help-0

[wary badge]

Sed

I wish graphs were continuous

[novel spruce]

what is the problem?

what does sum(alpha^3) mean?

is alpha a vector or a list? are beta and gamma labels for alpha_2, alpha_3?

i'm trying to understand the context

[rigid wind]

wack

[alpine sable]

Is th ere something wrong with the question?

Or does it simply need more attention?

[novel spruce]

reading that now

god that's abusive notation

ok i don't think i can help and ive gotta go sleep, you probably have to apply the fundamental theorem of algebra somewhere to cancel the roots but i don't have any other ideas (and i don't know what you meant by your original question)

[night saffron]

Hey everyone, can I please get some help with parts b and c for this question on lines?

[alpine sable]

anyone help me

[steep mortar]

10x+y=10

[alpine sable]

ik this seems stupid but i started algebra 4 days ago

i got most of function questions correct

i just

-2x
x = 2

thats it

i just dont understand

-2(2) + 10?

[split oriole]

X+y=10

[alpine sable]

oh

im so fucking stupid

I dont understand it

[dry berry]

wdym

[alpine sable]

im just asking for a friend

[tough hatch]

you have to solve for x

[ancient saddle]

Hello, what have you tried so far?

[alpine sable]

for the triangle do (5x-1)^2 + 6x^2 = BC^2

and solve as follows

(using pythagoras' theorem)

then solve for x

[dry berry]

idk if bc = wy

but if it is just use it

[alpine sable]

yeah

if you find x you can check whether it's equal

[olive pawn]

Are there any intellectual gigachads around that are comfortable with highschool physics

[alpine sable]

can anyone help me with 11 question of math problem?

[olive pawn]

<@&286206848099549185>

[dark granite]

maybe. It would help if you actually post your questions.

[alpine sable]

oh um ok let me send them-

[olive pawn]

What's jawaban anda

[woven echo]

name i'm guessing

or maybe its uh

[alpine sable]

its like our answer

[woven echo]

a different language

oh

[alpine sable]

whats our answer

[olive pawn]

i think it's a

[alpine sable]

its in bahasa indonesia

[olive pawn]

devil summoning ritual

[alpine sable]

ive been struggling with those questions for hours ;-;

[olive pawn]

jawaban anda sounds like something cultists would say while spinning in a circle

[alpine sable]

oh no-

it means "your answer"

[olive pawn]

if there's anyone that can help me with some homework I'll be indebted to you

Oh lol

what language?

[alpine sable]

bahasa indonesia

[olive pawn]

damn hello sea bro

[placid zinc]

You're missing the set for 1 in your screenshot

[woven echo]

yea i was gonna say

no clue what the original set is

[placid zinc]

That's okay, we can do 2

2 is the set of all whole numbers between 50 and 70

[alpine sable]

oh rly-

[placid zinc]

... Not clear if that includes 50 and 70 themselves, but we'll know in a bit haha

[alpine sable]

i dont know actually the teacher just sent that to me ;-;

kinda confused

[placid zinc]

Question 2 uses the set of all whole numbers between 50 and 70
With me there?

[alpine sable]

yes

[placid zinc]

2a asks for the subset that is all multiples of 5

[alpine sable]

ok

[placid zinc]

"Subset" meaning you take the elements out of the original set

[woven echo]

(similarly there should be a 1. that defines the original set above 1. a.)

or there's no way to answer those

[placid zinc]

So 2a is asking
"Out of all whole numbers between 50 and 70, pick out the ones that are a multiple of 5"

[alpine sable]

oooh

[alpine sable]

above 1 a is p = {whole numbers less than 30}

[woven echo]

same idea there then

[rigid wind]

i was tripping like even numbers belonging to $\mathbb{R}$ ?

[ocean seal]

Vee

[woven echo]

that defines your original set, then you use the rule to define the subset from that in 1.a. 1.b. etc

[alpine sable]

oooh ok ok

what am i doing wrong am i not supposed to just +-360°?

[paper grotto]

can someone help me w my homework

[vale wigeon]

i think the issue is you're putting the degree sign into the answer box when it's not supposed to be there

try writing just 480, -240 and 60, -660

[keen salmon]

Can someone help me with this

[light sparrow]

they will certainly be nicer ways, but I started with saying that |z-wk|^2 = (z-wk)(z-wk)* where the '*' denotes the conjugate

so thats (z-wk)(z*-w_k *)

and then if u expand it out you get 2 - w_k z* - w_k * z

and then we wanna sum the RHS from k=0 to n-1

so you can see the 2 will turn into 2n with the sum, so the remaining bit should sum to zero

i can give more details if u want

[rich basin]

How would we solve this problem with a problem where the observer is stationary and some ambulance is approaching it with a velocity of 10 m/s

[lyric ocean]

I know this is a dumb question but is the answer of this question -1?

[carmine lion]

lmao what

[rigid wind]

2x0-1

[alpine sable]

LMFAO

[primal lintel]

Hey all, so for an assignment I have, I've basically got to replicate a graph however I'm stuck on this one

The green line more specifically, I've tried messing about but I can't seem to get it right. Does anyone have a few pointers?

[alpine sable]

yeah, so, with graphs, you can usually use the roots to help create a factorised equation of the curve

for example (x-1)(x+1)(x+2) is a cubic with roots 1, -1, and -2

the way you determine whether it's a quadratic, cubic or quartic is by counting the number of stationary points and adding 1

if there are 2 stationary points, add one and you get 3. The three is for a cubic

[primal lintel]

Oh ok, but in my case it would be a quintic?

[alpine sable]

correct

as you can see though, you have 4 roots instead of 5

4 intersections with the x axis

[primal lintel]

So it would be structured like
(x + 1)(x - 2)(x + 3)(x + 2) ? (not right values obv)

[alpine sable]

yes

here, the missing root would just be an x

so following your example, (x)(x+1)(x - 2)(x + 3)(x + 2)

assuming there is a repeated root

[alpine sable]

that's a repeated root

[primal lintel]

So I've got the structure I guess you could say correct, but how I would I go about getting the values?

[alpine sable]

hold on, let me get desmos up

[primal lintel]

Ok ok, I get what you mean by a repeated root

This explained it well

[alpine sable]

i may not have helped as much as I thought i would've

trying to graph the original graph

[primal lintel]

ah no no no, you're helping a tonne

[alpine sable]

i might need someone to tag team

the issue is that the stationary points are just off

[jade birch]

u got the roots wrong

[alpine sable]

ok yeah

[jade birch]

,w graph (x+1) (x-2) (x-5) (x-6)

[ocean seal]

Results provided by WolframAlpha

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Requested by .itsjustnai#9187

[alpine sable]

with a repeated root, it's not (x), you square the bracket that is repeated

apologies

,w graph (x+1)(x-2)(x-2)(x-5)(x-6)

[ocean seal]

Results provided by WolframAlpha

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

Requested by bladee fan#4629

[jade birch]

oh i didn't copy a term

[alpine sable]

repeated root at x=2

[primal lintel]

I got something similar

Put a 0.1 at the beginning

[alpine sable]

yeah, but it's the why that's bugging me

[primal lintel]

@alpine sable thanks a lot for the help

Think that looks fairly accurate to the example

[alpine sable]

yeah, np, but I would really suggest understanding the need for the 0.1

[jade birch]

btw, are we sure it's 1/10 ?

[alpine sable]

I'm assuming that you'd differentiate the equation and get approximate coordinates of the stationary points

,w differentiate (k)(x+1)(x-2)(x-2)(x-5)(x-6)

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by bladee fan#4629

[primal lintel]

I understand that the smaller the coeffecient would be, the more flat it would be

And I suppose I was just looking for the graph to be less huge

[alpine sable]

actually, the coefficient here (0.1) affects how much you stretch the vertical axis

[primal lintel]

Oh that makes sense

[alpine sable]

how much you expand or shrink the verticalness of the graph (for lack of a better word)

y = a f(x) and y = f(x) + a
these two affect the vertical axis, where a is a constant. first one applies scale factor of a, second one shifts up by the value of a

f(x) is any function like x^2 + 4x - 12

y = f(a*x) stretches x axis by scale factor of 1/a
y = f(x - a) moves the graph on the x axis by the value of a
notice how it's (x-a) [negative] on the second line

[carmine lion]

isn't it "dilation"

[primal lintel]

@alpine sable sorry for the questions, but how would I replicate a graph like this

without seeing where the part on the right ends exactly

(talking about the gray shaded one), with the previous equation, we could see all the points however with this one I'm not sure how to approach it

[quartz oxide]

Hmm, what are you trying to find? In particular

[primal lintel]

The equation of the gray shaded line

[alpine sable]

not sure of the exact terms honestly

we're solving another question right now

please try another channel

[quartz oxide]

Well, we happily assume it is cubic, Then you can reconstruct the equation with the roots (0, -7, -7)

I think?

[alpine sable]

yes, i agree

[quartz oxide]

The only annoying thing left is the stretch coef

[primal lintel]

ah thank you

😆

[warped condor]

help

[umbral hatch]

hm start by simplifying

[warped condor]

idk lol

i just needed the answer

not smort

[umbral hatch]

#❓how-to-get-help

[alpine sable]

7. When asking for help, do not insist on getting just the answer; we are here to help you learn, not cheat.

[alpine sable]

Just try all options lol

[harsh belfry]

I am completely lost right now. I'm not sure on where to start with this question.

Usually I'm given some rules to follow that give me an idea of what to do. But I'm unfamiliar with what steps to take given the information.

[placid zinc]

I'll use h instead of Δx for ease.

So f(x) = x³
What's f(x + h)?

[harsh belfry]

f(x^3+h) simplified

x^3+h

[placid zinc]

f is the "cubing function". That is, it takes its input, and cubes it

[harsh belfry]

||Brain fart moment sorry haha||

ok

in this scenario it would be

[placid zinc]

So what you've got above is wrong.
x³ + h is not the cube of x + h

[harsh belfry]

Would it perhaps be:
(x+h)^3

[placid zinc]

Very nice that's exactly it

[harsh belfry]

ahhhh

so when I am given the above question

`(x+hx)-(x)

   hx`

i would cube the entire thing?

or would I do this

(x+hx)^3

(x)^3

over hx

[placid zinc]

So you've got
f(x + h) - f(x)

        h

[harsh belfry]

only the top two would be cubed if im following your example

[placid zinc]

Which is quite different than what you've written, be careful

You've correctly identified that
f(x + h) = (x + h)³

[harsh belfry]

(x + h)^3 - (x)^3

          h

then I would simplify from there?

[placid zinc]

Then yeah! That looks good! You're good to simplify.

[harsh belfry]

oh sorry if I misunderstood, what happend to hx?

did the x get cancelled out

[placid zinc]

Sorry my notation change is confusing. I simply let Δx = h

So I could type faster

[harsh belfry]

👍

[placid zinc]

(You'll soon see that h is more standard for this variable)

[harsh belfry]

Thanks a whole bunch!

[placid zinc]

Good luck with it! Feel free to ask if you have any other questions about it.

[harsh belfry]

🙇‍♀️

[alpine sable]

Is there any reason why h is used often?

[placid zinc]

I have no clue haha

[harsh belfry]

Surprisingly my professor also uses h in class even when writing on the board.

Haha.

[placid zinc]

Can't mix it up with x like you can with Δx

Δx is pretty bad and only to teach that this is a "change"

But not sure why h is the usual

[alpine sable]

I think h usually represent some change in a variable as it approach 0

[harsh belfry]

I've been treating Δx the same as I would any other variable... am I wrong in doing that?

[placid zinc]

That's absolutely correct

[alpine sable]

While delta x is just some change

[placid zinc]

The limit will wipe it always

[harsh belfry]

Should I omit the x and always use delta?

^

[alpine sable]

not sure, but probably not since you need to be clear what change were talking about

[placid zinc]

Δx means "change in x" and is itself the variable

You can use any label you want though. Δ by itself would be weird but you could

[harsh belfry]

I'll just keep it the same then

I should absolutely be treating deltax as a single variable right

[placid zinc]

Soon you'll swap that to h and never look back

[harsh belfry]

so if my x in a question changes, does the delta stick around

is deltax seperate from regular x?

[placid zinc]

x and Δx are separate, yes

[harsh belfry]

got it!

Alright I will fill out the rest of this homework. I really appreciate it man!

❤️

[placid zinc]

Good luck!

[harsh belfry]

Sincerest thanks.

[glad blaze]

Its late at night by me and i cant think and scared to make mistakes, can someone help me with this one quik

[harsh belfry]

Just wanted to make sure (x+hx)^3 would turn into:

right?

@placid zinc

or would it actually be

[shut elk]

,wolf expand (x+xh)^3

[umbral hatch]

isnt it just 1.1+0.2 and 2.5+ 0.2 im probably very wrong or overthinking

[ocean seal]

Results provided by WolframAlpha

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

Requested by eis#1282

[shut elk]

thats what i thought.

but then the 160cm width information is superfluous.

[umbral hatch]

it said 2.2.1

maybe there are more questions

[shut elk]

yep, you're right, well noticed.

[glad blaze]

160 cm is 1.6m

[harsh belfry]

@shut elk ah so i should expand it as such?

[shut elk]

vin, you should use another channel

[glad blaze]

there are

[harsh belfry]

I was in this channel for the last 15 minutes

[umbral hatch]

oof

[shut elk]

ah my bad

yea didn't read, sorry, yoda should use another channel

i'm not familiar with functions so i can't really help with that

[harsh belfry]

all good.

[glad blaze]

Theres all of them

[shut elk]

Yoda, use another channel.

find a channel that hasn't been occupied in the last 15 minutes, as per #rules

[alpine sable]

It should be x³+h³+3x²h+3xh²

[harsh belfry]

ty!

[alpine sable]

Or I write cube expansion as x³+h³+3xh(x+h) its clean

[shut elk]

this makes sense to me, like we input (x+hx) into f(x)=x^3 right?

[alpine sable]

Ist h not hx
Cause they assumed ∆x = h

[shut elk]

ohhh

so (x+h)^3?

[harsh belfry]

yes so as it was explained to me
f(x+Δx) becomes

(x+Δx)^3

and Δx is treated as a single variable separate from x

[alpine sable]

Yes

[shut elk]

nice

[harsh belfry]

I was just making sure I wasnt an idiot

which it seems I was

thanks again for the clarification

[humble tinsel]

may i get a bit of help?

i am stuck at finding the poles of this thing

[dull iron]

hello

please i want to know how to calculate the intercept between an hyperplan defined by three points and the f1, f2, f3 axis. i want to know the values of a1, a2, a3.

[alpine sable]

stop fucking spamming ur question everywhere

it makes people wanna not help u

its not difficult to follow simple rules

[umbral hatch]

lol

[humble tinsel]

meanwhile im having a mental breakdown

i literally have no idea how to solve the integral posted up there

[sudden crypt]

so you need the poles?

[dull iron]

Sorry, i didn't read the rules

[humble tinsel]

i got the poles in the end

but im stuck at the residues part

i gotta solve it with residues

[sudden crypt]

hold on from where to where does your \gamma go?

[humble tinsel]

thats the part

i do not know

the module says where it goes

i do know the solution is the sum of the residues

i have the formulas

but i am stuck at finding them

i know the poles are +- radical of 2i

[sudden crypt]

Ah you can rewrite it to x^2 + (y-1)^2 = 2^2 so the way is a circle centered at (0,1) radius 2

[humble tinsel]

yea

[sudden crypt]

do you know the square roots of 2i?

[humble tinsel]

i kinda guessed

[humble tinsel]

in what way

the actual numbers

i do not

[sudden crypt]

oh, you need that

the square root of i is (1+i)/sqrt(2)

so square root of 2i is?

[humble tinsel]

2+i ...

/ sqrt 4

so 2+i/2

[sudden crypt]

well its sqrt(2) * (1+i)/sqrt(2) no? and thats just (1+i)

and actually you have 2 roots, +-(1+i)

[humble tinsel]

wait that makes things so much easies

[sudden crypt]

so which ones are inside of the circle?

[humble tinsel]

so lemme get it

imma write what i got

basically this

[sudden crypt]

yup

[humble tinsel]

and i've got two poles

next

the circle

[sudden crypt]

yeah, now which poles are inside the circle

[humble tinsel]

if its a cirle with the r of 2

[sudden crypt]

remember that you only calculate the residii which are inside the path

[humble tinsel]

yes

like so?

[sudden crypt]

its centered around (0,1) and it should be a bit higher

[humble tinsel]

oh yea wait

yea

now its coming togheter

so no z2

[sudden crypt]

thats centered around (1,0) but yeah, no z2

[humble tinsel]

i

am dumb srry

havent studied for a while

this is my first day back in it

i have a big test in a week

[sudden crypt]

anyway, do you know which order the pole at z1 is? you need it to calculate the residue

[humble tinsel]

fixed

order 2

[sudden crypt]

looks good 👍

yeah, do you have the formular then or do you need it?

[humble tinsel]

i have it

this one right

[sudden crypt]

yes

[humble tinsel]

i'll get to writing the residue

now do i just do the squares and stuff]

?

excuse my handwriting btw

i know im bad at it

[sudden crypt]

I usually do it by factoring out (z^2-2i)^2 so you can cancel

[humble tinsel]

i tought of it but how do i

[sudden crypt]

so (z-1-i)^2 (z+1+i)^2 since you already calculated the roots

and you said they were order 2

[mortal void]

is it free

[humble tinsel]

not really

[sudden crypt]

um busy channel?

[mortal void]

i need help on something very basic please

[humble tinsel]

im the one needing help here but i think there are other channels

[mortal void]

okay

[mortal void]

can you help me till then you get help yourself

really its so basic question i just need to confirm my doubt thats all

[humble tinsel]

im not the smart one here

[mortal void]

it will take few second thats all

[glass lichen]

Channel is in use.

[humble tinsel]

back to it

i didnt undestand what i need to do

i know i kinda need to simplify the thing under the fraction

but how do i do the factoring

[sudden crypt]

you have to factor $(z^2-2i)^2 = (z-1-i)^2\cdot(z+1+i)^2$

[ocean seal]

T0lgi01

[humble tinsel]

wow that is a equation bot

[sudden crypt]

well you factor a polynomial by multiplying all (z-root)

a TeX bot yes

[humble tinsel]

nice

so

[sudden crypt]

if you have a polynomial $x^3+6x^2+11x+6$ and you know the roots are $-1,-2,-3$ then you can factor the polynomial by $(x+1)(x+2)(x+3)$

[ocean seal]

T0lgi01

[humble tinsel]

OH

that cleared that up

[sudden crypt]

same spiel here, you know the roots are +-(1+i) and of order 2 so you know how to factor

[humble tinsel]

i got it

wait

do all residue exercices use this thing

[sudden crypt]

usually, thats the gist of doing (z-z0)*f(z)

[humble tinsel]

right there

its just the roots thing

holy cow

that is amazing

[sudden crypt]

it is

Fun Fact I have my complex analysis exam tomorrow

[humble tinsel]

i have it in a week

lemme do the thing now

[sudden crypt]

oh and sorry I have to prepare food now, I'm back in like 45 mins, hopefully somebody can help in the meantime

[humble tinsel]

im ok now

i literally can do the whole thing

i am baffled at my stupidity

have a nice day

thank you

and good luck on the exam

[alpine sable]

how is y = 2x - 2 exactly proportional

i thought b must be 0 for something to be proportional

[glass lichen]

directly proportional, yes

$y=mx+b$ with $b\neq 0$ is called partial variation

[ocean seal]

Mosh

[humble tinsel]

i got here in the end

i just wonder if its ok for it to end up as 0

[atomic whale]

Since Nobody Helps You On A Math Question On This Server Then I Should Leave This

Bye Daddy's

👋

[humble tinsel]

other than that im more than ready for this type of exercise

[alpine sable]

when is something that?

[glass lichen]

y=mx

is direct proportionality b/w y and x

[alpine sable]

but how is y=2x+2 direct proportional since b is set to 2 there

[glass lichen]

what?

[glass lichen]

i thought b must be 0 for something to be proportional

directly proportional, yes

[alpine sable]

well yes but the other thing

[glass lichen]

I never said y=2x+2 was directly proportional

so dont put words in my mouth

[alpine sable]

i mean

what makes a linear equation partial varistion

I haven't heard about that

[glass lichen]

Read what I wrote.

[alpine sable]

oh

[glass lichen]

If you're asking for help, you should be reading what's said

[alpine sable]

It was a fault by me, I didn't even notice that u wrote that

that should be pretty simple though, although i have a question pretty similar to this

[glass lichen]

No

[alpine sable]

how do you find the function for a line that is orthogonal to the function for another link

[glass lichen]

"another link"

[alpine sable]

That just proves how bad google translate is

I mean, if you for example have y = 2x + 3, how do you find the function of a line that is orthogonal to that

[glass lichen]

Are you given a point you want the lines to cross at?

[alpine sable]

Nope

[wary stream]

I think something along the concept of slope should be negative reciprocal

[alpine sable]

I need a function of another line that makes a right angle with the other line

[glass lichen]

Then you cant find an equation

[wary stream]

Y intercept would be hard to find though

[alpine sable]

yes but how

[quartz oxide]

Any two lines that form a right angle have slopes with product -1

If you have the original slope then you can find the req’d slope

[wary stream]

Isn't negative reciprocal? Not just negative

[quartz oxide]

Ok my wording might be a bit weird

[alpine sable]

give an example

[wary stream]

2, negative reciprocal is -1/2

[glass lichen]

dont ping me.

[wary stream]

Don't ping people

[alpine sable]

that's also easy, just turn the fraction around

2 = 1/2

[glass lichen]

no

2 != 1/2

[wary stream]

It's negative reciprocal

Dude stop

[quartz oxide]

He wants to get banned it seems…

Lmao bye

[glass lichen]

[alpine sable]

! means reciprocal? since 2 = 1/2 is not a true statement

[glass lichen]

no

2 does not equal 1/2

[wary stream]

No, it's means that statement is not true

[alpine sable]

that's what i wrote

[wary stream]

Notice how I labeled things

[glass lichen]

You said 2 = 1/2

[quartz oxide]

Dudes just messing with you lol

[alpine sable]

smhsmh

! means reciprocal? since 2 = 1/2 is not a true statement

[gray isle]

if you're familiar with basic coding, **!= **is what's used to denote not equal to

[alpine sable]

which is \neq in latex

[quartz oxide]

2!=2
True or false

[alpine sable]

but well okay

false

[quartz oxide]

Ok let’s be serious now

[alpine sable]

wtf? i've been serious all the time

[quartz oxide]

I mean get back to the problem

So if you know the slope of a line, you can find the slope of any line perpendicular to it

[alpine sable]

yeah how

[wary stream]

I told you how

[alpine sable]

tell it again then

[wary stream]

Negative reciprocal

[alpine sable]

how do you find that?

blocked ElYoni and reported

[quartz oxide]

I ripped this off the internet

[wary stream]

Like what Elon mass posted

[alpine sable]

bruh how tf do you you find the nehative value of that

[gray isle]

don't overthink this

[wary stream]

Use the original function given

[quartz oxide]

Kick this guy again bruh

[glass lichen]

eh, just blocking them

[alpine sable]

example 2x - 3

ye, just block them

[quartz oxide]

Slope is 2

[alpine sable]

reciprocal or whatever is 1/2

[wary stream]

Find the negative reciprocal of the slope

[gray isle]

yes, reciprocal of 2 is 1/2
now whats the negative of 1/2

[glass lichen]

<@&268886789983436800>

[alpine sable]

-1/2

[quartz oxide]

basically find x where 2x=-1
ok you got it

[gray isle]

that's pretty much it

the negative reciprocal of 2 is -1/2

[quartz oxide]

-1/2 is the slope of perpendicular line

[gray isle]

and note that if you multiply 2 and -1/2 together you'd get -1

[alpine sable]

and you always need the negative reciprocal?

[quartz oxide]

That’s the rule

[alpine sable]

yes since negative reciprocal equals -1 and positive reciprocals equals 1

[wary stream]

To find a perpendicular line to the original, yes

[gray isle]

i mean its the relationship of non-vertical/horizontal perpendicular lines

[alpine sable]

reported to ModMail for good reason

[gray isle]

yes since negative reciprocal equals -1 and positive reciprocals equals 1
what?

who said anything about negative reciprocals and positive reciprocals equalling -1 and 1

[alpine sable]

the reciprocsl of 173 is 1/173 and the negative reciprocal of 173 is 1/-173

[gray isle]

yes, last i checked 1/173 and -1/173 aren't 1 or -1

[alpine sable]

no

that's now what i meant

[wary stream]

You're going to confuse yourself even more with random statements like these

[gray isle]

write what you mean clearly, otherwise we're not going to know what you mean or whether you actually understand

[alpine sable]

the reciprocal times the number you took the reciprocal value of is 1 if you don't change it to minus and stuff

[gray isle]

yes

$a \times \frac{1}{a} = 1$

[ocean seal]

ℝamonov

[alpine sable]

Yes

so, the function of a linear line that is orthogonal to y = 2x + 3 is -1/2x + b

do you put the minus before 1 or 2 here?

[gray isle]

doesn't matter

$-\frac 12 = \frac{-1}{2} = \frac{1}{-2}$

[ocean seal]

ℝamonov

[gray isle]

the leftmost form is preferred

[alpine sable]

alright

[gray isle]

also -1/2x is sucky notation

you're better off just writing -x/2

[alpine sable]

what if you were to find the reciprocal value of -1/2x and 1/2x

[gray isle]

just apply the definition of the reciprocal

[alpine sable]

imma just notate it like this for now

[gray isle]

the reciprocal of a is 1/a

simplify the result if needed

[alpine sable]

yes, that's easy for me to remember

[alpine sable]

1/-0.5x and 1/0.5x

[wary stream]

Are you trying to take the reciprocal?

Because that's wrong

[alpine sable]

yes

[wary stream]

You just took the negative of that value

[gray isle]

ugh this is why that notation sucks

$-\frac12 x$ is your original expression. are you trying to take the reciprocal of the whole thing or just the coefficient and then multiply that back to x?

[ocean seal]

ℝamonov

[alpine sable]

oh it must be an error that x is there

what is the reciprocsl of 1/2 and -1/2 and 3

[wary stream]

$$a \implies \frac{1}{a}$$

[gray isle]

eeep

[wary stream]

That's the reciprocal

[rigid wind]

are we still in the og problem of finding perpendicular slopes or just 1 divided by things

[gray isle]

bad eq sign

[ocean seal]

dldh06

[gray isle]

$\text{reciprocal}\br{\frac ab} = \frac ba$

[wary stream]

Better?

[ocean seal]

ℝamonov

[alpine sable]

reciprocal of 1/2 is 2/1 and 3 is 1/3 and -0,5 is 1/-0,5

[gray isle]

2/1 and 1/-0.5 can be simplified

[alpine sable]

2 and -2

[gray isle]

yes

[alpine sable]

but

If you for example had y = 3x + 2 and you were to find a function for a linear equation that is orthogonal to that line

It's always the negative reciprocal?

so 1/-3x and not 1/3x

[gray isle]

yes, it will pretty much always be the negative reciprocal (unless you have horizontal and vertical lines)

that's the property of orthogonal/perpendicular lines

[alpine sable]

So the function of the line that is orthogonal to y = 3x + 2 is y = 1/-3x + b? Right? How do you find b though?

is that impossible?

[rigid wind]

only the slope determines orthogonality

infinitely many b

[alpine sable]

so all b basically works?

[rigid wind]

imagine dragging the line along the other line

so they intercept at different point

but don't change the orientation

are they still perpendicular?

[alpine sable]

it doesnt matter what b is basically ok

they will still hit each other

but

[wary stream]

This channel is busy

[alpine sable]

how do you find the function of a line that is parallel to y = 3x + 2

[rigid wind]

paralel = same slope

intuitively

again, b only determines intercept, the "angle" or "orientation" of the line is determined by slope

[quartz oxide]

so the line ur looking is y=3x+b for some b

[wary stream]

A parallel line has the same slope to the original

[quartz oxide]

(But preferably, y’know, b≠2)

[alpine sable]

so it is a must they have the same slope but you can choose all b values

[merry idol]

Could someone explain this to me?

[jade birch]

you need help finding x?

[merry idol]

Yes.

[shut elk]

rule of multiplication and rule of subtraction for logs

logs

i think.

[jade birch]

for the second log apply rule for the powers

[merry idol]

Should I put 10 as the base?

[jade birch]

Yeah

when the base is not mentioned it is 10

[wary stream]

Yes, if no base is there, it's normally assumed as a base of 10

[jade birch]

After that this is a quadratic in disguise

let m=log x

[merry idol]

So should I put "(log 10^x)^2"?

[jade birch]

and then solve for m and then for x

[wary stream]

You don't have to write $\log_{10}$ every time

[ocean seal]

dldh06

[wary stream]

Leaving it as $\log$ is valid too

[ocean seal]

dldh06

.itsjustnai

[jade birch]

is what want

[merry idol]

I'm confused. SAHUSHAUSAH

[jade birch]

Ok look

[quartz oxide]

This is all you need actually

[jade birch]

forget the base

totally irrelevant for now

[jade birch]

what you need to do is apply this to the second term

[wary stream]

<@&268886789983436800>

[jade birch]

<@&268886789983436800> rules say no self promo?

[sly mantle]

b&

[jade birch]

ty 🖤

[merry idol]

Let me see if I'm right...

So should be "2 * 4 log x" ?

[jade birch]

go to another channel, read #❓how-to-get-help

[jade birch]

yes

8logx is what you end up with

now ur whole expression is

[merry idol]

And with the first term I do the same?

[jade birch]

log²x-8logx=0

no

the first term the logarithm is squared, not the x

[merry idol]

Right, right.

[jade birch]

that rule only applies for the things inside the log, not the log itself

does this remind you of a quadratic?

[merry idol]

Bhaskara?

[jade birch]

if you let logx=m, you get m²-8m=0

[jade birch]

what

[merry idol]

Formula of Bhaskara.

Quadratic function?

x = b^2 +- ...?

[jade birch]

ax²+bx+c=0

this

[merry idol]

Oh

Yes, yes.

I understood.

[jade birch]

a=1, b=-8, c=0

[jade birch]

so now solve for m

[merry idol]

OH!

THAT'S IT!

[jade birch]

Got it?

[merry idol]

Magic, really.

HAHAHAHAHAA

I got it.

[jade birch]

Nice

[merry idol]

Thank you

[jade birch]

No problem

[merry idol]

@jade birch
So the answer is -8?

[ionic jewel]

A = 3,2,1
B = 2,1
C = 1

think that should disprove it untill my mental math is gone

[jade birch]

No, it's 8

[alpine sable]

-8 would give you 128 lol not a solution

[jade birch]

But that's only for m, you need to sub back what m already is, and that is logx

[merry idol]

I used this:

[alpine sable]

quick question to settle an argument: if you do a 1/100 thing twice, is that 2 1/100 chances or 1 2/100 chance

[jade birch]

you dont have to

lets look at
m²-8m=0

[alpine sable]

just solve through intuition

[jade birch]

you can factor an m and get m(m-8)=0

from there m=0 or m-8=0

[gray isle]

can you show the quadratic formula led you to m=-8

[jade birch]

because A×B=0 is true if A is 0 or B is 0

[merry idol]

Yes...

[jade birch]

Also yeah, can you show how you got -8

[merry idol]

I used delta, and I got b ( b = 8) ^2 - 4ac (a = 1, c = 0)

8^2 = 64
4 * 1 * 0 = 0

64 - 0 = 64

[jade birch]

yep, delta is indeed 64

[merry idol]

x = -8 +- root of 64/2*1

[jade birch]

there

[merry idol]

(x = -8+-8/2*1)

[jade birch]

your b is -8

not 8

[wary stream]

[jade birch]

so -b would be just - (-8)

[wary stream]

@merry idol

[wary stream]

For this

[merry idol]

So I will have two x?

[wary stream]

Use parentheses

[jade birch]

of course

a quadratic equation has two solutions

[merry idol]

So this is the result?

[jade birch]

what are you refering to?

[merry idol]

x1 = (8+8/2) = 16/2 = 8
x2 = (8-8/2) = impossible

[jade birch]

ey buddy, for real, use

[wary stream]

That's possible

[gray isle]

[wary stream]

But legitimately use parentheses

[jade birch]

and yes ur half correct

but please

m1=8 and m2=0

[gray isle]

use parentheses properly

[wary stream]

Not like that

[gray isle]

\verb|8-8/2| reads as $8 - \frac82$

[ocean seal]

ℝamonov

[wary stream]

Parentheses for fractions

[jade birch]

x1 = (8+8) /2 = 16/2 = 8
x2 =(8-8) /2 = impossible 0

this is what we mean

[merry idol]

But why 0?

[jade birch]

because you get 0/2

[gray isle]

what's 8-8

[jade birch]

that's just 0

[merry idol]

8-8 = 0
And (0/2) = impossible

Not?

[gray isle]

no

[jade birch]

not yet

[gray isle]

why would 0/2 be impossible

[jade birch]

we are solving a quadratic

forget the logarithms

[wary stream]

If it was divided by 0, then that's impossible/undefined

[merry idol]

How I determine what is 8 and what is 0?

[jade birch]

It doesnt matter which is which

[wary stream]

What do you mean?

[gray isle]

wdym

by determine what is 8 and what is 0

[wary stream]

Those are the solutions to that equation

You have two solutions

[rigid wind]

did we really go from m^2 - 8m = 0 to here?

[jade birch]

wdym?

[merry idol]

But these two solutions should be put how in the log?

[jade birch]

we havent gotten there

tell me

do u understand why 0 is a viable solution?

[merry idol]

Because any number times 0 is 0.

[wary stream]

One at a time

[jade birch]

Yeah

So now we can move one

we're doing it one by one

FIRST: m1=8

Can you do this one alone?

[wary stream]

You plug in 0 as x, simplify, then x = 8

Or whatever order

[jade birch]

Also

can I please clarify

[woeful stag]

R we solving a quadratic here

[merry idol]

[jade birch]

that m1=8 and m2=0 NOT x1 and x2

[merry idol]

Where did m1 come?

[jade birch]

jesus

can

yall just

[woeful stag]

Lol this chat is getting tense

[jade birch]

take a break

for fucks sake

thank you!

@merry idol lets move back a bit so u underatand where m1 and m2 got there

we got to this point

log²x-8logx=0

remember this?

[merry idol]

Yes.

[jade birch]

Now, we said, let logx=m, and everywhere we saw logx we wrote m instead

and got to

m²-8m=0

[merry idol]

Yes, yes.

[jade birch]

and a quadratic was born

and we solved that quadratic right?

[merry idol]

Right.

[jade birch]

what were the solutions to it

[merry idol]

8 and 0.

[jade birch]

m1=8 and m2=0

indeed

but we still need to find x

[merry idol]

Ah, I understood this.
You changed x of quadratic to a m.

I was lost, but now I undestood. shauhsuas

[jade birch]

okay

yes thats what we did

Now we have m and x right here

m=logx

and you know that in one case m will be 8 in another one m will be 0

from the quadratic we solved

[merry idol]

Yes.

[jade birch]

So now you take m=8 and substitute it in m=logx and solve for x

Can you solve for x by yourself?

[merry idol]

No.

[jade birch]

so first we know that m is 8 so we can write
8=logx

right?

[merry idol]

Right.

[jade birch]

now what's confusing you here

the base is 10

[merry idol]

0,8?

[jade birch]

why the 0?

we're solving for 8 right now

That's another case, or equation if you would, that we'll solve later

[merry idol]

Okay.

[wary stream]

This whole substitution process you did made it confusing

[jade birch]

well rip me then

Are you aware of this logarithm property

[wary stream]

@merry idol Repost the problem, please, so no need to scroll

[jade birch]

$\log_{a}{b} = c <=> a^c=b$

[ocean seal]

.itsjustnai

[woeful stag]

First off, define the restrictions for the problem

What range are we limited to? @merry idol

[jade birch]

...

i love you all

[merry idol]

HAHAHAHAHAHAHA

[woeful stag]

Am i far back from where you are right now?

[wary stream]

I would have factored out a log then zero product property, instead of this substitution method

[woeful stag]

Lol

[jade birch]

i was gonna explain the range when we got to m=0

[jade birch]

literally same thing

[wary stream]

So log x (log x - 8) = 0

It's less confusing

[jade birch]

Go ahead

[merry idol]

m = 0
m = log x
log x = 0?

I'm getting crazy. HASHUAHSUAHS

[woeful stag]

Let m = log x, now use that variable to solve the quadratic

[wary stream]

Because you added in more letters like m and now we have to keep track of m

[woeful stag]

@wary stream well writing it down helps

[jade birch]

he is writing it down

but man

look,

I'll write it all out in detail for you

because I can't keep doing this with everyone throwing in different ways to solve the same thinf

[wary stream]

I'm just saying, throwing in more letters and substituting can get overwhelming

[woeful stag]

My bad you go ahead

[jade birch]

i understand

go ahead

continue

because Im not

[merry idol]

;-;

[woeful stag]

Luis, i believe you understand that if at least one factor is = 0, then the whole expression = 0

So in our case -> log x * (log x -8) = 0, we have two factors, can you point them out for me?

[merry idol]

I don't read in English very well. SHAUSHAU

[woeful stag]

What language?

[merry idol]

Portuguese.

Two factors... "log x"

And "(log x - 8)"?

[woeful stag]

Yes exactly

[merry idol]

Ok.

Then?

[woeful stag]

Exactly this ^

The idea is to find where logx = 0

And logx - 8 = 0

And if it fits the restrictions, then it is a solution

[merry idol]

Ok... I will see it again to be sure that I understood.

Thank you all, friends.

[wary stream]

I know that you're helping but try to prevent from giving out full solutions and work

[jade birch]

can you please let me buy you a gun so you can shoot me dead

[woeful stag]

Yeah, i get youve been working on this for a while but i have to agree with dldh here

[merry idol]

Thank you, .itsjustnai.

You have patience.

[jade birch]

it is not giving out full solutions because this is just everything that I explained step by step written out neatly.

a summary if you would

[wary stream]

Still, don't do people's work for them

[jade birch]

I'm not?

[wary stream]

You kinda did by doing the whole thing

[jade birch]

Wouldn't have had to if I was allowed to explain

[wary stream]

Your explanation was kinda convoluted

[alpine sable]

Can someone help me with this? I'm following this video https://www.youtube.com/watch?v=QJW6qnfhC70 and on 4:29 it says 16 * .8125 is 1. But when I do this on a calculator it gives me 13 instead. How are they getting 1? Please @ or DM me since messages can get lost

[lilac lantern]

i dont see any "16 * .8125" multiplication in the video

[wary stream]

He's doing 29/16

[alpine sable]

Yes but how is he getting the 1 unless he is not including the digits after the point?

There is multiplication, in the audio he explains he multiplied 16 by .8125 to get 13, so I understand better now

[wary stream]

So the audio is correct?

But writing is not?

[lilac lantern]

oooh

thats the remainder

16* .8125 to get the remainder

29/16 = 1.8125 = 1 remainder 13 if you were to do the division by hand

[alpine sable]

Yes the remainder is 13 but where is 1 coming from?

Hmm

[wary stream]

The quotient

[lilac lantern]

yup

[alpine sable]

I see

Alright, thanks!

[lilac lantern]

np

:D

[alpine sable]

;D

Hayo

[gray isle]

draw a proper diagram

you should have some compass axes with indications of where North is, the location of the boats and port etc

[mystic sinew]

Anyway to further simplify this?

[sage bronze]

yes

[mystic sinew]

Other than making bs power negative

[sage bronze]

use $\log_a (xy) = \log_a x + \log_a y$

[ocean seal]

HELLOBELLO

[mystic sinew]

no I am trying to go in the opposite direction

[sage bronze]

ah

ok

[mystic sinew]

is what I started with

[sage bronze]

alr then it looks like

thats all u can get to

i thiink

[mystic sinew]

I could probably take x out out tho

like (c^x)/(b^x) = (c/b)^x

[sage bronze]

ok wait lemme

check

[mystic sinew]

ah yeah

[mystic sinew]

you can simplify this further

if you take x out at the start

and then multiply c/b and (1/b)^logwhatever

[sage bronze]

hmm

[grave saddle]

can someone help me simplify this

exclude the 6.
its the question

isnt it just a standard a/b * c/d = ac/bd

[whole herald]

you can try taking out common factors

for example

2x-8 = 2(x-4)

and then you can cancel out terms

[grave saddle]

i did not think of that

i see the solution now. thanks man

[whole herald]

np.

[gleaming sandal]

Hello

Can someone please double check my answers? Ty in advance

[fluid moth]

Hi - can someone please help me understand what a unit is in statistics?

i believe that the unit is the measurement of the observation - does that sound correct?

im covering statistical variables right now and this is the definition that is provided:

[ancient saddle]

Hello, ii and vi are wrong

[fluid moth]

actually saying this out loud kind of helped... so Unit could mean:

population of 100 people
unit is the most basic building block of the population / 100 people

unit in this case is one person?

[gleaming sandal]

Really? Could you please help me find the error

[ancient saddle]

I think that's correct

it coincides with "a member of the population"

[gleaming sandal]

@ancient saddle I fixed ii to 6

But I still see no problem with vi

[fluid moth]

thank you ! it makes sense to me now because immediate after comes in the descriptions of population and samples. so i envision "unit" to be the basic building block that makes up the population we are interested in analyzing

[ancient saddle]

Ok, it's correct, for vi notice that there is a horizontal asymptote as x approaches -infinity

[gleaming sandal]

Oh!

I see it now

Is 1 correct?

[ancient saddle]

yes 👍🏽

[gleaming sandal]

Thank you

[formal dock]

Is this channel busy?

Could someone help me with this

[topaz scaffold]

Horizontal line test

If the line only crosses a 1 point then you only have 1 solution for x

[formal dock]

Thanks

[stark wadi]

quick help anyone?

[final ember]

Interior and exterior angle

a is 90 cause its supplameteraly

[stark wadi]

i forgot how to use exterior to solve

a and b is 90 i got both

[final ember]

yes

[stark wadi]

e 132??

[final ember]

c is 180-138

cause its also supplementary

[stark wadi]

Alr

[final ember]

do same thing. Get d to solve for e

nvm its not exterior and interior

only supplementry angles

[stark wadi]

is e 132

so d 48