help-27

[tame palm]

That's written on Onenote for Windows.

No worries. It happens. That's why there's the meme. 😉

[glossy solar]

alright, thank you so much kookiemon. i apologize for the 5th grade math hassles

the music stopped when my foster mother stepped in

@tame palm tysm

.close

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[formal torrent]

can u do smth with this or do u have to calculate all of it or is it just 0

[restive river]

transpose matrices?

[formal torrent]

yea

[restive river]

it is 0

[formal torrent]

okay ty

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[formal sierra]

where did he get sqrt(2)/2 from

both x and y

[uncut yew]

Unit circle

[winter torrent]

,tex .unit circle

[woven radish]

[formal sierra]

do i need to know thag

[uncut yew]

Yes

[winter torrent]

tbh yeah at least the first quadrant is worth memorizing

[devout snow]

@formal sierra Has your question been resolved?

[formal sierra]

yeah i am familiar about the first three on the first quadrant. but do i need to know why it is that value?

also, what if i get a question that asks me to find the value of an angle that is not the first three

[devout snow]

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[toxic meteor]

Can someone help me with these 2?

[toxic meteor]

Or at least help me find the vision

[devout snow]

@toxic meteor Has your question been resolved?

[toxic meteor]

<@&286206848099549185>

[toxic meteor]

^

I just need a formula or something I’m lost

[toxic meteor]

What formula do I use for this one

<@&286206848099549185> please 😭

I just need a formula

[supple knot]

Did you look in your notes/book for average velocity

[toxic meteor]

She didn’t teach this section

Cuz we’re “supposed to know it”

💀

[supple knot]

The one inside red box

Your y is the image's s

Watch the video if you're still lost
https://youtu.be/AwxT1xjMP9g?si=1h8cDrZ1S-50nGCR

[toxic meteor]

Thank you bro

🙏

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[little helm]

QUICK QUEStion

[little helm]

next month i will study maths in university

and i wanted to ask how i can prepare myself optimal for analysis 1

[vapid nest]

honestly I just read rudin

wonderful dude

you can get urself a free pdf

[little helm]

and which device i should buy some of my friends said 2in 1 tablet for excel and writing and other said ipad

[little helm]

what do you mean by rudin?

[restive river]

I'm not saying that rudin is bad, but its style is too dry for me.

[vapid nest]

"principles of mathematical analysis"

by rudin

[little helm]

ok

i will look

[little helm]

but?

just suggestions

[vapid nest]

just get a laptop

eventually learn how to latex

and get some notebook scratch paper

[little helm]

is it dificult?

[vapid nest]

no

[little helm]

do you have some good laptops for 600-800€?

[devout snow]

@little helm Has your question been resolved?

[sturdy mango]

try buildapc discord

[little helm]

kk i will

and do you guys habe any tips for maths study

for example my perfomance is underwhelming even if i try hard

[agile elbow]

The only tip for maths is practice

and never lose patience

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[tulip cave]

How do I do question 8

[supple knot]

Simplify then use power rule twice

,tex .exp rules

[woven radish]

pizzanator

[tulip cave]

x^1/2 (x^1/2 +1) ?

[supple knot]

Yes

[tulip cave]

How do I do question 9

.close

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[vivid estuary]

You have gone for a four mile run. You ran the first two miles at 12 mph. You ran the last two miles at 10mph. What was your average speed over the entire run?

[vivid estuary]

This is just 4/(30/11) = 10.91 right?

[lyric hornet]

[vivid estuary]

I'm not exactly sure why either but I understand why its 10.91 lol

is (initial speed + final speed)/2 not allowed here?

I got 10.91 from total miles over total time, he ran 4 miles, and first half he ran at 12mph thus it takes him 1 hour to run 12 miles thus he ran for 1/6 hours and same reasoning for the second part, he ran for 1/5 hours

4/(1/5 + 1/6)

@lyric hornet do you know why 11 is incorrect

ah

is it because we dont not have a straight line

but a piece wise function

so we can not use that formula

wait nvm

[lyric hornet]

^ this is correct :)

[vivid estuary]

why ins't (10 + 12)/2 correct

[lyric hornet]

that would assume you spent an equal amount of time running at 12 mph nad 10 mph

whereas here you have only ran the same distance at those respective speeds

not necesairly the same amount of time

[vivid estuary]

hm ok I think I see

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[restive river]

pls help <@&286206848099549185>

[acoustic leaf]

your inequality signs are backwards, -5 is not greater than 5

[restive river]

oh is it like this -5<x<5?

does this work (-5,5)?

yes but it seems that 5 and -5 are included in the interval

wdym

-5 and 5 are in the interval

-5<x<5 means -5 and 5 are out of the interval

but its using parentheses

oh... we did it differently at my school, my bad

still dont work

anyone know what i did wrong

yeah

i just reread the question

it says an absolute value inequality

[uncut crow]

tf

mold in help channel

[restive river]

so like | x |

you know how to turn -5<x<5 into an absolute value inequality?

no

how

well for starters

| x | < y

this would be the same as saying

x > -y AND x < y

or in the words; -y < x < y

oh so how does it go with -5 and 5?

[restive river]

substitue 5 for y in this equation

| x | < 5 like this?

yup

okay lemme check

it worked tysm

you're the first person ive ever helped 🙏

good job

so how do i exit the help room

do .close

.close

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[stark shuttle]

Hello

[stark shuttle]

@strange arch

Sorry for the ping but is this a good explanation?

From earlier

[uncut crow]

it would be better to give a counterexample

i would not call this a proof

[stark shuttle]

I'm not doing discrete mathematics though

[uncut crow]

so what loll

[stark shuttle]

Meaning this is sufficient

[dense lynx]

[uncut crow]

okay i have no further comment then lol

[stark shuttle]

Thanks for the rec but we can take this easy 😉

This is only calc 1

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[vast violet]

why is cos being used ?

sry

i see why it is negative becuz its going to the left

but why Cos60

cos just adj/hyp???

[flint spire]

because Bx is adjacent to the angle, it is not opposite to it, cant bee Sin(60°)

Sin(60°) would be for By

[vapid nest]

yes but we are multiplying by the magnitude of the hypotenuse (thus cancelling it out)

to get the magnitude of the adjacent side

which would be $B_x$

[woven radish]

nosqldb

[vast violet]

ohhh

[vapid nest]

mhm ".close" if that answered ur doubt

but I'm still here if you need more guidance

[vast violet]

thank u so much

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[gentle wagon]

is this correct

i said positive on all of them cause the derivative of e^x is always e^x and e^x is never negative

[rich lintel]

yes

assuming x is real that is

[gentle wagon]

yep

ok what about this

[rich lintel]

uh i think so but im not sure about the concave up/down because the function could be concave down on another part

but i might be reading too much into it

[gentle wagon]

ye i think its right cause my textbook says this:

f'(c) is < 0 and f''(c) is > 0

[rich lintel]

the relative max/min stuff is right

[gentle wagon]

oh

[rich lintel]

im just not sure about concavity because it doesnt specify where

[gentle wagon]

i said concave up cause i think its increaing

f'(3) = 0 and f''(3) = 2

f''3 is greater than f'3 so i guess that means increasing?

[rich lintel]

when the second derivative is greater than zero the function is concave up at that specific point, issue is the question doesn't specify where the function is concave up so you can have a portion of the function be concave down, while at x=3, the function is concave up.
also increasing is only when the second derivative is greater than zero

[gentle wagon]

ok so im half right😭

[rich lintel]

a function doesn't have to be necessarily concave up to be increasing

so you can have dy/dx>0, but d^2y/dx^2<0, and that would look like a logarithmic function

[gentle wagon]

hm

but its likely that this doesnt apply here

[rich lintel]

yeah i would say try what you had

if not then it would be that f is both concave up at one point and concave down at another since it doesnt specify where on f it is concave up/down

[gentle wagon]

i see

what abt here

i think its false

cause 1/0 is undefined

and no matter the derivative its always undefined when x = 0

undefined isnt a point of inflection

[rich lintel]

yeah, its a defined point where the second derivative changes signs

and at x=0 its undefined

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[undone bane]

The first 5 terms in this sequence are d(1)=1, d(2)=2, d(3)=6, d(4)=24, d(5)=120. We are wondering what type of sequence it is. The answers are arthetic, geometric, and neither. I'm leaning torward neither but I feel like it could be geometric because of the pattern with the growth factor where its like x/1.

[supple knot]

Try finding a growth factor

[undone bane]

wdym?

2,3,4,5?

hello?

[supple knot]

This growth factor isn't a constant

So it's not geometric

[undone bane]

ok

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[torn rock]

Working with negative/fractional exponents. -12^2 x^-5. Why is the final answer negative (-144/x^5)?

[torn rock]

Shouldn't -12^2 be just 144? Making it 144/x^5?

[acoustic leaf]

the conventional order of operations says -12^2 = -(12^2)

[smoky nimbus]

$-12^2 \neq (-12)^2$

[woven radish]

CaptainNova22

[tame palm]

By convention, the negative sign is not part of the value that is being raised to the second power.

[torn rock]

got it, thanks

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[thin wren]

what's the formula for this
bc its a sphere its a 3d space

[acoustic leaf]

the electric field due to a uniformly charged sphere outside that sphere is the same as the electric field due to a point charge with the same center and charge

[thin wren]

can I get the formula?

[acoustic leaf]

the formula for the electric field of a point charge is given by coulomb's law

[thin wren]

Kq/r^2

for point charge

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[sturdy mango]

is it possible

[sturdy mango]

to use PnC

for these?

anyone with idea of stereoisomerism?

[supple knot]

What's PnC

[sturdy mango]

permutation and combinations

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@sturdy mango Has your question been resolved?

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@sturdy mango Has your question been resolved?

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[rain imp]

Question 16

[visual hazel]

,rcw

[fervent hornet]

use the properties of the sum of angles in a triangle

[rain imp]

Sum of all angles is 180?

[fervent hornet]

yes

[rain imp]

So definitely not equa triangle

I chose none of these in the exam

[fervent hornet]

its c

[rain imp]

Ok thanks

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[lament schooner]

whats tr ( ) in linear algebra

[lament schooner]

is it At

[visual hazel]

should be trace, which is the sum of the diagonal elements

[lament schooner]

okay ty

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[marble quail]

$M={(x,y); x^2-y^2 \le 2}$

[woven radish]

Merineth

[marble quail]

Does someone know how I go about drawing the graph for all x and y?

$\frac{x^2}{2} - \frac{y^2}{2} \le 1$

Not sure if this helps

[woven radish]

Merineth

[rotund umbra]

https://youtu.be/TSapwHbI9EQ

You can plot the graph for equality, and then pick another point to test if the equality is that side.
For example, x^2 - y^2 <= 2 at x=0 and y=0, then that's the side the inequality holds..

[marble quail]

Watched it and don’t get it

When y = 0 x has to be sqrt(2) that I know for certain

If y = 2 then x = sqrt(6)

I guess that’s a way to graph it?

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[wooden pike]

We must simply this. The tutor (video) has solution: \frac{20c^2}{9a^2}

My solution is \frac{5}{9a^2}

[stone stump]

god these fractions are awful to read

you probably misread them. which is easy to do

$\frac{\left(\frac{2c}{3a}\right)}{\left(\frac{\left(\frac{3a}{5}\right)}{2c}\right)}$

[woven radish]

Denascite

[stone stump]

well ok maybe a bit too many parentheses

[wooden pike]

There is a fragment where they show you how they get to 3a/10c. But if I use this way to solve another problem, it's completely false

[wooden pike]

ok like this indeed

[stone stump]

well then you probably misapply it

$\frac{\left(\frac ab\right)}{\left(\frac cd\right)} = \frac ab \cdot \frac dc$

[woven radish]

Denascite

[stone stump]

thats what they are doing

[wooden pike]

Yes, I understand. Thanks for the clarification.

So you come to the same solution as the teacher?

[stone stump]

yes

but like tbh, the notation is just garbage

[grand siren]

tbh my solution to this is "go yell at the person who wrote that mess of fraction lines until they write brackets in", but given the interpretation that they obviously intended (obviously based on what the rest of the solution is like, i would not have guessed it just from looking at the problem), yeah 20c^2/9a^2 looks right

[stone stump]

it could also nearly be $\frac{\left(\frac{\left(\frac{2c}{3a}\right)}{\left(\frac{3a}{5}\right)}\right)}{2c}$

[woven radish]

Denascite

[grand siren]

yeah that's what i initially thought

[stone stump]

I think the one fraction dash is minimally longer

but its barely visible

[grand siren]

$\frac{\frac{\frac{2c}{3a}}{\frac{3a}5}}{2c} \neq \frac{\frac{2c}{3a}}{\frac{\frac{3a}5}{2c}}$

[stone stump]

its just bad notation

[woven radish]

bee [it/its]

[stone stump]

very easy to mess up reading it

[wooden pike]

Oh yes I think I misread it then

They gave us this bs after that. I got up with 150ab/18 but it was a/3b

[stone stump]

thats much clearer

[wooden pike]

ah yes

I got it now too

i've misread the first one

thanks @stone stump @grand siren

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[hybrid kayak]

I need help with vector valued functions and curves

[hybrid kayak]

Aren't these supposed to be tangent?

Did I do anything wrong?

g(t)=(4sint, cost(t))

isn't the derivative supposed to be the tangent vector to the curve at g(t)?

[sullen island]

yeah

how did you draw that ?

@hybrid kayak

[hollow ice]

The red vector looks like it points to the end point of the gamma'(t) vector

[sullen island]

ah yeah right

[hollow ice]

so I think red = gamma'(t) - gamma(t)

[hybrid kayak]

the red is supposed to represent gamma'(t)

[hybrid kayak]

do you mean the code?

[sullen island]

if you have it sure

[hybrid kayak]

I can share it after I finish fixing it

But I just copied from a bunch of people

[sullen island]

what bacterio is getting at I think, is that if you want to draw the derivative vector like this

you need the starting point of the red vector at gamma(t), which you did already

but the end point should be gamma(t) + gamma'(t)

if you want to translate the vector from the origin, you also have to translate the endpoint

[hollow ice]

All the vectors are starting at origin, and should be moved to the tip of gamma so they help visualize what they represent

[hybrid kayak]

ooooooooooh

ok thanks

I miss interpreted this so bad

Imma try to fix this and share it here

I think I got it

Now I have to change the other vectors

The other*

not brown = gamma(t) + gamma''(t), right?

gamma''(t) starting at the origin

[sullen island]

well you could start the brown vector after the red if you want

to continue like you did for red and black

i.e. brown starts at gamma(t) + gamma'(t), ends at gamma(t) + gamma'(t) + gamma''(t)

[hybrid kayak]

but brown is the acceleration

and the book places it at the tail of gamma(t)

[sullen island]

alright if you want

[hybrid kayak]

It looks kinda ugly ngl

the vector goes right back to (0,0)

Maybe I should pick another example

because I used t=pi/4

and then sint = cost

[devout snow]

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[woven radish]

l'agit

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[broken hinge]

not really sure how to deal with that last question. i figured it would just be <-489,592> but i guess not

[drifting sierra]

Are you given a definition of proj?

[broken hinge]

its the projection of vector v onto vector b

i havent been told what v or b is though

[drifting sierra]

By definition I mean some kind of formula involving v and b

[broken hinge]

no, i havent

[drifting sierra]

Ok so I guess this is an exercise to build up to a formula and maybe some intuition

Do you understand, geometrically, how to make a projection?

[broken hinge]

yeah, mostly

[drifting sierra]

So what do proj_b(v) and b have in common?

[broken hinge]

vector b right?

[drifting sierra]

Yes

I mean what property do these two vectors share

[broken hinge]

not sure what you mean

[drifting sierra]

$proj_{\textbf{b}}(\textbf{v})$ is one vector, $\textbf{b}$ is another

[woven radish]

Nel

[drifting sierra]

They share a property

[broken hinge]

oh ok

[drifting sierra]

What are some properties of a vector?

[broken hinge]

you mean like magnitude, direction?

[drifting sierra]

Yes

[drifting sierra]

So what do these two have in common?

[broken hinge]

ohh wait nvm i figured out the answer im so dumb

.close

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[tulip cave]

Lowkey don’t understand how my teacher did any of these questions and where she pulled out the 3 from 😞

[agile elbow]

In which question, do you have the problem with 3 ?

[fervent hornet]

which part are you confused on?

[tulip cave]

First one

[agile elbow]

She just put the value of x = 3

[safe inlet]

you just use the formula of a derivative

nx^n-1

[tulip cave]

Right but where did the magical 3 appear from

[safe inlet]

she just might've used a random value

or the question might've asked the value of f(3)

I mean f'(3)

[tulip cave]

What about this question

Idk how to do this

[safe inlet]

oh that

use this formula

nx^n-1

and after you can just plug in t = 2

[agile elbow]

So you are given the equation of displacement here and you have to find velocity at a particular time. To find velocity from displacement equation you Just have to differentiate it, after with you will get 12-10t. Then put the value of t = 2 sec

[fervent hornet]

know that the derivative of s with respect to time gives the velocity so you differentiate s wrt to t to get the equation for velocity them plug in t=2

[tulip cave]

Is it -8 ?

The answer I mean

[safe inlet]

-2

It's 2

[tulip cave]

Oh

[safe inlet]

my bad

[fervent hornet]

yes

[safe inlet]

when you differentiate displacement you get velocity of particle

[agile elbow]

@tulip cave All understood? Any doubts?

[tulip cave]

Yess I think I get it now

Tyyyy

[fervent hornet]

close the channel if you are done

[tulip cave]

.close

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[tulip cave]

[devout snow]

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[tawdry schooner]

How do I write an expression like this? Where "x" is increased by "y" each time, but each time "y" is increased by "z" sorry if it was a bad explanation, but here's an example:
1+4 = 5
5 + 4 +4 = 13
13 + 4 +4 +4 = 25
25 + 4 +4 +4 +4 = 41
etc.

[topaz axle]

it's a quadratic

2x²+2x+1

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[visual crypt]

how can i start solving this to get answer 66? pls help

[safe knoll]

can u try to write it as a mathematical equation?

[visual crypt]

i dont know how to do it 😓

[lost wave]

who knows statistics

[safe knoll]

the dude climbed 1/3 of the way
if he climbs 11 more steps it becomes 1/2

lets say the entirety of the staircase is x
he climbed 1/3x and then took a break
if he climbed 11 more then it becomes 1/2x

1/3x + 11 = 1/2x

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[tiny dagger]

Could someone tell me how to show the maximum value of x part please

[devout snow]

@tiny dagger Has your question been resolved?

[tiny dagger]

<@&286206848099549185>

[supple knot]

did you get the equation x^2 tan^2... = 0?

you maximize x by differentiating with respect to theta

[devout snow]

@tiny dagger Has your question been resolved?

[tiny dagger]

yes

[supple knot]

yea then do this

[tiny dagger]

how

[supple knot]

solve for x using quadratic formula

write x = f(theta). then x is maximized (or minimized) when f'(theta) = 0

[tiny dagger]

i tried that

it didnt work

[tiny dagger]

<@&286206848099549185>

[supple knot]

show your work

[tiny dagger]

it doesnt come up to a proper solution

can you please just show me i have to go to sleep in like 10mins

[supple knot]

no

[tiny dagger]

...

[supple knot]

!noans

[devout snow]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[tiny dagger]

at least explain then or something

[tiny dagger]

blud i know ive been here for like the past 2 years

but anyways

continue quickly please

[flint spire]

dont try to isolate dx/d0

differentiate implicitly and then set dx/d0 = 0

wherever you find it

[devout snow]

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[devout snow]

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[prisma lodge]

the question asks "estimate the rate of change at x=1 for the function f(x)=....)
Its giving me the function and the x value, but i thought i was supposed to get another x value, so i dont know what formula im supposed to use

[gusty nexus]

"derivative"

[prisma lodge]

thanks

.close

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[gusty nexus]

no problem

[devout snow]

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[oblique mulch]

My final answer is grossly incorrect but idk why

[vivid silo]

you got rid of the sin at the last step

[devout snow]

@oblique mulch Has your question been resolved?

[devout snow]

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[supple knot]

you subtracted the sum to m, not sum to m-1

[terse solar]

the issue is that the sum is inclusive of m

your answer would be true if it was a sum from k=m+1 to k=n+3, but it's from k=m to k=n+3

yeah lol

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[glossy plover]

Why is it not B?

[glossy plover]

This is the work I did

Don’t mind me accidentally using a 2 instead of an x

[upper schooner]

check what the actual question asks you...

You're forgetting something ⛓️

[glossy plover]

I thought I did chain ruleeeeee

Also idk what to do w the absolute value thing

[upper schooner]

You need to do it again

What's the derivative of pi/x?

[glossy plover]

Wait why

Erm

How do I do that…

[upper schooner]

(and because the insides of that cos is a "more interesting" function: for another one, remember that, say, cos(ax) differentiates to -a * sin(ax) for any constant a...)

[upper schooner]

do you know how to differentiate 1/x?

[glossy plover]

no…

[upper schooner]

are you sure?

[glossy plover]

still no…

[upper schooner]

Do you know how to differentiate something like x^n?

[glossy plover]

Yes

[upper schooner]

Can you write 1/x in that form then?

[glossy plover]

X^-1?

[upper schooner]

Yep, and that differentiates to...?

[glossy plover]

So just -1 then?

[upper schooner]

(how do you mean "just -1"? That it differentiates to -1, or...? If the former, then )

[glossy plover]

-1x^-2?

[upper schooner]

Yep

So then, pi/x differentiates to -pi * x^{-2}, just multiply the derivative of 1/x by pi as well

With that said, what does cos(pi/x) end up differentiating to, with that and the chain rule in mind? ⛓️

[glossy plover]

-sin (pi/x) * -1pi^-2

So is this how I would set up the rest?

[upper schooner]

-1pi * x^{-2} but basically yep

Replace it like that and make some simplifications, you'll get there

[glossy plover]

Oh got it!! Thank you!!

.close

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[cedar flint]

Im not sure how to do this question here

I dont really understand how to get the area, waht the partition exactly is and what the sample point is

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[lusty igloo]

i need help with this
Image
i used s=r(theta), so i pluged in 11 for r and 20 for theta
and i got 220, which is wrong

[frozen stump]

the radian measure

not degrees

oh i see

[lusty igloo]

so i multiply it by pi/180?

[frozen stump]

theta isnt 20

youre tying to find theta

[lusty igloo]

oh

how do i do that with what ive been given

[frozen stump]

s is the arc length

so sub 20 into s

[lusty igloo]

so 20 = 11 (theta)
9 = theta?

[frozen stump]

:,)

divide mate

not minus

[lusty igloo]

oh right

20/11

[frozen stump]

ye

[lusty igloo]

do i leave it like that or divide it and get the decimal number

[frozen stump]

what does the q say

[lusty igloo]

Do not round any intermediate computations, and round your answer to the nearest tenth.
idk what this means

[frozen stump]

hint is

nearest tenth

[lusty igloo]

so decimal form

[frozen stump]

yep

[lusty igloo]

and thenths place is 1.x

[frozen stump]

yep

[lusty igloo]

epic

ok

A circle has a radius of 6 fr. Find the length s of the arc intercepted by a central angle of 159 deg.

do i plug in it an s = 6(159deg)
or do i turn 159deg into radians first and then plug it into theta

[frozen stump]

make it into radians

these formulas are radian formulas so you gotta use radians

[lusty igloo]

ok

so its 159pi/180?

[frozen stump]

ye

[lusty igloo]

ok

epic

last one

A circular arc has measure 7 and is intercepted by a central angle of pi/3 radians. Find the radius r of the circle.

do i plug it in as 7=r(pi/3)?

[frozen stump]

yep

[lusty igloo]

i divide both sides by (pi/3) to isolate r?

havent done this stuff in a while

[frozen stump]

yepyep

[lusty igloo]

epic

tysm

actually

can you help me with these last few

A circle has a radius of 3.5. A sector of the circle has a central angle of 2pi/3 radians. Find the area of the sector.

do i use (1/2)(r^2)(theta)?

[devout snow]

@lusty igloo Has your question been resolved?

[lusty igloo]

<@&286206848099549185>

plz, i need guidance

.close

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[restive river]

so here is how i set up the equation

now, i dont think i know how to solve this with the tools i have learned thus far

i just learned seperable and integrating factor technique for first order linear equations and this is nonlinear

is there something i need to learn to solve this?

[woven radish]

Derivative

Derivative

[restive river]

thanks for the advice!

i dont want any help other than giving me a hint of what technique i must learn. The rest I can figure out myself. As long as I have the starting equation good, the rest is just algebra and math

[upper schooner]

Seeing you've learned separable differential equations, do you have an idea of where you'd follow from what you found?

[restive river]

well i should try to see how to solve nonlinear first order differential equations

unless i try to bring the y(1-y) to the other side and do partial fractions which is something i completely forgot how to do

ah well

i guess i gotta remind myself of that 😭

thanks for the hint!

.close

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[restive river]

.reopen

[devout snow]

✅

[restive river]

.close

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[candid lance]

got no damn idea on how to solve it

[devout snow]

@candid lance Has your question been resolved?

[tall linden]

Hint: use dot product.

Also, your username is kinda unfortunate. It has a dirty meaning.

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[placid trout]

heres the answer

can someone explain how they knew to use e

and what is ln

gonna go to sleep please leave this open

actually you can close when its answered ill check message logs

[finite briar]

It's called a logistic growth model. If you are doing these questions you should be familiar with it

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[sudden gull]

I'm wondering how to do the negative base log

[visual hazel]

explain?

[sudden gull]

I want to see if the negative base log is possible, for something such as $\log_{-2} -8 = 3$

[woven radish]

Makenna

[flint spire]

it is possible, but it only exists for specific values

base -2 log for example, you get a result when you input 1, -2, 4, -8, 16

or when you input -1/2, 1/4, -1/8

[sudden gull]

can it be generalized ( Of course assuming in the complex plane )

[flint spire]

yes, it works in C normally

ill show you why it doesnt work in R, but works in C

do you know the change of base rule?

[sudden gull]

of course...

I'm trying to explain via complex analysis 😭

[flint spire]

okay okay 😛

so in R, it doesnt work because $\log_{-2} (x) = \frac{\ln{x}}{\ln{-2}}$

[woven radish]

Emily

[flint spire]

but ln(-2) has no real value

in C, it is not a problem at all

$\log_{-2} (z) = \frac{\ln{z}}{\ln{-2}}$

[woven radish]

Emily

[sudden gull]

of course, ln(2)+i pi

[flint spire]

ln(2) + i (pi + 2pi k)

yeah basically

[sudden gull]

right, because of riemman surfaces

[flint spire]

so yeah, thats the thing about negative bases

[sudden gull]

$e^{\ln(-2)}, e^{\ln(2)+i\pi}$
$\ \ln(-2)=\ln(2)+i\pi$

[flint spire]

yes

[woven radish]

Makenna

[flint spire]

yeah yeah

in C its fine

[sudden gull]

mhm

[flint spire]

but in R, it only exists for specific values

the reason is..

$\log_{-2} (x) = \frac{\ln{x}}{\ln{-2}}$

[woven radish]

Emily

[flint spire]

if x is a power of -2

$\ln((-2)^{y})= y \ln(-2)$

[woven radish]

Emily

[sudden gull]

I was thinking, say $\log_{-a}(x) =\frac{\ln(x)}{\ln(-a)}$
$\ = \frac{\ln(x)}{\ln(a)+i\pi}$

[flint spire]

so it cancels out with ln(-2) and you get a result!

[woven radish]

Makenna

[flint spire]

yeah, it works normally in C

[sudden gull]

mhm

[flint spire]

for R it works only if x is a power of (-a)

[sudden gull]

is there anything specifically proving that this is valid?

[flint spire]

what, that in R it works only if the input x is a power of (-a)

?

[sudden gull]

I guess better question is proving change of base rule works for these type of numbers

[flint spire]

i think we are running in circles xD

it works, no wonder

its just that the ln(-a) cant be evaluated in R, but can be normally evaluated in C

thats simply what makes negative base log in C

[sudden gull]

yeah

assuming both inputs are negative

$\frac{ln(x)+i\pi}{ln(a)+i\pi}$

[woven radish]

Makenna

[sudden gull]

if you plug in x=8,a=2

does that actually work

[flint spire]

you cant plug in x=8 and a=2

[sudden gull]

why is that

[flint spire]

this works only if input of log in negative

and base is negative

[sudden gull]

yes..

[sudden gull]

this is assuming both inputs are negative

[sudden gull]

I guess I'm asking why doesn't this work for our explain log base -2 of -8

[flint spire]

ah wait, now i understood

you want to test the formula for x=8 and a=2

we shoul be getting 3 right?

[sudden gull]

yeah, should get us 3

[flint spire]

it works

[sudden gull]

it does?

[flint spire]

it is not working for you because your definition lacks generality

[sudden gull]

well, how do I generalize it

[flint spire]

ln(-2) is not only ln(2) + i π

ln(z) is a multi-output function in C

ln(-2) is actually ln(2) + i (π + 2πK)

[sudden gull]

Yes, being that every phase it repeats

[flint spire]

yesss

[sudden gull]

the pain of complex logs

[flint spire]

so the formula is $\log_{-a}(-x)=\frac{ln(-x)}{ln(-a)}=\frac{ln(x) + i (\pi + 2 \pi K)}{ln(a)+ i (\pi + 2 \pi m)}$

[woven radish]

Emily

[flint spire]

now this is general

for all pairs $(K,m) \in \mathbb{Z}^2$

[woven radish]

Emily

[sudden gull]

some set theory person is going to yell at you -

yeah

lmfao

[flint spire]

sooo, if you take log -2 of -8

there will be infinity of results

[sudden gull]

I was going to say you need to define the two variables as within the set of whole numbers?

[flint spire]

so if you take log -2 of -8

there will be infinity of results

all of them complex

but one, only one of them

will be real, our 3

you get it by letting m=0 and K=1

try it 😛

all other combinations of values of m and K will give complex numbers as answers

[sudden gull]

😭

[flint spire]

do it by hand, what 😛

[sudden gull]

aaaa

fine

how do I solve this 😭

[flint spire]

$\frac{ln(8)+i(\pi + 2 \pi)}{ln(2)+i \pi} = \frac{ln(2^3)+ i 3 \pi}{ln(2)+i \pi}$

[woven radish]

Emily

[flint spire]

carry on!

[sudden gull]

AAAA

can we factor 3 out??

[flint spire]

yes

[sudden gull]

and it just becomes 3*1

woaaah

[flint spire]

lol

[sudden gull]

can you explain the motivation of why you go down the spiral and why it works

[flint spire]

you mean why we could find only one real answer

in a sea of an infinite number of complex answers?

[hardy mantle]

nahh what is this i'm cooked when i start learning this

[sudden gull]

nah you're good bro

OMG WEEBER

[sudden gull]

well, why does going down the phases work

or up phases I guess 😭

[flint spire]

i didnt understaaaaand your questiiiion 😛

if you chose log -2 of -10 for example

then even if you try all combinations of K,m

the result will always be complex

cant find a real answer

but you chose log -2 of -8

and you know that 8 is a power of 2

[hardy mantle]

3 😸

[flint spire]

logically there must be a real answer

[sudden gull]

mhm

[flint spire]

in a sea of infinite complex answers

[sudden gull]

yeah

[flint spire]

it requires some brain cells at first

to grasp

[sudden gull]

Yeah, I get it

[flint spire]

but you dont need to dive into this too much

you wont be seeing negative log bases at all

haha

[sudden gull]

it's because of the non-uniqueness of the complex log

[flint spire]

yesss, we say the complex logarithm is multi-valued

[sudden gull]

similar to how 1^x is always 1 for the reals

[sudden gull]

I'm aware

[crimson crypt]

Hello I have an assignment but I can't understand I've gone through all our lesson but still nothing so I hope any of you guys help with an explanation thank you(number 5 and 10 only are the ones I can't understand)

[sudden gull]

it's a bit like a nullity

[flint spire]

!occupied

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[sudden gull]

oh, this isn't that bad

[crimson crypt]

Uhmm wdym?

[flint spire]

he has an open channel already 😛

[crimson crypt]

Oh j didn't see sorry mb

[flint spire]

https://discord.com/channels/268882317391429632/1018703538517454919

so yeah, any more questions Makenna?

i adore complex lol

hope i cleared your doubts about negative base log

[sudden gull]

we should talk about it more haha

[sudden gull]

I love complex analysis too, though I'm not sure how to learn it

[flint spire]

youll have courses on complex ig

[sudden gull]

I don't think my high school is going to be offering complex analysis anytime soon

I know a bit about it, but I don't know a lot of the fine details

[flint spire]

oh, so you're a high school

your profile says undergraduate

thought you're uni xd

[sudden gull]

oh yeah lmfao

can't let people think I'm a lowly highschooler 😭

[flint spire]

haha :p

so dont anticipate, youll get to learn cmplx sooner or later

[sudden gull]

haha I want to learn nOw though!!

I wish I was in uni for math haha

[flint spire]

try YT

[flint spire]

why not, make it happen!

[sudden gull]

how :c

[flint spire]

get into a math uni :p

[hardy mantle]

khan academy fr fr 🔥

[flint spire]

oh yeah, Khan Academy, i totally forgot

[sudden gull]

I have bad grades tho 😭

[flint spire]

gotta chase them dreams and make them a reality

[hardy mantle]

bro my friends keep making deez nuts jokes every time i mention khan academy istg and i fall for it every time 😭

[sudden gull]

teach me the ways

.close

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[woven radish]

24tudor24

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[inner ibex]

how do i find just Z

[vast drift]

(z+w) + (z-w) =...

[devout snow]

@inner ibex Has your question been resolved?

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[long pasture]

looks nice, what have you tried?

[fathom flint]

im clueless

i have worked on the first equation

and but the second one is just

...

[long pasture]

well, it says the 2nd equation has equal roots, so we can do:
∆=0

which will give us pretty nice results

[fathom flint]

yes

whats delta

b2-4ac?

b^2

[fathom flint]

they mixed three chapters in this question

Quadratic trigno equations and logarithms

[long pasture]

which actually makes this a very nice question

[fathom flint]

ye but that screwed my exam

[long pasture]

hint 1:
log_c ab = (log a + log b)/(log c)

[fathom flint]

i literally saw that question and left the entire section

[long pasture]

I understand....

[fathom flint]

ye

[long pasture]

so, can you simplify ∆=0?

[long pasture]

it's a lot easier than it looks here

so.... how's your working going?

[devout snow]

@fathom flint Has your question been resolved?

[placid trout]

Oh I see now

So how did they get ln2 = 2k

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[restive river]

hi

[restive river]

how do i find equation of planes passing through two known points and making some known angle with another fixed plane

help

guys

qyuicj

<@&286206848099549185>

[steep tide]

this is horrible

Whats an equation of a plane?

[restive river]

UH

you should know it

if you can help me

it basically would mean i know some point on plane and its normal vector

GUYS

by equation i mean vector equations of the planes

<@&286206848099549185>

[devout snow]

@restive river Has your question been resolved?

[restive river]

.close

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[thorn kernel]

if acot+bcosec= p and bcot+acosec =q find p^2-q^2

[thorn kernel]

<@&286206848099549185>

.close

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[plain dust]

im confused ive done:
(2-√x)(2-√x)/(√x)
i then rationalise denominator
(4-4√x+x√x)(√x)/x
(4√x-4x+x√x)/x
then divide by x
(4√x)/(x) - 4 + 1√x
then i can rewrite this as
(4/x)√x - 4 + x^1/2

now what

[olive jasper]

Numerator is (a-b)² form, find the a²-2ab+b²

[plain dust]

2^2 -4√x + x

[plain dust]

huh wdym

[olive jasper]

Now break all parts like
(a+b+c)/d = a/d + b/d +c/d

[plain dust]

(2^2)/(√x)+(-4√x)/(√x)+(x)/(√x)

[olive jasper]

Now do you know we can write
1/a^n = a^-n?

And
a^n/a^m = a^(n-m) too

[plain dust]

wait

i think i know

would u rewrite √x as x^1/2

[olive jasper]

Yep

[olive jasper]

So what will be 1/√x if you look at this

[plain dust]

(1+x)^1/2

WAIT

1/x^1/2

1X^-1/2

[olive jasper]

Yes

Now proceed like that

And you will reach the result

[plain dust]

but how would i rerite x/x^1/2

[olive jasper]

Like this

x can be written as x¹

So x¹/x½

[plain dust]

now i have

(2^2)x^(-1/2) + -4x^(-1/2) + (x^1)/(x^1/2)

[olive jasper]

Nope check 2nd term again it was
-4√x/√x

[plain dust]

would be - 4

[olive jasper]

Yep

[plain dust]

now how do i put x/x^1/2 into the form x^1/2

i got 2 terms

last one is weird tho

[olive jasper]

Like this ^^

Read what i said there

a^n/a^m = a^(n-m)

[plain dust]

x(1-1/2)

x(1/2)

[olive jasper]

Yep

[plain dust]

tysm

for the help

[olive jasper]

No problem

[plain dust]

thanks

.close

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[trail mason]

Hi. I don't know how to tackle this. If there was no nth root, I'd use squeeze theorem showing, that whether (-1)^2n= 1 or (-1)^(2n+1)= -1, 4^n "dominates" and the whole expression approaches infinity. The nth root is giving me trouble though. A hint of how to approach this should be enough. Thanks is advance ❤️

[trail mason]

arctg is arctan

I managed to get to a solution, but it required using squeeze theorem twice, so I'm still looking for a better one. <@&286206848099549185>

[oblique belfry]

Usually you factorize by the fastest growing term. What is it here?

[trail mason]

I don't remember why but I wanted to avoid that. I'll try to find the reason.

[trail mason]

Oh okay, I remember now. There was this limit below to which I applied that and got inf-inf, called it a day and said limit is 0 even though it's 2 and I started to subconciously avoid it. Thanks for helping me recognize that, I can take it from here. ❤️

.close

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