help-13

[teal wraith]

yeah

[compact crown]

but the way u said it looks easier

instead of dividing one by one

[teal wraith]

1/2+1/12 also works

[teal wraith]

yew

but make sure u apply it only when the denominator is same

or your answer is gonna be incorrect

[compact crown]

ohh

so it being 7/12

u mean 12?

[teal wraith]

?

i meant 60

[compact crown]

u said the denominator

ohh

right 60 sorry

60 is on the bottom for both

like we're dividing both 2 that number

[teal wraith]

Correct

[compact crown]

but adding looks easier

i understand this now thank you

.close

[cedar kiln]

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[cedar kiln]

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[sudden vessel]

Yoo

[sudden vessel]

1b

How do I do this?

<@&286206848099549185>

[steel fractal]

Can you show your work?

[sudden vessel]

?

[steel fractal]

What did you do

Or think of

[sudden vessel]

Nothing

What adds to 13?

[steel fractal]

alright..

[lusty pawn]

split the frac

[sudden vessel]

Then divide it

Like if it's 5pi/12 I do 3pi/12 - 2pi/12

[steel fractal]

Maybe the thing you should do it first convert it into an acute angle?

[sudden vessel]

Which equals pi/4, and pi/6

But for this idk what to do

[steel fractal]

uhuh, correct

[sudden vessel]

How?

[steel fractal]

Let's start by converting this into an acute angle

wkt sin(pi + x) = -sin(x)

[dire geode]

3 + 10 = 13

[steel fractal]

Just write 13pi/12 as 12pi/12 + pi/12

[dire geode]

3/12 = 1/4 and 10/12 = 5/6

[sudden vessel]

Mb

[dire geode]

[steel fractal]

LMAOO

[sudden vessel]

Then it equals pi + pi/12?

[steel fractal]

Yes

[sudden vessel]

Ok

[steel fractal]

And sin(pi + pi/12) = - sin(pi/12)

[steel fractal]

And 1 = 3 - 2 and we know that 3 and 2 are factors of 6✨

[steel fractal]

yupp

[steel fractal]

.

[sudden vessel]

How?

Why is it - now?

[steel fractal]

Oh that?

Did you learn allied angles?

You can tell me if you didn't

[sudden vessel]

Nope

[steel fractal]

I'd be glad to tell it

[sudden vessel]

Allied?

I never heard of it

[steel fractal]

Yea

So you don't know cos(pi/2 - x) = sin(x)?

That conversion are allied angles

[sudden vessel]

is it this?

[steel fractal]

Jus asking cuz most people don't know the names..

[steel fractal]

Which?

[steel fractal]

Yes

[sudden vessel]

Oh ok

[steel fractal]

But there is a whole lore there

[sudden vessel]

The final answer should also be 1-sqaureroot3/2sqaureroot2

[steel fractal]

Yes.

it is

[sudden vessel]

The teacher told me to use compound formulas

[steel fractal]

We will..

[sudden vessel]

But anyways continue

[steel fractal]

Mhm.. so one of those formulaes is sin(pi+x) = -sin(x)

Or wait..

We can do what Riemann told

Sin(10pi/12 + 3pi/12) because you haven't studied allied angles theory in deep before..

I mean for the problem, that's the solution but You can dm me later if you wnana know more

Anyway..

sin(5pi/6 + pi/4)

Sin(5pi/6)cos(pi/4) + sin(pi/4)cos(5pi/6)

[sudden vessel]

Woah

5?

4?

Where did those numbers come from

[steel fractal]

(rt(3)/2)(1/rt(2)) + (1/rt(2))(-1/2)

[steel fractal]

Alright arlight

13 = 10 + 3 as stated by riemann before

[sudden vessel]

Yea

[steel fractal]

13/12 = 10/12 + 3/12

[sudden vessel]

Yea

OHHHHH

WAIT

[steel fractal]

Cancelling out that 2 in the first term and 3 in the second term

[sudden vessel]

divide the 10 by 2

=

5pi/6

[steel fractal]

Yes.

Yayyy

[sudden vessel]

Then pi/4

?

[steel fractal]

Divide the 12 by 3

[sudden vessel]

Ohh okok

[steel fractal]

and 3 by 3

[sudden vessel]

Tyty

[steel fractal]

no problems

So back read again

[steel fractal]

.

[steel fractal]

.

So rt(3)/2rt(2) - 1/2rt(2)

{-1 + rt(3)}/2rt(2)

That's your answer

Got it?

[sudden vessel]

Ok so this is sin(a+b) which is sinacosb+cosasinb

?

[steel fractal]

yes

[sudden vessel]

And I use the special triangles

Perfect

Tysm

[steel fractal]

Yes

Anytime!

[sudden vessel]

Can u help with one more?

[steel fractal]

Sure!!

[sudden vessel]

Thanks

[steel fractal]

:>

[steel fractal]

Ohh alright aright

23 = 20 + 3

23pi/12 = 20pi/12 + 3pi/12

23pi/12 = 5pi/3 + pi/4

Cancel the factor 4 in the first term.. and 3 in the second term

So sec(23pi/12) = sec(5pi/3 + pi/4)

[sudden vessel]

Wym?

[steel fractal]

Now we don't have direct formulaes for secants.. but we do know secant = 1/ cosine

[steel fractal]

Look, 20 = 5x4 and 12 = 3x4

[sudden vessel]

Yea

[steel fractal]

Cancel out the 4's in the first term

[sudden vessel]

Oh okok

Then how would I use compound angle formula for this?

[steel fractal]

Alright alright

So as I was saying

[steel fractal]

.

So, the thing is we'd say sec(5pi/3 + pi/4) = 1/cos(5pi/3 + pi/4)

got it?

[sudden vessel]

Yes

Wait so

Look

[steel fractal]

Alrightt

[sudden vessel]

Cos(a+b) = cosacosb-sinasinb

?

Then I use special triangles

[steel fractal]

Yes

Yes

[sudden vessel]

Perfect

Tysm

[steel fractal]

But rmember we'er finding secant

[sudden vessel]

Uhuh

[steel fractal]

You'll have to reverse the fraction you got for the cos

[sudden vessel]

Wym

[steel fractal]

Well, sec = 1/cos

[austere pawn]

yes, because sec(x) = 1/cos(x)

[sudden vessel]

Yea?

[steel fractal]

The thing is.. we're finding sec(5pi/3 + pi/4)

[sudden vessel]

I only understand it up to here

[steel fractal]

So we'll have to reverse the fraction we got for cos(5pi/3 + pi/4)

[austere pawn]

wait...

[steel fractal]

Yes?

[austere pawn]

why dont you use sec(2pi - pi/24)

[sudden vessel]

Can u write it on paper?

I'm a bit lost

[steel fractal]

Well.. I tried to.. but Anthony doesn't know allied angles

[steel fractal]

hold on

[sudden vessel]

Alr

[steel fractal]

Sorry I don't have any paper avaliable

but that's what I mena

try evaluating the cos first..

Find the value of cos(5pi/3 + pi/4)

[sudden vessel]

Uhuh

I unde u gotta put it under 1

But what do u do after that?

[steel fractal]

Ohh what's the reciprocal if 2

Anthony?

[sudden vessel]

Wym? 2

Where is 2?

[steel fractal]

No not the 2, it was never in the question

I was asking what do you say about the reciprocal of a number say 2

What's the reciprocal of 2??

[sudden vessel]

1/2?

-2?

[steel fractal]

1/2

And the reciprocal of 1/2 is 2

So the reciprocal of any real number a/b is b/a

a,b not zero

[sudden vessel]

Oh ok

So what do we do now?

[steel fractal]

Just tell me what you got for cos

cos(5pi/3 + pi/4)

[sudden vessel]

That's it?

now it becomes 3/5pi?

Idk

This doesn't make sense to me

[steel fractal]

No no no

It doesn't become 3pi/5

Just tell me the cos of (5pi/3 + pi/4)

using the compound angles formulae

[sudden vessel]

Cos(a+b) = cosacosb-sinasinb
= cos(5pi/3)cos(pi/4)-sin(5pi/3)sin(pi/4)

[steel fractal]

Yes

[sudden vessel]

Then I use special triangles

And solve it

[steel fractal]

Yes

Solve and tell me the answer

[sudden vessel]

So what's the point of putting it under 1?

[steel fractal]

I'll explain what to do later

[steel fractal]

that's for that answer you get

[sudden vessel]

Ok give me like 2-3 minutes

Ima do it on my phone

[steel fractal]

Ofcofc

[austere pawn]

sec(2pi - pi/24) = sec(pi/24) = sec(pi/8 - pi/6) = 1/cos(pi/8-pi/6) = 1/(cos(pi/8)cos(pi/6) + sin(pi/8)sin(pi/6))

[steel fractal]

Yes that's what I was going for

[austere pawn]

wait, cos(pi/24) = ±sqrt((1+cos(pi/3-pi/4)/2)

[sudden vessel]

@steel fractal

We flip the sign right?

Instead of it being 1-sqaureroot3

I put 1+sqaureroot3

[steel fractal]

No no no

we do not flip the sign

we flip the fraction

[austere pawn]

wait, I think you are not meant to put 1/2, 1/sqrt(2), sqrt(3)/2 and 1/sqrt(2) inside cos and sin

[steel fractal]

cos and sec are reciprocals, as in fractions

[steel fractal]

yea... you're not supposed too

[sudden vessel]

Huh?

What's going on

[austere pawn]

You should remove the cos and sin on the last line

[sudden vessel]

WAIT

[austere pawn]

cos(5pi/3) = 1/2 ...

[sudden vessel]

So I flip it?

Wait wait

Hold on

[steel fractal]

the line where you wrote cos(1/2) and stuff

[sudden vessel]

Wait listen

[steel fractal]

yes

[sudden vessel]

It's supposed to be 1-sqaureroot3/2sqaureroot2

BUTTT

I flip it

And then I get

2sqaureroot2/1+sqaureroot3?

Right?

That's what the final answer says

[steel fractal]

Yes

That is true

But you did two mistakes in the process

[austere pawn]

that is what secant does

[steel fractal]

What clonesolopros said.. secant inverts the behaviour of the cos

[sudden vessel]

But I still got the final answer correct?

So it should've been flipped while it was inside the brackets?

And not after?

[steel fractal]

YEA XD, one of them was your representation of stuff and the other is ignoring a "-" two times in a row

[steel fractal]

no, secant means that the end product of cos is flipped.. the end product and not the inside stuffs

[sudden vessel]

Oh ok

So I'm right

Can u circle my mistakes if possible?

Cuz my teacher will take marks off on the test

[steel fractal]

I can't do that on this device

but

I can try to tell you where you went wrong

[sudden vessel]

Ok tell me

[steel fractal]

Last but one step.. writing cos(1/2) is wrong.. that's the representation mistake.. don't write cos(1/2) and cos(1/rt2)

[sudden vessel]

Why?

Isn't that what it's supposed to be?

[steel fractal]

No.. You see, cos(5pi/3) = 1/2

[sudden vessel]

Yea and I wrote 1/2

[steel fractal]

Not cos(5pi/3) = cos(1/2)

You wrote the cos again

[sudden vessel]

I always do that

[steel fractal]

@austere pawn was trying to tell you this mistake

[sudden vessel]

Idk I always do that

[steel fractal]

Oh it gives out another meaning

[sudden vessel]

Oh

I wont do it anymore ig

What's my other mistake?

[steel fractal]

Well, in the same step

sin(5pi/3) is -rt3/2

[sudden vessel]

-?

[steel fractal]

the minus outside and the minus inside cancel out to give a plus

[steel fractal]

minus

[sudden vessel]

Yea?

[austere pawn]

Maybe after the line where you wrote 1/cos(5pi/3+pi/4), you started writing with the formula of cos(a+b).
its not like a mistake, but it doesnt quite make sense the way you put it

[sudden vessel]

I'm confused

[sudden vessel]

I wrote the formula

That's why

[steel fractal]

I think you forgot to write a minus

Look at it

[sudden vessel]

Where?

[austere pawn]

you mean it should be 1-sqrt(3) at the top?

[steel fractal]

The second term in the same stepp

[steel fractal]

no.. not exactly

[sudden vessel]

Idk what ur talking about tbh

[steel fractal]

The step where you wrote sin(root3/2)

[sudden vessel]

I still got the final answer right

[steel fractal]

Oh alright alright

[sudden vessel]

I don't think my teacher cares

I always did it lmao

[steel fractal]

Yea alright.. It was jus a typo or smth

[sudden vessel]

Easier for me to understand 😭

[steel fractal]

I GUESS LMAO

[sudden vessel]

But anyways thank u

[steel fractal]

But be careful.. Universities are stricter

[sudden vessel]

I appreciate the help

My teacher moved the test to Wednesday

[steel fractal]

Anytime Anthonyy

[sudden vessel]

Yea ik

[steel fractal]

Ohh good luck!!

[austere pawn]

sin(5pi/6) = 1/2

[sudden vessel]

Tyty

[steel fractal]

Bye anthony!!

[sudden vessel]

.close

[cedar kiln]

Channel closed

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[sudden vessel]

Cya

[steel fractal]

Cya

[austere pawn]

cya

xd

[cedar kiln]

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[native anchor]

can anyone help with composite functions?? i can do the first step, i put an example below and i undrstand to do f(3x+5) but subbing in f(x) is confusing me

[native anchor]

also please ping me if you reply!!

[oak yarrow]

Have you tried anything?

[rocky harness]

Think of it this way: f takes whatever you give it (say x) and makes it into x^2-2. So if i want to find f(3x+5), i am giving 3x+5 to f. So what will f make 3x+5 into?

[native anchor]

omg is it (3x+5)^2 -2

[oak yarrow]

Yes

[rocky harness]

Yes

[native anchor]

thank you!

[oak yarrow]

Composite functions tend to be very ugly but it's mostly just substitution

[native anchor]

if theres a number before the x^2 does it go before the bracket?

[rocky harness]

Well you tell ne

Say f takes x and makes it into 3x^2, what will f make 3x+5 into

[native anchor]

does it matter if i square it or multiply it first

[rocky harness]

3x^2 means 3*(x^2)

[native anchor]

3(3x+5)^2 ?

[cedar kiln]

@native anchor Has your question been resolved?

[cedar kiln]

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[untold blade]

how can i solve for x

[dire geode]

can you show the original question

[untold blade]

okay

this is the solution

i got the number right but i just forgot how i can solve for x (aka c)

[dire geode]

do you know what that symbol means

the graph in blue

[untold blade]

graph it

use desmos or sum? 😭

idk

but it should be solvable by hand

[dire geode]

probably means to use a numerical solver

it's not

if it could be solvable by hand they wouldn't give an approximation

[untold blade]

oh ok

so theres no way i could solve it by hand?

[dire geode]

or just eyeball it by graphing

[untold blade]

i thought u can use log and stuff

lol okayy

ok ty

[dire geode]

logs won't get you very far

but feel free to try

[untold blade]

na i dont got time but thanks

.close

[cedar kiln]

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[haughty walrus]

I don't understand why the answer we were given is 576?

[winter moss]

24^2

essentially

ill use L for letter and # for number

the lisence plate is

LLL ####

but

she wants the numbers to be her phone number

and the first letter to be M

so MLL 1234

that leaves only two variables

so 24*24

[haughty walrus]

AHH I SEE. THERE'S ONLY ONE WAY FOR THE PHONE.TYSM.

.close

[cedar kiln]

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[lime yew]

can i get help with this task?

[cedar kiln]

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[lime yew]

hello?

[twilit escarp]

Open a new one

Can't do anything unfortunately

[cedar kiln]

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[old lion]

Hi i need help i wanna learn high lvl math like topology, abstract algebra Calculus III etc where can I start

[dull oxide]

What is your current level of math education?

[old lion]

My current level is i know the basics of calculus and know what a matrix is. But i dont know trigonometry and complex imaginary numbers very well

[dull oxide]

Definitely review trig. Have a basic comfort with imaginary numbers. Really as long as you get i²=-1, the rest will come if your algebra is decent.

Define "basic calculus". What topics have you covered?

[old lion]

I know like what a derivative is and a limit i know the chain rule and L opitals rule. For Calc II i know the definition of an Integral its use and how to solve basic lvl integrals

[proper mortar]

get a book about some topic and just try and work through it

[azure horizon]

practice integrals more on khan academy; khan academy eventually does some basic stuff with vector calculus

you can also look at paul's online notes for more calculus stuff

then for topology or abstract algebra, i think you just want to find a textbook and start sloooowly chipping away at it

[proper mortar]

do you know basic logic and set theory?

[azure horizon]

oh yeah you need set theory

[old lion]

Yea i know set theory

[azure horizon]

ok

[old lion]

What about topology

[proper mortar]

to get into these higher topicsc like abstract algebra, I think starting with some linear algebra would be best

[old lion]

I’ll start learning these topics. Thanks for the help.

[dull oxide]

This graphic is entirely opinion based:

• Solid arrows mean you should absolutely know the base subject before going to the next subject.
• Dashed arrows mean that it is helpful to know this material, but not absolutely required.
• Subjects in bold mean that you should be really good at them before trying to work out harder things
• Subjects in red mean that you better be near perfect

@old lion 👆

I left out a lot of other math courses, focusing more on what topics sounded like you had an interest in learning

[cedar kiln]

@old lion Has your question been resolved?

[old lion]

Thank you so much I appreciate it endlessly

[cedar kiln]

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[livid hollow]

Please help

[lofty topaz]

What is the girth?

Is it the width or the height?

[livid hollow]

It is in the diagram

It is the 4 sides added

Like the circumference but it’s a box

[lofty topaz]

Ok, since the width = height = s (Assume it is s). Then the grith = ?

[livid hollow]

It is 2(w+h)

[lofty topaz]

But the width and the height are ||the same||.

[livid hollow]

Yeah

[lofty topaz]

So, 2(w + h) =?

[livid hollow]

Ok

L+g=108

[lofty topaz]

l + ||4s|| <= 108

[livid hollow]

Yeah

And l times s squared is area

[lofty topaz]

Yes, we will find the formula for the volume.

$l + 4s \le 108$\
$\max(l \cdot s^2) = ?$

[wraith dagger]

Roman_Garland

[livid hollow]

Yeah

[lofty topaz]

@livid hollow Are you familiar with finding the maxium or minum values given these equations by calculus?

[livid hollow]

Ohhhhhh

Yeah you right

Derivative

So maybe Deriv of second one

[lofty topaz]

Yes.

[livid hollow]

So 2s+1=0

Wait

No

Product rule

Hold on

[lofty topaz]

l = ? in terms of s

l + 4s <= 108 so ||l <= 108 - 4s||

[livid hollow]

Ok

Then derivative of that?

[lofty topaz]

Yes, find the appropriate value for l and plug it in into the volume formula

Then, take the second derivative.

[livid hollow]

Wait I don’t get it

[lofty topaz]

Yes.

[livid hollow]

Wdym

[lofty topaz]

We haven't got the exact value just an estimate.

[livid hollow]

Bruh

We only have equations

[lofty topaz]

l <= 108 - 4s

[livid hollow]

What do I do with that?

Oh

Plug it in

Okay

[lofty topaz]

Ok, try and give me feedback.

[livid hollow]

108s^2-4s^3?

Okay

I understand

[cedar kiln]

@livid hollow Has your question been resolved?

[cedar kiln]

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[crimson sedge]

<@&286206848099549185>

[coral jewel]

please dont start a help channel with a ping

whats your question?

[crimson sedge]

Wait a minute what do you mean with ping

Sorry I'm just new to this server and I get banned every time

[opaque root]

I wonder why…

[coral jewel]

[crimson sedge]

Okay so this is what I need help with it's not a quiz just it's the website name it's a sign for homework and I've been stuck on calculus

One second I'm going to take a screenshot

Okay

I'm just doing it on a tablet because I'm not going to do it on anything else I'm just don't want to get on the computer I'm lazy

[blazing zephyr]

apply power rule

[opaque root]

What is your question

[crimson sedge]

Uhm this is my homework absent homework I have to turn it in on Monday well I got it do the turn and thing once I'm done with the thing

I didn't really study sadly

[opaque root]

And what is your question

[crimson sedge]

I don't understand the question

Like what is it asking me I don't know how to find the answer

[opaque root]

You do not know what is the question asking to you?

[crimson sedge]

Yes

[opaque root]

What can you identify in your exercise?

[crimson sedge]

I know that there is an fx and there are numbers

[opaque root]

And what you do not recognize?

[crimson sedge]

The numbers at the top and the X I don't know the missing numbers

Uh

[bleak viper]

do you know what f(x) denotes?

[crimson sedge]

I already answered the question I have a new one

It looks hard

[bleak viper]

i dont see where u answered that question

[crimson sedge]

I just got it done

I didn't take a picture I have a new question

It looks challenging

Why is 11th grade so hard 😰😰😰

[bleak viper]

have you learnt something like "area between curves"?

[crimson sedge]

Well we learned area and literally probably late kindergarten everyone knows what area means

[bleak viper]

i didnt ask about "area"

i said area between curves

[crimson sedge]

I didn't pay attention but we were learning it and the teacher was just blabbing and drawing stuff on the Smart board

I was just talking

And demonstrating slides and it was boring

And then of course she had to assign a homework assignment over when I was sick so now I have to turn it in on Monday

[bleak viper]

should've paid attention in the class

[crimson sedge]

You actually pay attention?

[bleak viper]

nah, I pay tuition fees, thats it

[crimson sedge]

Did you get good grades

[bleak viper]

obviously you pay attention in the class, what else will you do in there

[crimson sedge]

I just talked to my friends all the time about how boring the classes and then we get to lunch and maybe if it's a good I can enjoy it

The classes suck I'm only in a few clubs also

[bleak viper]

then atleast study from the textbook

[crimson sedge]

But it's boring you feel me it's is so boring I don't want to take notes all the other students do it I don't want to though

[bleak viper]

i can tell you rn how to do this specific question, but what will you do if a slightly modified question comes in exam

[crimson sedge]

And then I just get for us to write random shapes pretty much down and fail the class

I don't know

I failed last exam

I got like a c minus I guess it's not a fail but we got a report cards today

[bleak viper]

here, ill suggest something

[crimson sedge]

We have an essay on social studies coming up I already finished one essay I forgot the name of it but I did fine

[bleak viper]

open your textbook and study

then do these questions

[crimson sedge]

And my reading grade sucks

I don't have my textbook at home bro I just I'm in my bedroom trying to do this homework and I only have a couple sheets of paper and a lamp over my head and I'm in a chair so I don't know what to do

[bleak viper]

you solve that question by finding intersection points of the two curves (you have graph given so you can find easily from there) then integrate f(x) - g(x) (curve 1 - curve 2) from intersection point 1 to intersection point 2

[crimson sedge]

Okay well I have 20 questions I think and I'm not getting anywhere

I just stare at the screen because I didn't take notes and even if I did I didn't take them home

Yay I got it wrong 💀💀💀

And I forgot you can't go back we might as well just do the next question

Apparently this is jumping to trigonometry one second I'm going to delete some storage and come back

[bleak viper]

i cant really help if you dont even know anything about the question

[crimson sedge]

Ok

Here I go first the question

[bleak viper]

again, i suggest you to go through your textbook and then do these questions, or if you dont have textbook then watch some lecture on youtube

[crimson sedge]

Okay here's the new question I'm just going to show you

I forgot to study for this LOL and I only paid attention half the lesson

I got some information in my books though

[bleak viper]

ill just tell you what it needs, you can then learn about it and use it

cosine law

[crimson sedge]

Like I looked what the teacher did for the settings what does it mean law of whatever it says and all this stuff why does it have to be both of degrees and the other why

Did you already get through the 11th grade

[bleak viper]

yes, done with hs

[crimson sedge]

Did it seem hard to you

I am so scared because there is a math test coming up and I will treasure my moments till SATs

It just says assessment 3 lesson four and I have to study it

[bleak viper]

not really

[crimson sedge]

Oh

[bleak viper]

it seems hard to you because you havent studied anything

maybe it will still be hard after you study, but you will atleast know what you are doing

[crimson sedge]

Should I drop out

[bleak viper]

i cant say anything about that

[crimson sedge]

My friends have been pressuring me into doing it

Anyway so there's 13 23 and X but I think there's more numbers

And the X has a degree sign so it must be degree

And I have to round my answer to the hundredths place

So I get my answer and then I have to round it so I get my

[bleak viper]

dont listen to anyone, ask yourself first and talk to someone reliable about future plans, then decide what you want to do

[crimson sedge]

Is this a two-step problem or only one step I got a paper to help me

Ok

[bleak viper]

yes

[crimson sedge]

I just have to get an answer and round it

[bleak viper]

first find the answer

yes

[crimson sedge]

Am I using multiplication or division

[bleak viper]

cosine law

[crimson sedge]

And then I use calculus after doing that or I don't know

Ok I will search it up real quick

Okay let me think

6.49?

Oh I got it wrong

Close!

[cedar kiln]

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[obsidian crescent]

hi!! this is a rotation of axes problem from precalc i think, but when i try to do the (a-c)/b thing it ends up really funky. the teacher said we should recognize all values and no calculator would be necessary, but i keep getting cot(2θ) = (6-9)/4 = -3/4, which is funky... can anybody correct my reasoning? or is this just an outlier that we need a calculator for?

[obsidian crescent]

heres wat the answer key says i should get, btw. convenient that the angle of rotation isnt explicitly stated anywhere for reference

[sharp lotus]

what is the actual question?

[obsidian crescent]

"in problems 47-52, rotate the axes so that the new equation contains no xy-term. analyze and graph the new equation"

this might not be precalc either, the class is called elementary functions

i heard it was mostly precalc tho

[sonic thicket]

Why do you need to know the value of ∅

[obsidian crescent]

i use θ as the reference angle from which i create new axes, x' and y' - if i do it right and substitue x' and y' for x and y in the original equation, ideally it eliminates the 4xy term and just leaves me with a shape i recognise

[sonic thicket]

You need Cos∅ and Sin∅ right?

[obsidian crescent]

sure, that works

right now i know cos2θ and sin2θ

oh mb im stupid

i got it from here i think

expansion formulas?

thankss

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[sonic thicket]

Sure

[cedar kiln]

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[valid ingot]

Hi why is ob = oc

[final meteor]

radii of the same circle

[valid ingot]

What is radii

[final meteor]

radius of the circle

both OB and OC are the radius of the circle so theyre equal

[valid ingot]

Oh

[crimson sedge]

Plural of radius is radii

[valid ingot]

Why in (b) u cant use angle at centre twice angle at circle

[cedar kiln]

@valid ingot Has your question been resolved?

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[gentle ether]

Why is this process wrong?

[cedar kiln]

@gentle ether Has your question been resolved?

[gentle ether]

The book suggests to use Hopital's Theorem but i wanted to try solving it without the theorem.
I just don't understand how to know if i am doing the process of simplifying is wrong or right.
Where's the wrong step in this exercise?
Where did i do the mistake?

<@&286206848099549185>

[earnest socket]

you're doing arithmetic with limits that don't exist

the limit laws only allow you to separate limits when each individual limit exists by itself

[gentle ether]

In my book i've noted that "The Addition theorem can be applied ONLY if the limit of both functions exist", is this the case?

[earnest socket]

but lim x to 0 of 1/x^2 does not exist

[gentle ether]

It does, it's + infinity

i mean, lateral limits are equal

[earnest socket]

well by exist it means finite

limit laws only allow you to separate limits when each individual limit is finite

[gentle ether]

Let me note that

[earnest socket]

in general, limits that are +- infinity are not said to exist

[gentle ether]

That's it?

I mean, i don't understand if i am doing the exercise well.
I want to understand if the steps i am doing are right, is there a way?

[earnest socket]

if I can't use L'Hopital I would probably use the series expansion of sin(x)

[gentle ether]

Also, how do i know if i have to apply the Hopital's theorem or is there a way to simplify the limit?

[gentle ether]

An other method?

[earnest socket]

not sure

[gentle ether]

Alr, i gotta study the theory part harder then

[earnest socket]

you can do a quick check by seeing if you get 0/0 or infty/infty

it's possible that in some of these cases you can still solve it by simplification, but that's just intuition at that point

[gentle ether]

Alr, thx for your help

[earnest socket]

all good

[gentle ether]

Gotta work on theory more, thx : )

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[formal nest]

how did we find the pattern ?

double factorial ??

[hollow trail]

do you know the definition of double factorial?

[neat raven]

double factorial is really a helpful notation

[formal nest]

no

[hollow trail]

,w define double factorial

[wraith dagger]

Results provided by WolframAlpha

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

Requested by cloudedhorizons

[formal nest]

is there a proof ?

[hollow trail]

so if n is an odd number then n!! is the product of all prior odd numbers and if n is an even number then n!! is the product of all prior even numbers

[formal nest]

or should i just believe it

[hollow trail]

n!! is not (n!)!, it's a new function which has that definition

[neat raven]

yes\\

[formal nest]

oh

[formal nest]

i thought it was this

[celest flume]

there is no proof, it is a definition

[formal nest]

how did they turn 2k!! into (2^k)k!

without the knowledge of the double factorial, would there be another way to find the pattern?

[hollow trail]

,align (2k)!! &= (2k)(2k-2)(2k-4)\cdots(6)(4)(2) \ &= (2\cdot k)(2\cdot[k-1])(2\cdot[k-2])\cdots(2\cdot3)(2\cdot2)(2\cdot1) \ &= 2^k k!

[wraith dagger]

cloud

[formal nest]

this is incredible

i see now

thank you so much

[neat raven]

great

[cedar kiln]

@formal nest Has your question been resolved?

[formal nest]

do you also know how to show the same process, but for 2k+1 ?

[vague rapids]

||(2k+1)!!*(2k+2)!!=(2k+2)!||

[formal nest]

wat

[vague rapids]

think about it

and for even double factorials, you already know the trick

[cedar kiln]

@formal nest Has your question been resolved?

[cedar kiln]

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[wild belfry]

Im not really sure what to do here

Idk how cos(a) relates to sin(y)

[dreamy void]

If α = 0 you get cos(0) = 1
Νow what is γ for sin(γ) = 1?

[wild belfry]

y = 1

[dreamy void]

hmm no

[wild belfry]

Oh ya

0

aswell

[dreamy void]

no

[wild belfry]

💀

Pi/2

[dreamy void]

yes

[wild belfry]

🤦‍♂️ 🤦‍♂️ 🤦‍♂️ 🤦‍♂️

Good morning Odie

[dreamy void]

keeping your forehead warm

Ok so for you to understand, γ depends on the value of α

Thats the relation they have

They want now an expression for γ in terms of α given cos(α) = sin(γ)

[wild belfry]

y = pi/2 - 0? Or y = 0 - pi/2?

[dreamy void]

no in terms of alpha

[dreamy void]

That would be a constant relation where α has no impact on γ

[wild belfry]

y = pi/2 - a? Or y = a - pi/2?

[dreamy void]

The first one

[wild belfry]

How come its not also the second one?

[lyric narwhal]

Odie weren't you a helper?

I swear I remember you with a green name

[wild belfry]

No... im not smart enough 🥹

[lyric narwhal]

Oh you have emeritus

[wild belfry]

I had a blue name hehe

[lyric narwhal]

Yeah

[lyric narwhal]

Thats not true lol

[wild belfry]

It is I tried to help before but I always ended up giving the wrong advice 😅

Or saying incorrect things

Or making mistakes

Maybe after I pass this exam ill try again hehe

[viscid condor]

You can always get better

[wild belfry]

I hope so! I want to be able to help people lol

Ppl here have already helped me so much

[viscid condor]

Helping others helps you too

[wild belfry]

I really dont think im ready yet 😅

[dreamy void]

arcsin(cos(α)) = arcsin(sin(π/2 - α)) = π/2 - α if α is between 0 and π/2

[wild belfry]

So you did
sin(y) = cos(α)
y = arcsin(cos(α))
right?

[dreamy void]

Yea

[wild belfry]

and cos(α) = sin(π/2 - α) is a rule right? I forget the name of those rules

[dreamy void]

Basically we want sine to be 1 at α = 0 not 0 so we do π/2 - α so that it starts at π/2 where sine 1

[wild belfry]

Aaaaaaah

Oke I think I get it now

😄

Thank you for explaining I think I understand it now!!

❤️

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[cursive bloom]

can someone help me solve this question im not sure i did it right

[viscid condor]

Looks good

[cursive bloom]

it does?

i thought if a number isnt in A' and isnt displayed on B' it must be on B' is that the right logic

[viscid condor]

Yeah

And the common of a` and b' should be outside of both a and b

[cursive bloom]

ok thanks a lot

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[ruby path]

i want help in complex numbers

[ruby path]

like how can i solve i^31

[chrome quail]

what is i^2

[ruby path]

-1

[eternal gale]

You can do that simply by dividing by 4

The power 1-4 for i repeat themselves

Whatever the remainder is you put that to the i

[ruby path]

31÷4= 7.75

[eternal gale]

No the remainder

Not decimales

[ruby path]

can you give an examlpe

example*

[eternal gale]

So like if it was 21

21/4 is 5 remainder 1

So i^1

Which is just i

And that would be what i^21 also is

[ruby path]

if it i^31

[eternal gale]

31/4 is what?

[ruby path]

7.75

[eternal gale]

With the remainder

No whole number

How many 4’s can you evenly put into 31 without a decimal

[ruby path]

7

[eternal gale]

Yes so 4 x 7 is 28

31-28 is

[ruby path]

yes

4

[eternal gale]

No

[ruby path]

sorry 3

[eternal gale]

31-28

Yessss

That’s the remainder so now do i^3

[ruby path]

so its i^3

?

[eternal gale]

Yesss

[ruby path]

ok tysm

[eternal gale]

You’re welcome

the trick is, if you divide by 4 and the remainder will be the answer since it repeats itself every power of 4, so i^1 is i, i^2 is -1 i^3 is -i i^4 is 1

You can see it repeats

Just a little trick 🙂

Hope that helps goodnight!

[ruby path]

tysm

bye

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[crimson sedge]

anyone who can help me with the rotations im confused rn

[cedar kiln]

@crimson sedge Has your question been resolved?

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@crimson sedge Has your question been resolved?

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[tardy forge]

can I get some help

[cedar kiln]

Please don't occupy multiple help channels.

[pastel vault]

.close

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[crimson delta]

think about how the graph could look like

[eager hemlock]

It doesn't have exact expression

[crimson delta]

lets say n=3

how could a graph with 3 roots look like

what could the derivatives look like

is it possible that the second derivative is nonzero?

take a pen and paper or open paint

and actually draw stuff

[crimson delta]

yes

so what can you tell me about the relationship of the number of roots and locations of those etc

[eager hemlock]

f"' Will never be equal to 0

So here n=3, f has at most 3 roots

I think that this is somewhat related to IVT but I'm not very sure

[cedar kiln]

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[wild belfry]

The green is the first step of the solution to the question

I dont understand where they got the numerator from?

Like the denominator is the same

And they multiplied it by 1/2sqrt(x) because thats the derivative of u which is sqrt(x) + 1

But how did they get 2((sqrt(x) + 1) - 1) in the numerator?

[pseudo sage]

• 1 - 1 cancels out

[pastel vault]

they want to u-sub u = sqrt(x) + 1

that's why they wrote it like that

[pseudo sage]

no doubt

so let u = sqrt(x)+1

[wild belfry]

I still dont understand sry

Where did it come from?

[pastel vault]

try substituting u = sqrt(x) + 1

what is du now?

[pseudo sage]

they multiplied both the bottom and the top by 2 time sqrtx

[wild belfry]

1/2sqrt(x)

[wild belfry]

Oh so the multiplication by 1/2sqrt(x) is not from the u

[pastel vault]

yeah $1 = \frac{2 \sqrt{x}}{2 \sqrt{x}} = 2 \cdot (\sqrt{x} + 1 - 1) \cdot \frac{1}{2 \sqrt{x}}$

[wild belfry]

they just did it by themselves beforehand

[pseudo sage]

yeah they haven't substituded yet

[wild belfry]

Okokok

I see now

Yeah that makes sense

[pastel vault]

replace the 1

[wild belfry]

Thank you everyone!

[wraith dagger]

south

[pastel vault]

finally

np!

[wild belfry]

❤️

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[thorn idol]

How can i put in my calculator a fracture for 0,10 example

[thorn idol]

So i got 0,10

but now i want it in a fracture

on my calculator

[tropic jay]

Fraction?

[livid hound]

fracture?

[thorn idol]

as in 1/10

[tropic jay]

Put 1/10

[thorn idol]

i mean my answer is 0,10 for example

and i want it to transform it to 1/10

[livid hound]

if you're ona casio, there should be something like $\boxed{a \ b/c}$

[wraith dagger]

ℝαμOmeganato5

[thorn idol]

yea got that one

how do i use that function ?

[livid hound]

just press the button

and it should do the conversion

or use that button instead of the division symbol

[thorn idol]

okay that worked

So i did Cos 330

how can i get the answer in 1/2 √3

[livid hound]

depends on whether your calculator is capable of displaying radicals in the output

[thorn idol]

So i do cos 330 and than a \ b/c

that should give me this answer as in the picture

[livid hound]

depends on whether your calculator is capable of displaying radicals in the output

[thorn idol]

yeah alr, i got a cheap calculator

so that might be the problem

ty 🙂

.close

[cedar kiln]

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[cedar kiln]

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[neat raven]

Join A and B.

Infer that angle ADE = angle ABE

Recall that angle ABC = 90 deg (since AC is the diametre)

[valid ingot]

what do now

[neat raven]

Now, do addition and subtraction.

[valid ingot]

why is this

[neat raven]

Why this is true?

[valid ingot]

Ye

[neat raven]

Angles in the same segment are equal in measure

[valid ingot]

what is segment

help pls

[neat raven]

Bro

[valid ingot]

but it goner outside the line

[neat raven]

What

The angles will be the same since the lines cross though A and E

[valid ingot]

what

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[cedar kiln]

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[nova mesa]

.open

Uhh

[nova mesa]

Okay it opened good

So I have this math exam that I’m studying for and in the answer key worksheet the teacher put these 2 answers for the questions that are in this screenshot

Does anyone know how the teacher got these answers? And if so please tell me how.

[neat raven]

x^4 - 625 = (x-5)(x+5)(x^2 + 25)

[nova mesa]

How can I get the answer through a calculator?

[neat raven]

,w x^4 - 625 = 0

[wraith dagger]

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Requested by anshulyolo121

[nova mesa]

When I do this on the calculator it just says -5 how do I get the full answer @neat raven

[neat raven]

show

the primary answer is 5

[runic garnet]

bro dont use calculator

its bad

[nova mesa]

What do i use then bruh

[fierce garden]

Your brain.

[nova mesa]

,w x^5 - 81x = 0

[wraith dagger]

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Requested by madvillain98

[nova mesa]

<@&286206848099549185> can someone help :)

[tribal jackal]

No

[nova mesa]

This is really helpful

[late otter]

ill try, just let me solve it

[nova mesa]

Okay

[late otter]

what have you tried

@nova mesa

[nova mesa]

Well what I’m trying to understand is how my teacher got the answer of x^4-625=0 using the calculator and when I do that it only shows -5, but I want to know how he get the other numbers

[late otter]

easier to do by hand

[nova mesa]

How to do by hand again 😭😭

[late otter]

begin by taking the root of both sides

$x^4 = 625 \implies x^2 = \pm \sqrt[625] $

$x^4 = 625 \implies x^2 = \pm \sqrt{625}$

[nova mesa]

Oh

Then what do I do?

[wraith dagger]

caspar

[late otter]

take the square root again

[nova mesa]

Nvm I think I got it

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[dapper imp]

Can I shorten (x-1)^2 ?

[runic garnet]

wdym by shorten

[dapper imp]

can I do this?

idk english math words sorry xD

[hard wolf]

no

please dont

that is a sin

there is addition and multiplication

subtraction not multiplication

[final meteor]

bro needs to be locked up

[hard wolf]

someone stop him

[dapper imp]

ok thank u xD SORRY, but it makes sense now

tysm

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[cedar kiln]

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[frigid cloud]

What’s formula for half circle?

[cedar kiln]

Please don't occupy multiple help channels.

[frigid cloud]

<@&286206848099549185>

[dire geode]

!15m

[cedar kiln]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.