help-17

[forest plume]

yeah like a phase shift or w/e

[crimson jetty]

you translate one, so these are the same

exactly as youve drawn

and then their sum is arrow from the start of the 1st

to the end of the 2nd

So this will be the sum of the 2 vectors you drew

does that make sense?

[forest plume]

yeah

[crimson jetty]

so to answer this questin

you will have a vector starting and ending in the same place

this is the 0 vector

it has 0 magnitude, and is the only vector with no direction

ok?

[forest plume]

ok

[crimson jetty]

And you see adding the original magnitudes

had nothing to do with the sum

the original magnitudes couldve both been 1

1 + 1 -> 0 does not match

going back to your original question

we are talking about 2v

now this is scalar multiplication

but you can also think 2v = v + v

[crimson jetty]

Using this idea, you can answer the original Q

You want to know what twice this vector is

[forest plume]

well it's probably A since it's 2x as long as the length from O to B

oh so v = B

like you said OB

C = 1/2v

a = 2v

[crimson jetty]

no

[forest plume]

the path from O to A begins at the origin and ends at A

[crimson jetty]

,,\overrightarrow{v}=\overrightarrow{OB}

[crimson jetty]

but youve got the right idea

,,2\overrightarrow{v}=2\overrightarrow{OB}

[forest plume]

so you have to include O?

[crimson jetty]

,,2\bs{v}=2\overrightarrow{OB}=\overrightarrow{OB} + \overrightarrow{OB}=\overrightarrow{OB} + \overrightarrow{BA}

[crimson jetty]

To specify an arrow, you have to specify its start and end point

so we write vectors like this.

[forest plume]

that makes sense

[crimson jetty]

So using the ideas we talked about

this is whats going on

OB = BA because we are allowed to translate vectors

and finally OB + BA = OA

because B is the start and endpoint of the 2 vectors youre adding

[forest plume]

it is going to the left though, does this mean that the vector is .. negative?

[crimson jetty]

not at all, that doesnt make sense

to talk about

[forest plume]

it doesn't go to the right and up

so just curious

[crimson jetty]

yes, but thats just one of the directions

in a circle of rotations

there is no idea of negatives going on here

,,2\bs{v}=2\overrightarrow{OB}=\overrightarrow{OB} + \overrightarrow{OB}=\overrightarrow{OB} + \overrightarrow{BA} = \overrightarrow{OA}

[forest plume]

it's more like north west

[crimson jetty]

just to conclude, this is exactly the idea your question wants you to understand

[forest plume]

we define that as up here

[crimson jetty]

when it comes to negatives and vectors, there is something unrelated to this though

,,-\overrightarrow{XY} = \overrightarrow{YX}

[crimson jetty]

and the reason why this makes sense is because

,,\overrightarrow{XY} + \overrightarrow{YX} = \bs 0

[crimson jetty]

adding itself and the negative gives you the 0 vector

the last thing that youre confused about that doesnt matter for this question is coordinates

you can use coordinates to describe vectors, but these are still different from points

and it isnt useful for this question

[forest plume]

ok

[crimson jetty]

When someone writes this, they mean the vector going from (0, 0) to (1, 2)

[forest plume]

I also have another question if you can help me, thanks

https://discord.com/channels/268882317391429632/486844875632017408

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[edgy phoenix]

Hi i have question so when i need to find the slope of a line by its graph
slope = y2 - y1 / x2 - x1
i will use this formula but out of the 2 points i choose from graphs which will be x1 y1 and which will be x2 y2

[crimson jetty]

with a real example, try both ways

[edgy phoenix]

so it doesn't matter any point can be x1 y1 or x2 y2

[crimson jetty]

yes, for a straight line

you can find its equation with any 2 distinct points

[edgy phoenix]

ok thanks for the help

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[coral verge]

hello

[coral verge]

when you are identifying points on the plane does the x axis come first or y axis

[lime gorge]

X axis comes first

For example

(2,3)

The x part is the 2

The y part is the 3

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@coral verge Has your question been resolved?

[coral verge]

how do you identify transformations on a grid

hello

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[desert glen]

How am I supposed to find the original function here?

[desert glen]

for #41, specifically

.close nvm

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[chrome coral]

.Help

[chrome coral]

Pls someone help me

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[gleaming karma]

I have absolutely no clue what I'm doing here

[gleaming karma]

I've been out of school for awhile so I'm catching up on work I missed and I've never done this before so Idk what to do

[edgy sapphire]

it's mostly just a visual thing, it's like asking you to complete a four-leaf clover given only the top leaf

rotational symmetry of order 4 means that you can keep rotating that shape around 1/4 of the way and drawing what you get

[gleaming karma]

Thanks man

Thst helped alot

[edgy sapphire]

👍

[gleaming karma]

Damn that was alot more simple than I thought

Uhhhh

Thanks again

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[woeful snow]

How would I go about writing this?

If what I did so far is correct, im stuck at

33tan(39)=x

apparently another way of writing it is

X= 33
————
tan(49)

How to I go about solving for X after getting to this point?

[lime gorge]

Calculator

Or if they accept answers of that form, 33/tan(49)

[woeful snow]

I’ve gotten around different answers from 3 different places..

[lime gorge]

Huh? Wdym

Ok it says nearest tenth

U need calculator

[woeful snow]

Normal calc gives me .63

[lime gorge]

Make sure u have it on degrees

Not radians

[woeful snow]

Ooooooo

[lime gorge]

Yea I realized that here but just wanted to make sure lol

[woeful snow]

I got the same thing using Deg

Mathway gives me 37.92

Gauth gives me 28.68

:pain:

[lime gorge]

,w 33/(tan(49 degrees))

[twin meteor]

Results provided by WolframAlpha

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

Requested by northsteve

[lime gorge]

There’s ur answer

[woeful snow]

🙏🏽

lifesaver

thanks

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@upbeat fractal Has your question been resolved?

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[daring forge]

hello

[daring forge]

how to do r/3 + r/5

[thin vale]

Make common denominators

[daring forge]

so lcm

[thin vale]

So, make common denominators

[daring forge]

so lcm?

[thin vale]

The common denominators can be anything

[daring forge]

do i use Lcm

[thin vale]

you just need to make common denominators

[daring forge]

alr

[thin vale]

it would be easy to make them the lcm, but you could make them something else also

[daring forge]

so Lcm

i get it

[daring forge]

i have been asking you that but ok

alg

[thin vale]

"so lcm" isn't much a question

and I can't tell what you're asking by it

it isn't necessary to make them the lcm, but you could do that

[daring forge]

wait how to make the common denominator

[thin vale]

you could multiply the first fraction by 10/10 (since this is equal to 1 it leaves it unchanged) and multiply the second fraction by 6/6 (since this is equal to 1 it leaves it unchanged) then you would have
10r/30 + 6r/30

as an example

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[daring forge]

thanks bro

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[coral oasis]

help plz, Idk how they got the answer.

[quaint marsh]

They're just reading off the graph as far as I can see. So for (a) you read up from 5

And for (b) you look for the x-value where the two lines meet

[coral oasis]

can you explain?

[quaint marsh]

So if you want to know how much interest you paid in year 5

You go to year 5 on the graph (the x axis)

Then you see where the red line was at x=5

And you see it's at around 740

Same deal with (b)

You see where the two lines cross, because that's when the interest and principal are equal (at the same height at the same time). Then you check what year that happens in by reading down from that crossing, which is about 10.5

[coral oasis]

how did you see it exactly see it on 740?

[quaint marsh]

I didn't. But you can see it's slightly below halfway

It says "approximately" so as long as you're close it's fine

[coral oasis]

I can't approximate

but ig

@quaint marsh is there a math way to solve it?

[quaint marsh]

This is what they want you to do.

They haven't given you equations, so it's just reading off the graph

[coral oasis]

i hate math

thank you so much for helpping me out have a good night.

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[nova fulcrum]

hi, i tried alsing this yesterday but i could not finish it

[nova fulcrum]

$\int \sin^{(\ln x)}x\left(\frac{\left(\frac{\cos x}{\cot x}\right)\ln(\sin x) + x \sin x \ln x \cdot \cot x}{x \sin x}\right) , dx$

[twin meteor]

Alex

[nova fulcrum]

someone said something about the derivative of sin^(f(x))(x) but even with that hint i could not find the correct subtitution

[unborn wind]

is the last cotx inside log or outside

[nova fulcrum]

Outside

[unborn wind]

ok suppose y=sin^ln(x) x

are u there??

[nova fulcrum]

yes

[unborn wind]

now do d(ln(y))/dx

[nova fulcrum]

why the derivative of ln(y) and not the derivative of y?

And dx or dy?

[unborn wind]

d(lny)=1/y dy

[nova fulcrum]

yes

[unborn wind]

so that the power comes down and it becomes easier to get derivative

[nova fulcrum]

ok si i get 1/y but y = sin^lnx(x)

So i get 1/sin^lnx(x)?

[unborn wind]

thats the lhs

1/y dy/dx= d(ln(x))(ln(sinx))/dx

now do rhs

[nova fulcrum]

lnsinx/x + cosxlnx/sinx

[unborn wind]

yeah

so dy/dx = (y)( )

and this is also the thing u need to integrate in the question

[nova fulcrum]

omg sinxcotx is cosx and cosx/cotx is sinx

[unborn wind]

yep

[nova fulcrum]

i just have to split in two fractions cause denominator is xsinx

so the integral is solved likw sin^lnx(x)?

this was a weird integral

thanx!!

[unborn wind]

wc

[nova fulcrum]

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[ionic birch]

can i get some help with this?

so far i've gotten

(h,k) = ( -3 ,1 )

p = -0.5

focus = ( -3.5 , 1 )

[unborn wind]

what do u want help with

[ionic birch]

how do i find the rest, if these are even the correct answers i have

[unborn wind]

yeah those answers are correct

do u know how to find the rest in a normal parabola - y^2 = 4px??

@ionic birch

[ionic birch]

not really... first time

[unborn wind]

u should try asking your teacher or maybe see a video on it because trying to understand it through text would be tough

[unborn wind]

do u know what latus rectum is?

[ionic birch]

can't do that lol thats online too

[ionic birch]

is that like |4p|

[unborn wind]

yeah thats the length of latus rectum

its not the latus rectum itself

latus rectum is a line passing through focus that is perpendicular to axis of symmetry

ok tell me everything u know about parabola

@ionic birch

[ionic birch]

idk... its a parabola lol

looks like a u

[unborn wind]

what is focus?

[ionic birch]

that thing next to the middle of the parabola

[unborn wind]

parabola is the locus of all points who are at equal distance from directrix and focus

u need a whole lecture on parabola

[ionic birch]

why

[unborn wind]

why not

[ionic birch]

i cant talk to the teacher its just online

[unborn wind]

what about youtube video

[ionic birch]

i just come here

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[delicate night]

hi, im really confused and have no idea how to do this problem, if a satifies the conditions in the first image, how do i figure out the value for the second image?

[drifting terrace]

try writing out the first few terms of the required thing

[delicate night]

i have tried replacing j with i-1 but i dont understand how a(subscript(i+10)) can be obtained from the original conditions

[drifting terrace]

you can do that but its not necessary

[dense jay]

Put values of j and write the terms

[dense jay]

It's a1 to a20

[drifting terrace]

just actually write out what the sum is supposed to look like

sigma notation is hard to read if youre not completely familiar with it

[delicate night]

what do you mean by this\

[drifting terrace]

for example when j=2 it is a1+a11

when j=3 it is a2+a12

[delicate night]

yes but the values for when j is the index is not given so you need to convert it to i first

[drifting terrace]

observe the pattern

the sum would look like
(a1+a11)+(a2+a12)+(a3+a13)+...+(a10+a20)

[dense jay]

Treat j just as a variable

[drifting terrace]

can you find what it is equal to now?

[delicate night]

could you explain further? im still a bit confused

since the original conditions is all thats given wouldnt you have to reindex the sigma notation first in order to subsitute the values?

[drifting terrace]

do you know how you go from the sigma notation to this

[delicate night]

yes

how would you proceed from there?

[drifting terrace]

now look at what youre given

the first one says
a1+a2+a3+...+a10=17

the second one says
a1+a2+a3+...+a20=-1

[delicate night]

so would the answer be 16?

[dense jay]

Ig it's -1

[drifting terrace]

yeah its -1

[delicate night]

oh

wait

yeah

im a bit slow

[drifting terrace]

if you added the two things together you would get duplicate a1 to a10

[delicate night]

thanks a lot

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[fast quarry]

hi i need help with some linear algebra please

[fast quarry]

i have done i) and ii), but i dont know how to do iii)

here is my workings for i) and ii)

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<@&286206848099549185>

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.reopen

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✅

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[chrome herald]

Hi, first time using this channel. I´m a little rusty in multivariable calculus. I'm not sure how to solve the integral in d. I know the curl is (0,0,0) and the divergence is 0. This is a revolution surface and don't remember how to parameterize it.

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.reopen

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✅

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[mighty stone]

its C, not D, right?

[hybrid flicker]

yes it's C, in the second quadrant sin > 0, cos < 0

[mighty stone]

so how did they get D?

[hybrid flicker]

they got it wrong

[mighty stone]

alr thx tho

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[vast shale]

How do I find the probability of the shaded region?

[vast shale]

It’s the probability that a randomly chosen point in the figure lies in the shaded region

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[hexed ivy]

Can someone help explain

[vast shale]

we'd need to see the whole question

[sweet flower]

Not enough info here

[vast shale]

exactly

[hexed ivy]

K

[vast shale]

it depends on your answers to previous steps of the problem

[vast shale]

ok

is this a multi question problem or is that it

[hexed ivy]

I wrote because the difference in means is low, there is no random chance

[vast shale]

nononno that's not how it works

[hexed ivy]

It’s pick the choice and explain

[vast shale]

you have to calculate the p value

[hexed ivy]

What’s that

[vast shale]

ok

it's the probability of achieving an event = to or more extreme than the one we observed

[hexed ivy]

How would I find that

I forgot to also add this

[vast shale]

see

that's important information

[hexed ivy]

I haven’t been thought about p value yet

[vast shale]

you sure?

you can't answer the question without it

[hexed ivy]

I don’t think so

How do u calculate it

[vast shale]

u need the standardized test statistic

[hexed ivy]

R u talking bot margin of error

[vast shale]

no

standardized test statistic is part of what makes up the margin of error tho

[hexed ivy]

Standard dev?

[vast shale]

that's also part of it

[hexed ivy]

Yea I don’t think I’ve been thought it yet

How would u explain it in like standard dev or margin of error

[vast shale]

why are you even doing this problem

[sweet flower]

You don’t need a t or z test for this you can use chi squared

[vast shale]

oh

bruh

[hexed ivy]

What even is that 😭

[vast shale]

dude

honestly

ask your teacher

no point doing a problem u haven't been taught

[hexed ivy]

Can u explain it in terms of difference in means

Or nah

Well can u also help me answer other questions if possible?

[vast shale]

have u learned significance tests

[hexed ivy]

Nope I started stats like a week ago

[vast shale]

maybe ur teacher wants you to use a calculator to get all the info

LMFAO

[hexed ivy]

Yeah

[vast shale]

yeah ok buddy

[hexed ivy]

It says use technology needed

[vast shale]

this ain't happening

[vast shale]

oh

well

tech is needed for the chi-sq cdf

[hexed ivy]

I have learned normal cdf

[vast shale]

your teacher doesn't necessarily want you to just straight chi-sq gof

tech is needed regardless of whether you want to go through the process or just cheat it and use the p value the calc gives u

[hexed ivy]

Can u give me an example of an explanation u would give

[vast shale]

well

u need a null and alternate hypothesis

[sweet flower]

Can you use a table?

[hexed ivy]

Yea I got a ti 83

Explaining I used a calculator works?

[vast shale]

no

[sweet flower]

No

[vast shale]

lmao

"I used a calculator to get the answer"

[hexed ivy]

Well ima just leave it blank for a bit

[vast shale]

wonderful explanation

[hexed ivy]

Can u help me with another question?

[vast shale]

ig

imma bet you don't know how to do that either

ok

we need to see the full question

[hexed ivy]

Wait sec lemme edit

[sweet flower]

okay and what have you done so far?

[hexed ivy]

I just plugged into a calc

[vast shale]

plugged what

[sweet flower]

and got what?

[hexed ivy]

The values into table 1 and table 2

[vast shale]

and?

[hexed ivy]

I just got the mean ox and stuff

[vast shale]

ok

so do you have the answer to question a

[hexed ivy]

No I don’t have the difference in means

[sweet flower]

do you have the means?

[vast shale]

then get that lmao

[hexed ivy]

Do I add all of them?

[sweet flower]

yes

[vast shale]

do you know how to take a mean

[hexed ivy]

How do I get the blank ones

[vast shale]

ok

the blank doesn't mean anything

that just means the sample size is less

[sweet flower]

you dont have that info, so you only take the mean for the first 5 on the right

[hexed ivy]

K

[vast shale]

can i be honest with u @hexed ivy

[hexed ivy]

Sure

[vast shale]

it feels like you haven't actually learned anything and you're just trying to brute force your way through a bunch of random homework problems for no reason

[hexed ivy]

Rn it’s all just calculator use

[vast shale]

that doesn't even make sense

[hexed ivy]

To find mean and sd

[vast shale]

then why were you trying to do a problem with significance tests

[hexed ivy]

Idk that’s the hw he gives

[vast shale]

something's not adding up

[hexed ivy]

I’ve only done margin of error, mean, standard deviation, and normal cdf

[vast shale]

bruh

[hexed ivy]

Alright thx for the help ima try on my own

.close

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[lime kraken]

why does this converge to 0

like i feel like since the first term ln(n+1)

it has +1

n to infinity is alwaus gonna be a little more than 0

[feral light]

no

use l'hopitals rule

nvm use ln properties

[lime kraken]

yeah i did LH

and i got 0

just feels a bit counter intuitive

[feral light]

nice 👍

um how

[lime kraken]

cuz

ln9999 - ln9998

is always gonna be positive never gonna reach 0

first term always gonna be a little bigger

[dull bear]

log properties (and the fact that ln is continous) is probably a better way to see it tbh

[lime kraken]

yeah its just ln(1+1/n)

so ln1 = 0

like this it makes sense

but

[lime kraken]

this still feels like to me

i might be drunk tho lol

anyway tysm

.close

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[dull bear]

.(similarly, you have that sqrt{n + 1} - sqrt{n} goes to zero, does feel a bit trippy, but those sequences "increase really slowly")

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[dense elk]

In line 6th where they say that from the "hypothesis" we have |Xk|=1

could anybody tell me

which hypothesis are they talking

[wraith tangle]

I guess they are talking about the above equation

[dense elk]

how

like

it can be

xk=1 or xk=-1

with the help of above equation?

[frozen bobcat]

in the question: "All the roots of P are complex numbers with modulus 1"

[dense elk]

Oh fuck

my bad

thanks buddy

☠️

my level of dumbness

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[sage dew]

try multiplying and dividing one of the terms by (1-cosθ)

[polar phoenix]

SIMPLIFY

[sage dew]

consider trying it out and see what you get

[polar phoenix]

bro

Ok but I don’t it starts like that

[sage dew]

I don't know what that means but sure

[polar phoenix]

THATS WRONG

[sage dew]

show your work

[polar phoenix]

One sec

@sage dew

[sage dew]

no

I said just one term

not both

[polar phoenix]

EXACTLY

So get rid of one on the bottom

[sage dew]

get rid of what on the bottom?

[polar phoenix]

The fuck

Lmfao

Get rid of the one I put on the left side

OH

That would literally cancel

Or become a cos^2

[sage dew]

now you changed the quantity

[polar phoenix]

Dude

What

[sage dew]

when you want to keep something the same, you multiply and divide by some quantity

by only dividing by 1 - cos, you are changing the quantity

[polar phoenix]

YOU SAID 1- cos

[sage dew]

and that's not the term you should be doing this operation on, to begin with

[polar phoenix]

It should be 1+cos

[sage dew]

said what about 1-cos?

[polar phoenix]

SIMPLIFY

[sage dew]

seems like I said multiply and divide

idk tho

[polar phoenix]

I’m lost

<@&286206848099549185>

WE NEED A SECOND PERSON

[sage dew]

multiply and divide only ONE of the terms by (1-cosθ)

which term do you think needs this?

[polar phoenix]

Sin

[sage dew]

sin / 1+cos ?

that term?

[polar phoenix]

Yes

[sage dew]

yes

now multiply and divide that term and that term only, by 1- cos

and see what you get in the denominator

[polar phoenix]

Excuse the hand writing

is that it

[sage dew]

you forgot to multiply that term by 1- cos as well

[polar phoenix]

BRO WHERE

ITS THERE

[sage dew]

that looks like it's a division; if thats the case then you forgot to divide as well by 1 - cos

[polar phoenix]

Bro

WRITE IT DOWN IM A VISUAL LEARNER

[sage dew]

you know that it's permitted to ask that like an actually respectable civilized person

<tri> could you please write this down I'm more of a visual learner

of course Inno no problem

[polar phoenix]

sorry

[sage dew]

alright, let me type this in latex

$\frac{sin\theta}{1+cos\theta}\cdot \frac{1-cos\theta}{1-cos\theta}+\frac{1+cos\theta}{sin\theta}$

[twin meteor]

Triaxyz

[sage dew]

as you can see

one term is being multiplied and divided by 1 - cos

[polar phoenix]

That’s literally wrong

[sage dew]

we're doing this because it simplifies the denominator really nicely

[polar phoenix]

Bc look

THATS WRONG

[sage dew]

I'll wait for an explanation as to why

[polar phoenix]

Where is the negative

[sage dew]

the objective is to simplify the trig that is given

what I suggested was a trick to simplify the denominator

which you're refusing to do

what exactly do you want from this server?

[polar phoenix]

help

[sage dew]

then take it

[sage dew]

expand this out and write down what you get from expanding this out

[polar phoenix]

I think it’s wrong

I think I got it wrong

[sage dew]

just show me what you tried

[sage dew]

the 1 + cos's dont cancel because they are not being multiplied

[polar phoenix]

This is horrible

I’m so stupid

[sage dew]

additionally, the point of multiplying by 1 - cos was to expand out the numerator to get a simpler form of it

[polar phoenix]

OHHHH

WAIT

I just worked backwards

Hold on

Is it like that

[sage dew]

no, the 1 + cos and 1 - cos are not the same quantity so they don't cancel

hint: try expanding the denominator of that term, which is $(1+cos\theta)(1-cos\theta)$

[polar phoenix]

Oh my fucking god

[twin meteor]

Triaxyz

[sage dew]

$\frac{sin\theta}{1+cos\theta}\cdot \frac{1-cos\theta}{1-cos\theta}$ becomes $\frac{sin\theta \cdot (1-cos\theta)}{(1+cos\theta) \cdot (1-cos\theta)}$

[twin meteor]

Triaxyz

[sage dew]

are you sure you expanded the denominator correctly?

you're missing a term

[polar phoenix]

Bro

I’m about to give up

[sage dew]

just explain to me how you foiled the denominator

[polar phoenix]

I don’t know

It just made sense

<@&286206848099549185>

[sage dew]

then let's work it out together

[polar phoenix]

<@&286206848099549185>

<@&286206848099549185>

I’m dropping out

[wraith tangle]

??

[sage dew]

k so anyway $(1+cos\theta)(1-cos\theta)$; foil the '1' on the left term to the two right terms, then foil the $+cos\theta$ to the two right terms as well so the final result is $(1+cos\theta)(1-cos\theta) = 1 - cos\theta + cos\theta - cos^2\theta$

[twin meteor]

Triaxyz

[polar phoenix]

I SAID COS^2 the first time

I’m dropping out

Bro

Bro

E l

Rrr

R

R

[sage dew]

I literally cannot see it in your work

[polar phoenix]

I DIDNT WROTE IT

WRITE

[sage dew]

then that's not my fucking fault

[polar phoenix]

BUT I LITERALLY SAID IT

I want another helper

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[clear shoal]

Don't spam

[sage dew]

you never said cos^2 at any point during this conversation

[polar phoenix]

YES I DID

[vast shale]

just cross multiply

[polar phoenix]

BROOOOO

ITS SIMPLIFY

y’all about to make my grade go down

[sage dew]

ok

[vast shale]

do you know half angle formulae

[sage dew]

it's our fault that you're paying zero attention in class

makes sense

when I've spent the last 40 mins trying to help you

[polar phoenix]

BITCH MY GRADES ARE GOOD

It’s just this problem

[sage dew]

and we're trying to help you solve it but you're the most unwilling person I've ever met in my entire life

[vast shale]

you'd be thrown out of academia for such behaviour

[sage dew]

I (we) would really appreciate it if you could show some dedication and not throw hissy fits when someone doesn't give you just the answer

[polar phoenix]

these are just pythagorean identities not half angle

[sage dew]

exactly

and I was trying to lead you straight into a pythagorean identity with what I was doing

but you weren't willing to work it out

[vast shale]

you know what

get a triangle

ok ?

[polar phoenix]

Born

[vast shale]

right angeled triangle

[polar phoenix]

Vien

[vast shale]

literally

[polar phoenix]

VIEN

This isn’t a triangle moment

[vast shale]

write cosine and sine in terms of

sine and cosine

and substitute them

[vast shale]

i think it is

for you atleast

and its not wrong

its literally the most fundamental way to do this

if you were to listen to @sage dew carefully you wouldve been done with it in seconds

[sage dew]

it literally took me 3 lines to finish

this should have been a 5 minute help channel

[polar phoenix]

CLOSE THE FUCKING ROOM NOW

I don’t know how to do it

.close

[vocal sleet]

Channel closed

Closed by @polar phoenix

Use .reopen if this was a mistake.

[vast shale]

@sage dewi feel bad for you

[sage dew]

the whole interaction was hilarious dw

[polar phoenix]

.reopen

[vocal sleet]

✅

[polar phoenix]

.reopen

I can’t give up like that

COME BACK

HELP

[wraith tangle]

👀

[sage dew]

are you gonna get pissed again for getting showed multiplication tricks or are you going to actually work them out and later understand why they're being used

[clear shoal]

So much yelling lol

[polar phoenix]

yes

OK

SO

nah

i give up

i cant

do it

[sage dew]

you just said you couldnt give up

and less than 5 mins later you say you give up

[polar phoenix]

how tf am i an engineering student

[sage dew]

do you want to finish the assignment or not?

[polar phoenix]

BRP

I CANT DO IT

LIKEEEEEEE

[sage dew]

I was literally doing the problem for you

asked you to foil out a simple expression and you couldn't do it then I proceeded to do it for you

[polar phoenix]

I NEVER GOT TAUGHT FOIL

ALL I KNOW IS FOIL IN THE KITCHEN

[sage dew]

then I agree, how in god's name are you an engineering student

do you want to learn foil for this problem or not?

[wraith tangle]

🗿

[sage dew]

https://youtu.be/nyk3UGwCAms?si=hCWY9FsUj8-KBAdj

[polar phoenix]

I wanna

Give up

Bc

I’m a visual learner

I NEED SOMEONE TO SHOW ME

[sage dew]

madam

if I may direct your attention to the video link I just posted

which is a video

that contains visuals that make you learn

[visual harbor]

if it helps, (x+2)(x-1) you would want to FOIL, [first, outer, inner, last terms]

[sage dew]

they have no idea what that means

they've never heard of the term before

[polar phoenix]

BLAME HIGH SCHOOL

[visual harbor]

foil itself doesn’t mean anything, it’s the acronym

first terms being x, outer being x and -1, inner being 2 and x, last being x and -1 again

use the appropriate signs to get that polynomial function

[vast shale]

i haven't either i don't think it requires a specialized method you ancan just intuitively get the idea

like

[sage dew]

I posted a video that doesn't require you to know the acronym and shows you how to do it

by the looks of it they have refused to watch it

'visual learner'

actually literally unhelpable if they outright refuse to learn about the one thing required to turn this into a -2 second problem

or any other method as a matter of fact

[polar phoenix]

I can’t do text tutoring

[sage dew]

then watch the video I provided

[polar phoenix]

I’m looking for an actual tutor tmrw

[sage dew]

not even the entire thing

[polar phoenix]

THAT DOESNT HELPE SJSDODBDKSDISMXJDJXNDHX SHXBDIDHSJXNSJZBSOZNS JD

[sage dew]

just the first 5 minutes gives you the general idea

in what way does the video not help?

[visual harbor]

what helps you? if it’s not a video or text

in person tutoring?

[polar phoenix]

someone giving me an answer

Lmfao

And in person

[sage dew]

called it

[visual harbor]

foiling is critical in engineering , literally any stem major

do not skip out on it

[sage dew]

joins virtual discord to ask for help then claims nothing except non-virtual, in-person tutoring is the only way they can understand

[polar phoenix]

Bro

WELL

MATH IS JUST NOT MY STRONG POINT

[visual harbor]

it’s hard yes, but don’t refuse to learn how it works, lol we’re just simply trying to help

[sage dew]

and we're giving you every tool known to mankind to try to help you understand it but you're completely unwilling

[polar phoenix]

no tf I’m not

I’m just tired

I just don’t get it

[sage dew]

then go to sleep, wake up well rested, and watch the first 5 minutes of the video to understand how to foil

[empty python]

Suck it up tbh stop being lazy

Go to bed wake up early willing to put in the work

So many excuses man

[sage dew]

im sayin

[empty python]

Close this channel

[polar phoenix]

No bitch

Ima keep it open to piss u off

[empty python]

Ur just embarrassing urself atp

[polar phoenix]

Ur supposed to be deleting discord 3 days ago

Lmfao why are u here

[sage dew]

are you just frustrated that someone didn't give you the answer upfront

[polar phoenix]

Yes

[empty python]

<@&268886789983436800>

[polar phoenix]

OK I AM

[empty python]

u r abusing the purpose of this server

[polar phoenix]

I been trying to get help for the past 2 hours

Hello

[sage dew]

lmfao

[empty python]

…

[empty python]

….

Ur definition of help is someone giving u the answer

[clear shoal]

You're very patient lol

[empty python]

I’m debating contacting mod mail or not tbh

[polar phoenix]

I’m mentally ill

[sage dew]

I agree

[empty python]

excuse after excuse

[regal parrot]

Everyone focus on the problem

[empty python]

Have u read this chat

She just wants the answer

[regal parrot]

oh i didnt see this

[sage dew]

you should totally start from the pinned problem it's a hilarious read

[empty python]

Fr

[regal parrot]

@polar phoenix I've muted you for a day. Quit demanding answers, we do not allow helpers to hand out answers here.

Feel free to open a new channel when your mute expires.

.close

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[paper stratus]

I'm not sure how to do 5

[jade anvil]

how many coins are there in 5?

[paper stratus]

10

2 outcomes for each so 20

[jade anvil]

no

lets try a smaller case

[paper stratus]

as in 20 diff outcomes

ok

[jade anvil]

write down all the outcomes for 3 coins

write them down and show me

[paper stratus]

ok

do u mean just outcomes or the way they are arranged

like

hht and thh

they are technically the same outcome but different arrangement

[jade anvil]

yes these are different outcomes

[paper stratus]

ok

[jade anvil]

good

how many outcomes are these?

[paper stratus]

8

[jade anvil]

what can we write 8 as?

something in terms of 2 and 3

[paper stratus]

ohhhh

2^3

and then its 2^10

[jade anvil]

because there are 3 coins and each coin has 2 configurations

good

2^10 is correct

[paper stratus]

2 outcomes

and 10 coins

does that work for everything

[jade anvil]

yes

[paper stratus]

u can put the amount of possible outcomes from 1 thing as the base value

[jade anvil]

try for a pair of dice

[paper stratus]

and the exponent as the amount

6^2

so 36

[jade anvil]

they will have 6^2=36 outcomes

yes

[paper stratus]

ohhh

thank you man

preciate the help

[jade anvil]

no problem

[paper stratus]

.close

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[vast shale]

how come?

[vast shale]

does $\floor*{\frac{2x+3-1}{2}}$ simplify down to $\floor*{x + 1}$?

[twin meteor]

tree bark enjoyer

[edgy gulch]

3-1 is 2

2x+2 is 2(x+1)

2(x+1) / 2 is x+1

[edgy gulch]

^

[vast shale]

yes

so how come my floor function is wrong

[edgy gulch]

oh fuck i thought you asked how

sorry mb

[edgy gulch]

wait isnt floor(x+1) just x+1?

because the domain is just integers

[vast shale]

true lol

ty

.close

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[ember bloom]

how would you find the radius

[kind light]

where is q

[vast shale]

yes

[ember bloom]

.close

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Channel closed

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[kind light]

whar

[vast shale]

it is clear the question

circumradius

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[vast shale]

is the highlighted bit just implying that f(y_2) < f(y_1)?

[vast shale]

im getting $f(y_1) = 4 + 5\cos(x+\pi)$ and $f(y_2) = 4 + 5\cos(x+3\pi)$ which i think simplifies down to [f(y_2) > f(y_1)] [\cos(x+3\pi) > \cos(x+\pi)] which is true so...?

[twin meteor]

tree bark enjoyer

[vast shale]

oh wait i dont think thats true for some value of x? is that enough to prove that its not eventually increasing?

[river minnow]

cos(x + 3pi) > cos(x + pi) is true? Are you sure about that?

[vast shale]

woops nvm

it seems to be false for all values of x i think

[river minnow]

Not eventually increasing means past any point you always can find a pair of points y1, y2 with f(y1) >= f(y2) despite y2 > y1

[vast shale]

wait isnt that what the statement says?

[river minnow]

No, it says the opposite

[vast shale]

or do you mean f(y2) < f(y1) despite y2 > y1?

[river minnow]

I negated the statement

[river minnow]

Yes, my bad

[vast shale]

oh

right yh

[vast shale]

so can i use some arbitrary value of x that disproves f(y2) > f(y1) using this expression? would that be an acceptable proof?

[vast shale]

^

[river minnow]

x has to he arbitrary to disprove the statement, yes

[sinful drum]

No

[vast shale]

how come?

it seems to be false for any x in R if i chuck it in my calculator

altho i guess it makes sense that it is not a solid proof

[sinful drum]

Using just one value of ( x ) to disprove ( f(y_2) > f(y_1) ) isn't enough for a solid proof because you need to show the inequality holds true for all possible values of ( x ), not just one.

[twin meteor]

Codelazy

[vast shale]

yeah makes sense

[sinful drum]

I know I always make sense

[vast shale]

how should i go on about proving it? i kinda forgot my trig

[sinful drum]

To prove ( f(y_2) > f(y_1) ) using trigonometry, you'll need to examine how the function behaves for different values of ( x ) that satisfy the given conditions.

[twin meteor]

Codelazy

[sinful drum]

Did you get it

[vast shale]

kinda but didnt we just talk about how testing some values is not enough of a proof? im confused

i think i can just use trig identities for this tbh

ty for the help

.close

[vocal sleet]

Channel closed

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[river minnow]

You are confusing x with y1 and y2

x is arbitrary, y1 and y2 should be chosen according to x

[vocal sleet]

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[gloomy thicket]

Zoom in if you must thanks

[fervent wasp]

,rotate

[fervent wasp]

!status

[vocal sleet]

What step are you on?
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2. I have begun but got stuck midway.
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[fervent wasp]

@gloomy thicket

[gloomy thicket]

7

Pls solve the wuestion with working please

@fervent wasp plsss?

@onyx marsh help pls

[vocal sleet]

@gloomy thicket Has your question been resolved?

[fervent wasp]

I’m not allowed to do that

!nosols

[vocal sleet]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[gloomy thicket]

Oh sorry

Then 1

I will explain how I did this, now I know that FC is 2/3, and that CE is 1/2. But i'm not sure how to get perpendicular height to find the area of the triange FEC

@fervent wasp

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@gloomy thicket Has your question been resolved?

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@gloomy thicket Has your question been resolved?

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[vast shale]

not sure how to do this more formally. for part b, i can imagine in my head that there are 5 combintations

[vast shale]

but for part c i can visualise but its more annoying and dont think i should do it that way (given that the sample can be way bigger)

[torn oracle]

I assume you could use combinatorics to provide a more formal solution

That would also help with solving c

[vast shale]

yeah ive been trying to do that but cant really wrap my head around it

[fading plume]

it's 5 choose 1 right

[torn oracle]

Well you have to have 3 heads and the 2 remaining tails can be obtained anywhere in the sequence except where the other is obtained

[hybrid flicker]

maybe think about this : if you need exactly x amount of heads, you kinda need to CHOOSE which coin toss(es) result in head

[vast shale]

right

[fading plume]

oh that's just 5, so you can do
TTTTH
TTTHT
TTHTT
THTTT
HTTTT
which obviously generalizes to n solutions for n coins

[hybrid flicker]

yes but for exactly k heads among n coin tosses, this strategy won't work

[fading plume]

but yeah for (c) you'd have to do n choose k

[torn oracle]

I thought c should be 20

You have 5 possible positions for the first tails and 4 for the second tails

Heads can be obtained anywhere else in the sequence

[hybrid flicker]

except what does "first" and "second" mean

there is no order in choosing the positions of tails

so you overcounted

[torn oracle]

First and second is

A tails can not be obtained on the same position as another tails

[hybrid flicker]

yes but

imagine

TTHHH

how do you choose it?

1st tails is 1st position, 2nd tails 2nd position?

[torn oracle]

T chooses position one of 5 and tails 2 of 5

[hybrid flicker]

Or 1st tails is 2nd position, 2nd tails 1st position?

which one is it?

bc when you do 5*4 you count both of those

even though they result in the same

[torn oracle]

Ah yup