help-0

[sleek timber]

,rotate

[lone heart]

@sleek timber Has your question been resolved?

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@sleek timber Has your question been resolved?

[runic glacier]

first of all, you should be careful of the subtitution you are applying

$u = \frac 19 \ln x \implies u^2 = \frac 1{9^2} \ln^2 x$

[ocean seal]

shsgd

[runic glacier]

instead, you want

[u=\frac 13 \ln x]
[dx = 3x du]
[ \implies \int \frac 1{\sqrt{1-u^2}}du ]

[ocean seal]

shsgd

[runic glacier]

for the first term

[sleek timber]

Oh yeah

[runic glacier]

with the same substitution for the second integral:

[ \int \frac 1{2x}\cdot \frac{\ln x}{\sqrt{1-\frac 19 \ln^2 x}}dx ]
[ = \int \frac {3x}{2x}\cdot \frac{3u}{\sqrt{1-u^2}}du ]
[ = \frac 92 \int \frac u{\sqrt{1-u^2}}du ]

[ocean seal]

shsgd

[runic glacier]

so now you have
[ \int \frac 1{\sqrt{1-u^2}}du - \frac 92 \int \frac u{\sqrt{1-u^2}}du ]

[ocean seal]

shsgd

[sleek timber]

Ok Ty

.close

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@verbal galleon Has your question been resolved?

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[torn gate]

um do you know the answer?

i tried but im not sure if my reasoning is correct

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[steep jacinth]

.reopen

[austere charm]

it would be A. right?

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[austere charm]

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[stark spindle]

Can anyone help me on this? I’m struggling

[stark spindle]

<@&286206848099549185>

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[versed halo]

i need help with stats and probability,

1. wtf is it?
2. Can you teach me at least the basics beyond common sense
3. can you give me some problems?

[balmy grail]

Start here:
https://www.khanacademy.org/math/statistics-probability/probability-library

[fleet crown]

Welcome to the world of borderline evil math

Enjoy

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[frigid rapids]

Find the surface integral of the paraboloid z=4-3x^2-3y^2 when 1<z<4 and the vector field F is (2xy^2, -y^3/3, z(1-y^2))

[frigid rapids]

So far here is what I have:

I take paremeterize the 4-3x^2-3y^2 to get <rcos, rsin, 4-3r^2>

I take the partial derivative dr and dθ

to get cosθ, sinθ, -6r and -rsinθ, rcosθ, 0

then I take the cross product of those and get 6r^2cosθ, 6r^2sinθ, rcos^2(θ)+rsin^2(θ)

then I dot product that with my vector feild, converted into my cords using <rcos, rsin, 4-3r^2> to get:

12 r^5 cos^2(x) sin^2(x) - 2 r^5 sin^4(x) + r (4 - 3 r^2 (1 - r^2 sin^2(x)))

then i take this integral ∫0 to 2pi∫0 to 1[12 r^5 cos^2(x) sin^2(x) - 2 r^5 sin^4(x) + r (4 - 3 r^2 (1 - r^2 sin^2(x)))] drdx

which i think is my surface integral

and i get 13pi/4

[cinder compass]

just use

$\int_M \dd{\omega} = \int_{\partial M} \omega$

[ocean seal]

xd

[frigid rapids]

can i get some more elaboration? i dont get what that is saying

[cinder compass]

no

kidding

[frigid rapids]

lol?

[cinder compass]

[frigid rapids]

im pretty sure my answer is either supposed to be 3pi/2 or pi, but really dont see what im doing that wrong to not get there

[frigid rapids]

oh wait you gave me stokes theorem

sadly i need to use surface integrals

the whole problem was calculating divergence theorem, and for part b, im supposed to verify the divergence theorem by directly computing the surface integrals

<3

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@frigid rapids Has your question been resolved?

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[alpine sable]

im stuck

[teal gulch]

(BC)^-1 isnt always the same as B^-1C^-1

A^T*(A^T)^-1 = I, then you get (BC)^-1 BC^2

BC^2 = (BC)C by associativity

so u get (BC)^-1(BC)C

[alpine sable]

(AB)^-1 = B^-1A^-1

[teal gulch]

oh yeah ur right sry i misread

[alpine sable]

oh i didnt know A^T*(A^T)^-1 = I

i see it in my book!

thank youuuuu

[teal gulch]

np

[alpine sable]

.solved

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[heady field]

can somone explain the secnod part of this quesiton?

nvm'

.close

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[rose lichen]

How do I do

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[cosmic tinsel]

I got the wrong domain for F

Please explain

ans key says it must be -3>=x, 3>=x

[vital nova]

x € [-3,3]

[cosmic tinsel]

?

[vital nova]

Domain of x

[-3,3]

Since the polynomial is in root

So the polynomial should be >=0

What's ur ans ?

[cosmic tinsel]

Red

Underlined

Is the domain I got

I just got two values and didn’t know what to do

Like ofc after graphing it I can see why the domain is what it is

[vital nova]

The graph would be parabola

@cosmic tinsel

For reference check (d) part

[cosmic tinsel]

No this is the graph

I’m confused

I think I’ve graphed it correctly

[vital nova]

Uhh

@cosmic tinsel

Ur graph is correct

Mb

[cosmic tinsel]

What’s wrong with it

Almost?

[vital nova]

It's correct

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[manic raft]

anyone know how to do this question?
i don't know where to start because it doesnt say anything about a changing rate

[manic raft]

This is all i got

[alpine sable]

2L + 2W = 820

Perimeter equation

Then area is LW = A

Perhaps that can help

[manic raft]

its asking for area tho ;-; idk how to maximize it

[regal dragon]

u want A(L)

[alpine sable]

Solve for W in the perimeter equation

And plug

Perhaps

[raven lark]

find the vertex of the parabola

you have 2W + L = 820

so L = 820 - 2W

since A = L*W

then A = (820 - 2W)*W

solve for the maximum value in the parabola, then you have W

and plug it into equation to find L

[manic raft]

wait why is it 2w

@raven lark

i thought it was 2l +w

[raven lark]

oh yep, 2L + W

my bad

[manic raft]

do i do it the other way around?

[raven lark]

well if 2L + W = 820

then W = 820 - 2L

[manic raft]

ok working on it

@raven lark got it thanks

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[chilly dagger]

how many trees are possible from n vertices that have exactly n-2 leaves?

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@chilly dagger Has your question been resolved?

[charred flint]

you're mostly just picking where the extra vertex goes and how many leaves are under it, since you already have the head and n-2 leaves

[prime badge]

hypothetically you put some into a and the rest into b

b can't be 0, so there's n−2 options

but if this is not a tree then there's something else going on

[chilly dagger]

U mean like the one on the right?

But for like 6 vertices like the one i sent, wouldnt both the left and the right be different as well

[charred flint]

red being the extra

[chilly dagger]

Yea like if u take one of the nodes attached to red and attach it to the black root instead wouldnt it count as a different tree or no?

[charred flint]

different tree yea

you pick how many go under red, then pick where red goes

if there's n nodes and k under red, there are (n-k-1) spots it can go)

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@chilly dagger Has your question been resolved?

[chilly dagger]

so is it like every node except root has n-k-1 spots it can go? so its like total is n*(n-k+1)?

[charred flint]

it changes depending on how big the red is

like if it's most things under red it can only go in like 2 or 3 spots, so it's not a simple multiplication

I'd probably just write it out for n=6 and see what it looks like, but it's related to 1+2+3+...+x=x(x+1)/2

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[boreal grove]

i have a math project for graphing and im supposed to draw some stuff on my ti 84 plus ce but i cant figure out why its unable to draw a circle for me , ive tried the semi circle equation , expressing standard form in terms of y = ... , but they all dont work TT if anyone could help would be greatly appreciated

[raven lark]

check your window settings

[boreal grove]

ah it looks like this

[hushed locust]

press "zoom" and select "zstandard", see if it looks more normal after that

[raven lark]

yea your x values are too low

needs to extend to positive

[boreal grove]

ohh ok ill try that

[raven lark]

also try this

[boreal grove]

it still looks odd w semicircle equation TT ill try expressing the standard equation in terms of y = ..

[hushed locust]

can you show the equation?

[boreal grove]

ouh yea give me a sec

[boreal grove]

this is the circle im trying to graph

[hushed locust]

1. it's too far left, we want to adjust our x-values. go to window and select Xmin = -20, xmax = 0
2. we want it to look "circular", rather than stretched out. go to zoom and select Zsquare

[boreal grove]

ouh yea its starting to look more like a circle just incomplete

i managed to get the bottom half but uh its kinda disconnected

[raven lark]

thats normal

circle graph on ti 84 is disconnected

[boreal grove]

ohh well will i just have to work with this 🥲 i hv to do a drawing on my gc for my school project and it requires a bunch of circles

[hushed locust]

if you go to "apps" there may be a "conics" app

[boreal grove]

where can i find apps

[hushed locust]

the button

[boreal grove]

oh i see ot

OH

this thing

THANKS ill see if it works

[boreal grove]

oh is it only for use for 1 graph though ? is it possible to add more graphs to it

[hushed locust]

only seems to support one circle at a time unfortunately. the only other thing I can think of is to use parametric equations for them (this is how the ti-84 does it for the conics program, internally). alternatively if you don't care about the equations (just the shapes) you can use cabrijr (also in apps)

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[frank gate]

Help plssss

<@&286206848099549185>

Can't seem to get to the answers

[alpine sable]

Helpers comming with the milk.

Is fg means f(g)

!15m

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[frank gate]

Oh sorry

didnt saw it

[frank gate]

yea i know

but i cant get to the answer

[alpine sable]

!status

[lone heart]

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

[frank gate]

im typing

my

steps

pal

g(5x+1)=5x+12
let y=5x+1 ==> x=(y-2)/5
g(y) = 5((y-1)/5) + 12
=y-2+12
=y+10

[vague river]

so g(x) turns 5x+2 into 5x+12

[alpine sable]

I think g is x+10

[vague river]

g(x) would equal x+10

yea

[frank gate]

but the answer is
fg x x ( ) = + 5 52

[vague river]

f(x+10)

[vague river]

yea

that makes sense

[frank gate]

which of my steps is wrong

[vague river]

where is the y coming from

[frank gate]

its an variable

where i let y=5x+2

then i find what is x

then i sub in

[alpine sable]

f= 5x+2
g=x+10
f g = 5(x+10)+2

5x+52

[vague river]

^

[zenith dew]

Can someone help me?

[vague river]

just look at how g transforms f

g adds 10 to f

so g(x) = x+10

and now you have f(g(x)) = f(x+10)

[frank gate]

why is g x+10 ?

[zenith dew]

X²+4x-2x-8
x(x+4)-2(x+4)
How how ? Like how +4?

[vague river]

because g adds 10 to f

[alpine sable]

gf :x+12

[frank gate]

then how do i write in a proper solution?

just write g=x+10?

[alpine sable]

See ur f function, it needs+10 to become the gf function,so g :x+12

[frank gate]

yea i know

how do i write in my answer sheets

i know ur solutions i just wanna know how do i writee in the answer paper

cause if i write g=x+10 my teachers would just mark me wrong

[vague river]

f(x) = 5x + 2

5x + 12 = (5x + 2) +10 = (f(x)) +10

[frank gate]

how do i get rid of the f

then

[exotic belfry]

and that would be ok, as youre not asked to write g. you are asked answer fg.

[frank gate]

but i need to write the whole solution

from the top to the bottom

[frank gate]

:0 thanks

[alpine sable]

Hope this helps

[frank gate]

how bout this question

[exotic belfry]

!nosols

[lone heart]

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.

[frank gate]

i just need to know how to get rid of f

[frank gate]

i got the solutions that use a new variable 'y'

[alpine sable]

I think u can solve it by own now

[frank gate]

but this solution can't be used

[frank gate]

on this question

[alpine sable]

Just observe the pattern

[vague river]

what does g do to (x-2) to turn it into that polynomial

it has to multiply it by something

[frank gate]

Can't i make it a new variable to solve?

i used it on almost all of my other questions

[frank gate]

but i can't seem to use it on this question only

[alpine sable]

Use completing the square

U will find g:x²+4

If u square x-2 and add 4 , u get gf so g = var²+4

[frank gate]

:0

i get it

thanks

.close

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[spiral thistle]

bro

[spiral thistle]

why isnt this -tan^2x

I thought with a natural log u could do u'/u

so I did -sin^2(x)/cos^2(x)

which is why I got -tan^2x

but apparently its A

the key says A

[hushed locust]

you have to apply the chain rule to the derivative of cos^2(x)

[spiral thistle]

so I would get 2cosx * -sinx

how do u get -2tan(x) from that

[hushed locust]

,, \frac{2 \cos x (-\sin x)}{\cos^2 x}

[ocean seal]

cloud

[spiral thistle]

ohhhhhhhhhhhhhhhh

so u still use that natural log formula

but to find the derivative of u

u gotta use the chain rule

got it

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[lethal anchor]

The f(x)= 7√x + 50 function shows the average height of children in centimeters until about sixty months old, where (x) is the length of time after birth (in months). What is the average growth rate in the interval [0,25]?

[lethal anchor]

I got 1.4 cm per month but AI got 2.6 so I want to know your opinions

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@lethal anchor Has your question been resolved?

[crude schooner]

what was yur working

[lethal anchor]

its a high school math exam question

[crude schooner]

average = change in height /25

=f(25)-f(0)/25

[lethal anchor]

yes i done that and i got 1.4 but AI confuse me with 2.6

.close

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[alpine sable]

PLs can someone help me with this

[lone heart]

Please don't occupy multiple help channels.

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[lethal belfry]

well

what have you tried

[whole mason]

dont really know how to start

[lethal belfry]

know pythagoras theorem?

[whole mason]

yuh

[neat folio]

Try finding the value of t first and then find the angle w

Using inverse trig functions

[topaz nacelle]

or law of sines

[lethal belfry]

or just pythagoras theorem?

solve the resulting quadratic

[topaz nacelle]

how do you get the angle from pythagoras theorem

[arctic lintel]

by finding t?

[topaz nacelle]

i know

they want to find w

still need law of sines

[whole mason]

2.828?

[neat folio]

I can't check sorry

[whole mason]

i got t

but now what should i do?

(2t+3)

<@&286206848099549185>

um so

?

[lone heart]

@whole mason Has your question been resolved?

[frank gate]

whats this?

[whole mason]

t cm

[frank gate]

is it 2t+3cm

[whole mason]

yuh

[frank gate]

for the other angle?

oh

use pythagoreous theorem

(2t+3)^2 = t^2 + 5^2

[frank gate]

what does the question ask for

[whole mason]

the diagram shows a right angled triangle

[frank gate]

yea

[whole mason]

find the value of W

[frank gate]

wheres w?

this?

[whole mason]

yeahh

[frank gate]

what did u get for t

[whole mason]

2.828

[frank gate]

ok

u need to use

sin,tan,cos

do u know what it is?

[whole mason]

yuh

[frank gate]

apply it

so do u know how to finish it?

did i solve ur question @whole mason ?

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[supple harness]

Hi, a complex symmetric matrix should be diagonalizable by a unitary matrix. Yet, I'm failing to prove that in python. What am I doing wrong?

a = np.asarray([[1+2j, 1+2j],
                [1+2j, 5+18j]])

np.linalg.eig(a)[1] @ np.linalg.eig(a)[1].conj().T

output:

array([[ 1.00000000e+00-1.63711923e-20j, -1.70276373e-17-5.49600332e-02j],
       [-1.70276373e-17+5.49600332e-02j,  1.00000000e+00-1.58748534e-19j]])

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@supple harness Has your question been resolved?

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@supple harness Has your question been resolved?

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[sonic cypress]

Is there an easy trick to find the common denominator with fractional x?

[cinder tundra]

Could you elaborate your question? As Im understanding the question, you only need to multiply by 1, and changing that one by y/y, where y=what you need to make denominator equal

[sonic cypress]

Here’s a more simplified version of my question

How do you go from the left to the right?

[cinder tundra]

You want to do only left, right?

[sonic cypress]

My teacher wants common denominator

[sonic cypress]

Yeah starting from left side

Ok so my question is

How do you know that ‘6’ power goes on the denominator?

There’s gotta be a way/method to find that out

[cinder tundra]

I actually got another solution so give me a moment in case i am not looking correctly

[cinder tundra]

No this is wrong

You are missing a minus

Before x^(15/4)

You first do the fractions normally

You will get in the denominator x^(14/3)

After that, you multiply numerator and denominator by the thing that will make x^(14/3) = x^6

Which is x^(4/3)

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[waxen turtle]

log_6(x-5)=2-log_6(x)

[waxen turtle]

idk wat to do I tried turning it into exponential but idk wat to do

[quasi vector]

!show

[lone heart]

Show your work, and if possible, explain where you are stuck.

[waxen turtle]

oh waiy

can't I add the logs

fr

and combine them together

[split spire]

Yes

[quasi vector]

Yes

Make sure to check the domain of both logs

At the end

[waxen turtle]

ok

I'm gone

.close

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[fervent grove]

channel 0 fr

[fervent grove]

hello

can I ask something fr

fr

fr

e I mea

[lone heart]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[fervent grove]

oh cause I already ask

if I ask

fr

I meant can I ask another question

[heady oyster]

Go for it.

[fervent grove]

If someone does the floor function of the square root of something times the square root of something else

like

[pseudo trellis]

Is there anyone good at discrete math?

[heady oyster]

Don't comment in everyones channel.

[fervent grove]

$\floor{\sqrt{109}\cdot\sqrt{k}}$

oh I wrote it wrong

oh

[ocean seal]

MichaelJackson

[fervent grove]

and I want to do that like for all the k from 1 to 27

and then add them

[fervent grove]

if I know how much all the k's floor function together are

can I use it on like \sqrt{109}

no right

[fervent grove]

what problem fr

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[lone heart]

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as this action is irreversible, and this channel may abruptly lock.

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[ornate flicker]

My math question is or what I think is trigonometry, and the topic is about "Modeling with Functions". My class has just started this and I wanted to get a head start since my teacher is a intern and the way he teaches isn't really helpful.
Some examples of the work we did are shown on the image, I just want to have a good understanding on it and we have to memorize the linear formula, and what a linear graph looks like and etc like different types of graphs... I hope this isn't too much, hopefully someone can help me, thank you for your time.

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@ornate flicker Has your question been resolved?

[ornate flicker]

<@&286206848099549185>

.close

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[fair raft]

use substitution

any variable like u, set u = cosx

and then turns into a quadratic

[agile blade]

I did then got (2x+1)(2x+1)

[fair raft]

4u^2 - 4u + 1 = 0

[agile blade]

yeah that should be (2u+1)(2u+1) right

[fair raft]

so u = 1/2

[agile blade]

yeah for cosx=1/2

[fair raft]

yes

you want to work out x?

[agile blade]

wait shouldn't it be -1/2?

[fair raft]

no its not u=-1/2

sorry i meant

its not u = -0.5

its u = 0.5

perhaps u did the factorisation wrong?

[agile blade]

honestly I kinda forgot how to factor so that was my best guess

[fair raft]

which method, did you use?

• x method or quadratic formula?

[agile blade]

I don't know if it is called the +x method but I didn't use the quadratic formula

[fair raft]

AC method*

did you do 4 multiplied by 1

and then work out what two numbers add to get -4

[agile blade]

I tried that then forgot what to do

[fair raft]

okay

one second then

ill work it out myself?

[agile blade]

so it would be -2 and -2

[fair raft]

yes seems right

perfect!

[agile blade]

then it would be 4x^2-2x-2x+1

[fair raft]

yes

[agile blade]

then it would be (-2x+1)(-2x+1)?

[fair raft]

seems good

to me

yep

[agile blade]

yeah so it would be positive 1/2

[fair raft]

correct or you could do (2x-1)(2x-1)

yes

so do you understand how to do it now? @agile blade

[agile blade]

then cos would equally everything on the unit circle that is 1/2 so pi/3 and 5pi/3

yes

[fair raft]

great

[agile blade]

thanks I completly forgot how to factor

[fair raft]

np

[agile blade]

.close

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[alpine sable]

how would i solve this

sorry about miserable notation

[vapid drift]

basic subtitution

theta/2 = x or smth

and tan(x)= sqrt(3)

solve that

[alpine sable]

so it is acceptable to use the table values

[vapid drift]

yeah

u should just know it, but yes

[alpine sable]

yeah?

[vapid drift]

yeah i think so

now reverse the sub back

so theta/2 = pi/3 + pin

and after solving for theta consider the domain

0<=theta<=2pi

for your solutions to lay there

[alpine sable]

👍

appreciate it

.close

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[proud wyvern]

Is this right?

[subtle light]

close, you also have to consider that (-1)^n

if you want to use your way, you can use that if you show the absolute convergence of the series

which in tern means that the original series would also converge

[proud wyvern]

I don’t know what other test I could use I know for sure I can’t use the direct comparison test or limit comparison

[subtle light]

alternating series test

[proud wyvern]

For alternating series test limit as n approaches infinity should be 0 and a decreasing sequence

[subtle light]

oh wait right

divergence test would do fine

just include that (-1)^n and compute the limit again

[proud wyvern]

I’m not familiar with limits involving (-1)^n

[subtle light]

so it’s essentially the same as what you had there, but whether the result is negative or positive depends on what infinity is

either even or odd

since we don’t know that, the limit as n approaches infinity will alternate between -2/5 and 2/5

hence the limit would not exist

[proud wyvern]

So if I take the limit of something with a (-1)^n term is it safe to say it will always diverge

[subtle light]

not always

if the other part, not including the (-1)^n, goes to 0

the limit would exist

[vapid drift]

not really

i think 1/n*(-1)^n would converge for example

[proud wyvern]

Going back to the absolute convergence test if I did use that test the (-1)^n term disappears and the series would diverge so what does that tell me about my og series

[subtle light]

nothing

yeah it would be inconclusive

so the only way is just the divergence test

[proud wyvern]

In this case is the divergence test the easy way out. The ratio test would be a hassle

[subtle light]

yeah definitely

[proud wyvern]

Because I thought for the divergence test you excluded the alternating part

[subtle light]

that’s more the alternating series test

divergence test takes the entire a_n

[proud wyvern]

If I used the divergence test for this a_n what would it be

[subtle light]

0

since 1/n goes to 0

[proud wyvern]

If it was a regular 1/n it goes to 0

[subtle light]

yep

and that would too

since the (-1)^n only alternates between -1 and 1

it can’t get bigger than that

[proud wyvern]

Can I say if limit as n approaches infinity of a_n converges then limit as n approaches infinity of (-1)^n a_n should also converge and vice versa

[subtle light]

only the first part

(-1)^n a_n converging doesn’t say anything about a_n

only if it is the other way around then it’ll be correct

[proud wyvern]

Does this also work for divergence

[subtle light]

for divergence then it would be if (-1)^n a_n diverges, then a_n must diverge

not the other way around

[proud wyvern]

I don't recall learning this in specific unless it's applied in some other context

[subtle light]

think of the direct comparison test

(-1)^n a_n would be smaller than a_n

so if the smaller one diverges, the bigger one must diverge

and if the bigger one converges, the smaller one must converge

[proud wyvern]

Wait you can use direct comparison for an alternating series?

[subtle light]

yeah

wait

did it require for both series to be positive?

[proud wyvern]

I think so

[subtle light]

well maybe don’t put the name direct comparison test on it then

[proud wyvern]

This what I remember

$$0 \le a_n \le b_n $$

[ocean seal]

Unknown

[proud wyvern]

If sum of bn converges then sum of a_n has to converge too

[subtle light]

yep

so the thing is our (-1)^n a_n isn’t really always less than 0

it is sometimes greater than 0

so we can’t really use this logic i suppose

think back to absolute and conditional convergence

if we deem that our original series diverges, then there is no way that the absolute value of it would converge

since whatever that sum of our original series is, the absolute value version would be much bigger as we are adding more terms instead of subtracting

[proud wyvern]

I might be wrong but this what I recall

[subtle light]

yeah that’s right

but there wasn’t a single case

where a_n diverges and |a_n| converges

it wouldn’t make much sense since for the absolute value, we would be adding all of the terms instead of subtracting some of them

[proud wyvern]

Do you know where I can find practice of limits with these alternating components or the name of it

[subtle light]

hmm you can try alternating series test problems

but instead of using that, use the divergence test

to see if it works

[proud wyvern]

I’m just making a random example but where could I go with this

I know the second limit goes to infinity

[subtle light]

yeah so we know that

since (-1)^n goes between -1 and 1

as n gets closer to infinity

it’ll alternate between negative infinity and positive infinity

hence the limit doesn’t exist

[lone heart]

@proud wyvern Has your question been resolved?

[proud wyvern]

So why does $$\lim_{ n \to \infty} \frac{(-1)^n}{n}$$
Become a special case

[ocean seal]

Unknown

[proud wyvern]

Or well, I'm talking about the sum

I found this online and looks similar to my situation

[subtle light]

mm that doesn’t seem right

the divergence test doesn’t ignore the negative

but regardless, it would diverge by it

it’s just that the work is slightly wrong

[proud wyvern]

Instead, what should the work be

[subtle light]

with the (-1)^n

[proud wyvern]

I can't seem to wrap my head around this

[subtle light]

you would do $\lim_{n\to\infty}\frac{(-1)^n(5n-1)}{4n+1}$

[ocean seal]

y0shi

[subtle light]

and the limit would not exist

hence that is not equal to 0 and diverges by the the divergence test

[proud wyvern]

Is there a way to show the $$\lim_{ n \to \infty} (-1)^n $$ in general

[ocean seal]

Unknown

[subtle light]

so here’s the thing, you technically cannot separate the limit into two products as that requires both limits to exist

but this limit doesn’t

so you kinda just have to think of this more conceptually

imagine we have a really big number that is odd

the sequence would give us a number close to -5/4

the next term would give us a number close to 5/4 since it would be even

[proud wyvern]

I was thinking of using natural logs in the limit like the e limit but the (-1) could be a problem

[subtle light]

so it depends on whether our “big number” is even or odd

yeah don’t do that

limits are conceptual

no work needs to be shown

[subtle light]

you can jump from here to DNE

but you have to understand why it is

[proud wyvern]

Only way I see it is if the sequence is a_n =(-1)^n then the sequence diverges

[subtle light]

yes and that’s because it’ll alternate between -1 and 1 when n gets extremely large

the same idea applies to when you have other bits attached to it

it’ll essentially just be what the limit would be when that other part goes to infinity but it will alternate between negative and positive because of the (-1)^n

[proud wyvern]

In this case the (-1)^n term takes over?

[lone heart]

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[subtle light]

.reopen

[lone heart]

✅

[subtle light]

well the (-1)^n term alternates between -1 and 1

hence making the other bit either positive or negative

so if that other part, as it approaches infinity, goes to 5/4

the limit would alternate between -5/4 and 5/4 because of that (-1)^n

the (-1)^n term just basically alternates the terms between positive and negative

[proud wyvern]

I was about to say, why isn't $$\lim_{n \to \infty} \frac{(-1)^n}{n} =\infty$$

[ocean seal]

Unknown

[subtle light]

well because as n gets really big

the 1/n bit would go to 0

so it doesn’t matter if it switches between -1 and 1

since it’ll just be -0 and 0 which is just 0

[proud wyvern]

makes a little more sense so basically it depends on the terms that don't include the (-1)^n

[subtle light]

yeah basically

[proud wyvern]

Well, thanks again for helping me on this scenario. Not sure if it's against the rules but I might make another help channel for another problem

[shy dove]

You can definitely close this one and open another one without issues haha

No mods will chase after you

[proud wyvern]

Thanks for the clarification

.close

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[lethal salmon]

Mmm it didnt change lol

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[steel crescent]

image one is for context
in image two, the question, all i have to do is factorize a(x) then set those factors = 0 and that's my a and b correct?

[lone heart]

@steel crescent Has your question been resolved?

[steel crescent]

oh thanks yeah, i was just double checking ^^

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[wise ore]

no idea where to start

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@wise ore Has your question been resolved?

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[coarse elm]

What does question b) mean?

I dont understand the "meaning of the value for the axis of the curve"

[paper mango]

symmetry is probably missing

"symmetry axis"

[coarse elm]

ok so what would i write then @paper mango

[paper mango]

If it's meant to be the symmetry axis then it's the mean

[coarse elm]

kk ty

.close

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[granite rune]

how would i write df/dg in lagrange notation

[gritty bramble]

f'(g)?

[granite rune]

where g is a function as well

..nevermind

thanks

so basically

the chain rule in leibniz notation (if we switch the letters around) is df/dg*dg/dx

[gritty bramble]

f'(x)/g'(x)

[granite rune]

so with lagrange notation thats f'(g(x))*g'(x)

thank you!

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[agile dagger]

How to find median of this stem leaf plot

[agile dagger]

This is what I did

Someone pls come here

https://tenor.com/view/deadpool-gif-26545415

<@&286206848099549185>

Bro Ik u see this

I’m cooked fr

[long axle]

Do u know how to read a stem and leaf plot

[agile dagger]

Yes

[long axle]

Do u understand the concept of median

[agile dagger]

Yes

Did u not see my work

Scroll up

[long axle]

Oh, yea lemme check it out

Ok so what makes u think 32 is wrong?

[agile dagger]

The answer key

[jovial ferry]

Ok but like Stem - leaf graphs are the worst way to show data

[jovial ferry]

what does it say

[agile dagger]

8.5

[long axle]

32 seems right…

Are u looking at the right problem

[agile dagger]

Yes

[long axle]

Well here’s the thing

It’s between the 8 and 9th term

[agile dagger]

OHHHHHHH NVM

[long axle]

So the median is the “8.5th” term

[agile dagger]

I need glasses

My bad

.close

[lone heart]

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[jovial ferry]

this dude..

[agile dagger]

Hey it’s not my fault

These were the eyes I was born with

https://tenor.com/view/cute-sad-eyes-cat-please-gif-15746035

[jovial ferry]

ok bro

[stray cedar]

Wsp

Happy new day

[long axle]

Ur on the right side of the world my bueh

[stray cedar]

Where u from

I'm in usa

[jovial ferry]

@stray cedar

I thought u were in a hurry?

[stray cedar]

What hurry

[lone heart]

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[rich drift]

is there easier way to solve this other than brute forcing?

[steep rover]

you can definitely simplify this further

im not too familaiar with column operations, but if you subtract row 1 from the rest of the rows

you should have 0's in the first column besides row 1

this makes it a 3x3

for row operations, if two rows are interchanged, the determinant switches in sign, but for adding and subtracting rows, the determinant is unaffected

[rich drift]

thanks

[steep rover]

and multiplying by a constant

scales determinant by that constant

[rich drift]

i found video about that on yt

.close

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[lone heart]

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[alpine sable]

how do i find the probability that a thrown dart will hit somewhere inside the shaded region? i got pi / 4

[alpine sable]

what i did

A of shaded = 6^2 = 36
A of circle = pi (3^2) = 9 pi
Probability of shaded = 9 pi / 36 = pi / 4

[raven lark]

the area of the shaded would be 36 - 9π

[alpine sable]

dont u have to find the area of the entire shaded region

so you can find the probability

[outer lodge]

!status

[lone heart]

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

[outer lodge]

@alpine sable

[alpine sable]

4

[outer lodge]

okay so i think A of shaded is calculated wrong

[alpine sable]

how so

[outer lodge]

see area of shaded will be everything in square except the circle inscribed in it

[alpine sable]

ok

[outer lodge]

do you get what i am saying?

[alpine sable]

yes

[outer lodge]

now calc. again

[alpine sable]

63 - 9 pi

[outer lodge]

not 63

36*

[alpine sable]

36

36-9 pi

then what

[outer lodge]

now you have shaded region area

and also the total area

so prob will be shaded / total

and thats your answer

[alpine sable]

oh

i see

[outer lodge]

now calculate final answer

[alpine sable]

-9 pi

[outer lodge]

can probability be negative?

[alpine sable]

according to google, no

[outer lodge]

then you have calculated it wrong

[alpine sable]

0.215

but thats not a probability

[outer lodge]

0.215 is the answer

[outer lodge]

how come?

[alpine sable]

its not

doesent it need to be in a form like "1-x" since all probabilites add up to 1

[outer lodge]

yes, if u calculate the prob of unshaded region it will be 0.785

and sum of them is 1

[alpine sable]

so would it be 1-0.785?

[outer lodge]

yes this is also an alternative way to answer this

calculate unshaded subtract it from 1 you will get shadeds prob.

[alpine sable]

now i get it

[outer lodge]

but keep in mind this seems easy in only those questions who has binary possible outcomes

dont try to use this in more than 2 possible outcomes question

[alpine sable]

ok ill keep that in mind

[outer lodge]

if your doubt has been solved the close this channel

keep doing maths

[median oar]

you can always ask about P(not A) though

your P(A) and P(not A) is "binary" and will always add up to 1

[alpine sable]

oh

[median oar]

like P(roll a 1 on a fair 6 sided dice) and P(not roll a 1 on a fair 6 sided dice)

yes you can roll other things as well but you can group them all into the "not 1" event

[alpine sable]

i see

.close

[lone heart]

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[lone heart]

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[chrome tapir]

how does this work?

[chrome tapir]

how did -1 + 1/2 equal -1

oh

im stupid

.close

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[grizzled burrow]

y=4x^{2}-48x+7

[grizzled burrow]

find teh vertex

and aos

im at y=4(x^2-12x)+7

[granite rune]

hiii

[grizzled burrow]

helo

[granite rune]

so

lets factor this

u know how to do that or

[grizzled burrow]

this or y=4x(x-12)+7

[granite rune]

hmm

alright

so

lets get this into a(x-h)^2+k (vertex form)

complete the square for x^2-12x

[grizzled burrow]

hmm idk what to do for that

[granite rune]

lets recall something okay

[grizzled burrow]

ok

[granite rune]

(x-a)^2=?

[grizzled burrow]

x^2+a^2

[granite rune]

what grade are you

not trying to insult you just asking

[grizzled burrow]

oh shoot

forgot the -2ax?

[granite rune]

yes

[grizzled burrow]

9th

[granite rune]

ok makes sense

[grizzled burrow]

mb 😭

[granite rune]

8th rn

[grizzled burrow]

ohh

[granite rune]

math nerds like me when (a+b)^2 = a^2+b^2

p a i n .

[grizzled burrow]

😭

anyways whats next

[granite rune]

anyways, back to the question

completing the square

so

a is just some real number okay

some constant

so, a^2 is a constant as well

now lets take a look at the -2ax term again

and then at your factoring so far

y=4(x^2-12x)+7

lets complete the square for x^2-12x, then subtract the constant that we added (a^2)

first, we try to find a, then find a^2 right

do that

[grizzled burrow]

so how would it look

[granite rune]

-12x is -2ax

[grizzled burrow]

yes

i see

so we are missing

[granite rune]

find a, then a^2

[grizzled burrow]

6?

[granite rune]

so whats a^2

hello?

[grizzled burrow]

36

[granite rune]

yes

[grizzled burrow]

sorry mb

[granite rune]

so

back to y=4(x^2-12x)+7

now lets complete the square and add 36 so that we can make it (x-6)^2, and turn it into vertex form

but wait, we can't change the equation

so we must subtract what we add

[grizzled burrow]

from 7?

[granite rune]

yes

[grizzled burrow]

ok

so

[granite rune]

4(x-6)^2+7-36*4

[grizzled burrow]

huh

[granite rune]

4(x-6)^2+7-144

because the a^2 (36) inside a coefficient of 4 is just 4*36

[grizzled burrow]

ohh

wait

why the 4 multiplying at the end

[granite rune]

4(x^2-12x+36)+7-4*36

[granite rune]

distributive property

brb

back

[grizzled burrow]

welcome back

i dont understand the prop in this case

[granite rune]

so

you know what here's a vid that'll help

https://www.youtube.com/watch?v=pf9LkX8hpTQ

[grizzled burrow]

ok

we dgood i think

[granite rune]

gtg bye

[lone heart]

@grizzled burrow Has your question been resolved?

[lone heart]

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[lone heart]

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[shadow tiger]

How do you isolate dy/dx here?

[proud ingot]

yoou pass the under part to the other side mmultiplying

then the y goes witha negative sign to the left

then u can bring the left sided dy/dx dividing

[shadow tiger]

You mean this?

This just cancels out dy/dx tho

I wanted to isolate for it

[proud ingot]

ah ok mb one sec

[pale glen]

on the second line

move -y to the right

move dy/dx to the left

factor out a dy/dx

[pale glen]

also the x vanished here

[shadow tiger]

Yeah just noticed, and fixed it based on what you said

But dy/dx still needs to be isolated tho

ignore the first 2 lines

okay you know what

[pale glen]

,,\frac{dy}{dx}(u)-y=x\frac{dy}{dx}

[ocean seal]

Renz

[pale glen]

you have this right

[shadow tiger]

maybe i made other mistakes along the way but here's the original question

[pale glen]

u is the e^y xy ln3 thingy