help-27

[restive river]

Tysm

[devout snow]

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[stiff acorn]

Can someone please help me with Question number 247 please this is what I have done

[devout snow]

@stiff acorn Has your question been resolved?

[stiff acorn]

<@&286206848099549185> Someone?

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[flat stratus]

Hello, i would like to know how to show working for:
explain what happens as k gets closer to 0 and what happens as k gets closer to infinity for the equation: |z-(1+i)| = k|z-(2-i)|
i know that as it gets closer to 0 the circle gets closer to 1+i, and vice versa to 2-i, but idk how to show working out.
and that its a straight line if k=1 (i think)

[devout snow]

@flat stratus Has your question been resolved?

[long pasture]

if i remember correctly, it's a family of circles that passes through the 2 intersection of the the 2 circles when the circles are large enough

and yea, the 2 intersections will pass through the straight line when k=1

[flat stratus]

family of circles?

so like a range of circles

[long pasture]

yes, lemme grab a link

something like that

https://math.stackexchange.com/questions/2628001/what-exactly-is-family-of-circles

[flat stratus]

lemme read

not exactly

[long pasture]

oh?

[flat stratus]

like this

the 2 dots are the points which z - it

and the black circle is when k gets closer to 0

and red is infinity

they get smaller the more extreme k is

[long pasture]

i see

[flat stratus]

yea, i just dk how to show it as working

[long pasture]

anyways, if you gotta show working, I'd perfer to use
z=x+yi

[flat stratus]

yea definitly

[long pasture]

then it will be in the form of
(first circle with radius 0)-k(second circle with radius 0)=0

[flat stratus]

oh so i can explain circles as there are x^2 and y^2 left over when k=/= 1

hmmm

[long pasture]

and the simplify it to get a circle equation

[flat stratus]

oh yea i see

[long pasture]

(1-k)x²+(1-k)y²+Dx+Ey+F=0

something like that

[flat stratus]

mm yea i get the expand

[long pasture]

note that it will be interesting for 0<k<1

[flat stratus]

cuz quick shrink and it is positive

[long pasture]

when k get closer to 1

[flat stratus]

it gets bigger until line

[long pasture]

and after 1 it will switch sides XD

[flat stratus]

mm yea i think thats a good enough explanation for the question

i hope

anyways thanks you for helping :D

i think this is good for not uni maths

[long pasture]

cheers!

[flat stratus]

:D

[long pasture]

indeed

[flat stratus]

.close

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[hard knot]

Uhhh, Part B

So

I thought its y=y -> 4cosx -2 and then integrate it

for your values of A & B

But its not, your supposed to use

y = 2cos x + 2
it says on the markscheme

Can u also use 4cosx - 2? or no

Why????

{I think ik why, its cause both y values r basically reflections of eachother so you can use either one, or u can use them combined, i think)

Need someone to check this tho :3

Bc im confused

[manic condor]

I think 4cos(x)-2 is correct. It makes sense. I don't see how integrating 2cos(x)+2 from A to B gives R1.

[hard knot]

Oh lol, i didnt read the markscheme properly my bad

[manic condor]

Are you sure that's what your mark scheme says? Maybe they didn't say that.

[hard knot]

They foundthe difference in two areas, y 1 and y 2

[manic condor]

Ah. They did separately.

[hard knot]

Silly me

my bad on that

thank you haha,

ill read better

.close

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[feral rain]

Hello, this is the last two questions on my math contest that i didnt have and i dont have any
idea how to solve can anyone explain?

[ocean yacht]

,rotate

[feral rain]

sorry

[ocean yacht]

no probs

the feature is meant for it :)

[feral rain]

took the image on phone because the sheet wasnt released on the internet

im only in grade 8 so i really have no idea how to solve them

[ocean yacht]

oh

[feral rain]

its a pretty hard math contest

i dont think anyone got to last questions

[ocean yacht]

well I think we can begin with the fact that the area of all parts are equal

[feral rain]

yea so i thought that all the height and base is the same

for the 4 smaller tria

i dont know where to go after that tho

[ocean yacht]

$ar(\Delta ABD) + ar(\Delta DBE) + ar(\Delta DEF) + ar(\Delta FEC) = ar(\Delta ABC)$

[woven radish]

Wither

[ocean yacht]

let $ar(\Delta ABD) = K$

[swift oasis]

I think in ∆DEF and ∆EFC, if you take base as EF, then the perpendicular height is same

[woven radish]

Wither

[feral rain]

it says all images are not up to scale

[swift oasis]

oh

[feral rain]

yea

they're only for refrences

[feral rain]

i still dont know what do 💀

[ocean yacht]

we can find the area of one triangle

[feral rain]

oh yea

[ocean yacht]

4K = Area of ABC

[feral rain]

why 4 and not 3

oh bcz

1/2

[swift oasis]

because the internal lines divide the triangle into 4 triangles of equal areas

[ocean yacht]

yes

[feral rain]

oh yea

and the base for ABD must be 120 right

[swift oasis]

and you can calculate the area of equilateral triangle

[feral rain]

or is the refrence picture completely not up to scale

[feral rain]

legit havent learned that lmao

[ocean yacht]

it doesnt matter

[feral rain]

even in advanced classes

[swift oasis]

AB's length is 120

[feral rain]

wait small problem

the contest is

[ocean yacht]

$Area = \frac{\sqrt{3}}{4} a^2$ where a is the side

[woven radish]

Wither

[feral rain]

no calculators allowed

[swift oasis]

No problem

[ocean yacht]

yeah its simple math

[feral rain]

u can find root 3 that easily?

[ocean yacht]

not very complex to perform

[swift oasis]

Each angle is 60°

[ocean yacht]

we usually know it

[swift oasis]

In ABC

[ocean yacht]

but you can use long division to do it

[feral rain]

oh ok

[swift oasis]

√3 = 1.734

a = 120

[ocean yacht]

so we can now calculate area of each triangle

[swift oasis]

But how to measure the length of FC?

[feral rain]

yea

[swift oasis]

we can get the area of DEF and EFC

And FC is the common side in both of them

so it will be the base for both triangles

but if we don't know the height or the triangles are right angles, then idk how to solve further

[feral rain]

yea

[ocean yacht]

idk why do I think of conservation of angular momentum here suddenly

[feral rain]

i got 1558.85 for the area

[swift oasis]

[feral rain]

what next now 😅

[swift oasis]

Divide by 4

[ocean yacht]

lol, its kinda used in Keplers laws

and the principal here is kinda same

[feral rain]

what?

explain

[ocean yacht]

the constant areal velocity

[swift oasis]

I haven't studied gravitation till now

[swift oasis]

Oh I remember

[ocean yacht]

yeah

[feral rain]

can we solve the problem now bruh

[ocean yacht]

we need trig for this ig

[feral rain]

i wanna flex to my friends that i did it

is there a simpler way

i dont think any 8th graders know trig

[swift oasis]

ABC = 1558.85 divided by 4 will be the area for each triangle

[feral rain]

i meant this

[ocean yacht]

real

[ocean yacht]

oh, its based on vectors and trigonometry

[swift oasis]

Some of them do, but atm I am not sure how to apply trig when we don't know how it divides the triangles

[feral rain]

ah ok

[feral rain]

yea this is an international math contest

so the top ones out there prob know

[swift oasis]

That's why the questions are not that easy

[feral rain]

im pretty sure only 1 kid in 8th grade at my school is learning trig

[fervent sundial]

[feral rain]

maybe we can try question 30

[fervent sundial]

what's the question?

[feral rain]

might be easier

[swift oasis]

@fervent sundial

[feral rain]

question 30

[swift oasis]

The figure is not to scale btw

[fervent sundial]

right, what have you done?

[feral rain]

literally nothing

bcz idk what to do

[ocean yacht]

nothing? we've tryed to help him using the fact that the areas are same

[feral rain]

for question 30 tho

[fervent sundial]

Do you see that this is 3 similar triangles?

[feral rain]

yea

[fervent sundial]

each one of those has side lengths x right?

[feral rain]

ye

bcz 5 equal parts

[fervent sundial]

okay so what's the ratio of the area of the smallest triangle to the biggest triangle

note we're only working on whatever the purple contour marked out (3 triangles)

[feral rain]

tbh idk

because there might a formula or something i didnt learn

[fervent sundial]

there's no formula

what's the ratio of the lengths of the smaller triangle to the biggest triangle?

[feral rain]

1:1

[fervent sundial]

clearly not

[feral rain]

sorry

i thought u meant base

[fervent sundial]

the small triangle has side length x (whatever you want to call that side)

The big triangle has side length of 3x (again whatever you want to call that side)

[swift oasis]

If it is 1:1 then both are equal, how can it be there any smaller and bigger sides

[feral rain]

how do we know that tho

[fervent sundial]

I assume you can answer this now

[feral rain]

just by seeing the picture?

[fervent sundial]

cuz x + x + x lol

[feral rain]

oh i thought u meant the other length

[swift oasis]

No

We are working on the information we already have

[feral rain]

yea so 1:3

[fervent sundial]

do you follow how we proved that the triangles are even similar to begin with?

we used ASA

[feral rain]

angle side angle right

atleast thats what i learned ASA to be

[fervent sundial]

the red angle is shared for the smallest triangle and the biggest triangle

[swift oasis]

we could also use AAA ig, as 1 angle is common, there is perpendicular at every point, then the 3rd angle is also equal

[fervent sundial]

The red angle is 90

[feral rain]

ohhh

[fervent sundial]

from AA, you already know that these two triangles are similar

[feral rain]

yea

[fervent sundial]

anyway back to where we were at

what's the ratio of the side lengths of the smallest and biggest triangle?

[feral rain]

1:3

[fervent sundial]

and the area is the multiplication of two side lengths right?

if each side length is in the ratio of 1/3 then the area is in the ratio of 1/9

cuz 1/3 * 1/3

[feral rain]

yea

[fervent sundial]

,, \frac{A_s}{A_B} = \qty(\frac{l_s}{l_b})^2 = \qty (\frac 13)^3 = \frac 19

[woven radish]

kanna

[fervent sundial]

anyway

[feral rain]

mhm

[fervent sundial]

so doing some algebra, we have that the big area is 9 times the small area

[feral rain]

ohhh

makes sense

[fervent sundial]

what should we do next? Lol

[feral rain]

we already know the shaded area is 10 cm^2

soo

idk

[fervent sundial]

Our goal is to find this btw if that wasn't apparent

[feral rain]

ok so the 2nd biggest triangle

[fervent sundial]

can you find the ratio of the middle triangle's area and smallest triangle's area?

[feral rain]

well the middle triangle area should be 1/4 the ratio of the small triangle area

[fervent sundial]

good

well not phrased properly but i understand you

4 * smallest triangle = middle triangle

[feral rain]

yea

[fervent sundial]

Middle triangle is everything btw

[feral rain]

i gotta go to school in 10 mins

ye

[fervent sundial]

Okay lol anyway

[feral rain]

u think this can be done in 10 mins

[fervent sundial]

yeah we're almost done

[feral rain]

alright

[fervent sundial]

,, \frac 19 = \frac{A_s}{A_b}

we had this before right?

[woven radish]

kanna

[feral rain]

mhm

[fervent sundial]

,, A_b = A_m + 10

[woven radish]

kanna

[fervent sundial]

do you agree with that?

[feral rain]

whats ab and am again

sorry

[fervent sundial]

A_b = area of big triangle

A_m = area of middle triangle

[feral rain]

can u explain why is that?

[fervent sundial]

area of middle triangle + 10 = area of big triangle

[feral rain]

ohh

yea

mb

[fervent sundial]

and we had that area of middle triangle = 4 * area of small triangle right?

[feral rain]

ye

[fervent sundial]

,, \frac 19 = \frac{A_s}{A_b} = \frac{A_s}{A_m + 10} = \frac{A_s}{4A_s + 10}

[woven radish]

kanna

[fervent sundial]

finally, we have everything in terms of one variable (area of small triangle)

[feral rain]

yea

[fervent sundial]

,w 1/9 = a/(4a + 10)

[woven radish]

Results provided by WolframAlpha

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

Requested by kannaaaaaaaaaaaaaaaaaaaaaaa

[fervent sundial]

area of small triangle is 2 from algebra

[feral rain]

so the medium triangle is 8-2

and 6

[fervent sundial]

yes

so what's the area of the entire figure?

[feral rain]

12+10+13

thankss

i understand now

[fervent sundial]

,calc 12 + 10 + 13

[woven radish]

Result:

35

[swift oasis]

I think

[fervent sundial]

can you find out what you missed lol

[feral rain]

+10

[swift oasis]

It's 10×2 + 12×12

[feral rain]

lol

[fervent sundial]

yes

[feral rain]

tyyy

ill be flexing to my friends now

[swift oasis]

Cuz those two parts of pentagon occur 2 times ig

[feral rain]

yea

[swift oasis]

.close if your queries have been solved

[ocean yacht]

what about the first one?

I think I found a solution

[swift oasis]

Can you share?

I've tried it in the meantime, but it's messed up

[ocean yacht]

sure

dm maybe

or should I put it here?

[swift oasis]

Ig you should put it here

If there will be any issues, then we might get some help lol

[swift oasis]

But it says the figure is not to scale

what if FC != DF ?

[ocean yacht]

its midpoint

cuz the triangles have same area

[swift oasis]

oh yes

that's the point I was missing

i took it DF as y and couldn't solve further

thanks @ocean yacht

[ocean yacht]

np

[devout snow]

@feral rain Has your question been resolved?

[devout snow]

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[willow urchin]

I got the 4 Terms (Not Shown) but not getting how to write the general term

[willow urchin]

nvm i got it

.close

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[rare swallow]

XD why is this incorrect?

[devout snow]

@rare swallow Has your question been resolved?

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[fossil locust]

The covertices are not necessarily the ones that share the same x-coordinate

[fossil locust]

They're the ones on the minor axis

So for this ellipse the major axis is up-down, and the minor axis is left-right

So you need the other pair of vertices

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[trail pawn]

how to solve for mean,median and mode

[floral ridge]

mean is sum of observations/number of observations

median is the middle of the dataset (arranged in descending or ascending order)

mode is the observation which occurs most frequently

[trail pawn]

what if theres no descending or ascending order?

i dont understand

[meager yarrow]

Rearrange it yourself

[trail pawn]

by ascending?

[meager yarrow]

Yeah

[trail pawn]

what if theres a repeating number

[floral ridge]

arrange it then

[floral ridge]

let's say original data was 1,3,1

ascending order would be 1,1,3

[trail pawn]

ohh

then number 1 ascending order is 2,3,7,8,8,9,10,13,14?

[winter patrol]

yes to your updated result

[trail pawn]

now to solve that for mean

i use the x=Ef/n right

[devout snow]

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[sharp sable]

I need to send my answer in about 30 mins can someone help me understand this and tell me the answer

[devout snow]

Please don't occupy multiple help channels.

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[calm crater]

Hello, I think there is an error in my maths book, could you confirm for me?
I can't find the same derivative, I come with e^(-x^2)(1-2x^2)

[hasty saffron]

Could you show your work

[hasty saffron]

Here if there's a -x² in final line then it should be right

[calm crater]

i will do it again i have erase it whait

[hasty saffron]

Within exp I mean

[calm crater]

@hasty saffron

[onyx rune]

but f(x)=-1/2e^x^2

you diffrentiated wrong thing

[hasty saffron]

$\int xe^{-x^2} dx$, this is what you've to find

[calm crater]

the book whent from

to the lambda of x

yes

[woven radish]

Sulphur

[hasty saffron]

Missed the dx

[calm crater]

I don't understand what you want to tell me

[hasty saffron]

How did you integrate this

[calm crater]

integration by part

but why do you ask

i have to diferentiate not to integrate

[hasty saffron]

Coz I didn't quite understand what you sent in this pic

[calm crater]

ok sory

ok

[hasty saffron]

We are going from λ' to λ

[calm crater]

yes

[hasty saffron]

So why differentiate?

[calm crater]

ooooo fuck

mannn

i'm soo dumb

sorry

[hasty saffron]

C'est d'accord

[calm crater]

oui oui 🥖

[hasty saffron]

Lol

[calm crater]

sorry for the disturbance

and ty to tack carre aboute a dumbass like me

❤️

.close

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[hasty saffron]

It's all cool

[devout snow]

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[frail sun]

On the answer key, it says this limit is just infinity. However, I get -6/0, meaning it should be -infinity?

[frail sun]

I just plug in 1 for the x values to find the -6/0

[woven radish]

Someone

[frail sun]

The answer key just says infinity, which is where I'm very confused

[winged wasp]

Since the numerator is negative and the denominator 2 x 3 − 14 x + 12 approaches zero and is less than zero for x near 1 to the right, the function increases without bound

so positive infinity

you can see it more clear if you use Lopitals rule

[frail sun]

I see, I'll try Hospital's rule really quick

[frail sun]

I got -1/8 with Hospital's rule

[woven radish]

Someone

[winged wasp]

use it 1 more time

[frail sun]

is there a way to know when to use it twice?

[winged wasp]

ı am assuming you took the derivative correct

[frail sun]

this is my first time really using the rule, sorry hahaha

[winged wasp]

no problem but my fault. you cannot do lopitals in this sitaition

you can only use lopitals in 0/0

[frail sun]

yeah, that's what i also thought

[winged wasp]

it is better to understand way function works by plugging values

like 1.2

then 1.1

it will get larger and larger and larger

you can plug in 1.000001

[winged wasp]

but this is way better solution

[frail sun]

I see

plugging in 1.2 gives me +

that's really weird just 1 gives me - and -infinity

[winged wasp]

that is why limits are kinda tricky

we do not care what happens at x=1

[frail sun]

Thank you very much for your help!

[winged wasp]

Your welcome

@frail sun ı think you need to close the channel now

[frail sun]

.solved

[devout snow]

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[lavish pebble]

help

[lavish pebble]

alright so im an 8th grader right

and i have absolutely no idea on how to solve polynomial equations

like absolutely no idea

and i got a test in 5 days for 15 points which determines if i pass the class

and if i dont then i gotta go to recuperation for maths

so and i cant find a turorial that helps me understand

so i need help

with understanding polynomial equations

and also quotients of monomials

and zero and negative exponents yeah

i feel so dumb rn smh

[jaunty mantle]

Do you have some examples?

[violet wind]

You'll probably have better luck checking out Khan academy then getting someone to teach you a whole course

Then ask questions when you get stuck

[lavish pebble]

oh boi i got like 20 of each theme

[lavish pebble]

dude

wth is khan academy

[violet wind]

Website that has lots of free math education content

[lavish pebble]

oh so its free?

[violet wind]

Yeah

[lavish pebble]

ill check it out then

[soft nest]

https://www.khanacademy.org/

[lavish pebble]

thank you

soooo

how do i get someone to teach me a course?

[oak yarrow]

thats the sad part - you most likely won’t 😭

and so is the case with literally anyone else not having a teacher on speed dial

[lavish pebble]

oh dang

[violet wind]

Hire a private tutor

[lavish pebble]

how do u expect me to hire a private tutor for a exam in 5 days as an 8th grader

[violet wind]

I don't expect you to do anything. You asked how you could get someone to personally tutor you and I gave the only correct answer: pay them money

Unless you mean on Khan academy

[lavish pebble]

yeah thats what i meant

[violet wind]

Ah ok

[lavish pebble]

yeah

[violet wind]

There should be a section for 8th grade math somewhere on there

[lavish pebble]

yeah i got there

but cant find polynomial equations at all

oh man im doomed

[violet wind]

https://www.khanacademy.org/math/algebra-2-fl-best/x727ff003d4fc3b92:more-on-polynomial-equations-functions-intr

Maybe this?

Seems like you'll have more luck under algebra 1 and algebra 2 then 8th grade

[lavish pebble]

yeah it might be it lemme check it out

[devout snow]

@lavish pebble Has your question been resolved?

[lavish pebble]

probably yeah

[devout snow]

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[lapis shadow]

How does one approach these

[heady plinth]

First one seems pretty straightforward

There’s no way concatenation turns it finite

When one of them is infinite

Don’t know how to rigorously justify it but it just seems obvious idk

[lapis shadow]

but it doesn't turn uncountably infinite?

[heady plinth]

No, countable * countable is countable

Like for example you can think of rational numbers as a composition of two integers

If you had an infinite number of languages it would turn uncountable even if they were all finite tho

[devout snow]

@lapis shadow Has your question been resolved?

[lapis shadow]

okay so I'll try find a way of proving this, thanks

what are your thoughts on part two

[heady plinth]

No idea sorry

[lapis shadow]

<@&286206848099549185>

[lapis shadow]

Also these two, I believe the second one of these is countably infinite but providing an adequate proof is what i'll need help with

the first one idk

the second one, the yield can be sorted into countably infinite sets, e.g.

• A set of "01" n times, followed by "0"
• A set of "01", followed by "0" n times

so on so on

each one is a new set

and there's a theorem that

The union of at most countably infinitely many countably infinite sets is countably infinite

So I believe this set is countably infinite

but I don't know how to word it exactly

I believe the first one is uncountably infinite, simply because the set of complex numbers is uncountably infinite

[lapis shadow]

<@&286206848099549185>

[faint zinc]

The first one is finite.

There are exactly 8 solutions. (up to multiplicity)

@lapis shadow

This is because polynomials of degree n have n solutions (again, up to multiplicity)

[lapis shadow]

@faint zinc what about these two?

and am i correct about the language L which is strings of '01's?

[faint zinc]

The first one is countably infinite, as you supposed.

And any regular language is comprised of only finite strings, which means that it is also countable.

[lapis shadow]

Okay, so I'll use this to extend the proofs myself

[lapis shadow]

is this idea good too?

[faint zinc]

I'm not certain what you are referring to here.

This is probably my fault for not reading carefully

but can you help me out?

[lapis shadow]

Sorry, I was trying to elaborate on the idea that the Language L over the alphabet A consists of countably infinite countably infinite sets

Meaning Language L is countably infinite

[faint zinc]

If a language consists only of finite length strings, then it is countable.

because membership of L requires that it not end with a 1, it is not clear to me that infinite strings would be disallowed.

in other words 01{0...} seems to be allowed.

[lapis shadow]

infinite strings seems to be allowed

[lapis shadow]

yes

[faint zinc]

if this is the case, then it is uncountable

[lapis shadow]

oh?

[faint zinc]

And you can prove it using the diagonal argument.

consider the following subset of L consisting of the string 01 followed by any infinite binary non-terminating sequence

If we list this sequence out:

01 01011011011000111...
01 10001010011010001...
01 00000100110001101...
01 01011101100110001...
...

Then flip all of the values on the diagonal, this will make a few entry that is different from each member of the list.

but is still a valid member of the subset of L

therefore, this subset of L cannot be enumerated

and is uncountable.

and because L has an uncountable subset, it too is uncountable.

[lapis shadow]

Okay so we have:

• z E C question: Finite
• Language L over alphabet A: uncountably infinite
• L1 ° L2: Countably Infinite
• Following question: Countably infinite

yes?

[faint zinc]

That's my understanding

[devout snow]

@lapis shadow Has your question been resolved?

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[visual hatch]

I need help again 😔

[visual hatch]

how do i solve this

uhm its pi/180

[dense jay]

this is what youd multiply a degree result by to get the equivalent radian one

flip it and youll do the reverse

[visual hatch]

how?

can you explain it visually?

[cinder kayak]

just use π = 180° and ull get the answer

[visual hatch]

ok let me send a picture of what i think you guys are saying

[dense jay]

pi radians is equivalent to 180 degrees, so dividing a radian value by pi gives the you the number of pi's, you then multiply that by 180 since the number of pi's in radians is equivalent of the number of 180s in degrees, same ratio

[visual hatch]

dont give me the answer

[cinder kayak]

ok

[visual hatch]

so 5pi/3

do i divide that by 180?

what does pi=180 mean?

[cinder kayak]

no

[visual hatch]

pi is 3.14 and 180 is 180 degrees

[cinder kayak]

substitute pi with 180

[cinder kayak]

no dont use that

were talking radian measure

[visual hatch]

oh im sorry

[cinder kayak]

so pi in radians is 180 in degrees

no its fine

[visual hatch]

okay pi in radians is 180

wait i dont understand

Like this?

[dense jay]

the measurement of an angle pi radians is equivalent, not equal, to 180 degrees as a measurement

[cinder kayak]

bro

[dense jay]

other way, 180/pi

[cinder kayak]

you know how some questions are like what is x+5 when x=3?

[visual hatch]

yes

[cinder kayak]

just imagine its the same with this

pi = 180

substitute

[visual hatch]

oh pi is like x okok

[cinder kayak]

yes

only here

when u convert radians to degrees

[dense jay]

ah did not see the division

[visual hatch]

uhh

Guys I don’t mean to make you all mad but I still don’t understand

How do I solve it?? Do I put in my calculator “5pi/3 x pi/180”

Oh

Would both pi there cancel each other out?

What do I do now?

thank you

perfect thank you

thank you!

i needed that

also

ill take note of that, i was looking at degrees-radian and i wondered what formula i was using

so thank you

How do I solve 5?

180/2?

90?

perfect degree?

oh crap

yes

-90

yeahh!!

thank you

[cinder kayak]

you got it?

[visual hatch]

yes

:>

does anyone know where i went wrong on this?

3.65 is the radius

radians

i think

oh

so 0 is radians

i wont do anything to it right?

cuz they didnt give me a degree

0r?

lol the 0r

operating room

waot waot

wait

so i would multiply both?

3.65(13.8)

?

you are a genius

thank you

I don’t know any math ☹️🧍‍♀️

I know how to use the matrix trick

To find the uhhh

Polynomial

I think

Idk I have a hard time in math lol

And I’m taking trig lolol

Gotta love being a bio major

Wait

It’s not matrix

It’s SYNTHETIC DIVISION

God I LOVE doing those

But I suck at math 🙃

It’s finding the polynomial equation

Like u see that equation on top

Wait

idk how to explain it

but i love doing those for fun

so basically youre given a number

x=2

youre gonna use that to solve the rest of your equation

lol 🫠

i dont wanna bore you with it

but its very fun to do imp

imo*

[devout snow]

@visual hatch Has your question been resolved?

[visual hatch]

No

🫠

I still got a question but I’m eating

[devout snow]

@visual hatch Has your question been resolved?

[visual hatch]

@storm kiln

do i use the other formula for this?

wait what?

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[visual hatch]

2

Yes

It’s 2.52

oh

yes

yes

ohh

we divide?

2.738095238?

o

2.738?

thank you!

i can close this now

.close

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[devout snow]

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[lunar lance]

how does the -1/3 become an exponent after step 4

[restive river]

because if it's at the front you can move it to the exponent

log rules no ?

[lunar lance]

damn

that was way easier an explanation than i expected

thx

.close

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[restive river]

why does he look at the 60 degrees

in the unit circle would he not look at the 300 degrees

because 300 degrees equals 5pi/3

[meager yarrow]

But it’s -5pi/3 not 5pi/3

[restive river]

so does he get the refernce angle

if it's negative

360-300

to get 60

[meager yarrow]

Yeah you can do that

[restive river]

oh okay

thanks!

.close

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[restive river]

how come he is multiply criss cross

[restive river]

instead of across

how do i know when to multiply across then criss cross when it comes to dividing fractions

.close

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[tender relic]

hey, could someone help me out with questions 9 and 13?

[tender relic]

these are my answers so far.

Don’t know where to go on from there.

[devout snow]

@tender relic Has your question been resolved?

[tender relic]

<@&286206848099549185>

[dense jay]

subtract one from the other (fx and fy)

[tender relic]

ur talkin about 9 or 13

[dense jay]

9

[tender relic]

wdym subract

[dense jay]

in 13, what does this say?

[tender relic]

both x and y =0?

[dense jay]

in the same way youd solve any simultaneous equations, you can subtract one from the other

[dense jay]

thats definitely not what that says

oh its a cos

[tender relic]

undefined?

impossible

[dense jay]

are you just saying random things?

[tender relic]

no

[dense jay]

because youre saying some pretty random stuff when i was only asking what you wrote

now i know its a cos

anyway

[tender relic]

cosy=0 then y=pi/2

[dense jay]

e^x is never 0, so in both of them you can divide by it

[tender relic]

yes

[dense jay]

where is there a cos x, anywhere

[tender relic]

and siny=0 then y=0

[dense jay]

again, where is there a cos(x)

you have a cos(y)=0 and a sin(y)=0

[tender relic]

yes

therefore y= pi/s and 0

right?

[dense jay]

i mean, y has infinite values thatll satisfy that

[tender relic]

mhm

they didnt put range

or domain

the books answer is weird

its just a "none"

[dense jay]

yeah

because there arent any

you cant have cos(y)=0 and sin(y)=0 simultaneously

[tender relic]

since we dont have ranges or domains of y?

[dense jay]

just doesnt happen

thats irrelevant

[tender relic]

fuck that question

[dense jay]

its the fact that you cant have fx=0 and fy=0 at the same time

[tender relic]

yh yh i think i got it

im still not sure about q9

or maybe bc its 4 am and my brain aint working

wtf thats simple maths

[dense jay]

just simultaneous equations
like if i had a+b=0 and a-b=0 i can subtract 1 from 2 and get -2b=0 or something like that

thats what i meant by subtract one from the other

[tender relic]

that leaves me with 1-1 + y^2 - x^2

[dense jay]

=0

sure

[tender relic]

so we can say y^2 = x^2

yh wtf am i doing

ok

so

1+2x(x)^1/2 + x^2 =0

now i solve for x

fuck that 1

[dense jay]

where did y=x^1/2 come from

[tender relic]

from y^2=x^2

so

oh

[dense jay]

might want to think that one over

[tender relic]

wait

OH

OH

fucking hell

[dense jay]

y=+-(x)

[tender relic]

yes yes

wait

that means

1+2xy + y^2 =0

we know y^2 = x^2

so y=x

so 1+2x^2 + x^2 =0

so 1+3x^2 =0

what

oh

x is positive or negative

we neglict the positive

we take the negative

that means

[dense jay]

y=+-x, two cases my friend

y=x and y=-x

one of them, the one you just chose (y=x) doesnt work

because theres no x thats going to satisfy 3x^2=-1

[tender relic]

yes yes

Is that rigjt

[dense jay]

you should still show the y=x attempt and say why it doesnt work, but beyond that it looks good

you just need to classify those points now

[tender relic]

yeh theyre both saddle points

great

thanks a lot for the help

[dense jay]

np

[tender relic]

.close

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[lofty bay]

#help-27

[lofty bay]

I need help with this

@untold crow

Hi

I need to finish this as soon as possible and I don’t understand how to do it

I have to submit my homework in like 15-20 mins

[untold crow]

What part of the question don’t you understand?
We have a function f(x) that corresponds to the graph you see there. The format of your answers would be written as x E (x₁ , x₂), though why they say “y” I don’t get.

[lofty bay]

Ok so I got these answers

But I need the steps

So for the first one I got Which is (-♾️, 2) U (♾️,2) U (-1,1)

B) (1,2)

C) (-♾️,-2)U(-1,0)

I don’t know for D

Are those answers corrext?

If so I need the steps for it

Or should I just put the answers down

Are you there @untold crow?

.close

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[tall fern]

How do I know if a sequence is geometric or not?

[tall fern]

thanks

.close

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[hardy crag]

can someone please help with this question

[flat stratus]

so let's say there is x amount of ppl and a is average age now, the total age present is x*a, if 4 10 year olds leave then average is a-1

and if 4 22 year olds arive then average is a+1

if u put that into equations it could be visually more solvable

[hardy crag]

oh alright

thank you

.close

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[rare current]

is our prof a devil for giving us this

[rare current]

is there a way to solve this other than hand multiplying the matrix 3 times

coz even when I did that and checked it was correct my final answer lead to an impossible solution

[flat stratus]

HOLY

well it's undergrad so it seems not toooooooo bad

[wicked turtle]

hint

do you know how to find the characteristic equation of B

[rare current]

does that have to do with eigen values? we haven't done them in this class

[wicked turtle]

yes it is very related to eigenvalues, they are the roots of the characteristic equation

and there's a theorem called the cayley hamilton theorem

which says that a matrix is a solution to its own characteristic equation

[rare current]

lemme google that shit real quick

ok yah this hamilton thing is literally the perfect thing for this problem but I still managed to mess up the tedious steps 💀

I hate these types of questions so much

[wicked turtle]

haha yea

it makes the problem a lot easier but there's still messy algebra to calculate the polynomial

[rare current]

and yah when I plug it into wolfram it's right

[wicked turtle]

nice

[rare current]

broo it's soo much annoying tedious math

[wicked turtle]

this is why computers exist haha

[rare current]

like there's no way I'm trusting myself with this during the exam

2x2 is max for me to do with reasonable accuracy

[wicked turtle]

yea, 3x3 determinant involving variables is ugly for an exam

[rare current]

hopefully he doesn't pull a 3x3 for this

he didn't even teach us about hamilton so this one was nasty to begin with

[wicked turtle]

that's surprising

i wonder how the hell he expected you to solve this

[rare current]

I hand multiplied until B^3

still got it wrong

[wicked turtle]

as you said, this is like a textbook example for using cayley hamilton

[rare current]

yah

thanks tho

definitely a cool tool to have for the exam if this did show up

[wicked turtle]

especially if he gives you a reasonably "nice" matrix

like say upper triangular

where you can just read off the eigenvalues

[rare current]

yah

[devout snow]

@rare current Has your question been resolved?

[rare current]

ok after literally my 3rd time redoing the hamilton thingy, I finally got the right answer 0 of errors

main thing i learned from this small experience is for large enough computations like this one I should definitely break things down as much as possible cuz I don't have enough ram in my brain

I'll make mistakes otherwise

[wicked turtle]

yea

so many opportunities for sign errors among other things

[rare current]

ok so my exercise sheet followed up with "use this to find B^-1"

this is the solution which I can't seem to grasp

non of this is in the slides and our prof did NOT go through this

do you know what's going on here?

[fossil locust]

They rearranged to find B^(-1)

So if AB = I, then A^(-1) AB = A^(-1) I = A^(-1)

So B = A^(-1)

The first step they did was to rearrange for I on the RHS

So $B^3 - 9B = 9I_3, \frac{1}{9}B^3 - B = I_3$

[woven radish]

south

[fossil locust]

And then factor out a B to get (B)(matrix) = (identity matrix)

[rare current]

ok yeyeye I see it now

thanks brother

[fossil locust]

No worries

[rare current]

fuck my brain is so fried I coudln't even do the more basic thing lmao

[fossil locust]

It's alright, npnp

[rare current]

I'm so screwed in the exam 😭

[devout snow]

@rare current Has your question been resolved?

[devout snow]

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[glad shell]

so im stuck on a question but i checked the answer key now im more confused, I figured out the first "find x" part where it says segment DC is 4 but i just dont understand how the teacher got the random angle measurements like 20

[glad shell]

nvm i figured it out sorry yall

.close

[devout snow]

Channel closed

Closed by @glad shell

Use .reopen if this was a mistake.

[devout snow]

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Remember:
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[zinc pecan]

i have dumb question

[zinc pecan]

how he did go from first step to seconde one

i know its dumb question but

[jaunty mantle]

Probably the conjugate?

[zinc pecan]

yeah thx

i got it now

[formal sierra]

correct

don't forget the parenthesis btw

could cost you a point depending on your teacher

[zinc pecan]

yeah our teacher he is just cool, in final exam i will need it

Btw E(0-)

is it 1 or -1??

[formal sierra]

what's E again?

[zinc pecan]

parte entier or something like this

like this E 0- it goes from left to right into 0

and E 0+ goes from right to left into 0

nvm 0- its -1

[devout snow]

@zinc pecan Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hollow shore]

Is the last done incorrectly especially the deonmiator??

[hollow shore]

also i wanna know how we got to the last step

[stuck field]

yeah it's wrong

[woven radish]

! What the hell am I doing here?

[stuck field]

And to get there, you're using the fact $\sqrt{ab} = \sqrt{a}\sqrt{b}$ when a,b $> 0$

[hollow shore]

thats what I was thinking

[woven radish]

! What the hell am I doing here?

[hollow shore]

is there a yt video i could watch?

[stuck field]

Nothing for this specific problem.

But laws of exponents/surds.

I guess a video on that.

[hollow shore]

How would I know what I could draw to the graph?

[stuck field]

What's that supposed to mean?

[stuck field]

I'm asking what was your question again?

[hollow shore]

how to draw the graph

from the given function

[stuck field]

Well you'd differentiate the function to see where its increasing and decreasing. Then double differentiate to see if it's convex or concave.

Then you'd also look for points like x = 1, where it's not defined.

Etc etc.

[hollow shore]

ohh so if we look at c)

we draw like a hidden vertical line

and we know when the the curve is up or down

How come the first one is equal to 0 meanwhile the other is greater than 0?

Oh is it because x^2 + 1 is always greater than 0 for all x

[stuck field]

Correct.

So you only look at tbe denominator.