to

[peak siren]

$\log_2 x = 8 \ 2^8 = x$

[bronze gust]

Is 8

[flat frigate]

Climb

[bronze gust]

To get x

Therefore x=2^8

Yea

[austere cypress]

if x = 8 then 2^x = 8

if log2(x) = 8 then 2^(log2(x)) = 2^8

[dense sphinx]

Ah, how do we solve it then?

[bronze gust]

x is simply equal to 2^8

[austere cypress]

$2^{\log_2(x)}$ = ?

[flat frigate]

kaue

[dense sphinx]

How do we solve equations like 4^x= 16

Or ln (x) = 1

[austere cypress]

log base 4 both sides

e^ both sides

[bronze gust]

I mean you can do this just by observation because 4^2=16 is a pretty common power

[austere cypress]

if you have log, then exponentiate. if you have exponentation, then log

[dense sphinx]

Yeah, but I couldn't think of a different example.

[bronze gust]

If you wanted to use logs then
$x=\log_4(16)$

[flat frigate]

denzio321

[dense sphinx]

So, if I have ln(x) = 0

I would have to do

e^x= e^0?

[austere cypress]

the LHS is ln(x), not x

you have e^(ln(x)) = e^0

[dense sphinx]

Oh.

So e^(ln(x} = e^0

[dense sphinx]

what's next?

[austere cypress]

can you simplify e^(ln(x)) ?

[dense sphinx]

I'm not sure.

Can I?

[austere cypress]

what's the definition of ln(x)?

[dense sphinx]

e^something=x?

[bronze gust]

That something is ln(x)

Tbh I think you should try some khan academy

[austere cypress]

e^x and ln(x) are opposite functions.
if you apply ln and then apply e^, you get x back
if you apply e^ then apply ln, you also get x back

ln(5) = 1.609...

e^(1.609...) = 5

so e^ln(5) = 5

[dense sphinx]

First I gotta pass my test, then Khan Academy.

[bronze gust]

Want some practice qns

[dense sphinx]

qns?

I do not know what that is

[bronze gust]

Questions

[dense sphinx]

Yeah.

[bronze gust]

Kk

[dense sphinx]

Derivatives, limita

vectors

functions

max min

And finally integrals which I have yet to study the.

[bronze gust]

Alright gimme a sec

[dense sphinx]

btw

i would like if you could give me some general math questions

so I can see where I'm failing and see what knowledge I'm missing.

Fuck, now I want Logarithms questions

yeah.

Logarithms are my passion.

[bronze gust]

A circle with radius r starts to expand where dr/dt=0.5
(t is time) calculate the rate of change of its circumference

@dense sphinx

[dense sphinx]

Alright.

Maybe tomorrow.

Power died. xD

are you okay with me sharing the solution tomorrow?

[bronze gust]

Sure

[dense sphinx]

btw 2e^x + e^-x

it doesn't have max nor min right?

Because, well.

e^n will never be negative

right?

So my answer was no max nor lima

[bronze gust]

Well the derivative of that is
2e^x-e^-x

So I think it could possibly be negative

[dense sphinx]

Yeah, fuck just figured that out.

[dense sphinx]

Wait.

Is not that a good logarithm exercise

[bronze gust]

There is one time you need to do a log

[dense sphinx]

2e^x-e^-x=0

[bronze gust]

Mhm

[dense sphinx]

Like

Equations?

[bronze gust]

Do you know about u substitution

[dense sphinx]

what is that?

No, I probably do not know about that

[bronze gust]

Sorry gtg

Cya later

[dense sphinx]

alright.

[safe radish]

@dense sphinx Has your question been resolved?

[safe radish]

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[safe radish]

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[steady sail]

hey so i don't really understand how the determinant can be used in equations

for example, we know that det(AB) = det(A)det(B)

so does that mean that det(AB) = det(A)det(B) = det(B)det(A) = det(BA) ?

Also, if i have the equation A=B can I turn it into det(A) = det(B)
or in the same way AAB = B^3 => det(AAB) = det(B^3)

[solar hazel]

yes to all

[steady sail]

alright thank you i might be back with more

.close

[safe radish]

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[lean otter]

lol

[steady sail]

.reopen

[safe radish]

✅

[steady sail]

wait i forgot to ask

can i divide with the determinant since its a number and not a matrix?

[solar quartz]

Yes if its not 0

[steady sail]

ok thanks

.close

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[full lotus]

Hi, I'm struggling on calculating phi

[full lotus]

So, I'm working on this

I have to calculate that integral on W

I have that the radius moves between 1/2 and 3

then θ between pi and 3/2 pi

but idk how to calculate phi

I'm cool with double integrals, but I'm really struggling with these

[vagrant ice]

should be just from 0 to pi/2

[full lotus]

why?

[vagrant ice]

because phi is the vertical angle

[full lotus]

I want to learn how to calculate it

[vagrant ice]

so the bounds $x \le 0, y \le 0, z \ge 0$ are one of the octants of the 3D plane

[flat frigate]

southlander!

[vagrant ice]

you're dividing x into 2, y into 2, and z into 2
(positive and negative)

so there are 8 possible regions

[full lotus]

so there are 8 possible regions
yes

[acoustic goblet]

You need to define your coordinate transformation at first. There are multiple conventions, or am i stupid?

[vagrant ice]

yes absolutely

I just looked at the problem and their working, and figured out that theta was the angle on the xy-plane

it's confusing cause there are many different conventions

[full lotus]

I drew the region first

to figure how the radius and theta moves

so for example if we were to calculate the whole sphere, phi would be 2pi?

like if we didnt have restrictions on x, y and z

and had only the region between both spheres

phi would be 2pi?

[vagrant ice]

no, it would span pi radians

so -pi/2 to pi/2 or 0 to pi

[vagrant ice]

you can rotate this short red line 180 degrees around the z-axis

so you only need half of the 2pi for phi

[full lotus]

isnt there a calculation I can do? 😄

[vagrant ice]

no

you have to keep imagining what happens with the angles when you move the point around

or you could use Geogebra or Desmos in 3D

[full lotus]

so if I where to calculate the whole sphere, phi would = pi because of these black lines?

[vagrant ice]

instead of changing the vertical angle phi

[vagrant ice]

just go around, add pi radians to the angle theta
then your angle phi will remain the same

[vagrant ice]

yeah so those two black lines going down from the origin would have the same angle phi

so by symmetry you only need to cover half the sphere, the left and the right half on your diagram

[full lotus]

makes sense

ok I'm trying to make my mind up

so phi here moves from 0 to 1/2 pi?

[vagrant ice]

no, you need to do the negative z-coordinates as well

so -pi/2 to pi/2

[vagrant ice]

oh but for your original question it does

since you are only considering z >= 0 there

[full lotus]

Yes

hmm

Ok I'll try with other excercises also

I'm kinda cooked for tomorrow 🤣

[vagrant ice]

yeah basically there are only a few configurations

you're going to do a lot of questions where literally they only changed the numbers

and the question structure is exactly the same

[vagrant ice]

for this topic, triple integrals without any flux or divergence theorem or whatever

[full lotus]

perfect

[vagrant ice]

I recommend your textbook and OpenStax textbooks as well

[safe radish]

@full lotus Has your question been resolved?

[safe radish]

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[dense sphinx]

guys

[dense sphinx]

help me with this shit

so my derivative is 2e^x - e^-x

now, how can I make an ecuation so I can find the values of X that make my derivative zero?

[vagrant ice]

great, so let e^x = u

then you have $2u - \frac{1}{u} = 0$

[flat frigate]

southlander!

[vagrant ice]

do you know what to do next?

[dense sphinx]

what.

I don't get it.

[vagrant ice]

try multiplying both sides of this by u

oh wait you don't know that $e^{-x} = \frac{1}{e^x}$?

[flat frigate]

southlander!

[dense sphinx]

yeah

and I did that

so

I got

(e^x)-(1/e^x)

[dense sphinx]

then I end up with 2* e^2x/e^x-1/e^X

well

2*e^x-(1/e^x)

as we can tell, the denominator is different from e^x

so in order to get e^x at the bottom

we need to multiply 1 * e^x

[vagrant ice]

yes!

right I forgot the original question

[dense sphinx]

and then we get

[vagrant ice]

yes so you have $2e^{2x} - 1 = 0$ then

[dense sphinx]

no?

[flat frigate]

southlander!

[dense sphinx]

I get (2*e^2x/e^x)-1/e^x

= 0

[vagrant ice]

can you multiply both sides of $2e^x - e^{-x} = 0$ by $e^x$?

[flat frigate]

southlander!

[dense sphinx]

CAN I DO THAT?

WHEN?

[vagrant ice]

ofc

you can always multiply both sides by the same thing

[dense sphinx]

OKAY THAT'S SOMETHING NEW

OKAY SO YEAH

FUCK

[vagrant ice]

algebraic equations is the process of doing the same thing to both sides

so you can also divide both sides by the same thing
Just check your denominator is not 0

cause you know, dividing by 0 is undefined

you can also raise e to the power of both sides

[dense sphinx]

OKAY OKAY SO

[vagrant ice]

really any operation you can think of

[dense sphinx]

SO basically

[vagrant ice]

unless it makes something undefined, you can do

[dense sphinx]

if I have something messy like that

I can just multiply by the number I want

at both sides?

[vagrant ice]

yes

by the expression also

doesn't have to be a literal number, like e^x is not a number

[dense sphinx]

can you show me examples where I can do that

[vagrant ice]

one sec I'll link a YT video or two

[vagrant ice]

have you never seen this kind of working before?

https://www.youtube.com/watch?v=Z-ZkmpQBIFo

this video btw

[dense sphinx]

yeah

[vagrant ice]

great

I guess you learned something new

that this principle is super useful and can be applied in a ton of different situations

[dense sphinx]

Yeah like

I knew that you could like

[vagrant ice]

https://www.youtube.com/watch?v=yNgmVu0R_T8

here's another example

[dense sphinx]

do that but only if you had

the x

there

[vagrant ice]

this goes through the subs I was talking about earlier

[dense sphinx]

I didn't know you could do it with pretty much everything you want

[vagrant ice]

u = e^x for the first 2
u = e^(2x) for the 3rd

[dense sphinx]

I have a question

let's say instead of e^x at the bottom

I have idk, 2

can I multiply everything by 2?

[vagrant ice]

like $2e^x - \frac{1}{2} = 0$ or what?

[flat frigate]

southlander!

[dense sphinx]

like both 2e^x and1 being divideed by 2

[vagrant ice]

oh yeah if $\frac{2e^{2x} - 1}{2} = 0$

then yes just multiply everything by 2

a bit of work after that shows that e^(2x) = 1/2

[dense sphinx]

Okay now

I did end up with 2e^2x -1

then that becomes e^2x= 1/2

what's next?

[flat frigate]

southlander!

[vagrant ice]

then great, you can take the logarithm of both sides

[dense sphinx]

so my guess is

[vagrant ice]

$\ln(e^{2x}) = \ln(1/2)$

[flat frigate]

southlander!

[dense sphinx]

yeah

so my guess is

and correct me if i'm wrong tho

ln e^x = x

and then 2 goes out

so 2*x= ln (1/2)

finally ln (1/2)/2

[dense sphinx]

is that correct?

[vagrant ice]

this is correct

so yes you can replace x with 2x

[vagrant ice]

so this reasoning is correct!

well done

x = ln(1/2)/2 indeed

[austere cypress]

or -ln(2)/2

[dense sphinx]

why is that?

why -ln(2)/2?

ah

my bad

[austere cypress]

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

[dense sphinx]

I get it know

[flat frigate]

kaue

[dense sphinx]

yeah

alright

now

how can evaluate it

[austere cypress]

normally you just let it be like that

if you want a numerical approximation just use a calculator

[dense sphinx]

no but like I gotta find max and mins

so I gotta evaluate that thingy with numbers smaller than x and bigger than x

[safe radish]

@dense sphinx Has your question been resolved?

[safe radish]

@dense sphinx Has your question been resolved?

[dense sphinx]

Okay, I solved ln1/2/2

which is about -0.34

BUT HERE'S THE PROBLEM BUDDY

what if they don't allow me to use calculator during my test

I wouldn't be able to assign a numerical approximation to my X, let alone my Y

[dense sphinx]

ALRIGHT

SO

NO MAX NOR MINS IT SEEMS

nevemind

done

DONE

[dense sphinx]

guys

what if they don't allow us to use calculators tho

[dense sphinx]

guys

when someone asks me

why is zero not a critical point here if it makes the derivative not exist

what can I say?

Zero is not a critical point because critical points are part of the domain.

And zero is not part of the domain as ln (0) is not defined

[safe radish]

@dense sphinx Has your question been resolved?

[dense sphinx]

FUCK yeah i'm doing my exercises correctly!

.close

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[torpid spindle]

I was trying to find any complex solution to this but I struggled a lot with that

[torpid spindle]

Im thinking atp that there is no solution at all, not even a complex one

and 17/4 doesn't work because it's gonna give 1/2 instead of -1/2

[pale lily]

its not solvable

as is

it always produces a non negative value

[torpid spindle]

I'm in a class w 15-16yr olds, I think that's grade 9 or 10 in your system

[torpid spindle]

so there wouldn't even be a complex solution?

[pale lily]

i mean

17/4

is just solving for x

thats the answer in real numbers

but not complex

the answer is probably just

no real solutions

[torpid spindle]

I was thinking there could be some sort of solution that gives a negative value like that

[torpid spindle]

that's the answer but I was asking the math teachers if there was any complex solution and he just guessed it was -1/(5i+4) which I checked, isn't correct

[pale lily]

i mean

theres no need

for a complex solution

x=17/4 is a real number

but

u just cant solve that equation

with it

[torpid spindle]

I just wanna figure out if there is any, it's rlly not needed but I'd like to know

[pale lily]

i can ask chat gpt if u want lol

[torpid spindle]

it couldn't give me any

it was telling me there was no complex solution which confused me

[pale lily]

its probably right

this is a pretty basic math concept

i doubt it would get it wrong

[torpid spindle]

I dont trust it anymore, it was telling me 17/4 was a real solution to it

[pale lily]

it is real

[torpid spindle]

but it's not a solution

[pale lily]

the complex solution

is 17/4

there are no real number solutions

but

17/4

doesnt satisfy

the orignal equation

so

there are just none

i guess i could be wrong

but im just using common sense here

[torpid spindle]

Why would this be a complex solution

It doesn't involve any imaginary numbers

still kinda confused

[pale lily]

it doesnt need to

5 + 0i

is a complex number

but it just equals 5

[torpid spindle]

But it wouldn't be on the imaginary plane of numbers so it should just be a real number

[pale lily]

just curious why are you trying to do this just wanna know?

[torpid spindle]

something like e^(pi*i) would be a real number too

[torpid spindle]

Curiosity and I just want to get an answer to a question I've been trying to solve since this morning

[pale lily]

have u used something like

symbo lab

it will solve the equation for u

if its possible

[torpid spindle]

Nope never heard of that, imma try it

[torpid spindle]

Yea that's for real answers

[pale lily]

im like 99% sure its either auto done

or there is a option

to include complex solutions

im not too familair with it but its a pretty advanced tool

[pale lily]

this is for complex numbers

[torpid spindle]

It specifices it's only to real numbers, meaning complex numbers could possibly make it negative

[pale lily]

x:∈:ℂ

means

x

has to be

complex

[torpid spindle]

oh okay

Imma still wait for somebody else to hop in to verify ig

edit: I realized how stupid of a question that was wow

[safe radish]

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[karmic mantle]

So like basically im studying for my calc exam (this is a practice test) and this prof is using desmos but im not sure how i would get the bounds in an exam setting. I do have a TI-84 tho

[karmic mantle]

not really sure how to use the TI

[onyx narwhal]

i think a youtube video would be your best bet

[karmic mantle]

oh fr

do u know a good one?

[onyx narwhal]

to figure out how to use the calculator anyways

[karmic mantle]

yea fair enough i just never had a situation where the teacher himself is using desmos to do the problem lmaoo

[onyx narwhal]

but to find the coordinates for where the two lines meet you can just set cos(x^2)=x^2-2 and solve for x

it looks like that is what he is doing but just using desmos

if i remember right (havent been allowed to use a graphing calculator on exams in a while) there should be a mode to directly find the intersection of two lines you graphed

[karmic mantle]

oh yea thatll def save me time

cus im pretty sure im allowed to so long as i explain it

[onyx narwhal]

yeah if you're allowed to use one on your final i'd learn as much as you can about what it can do for you to be honest lol

very useful

[karmic mantle]

okok thats solid

thank you

!!

[onyx narwhal]

of course, good luck with your final

[karmic mantle]

thanks!

[safe radish]

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[steady loom]

I need help with b)

The hint given is that for any group G, [G:Z(G)] is non prime

or particularly n/m >= 4

but I cant seem to manipulate it to get anywhere

[safe radish]

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[safe radish]

@steady loom Has your question been resolved?

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[odd nest]

How to calculate

4^2 + 5^3?

[pale lily]

4 times 4

is 16

5 times 5 times 5

is 125

125+16 = 141

[cedar owl]

Vrai

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@odd nest Has your question been resolved?

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[dense sphinx]

I need help.

[pale lily]

very specific

[dense sphinx]

gotta find second derivative of this.

So far

I have a long ass shit

[pale lily]

whats the first derivitive

[dense sphinx]

quite simple

[echo bronze]

Just bruteforce it

[dense sphinx]

-10x/(x^2-4)^2

[pale lily]

wait now i gotta fact check that

[marsh walrus]

just use the bot

[echo bronze]

It's right

[pale lily]

idk how

[marsh walrus]

,w second derivative (5)/(x^2-4) + 2

[pale lily]

so whats your issue with finding the 2nd one if u found the first?

is this right? 🤔

[pale lily]

ok well this is right either way

[marsh walrus]

oops

[echo bronze]

It low-key looks wrong but wolf can't be wrong

[marsh walrus]

idk why they write it this way

[pale lily]

wait no

u found the 2nd derivitive

of the orignal problem

lol

[marsh walrus]

yea

[pale lily]

o i thought u were fact checking his first deriv

[dense sphinx]

Yeah the problem is

in order to find the second derivative

I gotta do this:

[echo bronze]

Bot using product rule instead of quotient rule is so real

[pale lily]

there is never a instance in calculus where you HAVE to use the quotient rule i dont think and im happy every day cause of that

[dense sphinx]

Wait

lemme write it

and send a picture

[echo bronze]

😭 I'm a quotient rule hater too

My lazy ass can't remember ANOTHER formula when this one works perfectly

[pale lily]

its not even that i cant memorize it its literally already in my head

im just not using that shit

be fr

thats like driving a toyota over the porsche in your driveway

[echo bronze]

Only downside is it looks less clean when done

[dense sphinx]

So, this is my problem.

I do the whole formula.

I factor it.

However, now there's a big ass problem.

I cannot make my second derivative zero, EVER.

Did I do something wrong, perhaps?

I cannot spot my error.

Wrong sign

BUT WHY

alright

so yeah

there are no real solutions

FUCK

BUT WHY

WHY DO I GET THE OPPOSITE SIGNS

[safe radish]

@dense sphinx Has your question been resolved?

[dense sphinx]

<@&286206848099549185>

[delicate sphinx]

This is a bit blurry, can you send a better photo?

[dense sphinx]

Alright.

I can do better.

I can draw it.

Nah

Just gonan take a picture. xD

[echo bronze]

You used the 2nd derivative instead of the first

Wait

What's the question?

[dense sphinx]

gotta find where it's concave or convex

[echo bronze]

You mean min/max?

[delicate sphinx]

Are you not sending a better photo?

[dense sphinx]

yeah but like

in a few moments

[echo bronze]

If you mean min/max then you need to plug in the x values from your first derivative where you equate dy/dx=0

[dense sphinx]

Alright, here.

So according to symbolab and WolframAlpha

THIS IS WRONG.

Like, I cannot factor that as 10(x^2-4) *-(x^2-4)+4x^2)

Instead, it says it should be -10(x^2-4)*(x^2-4)-4x^2

Okay, but why?

Me don't get it.

What do you think @delicate sphinx

[delicate sphinx]

Does that say $-10 * (x^2-4) * (x^2-4) + 40x^2(x^2-4)$?

On the first line

[dense sphinx]

Remove the first - and yeah.

[dense sphinx]

I mean, it's just -10*(x^2-4)*(x^2-4)

The rest is indeed correct.

[flat frigate]

CaptainNova22

[delicate sphinx]

So that?

[dense sphinx]

Yeah.

[dense sphinx]

So, what did I do wrong.

[delicate sphinx]

How are you typing it into symbolab/wolfram?

[dense sphinx]

Second derivative of 5/(x^2-4)+2

[delicate sphinx]

Can you show your full work then?

It's hard to understand what you're trying to do

[dense sphinx]

Alright.

Lemme write once more then.

Gonna try to make it as clean as possible.

[delicate sphinx]

Because you showing this and saying that you searched on wolfram for "second derivative of 5/(x^2-4)+2" does not correlate at all, unless you show the full work

[dense sphinx]

Here.

Better quality=

Now, as you can tell

the fucking problem is that I get the opposite sign.

[delicate sphinx]

So you're asking about the factoring of this? $-10 * (x^2-4) * (x^2-4) + 40x^2(x^2-4)$

[flat frigate]

CaptainNova22

[dense sphinx]

So, what did I do wrong.

Yeah.

[dense sphinx]

Yes, absolutely correct.

Why must it be -10 and not 10

as you can see

Symbolab will give you the same result I get but with opposite signs.

[delicate sphinx]

Well here, if you look at it closely, (-3x^2 - 4) = -(3x^2 + 4)

So then -10 * -(3x^2 + 4) = 10 * (3x^2 + 4)

[dense sphinx]

So my Answer is absolutely correct?

[delicate sphinx]

If your answer results in 10(3x^2 + 4)

[dense sphinx]

Well, I mean

-(x^2-4)

That becomes -x^2 + 4

4x^2-x^2 = 3x^2 +4

FUCK

SO I SPENT ONE HOUR FOR NOTHING? FUCKING SHIT.

[dense sphinx]

Thank you captain nova.

[safe radish]

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[cerulean stream]

I'm wondering what to do to find the inverse of F. I have no idea how to solve to find it. Where do I start? If it was something like y=6x+7 I could figure that out easily and just solve for y.

[light shoal]

it's not invertible..

try computing F(1,0) and F(2,0)

they're both equal to 0

[plucky elk]

!original

[safe radish]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[faint seal]

What does the inverse of a two variable function mean?

[plucky elk]

2^-1 = 1/2 /s

[slim lion]

latex pls 🙏

[plucky elk]

Obviously a function of 1/2 variable

[faint seal]

So true

[safe radish]

@cerulean stream Has your question been resolved?

[vagrant ice]

1^(-1) = 1, ah so the inverse of a one-variable function is also a one-variable function

thanks!

[safe radish]

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[lean otter]

any idea what you do after this?

[lean otter]

@eternal kite

[plucky elk]

Where's the question

[lean otter]

here you gp

we have to find the particular integral

[plucky elk]

Is D = d/dx?

[lean otter]

yep dw i got it though

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[lean otter]

no

[lean otter]

yes and im lost again lol

we have to divide x/D^4-3D^2'

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[lean otter]

@meager igloo

pls help

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[plain night]

Ive replaced every distance with its length and cant calculate FC (pls ping me)

[safe radish]

@plain night Has your question been resolved?

[plain night]

<@&286206848099549185>

[safe radish]

@plain night Has your question been resolved?

[plain night]

<@&286206848099549185>

[safe radish]

@plain night Has your question been resolved?

[plain night]

<@&286206848099549185>

[safe radish]

@plain night Has your question been resolved?

[plain night]

<@&286206848099549185>

[sour herald]

@plain night

I think I may be able to help you

∆ ADE is similar to ∆ FCE

Because they share a common 90° angle and a vertically opposite angle

If two triangles are similar

There's this property

a/A = b/B = c/C

Where a,b,c and A,B,C are the respective length of the side of small triangle and the bigger triangle

So here,

CE/DE = FC/AD = FE/AE

We have the values of
CE = 2
DE = 3
AD = 2

When we put the values

We get

2/3 = FC/2

FC = 4/3 units

[plain night]

.close

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[forest gyro]

help

[safe radish]

Please don't occupy multiple help channels.

[forest gyro]

Mark the relationship between the two marked angles:

1Alternate angles between parallel lines
2The vertex angles are equal
3The sum of the adjacent angles is 180°
4Corresponding angles between parallel lines
5None of the options
Calculate x:
x=
Answer to answer element 2

Calculate the size of the marked angles:

i didnt listen in class

xD

[worldly herald]

do we know that AB is parallel to CD? if yes then 8x + 5 would be equal to 10x-7

you can solve that to get x

[forest gyro]

oh ok

ty

[worldly herald]

only if you know AB || CD though

[forest gyro]

i will try now

How to calculate the size of the marked angles?

???

.close

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[lean otter]

How is it defo prime when it says 20%

[lean otter]

It says less than 5 but there are only 4 then not 6

[rugged arch]

what do you mean

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

It says find the 6 numbers then it says number chosen is less than 5

And in the tutorial they just ignore the 1/3 thing and just cross out the ones over 5

I sent wrong pic here

[lean otter]

<@&286206848099549185>

[safe radish]

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[lean otter]

Huh

.reopen

[safe radish]

✅

@lean otter Has your question been resolved?

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[mortal jolt]

In a Trapezium ABCD where ab is parallel to cd and the daigonals ac and bd intersect at a point 'o' if a line is drawn from a point 'p' on the side ad to a point 'q' on the side cb passing from o and parallel to ab proove that po = qo

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Please don't occupy multiple help channels.

[lean otter]

@mortal jolt stick to one channel

.close

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[odd nest]

Is this correct?

[solar hazel]

,rotate

[safe radish]

@odd nest Has your question been resolved?

[lean otter]

bro lost bros banner

[lean otter]

yes thats correct

[solar hazel]

😭

[odd nest]

Ty

[lean otter]

np

[odd nest]

Find x and y

I found y = 6,67 and now I’m completely confused with x

I think x = 18 check it out @lean otter

X and 6 are similar

I know x/6 but

Do I do

20 / 6,67?

I’m completely confused

Maybe

X / 6 = 6,67 + 10 / 6,67?

[lean otter]

for x, i got 9 tbh

because

8 / 12 = 6/x
8x = 72
x= 9

for y, its 6.67

@odd nest u get it? or do u want me to explain it?

[odd nest]

@delicate sphinx Confirm?

[lean otter]

dang

..

[odd nest]

I can also do

6,67 / 16,67 = 6 / x?

6,67 x

100,02

X = 15

@lean otter ??

[lean otter]

what is that

💀

with ur method

u should do

6.67 / 10 = 6/x

x = 60/6.67

= 9

[odd nest]

Why?

Why can’t I do 8 / 20?

Left side ?

[lean otter]

u could, but u have to do the same for the left side

so like

8/20 = y/y+10

same for x

[odd nest]

I did that

It’s giving result for y not x

[lean otter]

6,67 / 16,67 = 6 / x?

this is wrong because u should have x+6 as ur denominator

[odd nest]

Why x+6?

[lean otter]

on the left side, u added the side from the small triangle, and the rest of the side, as ur denomintor

U should apply that for the other side.

[odd nest]

It’s

6,67 / 16,67 = 6 / x

[lean otter]

6,67 / 10 + 6.67 = 6 / x + 6

6,67 / 10 + 6.67 = 6 / x + ||6 ||

[odd nest]

Why + 6?

Let’s say x is 10

It’ll be 6 / 10