help-13

[hoary charm]

so u expand right side and collect terms

then directly compare the coefficients?

[crimson sedge]

yup

exactly

[hoary charm]

i see, why is this something we can only do with a linearly independent set

[crimson sedge]

if we dont have a basis, we might miss something

eg, we cant write $(1,1,1)$ in terms of only $(1,0,0)$ and $(0,1,0)$

[wraith dagger]

Toby

[hoary charm]

but isn't a set thats smaller than a basis also linearly independent

wait nvm, ok but I mean a non Lin independent set containing a basis

[crimson sedge]

well it needs to span the whole space for it to work

it could technically be linearly dependent and still work, but we dont have to use the linearly dependent thing

basically, what we were trying to do was to write an arbitrary thing (eg a_0+a_1x+a_2x^2) in terms of the given spanning elements

[hoary charm]

ok I think I got it..

[eternal sphinx]

haylp

i have test on friday

algebra 1

aaahhhh

[crimson sedge]

#❓how-to-get-help

[eternal sphinx]

oh

soory

for barging in

[hoary charm]

I think im ok here

thanks for the help again toby

[crimson sedge]

yw :)

[cedar kiln]

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[outer hound]

Hey

[outer hound]

I need help with a algebra exercise

Being that E is a vetorial space on IK. a and b belong to IK and u and e belong to E

If au=av, then u=v?

If au=bu, then a=b?

If au+bv=bu+av, then a=b or u=v?

Which are true and which false

[crimson sedge]

$IK=\mathbb{K}$ is a field?

[wraith dagger]

Toby

[outer hound]

Yeye

That s what I meant by IK

[crimson sedge]

think about $\mathbb{R}$ as a vector space over $\mathbb{R}$ and come up with a proof or counter example

[wraith dagger]

Toby

[crimson sedge]

ie, are any of these true over R?

[outer hound]

Okok let me think about it

I am still very new to this so I dont understand much just saying

a) and b) are true over R

c) isnt tho

[crimson sedge]

what if a=0 for the first?

[outer hound]

Hmm then that s false ye

Always forget the 0

[crimson sedge]

yeah, if it goes wrong, its usually 0

now come up with similar counter examples for the others

then generalise to an arbitrary vector space

[outer hound]

So you are telling me b is also false?

[outer hound]

What s an arbitrary vetor space?

[crimson sedge]

E over K

[outer hound]

Sorry but my classes are not in english so Idk all the terms

Ah ok

The same thing goes for b) no?

If u=0, doesnt mean that a and b are the same

For c, it s false in examples that a and u are 0 for example or b and u or b and v or a and v

[cedar kiln]

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[outer hound]

No

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[shy wyvern]

Hi

[shy wyvern]

Can someone teach me

Algebra and a geometry

Because I wanna learn

My teacher won't help me

[worldly walrus]

"ask your math question in a clear, concise manner"

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[bold hazel]

is this valid

[bold hazel]

so far

my textbook does it kinda weird

whenever there's u-substitution

normally I do it like this

is that weird

the du is kind of like, a factor, isn't it?

[obsidian tinsel]

It is!

[bold hazel]

interesting

ic ic

[obsidian tinsel]

You remember doing Riemann Sums with rectangles? Rectangle is height times width; so for an integral, figuratively, the function is the height and the width is the dx

[bold hazel]

I remember Riemann sums yes

hm ok

kinda makes sense

ty

[obsidian tinsel]

Np

[bold hazel]

:p

[obsidian tinsel]

😄

[bold hazel]

.close

[obsidian tinsel]

: D

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[hollow minnow]

If it’s an expression of u I wouldn’t put it outside

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[bold hazel]

is this valid? been a while since I've done derivatives

[bold hazel]

done did derivatives

I'm not sure I'm thinking about this the right way

[obsidian tinsel]

Absolutelycertainly correct

Saw ur other post, and Ye u r hearing the right direction

[bold hazel]

awesome... second guessing myself because it feels like the book will skip steps

and I need to do all steps very explicitly

[obsidian tinsel]

Sounds to me you will end up being a god mathematician whose work anyone will be able to understand clearly

[bold hazel]

https://tenor.com/view/i-am-a-generous-god-xerxes-300-youre-welcome-gif-19690831

ty

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[solid juniper]

what?

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[old sinew]

I have a question, why is it that the slope is being multiplied to x in a linear function

[old sinew]

<@&286206848099549185>

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[old sinew]

.close

oh pog XD

[old sinew]

/close

.close

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[real crane]

i need

[real crane]

help

uhm

[real crane]

uhhhh

what if its not a math question

can i still receive help

??😭

[livid hound]

Is it related to math in any way

[real crane]

no

its about a skit and daoism

like i need to write a skit

in my group for class

tmr

[livid hound]

then no

[real crane]

😔😔

sadg

e

okay

.close

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[sick rock]

how do i solve this problem? not sure what it’s asking and need a step by step guide through

[cedar kiln]

@sick rock Has your question been resolved?

[sick rock]

<@&286206848099549185>

[gilded wigeon]

what problem are you even asking for help with

43?

If you don't have work here most people will not do it for you.

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[cosmic marten]

Can someone help me solve triangle 5 and 6. Then explain how you solved it to me please. I can do the rest on my own

[tropic oxide]

pythagorean theorem

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[proud forge]

is my proof correct?

<@&286206848099549185>

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[amber thicket]

quick question, what is -1 raised to the power of 2?

[hollow minnow]

If you mean (-1)^2 then it’s 1

But if you mean -1^2 then it’s -1

[amber thicket]

to put it in the context i mean this

[hollow minnow]

This would be (-1)^2

Which is -1 x -1

[amber thicket]

what is the difference between those?

arent both of them -1

[hollow minnow]

(-1)^2 = -1 x -1

-1^2 = -(1)^2 = -(1 x 1)

[amber thicket]

oh okay

.close

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[median bay]

how do i go from here

[median bay]

.close

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[nocturne cedar]

can someone help me what equation is this? and what are the rules specifically

[worn wave]

Let me ask you

what’s the square of 5?

[nocturne cedar]

25

[worn wave]

Okay, what’s the square of -5 then?

[nocturne cedar]

still 25

-5^2 is still 25 or -5 x -5 = 25

[worn wave]

So when you found a perfect square number

And you decided to square root it

It can either be a positive or a negative

sorry I just realised your question is a bit unclear, what do you mean by rules?

[nocturne cedar]

I wanted to know what kind of equation this is

because it just shows how it is solved yet I dont know what equation is this

[worn wave]

I see

In this case

If you expand it and make the equation equate to zero by moving the terms, you’ll get what’s called a quadratic equation

If my observation is not wrong, this is part of the step to solve it using the completing the square method

[nocturne cedar]

ah okay

now then can you teach me how to turn this equation into a standard form quadratic equation?

nevermind

.close

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[crimson sedge]

Idrk what to do

[crimson sedge]

Can I get some help with part iii?

Got this but $\theta_2$ is not coming out to be $\frac{4}{\sqrt{42}}$

[wraith dagger]

idecanymore

[reef bane]

https://cdn.discordapp.com/attachments/875939621547180103/1034791906443538473/image.png

you have to try and find what alpha is and take the negative of that

[crimson sedge]

Why did you take the point there

It says shortest distance to the circle

[reef bane]

for arg(z-1) to be the smallest

it has to be the most negative value it can be

[crimson sedge]

I was told

[reef bane]

it didnt say the distance has to be the smallest

[crimson sedge]

That by smallest it's just referring to magnitude

[reef bane]

for c) its saying the arg has to be the smallest

[crimson sedge]

Oh wait but then it could just be zero

Ohki thanks

[reef bane]

a hint for how to find alpha

you have to break it up into 2 triangles

[crimson sedge]

I'll find it

Nws

[crimson sedge]

Bit of a problem

I'm getting $\frac{4}{\sqrt{57}}$

Not 42

[wraith dagger]

idecanymore

[reef bane]

should be sqrt(58)

and thats arcsin

the answer has it in terms of arctan

so you need to convert it

[crimson sedge]

,w sqrt(8^2+3^2-4^2)

[wraith dagger]

Results provided by WolframAlpha

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Requested by idecanymore#5738

[crimson sedge]

No I just found the length of the adjacent

Using pythagoras

[reef bane]

https://cdn.discordapp.com/attachments/875939621547180103/1034796589211996241/image.png

so in this case y is the distance

and thats sqrt(7^2+3^3)

[crimson sedge]

The length you've written as y is just $\sqrt{8^2+3^2} = \sqrt{73}$

[wraith dagger]

idecanymore

[reef bane]

its not 8^2 +3^2

its 7^2+3^2

[crimson sedge]

It ia

[reef bane]

it doesnt start from the origin

it starts from (1,0)

[crimson sedge]

Oh shit

Lmao mb

[reef bane]

so y is the hypotenuse of the triangle with angle gamma

we get arcsin(4/sqrt(58))=g

and you can convert it into arctan

same with the other triangle

[crimson sedge]

Yeah uhh

It's 42 now

Nws

[crimson sedge]

Nah you can just find adjacent

,w sqrt(7^2+3^2-4^2)

[wraith dagger]

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Requested by idecanymore#5738

[crimson sedge]

So you get tan theta as 4/root(42)

Thank you so much @reef bane

[reef bane]

nws

[cedar kiln]

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[mint canopy]

is it true that for any events A,B,C of omega, that ( P( A \cap B) + P( A \cap C) + P( A \cap B^c \cap C^c ) - P(A \cap B \cap C ) ) is always equal to 0?

[mint canopy]

this is my reasoning:

[wraith dagger]

Lasha

[cedar kiln]

@mint canopy Has your question been resolved?

[mint canopy]

<@&286206848099549185>

[cedar kiln]

@mint canopy Has your question been resolved?

[cedar kiln]

@mint canopy Has your question been resolved?

[mint canopy]

<@&286206848099549185>

[crimson sedge]

Yo

Sup

[crimson sedge]

You called for stats man

Why

Wdym of Omega?

[mint canopy]

omega is the the solution space or whatever its called

[crimson sedge]

Wait lemme write your thing in latex I cba to zoom in

$P( A \cap B) + P( A \cap C) + P( A \cap B^c \cap C^c ) - P(A \cap B \cap C )$

[wraith dagger]

idecanymore

[crimson sedge]

Hmm wait

[mint canopy]

omega is the sample space

[crimson sedge]

No this statement's not true

[mint canopy]

Ω

[crimson sedge]

Definitely not true

[mint canopy]

then whered i make a mistake

[crimson sedge]

$$P(\Omega) = 1$$
$$P(A \cup B) + P(A \cup C) + P(B\cup C) - 2P(A\cup B \cup C) + P(A \cup B^C \cup C^C) + P(A^C \cup B \cup C^C) + P(A^C \cup B^C \cup C) + P(A^C \cup B^C + C^C) = 1$$

[wraith dagger]

idecanymore

[crimson sedge]

Here's your correct one

@mint canopy

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[crimson sedge]

what's the ideal mechanical advantage of the block and tackle?

[dire geode]

engineering server is in #old-network

[crimson sedge]

damn thats engineering?? i had that shit in my math textbook😂

.close

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[peak osprey]

need help with this. complex numbers

[sterile tendon]

since z is complex it can be written as re^itheta

and then 2-2sqrt(3)i is another complex number that can also be written the same way

[peak osprey]

thanks i'll try solving it in this way

.close

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[signal fiber]

hello

[signal fiber]

basically

i dont undertsand a math page

let me send it

[cedar kiln]

Please don't occupy multiple help channels.

[signal fiber]

ok

what is that

.close

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[bold hazel]

hoping I did this right

that's the problem

[mental trail]

d(t) = F(t) - F(0), always good to check

Also :
-You got an "x" in the expression of F

• be careful not to use the same variables between the function and the integral

[bold hazel]

oh, oops, ty

I'm not sure if I should write it that way or not

d(t) = F(t) - F(0)

and I'm not sure what you mean by not using the same variables between function and integral

so my integrand should have different variables than the anti-derivative?

I would think I'd have to use t in this case

since displacement is a function of time

anyway... I'm not going to overthink it, I think the grading criteria is a bit loose, this should be close enough I think

.close

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[grave cloud]

try to simplify the numerator

you get

also

hmmm

strange.. ?

i cant seem to simplify this, could you check if the problem you gave is correct ?

[cedar kiln]

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[glacial moth]

if A not less than B and B not less than A does that mean A = B?

[glacial moth]

should right?

[fair geyser]

yes

[cedar kiln]

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@glacial moth Has your question been resolved?

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[crimson sedge]

how am i meant to deal with this a and b?

[dire geode]

Treat it like a constant

2 and 3 if you like

[cedar kiln]

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[crimson sedge]

.close

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[gilded steeple]

Hi! I need help reviewing these questions I got wrong, gotta clear up the confusion.

[gilded steeple]

Give me a min

How is it A? How do you make it a quadratic equation?

I know the solution but I was kinda confused

I have no idea how to find the roots in this kind of equation

And that's all

[hushed spoke]

Easiest one would be to just plugging in the roots into the options

[gilded steeple]

Wdym? Sorry my Math vocabulary isn't that great

What's the equation here, in this type of equation at least

[gilded steeple]

<@&286206848099549185>

wait I know now

[gilded steeple]

Now I just need help with this one next

.close

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[urban locust]

does anyone know how to do basic proofs

[urban locust]

im suffering

<@&286206848099549185>

[hushed vessel]

please helpp

[urban locust]

💀

[hushed vessel]

i have to finish it now, lease can someone help

😭

[urban locust]

y u raiding my channel

<@&286206848099549185>

[eager sparrow]

Hey I got it @urban locust

[urban locust]

ok

im so confused

[eager sparrow]

Here

[urban locust]

proof

so like steps

[eager sparrow]

So first are the givens

[urban locust]

yeah

ima freshman so everything is limited rn

[eager sparrow]

Then after that, the third given is a property of an isosceles triangle

[urban locust]

ok

[eager sparrow]

After that is the two right angles, it's a property of a rectangle

[urban locust]

i didn't learn that yet

[eager sparrow]

Basically there's an exterior angle theorem at the top right

[urban locust]

we didn't learn about that yet

so limited

[eager sparrow]

Then, I dunno how to prove that without those

[urban locust]

how do you find that each vertex thing is 90 degrees

@eager sparrow

sry for ping

[eager sparrow]

I mean it says in the given

That both of the line segments are perpendicular

[urban locust]

it says that for only 2 angles

[eager sparrow]

Yeah, but if the lines are parallel then you can use the exterior angle or interior angle theorem

And also try to imagine the angles as triangles

It's very hard to do since I can't really show you
Im too lazy to draw it

[urban locust]

can i say they are isosceles

[eager sparrow]

Maybe if we can share screen since I have a drawing tablet

[urban locust]

but i don't have enough info for the rest of the triangles

[cedar kiln]

@urban locust Has your question been resolved?

[cedar kiln]

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[crimson blade]

Help with this (elimination method)

[crimson blade]

Am very lost help would be nice

[haughty wraith]

4x - 6y = -2

3x + 5y = 8

[crimson blade]

Yes and I multiplied bottom by 3 top by 4

[haughty wraith]

oh

what did u get

[crimson blade]

eliminated 4 and 3

[haughty wraith]

what did you get after this step

[crimson blade]

multiplied 3 x -6

-18

4 x 5

20

[haughty wraith]

what are your two equations

like]

write them out

[crimson blade]

-6y=-2

5y=8

[crimson sedge]

???

[haughty wraith]

dude

you multipled top one by 3

what is your new equation

[crimson blade]

12x-18y=-6

[haughty wraith]

ok

whats ur 2nd one

[crimson blade]

12x+20y=32

[haughty wraith]

ok great

now subtract

-18y-20y = ?

[crimson blade]

2y

[haughty wraith]

oh you did it other way

ok

what does that =

wait

[tame stream]

You need to subtract not add

[haughty wraith]

which are u subtrating for which?

12x-18y=-6

12x+20y=32

subtract and you get

-18y-20y = -6-32

-38y = -38

[crimson blade]

Yep

[haughty wraith]

y = 1

[crimson blade]

Wow

Math is crazy

Would’ve never ever thought to do that

alr thanks

.close

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[shrewd barn]

just need to know if these are right and if they arent how would i go about fixing them

[muted bear]

Your missing something called "windowframe convention" i believe

Dont mind the term

Basically id there are arrows, assume they go off the infinity

[cerulean star]

You're not getting what Domain and Range mean

[muted bear]

No i think they get it

Just that the arrows mean that it leeps going off to inifity

[cerulean star]

@shrewd barn define Domain and Range

[shrewd barn]

only vaguely

[cerulean star]

In your own words

As simply as possible

[shrewd barn]

domain is the amount of values seen at the top of a graph and the range is the amount of values on the side

i think

[cerulean star]

No.

Domain is the set of all input values (x) that a function relation CAN recieve and spit something out that makes sense

Range is those values it spits out (y).

[muted bear]

These arent functions

Theyre curves

[cerulean star]

True

[shrewd barn]

how would i go about finding either then

[cerulean star]

Fixed

[cerulean star]

Look at the graph and think about what is allowed to go in, and what can come out

You got the ellipse right.

Think about that from that point of view

Every input from -4 to 2 was allowed

The output ranged from -2 to 2.

[shrewd barn]

wouldnt it be the same for all graphs below for example the single linear one going from -1, 3 and -2, 4

[cerulean star]

For the line, is there any value x that IS NOT allowed?

What do the arrows mean?

@shrewd barn

[shrewd barn]

infinity

[cerulean star]

They mean they keep going

...(to +- infinity)

The curve continues infinitely

(Line)

Is there any value of x that does NOT belong to the line?

Yes or no will work

[shrewd barn]

anything past 3 or below -1?

[shrewd barn]

yes

[cerulean star]

You already said the arrows on the ends mean the curve (line) continues in that general direction forever, not to the edge of the graph on your paper

[shrewd barn]

oh yeah

so then wouldnt the graph as a whole belong

[cerulean star]

All values of x, all real numbers, belong to the graph

It takes all x as input, and gives all possible y's as output

[shrewd barn]

so the domain and range would be infinity -infinity?

[cerulean star]

Backwards

[shrewd barn]

got it

[cerulean star]

Always write from left to right,

• to +

[shrewd barn]

thank you was struggling with this for awhile

[cerulean star]

How about the v-shaped graph?

[shrewd barn]

the domain would be -infinity, infinity and the range would be 3, infinity?

[cerulean star]

Close

[shrewd barn]

since one part of the graph is a dot rather then an arrow

[cerulean star]

You got the range (set of all outputs) wrong

"What's the lowest point?"
"What's the highest point?"

[shrewd barn]

the lowest point of the graph is 3, -1 and highest would be wherever line b ends up since it is steeper

[cerulean star]

Only worry about the y-coordinate

For the Range

The graph is unbroken; continuous

So these questions about Domain and range are single intervals

The x-inputs range from -inf to +inf

The y-outputs range from -1 to +inf

[shrewd barn]

so -1 is the lowest point on the y coordinate

[cerulean star]

on the y-axis.

[shrewd barn]

my bad

the highest would be positive infinity then right?

[cerulean star]

I mean...it's not on the axis but we don't need to lose sight of the big picture here

[cerulean star]

Because there is no highest point. There is always a higher point

+inf

[-1,inf)

[shrewd barn]

alright thank you

[cerulean star]

Square bracket means left (or in this case, bottom) endpoint is INCLUDED

[shrewd barn]

could we go over the parabola one i think thats what its called

[cerulean star]

Ok

[shrewd barn]

range is -infinity, infinity im sure but the domain is what im not getting the most

[cerulean star]

Ok

[shrewd barn]

even though im sure its about same rules as the others

[cerulean star]

Imagine flattening the curve against the x axis.

That's the domain.

[shrewd barn]

the x value is infinity then

im assuming by trying looking at it from that perspective

[cerulean star]

Domain and Range are sets of values, not single values (usually)

If you flatten the parabola against the x-axis, like in photoshop

The left end goes all the way to -infinity

But there aren't any other points past x=2

[shrewd barn]

so (-inf, 2]?

[cerulean star]

Yes

Do you see it?

[shrewd barn]

yeah i get it more now

thanks for the help

.close

[cedar kiln]

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[quaint rune]

how to find the shortest distance between (0, 0) and a point in the parabola y=1/3x^2 - 9.

[quaint rune]

(no calculus needed)

[dire geode]

is it (1/3) * x^2 or 1 / (3x^2) ?

[quaint rune]

(1/3)x^2

[dire geode]

do you know the distance formula?

[quaint rune]

yes

[quaint rune]

but idk how it works on a parabola

[dire geode]

x = x and y = the formula for the parabola in terms of x

[quaint rune]

bc normally with straight lines its perpendicular line thats the shortest

[quaint rune]

but what is the shortest point though

straight line its the line perpendicular to the other line

but this is a parabola

[dire geode]

once you have the distance formula and picture, you'll know

[quaint rune]

i dont quite understand

because in order to apply the formula you need to know two coordinates

and right now we only know one which is (0, 0)

the other coordinate has to be the shortest line from (0, 0) to any point on that parabola

[dire geode]

yes

your distance will be in terms of a variable x

[dire geode]

use this to express your y^2 term in terms of x only

[quaint rune]

ok so what would the equation be?

[dire geode]

try it yourself

[quaint rune]

sqrt(x^2+y^2) = d?

[quaint rune]

but then how to make y^2 in terms of x

[dire geode]

yes

[dire geode]

.

[quaint rune]

yeah but how do you subsitute y^2 in terms of x

btw i gtg now, ty so much for your help ill look at this and figure it out tmr

[cedar kiln]

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[grave crescent]

So I've been stuck at this for a while now and I'm not sure what to do

I have vectors a and b such that |a|=3 and |b|=1, and the angle formed by a and b is π/3. If c=a+3b, find
|c| and the angle formed by a and c

[grave crescent]

I found that |c|=3√3 by squaring so that
|c|=|a+3b|
|c|^2=(a+3b)^2
And I found that |c|=3√3, but when I try to find the angle I get that cos(x)=(3√3)/2 which doesn't make sense

[cedar kiln]

@grave crescent Has your question been resolved?

[grave crescent]

<@&286206848099549185> help ._.

[cedar kiln]

@grave crescent Has your question been resolved?

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[bitter surge]

i dont understand q. 28

I hv no idea what the question is asking

this is what i think the question is trying to talk

The ans is 4x^2-28x+9= 0

@uncut veldt

plz pin me when you are ready , thank you👊

[cedar kiln]

@bitter surge Has your question been resolved?

[livid hound]

the work in the first image seems fine

[cedar kiln]

@bitter surge Has your question been resolved?

[bitter surge]

ohhh, yahh, cus i almost get the final ans haha

If u are interest in how to find,

4 times the whole formula. Thats because the alpha is different in 7 and 2.25, therefor times 4

[cedar kiln]

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[gritty belfry]

need help solving this ive completely forgot how to do it

[bold lotus]

do you know what angle BCA is

in terms of c

[gritty belfry]

it all adds to 180 i know tha much

[bold lotus]

this is an isoceles

[gritty belfry]

right so

c = 4c too

[bold lotus]

no

[undone halo]

what

[gritty belfry]

oh

[bold lotus]

the congruent line segments form equal angles with the non congruent side

[gritty belfry]

so A and b are equal??

[bold lotus]

no

$\angle BAC = \angle BCA$

[wraith dagger]

dog.

[gritty belfry]

how is A and C not equal

[bold lotus]

A and C are points?

[gritty belfry]

but equal angles

[bold lotus]

how are they equal?

oh shit

yeah A and C

[gritty belfry]

cos its isosceles

[bold lotus]

you are right

you said a and b first

[gritty belfry]

noo

[gritty belfry]

here

[bold lotus]

yeah the angles formed at vertex A and C are equal

[gritty belfry]

right right

[bold lotus]

thats not correct

[gritty belfry]

i meant like

point C is also 4c

[bold lotus]

yeah

[gritty belfry]

cos they equal

right

[bold lotus]

so whats the total angle in the triangle

[gritty belfry]

180

[bold lotus]

what abt in terms of c

[gritty belfry]

idk

4c + 4c + c = 180

but how do u find c

[bold lotus]

well you have 9c = 180

its pretty simple algebra

[gritty belfry]

oh right true

i didnt think of it in algebra

so would it be

180 / 9

20

got it thank u

.close

[cedar kiln]

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[dense yacht]

find a branch of the multiple valued function (z^2 − 1)^1/2
that is analytic in
the disk |z| < 1.

[dense yacht]

how would i start this problem

[cedar kiln]

@dense yacht Has your question been resolved?

[cedar kiln]

@dense yacht Has your question been resolved?

[rancid flint]

write $z^2-1$ in the form $re^{i\theta}$.

[wraith dagger]

Blaxapate

[cedar kiln]

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[dense yacht]

.close

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[solemn torrent]

hi

[solemn torrent]

Find the conjugate and modulus of complex number z=1+i

how would I go

About doing this

[wild spear]

for a complex number $z=a+bi$, the conjugate would be $z*=a-bi$ and $|z|=\sqrt{a^2+b^2}$

[solemn torrent]

is that the general rule

[wraith dagger]

nichoals

[wild spear]

for z = a + bi yes

[solemn torrent]

okay

wait so

OH

that’s it?

I just substitute the values of a and b?

[wild spear]

yes

[solemn torrent]

ty!

[wild spear]

you can imagine z in an argand diagram to understand it more thoroughly

[solemn torrent]

wait

[solemn torrent]

what is z* again

[wild spear]

complex conjugate

you can write it as $\bar{z}$ as well

[wraith dagger]

nichoals

[solemn torrent]

Wait

[solemn torrent]

What is an argand diagram?

Is it the reflection thingy

[wild spear]

a cartesian diagram but the x-axis becomes the real part and the y-axis becomes the imaginary part, simply saying

rowlet is the cutest and no one can change my mind

and also it reflects me (my hobby is sleeping)

[solemn torrent]

Is this right

[wild spear]

yes

[solemn torrent]

ohh thank you!

Q6.Express the complex number in the form of atib, where a, b E R and i = V-1, if z = (3 - 1)(1 + 21).

How about this?

[wild spear]

wait

thats the question? z = (3-1)(1+21)?

or maybe it's (3-i)(1+2i)

[solemn torrent]

Oh wait

I suck

YES

Q6

[solemn torrent]

Yep! You’re right

Do I just expand?

[wild spear]

yep

[solemn torrent]

Oh that’s it

[wild spear]

and whenever you see i^2, change it to -1

[solemn torrent]

Oh ok

[unique scaffold]

Anybody got good resources for factoring?

[wild spear]

this channel is occupied

[unique scaffold]

Where should I go to get help?

[wild spear]

and if you want book recommendations, there is a channel on that

#book-recommendations

[unique scaffold]

Thanks ig.

[solemn torrent]

YAY!

tysm!!!! @wild spear

[wild spear]

do you want help on a problem or books?
if help, #❓how-to-get-help
if book recommendations, #book-recommendations

[wild spear]

no prob

[cedar kiln]

@solemn torrent Has your question been resolved?

[cedar kiln]

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[rich spade]

Could someone give me a hint for where to start for this or something? The prof didn’t really go over it. I know the arc length formula, but I just can’t differentiate it when it’s plugged in

[rich spade]

Obviously can’t rlly use u sub or IBP

So i have no idea where to go

[runic garnet]

Show ur work

O wait u don’t know how to start, mb

Wdym by can’t differentiate when plugged in

[rich spade]

I mean

Integrate

Like here, can’t really integrate this

I’m probably being really stupid honestly

[runic garnet]

How’d u get +1/(8x^4)

[rich spade]

Oops

It’s supposed to be 1/16x^4 lol

I just rewrote it and smooth brained

[runic garnet]

lol yep

Ur teacher requires that u do this by hand?

[rich spade]

Yes

[runic garnet]

Hmm gimme a sec

[rich spade]

Ok this didn’t occur to me initially but could it possibly follow the formula A^2 + 2AB + B^2 so we can square the whole thing? He did something like that in class but it didn’t seem like it’d apply here

[runic garnet]

Hmm

For the x^4 + 1/2 + 1/(16x^4)? Or did u turn it into a fraction

[rich spade]

Yea for that

Can you just simplify it to (x^2 + 1/4x^2)^2?

[runic garnet]

U CAN

NICE

[rich spade]

Honestly no clue why my prof gave us something like this… lmao

He did one single example for this formula in class

But anyway

Ty 🙂

[runic garnet]

Sure np

I guess he just wanted to see if y’all were paying attention

xD

[rich spade]

Ig so lmaooo

…how do i close it again

[runic garnet]

.close

[rich spade]

Ty

.close

[cedar kiln]

Channel closed

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[cedar kiln]

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[opal umbra]

I don't understand how I can get the length of |BH| from the information provided in the question. Please help

[bitter finch]

notice that ABH and ABC are similar triangles

because they both have a right angle and an angle of 38 deg

[cedar kiln]

@opal umbra Has your question been resolved?

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[opal umbra]

Thanks yeah 👍

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[quasi swift]

This is going to sound dumb, but does anybody know any resources for how to find the center of the circle

[quasi swift]

Like I'm aware of the equation a little, but I wanna see it in a problem and try to work it out

Back in my sophomore year our teacher didn't teach us the circle unit at all because she was far behind that year

[south tundra]

Depends on what's given

[quasi swift]

So I'm pretty much clueless on geometry circles

[quasi swift]

uhh

I'll find a problem

This isn't center of a circle but idk how to do this either

[runic garnet]

Do u know the formula for circumference of a circle?

[quasi swift]

shit

uhh

pir^2?

wait that's area

(2pi)r^2

I think?

[runic garnet]

No

Just

2 * pi * r

[quasi swift]

o

okay so just divide it by 6.28

or no

I could plug it in to each

[runic garnet]

C = (2)(pi)(r)

Plug in 16pi for C

Then solve for r

Don’t turn the pi into a decimal

[quasi swift]

but wouldn't it be quicker to just plug in the circumference equation into the questions

[runic garnet]

Wdym?

[quasi swift]

Okay so there is A-E answer choices

If I just cut it in the middle and go to C the answer is 8. So 2 * pi * 8

If it's too low or too high I go to A/B or D/E

[runic garnet]

O plugging in the answer choices into the circumference formula? No that’s slower

[runic garnet]

Bro…

[quasi swift]

wat

That's right equation?

[runic garnet]

C = (2)(pi)(r)

Plug in 16pi for C

Then solve for r

[quasi swift]

that seems like it would take longer, but I will do that instead

[runic garnet]

No, it’s shorter

16pi = 2 * pi * r

How would u go from here

[quasi swift]

I'm very bad at algebra

Probably move 2pi

Over

[runic garnet]

Yes, how

[quasi swift]

Yeah that's the problem idk if you'd divide it or not

16pi/2pi = 8

8=r

[runic garnet]

Correct

U cannot use addition or subtraction here

[quasi swift]

What about this one

[runic garnet]

Do you know the standard equation of a circle

[quasi swift]

lol nah

I don't know anything about circles other than radius and diameter. And area maybe

[quasi swift]

Wtf

what is h and k

x and y?

oh

[runic garnet]

The coordinate of the center of the circle

[quasi swift]

what is x and y

the other point?

[runic garnet]

x and y are part of the equation

[quasi swift]

okay so the radius is 5 right

[runic garnet]

Just like for a linear equation there is for example y = 2x, here the x and y are on the same side

[runic garnet]

Correct

[quasi swift]

but the answer is J

because x^2 and y^2 don't make 5

It makes r^2

Which is 25

right?

[runic garnet]

correct

[quasi swift]

Also, where can I find an intro to functions?

I forgot since Algebra II

[runic garnet]

Intro to functions? What type of functions

Khanacademy could probably give you what you’re looking for

[quasi swift]

Well I wanna know how to answer the questions where it's like f(x) = 3x^2+9+4 | f(g)=5x^4 + 3 + 9. Find f(x(g))

[runic garnet]

Yea khanacademy is probably a good resource for all sorts of topics in those levels

[quasi swift]

Found an example

[runic garnet]

I’d recommend looking there, and a few channels on yt like the organic chemistry tutor are pretty helpful

[quasi swift]

I don't understand how I can be so bad at math lolz. I'm not this bad in any other subject

Like my math skill squared wouldn't compare to any other subject

[runic garnet]

lol, just keep at it

[quasi swift]

I'm gonna close this for someone else but, I'm probably gonna be back soon once I take a look at these prac probs

.close

[cedar kiln]

Channel closed

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[cedar kiln]

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[foggy elbow]

why convert n is an element of bZ to n = b * k for some k exists in Z?

never mind. saying it outloud in my head , it makes sense now

.close

[cedar kiln]

Channel closed

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[foggy elbow]

.reopen

[cedar kiln]

✅

[foggy elbow]

where did the red box come from?

i understand everything up until that part

[tough valve]

from the first part of the second line

[foggy elbow]

b = a * k, yes I see that now. thanks

[foggy elbow]

is this showing equivalency of n = b * h is also the same as n = a * l?

so because of that, bZ is a subset of aZ?

[tough valve]

i don't understand the question

[foggy elbow]

what exactly is happening in the whole proof? They start off with n being an element of bZ

[tough valve]

yeah in order to prove bZ is a subset of aZ, we need to prove any element in bZ is also an element of aZ

so, we take a random n from bZ and prove it's also part of aZ

[foggy elbow]

thanks,. and in the red box. i see it came from b = a * k1 for some k in Z

why specify k1?

a(k1 * k) = a * l

[tough valve]

b is a multiple of a

because a | b

so we can say b = a * k1

or b = a * WHATEVER_NAME_WE_WANT

[foggy elbow]

a | b if and only if b = a * k1. i see

what's with the a(k1 * k)?

well

specifically why (k1 * k) instead of just a * k1

[tough valve]

it's just a calculation of n

n = a * k = (b * k1) * k = b * (k1 * k)

[foggy elbow]

Oh makes so much sense now

thank you so much

.close

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[unborn locust]

Does the set E^n mean all column vectors with n rows?

[unborn locust]

Nvm

.close

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[granite eagle]

.

[granite eagle]

the third step is gibberish i tried

im supposed to express x in terms of pie

[mighty drift]

It's just the angle sum formula

[granite eagle]

mind elaborating?

[mighty drift]

To go from line 2 to line 3, it's just the formula for cos(a+b)

[granite eagle]

and?

[granite eagle]

.

[mighty drift]

What's x bar

[granite eagle]

its a variable

[mighty drift]

So should we find x as a function of pi and x bar ?

[granite eagle]

the question is phrased exactly as i asked it

[mighty drift]

Then x bar should have some formula as a function of x

[livid hound]

is that supposed to be
$\overline{x}$ or $\pi$

[wraith dagger]

ℝamonov

[granite eagle]

x has a range tho

pie

[mighty drift]

What

Pls don't write π like that. Wtf

[granite eagle]

both of u didnt read this

[mighty drift]

We did, but we were confused about the nature/role of x bar

[granite eagle]

okay

sorry

[mighty drift]

Which is actually just pi

[granite eagle]

any hints?

[mighty drift]

Start from line 2, not line 3

Cos a = 1 has known solutions

Then just use a = x/2 + pi/6

[granite eagle]

wow

okay

[mighty drift]

And solve for x

[granite eagle]

im stupid

thanks ppl