help-10

[ember rune]

okay

how do i get the equation of the lines?

[carmine hawk]

You should know that each line passes through a specific point (midpoint of each side), and the slope of those lines can be found from the slopes of the sides of the triangle

[ember rune]

so with side AB the midpoint is (1,8) right but idk how to get the equation

[carmine hawk]

Alright, now what is the slope of the line AB?

[ember rune]

is it 0?

[carmine hawk]

Yes, which is kind of bad in our situation since the slope of the perpendicular line can't be expressed with a real number.

[ember rune]

yeah that's probably why im a bit confused lol

[carmine hawk]

So, since the slope of the line is 0, that means the equation can be written as y=something

What line y=constant goes through (0, 8) and (2, 8)?

[ember rune]

y = 8?

[carmine hawk]

Excellent, now, what line is perpendicular to it, and goes through (1, 8)

How do we write vertical lines?

[ember rune]

hmm

to write vertical lines would it be x = something?

[carmine hawk]

Yup

[ember rune]

i'm not sure

[carmine hawk]

Alright, so we have the equation x = something.
We know it goes through (x, y) = (1, 8)

If I substitute that point, I should get

1 = something

Which means that constant is 1

Makes sense why now the equation is x = 1

that goes through the point (1, 8)?

[ember rune]

ahhh okay yeah

[carmine hawk]

Alright, you found one line, now do a similar process for another one, for example BC

[ember rune]

okay so the full equation is just x = 1?

[carmine hawk]

You will need to use negative reciprocal slopes though, it won't be like this case

[ember rune]

okay

[carmine hawk]

Yes, that's it

[ember rune]

okay

i'll try BC real quick

so i've got the slope as 1/3 and goes through the midpoint (1, 5) but idk how to make the equation from there

[carmine hawk]

The slope 1/3 is for the side of the triangle?

[ember rune]

it's the negative reciprocal of it

[carmine hawk]

Alright, do you remember point-slope form of an equation?

[ember rune]

not really

[carmine hawk]

A line that passes through a certain point (x1, y1) and has a slope m has the following equation

y - y1 = m(x - x1)

[ember rune]

ohh yeah

so would i plug in (1, 5) in (x1, y2) and the slope into m?

[carmine hawk]

Yes, x1 = 1, y1 = 5 and m = 1/3

[ember rune]

okay

i got y = 1/3x + 14/3, not sure if that's correct

[carmine hawk]

I think you missed a couple of signs

[ember rune]

okay

[carmine hawk]

wait, no

That looks good

[ember rune]

oh alright

do i set the 2 equations equal to each other or something like that to find the intersection?

[carmine hawk]

Precisely that, that should give you the center

[ember rune]

okay

[carmine hawk]

However, I think you have a miscalculation

[ember rune]

oh ok

[carmine hawk]

When finding the side BC, did you use (0, 8) and (2, 2)?

[ember rune]

i don't remember XD

[carmine hawk]

Ah, check your calculations again and see what you've plugged in

[ember rune]

ok

yeah i did

[carmine hawk]

So for one of the slopes you got -3 right, of one of the sides?

[ember rune]

yeah

[carmine hawk]

Oh, continue then, it should be fine

[ember rune]

okay

so would i do 1 = 1/3x + 14/3?

[carmine hawk]

y = 1 is not a perpendicular bisector

[ember rune]

how would i set up the equation

[carmine hawk]

You got two equations for the perpendicular bisectors, what are they?

[ember rune]

x = 1 and 1/3x + 14/3

[carmine hawk]

So, you need to solve x = 1 and y = 1/3 x + 14/3

[ember rune]

y = 1/3x + 14/3

[carmine hawk]

You can substitute x = 1 in the second equation

[ember rune]

ohh

okay

so it would be y = 5?

[carmine hawk]

Yes, which means the center of the circle would be?

[ember rune]

uhh idk

[carmine hawk]

You solved for the intersection, the intersection is a point, (x, y)

What were the values of x and y that you got

[ember rune]

the ones i plugged into the point-slope form?

[carmine hawk]

When you were solving

y = 1/3 x + 14/3```
which values for `x, y` ended up working, aka being the solution?

Don't overthink it

The first equation, which value for x satisfies x = 1

[ember rune]

1

[carmine hawk]

Alright, so the x coordinate for the circle is 1

Then, you solved for y, what was it?

[ember rune]

oh (1, 5)?

[carmine hawk]

Yup

[ember rune]

ah i see

[carmine hawk]

That is your circle center

[ember rune]

okay thanks a lot man

[carmine hawk]

Np

[obtuse pebble]

@ember rune Has your question been resolved?

[obtuse pebble]

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[balmy sandal]

How do I comprehend Row Echelon Form?

[nocturne minnow]

Do you have an example?

[balmy sandal]

I don't understand the whole thing it's driving me nuts

[nocturne minnow]

Row echelon is just a form for solving a system of equations

[balmy sandal]

That's why I don't understand it. The method doesn't make any sense to me. When I modify a row, I should have three equations instead of two.

[nocturne minnow]

What exactly do you mean?

[balmy sandal]

The whole thing. It makes me feel inadequate.

[nocturne minnow]

Like instead of thinking of it in matrix form, the equivalent form are equations. You multiply one equation by some constant, does it add another equation?

[balmy sandal]

Sorry I don't understand it at all

I think it's because there's multiple ways to do it and I really hate that

I prefer repeating the same steps

[nocturne minnow]

So for example [ 1 2 ¦ 3], can also be written as x + 2y = 3, correct?

[balmy sandal]

yes

[nocturne minnow]

So using your logic and stating that you would obtain an extra equation, if you modified a row, if we multiplied x + 2y = 3 by some constant, does it add an extra equation?

[balmy sandal]

yes

[nocturne minnow]

No it doesn't, it's just a variation of the same equation

[balmy sandal]

Why would something like R2+R1=the new R2 or R1? It should be a new equation

[nocturne minnow]

It's a linear combination of 2 equations

[balmy sandal]

you can't just say its the new R2 because it doesnt make sense

[nocturne minnow]

If you had, x + 2y = 3 and 4x + 5y = 6, how would you eliminate the x?

[balmy sandal]

well I guess but I still don't see how it could replace another equation

[nocturne minnow]

Row reducing is just an elimination process

[balmy sandal]

ok but how do I know which equation it replaces when I add the two equations or subtract them?

[nocturne minnow]

Which ever you want it to replace

It doesn't matter

[balmy sandal]

ok

What's the best way to do row and reduced echelon form? Like the way you prefer?

[nocturne minnow]

RREF, to me, is more useful when finding the null space

Row echelon is good enough in general

When finding solutions to a system of equations

[balmy sandal]

I just get lost when I have to find the reduced form

Like my brain goes blank

[nocturne minnow]

Reduced echelon form, the rules are, the pivot elements are 1s and all other elements in the pivot column are 0s, and the next pivot element is anywhere to the right and next row of the previous pivot

[balmy sandal]

thanks

but I still never where to start

[nocturne minnow]

You go from left to right

[balmy sandal]

ok thanks

[obtuse pebble]

@balmy sandal Has your question been resolved?

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[balmy sandal]

.close

[vale quartz]

I'm trying to understand how to integrate e^(ikx)dx. If you do it like a normal e^x function, you get

[warm shale]

AstroCode

[vale quartz]

But this is undefined when k=0.

However, if you plug in k=0 from the start, you get

[warm shale]

AstroCode

[vale quartz]

Which is valid

[brave bramble]

First one is correct for all values of k ≠ 0

Second one is correct for k = 0

[vale quartz]

So you just integrate it differently based on k?

[brave bramble]

Ye

[vale quartz]

It feels, like, piecewise

[brave bramble]

They are very different functions for different values of k

[vale quartz]

Ya fair

Ok cool. Thanks!

.close

[obtuse pebble]

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[unreal isle]

Oh boy, I don't even know which test to use for this one to start it off.

[gloomy trellis]

We are in same section lmao calculus 2 right?

[unreal isle]

Yep.

sure do love me a good summation to infinity

[mild ocean]

divergence test could work

pretty quick and easy

[gloomy trellis]

I mean I have been skipping through calclulus 2, but I know that converges equal to finding the limit and divergence is when going from -infinity to positive infinity

[forest sinew]

i think it converges

[mild ocean]

same

[forest sinew]

so thats not gonna be strong enough

[mild ocean]

oh wait i’m dumb

i forgot the definition of divergence test lol

[gloomy trellis]

XD

[forest sinew]

see if you can create a perfect square in the denominator by making the denominator smaller

[mild ocean]

use this if you want, https://tutorial.math.lamar.edu/classes/calcII/SeriesStrategy.aspx

[brave bramble]

Note this is "like"
n/√n³ = n^(-1/2) which diverges

[gloomy trellis]

I got a test next week tuesday ;-;

For sequence

[forest sinew]

alternatively

[gloomy trellis]

For me I just plug in calculator and figure out

XD

[brave bramble]

There's a comparison that should make this stronger, I'll think on it

[mild ocean]

good luck on your test if that’s what you do

[gloomy trellis]

Ye it's going to be pain in ass, but I definitely need to study

cuz I haven't been pay attention to calculus 2 until sequence hits

[mild ocean]

sequence was like my least favorite part of calculus 2

[brave bramble]

That sqrt sucks

[gloomy trellis]

me too

[forest sinew]

my favorite

[mild ocean]

that and maybe polar coordinates

[forest sinew]

i love sequences

[mild ocean]

taylor series was cool too but i wanted to get to vectors so much i didn’t even finish it all lol

[gloomy trellis]

appendix c was pretty interesting

I think that's the most easiest thing I have done in calculus 2\

[mild ocean]

what’s that

[gloomy trellis]

Look at imagery number

And changing into complex form

[unique solstice]

Imagery numbers is what english teachers call imaginary numbers

[brave bramble]

Limit comparison should be able to do this, just compare with 1/√n

But that's kinda cheaty

But I'm not seeing better

[unreal isle]

1/sqrt(n) is fine?

huh

I figure the n in the numerator would be an obstacle to that

[brave bramble]

It's necessary

If that n wasn't there this wouldn't work lol

So note I am not talking comparison test, but limit comparison test

[unreal isle]

Yeye.

[brave bramble]

Okay cool it's very badly named

[forest sinew]

hmm

[unreal isle]

Wait

[forest sinew]

how about this

[unreal isle]

n-1/whatever is 0 at n=1

[forest sinew]

\begin{align*}
\frac{n-1}{\sqrt{ n^3+3n+4}} &< \frac{ n-1 }{ \sqrt{n^3+3n} } \ &= \frac{ n-1 }{ \sqrt{ n(n^2+3) } } \ &< \frac{ n-1 }{ \sqrt{ n(n^2-1) } } \ &= \frac{ n-1}{ \sqrt{ n(n+1)(n-1) } } \ &< \frac{ n-1}{ \sqrt{ (n-1)^2(n+1) }} \ &= \frac{ 1 }{ \sqrt{ n+1 } } \ &< \frac{1}{\sqrt n} \end{align*}

[warm shale]

jan Niku

[unreal isle]

oh, you can eliminate a constant inside the square root and still have a lesser function?

[forest sinew]

youll need to cut off a tail

since this isnt defined for all n

i think letting n>1 works

im tired so there may be an error in there

[forest sinew]

more like uhh

you make the denominator smaller

[mild ocean]

constants basically do nothing in this context

[forest sinew]

then its being divided by a smaller number

[mild ocean]

so it’s fine to take them out if they’re being added or subtracted

[forest sinew]

if you got less people eating the same pizza

everybody gets more pizza

[forest sinew]

its not

[mild ocean]

wait really

[forest sinew]

at least not carelessly

[mild ocean]

i was talking about in the comparison tests

[unreal isle]

So what's the point of making bsubn ?

[forest sinew]

bsubn?

[unreal isle]

the second function with the constant removed

[forest sinew]

i mean there its not either, you need to be careful

[forest sinew]

its part of a chain

assuming i did everything correctly

i am very tired

i was trying to explain this to someone the other day

i think it made sense in the context of an integral

i should actually check i did that correctly though

[gloomy trellis]

Bruh I can't believe I have to do integral in physics so annoying

[forest sinew]

its wrong

[mild ocean]

oof

[brave bramble]

It's very impressive, but showing that you're less than a diverging series isn't valuable

[forest sinew]

[brave bramble]

(As this one also diverges, but happens to diverge slower than 1/√n, which is still cool)

[forest sinew]

wait

i was backwards

no i wasnt

but that is kinda cool

[unreal isle]

So is this valid?

i'm fuckin lost lmao

[unreal isle]

Since you know that it diverges, can you walk me through the steps to prove it?

[brave bramble]

So yeah. A limit comparison test with 1/√n

[unreal isle]

I don't have a good grasp on limit comparison test

[brave bramble]

That is, √n(n - 1) / √[n³ + 3n + 4] has a finite limit

[unreal isle]

is that the one where you divide the two functions?

[brave bramble]

So, your thing has the same behavior as 1/√n, which is divergent

[unreal isle]

wow i forgot how to take this limit 🤦‍♂️

[brave bramble]

(Basically, this test allows you to eliminate everything that isn't the dominant term. You care about a comparison with n/√[n³])

[unreal isle]

that makes sense

[brave bramble]

Divide top and bottom by √[n³]

To get the limit

[unreal isle]

Alright just to clarify

I should have (√[n³] * (n-1))/ √n^3 +3n +4 before I divide right

it's the n-1 in the initial problem that's got me a bit confused here

[brave bramble]

A limit comparison test with 1/√n
That is, √n(n - 1) / √[n³ + 3n + 4] has a finite limit

Divide top and bottom by √[n³] to get that limit

[unreal isle]

ahhhh, okay

.close

[obtuse pebble]

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[hushed star]

how do i find the extreme values for this?

[brave bramble]

Can you graph |x - 1|?

If not, can you graph |x| instead?

[visual kelp]

I recommend graphing |x-1| by starting from |x| and then seeing how you can manipulate |x| into |x-1|

[hushed star]

im not sure how

they didnt teach us that

[brave bramble]

,w graph |x|

[warm shale]

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[brave bramble]

So that's the absolute value function. It returns the positive value always. That is, |-3| = 3

[visual kelp]

I will only leave this here

[brave bramble]

And |3| = 3

[hushed star]

ahhhh i see

what would be the extreme values?

[brave bramble]

Shifting it to the right 1 unit gives |x - 1|

[hushed star]

they either want critical points, local max/mins, absolute max/mins or singular points

[brave bramble]

,w graph |x| and |x - 1|

[warm shale]

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[brave bramble]

If you can make that graph, you can answer all

[hushed star]

ok thank you!

[obtuse pebble]

@hushed star Has your question been resolved?

[obtuse pebble]

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[mystic plaza]

How do I find particle speed?

[short spruce]

gonna need more context than that

[mystic plaza]

It was question e

Relating to particle motion

E*

[short spruce]

velocity is the derivative of position with respect to time, acceleration is the derivative of velocity with respect to time

so acceleration is the second derivative of position with respect to time

you have the position equation

[junior inlet]

a. find the derivative

b. find the second derivative

(you only need the derivative for this problem i think)

[mystic plaza]

Wait so acceleration is another way to say speed

[short spruce]

no

velocity is the most similar to speed

[mystic plaza]

Or I mean velo

Yeah

[short spruce]

though velocity is a vector and speed is scalar

so not the same exact thing

but for the purposes of your question, yes

[mystic plaza]

So my answer to c should be the same as D?

[short spruce]

oh shoot

didn't read that

don't listen to me

[short spruce]

.

refer to that then

[gloomy trellis]

I was about to say that's physics xd

[mystic plaza]

Wait but what should I do for it

[short spruce]

velocity cares about direction, speed does not

[mystic plaza]

so I can consider speed to be the absolute value of velocity?

[short spruce]

correct

[gloomy trellis]

Just saying that speed = distance/ delta t and velocity is saying displacement over time

[mystic plaza]

Alr one more thing uh

Do I do like a sign chart for question f

[short spruce]

looks like it, yes

[mystic plaza]

Kk thank you!

[short spruce]

👍

[mystic plaza]

*thank you all

.close

[obtuse pebble]

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[obtuse pebble]

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[swift copper]

One sec. I will show my work.

$x*\frac{1}{1-(-3x^2)}$

[warm shale]

RESIDGE

[swift copper]

Then I first did the power series representation on the right one(the rational)
$\sum_{n=0}^{\infty}(-1)^n * 3^n * x^{2n}$

[warm shale]

RESIDGE

[swift copper]

What do I do with the remaining x on left side? Do i just multiply it to the power series?

[swift copper]

Whoops sorry, it's 3 rather than 7. So all the work I've shown should be a 7.

I did (-1)^n and 3^n

not the negative one

$x* \sum_{n=0}^{\infty}(-1)^n * 7^n * x^{2n}$

[warm shale]

RESIDGE

[swift copper]

Okay, I guess either way works.

Are you allowed to move the x inside even though it is not a constant

[swift copper]

Okay thank you.

alright ty it works in this form i guess

.close

[obtuse pebble]

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[obtuse pebble]

@left shell Has your question been resolved?

[gloomy trellis]

You have 60

And 90

What can you indicate from there?

@left shell sorry for ping

[left shell]

oh i got it lmao

i got 90

[gloomy trellis]

Oh

Sorry for late help xd

[left shell]

no its alright

[obtuse pebble]

@left shell Has your question been resolved?

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[timid silo]

hello plase i need help hommeork plase get in a call with me delta math asignment

[obtuse pebble]

@quiet vapor Has your question been resolved?

[quiet vapor]

@twin night

can you heIp me ?

[twin night]

no im busy watching league videos before falling asleep

my roommate told me "know your value and add tax" and you know that kinda stuck with me

thats why ive decided to just chill and work on my own stuff this semester

2nd sem is where the real fun is gonna be

[quiet vapor]

:>/

[brisk matrix]

mental health comes first

and league comes 0th

[twin night]

well its a combination of that with physical academic social emotional etc

basically my main goals to be achieved by the start of 2nd sem are

1. pass all my classes 2. get to 170lbs (im 160 currently, 150 when i came to campus) 3. get to know more people / become closer with the friends i already have

[junior inlet]

uh... use your calculator?

[obtuse pebble]

@quiet vapor Has your question been resolved?

[obtuse pebble]

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[pure nova]

pls help

[junior inlet]

can you send your question please?

[pure nova]

@junior inlet

[junior inlet]

just noticed the tabs on top...

i just deleted all my answers (hope you've never seen them)

I AM SO DUMB :(((((((

[pure nova]

no problm

i had finished the exap

exam*

5\25

:DDD

[junior inlet]

fortunate;y i took one screenshot

[pure nova]

.close

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

hey can someone just take a quick look at my math here to see if it looks right

[timid silo]

so basically im trying to find a polynomial based on the turning points

if better quality screenshot/pdf needed i can throw those in asw

just need to make sure the shi looks right

[obtuse pebble]

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[royal pulsar]

Hey! I'm studying the Laplace transform and I'm trying to figure out where 4/(p-2) came from in this specific exercise

[royal pulsar]

this Cauchy problem is to be solved through the Laplace transform. After noting

we get

my brain is having a bit of an xD moment and I can't for the life of me figure out where 4/(p-2) comes from

halp pls 🐱

[strong delta]

Maybe the Laplace from 4e^ 2t?

[royal pulsar]

fuck, yeah, it's literally 1/(p-2) multiplied by 4 from the Laplace table

thank you

🤣

.close

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[stuck zephyr]

lmao I forgot this server existed since my exams ended lmao

[jolly ginkgo]

You started a help channel

If you don't need help and have accidentally messaged here type .close

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[woeful otter]

Need help understanding this question. I just need to know how they got the expression after that i can solve the rest

[obtuse pebble]

@woeful otter Has your question been resolved?

[cold thistle]

It seems like they want it to be a cylinder so you could use the formula for cylindrical volume

$V = \pi(r)^2 \times h$

[warm shale]

lexitorius

[cold thistle]

Where h is the thickness given

[obtuse pebble]

@woeful otter Has your question been resolved?

[woeful otter]

Yeah well the answers says differently

the expression they gave was (nr^2)/(20)

[jolly ginkgo]

That's what final result is

You have to perform differentiation on volume to get that

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[topaz bridge]

i've always was thought to fractionize z out and then substitute the auxiliary variable for t=z^2, but i'm not sure if you can do so for complex numbers

[orchid wind]

yeah, complex no. confuse me

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[timid silo]

Why is this 0 and not -6?

[novel knoll]

what is derivative of 1/ln(x)?

[timid silo]

oh…..

lol

@novel knollif i put ln(x) in the denominator I get an never ending loop of ln(x)^power

[novel knoll]

what is cos(0)?

[timid silo]

0

but

lim > 0 for ln(x) is undefined

[novel knoll]

try again

[timid silo]

oops 1

[novel knoll]

so you can find the limit after applying L'Hopitals once?

[timid silo]

no because

ill show u 1 sec pls

[novel knoll]

yes you can, but go ahead

[timid silo]

no?

lhopital won't work because i can't get rid of ln(x)

[novel knoll]

ah okay sure lot of effort

[timid silo]

so what should I do?

it seems the answer puts sin at the denominator

but how would I know where to put what?

[novel knoll]

yeah that might be easier but you can get the result your way too

factor out -6cos(x)

apply L'Hopitals again

[timid silo]

it's easy to tell by looking at the answer but I prob won't be able to distinguish on an exam

if i take lhopital again, the top part ends up being zero from sin

and hence 0, right?

[short spruce]

you took the wrong route in solving that

[timid silo]

where?

[short spruce]

by switching 6sin(x) to the bottom instead of ln(x)

[timid silo]

I did it with ln(x) and it didn't work

[short spruce]

it definitely does

[timid silo]

@short spruce

you end up in a cycle of ln(x)^n

[short spruce]

oh shoot yeah

[short spruce]

this is still made more complicated that it needs to be though

1/sin(x)=csc(x)

[timid silo]

how would u solve it?

oh

u mean the way i did the derivatives?

[short spruce]

instead of flipping the sin(x) down into 1/sin(x), flip it to csc(x)

derivative of csc(x) is a lot nicer than 1/sin(x)

it all simplifies anyway but yknow

[unique solstice]

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[rigid void]

My first problem is that what my teacher mean by the of bank slope being 2/3? does the mean if this was a function it would be (2/3)x? my other problem is how determinate the ratio of the length (2/3)x? my problem is how he determinates the surface?

is (2/3) hm the line of the y axis?

why does he add 5+5?

I have solved almost all my problems all i need to understand is the meaning of bank slope 2/3?

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[errant quest]

https://cdn.discordapp.com/attachments/359052604149465088/910037809753108520/unknown.png
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— Yesterday at 10:25 PM
Campanula — Yesterday at 10:25 PM
how is this right
this does not make any sense at all
if we use this equation we would get
y=5.8x-23.2

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[obtuse pebble]

@vast mountain Has your question been resolved?

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[tribal creek]

hey guys so my teacher gave us a homework she said "see if sarrus method can be applied on a 4*4 matrix and i searched for answers but i didnt relaly understand their proofs

[tribal creek]

i tried to prove that it cant be applied with the number of diagonals

thne i foudn this and i got really confused now

https://regularize.wordpress.com/2011/06/24/sarrus-rules-for-4-x-4-second-try/

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[timid silo]

I'd like some help with this thx

[timid silo]

pretty sure the height isn't 12+ o - root(3)

anyone?

[obtuse pebble]

@timid silo Has your question been resolved?

[unique solstice]

w = 300/(h-12) + 4

w>0
h>0

A=300h/(h-12) + 4h
A=(300h+4h^2-28h)/(h-12)
A=(4h^2+272h)/(h-12)

A'=(4(h^2-24h-816)/(h-12)^2

h=12
h=12+8 sqrt(15)

It looks like you did good up until the step where you simplified the derivative

[timid silo]

@unique solsticeA=(300h+4h^2-28h)/(h-12) what happened here?

[unique solstice]

I just combined the 4h term into the fraction

[obtuse pebble]

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[obtuse pebble]

@graceful sparrow Has your question been resolved?

[graceful sparrow]

<@&286206848099549185>

[tired shell]

to simplify a square root you want to take out as many doubles as you can

like with the x^5 I can take out an x^2 to put an x outside

try to find what all the doubles are in 5^3 x^5 y^6

[graceful sparrow]

like this

[tired shell]

yup, and you can pull out a few more

[graceful sparrow]

i don't think you pull out from the term in the bracket

so idk

[runic obsidian]

yes you do, if I'm understanding you correctly. You can keep going

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[ivory willow]

hello, i just want to ask what is this question asking me?

[ivory willow]

part b

i dont understand when it asks to determine two polynomial equations which have the same set of solutions as that system

i dont understand when it asks to determine two polynomial equations which have the same set of solutions as that system

<@&286206848099549185>

[obtuse pebble]

@ivory willow Has your question been resolved?

[junior inlet]

uh
maybe they have the same stationary points?

[obtuse pebble]

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[jolly ginkgo]

They haven't mentioned how much a student gets

[timid silo]

So the question is wrong ?

[runic obsidian]

not if it gives u more information on another page, is it continuing an example that it started on the previous page?

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[placid walrus]

can anyone explain how it is E?

[obtuse pebble]

@placid walrus Has your question been resolved?

[placid walrus]

<@&286206848099549185>

[royal basin]

@placid walrus do you know what it means for two events to be independent

[placid walrus]

one event occurring doesnt affect the other

[royal basin]

can you write that in terms of probabilities?

[placid walrus]

pr(anb) = pr(a) * pr(b)

[royal basin]

okay, great, so are you able to check each answer option against that?

[obtuse pebble]

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[placid walrus]

oh ok got it ! thanks

[obtuse pebble]

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[manic violet]

dont know how to find the values of the a b and c but they all need to add up to 360

[dim patio]

Is this a parallelogram?

[manic violet]

no its a rhombus

[dim patio]

Give me a mib

[manic violet]

ok bett

[dim patio]

If it is a rhombus

Then you got c=108

[manic violet]

oh ok thanks

what about a and b

[dim patio]

a=b=360-108/2

[manic violet]

oh ok

thanks then

[dim patio]

Kk

[manic violet]

.close

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[lunar plank]

can anyone explain why i can find the inverse of function with 2 variables with inverse matrix please?
Source: https://math.stackexchange.com/questions/221148/how-do-we-find-the-inverse-of-a-vector-function-with-2-variables

[lunar plank]

I have been thinking this question for several days.

[obtuse pebble]

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[lunar plank]

.close

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[sullen vault]

What is the next number in this sequence?
52 56 48 64 32 ...
How do you did you find your answer?

[sullen vault]

I found it, it is +4 multiplied by -2

.done

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[queen fractal]

Maria, Andreas and Patric are running relay. Andreas runs in twice as long as Maria and Patric. Maria and Patrics times are 27min longer than Andreas. Together they have ran for 2h and 22 minutes. How long did each of them need?

[queen fractal]

I cant understand how he can run in twice their combined time but yet they run for 27min longer than him

I did (x+27)+(x+27)+2(x+27)=142(time in minutes)

But it doesn’t work

That would make X = 8,5

[obtuse pebble]

@queen fractal Has your question been resolved?

[queen fractal]

<@&286206848099549185>

[undone warren]

<@&286206848099549185>

[novel knoll]

From the picture it seems they mean Andreas runs twice as long as Maria. Patrik runs 27 mins longer than Andreas

[queen fractal]

That not true tho

Here’s from another book

[novel knoll]

Och means and

If you read the and as: “…Maria, and Patrik…”

It reads like that

[queen fractal]

But can you solve the problem my way?

<@&286206848099549185>

Nvm

[novel knoll]

It doesn’t make sense the way you read it

Like you said yourself

So no

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[astral rune]

is that the right way to use this math notation?

[astral rune]

I want to say: square root of y is the positive number which exists x^2 = y

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.close

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[obsidian condor]

Hi, I was able to write the equation for the following zeros x = -1 and x = 4. I am not sure by what the question means in part a), "state two functions that belong to the family."

[jolly ginkgo]

Write two equation for two different values of k not equal to 0

[obsidian condor]

oh okay

thx for the clarification

.close

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[naive fossil]

If the sub travels 30 ft/min, then after 5.5 minutes it will have traveled 30 ft/min * 5.5 min

[timid silo]

no

I'm going to submit that

.close

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[austere folio]

if i have a cylinder with radius r and height h. If I double the radius and height will the volume double aswell?

[timid silo]

If you doubled the height, the volume would double, yes

However, the radius term is squared so that would more than double the volume

because $V = \pi r^2 h$

[warm shale]

hvna

[timid silo]

So imagine you doubled the radius:
$V = \pi (2r)^2 h = V = \pi 4r^2 h$

[warm shale]

hvna

[austere folio]

ok thanks

that makes sense

.close

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[south current]

If I have a square matrix A, and I raise it to an exponent (Such as 3), what order do I multiply it? Do I do:
A * A^2
A^2 * A
Or does it not matter?

[urban schooner]

help

[south current]

I am 0.2 seconds ahead of you

[urban schooner]

nutj

[south current]

Eh?

[timid silo]

try it out yourself

preferably with a simple matrix

[south current]

ok

I've compared the top left values for the two matrices and they are the same value (In terms of a, b, c and d)

Yes that works

.close

[obtuse pebble]

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[south current]

Thanks

[obtuse pebble]

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[sinful grove]

(probability) if i have x cookies and r kids how do you find the distinct ways of distributing them?

[sinful grove]

.close

[obtuse pebble]

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[edgy fiber]

Hi guys can i ask you a problem related to matlab ?

[marsh juniper]

Send your question

Someone will answer If they can

[obtuse pebble]

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[amber bobcat]

Can anyone help me with the 3a

I literally need to write a proof

For Regression Analysis

🤣

[obtuse pebble]

@amber bobcat Has your question been resolved?

[fast kite]

plug the value of Y in the expression given in 3a, what do you get

[amber bobcat]

what do you mean?

[fast kite]

the expression given in 3a, is an expression in terms of Y right?

[amber bobcat]

hmm

thats the proof?

[fast kite]

yes

[amber bobcat]

didnt work for me

:?

[fast kite]

what did you get?

[amber bobcat]

-1/B0+B1

@fast kite

[fast kite]

where did the X go?

[amber bobcat]

B0+B1X

[fast kite]

right

so YTran = B0 + B1X

which means it is linear in X

[amber bobcat]

but its -1/B0+B1X

@fast kite

whats that -1?

[fast kite]

in the expression the raised to power -1 bit ln(...)^-1 ONLY applies to the term in the parentheses (...) not the whole expression

did you apply to the whole expression?

[amber bobcat]

no

OMG

YES

[obtuse pebble]

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[whole tide]

shoot wait let me rotate it

[obtuse pebble]

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[tardy tinsel]

can someone help me with this? i have a vague idea on how to get started but am unsure with the execution of it

[obtuse pebble]

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[tardy tinsel]

<@&286206848099549185>

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[mystic saffron]

how would you find the missing angle in the top quadrilateral

[hidden wigeon]

ok so

a right angle is 90 degrees

right

[mystic saffron]

yes

not h

the one next to 66

near 108 and 130

[hidden wigeon]

what should these 3 angles add up to

[mystic saffron]

BRO

YO

NO WAY

ok

i get it

thank you cat bread

.close

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[junior inlet]

UHH

i think this deserves a spot in the advanced maths channels

or just wolframalpha

[obtuse pebble]

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[magic portal]

What are independant and dependant variables

[magic portal]

Cause I kinda forgot what the difference is

[nocturne minnow]

Independent variables are the ones that get manipulated, dependent respond to the independent. Like y = 3x + 4, x is the independent because you can manipulate it, while y is the dependent because it responds to the changing x value

[magic portal]

so dependent variable is what you are calculating for right??

[nocturne minnow]

Yeah

[hidden wigeon]

yes

[magic portal]

Oh ok

now I remember both

thx

I prob will have more questions

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[brittle scroll]

how do you solve quadratics that are not of degree 2

[brittle scroll]

something like that for example

quadratic equation only works for those of degree 2 right

[nocturne minnow]

That is what quadratic means. It only deals with equations with a max degree of 2

[brittle scroll]

o ok

polynomials that are not of degree 2 then

[nocturne minnow]

Best option is just use a calculator

[brittle scroll]

well like

ik thats probably an extreme example

i chose random numbers honestly

but something simpler, is there a method for it?

if its not obviously factorable

[obtuse pebble]

@brittle scroll Has your question been resolved?

[signal cape]

There is no 1 single method that can factor any polynomial

For example, if you were to factor a cubic function (degree 3)

You can take the coefficient of the term with the highest degree, and the constant term, then factor both

Or you can use the cubic formula which is incredibly long and no sane person memorizes it

[obtuse pebble]

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[brittle scroll]

hm ok

[brittle scroll]

.close

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[ember geode]

hi

[ember geode]

.close

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[timid silo]

That'd make sense

As it approaches 0/0

[obtuse pebble]

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[timid silo]

.open

BRUH HOW DO I CLAIM THE CHANNEL

[timid silo]

.reopen

hi how do i do Quadratics

[royal basin]

by posting your math problem(s) here

also wdym by "do quadratics"

[timid silo]

teach me quadratics

.close

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[royal basin]

.....

[ocean topaz]

can you be more specific about what you need help with?

[oblique glacier]

please read #❓how-to-get-help as well to learn about what to do to get help as well; and how to claim channel, etc

[ocean topaz]

people can't teach you a full course here, but they can help you with specific questions

[obtuse pebble]

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[hybrid kraken]

https://i.imgur.com/hdE0hiS.png

[hybrid kraken]

For 4a, would it be False -> True, therefore the expression is always true?

[formal atlas]

Isn't it True -> False though?

[obtuse pebble]

@hybrid kraken Has your question been resolved?

[hybrid kraken]

For every n, there exists an m where m!=n
Actually yeah...

Since it is true-> false then the statement must be false

[dapper bloom]

Yep.

For that last one if it were true you'd have stuff like m=m+1 so 0=1 (which is obv untrue lol)

[hybrid kraken]

Btw, for 4b
If the not symbol was not infront of the left proposition, the statement would be True

if the not symbol is in front, would it instantly be false?

Or are there some cases where you can add not and it remains True?

[dapper bloom]

So if P is true then not P is false.

So we can't have P be true and not P also be true for any proposition, or any well formed formula in normal fol.

[hybrid kraken]

What if the "not" was located between the ∀m and En?

Would the same reasoning still apply?

[dapper bloom]

I don't think it's as simple.

Well I guess it depends on what ur meaning to ask.

To be clear I do not think something like $\lnot\exists x P(x,y)$ has a defined truth value without knowing what y is.

[warm shale]

DootDooter

[dapper bloom]

Are you meaning to ask what happens to the truth value of the whole formula of 4b if we do that thing you said to the not?

[hybrid kraken]

Yeah

For ex, if ∀m (not)∃n p(x) is True
would ∀m ∃n p(x) be False

[dapper bloom]

So $\forall m \lnot \exists n (m\neq n) \iff \forall m\forall n (m=n)$

But not all natural numbers are equal.

So if we make the change u mention the conditional now has a false antecedent (first part)

So it is vacuously true (the false implies true/false cases for truth value of a conditional).

[warm shale]

DootDooter

[hybrid kraken]

I see,
btw for 4a where where it is True -> False, the question ask to give the truth value. Would it be correct to say the truth value is always 0 (since true->false is always false)
What if there was a case where true-> True?

[dapper bloom]

So for the antecedent in 4a we know it is true by considering n and n+1 since n=/=n+1 for any n.

So like, let m=n+1 hence you know 4a has a true antecedent.

For the consequent if it ever were true we would have some m where every other natural number was equal to m. So in particular consider m=n+1 hence n=n+1 so that 0=1.

But 0 is not 1 so the consequent of 4a can never be true.

So it will always be True implies false.

[hybrid kraken]

I see, thanks

[hybrid kraken]

https://i.imgur.com/PWJXIKS.png

For this question, what is it asking?

I know that the only way for 6a to be false is if T->F

it says to "defining predicates p(x) and q(x) where this implication fails" does this means to set p and q to a truth value so that T->F?

All I know is that this means
[∃x p(x) ] ^ [∃x q(x)] is True
which implies ∃x [p(x) ^ q(x)] is False

[stuck zephyr]

ohhhh ok sorry

.close

[hybrid kraken]

im using

[obtuse pebble]

@hybrid kraken Has your question been resolved?

[obtuse pebble]

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[fathom tangle]

Question: Look at the venn diagram. The likelihood for A is 0,3, the likelihood for B is 0,5, and the likelihood of them coexisting is 0,1. What's the likelihood of neither A or B occurring

Really don't know how to solve this, answers that explain the thought process greatly appreciated

[obtuse pebble]

@fathom tangle Has your question been resolved?

[fathom tangle]

Still looking for answers 🙂

[plain owl]

Probability of neither A,B occuring could be written as
1 - P(A U B)

Can you calculate probability of A or B occuring?

[fathom tangle]

Not really

The formula is familiar

[plain owl]

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

[warm shale]

Euclid31415

[plain owl]

We have subtraction because we double counted probability A and B both occuring in P(A) and also P(B)

[obtuse pebble]

@fathom tangle Has your question been resolved?

[fathom tangle]

so P(A) + P(B) - P (A not B)

= 0.7

but thats the probability of a or b happening

so you take the probability of anything happening (1) minus probability of A or B happening = 1 - 0.7?

[plain owl]

Probability of neither A nor B happening=1- probability of A or B happening

[plain owl]

P(A or B)=P(A)+P(B)-P(A and B)

[fathom tangle]

Thanks! I got it 🙂

[fathom tangle]

New Question

The risk of dying after a heart attack is 5%. 10 people are taken to the ER one night due to heart attack. a) What's the probability that all 10 survive? b) How big is the risk that at least one dies?

How would you guys calculate this?

[plain owl]

When events A,B are independent:\\$P(A\cap B)=P(A)P(B)$

[warm shale]

Euclid31415

[fathom tangle]

Still kinda lost :/

[plain owl]

What is the probability that a patient survives after heart attack?

[fathom tangle]

95%

So 0,95

[plain owl]

What is the probability that two patients survive after heart attack?

[fathom tangle]

0,9025

oh

yes

0,95^10 yes?

[plain owl]

Yes!

[fathom tangle]

Hmm

okay so B

[plain owl]

You can think of the reverse of question (b)

How big is the probability that no one dies?

[fathom tangle]

0,05

wait

[plain owl]

We did in (a)

[fathom tangle]

no one dies is 0,58...

59*

0,5987...

[plain owl]

So what is the chance of atleast 1 dying?

[fathom tangle]

0,05

[plain owl]

It is 1-(0.95)^10

[fathom tangle]

oh wait

ur right

if 60% are likely to survive then the rest are not

which would be 40%

[plain owl]

~60% chance that no one dies

Which means ~40% chance that the event of no one dying does not occur.

[fathom tangle]

Yes

I have this question

You flip a coin 1,000 times in a row. The claim: The probability of the coin lands heads up each time is equal to the probability of which any other given sequence of heads and tails.

I would say that it's not equal because probability of landing heads up every time is 0.5^1000 right

[plain owl]

Yes

It would be equal though

For any specific sequence of 1000 coin flips

[fathom tangle]

So it's as likely that you get 1000 heads

as it is that u get 500 heads 500 tails?

[plain owl]

No!

That is because 500 heads and 500 tails can occur in many arrangements

But that probability is equivalent to getting 500 tails in first 500 throws and getting heads in rest of them

[fathom tangle]

Oh so it's saying that probability of landing 1000 heads is as likely as any other given combination of throws

[plain owl]

Given sequence means we also know the exact arrangement of H and T that occur

[fathom tangle]

yes

so the exact arrangement of 1000 heads is as likely as an exact arrangement giving 999 and 1

where lets say the first 999 are head last 1 is tail

[plain owl]

Yes

[fathom tangle]

okay thanks!!

[plain owl]

Probability of getting 999 heads first and tail at the end is also (0.5)^1000

[fathom tangle]

exactly