help-10

[astral ivy]

The midpoint of A and B is (-1/2, 3)

Slope is -5.5

So the equation is y - 2 = 5.5(x - 5) which is y = 5.5x + 29.5

[analog pasture]

I got something similar

y - 2 = 5.5(x - 5) which is y = 5.5x + 30

where did I go wrong

Prove that area of ∆ABM is half that of ∆ABC.

how do I prove this

i got 1 more of these

[astral ivy]

Oh wait I went wrong

[analog pasture]

after this

[astral ivy]

Ok let’s do the proof after this

[analog pasture]

for the first part

[analog pasture]

am i wrong

[astral ivy]

Nah Im graphing these lines to double check cause I got a nonsense answer

[analog pasture]

oh

bro how r u so smart

tho like fr

like I have a learning disability

but like ur smart

[astral ivy]

Nah dude just practice and experience haha

U got a learning disability? Doesn’t seem like it

[analog pasture]

srsly

but i got diagnosed for adhd when I was 10

[astral ivy]

You’re picking up on this stuff quickly

[analog pasture]

and ive been bullied so much

like beaten up in the bathroom and spit one 6th grade was horrible for me

damn

so the half will me

be

how tho

wait y - 2 = 5.5(x - 5) which is y = 5.5x + 29.5 this right

yea its right

u were right

I think

[astral ivy]

Jesus dude

That’s so messed up

I’m sorry man

[analog pasture]

nah I made great friends cause of it

Im happy now

happier than ive ever been

[astral ivy]

That’s great

[analog pasture]

you were right tho

just swaying

[astral ivy]

The issue was I did x2-x1/y2-y1, but it’s y over x instead

[analog pasture]

yea

[astral ivy]

So the slope is 1/-5.5

Which is -2/11

[analog pasture]

but ur values r right except slope

yea

[astral ivy]

So those are the new equations

[analog pasture]

damn nice

ur good at this even I made a mistake then

[astral ivy]

(1.333, 2.667) is precisely where they meet

Well done

[analog pasture]

yess

[astral ivy]

Lit dude

Ok so what is the next one?

[analog pasture]

umm

Prove that area of ∆ABM is half that of ∆ABC.

[astral ivy]

And what’s ABM here? ABC? Do they give you coordinates or something

[analog pasture]

like using the cordinates

from before

[astral ivy]

Oh ABC is the same ok

[analog pasture]

yea

[astral ivy]

What is ABM

What is M coords

[analog pasture]

An altitude is a perpendicular line dropped from one of the vertices to the opposite side. Here, AM is an altitude of ∆ABC. Find the Equation of AM.

we did it rn

i think

[astral ivy]

Hm

[analog pasture]

its fine we can skip that one and try this if you want

An altitude is a perpendicular line dropped from one of the vertices to the opposite side. Here, AM is an altitude of ∆ABC. Find the Equation of AM.

[astral ivy]

So they’re saying the area of ABM is half of ABC

Oh

[analog pasture]

yea

Prove that medians always divide each other in the ratio 2:1. That is, for each of the three medians, the distance from the vertex to the centroid is always twice as long as the distance from the centroid to the midpoint. You may use any of the medians to prove this point.

A

I mean this

one

or u wanna do the second main questions

sub questions

and also can I add u on discord

[astral ivy]

Yeah totally

Let's do the area proof right now

So one thing I just noticed

The dotted lines are altitudes

The only way for the smaller triangle to be half of the bigger triangle is if it's symmetrical across the line

In other words, it must be isosceles

Do you see?

[analog pasture]

yea

damn

so its not scalene

[astral ivy]

I guess not lol

[analog pasture]

lmao

[astral ivy]

Hm

[analog pasture]

yea

[astral ivy]

Ok does your teacher want you to like

Write out paragraph proofs

Or the stupid two column thing

[analog pasture]

paragraph proof

i think

[astral ivy]

Lit lit lit

Ok

[analog pasture]

yess

then we need to do the second question which has only 5 questions and is pretty easy

John is hiking. He is currently located at point A(25 ,90). He wants to take the shortest path to reach the highway L, which follows a straight line with equation

y=1/5x + 5

He takes a straight perpendicular path to the highway.

In the following graph, you can see the Highway Line L represented in red. The blue line is a line perpendicular to the Highway that passes through A.

lmao I only got 25 min for this

prbbly not enough time

the questions should be here

http://patemath.weebly.com/uploads/5/2/5/8/52589185/scan0148.pdf

u there @astral ivy

[astral ivy]

Oh jeez

25 minutes

[analog pasture]

yea

lmao

so we have 6 questions left in total

wanna see where david goes first

and then get back to

Prove that medians always divide each other in the ratio 2:1. That is, for each of the three medians, the distance from the vertex to the centroid is always twice as long as the distance from the centroid to the midpoint. You may use any of the medians to prove this point.

so davide

Find the equation of the perpendicular path that John takes to the highway.

B

[astral ivy]

Oh the John one is easy

[analog pasture]

yea

fr

so lets finish this itll probably take 10 min mac

x

[astral ivy]

y intercept is 5, slope is -5, equation is y = -5x + 5. Boom

[analog pasture]

just the Prove that medians always divide each other in the ratio 2:1. That is, for each of the three medians, the distance from the vertex to the centroid is always twice as long as the distance from the centroid to the midpoint. You may use any of the medians to prove this point. is hard ish

[astral ivy]

Yeah that's tricky

Gimme a sec I think I've proven that before

[analog pasture]

ooh

so what do i do for this

Find the equation of the perpendicular path that John takes to the highway.

its just the time is stressin me rn

[astral ivy]

@analog pasture this is the John one

[analog pasture]

yoo smart ass

did u graduate from hravrd

ur smart

or MIT

[astral ivy]

Lmao no haha

[analog pasture]

damn

Find the coordinates of the point, B, at which the perpendicular path meets the highway.

[astral ivy]

This is wrong whoops

Slope is right, y intercept isn't

[analog pasture]

oh ok

bro 16 min if u pull this of someway damn

[astral ivy]

It's y - 90 = -5(x - 25) which is y = -5x + 215

[analog pasture]

found it

lmao

sorry

[analog pasture]

for the second one right

oh no it isnt

yea its for the first one

[astral ivy]

This is the intersection of 1/5x + 5 and -5x + 215 which is (525/13, 170/13)

[analog pasture]

umm y r u helping me so much

no one ever helps me

[astral ivy]

Cause you need it

Okay so

Now the area one

[analog pasture]

Point D (30,15) is on the highway. Prove that AB<AD

[astral ivy]

Oh ok

[analog pasture]

yea lets do that one last

[astral ivy]

What's the coords of A and B here

[analog pasture]

the john one

r the cords

[astral ivy]

Kill me

[analog pasture]

yea

[astral ivy]

Ok

Can you plug in (25,90) to (525/13, 170/13) in distance formula

That's AB

[analog pasture]

ok

[astral ivy]

And then AD is (25,90) to (30,15) which is a distance of 75.166

Oh something went wrong

[analog pasture]

last one

[astral ivy]

Bruhhhh

[analog pasture]

no like fr

[astral ivy]

AB is 78 and AD is 75

[analog pasture]

According to your observations, which path will always be the shortest path. Justify your answer.

thats it

am i annoying u

yooo

@astral ivy

[astral ivy]

No ur good

[analog pasture]

ok

this and then were done with john

[astral ivy]

Ok

[analog pasture]

4 min

were cutting it close homie

its like a heist movie

[astral ivy]

The path from A to D is shorter than from A to B, since AD = 75.166 and AB = 78.466

[analog pasture]

or money heist

still wann do

[astral ivy]

What's nex t

Go go go

[analog pasture]

Prove that medians always divide each other in the ratio 2:1. That is, for each of the three medians, the distance from the vertex to the centroid is always twice as long as the distance from the centroid to the midpoint. You may use any of the medians to prove this point.

the hard one

[astral ivy]

Tough ok let's see

[analog pasture]

the final boss

[astral ivy]

Yup

[analog pasture]

3 mins

damn

[astral ivy]

Gimme a sec

[analog pasture]

u can do ittttt

2 min

1 min 30 sec

1 min

[astral ivy]

Nope way too hard lol

[analog pasture]

damn

ggs

[astral ivy]

That is way too hard for 30 mins

[analog pasture]

good game

[astral ivy]

Gg haha

[analog pasture]

lmao

u in colleg yet

causee ur good

[astral ivy]

Nah

Dude this median one is like

Jesus Christ

[analog pasture]

do u play valo

like its my main gamme]

so damn fun

[astral ivy]

Rly

[analog pasture]

yea

u do

play???

[astral ivy]

I'm like complete trash but I love the game

[analog pasture]

Im really good

[astral ivy]

I haven't played in a bit, in a rental house so I don't have a computer for now

What rank or whatever r u

[analog pasture]

radiant like I placed top 10 in ranking

so i feel like batman at school

like Im really good

but like I hide it yk

[astral ivy]

That's absolutely insane

Jeeeez

[analog pasture]

all the guys at my school play valo

and grind it

[astral ivy]

Haha rly

[analog pasture]

so I pretend to no know anything bout it

[astral ivy]

What grade r you in

[analog pasture]

10th

wby'

[astral ivy]

Lol prodigy in the shadows

12th

[analog pasture]

yessir

prodigyyy

[astral ivy]

That's sick

[analog pasture]

the next tenz

damn bro so colleg next year

wHERE u goin

imma just ride my legacy addmision to harvard thanks to my uncle

[astral ivy]

No clue yet, still applying

You have Harvard legacy?

[analog pasture]

so im stupid

[analog pasture]

yea

[astral ivy]

That's wow

Wow

[analog pasture]

but my uncles stacked

like even my parents r

[astral ivy]

What is he doing now lol

[analog pasture]

he's into quantum proccessing

and 5g

and 6g

like they use a polymer arround 5g phones

so they can recieve and stuff

and AI so yea he's smart I wanna be like him someday

[astral ivy]

That's really cool

Wow that's actually really really cool

[analog pasture]

rightttt

so i added u as a friend

we should play valo sometime

kk byee

u free at 7:00

u live on the east or west??

[astral ivy]

West

[analog pasture]

damn k

[astral ivy]

I can't play tho, in a rental house with no computer rn :(

[analog pasture]

lmao

kk tell me when u can

[astral ivy]

Probably in a month or two lol

[analog pasture]

k

ttyl

[astral ivy]

Ok see ya dude

Remember to close this channel if you're done for now

[obtuse pebble]

@analog pasture Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[robust sleet]

nice

[timid silo]

Quite a general query. Is there a method to calculate the equation of a line with seemingly random fluctuations such as the one above without the use of integrals?

I'm not great with Mathematics and haven't been taught Calculus of any sort. I'd prefer not to share what the points represent, but my closest approximations have all been hyperbolas of which the points have fallen very close to.

The upper bound for the points is π (which is the Y-value of the highest point in that image) and the points decrease to 2√2 as x approaches infinity.

The x-value of the furthest-right point in that image is 4. I haven't plotted many more points as of yet.

(The remaining points)

I imagined creating a straight line between each integer for an approximation. Creating a straight line between every half would be twice as accurate, between every eighth would be 8x as accurate and so on. Therefore an infinite quantity of straight lines between each infinitesimally distant point would create an "exact" solution. This sounds like the sort of thing Calculus messes around with, hence why I presumed it would be the go-to.

Any advice would be very helpful, if necessary I'll show my closest approximation.

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

<@&286206848099549185>

cant this be done some way using polynomials and vertex points?

im not sure myself but i think theres a way to do so

unloess you looking for the best aproximation of the lines that still hits all the points

I'm looking for an exact solution, you can't hit all the points with an approximation.

I have approximations that visually touch the points on Desmos to a degree, but that's frankly irrelevant.

[timid silo]

How would Vertex Points play into this?

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

<@&286206848099549185>

[glossy ibex]

look into methods of interpolation

[timid silo]

No idea what that even was until now, I'll look into it thank you.

Interpolation unfortunately is limited to approximation also.

[glossy ibex]

im not sure what you expect

[glossy ibex]

Interpolation hits every point. its unknowable what exactly happens between each point, you have to guess

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[willow chasm]

So limit is basically just the y value in the graph (with circles) and if they have continuity (arrows) just write infinity as the y value?

[balmy mortar]

If someone gave me this description I would have no confidence they actually understood what the concept of a limit was.

[willow chasm]

I don't understand limits so it's true kek

[strong sinew]

☠️ i have no idea how ppl have so much confidence in themselves i am talking about @balmy mortar she is not wrong but how do u say like that what if u get proven wrong ☠️

[strong sinew]

https://www.youtube.com/watch?v=kfF40MiS7zA&t=579s

u can watch this to understand what limit means

[willow chasm]

Thank you veru much bro

.close

[obtuse pebble]

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[balmy mortar]

I am saying that it sounds vaguely right but maybe not right, and I don't want to say it is right in case they don't fully understand it.

[obtuse pebble]

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[trim field]

transform sin(x)+cos(x) into a product

[balmy mortar]

1 . (sin x + cos x) ?

question unclear 🤔

[lucid flame]

product of what?

[trim field]

3, a

[leaden ibex]

I mean, there is a formula for that

Can you use that or do you have to somehow derive it?

[timid silo]

Relevant meme

[hollow sun]

yea you can just write $1\cdot(\sin(x)+cos(x))$, since the question was asked in a very general way

[warm shale]

Big xdddd

[hollow sun]

except the teacher said sth to it

[leaden ibex]

Probably wants this

[trim field]

yes

[compact shadow]

asin(x)+bcos(x)=r((a/r)sin(x)+(b/r)cos(x))=rsin(x+t) where r=sqrt(a^2+b^2), b/r=sin(t),a/r=cos(t) for some t

Like sin(x)+cos(x)=sqrt(2)((1/sqrt(2))sin(x)+(1/sqrt(2))cos(x))=sqrt(2)sin(x+π/4)

[trim field]

can you explain again, I don't understand

solution

[leaden ibex]

Looks like this

[trim field]

Aaaa

Tysm

[leaden ibex]

They just turned a cosx into sin(pi/2 - x)

[trim field]

But, why

and how

this I don't understand

[tardy epoch]

https://www.mathwords.com/c/cofunction_identities.htm

[trim field]

Tysm

.close

[obtuse pebble]

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[languid spire]

Anyone that could help me with plotting two equations in matlab and get the points where these two intersects?

[drowsy girder]

Matlab the programming language

[languid spire]

yeah

[obtuse pebble]

@languid spire Has your question been resolved?

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[timid silo]

oh

[obtuse pebble]

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[karmic cedar]

wouldn't it be a nightmare if there was a typo here

[warm shale]

DarQ (Shuri for honorable)

[haughty coyote]

You'll notice that the text says the row spaces of A and A~ are the same, so they also have the same dimension

[compact shadow]

Same. Since they are different by row transformation

[karmic cedar]

I see

.close

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[craggy aurora]

ok so for leter e, isnt that just plugging 6 into the given equation

to find the distance isnt it f(x)-f(0)

so id do f(6)-f(0)

i get 36 when i plug in 6, and since all have variable theyd be 0 so wouldnt final answer be 36

.close

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[calm scaffold]

So, I've so far determined tan(alpha)=-7/3. Im not sure how I'd solve it from there, supposedly arctangent?

[hollow sun]

yes

$\alpha=\arctan\left(-\frac{7}{3}\right)$

[warm shale]

Big xdddd

[calm scaffold]

Okay, -66.80. I knew that partt, Now it's looking for an angle measure, how would that be determined?

[hollow sun]

are you talking about that?

[calm scaffold]

No, Theyre looking for an angle measure to be determined from tan(alpha)=-7/3

[short spruce]

?

[hollow sun]

well it can be done graphically

[calm scaffold]

Sorry, meant -1.17

[calm scaffold]

Thats probably what it's looking for, I'm fairly lost in this part

[short spruce]

you literally said the angle measure here

[hollow sun]

you have a coordinate system, i is your x axis and j is your y axis, then you plot the vector there, and determine the angle between your vector and the x axis

[calm scaffold]

It said it isn't that.

Yes. Hence why I was asking for a follow up. They answered, I'll do that

[short spruce]

who is they

[calm scaffold]

Big xdddd#6971.

[short spruce]

they just told you to do exactly what you already did

you found alpha. you just need to determine quadrant relevant to the question

[calm scaffold]

If you read the problem, it asks for 360-66.90. It isnt just 66.80

because its 0<theta<360

[short spruce]

hence

[calm scaffold]

Someone else was answering and having another person just made it convoluted. Thanks though.

[obtuse pebble]

@calm scaffold Has your question been resolved?

[obtuse pebble]

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[proven plank]

help plz

[hybrid gull]

^^

have you tried anything?

[royal solar]

have you heard of chain rule

if yes, use that

@proven plank

[royal solar]

when x = 4, u = 0.6

right?

y = (u-4 +8)/u-4

[cerulean nest]

do you first differentiate for dy/du

[royal solar]

yeah, chain rule

[cerulean nest]

and then you sub in u for the answer you get?

or do you first find the derivative of u

[royal solar]

no,

wdym,

[cerulean nest]

what do you do sorry

[royal solar]

dy/du x du/dx = dy/dx

[cerulean nest]

right

[royal solar]

in all fairness, you could prolly sub in 0.6 at that point,

find both

multiply them together

and sub in x and u values

[cerulean nest]

thanks

[royal solar]

no worries,

wait, what happened to the guy who actually asked

[cerulean nest]

i’m not sure

i learned this yesterday though so i recognized it

[obtuse pebble]

@proven plank Has your question been resolved?

[proven plank]

im here mbb

i was trynna understand ur work

[obtuse pebble]

@proven plank Has your question been resolved?

[tardy epoch]

To calculate this chain rule
$\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$

[warm shale]

riemann

[tardy epoch]

You need to calculate three parts

$$\frac{du}{dx} = ?, \text{ when } \ x =4$$

[warm shale]

riemann

[tardy epoch]

$$u = ?, \ \text{ when }\ x=4$$

[warm shale]

riemann

[tardy epoch]

$$\frac{dy}{du} = ?, \ \text{when}\ x=4$$

[warm shale]

riemann

[tardy epoch]

not necessarily in that order

[obtuse pebble]

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[humble quest]

hm

[obtuse pebble]

Please don't occupy multiple help channels.

[humble quest]

@tardy epoch 🙏

[tardy epoch]

show the original question, i don't know what you're supposed to do from this

[humble quest]

prove the series of u_n is converging @tardy epoch

[tardy epoch]

what do they tell you about f?

[humble quest]

literally told u above lol

[tardy epoch]

it's impossible to tell what's given and you did

[humble quest]

thought u read what i wrote

[tardy epoch]

what's given and what did you do?

[humble quest]

ye

[tardy epoch]

that doesn't answer my question

[humble quest]

lmao

[tardy epoch]

all of this can be avoided if you just showed the original question

[humble quest]

@tardy epoch

[tardy epoch]

and translate it

[humble quest]

lmao

[humble quest]

the translation is this

if u don't understand that then its ur problem ig

[tardy epoch]

rude

[humble quest]

lol aight

[tardy epoch]

this is just a shit translation

[humble quest]

bias

anyways thx

[jagged dagger]

how'd you get mad at him for trying to help

let f be a continuous decreasing function on [0, + infinity] such that limit x --> (positive infinity) f(x) = 0

1. study the general term series

[obtuse pebble]

@humble quest Has your question been resolved?

[humble quest]

idk u tell me

[jagged dagger]

but is that the full question though? it just says "study the general term series"

that's what riemann was asking for

where's the actual q

[humble quest]

^ ?

[jagged dagger]

this isn't a full question

are you taking a test or something

[humble quest]

it is

no

[humble quest]

^

[jagged dagger]

ok post the actual screenshot of the page then

[jagged dagger]

is this test or no?

[humble quest]

this isn't a test lmfao which professor would give this tons as a test

[jagged dagger]

then why didn't you just post this when riemann asked earlier lol

[humble quest]

he said translation

i already gave my answer to the problem i just want him to go thru it lol

[jagged dagger]

"all of this can be avoided if you just showed the original question"

[humble quest]

https://cdn.discordapp.com/attachments/903430332324405288/950908764528181258/unknown.png

this the question r u blind?

[jagged dagger]

ok gl then

[obtuse pebble]

@humble quest Has your question been resolved?

[obtuse pebble]

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[proven plank]

help plz

i got to this part

[delicate bay]

did u use the quotient rule

?

[gilded needle]

,rotate

[gilded needle]

how did you get the first term in the numerator?

should be (1+x)^3 times the derivative of x^2 - x^5, which is what?

[proven plank]

i expanded it

[gilded needle]

Meaning what?

[proven plank]

Like i out the x^2 back into the equation

Put

[gilded needle]

yes I understand you did that

but you did not take the derivative of x^2 - x^5 correctly

it's not (2)(-5x^4)

[proven plank]

which step?

[gilded needle]

the first term in the numerator of y'(x)

is wrong

[proven plank]

.close

[obtuse pebble]

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[obtuse pebble]

@lusty echo Has your question been resolved?

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[timid silo]

hi

[timid silo]

here

may i ask for help

?

[strong vale]

just post problem

[deep mason]

yea just put ur actual question and someone will help you out

[timid silo]

\

hmm

hii

i need help

😦

guys

[timid silo]

ok

[timid silo]

alr

[strong vale]

https://tenor.com/view/yoda-patience-you-must-have-patience-gif-15254127

[timid silo]

hmm

how about you

can u help me

hii

welp

no one insteresting

to heko me

[strong vale]

u must have patience, wordy problems like this are not very popular, so they will take longer to get response. but someone with the time will come to help eventually

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

hi

[timid silo]

is 1hr a patience?

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

your a cute

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[grim mural]

anyone good on probaibilities?

[proven zephyr]

what's the question

[grim mural]

i cant seem to provide a proof for this

multiplication rule seem exponential

idk

[proven zephyr]

welp

im dumb

so ima just leave it to someone else

[obtuse pebble]

@grim mural Has your question been resolved?

[obtuse pebble]

@grim mural Has your question been resolved?

[glossy ibex]

does this help?

P(A | B) = P(A∩B) / P(B) --> P(A | B)P(B) = P(A∩B)

[obtuse pebble]

@grim mural Has your question been resolved?

[royal solar]

ahh. no worries. hope it made sense

[royal solar]

yeah, this chains

[obtuse pebble]

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[grim mural]

thank you

[obtuse pebble]

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[lilac grove]

How tf do I use Newton raphson to estimate

[short spruce]

https://www.youtube.com/watch?v=-5e2cULI3H8

[obtuse pebble]

@lilac grove Has your question been resolved?

[obtuse pebble]

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[lilac grove]

I have trouble with f'(x)

[short spruce]

how so

[visual wagon]

Answer ?

[obsidian isle]

What does it look like

[royal basin]

@visual wagon do not occupy other people's channels.

[visual wagon]

Ok sorry

[obtuse pebble]

@lilac grove Has your question been resolved?

[obtuse pebble]

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[craggy ferry]

For this problem do you have to rewrite it as ln(x)/(1/x^2)?

[short spruce]

yeah

[craggy ferry]

I found that when I just took the derivative without rewriting it I ended up with 2xln(x)+x. If I plug in 0 ln(0) is undefined

[short spruce]

you can't apply lhopitals if you don't have something in the form of +-inf/inf or 0/0

[craggy ferry]

How does rewriting it like so make it so that you are able to apply it?

[short spruce]

because you can't apply lhopitals if you don't have something in the form of +-inf/inf or 0/0

rewriting it gives you something in that form

therefore applicable

[craggy ferry]

I'm just confused because I thought ln(0) was undefined

[short spruce]

it is

[craggy ferry]

I just searched it up and it says ln(0) is also equal to infinity. So I guess since it's infinity/0 which equals infinity I use L'hospital rule

[short spruce]

ln(0) is undefined

the limit of ln(x) as x approaches zero from the right is negative infinity

[craggy ferry]

Oh ok I see what you are saying now.

Thanks

.close

[obtuse pebble]

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[inland pine]

can someone help me with this question

[jolly rock]

can anyone help me?

[idle thunder]

#❓how-to-get-help

[timid silo]

@jolly rock this one just got occupied

[inland pine]

.close

[obtuse pebble]

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[timid silo]

@inland pine you figure it out?

lmao nm

[inland pine]

oh no i thought someone else was using this channel so i went to a diff one

[timid silo]

no you were using it and someone else came in to it lol.

[inland pine]

ohhh lol my bad

[obtuse pebble]

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[obtuse pebble]

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[grave kestrel]

In this question they are asking that whether the two events are exhaustive. I understood the first part that the events are mutually exclusive but in the second part I don't know that if the events are exclusive or not.

[timid silo]

the rolling of the first dice is fixed, it will not effect the prability that a 5 will be rolled on the second die

wait no i miss read the question

im not sure

sorry

[obtuse pebble]

@grave kestrel Has your question been resolved?

[brisk oracle]

"In probability, a set of events is collectively exhaustive if they cover all of the probability space: i.e., the probability of any one of them happening is 100%. "

i.e., if you can imagine a scenario where neither A or B occurs, they are not exhaustive

[grave kestrel]

Okay thanks

.close

[obtuse pebble]

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[timid silo]

How to divide ➗ fast on paper ? Like
1500÷46?

[sage geode]

Look for obvious common factors?

In this example 1500 and 46 are both factors of 2

[elfin sage]

Write it as fraction and rewrite num and den with factors

[timid silo]

$\frac{1500}{46}= \frac{7502}{232}= \frac{750}{23}$

[warm shale]

aspwil

[timid silo]

or are you looking for an exact anwser and not simplist form

What if they are no fraction of 2

Exact

look for other numbers?

Yes

When I am in exam that's my mine problem

And there is no enough time

long division may be helpfull thne

Yes but fast

Alright thank you for your help 😊

this looks promising https://www.youtube.com/watch?v=X80zDVyDL_0
good luck

[timid silo]

Thanks that was really useful.

[obtuse pebble]

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[latent panther]

Anyone have any videos I can watch to solve more complicated derivatives like these?

[hollow sun]

you can solve these with chain rule, product rule and quotient rule

[latent panther]

Alright. Does organic chemistry tutor make good videos for this?

Also how about problems like this?

[obtuse pebble]

@latent panther Has your question been resolved?

[knotty nebula]

That’s just implicit differentiation

[latent panther]

@knotty nebula how about this?

[knotty nebula]

Product rule

[latent panther]

@knotty nebula this one?

[knotty nebula]

What ideas do you have on it

[latent panther]

Quotient and product rule?

[obtuse pebble]

@latent panther Has your question been resolved?

[latent panther]

<@&286206848099549185>

Can someone please give me the resources needed to do complicated derivative problems like these?

I really need help badly

please

[latent panther]

hello anyone? <@&286206848099549185>

[robust sleet]

they ain't complicated

just search on YouTube or Google

[latent panther]

Search what?

I dont know what to look up

@robust sleet

[robust sleet]

search derivatives

[latent panther]

all the videos I find on derivatives are not complicated derivatives like that

they are much simpler things like basic polynomials @robust sleet

[robust sleet]

http://faculty.bard.edu › Adv...PDF
Exercises: Advanced Derivatives - Bard Faculty

math.berkeley.edu/~kruckman/fall2010/9-29-problems.pdf

https://homepages.bluffton.edu/~nesterd/apps/derivs.html

simple 1 sec search

[latent panther]

@robust sleet Ok but these are problems I have no idea how to solve

I am trying to find a resource that teaches me how to solve them

[tardy epoch]

Like a derivative rules list?

[latent panther]

I just want to learn how to do these I am trying to do the thing Fractalogist sent me but I am just failing every single problem I dont get how I am supposed to learn these

[tardy epoch]

https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.math.ucdavis.edu/~kouba/Math17BHWDIRECTORY/Derivatives.pdf&ved=2ahUKEwjb54ewzrn2AhVHDEQIHcuxCYIQFnoECAwQAQ&usg=AOvVaw0I2oZK9n3eOc4MR0VHYluC

[latent panther]

I dont get how to learn from this

[tardy epoch]

You're gonna need to ask a more specific question then.

[tardy epoch]

Just try #3 here

[latent panther]

I already saw the solution for number 3

[tardy epoch]

Would you be able to do it again for different numbers?

Like 9 in the exponent in the first term

[latent panther]

Yeah do you have another version of it?

[tardy epoch]

You need help replacing 9 in the exponent?

x^7 becomes x^9

[shut ravine]

Is this already occupied?

[rustic harbor]

@latent panther The goal in differentiation is always to come back into something you know. For example, if you have a big fraction, you can always set the top part as a certain function u and the bottom part as v

[rustic harbor]

If there is a name besides the name of the channel "help-#", then yeah

The name in #help-10 right there shows who is being helped

The ones that are free are located above these @shut ravine

[obtuse pebble]

@latent panther Has your question been resolved?

[obtuse pebble]

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[misty valve]

I have tried 5pi/6, 11pi/6

Nothing I put is right

Idk what to do

Sorry

Wrong picture

I have tried 5pi/6, 11pi/6 nothing works

Well I just tried every single radian measure in the whole unit circle

It didn't take it

[obtuse pebble]

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[azure delta]

correct? pythagoras

i dont really know when i split something correctly or not

yes

yea a bit

i just got started w it

im 15 in norway we have reallly low standards here im just learning about this

they start of very low and kill us in high school with bunch of shit im in high school next year im preparing myself

alrighty

[obtuse pebble]

@azure delta Has your question been resolved?

[stable summit]

pro tip: if a^2 + b^2 = c^2 then (ak)^2 + (bk)^2 = (ck)^2 and vice versa

9^2 + 12^2 = 15^2 because if you divide all numbers by 3 you get 3^2 + 4^2 = 5^2

and (3,4,5) is the easiest to remember pythagorean triple

[obtuse pebble]

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[azure delta]

God damn i apprechiate that

[azure delta]

Ima screen shot this and come back tommorow ive been studying for 7h today+ 5h of school gotta go to sleep

Gn i apprechiate it

[obtuse pebble]

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[pallid crane]

$-a^2-9$

[warm shale]

Xerral

[pallid crane]

How can I factorize it?

[compact shadow]

Can’t factor it in real numbers

Unless you factor it in complex numbers

[pallid crane]

wdym

why I can't with real numbers?

[compact shadow]

a^2+9=0 doesn’t have a real root

[pallid crane]

i see

thx

[obtuse pebble]

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[digital fjord]

its my work on the left

answer key on right

im not sure hgow they got ^2

[river tree]

you don't need to take the natural logarithm of both sides of the equation.
Try to solve the derivative of f(x) using the chain rule first

[river tree]

notice that the square root of b^3 * x^2 * y is the same as (b^3 * x^2 * y)^0.5
that will let you use more logarithm identities to get numbers outside the logarithm

[obtuse pebble]

@digital fjord Has your question been resolved?

[digital fjord]

gimme a sec

[obtuse pebble]

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[inland spoke]

Hi

[inland spoke]

isn't y0 supposed to be -1/16, and m supposed to be -1/2?
or am I missing something?

[river tree]

you're confusing the slope with the y value. y0 is the y-value of the point, m is the slope, and at (4,1/2) the slope m=-1/16

[inland spoke]

isn't -1/16 the y value, since we plugged in the x value (4) and computed the y value

?

cause we end up with f'(x)=(-1/2)(x^-3/2)

[tardy epoch]

no

[inland spoke]

which is just like y=mx+b

[tardy epoch]

y = f(x)

$y_0 = f(4)$

[warm shale]

riemann

[tardy epoch]

calculate $f(4)$

[warm shale]

riemann

[inland spoke]

wait is it because the y value of a derivative is the slope of the original line?

[tardy epoch]

write mathematically what you mean

[inland spoke]

the definition os the derivative is the slope of the function at a certain point right?

[tardy epoch]

right

[inland spoke]

so you know how in a normal function, if we wanna find the y value we just plug in the x value

and the slope is already visible in y=mx+b

this is doing the opposite right?

because it's a derivative?

[tardy epoch]

you're being sloppy with your language

there are no "normal functions"

if you want to evaluate a function, yes you plug in the x value.

the "slope is already visible" only applies to equations of lines, but that's a very small class of functions

[inland spoke]

sorry I don't know how to explain this well

for example, a normal function like f(x)=2x+1

the slope is 2

and the y value at point a is f(a)=2(a)+1

but for this derivative function, it's doing the opposite. The derivative in this case is f'(x)=(-1/2)(x^-3/2)

[tardy epoch]

this is called a line, not a "normal function"

[inland spoke]

sorry

yea

[tardy epoch]

this is just the definition of the derivative

yes it gives you a slope

[inland spoke]

yea

but why is the y value 1/2

?

the y0

[tardy epoch]

look at your notes for definition of tangent line

[inland spoke]

oh

we plugged the x value in f(x)

I think I got it

thank you

have a good day

[tardy epoch]

[inland spoke]

.close

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[crimson carbon]

how would i go about solving this

hello

[odd stag]

if the solutions are those points then you already know two of the points on the line that intersects them

so you can just you y=mx+c

does that make sense?

[obtuse pebble]

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[high lily]

.close

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[uneven hamlet]

collinear means the vectors p,q are scalar multiples of each other

[junior hull]

yea I am having troubles with 17c

[uneven hamlet]

oh ok

did you find suitable values for a,b?

[junior hull]

you need to use the equation you got out of 17b first which is 0=2a-2b-18

a=9 and b =0

[uneven hamlet]

yep sure looks good

now you just have to make it a unit vector

[junior hull]

but im confused a little by the solution given by the text book

why is it squaring the values we gave it for a and b but then choosing to square the 18 from the equation

if it just square the equation would it not be 18^2+0^2+18^2

[uneven hamlet]

i think the book is wrong here but let me make sure...

[junior hull]

sure as hell wouldnt be the first time it was wrong

[uneven hamlet]

because you should divide by the magntiude of q

[spiral maple]

you want the norm of [9,0,6].

[uneven hamlet]

which is sqrt(9^2 + 0^2 + 6^2)

[junior hull]

exactly

so that would be the correct solution right? thats what I thought untill i looked at the textbook

[uneven hamlet]

yes that should be the correct solution, looks like the book is wrong

[junior hull]

alright thank you very much

.close

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[peak ermine]

Statistics

This might be a stupid question but:
"How many ways can you make change for a quarter? (Different arrangements of the same coins are not counted separately) Use only pennies, nickels, and dimes"

[uneven hamlet]

idk if there's a better way than just enumerating all the possible combinations...

but that sounds pretty brutal lol

[peak ermine]

Yeah I'm tryna figure out if there's any way other than that because my brain is fried rn

[true rain]

That's not really statistics, but combinatorics?

but uhhh I think you can enumerate

[peak ermine]

I'm not too sure at this point? It's in my elementary statistics course

[true rain]

Oh really ok

I feel like the best way to approach this is to start at the maximum amount of dimes, then maximum nickles

and count the number of ways

[uneven hamlet]

gl hf

[true rain]

^

[peak ermine]

Ahaa brain go wee woo
Thanks 😅

[uneven hamlet]

google says 12...maybe you can use that to check

and we can help you find any combinations you're missing

[peak ermine]

12's right

I guess it is just a manual thing

That's funky

I will most likely be back in some other chat later asking more questions but I'll close this for now

.close

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[small bloom]

given GDC where G is 20 degrees and DC is 10.3 cm, what is the range of values for side DG so that two possible triangle can be drawn? I know this is an ambiguous sine law problem, but how I start with so few values?

[obtuse pebble]

@small bloom Has your question been resolved?

[small bloom]

I figure I should try to find the height, but again idk how to solve this with so few values

<@&286206848099549185>

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[small bloom]

.close

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[manic crow]

idk what they are asking

[short spruce]

i believe they're asking the scale on the vertical axis per unit

[true rain]

true

unit probably means square

[manic crow]

the big ones right

not the small squares

[short spruce]

per unit

[true rain]

probably the small ones

[manic crow]

ohh ok thx

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[wintry stream]

when do you use the disk vs washer method?

[brave bramble]

Disk method integrates with the same variable as the axis you're rotating

And washer is opposite

[civic zealot]

????

[brave bramble]

Oop I said "washer" when I was thinking of shell

[civic zealot]

washer method is just the difference of two disks

You use it when the object doesn't touch it's axis of rotation.

[obtuse pebble]

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[balmy merlin]

so i have no idea how to do part c let alone start it

[gilded needle]

do you know how to find the local minimum in that interval?

[balmy merlin]

no

i havent done this in a while so i have forgotten

[gilded needle]

well it's either at a point where the derivative is zero (if there is such a point in that interval), or it's at one of the endpoints of the interval

[balmy merlin]

ah

so what equation should i use to start it off

[gilded needle]

you found the values of x where f'(x) is zero in part (b). Are either of those values of x in the interval [-5,5]?

[balmy merlin]

correct

not sure about the interval however

[gilded needle]

what aren't you sure about?

[balmy merlin]

like how is the interval [-5,5]

like ik its given to me

[gilded needle]

"the domain -5 <= x <= 5"

i.e. the domain is the interval [-5,5]

[balmy merlin]

oh i get it

sorry my brain was like what

but i get it

[gilded needle]

so in fact both of those two points are in [-5,5]

[balmy merlin]

so is there a certian equation to find the tangent line?

[gilded needle]

one point is at a local maximum and the other is at a local minimum

you need to work out which one is the local maximum first

[balmy merlin]

right

how do i do that

[gilded needle]

couple possibilities... do you know the second derivative test?

[balmy merlin]

no

[gilded needle]

ok, then how about evaluating f(x) at each of those two points and seeing which is bigger and which is smaller

the bigger one must be a local maximum and the smaller must be a local minimum

[balmy merlin]

so -5 is the local minimum and 5 is the local maximum?

.close

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[dreamy tree]

If an original graph has (1,0) is it like the inverse that has (0,1) or a reflection

[dreamy tree]

Simple question

[obtuse pebble]

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[rigid flare]

Hii! Our MPTS (Multiplinary Discipline Task) just came out, and I have this MPT for math. I don't have good ideas on what I should do for it, can you suggest me some good ideas? Thanks!

<@&286206848099549185>

[astral ivy]

are you good on questions 1-4?