help-0

[remote heron]

but a-a is equal to 0 for all a

so its actually never reflexive~

in your problem

$a \sim a \to 2 \mid (a+a)$

[ocean seal]

jan Niku

[remote heron]

do you think this is generally going to be true for a positive number?

[raw shard]

not to interrupt but is this supposed to look confusing without context lol

[remote heron]

or if not why not

can you split it into cases? do we know that a has to fall into certain categories?

[magic pine]

im stomped here

can I take a breather

im trying to absorb as much information as possible

[remote heron]

sure

just ping me, ill be around

[magic pine]

ok thanks

[meager barn]

how could you type that so easily and fast??

[remote heron]

i type a lot of math

[meager barn]

so its just a practice

[remote heron]

lol

[magic pine]

are you a professor

[remote heron]

nah undergrad

i should be doing homework

[magic pine]

woa

[remote heron]

but its hard

so i dont want to

[wary stream]

Same

[magic pine]

oh

I actually have a quiz 8 hours from now

[meager barn]

same

[alpine sable]

hi

[remote heron]

today is my work day

[magic pine]

about this

[remote heron]

about relations?

[meager barn]

doing it all day and night

[remote heron]

we should finish that example 😄

go get some water or take a walk or something

[wary stream]

Everyday is my work day, because engineering

[remote heron]

yea

im at an engineering uni

there is no off day

[wary stream]

I'm EE so my stuff is imaginary

[remote heron]

lol

[meager barn]

ohh, what engr are you doing?

[remote heron]

come join EE free shock therapy for stress

im CS/math

[alpine sable]

Im EE/CE

[remote heron]

nice

[meager barn]

I m also planning to do CS or SE

[remote heron]

good money

[alpine sable]

I finished though and now work

[remote heron]

but you wont get to take any cool math classes

[meager barn]

yeah, but its my passion rather

[magic pine]

this framework, can check for reflexive and symmetric?

i am cs too

[remote heron]

thats the definition of the relation, so its the tool youll use to check everything

ah, discrete math then? :p

[magic pine]

discrete structures

[remote heron]

checking for reflexive is checking if $a-a>0$

[ocean seal]

jan Niku

[magic pine]

I don't know why but i think structures and math here is used interchangeably

[remote heron]

check symmetric is if $a-b>0$ implies that $b-a>0$

[ocean seal]

jan Niku

[remote heron]

transitive similarly

youll use the definition of the relation heavily

i was gonna say Ric a lemme if you wanted to finish that problem you may wanna try to show

or take without proof

2*k where k is an integer is always even

[magic pine]

Can we finish the problem? But I don't think I'll have an answer

[remote heron]

yea

[magic pine]

Can I use that as a reference?

[remote heron]

the lemma?

yea

just for sake of focusing on the relation and not the number theory

or whatever you call it

so youre trying to show that its reflexive

so you wanna show that $2 \mid (a+a)$

[ocean seal]

jan Niku

[remote heron]

what do you say using that lemma

[magic pine]

this is my first time hearing lemma

[remote heron]

,w lemma

[ocean seal]

Results provided by WolframAlpha

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

Requested by jan Niku#2119

[remote heron]

i more just worry i dont want you to get stuck and hit a wall 😄

[magic pine]

so it's like a mathematical equation with pre-defined terms?

[remote heron]

which?

the relation?

[magic pine]

this?

[magic pine]

the lemma

[wary stream]

So unrelated but I like hitting walls in anger

[remote heron]

the lemme is just a helpful result

which hopefully its clear why its helpful and related here?

we want to show that a is related to a for all positive integers

in other words that a plus a is always even

the lemma tells us that "two times any integer is even."

you could maybe rewrite that as "any integer plus itself is even."

[magic pine]

oh

so the 2 there

is called even

?

[remote heron]

yea

have you guys seen divides before?

[magic pine]

i see!

[remote heron]

this is a silly relation to do if you havent

like a|b implies that b=ak

[magic pine]

what is k

[remote heron]

be better to work with something involving symbols youve seen before

some integer

like 3|9 read "3 divides 9" because 9=3*3

[magic pine]

so b is equals to a times an integer?

[remote heron]

yea

or a|b implies that a is a factor of b

so were saying "two numbers are related if 2 is a factor of their sum"

well if 2 is a factor of any number, we call that number even

but fr if you havent seen this before we can do a different one

i was just trying to come up w something different than the examples

[magic pine]

My head is like rewiring all those simple algebra

[remote heron]

lol lets do a different one

you should do a skeletal one theres no need to learn 2 things at once

are you okay with that?

[magic pine]

yes

[remote heron]

okay

[magic pine]

the most basic of basic

[remote heron]

yea

[magic pine]

uhm

can I give you

my work

regarding this

Can you check my work i mean

regarding

equivalence relation

[remote heron]

ye

[magic pine]

S = R where a = b if and only if |a| = |b|

I want to confirm if my answers are correct

and how would you solve it using this

[remote heron]

yours is different

[magic pine]

how so

[remote heron]

$a \sim b \to |a|=|b|$

[ocean seal]

jan Niku

[remote heron]

different relation

[magic pine]

what does that mean

[remote heron]

its a different relation

this is just a rewrite of >

if you add b to both sides

"a is related to b iff a is greater than b"

nothing to do with absolute value

well at least not directly

[magic pine]

so I cannot solve this

[magic pine]

using this?

[remote heron]

no, theyre different relations

[magic pine]

I see

[remote heron]

you could check them separately though

[magic pine]

that's why I was getting confused in the first place

[remote heron]

oh

😅

[magic pine]

xd

[remote heron]

well what do you wanna do

another example?

or try one of those?

[sonic lichen]

Would be super appreciated

[remote heron]

we could try one without weird symbols

and a smaller set

no infinite sets

so you can check directly if you want to

or need to

[magic pine]

Well, how would you prove if this is equivalance relation

oh wait,

scratch that

oh wait i thought there was a typo

yep

S = R where a = b if and only if |a| = |b|

[remote heron]

once you get a couple examples under your belt youll be able to do it 😄

lets try this

[magic pine]

ok sir

btw, after this i need* to learn partial orders and lattices tonight lol

[remote heron]

a relation $\sim$ on $S = {4,5,6}$ is defined by $a \sim b$ if $a\cdot b>0$.

[ocean seal]

jan Niku

[magic pine]

this is gonna be a long night for me xd

[remote heron]

just looking at this, what are your thoughts

like before trying anything

[magic pine]

can I translate it

[remote heron]

that dot is just normal ol multiplication btw

[magic pine]

into words

[remote heron]

ye

[magic pine]

ok

uhm

[magic pine]

A relation on set S is equals to 4,5,6 and is defined by a equivalent to b if a times b is greater than 0

is this correct

[remote heron]

yea

[magic pine]

so

I must prove that this is an equivalence relation

[remote heron]

yea

but just first like

can you think of any element in this set thats not gonna be related to any other?

what do you notice about the numbers?

how do you get a negative number out of multiplication

[magic pine]

you multiply it by another negative

[remote heron]

another?

idk its not important we can just try it

[magic pine]

to become positive

[remote heron]

do you think its reflexive?

is a*a>0 for all a in S?

[magic pine]

yes that is true

[remote heron]

whys that?

[magic pine]

because all the elements in S are positive

and a*a > 0

[remote heron]

would it be true if our set was all the real numbers

[magic pine]

no

real numbers include negative right

[remote heron]

yea

[magic pine]

omg

[remote heron]

but whats a negative times a negative?

[magic pine]

oh!

[remote heron]

but theres still a pathological number :p

[magic pine]

i got played by my own statement

[remote heron]

a negative times a negative is positive right

a positive times a positive is a positive

but what number times itself isnt positive

[magic pine]

yes

[remote heron]

?

[bleak ridge]

👁️

[magic pine]

none

[remote heron]

👀

its not important, just to get you thinking i was asking lol

0 breaks it

but thats not important here

were only looking at 4 5 6

[magic pine]

i see

[remote heron]

alright

try out symmetry

[magic pine]

it's very informative

[remote heron]

if $a\cdot b >0$ does that imply that $b\cdot a>0$?

[ocean seal]

jan Niku

[magic pine]

so, if Real numbers are the given set

it would be false because of the pathological numbers

?

[remote heron]

yea

but specifically because our relation is using >

not >=

[magic pine]

Noted

[remote heron]

okay, is it symmetric?

[magic pine]

yes

Aha

My weakness here is that I am having a hard time proving my statement

[bleak ridge]

In another channel probably

[remote heron]

make a generalization about the numbers in s

and our operation

[magic pine]

But If I were to prove it, I would substitute a = 4 and b = 5 then 4*5 > 0

[remote heron]

is ab=ba for all s?

[magic pine]

and ba = 5(4) = 20

20 > 0

therefore

true

[remote heron]

you need to make a general statement

[magic pine]

uhm

[remote heron]

|or a small set checking them all is okay

[magic pine]

I think I dont know how to

let me try

[remote heron]

sure you do

whats a very general statement you can make about s in S

all nonzero positives right

[magic pine]

ab=ba > 0 because if you substitute elements of S, it will not be equal to 0 or a negative integer

[remote heron]

well even thats not important

yea exactly

[magic pine]

if I were to give this in an exam paper, would this be considered correct?

[remote heron]

sorry i was walkin around

[magic pine]

no worries

[remote heron]

yea id say like

As multiplication is commutative, we have that ab=ba for all integers b and a. Then $ab>0$ implies by equality that $ba>0$.

[ocean seal]

jan Niku

[remote heron]

okay, how about transitive?

[magic pine]

woa, I forgot the properties of multiplication

[magic pine]

for transitive,

a=b, b=c => a=c right

if I can prove a=b and b=c automatically, a=c

[tardy plank]

can why there is an u in the denominator the first part on the second step ?

[remote heron]

its easier here because of the set were dealing with

so you can shortcut it if you want

but i would say like

we have no negative or 0 numbers in our set right

[magic pine]

yes

[remote heron]

well

lemme think

i mean you can just say that ab>0 implies that a and b are positive (even though we already know that)

same thing with bc>0

than ac>0

not a super illuminating example

but thats more or less the flow of one of these problems

you can extend it

try now Let $\sim$ be defined over $\bR \less 0 = {\pm 1, \pm 2, \dots}$ by $a \sim b$ if $\left| \frac{a}{b} \right| > 0$.

if you want 😄

[magic pine]

yes sirrr

[ocean seal]

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

[remote heron]

or you can probably think if your own examples now

[magic pine]

I don't want to waste a learning opportunity

[remote heron]

maybe youd like to try out $\geq$

[ocean seal]

jan Niku

[remote heron]

or so

there are a lot of these kind of things

maybe even like $\sim$ on $\bN$ by $a \sim b$ if $\sfrac{a}{b} \geq 1$ fails for which conditions?

[ocean seal]

jan Niku

[magic pine]

natural numbers are positive integers right?

[magic pine]

Reflexive: a/a >= 1 -> Yes, as all natural numbers divided by itself is 1.
Symmetric: a/b >= 1 -> No, 4/2 >= 0 is true but 2/4 >= is false. (I gave a counter - example)
Transitive: a/b >= 1, b/a >= 1 therefore a/c >= 1. Therefore, it is transitive

[remote heron]

yea

solve?

[green glacier]

Wait

I was gonna help but the message was dleeted

[magic pine]

This is right, right? xd

[green glacier]

Oh ok

But what is the question

[alpine sable]

Mom bakes cupcakes for a student party. In the morning he baked two-thirds and in the evening one-fifth of the total number of cupcakes. On the morning of the holiday, Mom baked another 16 cakes. How many cupcakes did the mother bake for the party in total?

[glass lichen]

You can use whatever symbol you want... frequency is typically f of nu though

[remote heron]

im not sure about transitive

[magic pine]

oh

[remote heron]

you want to show that like

if a/b>1 and b/c>1 then a/c>1

well equals there too

you know what i mean

[magic pine]

I see

thanks for correcting me

thanks for the help @remote heron

[remote heron]

you still have to show it :p

[magic pine]

oh!

[remote heron]

but its not bad

thats just the definition of transitivity

[magic pine]

isn't this the right answer?

[remote heron]

its just the definition

you need to apply some kind of logic

i mean its not bad you just say like

a/b is some number thats at least one

b/c is some number thats at least one

a/c is ab/bc

which is uhh

yea

[magic pine]

I see

[remote heron]

\begin{align*} \frac{a}{c} &= \frac{a\cdot b }{c \cdot b} \ &= \frac{a \cdot b}{b \cdot c} \ &= \frac{a}{b} \cdot \frac{b}{c} \end{align*}

[ocean seal]

jan Niku

[magic pine]

That's where I'm having hard time, proving the statements

[remote heron]

some number thats at least one

times number thats at least one

what can we say about that :p

[magic pine]

woa you're fast at coding

[magic pine]

it is transitive

[alpine sable]

?

yu there?

[remote heron]

it is

[magic pine]

so, that's about it

[remote heron]

but is it a equivalence relation?

[magic pine]

no they are not

[remote heron]

yea 😄

[magic pine]

the three properties must be met in order for it to be

xd

[remote heron]

there ya go

all these proofs flow more or less the same

the weird parts are gonna be the bits that are specific to certain relations

like divides or division here as creating those two fractions from one

but if you start from what you want and work backwards you can generally get there

good to practice a lot a lot with these

especially before equivalence classes if youre gonna see those

but i know you got other stuff to study too

[magic pine]

Where do you get sample exercises?

[remote heron]

hmm

if you have a book, that works

you may wanna define your own

or like

https://scholarworks.gvsu.edu/cgi/viewcontent.cgi?filename=8&article=1009&context=books&type=additional

heres this chapter of the book i used

[magic pine]

Unfortunately, we don't use books

[remote heron]

id say define your own and check them

$a \sim b$ on the $S = { x \in \bR : x < -2}$ if there exists some natural number $c$ such that $(a+b)*c = 3$

[ocean seal]

jan Niku

[remote heron]

or other weird structures

[magic pine]

Woa, is there any chance you have the main book pdf? I'm looking for resources about the topics, partial orders, posets and lattices

[remote heron]

yea

well it may not have that stuff

https://www.tedsundstrom.com/mathematical-reasoning-writing-and-proof

this is an intro proofs book

for math students, not discrete

[magic pine]

I see

dang

I've got a long way to go

[remote heron]

exciting 😄

[magic pine]

hey man, thanks for the help!

It means a lot to me

[remote heron]

good luck on your exam

[marble spruce]

Hello

I'm stupid and need some help 😄

[magic pine]

thanks again

[marble spruce]

If you roll 10d20, what are the odds in percentage that you'll get 2 or more 20s?

[green glacier]

Yes

[green glacier]

"Mom bakes cupcakes"
"In the morning he bakes"

[alpine sable]

I auto translated it

lol

My country doesn't have gender pronouns so it's odd.

[tawny fable]

Hi, I have a question:
I have to prove on the negative way, that for every pair of positive integers x,y - x^2 - y^2 != -1
Any help with that?

[green glacier]

Did they help you with the question

[gusty oyster]

Wait really where are you from if you dont mind answering?

[tawny fable]

anyone?

[thorn kindle]

Ok

So for positive integers x,y

-(x^2+y^2) != -1

[scarlet quest]

can someone help me with diff. eq? 🙂

[gusty oyster]

What's ur qs

[scarlet quest]

My brain is completely done: A car manufacturer has measured the acceleration of a particular car model. The acceleration ability a (t) = v´ (t) is different for different speeds: v (t). You experience this as a motorist, if you press the accelerator at low speed, it accelerates sharply, while there is not the same opportunity to increase the speed if you already drive fast.

Show that by approximation it holds that v´ = α · v + β, ie that there is a linear relationship.
Enter the constants α and β.

[tawny fable]

@thorn kindle are you there?

[gusty oyster]

Havent studied these models yet, sorry

[scarlet quest]

no worries 🙂

[crystal kiln]

How do i tell the difference between linear vs non linear differential equations?
So far i know the y' can't be multiplied or to any power, what else?

[woven river]

the answer

is this correct?

[crisp grove]

sum of 2 solutions is also a solution for a linear equation

[fresh quail]

$$" \answer {-\frac {9}{2} , \cos \left (16\right ) + \frac {9}{2}}"$$

[ocean seal]

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

[lethal dock]

If $a - \frac{1}{a} = 2$, then show that $(a + \frac{1}{a})² = 8$

[ocean seal]

JUGisMUG🎃

[small swift]

Hello

I am trying to solve this problem: https://gyazo.com/c2afd70ce54fae8f2b1a036851df5c06

I got my answer is 5

Is that correct?

[small swift]

<@&286206848099549185>

@wintry iris sorry i'm currently using this chat if that's cool

[next pawn]

its 1.857 i think

[green glacier]

hey

ill look at the problem

[amber iron]

hi

[green glacier]

sorry man im not familiar with linear algebra yet, i know im not supposed to say anything if i cant help but i already said i would look at the problem so yeah.

[amber iron]

im getting the wrong answer, anyone help me out setting this up in cylindrical?

any helpers?

[obtuse cove]

Help.

😭

[hybrid plume]

@obtuse cove

[low topaz]

79-41

=38

[trim canyon]

may someone please help me with this problem?

[lethal dock]

Someone?

[alpine sable]

whats 2+2x4

[warm brook]

[\left(a - \frac{1}{a}\right) = 2 \implies\left(a - \frac{1}{a}\right)^3 = 8 ]
Expand this out

[alpine sable]

what (a) equals to?

[warm brook]

Oh

[obtuse cove]

Thank you.

[ocean seal]

kirby

[warm brook]

I misread that lmfao

[obtuse cove]

Can you help me some more?

[lethal dock]

Why ³ there though?

Someone gave me this solution?

I think its good

( a + 1/a )² = a² + 2 + 1/a²
= a² - 2 + 1/a² + 4
= (a- 1/a)² + 4
= 2² + 4 = 8

This

And like they said the 4 there emerges from 0, like 0 = +4 - 4 so we can write that there instead of zero

And like a² - 2 + 1/a² + 0 makes no difference

[warm brook]

Yeah, I misread the original question, but this above would work, because 2^3 = 8, so then you'd expand it out and it should be equal to (a+1/a)^2

[amber iron]

helpers

[warm brook]

but that is probably better

[lethal dock]

I see

But I'm amazed that u can literally get any number from 0

Even a variable

[amber iron]

hi

i need some help setting this up with cylindrical, i dont know where my setup went wrong

[lethal dock]

Thats literally 16

[alpine sable]

WRONG!

you do 2x4 first

[lethal dock]

Oh crap

[amber iron]

<@&286206848099549185>

[lethal dock]

Right..........

[alpine sable]

consider transaction priority

[warm brook]

what was your setup

[amber iron]

integral from 0 to 2pi of integral from r1 to r2 of integral from 0 to 99 of (9-9r^2 - r^4 - 1) dz dr dtheta

i seriously feel like i need to redo this from the first step

answer is 31pi/6

[green glacier]

what does z=9-9 mean

[alpine sable]

can you help me i am in a number theory lcass and i have to prove comutativity in multiplacation and addition and asocciativity, with peano axioms thanks

[amber iron]

@green glacier 9-9(x^2+y^2)

[green glacier]

oh

[amber iron]

i think i even integrated the wrong region

[warm brook]

Yeah, the region is wrong, the bottom paraboloid is on the negative region, so it adds to the total volume

[amber iron]

so i'd have to split it up into 2 regions

[warm brook]

Also, consider that given
x = r cos theta
y = r sin theta
z = z
the change of variables is dV = r dz dr dtheta

idk if you did that

[amber iron]

yeah forgot bout that too

[stone hedge]

Heyy bros

[round pagoda]

Hey, why is u(tau)*u(t-tau) equal to zero for t < 0 and equal to 1 for t > 0 and 0 < tau < t?

[flat pine]

q 2 can someone solve and give explanation?

[stone hedge]

👋👋

[warm brook]

This channel is taken

[stone hedge]

Oh okay

[amber iron]

ok so how should my setup from -1 to 0 be?

[warm brook]

It should be set up in the same way as the other region

[amber iron]

integral from 0 to 2pi of integral from 0 to r^4 -1 of integral from 9-9r^2 to 0 of r(r^4-1) dz dr dtheta?

idk

i still feel like i messed up my second bounds

channel is not open

[sterile sparrow]

mb

[amber iron]

integral from 0 to 2pi of integral from 0 to 9-9r^2 of integral from 0 to 9-9r^2 of r(9-9r^2) dz dr dtheta?
for the second part

[warm brook]

I think the lower region is a region with height between z = -1 and 0, then a radius between 0 and 1, and finally a circle between 0 and 2pi
[\int_0^{2\pi} \int_0^1 \int_{-1}^0 r(r^4-1)dzdrd\theta]

[ocean seal]

kirby

[warm brook]

I don't think the bounds for the first integral are exactly correct, I'll have to verify it

r^4 - 1 = 9(1-r^2)

they intersect at r = 1

[ancient saddle]

$V=\int_0^{2\pi} \int_0^1 [9-9r^2-(r^4-1)]r, dr, d\theta$

[amber iron]

hmm

[ocean seal]

leonardogtf

[warm brook]

OH, yes this is correct, I was thinking these were functions of f(x,y,z), no triple integral should be needed

[ancient saddle]

the bounds of the integral describe the region of integration in the XY plane

then the upper vertical bound of the volume is 9-9r^2 and the lower bound is r^4-1

that's why they are subtracted

[frosty loom]

Can someone please help me with this? I don't understand how to do it.

[amber iron]

i don't get how the dr is from 0 to 1

isn't the outer bound always changing, not just 1

[warm brook]

@amber iron in the expression given by Leonardogtf, think about it like you're integrating from the top and bottom bounds, and integrating down on the top surface and integrating up on the bottom surface until the radius is 1

So it starts at 0 until they intersect

The surfaces intersect at r = 1

[rich basin]

can anyone

[amber iron]

thank you both

[rich basin]

(a)

[warm brook]

arg(z+1) = arg((x+1)+iy) = arctan(y/(x+1))
You want the arctan(y/(x+1)) = pi/3 that minimizes x^2 + y^2.. What if you set x = 0?

[verbal marsh]

Why is this true? Can't it just be like this

where x = 1/root2 is at the local minimum in the picture i drew

[alpine sable]

<@&286206848099549185>

[warm brook]

channel in use, and don't ping helpers immediately

[warm brook]

What is the f in question? You are correct in your concern

[faint valley]

How do I make 11/50 to percents

[faint valley]

cuz like it aint working

[alpine sable]

sorry

[warm brook]

The channel is in use, but write 11/50 as a decimal, then recall that a decimal is just the percent / 100

[faint valley]

oh ty but how do i write it as a decimal 😭

[verbal marsh]

yeah, or you could just say 11/50 = x/100, then algebra your way

[alpine sable]

0.22

[warm brook]

Okay, so with this equation, it's always continuous, so you don't have a concern here

[alpine sable]

@warm brook can you do me next? after this guy

[verbal marsh]

is the graph i drew not continuous?

i thought it is

[warm brook]

Uhh yes it is

Why is the there are no discontinuities highlighted then

[verbal marsh]

oh if you're asking literally, it's because i took a screenshot in the middle of the lecturer highlighting each text in a video

[warm brook]

Ahhh, okay that makes more sense

[warm brook]

Anyway, the function you are given is indeed the case that there are multiple local maxima

So that can happen

[verbal marsh]

yeah, the lecturer draws it out in the end, but is the statement "it is obvious that x is a local maximum" from these conditions kinda weird?

[verbal marsh]

these conditions

[warm brook]

Yes I see, the reason why is because there is a derivative of 0 at x = 1/sqrt(2)

so because f(0)=0 and f-> 0, it's not a minimal element

roughly speaking

It's a rather weird set of conditions

[verbal marsh]

the derivative would have been zero at x = 1/root2 if it was a local minimum too

[warm brook]

If it's the only zero in the interval (0,infty), then yes, these conditions work

and it'd be a local maximum because in order for f(0) = 0 and f-> 0, then f(1/sqrt(2)) > 0

you need to know it's the only zero in that interval, then you can use those conditions, so I agree, it may not be really that helpful

[verbal marsh]

that's true

i'd know it's the only zero by taking f'(x) = 0 and finding the roots of x yeah?

[warm brook]

Yes

[verbal marsh]

another zero can't sneak up on me if i use that method i'm hopinh

[verbal marsh]

that clears things up

[alpine sable]

is this channel available now?

[warm brook]

[f(x) = xe^{-x^2} \implies f'(x) = e^{-x^2} - 2x^2e^{-x^2}]
Then see that
[ e^{-x^2} - 2x^2e^{-x^2} = 0 \implies 1 - 2x^2 = 0]
Clearly there is only 1 positive x s.t. f'(x) = 0

[ocean seal]

kirby

[verbal marsh]

yep, have a good day @warm brook

[warm brook]

yeah you too

[warm brook]

yeah, and a note even using this method here doesn't have a zero creep up on you as e^{-x^2} is never equal to 0, so you can divide like that

[warm brook]

What is a stationary point (its definition)

[verbal marsh]

i don't get you, what method are you talking about?

[warm brook]

Oh I'm just qualifying the divide by e^{-x^2} in what I wrote down

[verbal marsh]

isn't it true that even if e^{-x^2} COULD = 0, i.e. it intersects the x-axis at some point, you could still divide like that?

[warm brook]

Yes, it just leads into an issue at that point, so you need to make sure there isn't a problem at such value of x

That would just be another 0 you will need to handle

[blazing dock]

Samantha swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 12 minutes. If the river flows at 4 mph, how fast can Samantha swim in still water?

How do I create the equation for this?

[verbal marsh]

sorry but how'd you handle it?

[warm brook]

It would suggest that at the value of x, there is another local extrema of the function, so you would need to double check that it is not a local maxima, which would actually lead directly to the problem you were originally concerned about

[midnight sand]

Dos anyone know what error intervals are?

[amber iron]

hi, is the channel open

[blissful valley]

yo i need help

[amber iron]

what am i doing wrong?

the answer is supposed to be 360pi

i used spherical here, x = p, y = phi, z = theta

for the answer to be 360pi, the lower bound of my second integral needs to be cos^-1(5/14). but where do i get that from?

[alpine sable]

hello

can somebody help me

i need help with

my sat

questions

[gloomy pumice]

Yesterday I asked a question but until now I have not been able to solve it: #help-2 message

[fading python]

Somebody plz help

[weary cloak]

omg i never get help here im leaving

[fading python]

Find”

[alpine sable]

burh

[bleak ridge]

,rotate

[magic geyser]

divide 10 by 4 what do u get

[blazing dock]

Samantha swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 12 minutes. If the river flows at 4 mph, how fast can Samantha swim in still water?

How do I create the equation for this?

nvm i've figured it out now ._.

[verbal marsh]

i'm too sleepy to efficiently ask you what's confusing me in the case if the function could equal zero, i'll just annoy my prof in office hours about it

[minor bloom]

so im using slope point formula for derivative stuff and i got the m and x1, but idk how to get the y1

[glass lichen]

Plug in the x value into the function

[minor bloom]

oh so in thsi case I have 1/x+2, x =1, y would be 1/3?

oh wait lmao

the function

is f(x) =

now isee

[tardy plank]

can someone explain this to me?

[novel pond]

anyone knows how to use excel and do regression model to get result for hypothsis?

[wicked breach]

[low topaz]

are there limits that approach things other than infinity and 0

[charred flint]

sure, just take a function that approaches 0 and add a number

[honest dew]

does anyone know how to do this

[robust flax]

how do we plot the probability distribution? i sort of just relied on computational procedure by plugging in numbers and got 3.54 but how can i express this graphically?

[charred flint]

for discrete sets you just put some dots on a graph

[wary stream]

Trig function. It gives you which one to use

[drowsy garden]

anyone know this

[nova wyvern]

What is the length of side c? use two decimal places.

howwww

[wary stream]

Law of sines

[drowsy garden]

so no one knows

alrighty then

[kindred warren]

@drowsy garden For any triangle, A/sin(a) = B/sin(b) = C/sin(c)

excuse my bad drawing

you can use that to find side C

[quasi tapir]

Is there a name for this mathematical sequence: 1,2,4,7,11,16,22,29,37,46,56

[gleaming sluice]

that looks similar to triangle numbers

[robust flax]

how would i compute the case k = 1 for example?

[lapis goblet]

Trying to find the equation for the elliptical parabaloid given the contour plot

Is this possible

[near escarp]

Hey

Im Brazilian and i have onde problema in math

I do know, and the last year i do have one study

Sorry, my english is very bad

[lapis goblet]

Just put the question

Someone will answer it

[near escarp]

The question is BR

[lapis goblet]

i only know French sorry

[near escarp]

a rational number A is represented below in its factored form. check the option that has a digit that can be placed in place of the exponent X so that A is a perfect square number

[subtle elbow]

help

[near escarp]

A) an even digit

B) a digit less than 2

C) an odd digit

D) A digit greater than 2

E) Any natural digit

@lapis goblet

[lapis goblet]

Try plugging in some numbers

And see what happens

[near escarp]

And i do knos speak french

Im braziliam

:v

[lapis goblet]

Utilisez quelqeus numeros pour ‘x’

Vois se qui ce passe

[near escarp]

I do know speak french !!!!!

Im brazilia

Rio de janeiro

[lapis goblet]

Do or don’t?

[near escarp]

Bolsonaro

[near escarp]

What

[lapis goblet]

nvm, you have to wait until someone can help

[near escarp]

Oh

Ok

Tranks for help

Good night

My love

[lapis goblet]

[near escarp]

😘

[compact orchid]

For question 3 I am a bit stuck. I found the derivatives of the two equations. K/s for the first one and then la(4)^a-1 for the second. From here I’m not sure because of the constants. I assume I somehow need to solve the derivatives by making x certain same values proving they are or not the same. But again, I don’t know what to do with the constants. Any help would be appreciated

By x I mean s

[outer notch]

6^(-76)

someone solve this please

[raw shard]

1/6^76

[outer notch]

what is that answer

Im asking

me and my friends are debating on it

[wary stream]

Use a calculator

[outer notch]

either 1/14r8x10^14 or 7.25278779 × 10^(−60)

[outer notch]

I did hes still debating with me

[wary stream]

Literally use the calculator, it's normally correct unless you typed it in wrong

[outer notch]

ill try again

[raw shard]

no one would do that by hand

[outer notch]

7.2527878e-60

[wary stream]

And so that's the answer

[outer notch]

so then do you know where my friend went wrong when he got 1/14r8x10^14

[wary stream]

I don't even know what the r means

[compact orchid]

<@&286206848099549185>

[raw shard]

@amber gulch do you see the pattern of how the angles are increasing?

so what would the larger angle be

aka the angle beside x

yes

bruh

not sure how

it should be 63

[kindred warren]

it's b

[wary stream]

Don't give answers

[kindred warren]

he said to give the answer

[wary stream]

Not the point of this server to give answers

[kindred warren]

he wanted the answer

[wary stream]

Don't care, don't give answers

Not the point of the server

[opaque totem]

woww what happen here

[neon igloo]

Help pls

[wary stream]

,rotate

[neon igloo]

The 1st qs

Hello

[devout summit]

Try representing BQ vector and BC vector as sum of the other vectors

[lethal dock]

How to solve ii

The second one

[devout summit]

You solved (i)?

[lethal dock]

Yes

[devout summit]

Then going to (ii) from there is similar

What did you do to solve (i)?

[lethal dock]

Hold on

[wary stream]

No

[devout summit]

You squared both sides correct?

[lethal dock]

Yes

[devout summit]

Do the same to the answer you got in (i)

[wary stream]

3 is a vertical stretch

Use the chart I gave

[tight locust]

can someone clear something up for me regarding cross product?

$a \times b = |a||b|\sin(\theta)n$

[eternal crown]

The LCM of 18, 10 and a number N is 180. Which among the following is a possible value of the number N? *
1 point
A. 24
B. 48
C. 27
D. 36

[little pier]

jesus christ people there's more than one channel

A person was already being helped by someone

[wary stream]

Add spaces between that a and slash

[crisp grove]

find the lcm

[little pier]

The etiquette is to respect the current question being answered and direct your question to a free channel

[wary stream]

And the b

[ocean seal]

EndTimes

[tight locust]

there we go.

n is defined as the vector perpendicular to a and b

but aren't there two of them?

[lethal dock]

$a - \frac{1}{a}$ = 2
= $(a - \frac{1}{a})² = 2²$
= $a² - 2(a * \frac{1}{a}) + \frac{1}{a²}$
= $a² - 2(\frac{a}{a}) + \frac{1}{a²}$
= $a² - 2 + \frac{1}{a²}$
= $a² + \frac{1}{a²} = 2² + 2$
= $a² + \frac{1}{a²} = 4 + 2$
= $a² + \frac{1}{a²} = 6$

[ocean seal]

JUGisMUG🎃

[tight locust]

how do you uniquely determine n?

[lethal dock]

How can I make lines-

[raw shard]

so many people in one channel

[wary stream]

It also depends on the function too

[tight locust]

i'll move to questions 1

[wary stream]

What function are you applying it to?

[devout summit]

Square the last equation you got again.

[wary stream]

Absolute value, quadratic?

Etc

[lethal dock]

How do lines work

[devout summit]

You write \\ while writing latex

[lethal dock]

Oh

[lapis hedge]

take a better picture

[lethal dock]

Got it

[wary stream]

If you want to mess around with latex, use #latex-testing

[lethal dock]

Ohh

[wary matrix]

find the angle between the plane a and the straight line passing through the origin and point M. Calculate the distance from point m to plane a. A (-3, 2) B (5, -4) C (1, 6)

[devout summit]

Did you get (ii)?

[lethal dock]

Doing it

[devout summit]

It should not be that difficult

[wary stream]

Write it in terms of f(x)

And use the table I gave

It helps

Because you aren't given f(x), you're writing g(x) = f(x) and what transformation needed

[devout summit]

@lethal dock Are you writing latex?

[wary stream]

Is there an f(x)?

[lethal dock]

Yep

[wary stream]

Like what is the parent function?

[devout summit]

Its not necessary. Don't write the whole latex it's the idea that counts

[wary stream]

Is f(x) = x^2?

f(x) = |x|?

If there is no parent function given and just f(x), you write g(x) in terms of f(x)

No

[devout summit]

I understand. What you did was correct

[lethal dock]

$(a² + \frac{1}{a²})² = 6²$

$a⁴ + 2(a² + \frac{1}{a²}) + \frac{1}{a⁴}$

$a⁴ + 2(\frac{a²}{a²}) + \frac{1}{a⁴}$

$a⁴ + 2 + \frac{1}{a⁴}$
\
$a⁴ + \frac{1}{a⁴} = 6² - 2$
\
$a⁴ + \frac{1}{a⁴} = 36 - 2$
\
$a⁴ + \frac{1}{a⁴} = 36 - 2$
\
$a⁴ + \frac{1}{a⁴} = 34$

[ocean seal]

JUGisMUG🎃

[wary stream]

No

[lethal dock]

Oh

[wary stream]

So if you have a vertical stretch of 3, g(x) = 3f(x)

No

[lethal dock]

@devout summit thenks for da help

[wary stream]

If there is a vertical translation up of 10 , it would be g(x) = f(x) + 10

Horizontal translation left by 5 units, g(x) = f(x + 5)

[lethal dock]

What u even need help with

[wary stream]

Make sense now? @alpine sable

I'm giving you examples

With my examples, you should be able to figure it out

Are you saying $$\sqrt{17} \cdot 3^7$$ or $$(\sqrt{17} \cdot 3)^7$$

[ocean seal]

dldh06

[lethal dock]

I get 44,301,660.833027

[wary stream]

Can you use a calculator?

So then use a calculator?

[tardy plank]

can someone tell me how 2 was derived?

[crisp grove]

g(2, -1) = 2*1=2

we want the level curve with level set 2

[misty mortar]

How do I solve this problem?

[crisp grove]

find the fixed points. falls into autonomous dynamical system

,w plot -5*(2-x)*(y-7)

,w plot -5(2-x)(x-7)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Ryuzaki#5323

[crisp grove]

check that, if a points starts from the left of 2, dy/dx there is negative, so the value will decrease and will eventually reach -inf, if it starts from the right or somewhere > ~4.5, it''' reach the point 7

with this u can have an idea on how the trajectories will behave

[misty mortar]

If it starts form the left of 2 shouldn't it be positive because the line is within the positive region

[crisp grove]

if it starts from 2, means it has dy/dx = 0. so it'll not mvoe

these kinds of points are known as fixed point

for a system $\dv{y}{x} = f(y)$, a fixed point is where $f(y)=0$

[ocean seal]

Ryuzaki

[crisp grove]

the stability depends on the value of $f'(y)$. for a fixed point $y_0$, it'll be attracting if $f'(y_0)<0$, repelling if $f'(y_0)>0$

[ocean seal]

Ryuzaki

[crisp grove]

all that means in Layman term is, if the slope of the graph where it crosses the x-axis is positive, then it'll be repelling, i.e. points will move away from it, if it's negative, then points will approach it

find which one is which in your case

[manic peak]

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[alpine sable]

Bro

[wary stream]

Don't troll

[alpine sable]

Are you 5 years old

[atomic lodge]

Anyone

Please help me

[tight locust]

find an expression for the perimeter of this fence

[eternal osprey]

What is the equation for implicit definition of derivative?

[wary stream]

Stop trolling

[sharp falcon]

Can someone help me

I don’t know how to do 2 step equations and need help with this

[violet canopy]

could i get some help with this please

[wary stream]

Just expand and simplify the left side

[lime wadi]

sup!

is this correct?

[vapid oak]

no

[raw shard]

another no

[vapid oak]

1. none 2. all except none 3. origin

[raw shard]

you shouldn’t give answers

[fair mesa]

Hello there, I have a question:

Let N be any whole number > 0

1. N*x > (N-1)*y
2. x < y
   If both x and y are positive numbers, find the minimum values for both x and y in terms of N
   Currently I have only tried rearranged them to no avail, any one have any ideas

[raw shard]

bruh

[fair mesa]

i mean couldnt you just put that into a calculator lol

[raw shard]

rewrite division as multiplication

yes

actually

just do it left to right

parentheses first

no, i don’t know any questions

[wary stream]

Just Google some

[fair mesa]

nvm i literally figured it out 2 seconds afterwards

[compact orchid]

I’ve asked this question before and it’s been a few hours and I can’t figure anything out if anyone can help me with question 3

My thought process. I found the derivative of both and need to find a value of s that only works for one to disprove the equitation

Or that the equations are equal

I know 0 doesn’t work, but that’s not enough proof it seems

I just don’t know how to find this value or values

The derivatives I found were for the first one k/s and for the second one las^a-1

[cursive crescent]

Just at a glance I see that q(s) and p(s) both represent the same thing, so you could set the equations equal to each other and see if it simplifies down to a constant or not, or solve for a variable to see when they’re equal along a variable, or whatever relationship you’re looking for

[lime wadi]

thanks!

[misty sphinx]

may someone help me with this i have no idea how to continue

[upbeat gorge]

If AD bisects angle A, what does that imply about the angles CAD and BAD?

[agile fulcrum]

how do i algebraically manipulate the left inequality to the right one

Since 0 < x < 1, 0 > (− x) > -1.

Since 0 > (− x) > -1, 1 > (1 − x) > 0.

Since 1 > (1 − x) > 0, x > x(1 − x) > 0.

thats what i did so far

i dont know what im doing

[inner sequoia]

how did they factor this

dont understand explanation

[sleek herald]

gcf of 4 is 4 bcuz 4/4 and 24/4

you can't divide 5 i n

5 in four

[inner sequoia]

i mean why is it 4x^3(x+6)

where'd that come from

[sleek herald]

take the least exponent

that's it

for ex 10x^5 and 5x^3

the gcf would be 5x^3

nonono

[inner sequoia]

where the shit did (x+6) come from

[sleek herald]

I don't know

[inner sequoia]

is it because 4x^4 / 4x^3 = x?

and 24x^3 / 4x^3 = 6?

[opal mesa]

If you multiply 4x^3 by x+6 you get 4x^3+24x^3

[inner sequoia]

how

[opal mesa]

Sorry 4x^4 typo

[opal mesa]

Yes

That is the gcf of the whole package so you factored 4x^3 divided the terms by 4x^3 and wrote it down

@inner sequoia you get it ? Sorry my explanation is really ass

[inner sequoia]

yeah i get it

[opal mesa]

Good

[inner sentinel]

for this question do i just simplify the value of f'(x) and g'(x)

[stiff pawn]

find the derivative of h(x) using chain rule and quotient rule

[misty sphinx]

definition of angle bisector?

[grizzled depot]

can u guys help me with this

Describe the error

22/7=3.14

[dire juniper]

how to solve for the hypothenuse of a right triangle given its two medians?

[lime kraken]

What should be the multiplier when a value is decreased by 25%?

[alpine sable]

what would be the angle of the black lines?

the angle of the green long ones is 60 on outside

what would it be for the black long ones

how do I calculate that?

[inner sentinel]

how do i solve this

[alpine sable]

it's a perfect hexagon

idk if that helps

how to calculate the angle onit

[grand fable]

interior angles of a hexagon are 120 degrees

internal angles of that triangle add up to 180

see if you can do something with that

[woeful pulsar]

what do the black lines connect to exactly?

[grand fable]

the vertex of the hexagon im assuming

would not make sense if they didn't connect tehre

[woeful pulsar]

tbh, I think just whack coordinate geometry or trigonometry

[alpine sable]

srry found out the issue

thank you for your time though

🙏

one of the lines was too long

[alpine sable]

the offset caused this

[robust nymph]

Clint wants to buy a new computer worth P35,000. He opted to pay it in equal
monthly payments for 3 months at 6 % compounded monthly. How much is his
monthly payment? How much is the total interest in all payments?

I got the R but how do I get the total interest?

[pulsar yarrow]

Just the total - principal should yield the total interest?

[robust nymph]

I don't have to do A = P(1+r/n)^nt

[pulsar yarrow]

Well yeah you use that lol to get the A

then A- P = interest

[robust nymph]

35,000 - 1064.77

[pulsar yarrow]

?

Did you use the formula you've written down

[robust nymph]

No

[pulsar yarrow]

A is not 35000 btw

[robust nymph]

What you said

[pulsar yarrow]

P is 35000

[robust nymph]

I mixed up

[pulsar yarrow]

I said A-P for which you have to calculate A

[robust nymph]

1064.77 - 35000

What is A

[pulsar yarrow]

A>P lol

[pulsar yarrow]

total amt. after interest

[robust nymph]

That's F

[pulsar yarrow]

principal is without interest that's why i proposed A - P

[pulsar yarrow]

What?

[robust nymph]

In our school F = total amt after interest

[pulsar yarrow]

It's the same thing i referred to it as A because the formula you posted

literally says A = something so that's why

[robust nymph]

Anyways I'll just do it

[pulsar yarrow]

Find total amount accrued with interest (which is A or F whatever you want) then that - P = interest money if that makes sense

[robust nymph]

$$F = R\frac{(1+j)^n-1}{j}$$

[ocean seal]

BrainDead

[robust nymph]

,c 1064.77\frac{(1+0.005)^36-1}{0.005}

Tf

Yeh

#bots

[cunning obsidian]

<_<

Those numbers which when divided by 2 will have a reminder of 1

Should be pretty straight forward as it’s a pure calculating q

Work out 9*34

[edgy hazel]

guys can u help

[alpine sable]

42

[cunning obsidian]

What do u even try to calculate these?

[cunning obsidian]

For questions like these I would group those numbers and see what numbers they can make

7*8=?
And how can we put in operators and thus make the result equal to 50?

Sorry I have trouble understanding

Did you mean “your dad” XD

[edgy hazel]

yea but i tried literally everything

[cunning obsidian]

[cunning obsidian]

Tip: try multiplying 8 and 7

[edgy hazel]

bro ive tried every single thing

8 times 7 then minus 3 minus 2 thats 51

[edgy hazel]

even tried with exponents and it didnt wokr

[cunning obsidian]

8*7=56 right

2*3=?

[edgy hazel]

omfg

[edgy hazel]

thanks so much

[cunning obsidian]

Also try other operators other than + and -

[edgy hazel]

yea ok

[cunning obsidian]

Have you tried calculating it

Also isn’t this elementary math

Are you underaged

Ya shall be at least 13 yo to use discord and to join this server

Try it yourself first

We aren’t here to do your hw

[loud cradle]

he's a troll.

@cunning obsidian

[cunning obsidian]

[cunning obsidian]

Isn’t this a “quiz”

[short lichen]

NO

[cunning obsidian]

Hmm do you know y=mx+b

[short lichen]

yes

[cunning obsidian]

And u know m is the slope?

[short lichen]

?

[alpine sable]

guys

I have a question

Gemma has the same number of sweets as Betty

Gemma gives 24 of her sweets to Betty

Betty now has 5 times as many sweets as Gemma

Work out the total number of sweets that Gemma and Betty have now

I tried solving it but I got confused

I did this

x=x

x-24=5(x-24)

but I found x=25

i mean 24

can somebody please help me?