help-38

[heady mica]

It’s abstract at first but listen me

[bleak maple]

Oh okay

[bleak maple]

Yeah, a little bit

[heady mica]

I want you to think about 2 * 3 + 2 * 5

We will count by two

[bleak maple]

Okay

[heady mica]

So no twos will in our job

We see that 3 + 5 is 8

[bleak maple]

Yes

[heady mica]

And since we treated 2 like 1 (basis for counting) we will multiply by two to convert it into 1 basis

[bleak maple]

Ohhhhh

[heady mica]

And if you were to calculate it

6 + 10 = 16

Think like we set the answer to be a

And multiply both sides by a number

(In our case it was 1/2)

[bleak maple]

Ohhh

[heady mica]

We could reverse it in the end and get answer

It’s useful in irrational numbers because we don’t actually calculate it

It provides us a shortcut

[bleak maple]

Yeah

[heady mica]

So a * some irrational + b * same = (a+b) * that irrational

[bleak maple]

Ohhh right

[heady mica]

And we want to get the same irrational to do it

[bleak maple]

Yes

[heady mica]

So we some 3 multiple on a

It was this

Wrong lol

This

[bleak maple]

oh

that's the anwser

??

[heady mica]

We multiply numbers to get our number and it provides a escape way in square root

[heady mica]

For a

If I did all of this and didn’t fail on summing

[bleak maple]

Okay, tysm! now i finally understand

[heady mica]

When you can’t deal with square roots, reverse it, take the square of it

[bleak maple]

Oh that's the point..

[heady mica]

And when you square it, you can find some full-squares in it and they can escape from square root

But 3 stays in root

[bleak maple]

Ohhhhh, that makes sense actually

i only know that we can't change 3 in root, that's it

[heady mica]

I didn’t solved the b but listen how I solve

[bleak maple]

Oh the b doesn't need to be sloved

solved*

[heady mica]

Ok

[bleak maple]

only a

[heady mica]

Whenever you struggle with something, try reversing it

[bleak maple]

Okay

[heady mica]

Square root is reverse of square

[bleak maple]

Ohhh

[heady mica]

You can understand squares easily but not square root

You ask “who’s square is that” and you normally do f(x) -> x^2 but it asked you f(?) = x

[bleak maple]

that's actually really helpful

[heady mica]

Like I liked how we multiply everything in roots

You square them all

And you could just multiply those who is rational like a^2 * b^2 = ab^2

And you could multiply smalls and get it in square root when you reverse it

[bleak maple]

ohhhh

ty

[heady mica]

No problem

[bleak maple]

now I finally understand

tysm!

[heady mica]

Always think about why and start constructing from start again

[bleak maple]

Ohhh

[heady mica]

I don’t believe in anything without proof

Math is all about proofs

[bleak maple]

Oh okay gimme min

[heady mica]

Ok

[bleak maple]

since i have 6√3 and -6√3, i crossed that cuz the answer is 0

idk is this good actually

[heady mica]

Yes they cancelled each other

You think adding (6 + (-6)) * sqrt(3)

And it’s 0

[bleak maple]

my teacher only said if u have the same number, but one is positive, and other one is negative, that the answer will always be 0

[heady mica]

Because they sum up to 0 and multiplying by 0 (if done finite) causes nothing

[bleak maple]

yeah

is my answer correct?

[heady mica]

Yes

It’s correct indeed

[bleak maple]

Oh okay, tysm for explaining!

[heady mica]

A trick here

You want 3 in radical to sum

So you can divide the things in radical by 3

If it gives you a complete square, then you can easily bring it out

Because they want it to be simple and calculateable

[bleak maple]

Ohh, I only partially rooted all the numbers

[heady mica]

You can use this method

I want to tell you something

Why this is in university idk

But square root is 1/2th power

Think about it

[bleak maple]

Why tho

[heady mica]

When you have a number x

And you want to raise it to 1/2

It will be simpler if you can write x as something *2

[bleak maple]

ohhh

[heady mica]

Squared*

And it will be square root indeed

And you can simplify 1/2 * 2 to 1

And get the square root

[bleak maple]

That's actually much faster method

[heady mica]

It’s why you can just divide all powers by two

It’s a bit trickier to see square roots inside those rationals but

For example take 7^3

[bleak maple]

okay

[heady mica]

You can arrange it like 7^2 * 7

And 7 comes rational

But 7^1/2 is not

And it’s the definition of sqrt(7)

So 7 * sqrt(7)

You can check it

sqrt(343)

Is 7 * sqrt(7)

When you regulate your number to prime powers, it’ll be easier to convert

[bleak maple]

is it 7^7?

[heady mica]

It’s 7^3

[bleak maple]

ops i typed wrong number

now i see

[heady mica]

Lol

[bleak maple]

It's 7^3

[heady mica]

Yes

[bleak maple]

Ohhhh

[heady mica]

And you could easily found this by yourself

When constructing maths

[bleak maple]

That's actually not hard

[heady mica]

When you understand a proof, you would say “I could invented it by myself.” For most of the theorems and proofs

[bleak maple]

oh okay

[bleak maple]

sorry

[heady mica]

It’s understanding

You could find it

[bleak maple]

oh

[heady mica]

People think math is hard

[bleak maple]

some points are

not all, but some are

if we don't concentrate.

[heady mica]

But it’s to understand yourself, nature and everything

[bleak maple]

You're right..

[heady mica]

It could be hard if you don’t see the proof to do something

But proofs is what makes understanding understanding

[bleak maple]

I tried a few times, but i didn't know where to start from, since I was very sick, and I wasn't been in school for few weeks..

And i literally forgot where to start from.

[heady mica]

It’s hard to be ill

[bleak maple]

yeah..

[heady mica]

And not to go to school is not considerable

The thing is most of the education systems depend on memorisation rather than questioning

And school math is to memorise a lot of useless stuff( it’s like at first) and forget it, the thing teaches in the school is great if you’re curious about everything

There is no “useless”, it’s just a little bit less connected than others to a topic

[bleak maple]

I know math, unless my lil sis, but i rlly don't like math at any point, if u understand me...

[heady mica]

Like we prove set questions by imaginary numbers

It’s all about excitement

And curiosity

[bleak maple]

yeah..

[heady mica]

Then why would I need to improve General Relativity and think about it?

It’s not because it’s important

It’s because we’re curious and do it

[bleak maple]

yeah, you're right.

[heady mica]

And it made us understand most of the things happening

Math is the heart of science, and it’s not a tool at all

It’s the thing what is science

[bleak maple]

Everyjob ur doing needs math..

every job*

[heady mica]

We don’t use maths in our jobs

It’s not about money

[bleak maple]

how not

[heady mica]

It’s about the understanding of nature and to find why we live

[heady mica]

Some people do it but it’s not true to sell maths

We try to think and find and generalise it

And we fail generalising %99 of the time but we progress

It’s all about curiousity

And people want it for just money

[bleak maple]

yeah

[bleak maple]

sadly that's true

[heady mica]

When I think, like I see my milk rotate and ask why?

Like this

I just want to learn why it rotates

More angle you make, more turns it’ll make

[bleak maple]

It depends on someone's curiosity level

[heady mica]

Like it breaks Einstein’s relativity theorem

[bleak maple]

literally.

[heady mica]

I said it, it was all about curiousity

Then you ask, “how can I effectively generate energy from that” and you just made something

That can help us

[bleak maple]

actually yea, I never thought in that way, I'm always like, it's just math, someone will send me a hw

[heady mica]

It’s the real math

The way of thinking

It was funny to think

And it’s the way which science progresses

[bleak maple]

Well, thank you so much with helping me, I don't have much time to talk, so sorry

[heady mica]

Bye then

[bleak maple]

bye!!

[heady mica]

You’re welcome

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[gusty cedar]

this is in the context of an algorithm, but i hope it still makes sense

[gusty cedar]

I just wanted a check of correctness, im not sure if i am misusing the summation symbol since my variable is counting down by 3

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[gusty cedar]

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[rugged latch]

can someone help me interpret this problem

[rugged latch]

what does it mean to find E[X_3]

[dry spear]

expectation?

[rugged latch]

yes, but X_3 specifically

if i have states 0, 1, and 2, how would i get 3, (if thats what its asking)

i can draw a state transition diagram

[zinc ginkgo]

You just calculate the probability X3=0 times 0 + probability of X3=1 times 1 + probability of X3=2 times 2

Relevant https://math.stackexchange.com/questions/1357649/expectation-in-markov-chain

[rugged latch]

OH!

thank you riemann

i totally forgot about searching up my problem lol

[rugged latch]

yeaaaa expectation, got it!

👍

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[zinc ginkgo]

It's nearly the same matrix lmao

[rugged latch]

yea, my professor probably just grabbed this example out of some textbook/resource and switched the numbers around a little bit lol

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[dusky pagoda]

LA qustion coming up!

[dusky pagoda]

I need help with these Linear Algebra proofs, I’ve completed i) with help, and now I’m looking to do ii) - iv).

[solid kiln]

binnet

binnet

[dusky pagoda]

<@&286206848099549185>

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[wraith hinge]

My question, isn't related to calculating something specific but with solving for an answer using complex numbers. It's an electromagnetics question, so you don't need to understand the basics or anything relating to it conceptually as I'll provide that information if needed (especially since it's mostly plugging numbers into formulae). Again it's more on how to deal with complex numbers in calculations. I have done part a, to a certain extent (until the imaginary portion, where I can calculate what I need to)- and know that part b and c are interrelated. Part d, as well though mostly with variables as I require all above parts in order to continue.

[wraith hinge]

The question is the following:

And what I've done so far, is basically along the lines of the following image:

For part a, I'm aware in order to find alpha, I need the real component of the following product but, I honestly don't know how to procede any further.

<@&286206848099549185>

[wraith hinge]

First of all, you're not the only person in history to think that complex numbers are "bullshit." It took centuries for mathematicians to accept their validity. However, there's a really simple way of looking at them that can help a whole lot.

You have some preconceived notions about what a number should be, and that means that you are restricting yourself to the real numbers. One pretty reasonable preconceived notion is that numbers have an order (in this technical sense). Complex numbers are not an ordered field.

Okay, here's the thing: Instead of looking for numbers (i.e., Real Numbers, the kind you're familiar with), how about you define a way to add, subtract, multiply, and divide pairs or numbers, which you can think of as points on a plane (i.e., the Cartesian plane). Here's how you do it:

(a,b) is a pair if a and b are real numbers.

[wraith hinge]

Let's say (a,b) and (c,d) are pairs. Then (a,b)+(c,d)=(a+c,b+d). That's just normal vector addition in two dimensions.

Similarly, (a,b)-(c,d)=(a-c,b-d).

Now the tricky part. You need to make a kind of multiplication that will give back the behavior you had on the real number line (because you're trying to extend the behavior of the reals). You can do this by defining (a,b)×(c,d)=(ac-bd,ad+bc). So if b and d are 0, you have (a,0)×(c,0)=(ac,0). That is, this definition of times yields the behavior you're used to when you are dealing with number pairs on the x axis, which you can think of as the real number line. Also, (1,0)×(a,b) = (a,b)×(1,0) = (a,b), so there is a multiplicative identity.

Division is a bit uglier: (a,b)/(c,d) = (ac+bd,-ad+bc)/(c2 +d2 ). Horrible, yes, but there's an intuitive way to think about it. Flip the y-value of the second pair, and multiply by that; then divide the length of the number pair you get by the square of the length of the second number. Notice that (a,b)/(a,b)=(a2 +b2 ,0)/(a2 +b2 ) = (1,0).

Okay, now you have a way of dealing with pairs of numbers that gives you back the normal behavior of the real numbers you're used to, as long as you restrict yourself to the x axis.

But now you can do more: Suppose there is a pair of numbers, and let's just call that pair of numbers x. Now, can you (yes, a human) find out what x could be if I told you that x×x=(-1,0)? Well, I'll just tell you the answer: (0,1) and (0,-1) will both satisfy the equation. We choose one of these and call it i. Then we give the pair (1,0) (the multiplicative identity) the special name 1, and there you have it: i2 = (-i)2 = -1.

Everything else comes from that.

So basically, when someone says "complex number", just think to yourself, "oh, they mean a pair of real numbers."

Hope this helped.

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[cedar prawn]

Hello

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Please don't occupy multiple help channels.

[granite sedge]

Hey

[cedar prawn]

hi

im stuck with the final part of this question

Im not sure if ive just read it wrong

I did -6+12/7

Would you be able to correct me where I went wrong?

[granite sedge]

you used Total Displacement / Total Time

right ?

[cedar prawn]

yea

I just dont know if I read it incorrectly

[granite sedge]

read what exactly

[cedar prawn]

the time and displacemtn values

displacement*

hmmm

would someone just be able to solve it

and tell the steps on how u did it?

[granite sedge]

First calculate Total Time

using =√((x₂ - x₁)² + (y₂ - y₁)²)

for both 2 segments

[cedar prawn]

OH

so

[granite sedge]

so total time is time taken for Segment 1 + time taken for segment 2

[cedar prawn]

for (3,-6) and (7,6)

[granite sedge]

and Plug the values into the formula

[cedar prawn]

ah ok

ty

[granite sedge]

and lastly divide the displacement you found by the total time taken to get the average velocity of the particle over the entire journey

[granite sedge]

Let me know when you calculate the answer

[cedar prawn]

ok

4sqrt10

[granite sedge]

what's the total time taken btw ?

[cedar prawn]

is that not it

I just put (3,-6) and (7,6) into the formula

[granite sedge]

.

[cedar prawn]

Is that what u do to calculate the total time

?

yea thats incorrect

hmm

[granite sedge]

i'm confused

[cedar prawn]

why?

[granite sedge]

it's √((x₂ - x₁)² + (y₂ - y₁)²)

did you use the correct values ?

[cedar prawn]

I think so

is (3,-6) and (7,6) correct?

[granite sedge]

i calculated the average velocity of the particle

[cedar prawn]

ah ok

[granite sedge]

and it's 0.857m/s

[cedar prawn]

thats incorrect apparently

wth

But shouldnt the time just be 7

[granite sedge]

that's what i thought too

[cedar prawn]

hmm

yea something weird is going on

I understood thi

this

something weird is just going on

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[cedar prawn]

@granite sedge I ffound the issue

they wanted it in fractional form

it was just 6/7

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[granite sedge]

lmao

[cedar prawn]

ikr

[granite sedge]

That's literally unfair

[cedar prawn]

I hate maths mechanics

ikr

Physics ITS ALWAYS DECIMAL

AS IT SHOULD BE

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[wraith hinge]

help

[lapis oak]

It is an equation for a parabola. for h(x) the axis of symm will be the st line x=2

For f(x) it should be x=4

Plot f(x) roughly upon a graph (y-2)=-2(x-4)²

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[wraith hinge]

can someone help me solve 54? i know to take the integral of the equation but idk how to integrate it

[twilit fern]

Hi
I think you can just open (1+e^t)²
So
(1+e^2t+2e^t)/e^3t
And then integrate this

[twilit fern]

And this is just
e^-3t + e^-t + 2 e^-2t

[wraith hinge]

alright, thank you

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[viral isle]

help from anyone?

[digital bolt]

find d and e such that e(Aj) + f(Ai) = (3, 1)

then A^-1 (3, 1) = A^-1 (e(Aj) + f(Ai)) = ej + fi

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[elfin olive]

Need help with my alek geometry but I suck at it can anyone help to explain this 🙏

[chilly goblet]

can u help me in mine its j basic geometry

j proofs

i dont understand it

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[indigo spear]

Wouldn't the solution here be the definite integral from 0->3 of r(t)?

but that isn't correct according to webwork

because integral of r(t) should give population function

[nimble stone]

,w integrate (450.268*e^(1.12567t)) from t=0 to t=3

[solid kiln]

Results provided by WolframAlpha

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

Requested by aldrnari_

[nimble stone]

you forgot the 200 initial ones

[indigo spear]

ohhhhhh

ty that worked

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[nimble stone]

np

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[silver star]

Can anyone find the recursive formula for this pattern? I know the denominator is n!, but I can't figure out a formula for the n_th term

[digital bolt]

can you find a formula for the numerators

[silver star]

thats the thing i cant figure out

[silver star]

it's supposed to be a recursive formula like the fibonacci sequence

where the nth number is made out of the previous numbers

[digital bolt]

where did you run into this?

[silver star]

it's actually a smaller problem for a bigger problem involving binary search trees and their height

[digital bolt]

go on

[silver star]

so for the nth term basically you are trying to find the average height, where the nth term is like how many nodes in the BST there are

so the denominator is the different combinations of n nodes we can have for a BST

[digital bolt]

hm

[silver star]

i literally got the sequence by drawing each tree

[digital bolt]

seems like it would get very annoying

[silver star]

it is

especially the 5th term

although i found a short cut to the amount of work needed to be done

[digital bolt]

the number of trees with 5 nodes and 3 high is dependent on the number of trees with 4 nodes and 2 high but also the number of trees with 4 nodes and 3 high but with a 2 high branch

and so on

so it feels very messy

sometimes things like these just don't have nice formulas

it's a bugger

[silver star]

there must be one

[digital bolt]

why

[silver star]

cause there must be a solution to this problem

[digital bolt]

why

[silver star]

else they won't give the problem

if there's no solution

[digital bolt]

who gave the problem

[silver star]

prof

[digital bolt]

professor is evil

[silver star]

agreed

[digital bolt]

oh

we can try the oeis lol

i always forget the oeis

[silver star]

what's that

[digital bolt]

https://oeis.org/search?q=1%2C4%2C16%2C80%2C456&language=english&go=Search

here we go

[silver star]

o

[digital bolt]

yeah no nice formula there

so if you find one you should put it on there ok

[silver star]

wait a second

ayo?

ayo??

formula not nice

but

thanks buddy

.close

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[neon kraken]

can someone explain this theorem intuively

[neon kraken]

I have seen tthe proof for th case where n = 2 where u integrate multiplite times I understand the steps but I don't understand it intuively

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[jaunty silo]

!15min

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[jaunty silo]

looks like linear regression problem

Is this from any lecture?

Is there a specific topic you're studying with this?

Do you know least square method?

or making linear regression model

Do you know any method to make linear regression model?

Like step by step on creating approximation in linear regression

[jaunty silo]

Sorry for being late

you should close this yourself

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[wet tapir]

i need help with this ☹️

[left oriole]

!status

[trim jolt]

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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

[wet tapir]

I dont know where to begin

1

[wraith hinge]

why dont u put 1k on the other side

[wet tapir]

oh ok

ty

[red widget]

Is this for factoring?

[wet tapir]

yea its for factoring

[red widget]

Or just solving

Then don't put it on the other side if its for factoring

[wet tapir]

ok

what do i do?

[red widget]

Well, do you know what a perfect cube is?

[wet tapir]

no

[red widget]

It's a number with an integer cube root basically

So 8 for example is a perfect cube, its 2^3

[wet tapir]

oh ok

[red widget]

Do you know what the cube root of 1000 is?

[wet tapir]

10

[red widget]

Yes so write it as 10^3

[wet tapir]

kk

[red widget]

So now you have

[wet tapir]

so is it like x^3-10^3?

[red widget]

$x^{3} - 10^{3}$

[solid kiln]

quevivamexico

[red widget]

Here you can use the difference of cubes

$(a-b)(a^{2} + ab + b{2})$

[solid kiln]

quevivamexico

[red widget]

Which is all equal to

$a^3 - b^3$

[solid kiln]

quevivamexico

[wraith hinge]

we onto something foreal foreal

[red widget]

So now that you have it written like a^3 - b^3 it should be simple to see what a and b are

And use them in the difference of cubes

[wet tapir]

ohh ok

[red widget]

Yeah ping me if you get lost

[wet tapir]

kk ty 😭

[red widget]

Someone else had a question like this, it took me a second to realize it was a cube and not squared haha

[wet tapir]

lol

[wet tapir]

@red widget im confused on this part

like what am i supposed to do 😭

[red widget]

That is all equal to a^3 - b^3

Can you see what a and b are when you have x^3 - 10^3?

[wet tapir]

so a is 1 and b is 10?

[red widget]

A is x

[wet tapir]

ohh

[red widget]

Yes so you can use those in the difference of cubes thing I showed

[wet tapir]

so is it it like (x-10)(x^2+10x+20)?

[red widget]

10^2 is not 20

but otherwise yes

oh shoot i put b2 instead of b^2 @wet tapir

[wet tapir]

oh 😭

[red widget]

$(a-b)(a^{2} + ab + b^{2})$

[solid kiln]

quevivamexico

[red widget]

There

[wet tapir]

ty

I multiplied them together and got x^3+10x+100x-10x^2+100x-1000 is that right?

[red widget]

dont multiply

that will get you x^3 - 1000

[wet tapir]

oh ok

[red widget]

thats the factored form

you cant be any more factored than that

[wet tapir]

oh 😭

im confused because in my textbook is says that the equation is like (a^2+ab+b^2)=(a-b)^2

@red widget

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[manic flame]

need help with this physics word problem

[subtle prairie]

What’s is acceleration?

[left gazelle]

For accn just differentiate the velocity eqn

[manic flame]

velocity/time

[left gazelle]

Do you know differentiation?

[manic flame]

yes i do

[left gazelle]

Yeah then dv/dx

[manic flame]

ah so i just differentiate v(t)=9t^2-4t+6

[left gazelle]

For position eqn
You'll need to integrate the velocity eqn

[left gazelle]

Yeah for accn👍

[manic flame]

ahh

thank you

[left gazelle]

No prob👍

[manic flame]

.end

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[flat meadow]

I need help to kjnow if im right

[tribal jetty]

ok

[flat meadow]

Idk if im doing the third one right or not and

ye I just want to check my answers or like the process

[tribal jetty]

can you show why you reached c) is the integral of x^2 - sqrt(x) ?

[flat meadow]

idk

I did it in my head

x=y^2 y=root x and x^2 is more than sqrt x

so like the integral would technically be that

[tribal jetty]

not when x is between 0 and 1

[flat meadow]

ah f

im actually done bro

[tribal jetty]

for example, 0.1 = (1/10), and 0.1^2 = (1/10)^2 = 1/100 = 0.01

[flat meadow]

ye no

I am kinda slow

forget that uh help with d

ya think im going the right direction ?

[tribal jetty]

here's some help with c

ok wait

[flat meadow]

thx man

I got c tho I was just uh

I didnt graph it

so I screwed up

uk what its fine

ill do it somehow

[tribal jetty]

can i see what you have in d)

[flat meadow]

Thats all i did

Idk if im doing it the hard way or what but

so do I just take the limits from 0,1 ?

idk

[tribal jetty]

its easier to find the area by taking horizontal segments rather than vertical segments

[flat meadow]

huh wait what

howd u graph it below the x axis

isnt there only one interseciton

?

[tribal jetty]

two intersections

look that both curves intersect two times

[flat meadow]

thats what I got when I put them on desmos

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[trail tusk]

@flat meadow x=y^2 is not the same as y=sqrt(x), it's the same as y= +-sqrt(x)

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[nimble rain]

can someone help me with how to start resolving this ?

[nimble rain]

the last part is the answer

[south latch]

this is just matrix multiplication

idunno what the zt part at the end is

is that meaningful in another language than English?

you have a 3x4 matrix multiplied by a 4x1 matrix, which produces a 3x1 matrix (has the outer dimensions of the matrices involved)

matrix multiplication is:
each row element in the first matrix multiplied by each corresponding column element in the second matrix.
and those products get added together and placed in the result matrix.

[nimble rain]

Its zł which is currency

[south latch]

ok

[nimble rain]

i know how for example multiplication of 3x3 x 3x3 is

but idk how to solve 1x4 or of different shapes ig

[south latch]

ok so

first matrix has rows {1,2,3}, second matrix has only the column {1}

to do the multiplication, you go across row i and down column j.

that puts the result of multiplying row i of the first matrix with column j of the second matrix in (i,j) of the new matrix

hopefully, you can make sense of the elements of the new matrix having coordinates (1,1), (2,1), 3,1), respectively

(a matrix with 3 rows and 1 column)

[nimble rain]

so it's like number of columns from the first one x number of rows in the 2nd ?

[south latch]

that's backwards

the dimensions of the new matrix is the outer dimensions of the input matrices

you are doing dimensions [3,4]x[4,1] -> [3,1]

3 rows, 1 column

[nimble rain]

okay

that i understand

so now knowing that how do i multiply them?

every row in mat1 times the one in mat2 column ?

[south latch]

yeah

each element of the row with each CORRESPONDING element of the column

[nimble rain]

so 150 * 150 * 140 * 130 * 40?

no

(150+160+165) * 40?

[south latch]

no

[nimble rain]

im having a hard time here and this is basic stuff 😭

[south latch]

150x40 + 150x20 + 130x100 + 140x50

[nimble rain]

ohhhhh

[south latch]

that's row 1 with column 1 -> (1,1)

[nimble rain]

that makes a lot of sense now

so now multiplying them we get

29000

[south latch]

ok

[nimble rain]

now i know

thank you so much

[south latch]

no problem

[nimble rain]

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[crimson rover]

if i know p(x)
p(y|x)

can i find p(x|y) ?

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@crimson rover Has your question been resolved?

[oblique valley]

@crimson rover Look for Bayes formula
You also need p(y)

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[worthy eagle]

If $\lim _{x \rightarrow-1} \frac{x^3-a x^2-x+4}{x+1}$ exists, find a

[solid kiln]

アキラ (>_<)

[worthy eagle]

!status

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2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
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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

[worthy eagle]

1

[left oriole]

hint: notice that the denominator goes to 0 as x-> -1
so if the fraction is going to have a limit, the numerator also needs to go to 0 as x -> -1

[worthy eagle]

so does this mean I plug -1 into the equation then solve for a?

[left oriole]

yea plug in x = -1, set equal to 0, solve for a

[worthy eagle]

alright got it, thank you

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[shrewd flame]

hello there, I was just wondering. Is there a difference between $f_x$ and $\frac{\partial f}{\partial x}$?

[solid kiln]

Crown

[stoic iron]

nope two notations for the same thing

[shrewd flame]

cool

had another quick question

[shrewd flame]

$f(x,y) = (x^{2} + y^{2})e^{-x}$

[solid kiln]

Crown

[shrewd flame]

if i were to take the partial derivative with respect to y

it'd just be 2ye^{-x} right?

[stoic iron]

yeah

[shrewd flame]

cool, thanks

for some reason through the use of calculator it was doing something different

it be like that sometimes

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[opal epoch]

So this is what I am studying

[opal epoch]

And this is my prof's answer

Why is it 6(hobo)/2 instead of (6hobo)/2?

[eternal adder]

they're the same thing

[opal epoch]

So no cancel out?

Just 6?

Not 3?

[eternal adder]

you could write it as 3h_0*b_0

but the point of writing (h_0*b_0/2) separately is that that's the formula for area

[opal epoch]

Oh I see

So next time if I solve it I just take x out of the (hobo)/2?

[eternal adder]

sure

[opal epoch]

Alrighty

Thanks

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[worthy eagle]

!1c

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[worthy eagle]

your channel is #help-3

[fading spruce]

yo

I need help

For a question

Here's the question

Name each polynomial by its degree and number of terms

3gn⁷ - 8d⁶ - 7y⁴s³ - 6z⁷k³ + 9d⁵y4

[worthy eagle]

!occupied

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[drifting goblet]

yo

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@drifting goblet Has your question been resolved?

[fair bison]

You already have a channel, so I'm closing this one

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[surreal eagle]

okay so somethings not clicking but I dont get what qualifies as a subspace?

by definition its this in my textbook

[terse nymph]

A subspace should satisfy those two and also that it contains zero vector

[nova spire]

subspaces are subsets of a vector space that are :

• non empty
• stable by addition
• stable by scalar multiplication
  in particular, 0 has to be in it, which can be a replacement for first condition

[surreal eagle]

so for 26.1 its not a subspace because of what exactly?

why is it not in W

[terse nymph]

What is W defined as

[surreal eagle]

it seems to be a simple concept but im missing something to make it clear

[nova spire]

it actually verifies none of : "stable by addition", "stable by scalar mult." "0 is in it"

and since those are the 3 necessary conditions for a subspace

choose your poison

[surreal eagle]

okay but what do you mean? for stable by addition, it adds up just like any of the previous examples no? im clearly misunderstanding the concept but to me theres nothing that differentiates it from the other question. how does its addition break it

[nova spire]

the sum of two vectors of W doesn't stay in W

because the third coefficient should always be the sum of the first two + 1

and when you add two vectors of W, the third coefficient is the sum of the first two + 2

which clearly doesn't "add up" in all meanings

[whole coral]

(more accurately, a subspace is [usually] defined such that you're a vector space under the same operations as the larger vector space, with this following as a necessary and sufficient condition [hence it being a theorem])

[surreal eagle]

so it being a plus 2 rather than a plus 1 is what breaks it? sorry, im just not quite seeing it the same way you are

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@surreal eagle Has your question been resolved?

[nova spire]

it is

because by definition, if the sum vector is written as [A, B, A+B+2]

it cannot be written as [A,B,A+B+1]

and so it, by definition, is not in W

[surreal eagle]

okay, i think i get it. and the same for the multiplication by a scalar part too right? for c not equal to 1

[nova spire]

yes

if c not equal to 1

then the scalar multiplication is written as [A,B, A+B+c]

since c is not 1, it doesn't match our definition for a vector in W

[surreal eagle]

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[wind gust]

i need help with number ten im stuck after taking one derivative

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[wind gust]

<@&286206848099549185>

[zinc ginkgo]

,tex .FTC2

[solid kiln]

riemann

[wind gust]

our lesson was on lhopitals rule idk if were supposed to use that

[zinc ginkgo]

Yes. Use l'hopital and fundamental theorem of calculus

[zinc ginkgo]

This is one version of FTC

[wind gust]

alr got it

tysm

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[blazing geode]

As the diagram illustrates, A and B are the centers of circles. Given the bigger circle intersects with the smaller at point B; and their radius are 2 and 1 respectively.

points C,D are line AB's intersection with these two circles.

If E is one of the intersection between these two circles then:

(1):CE=15

[bleak hedge]

we know that CEB is a right triangle since CB is the diameter of the circle A

using the pythagorean theorem and knowing that CB =4 and EB =1 (radius of B) we find that CE = sqrt 17

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[blazing geode]

shit, I forgot such important property of a circle

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[drifting rose]

can someone help me understand what I have to do here, I am currently revising and I don't know where to start

[drifting rose]

I also kind of forgot how to do all of this so a bit of detail per step would be nice, also 1a should just be enough

[kindred pier]

for 1a, you first want to draw the line y=0. Then, you want to think which side of the line has all the points where y is greater than 0. You can lightly shade that side, or just make a mental note

[drifting rose]

ok first, why y=0

[kindred pier]

Then, you want draw the line y=2x, and think of all the points (x, y) such that y is greater than 2x. Lightly shade that region. Finaklly, the answer is the doubly-shaded region along with the two lines you drew that form the region

[drifting rose]

I see

but where did you get y=0 and y=2x

I see that they are in the inequality however what understanding is it so that you can confidently say it is y =

[kindred pier]

Because $0\le y\le 2x$ means you must satisfy both $0\le y$ and $y\le 2x$. And $0\le y$ means that either $0=y$ or $y<0$.

[solid kiln]

SWR

[drifting rose]

ohhh

I understand

just another quick question

what requirements are needed which allows the inequality line to flip?

when its divided by something right?

[kindred pier]

when it's multiplied or divided by a negative number

[drifting rose]

hmm

if you are ok mind answering another one? solve x(x-1) > 0

I checked the answer and somehow x < 0 which is just wild imo

[kindred pier]

Yeah that is kinda unintuitive.

[drifting rose]

its x > 0 and x > 1 right

[kindred pier]

How I solve quadratic inequalities is solving x(x-1)=0. The solutions are x=0 and x=1. The inequality solution is then either

• x<0 and x>1, or...
• x>0 or x<1
  So I just test some value, like x=2. 2(2-1) is indeed greater than zero. So I deduce that the solution is x<0 and x>1.

I forget the precise way to solve it, this was always my approach

[drifting rose]

hmmm

alright, thanks

I got it now, thank you so much for the help

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[uncut saffron]

What does it mean to graph both lines on the same set of axis?

[knotty locust]

Weirdly worded

Just graph both the lines

on one of those graphs

and label them

I guess

I don't know why it would give you two graphs and then tell you to only use one of them though

[uncut saffron]

Oh okay lmao yeah i was confused with how they worded it and i thought they meant do both lines on both graphs which wouldnt really make sense either

anyway thank you tho!

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[last fossil]

im sure of D and F

i think C is wrong since either A or B would have to be the identity matrix

[nimble stone]

are you sure about D?

doubly sure?

[last fossil]

D is wrong just checked my textbook

so im ok with F

i think A works to

since all that were doing is adding 1 to the diagonal

[nimble stone]

dont think A works
(4 5)
(2 1) det is 4-10=-6
if you add I it becomes 0

simple counter

what about B

[last fossil]

ahh right

[nimble stone]

also do you understand why D is wrong?

[last fossil]

B i think you can use expand

[last fossil]

yeah, A and B swap positions but in the anser they dont

[nimble stone]

indeed

[last fossil]

E is wrong

i think its B and F

[nimble stone]

it is

[last fossil]

ah yup got it

thank you!

[nimble stone]

nw

[last fossil]

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[hallow osprey]

I got the answer A, but the answer sheet of this problem says E. Is there a specific formulas for swapping two variables, in this case x with y, to achieve E? Chatgpt and other models are all saying A.

[nimble stone]

chat gpt ew

ill check for you though

y(a-bx)=ax-b
ya-bxy=ax-b
ya+b=ax+bxy
ya+b=x(a+by)
(ay+b)/(a+by)=x

seems youre correct

[hallow osprey]

right? somehow the editor decided it was E and I'm confused

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[shrewd dagger]

how do i do 21 and 24 step by step😢

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[summer yarrow]

I can do a but cannot do b

this is binomial expansion btw

[quaint tusk]

r!(12-r)! = 12!/220
r!(12-r)!= 12!/ 11 (2)(10)
r!(12-r)!= 12(11)(10)9! / 11(2)10= 9!6 = 9!3! Since 6=3!
r!(12-r)!=9!3! So r =3 or 9

[summer yarrow]

ok tysm

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[frosty vapor]

Anyone know how to do this

[mellow tendon]

First find the f(g(x)) and g(f(x))

[frosty vapor]

Then?

[mellow tendon]

Then define the values of k that makes both defined
Just find them first and the rest will be easy

[wet dragon]

no matter what k is g(f(x)) is always defined

so just worry about f(g(x))

[frosty vapor]

What next

[mellow tendon]

Take g(f(x)) also

[mellow tendon]

,rotate

[wet dragon]

.rotate cw

shit

[wet dragon]

.rotate ccw

[frosty vapor]

I js found f(g(x))

[mellow tendon]

Ok write g(f(x)) under it

[wet dragon]

wait k is a positive real number ye

[frosty vapor]

Yes

[wet dragon]

f(g(x)) is always defined then

[frosty vapor]

So whats fhr answer

[mellow tendon]

Still you need to find g(f(x))

[wet dragon]

ye

[mellow tendon]

we now know that f(g(x)) is always defined for k in R+
We need to check g(f(x))

[mellow tendon]

,rotate ccw

[wet dragon]

-2sqrt(x)

[wet dragon]

brother

[frosty vapor]

Wait shit

[wet dragon]

.rotate cw

[frosty vapor]

Dleete

[mellow tendon]

Its ,

[frosty vapor]

Let me redo

[mellow tendon]

,rotate cw

[wet dragon]

yee ad that -2sqrt(x)

[mellow tendon]

No not quite correct

[frosty vapor]

Oops

[wet dragon]

idk looks defined to me for all k as long as x isnt negative

[frosty vapor]

Answer is [1,3]

[mellow tendon]

$$g(f(x)) = (-\sqrt{x}+ 1})^2+k = x - 2\sqrt{x} + 1 +k$$

[wet dragon]

weird

[frosty vapor]

Yeh

[solid kiln]

Sherif Player
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[frosty vapor]

?

[wet dragon]

is there anything in the question you forgot to add

[mellow tendon]

There is a point here

[frosty vapor]

No

[mellow tendon]

The function is defined when only 1 input gives us 1 output

[frosty vapor]

Whole q

[mellow tendon]

Ok I just checked it in desmos and both functions are defined for every value of positive k

[frosty vapor]

So k > 0?

[wet dragon]

ya

[frosty vapor]

Uhm thx 😅😅

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[rocky hull]

can someone explain this

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[sly mist]

can someone help me process the information and draw a picture of it

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@sly mist Has your question been resolved?

[sly mist]

ok i figured out a and b and part C

[kindred rapids]

15 degrees to what? the current?

[sly mist]

I think it’s just 15 degrees as an angle

I’m not sure

sry

I solved for x and y

[kindred rapids]

anyway, if it's to the current

as u had figured out c

[sly mist]

<28.9, 7.76> is my component or whatever and then for part b I just minus 7 so <28.9, 0.76>

yea

no

[kindred rapids]

use this time to times this "28.9"

[sly mist]

for part C?

[kindred rapids]

wait

why 7.76 was subtracted?

[sly mist]

Because the current is heading down stream of 7 FPS

[kindred rapids]

right or wrong?

[sly mist]

I don’t think the current would be going west

[kindred rapids]

what west

[sly mist]

it would be going south

[kindred rapids]

...

😅

[kindred rapids]

i asked u AT FIRST to verify WHAT 15 DEGREES TO

why u dont shou this that time

[sly mist]

I did

lol

[sly mist]

T

[kindred rapids]

where is the river

WHERE IS THE RIVER?

[sly mist]

In the question lol

[sly mist]

T

[kindred rapids]

....

anyway

[sly mist]

I mean it kind of says it

obliviously

[kindred rapids]

times this "0.76"

[sly mist]

ok

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[wraith hinge]

#help-48 message @kindred rapids

[wraith hinge]

sorry i was outside

i can continue our talk

anyways i think the point of mu_s is to verify that the box will even slide down to begin with

which i managed to calculate to be true

[kindred rapids]

slide what?

[wraith hinge]

Like, the box could possibly not even slide down the incline to hit the spring because the parallel-to-incline weight force is not stronger than the maximum static friction

so i suppose the point of that mu_s is to convince yourself that the box will be able to slide down the incline to hit the spring

[kindred rapids]

are u sure?

mu_s < tanθ

[wraith hinge]

i mean yeah if the angle was much lesser i'd suppose its not possible then

[kindred rapids]

it should slide down if there is no any other forces

ah i see

yes that make sense

[wraith hinge]

yeah so ig they just added that for you to self-verify

anyhow

I see what you mean now

let me recalculate and see if that gives the right answer of 1.04 m

Also, actually, i think i messed up recovering the correct work for the weight

uh

[kindred rapids]

uh?

[wraith hinge]

i will make x = 0 be where the spring is initially uncompressed so i can directly use the elastic potential energy

[kindred rapids]

wait, except english, what language u can use?

[wraith hinge]

Turkish and Arabic i suppose lol

but its okay english is fine

[kindred rapids]

ah alright

i though u can speak chinese tho because

[wraith hinge]

yeah sorry for the name its like

a gig the server is having