help-38

[tawny elk]

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[rugged latch]

Find the inverse of the function
y = x^4, x∈(0;∞)

[rugged latch]

y = x^4
x = y^4
y = 4thpowerrootx

now i found the inverse

I don’t understand where x∈(0;infinity) comes into play, what am I to do with that

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@rugged latch Has your question been resolved?

[limpid dawn]

Thats the range of your inverse function

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[spiral ocean]

Why is it $mg\sin{\theta} a$ not $mg\sin{\theta} b$

[solid kiln]

Average Calc Student

[spiral ocean]

Trying to find when the object would start falling

[wraith hinge]

nvm

[spiral ocean]

Plz help ):

[wraith hinge]

oh wait

do you knwo why its u mgcos theta b ?

[spiral ocean]

Moment = F x distance from center

[wraith hinge]

Distance from centre is a

[spiral ocean]

but its also b cuz the length of the base is 2b

[wraith hinge]

red point is given by -ai hat -b jhat , force at red point is given by - umg costheta i hat

cross product will give you ?

[spiral ocean]

This?

[limpid dawn]

If you change your pfp you will have aura debt forever

[wraith hinge]

aure debt ?

aura?

[wraith hinge]

cross product

thats the magnitude you wrote

[spiral ocean]

ok

gimme a sec

[wraith hinge]

also you need to simplify it

[wraith hinge]

nvm

just simplify it

by writing sin theta in terms of a and b

[wraith hinge]

suggest a theme and i will work on it

[limpid dawn]

Your pfp os goated

[spiral ocean]

wdym

[limpid dawn]

Do you know the definition of cross product

[spiral ocean]

yes

[limpid dawn]

Use that

[wraith hinge]

@limpid dawn

this is wrong, right ?
we should have a on both sides and thus they get cancelled

[limpid dawn]

I dont even know whars going on here

[spiral ocean]

idk why

[spiral ocean]

.

like

the book says that's the solution

[limpid dawn]

Why would it be not that can you tell your perspective

[spiral ocean]

i got mgsintheta x b from this

[limpid dawn]

Is this all there is

[spiral ocean]

This is all that the question provides

[still rose]

what are you trying to find

acceleration?

[spiral ocean]

the angle that makes the box tip over

olny under influence of friction force and gravity

[trim jolt]

@spiral ocean Has your question been resolved?

[wraith hinge]

you are taking this as your coordinate system right ?

[spiral ocean]

Yes

Wdym

After cross product, i removed the minus and compare the magnitude

If the one going clockwise is bigger then the block will tip

And fall

[still rose]

It's been 2 years since I touched physics

[spiral ocean]

I have to restart physics for my exam

And now I feel pain

[still rose]

and i got mgsin(x)(a) - F_s(mgcos(x)(b) = 0

[spiral ocean]

Could u

Show ur method

[still rose]

uhh

I don't have my phone with me right now

[spiral ocean]

Why is it

A and b tho

[still rose]

do you have any resources with you

[spiral ocean]

Nah

I’m outside rn

[still rose]

I try to find any resources

[spiral ocean]

Okie

[still rose]

http://adaptivemap.ma.psu.edu/websites/7_friction/7-2_slipping_vs_tipping/slippingvstipping.html

@spiral ocean

[spiral ocean]

I don’t understand the last part

Why is it the normal force not the friction

@still rose

@wraith hinge

[wraith hinge]

Friction = u x normal force

u is coefficient of friction

Wait up calc 3 victim and average calc student are different !

[spiral ocean]

What

Why is it N x OB tho

If friction is in the direction of OA @wraith hinge

[wraith hinge]

Gtg exam

[spiral ocean]

Gl

Nvm

I got it

Consider only contact forces

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[shrewd wraith]

Hey! Im doing complex analysis and I just feel like im missing something when solving a real integral by substitutions and so on

[shrewd wraith]

Here is the question

and my very wrong solution is

Now i know there are MULTIPLE errors in my solution, but my thinking was using homotopy, seeing that the upper bound of the integral is 0 and getting 0 as an answer. This did not work because the answer is first of all not 0. Second, Im pretty sure i pass by a singularity or something which means that the whole idea fails

And i am now unsure of what i should do. Find a primitive to the complex function?

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@shrewd wraith Has your question been resolved?

[reef shoal]

Idk anything about complex analysis but i like you handwriting

[shrewd wraith]

Thank you! hahahha

[wraith hinge]

No

[wraith hinge]

Since the block is moving in the direction of OA,the direction of friction will be opposite to it

[spiral ocean]

AO

[wraith hinge]

Yeah

[wraith hinge]

This is not phrased properly

Like if the block were moving down, but it's speed is decreasing

Then the direction of frictionAl force will be along OA

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[cedar jetty]

y = 6x – 1

how do i identify ordered pairs

[cosmic meadow]

Do you know what is an ordered pair?

[trim jolt]

@cedar jetty Has your question been resolved?

[cedar jetty]

pts on a table?

data

[hollow tangle]

Do you see that there will be infinitely many ordered pairs satisfying this?

@cedar jetty

The locus of these points will form a straight line

[cedar jetty]

ye

[hollow tangle]

Just put some random values of x

And find the corresponding vals of y

And that's your ordered pai

[hollow tangle]

I recommend numbers like -1, 0, 1

[cedar jetty]

awesome thanks

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[subtle topaz]

prove that if G is a point dividing one median in ratio 2:1 then the lines joining the other vertices to G will be medians

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[short spear]

How is the radius not from 2 to 4?

Oh nvm

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[celest eagle]

So uhh I was doing integration. Ran across this question and I have no idea what to do.

[vestal summit]

Integrate by parts 😉

[celest eagle]

sec²x dx/[sec(x)+tan(x)]^9/2

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[zinc ginkgo]

,rotate

[zinc ginkgo]

2(n-1) = 2 * n - 2 * 1 = 2n - 2

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[charred trail]

i would first recommend writing everything in terms of 3^(something) on both sides, and then you can compare the exponent

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[keen island]

Help

[keen island]

Hello?

[nimble stone]

Hello?

[keen island]

Could I have some support with this?

[nimble stone]

sure

any ideas?

[keen island]

No, #

[nimble stone]

alright, lets get some basics established then
$$\int_{a}^{b} A{f(x) dx}=A\int_{a}^{b} {f(x) dx}$$ where A is a constant
$$\int_{a}^{b} {f(x) dx}=-\int_{b}^{a} {f(x) dx}$$
$$\int_{a}^{b} {f(x) dx}=\int_{a}^{c} {f(x) dx}+\int_{c}^{b} {f(x) dx}$$ where $a<c<b$

[solid kiln]

AℤØ

[nimble stone]

those three should be enough to solve them all

[keen island]

hmm

so the first one should be -12

[nimble stone]

exactly so

[keen island]

next one 20

[nimble stone]

yup

[keen island]

last one 7

that one was quite easy you know

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[proper sluice]

what does the comma in 1 1/4 .0, 2+ 5/6 mean

[latent granite]

It's same as ×

1 1/4 × 0,2

[proper sluice]

oh is the comma decimal point

[latent granite]

Yeah

[proper sluice]

I see

okay what have you got for a and b

[latent granite]

Wdym exactly?

[proper sluice]

like have you got avalue for a

or b

like a = ?

b = ?

[latent granite]

For A I got 7/12, don't know how to get B tho.

[proper sluice]

okay first convert the fractions from a mixed to an improper fraction

[latent granite]

Yeah I suck at math

[proper sluice]

don't worry about it
you will get it over time

[latent granite]

B= 5/4 × 1/5 + 5/6
You mean this?

[proper sluice]

yes

[latent granite]

@proper sluice can you explain to me what was the point of those numbers here.
2-6:3+4×2 and the rest
What was being calculated exactly? And how does that add up to -7/19

[proper sluice]

is that supposed to be the answer?

[latent granite]

Yes

-7/19 is the answer but I don't get how did we get it

[proper sluice]

okay what have you got for b

and show me how you got the answer for a

[latent granite]

Yo my answer for A is wrong

One sec

[proper sluice]

👌

[latent granite]

It's ½×4/3-7/6, and that's

[proper sluice]

yes

[latent granite]

1/2

[proper sluice]

yes

have you got b yet

[latent granite]

One sec

[proper sluice]

👌

[latent granite]

130/120? It can't be that big

[proper sluice]

you can simplify that

notice the last digit

[latent granite]

/:10?

[proper sluice]

yes

[latent granite]

So A is 1/2 and B is 13/12.
A+B=38/24?

[proper sluice]

yes

[latent granite]

A-B= -14/24?

[proper sluice]

yes

wait

[latent granite]

Sorry but how does this end up as -7/19?

[proper sluice]

this should be negative

[latent granite]

True

[proper sluice]

sorry I just realised

sorry

[latent granite]

Nah it's ok

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[stray nova]

so in convolution ∫ f(τ)h(t-τ)dτ , when we shift the h(τ) function , why don't we substitute the value into the h(τ)

?

[zinc ginkgo]

what do you mean by "shift h(tau)"

can you write out on paper what you mean

using equations and such

[stray nova]

when we delay the function h(τ) to evaluate the convolution over a region.

[zinc ginkgo]

wot

[zinc ginkgo]

.

delay how

[stray nova]

suppose we've got the x(t) function (the red one) and the other function which is the h(t)

[zinc ginkgo]

wut

[stray nova]

and then i shift the triangle function

to evaluate the convolution

[zinc ginkgo]

what does your picture have to do with your question

which one is f and which is h

and are you plotting h(t - tau) or h(tau)

[stray nova]

im ploting h(t-tau)

plotting*

[stray nova]

the trinagle function is the h(t-tau) and the constant line is the x(t)

[zinc ginkgo]

yes that's what's happening visually

h(t-tau) is a different shifted function of tau for different t

,tex .horz trans

[solid kiln]

riemann

[stray nova]

yes , but mathematically speaking it doesn't make any sense to me.

[zinc ginkgo]

did you read this
#help-38 message

[stray nova]

because we don't plug the value into back to the h(τ), we're just saying h(τ-tau).

[stray nova]

i idid

[zinc ginkgo]

what is "the value"

[stray nova]

did

[stray nova]

suppose we shift the h(t) function by 2 right?

we're not plugging the value 2 into the h(t), we're just leaving it as it is, we're just saying h(t-τ)dτ instead of h(2-τ)dτ

[zinc ginkgo]

(f * h)(2) = int f(tau) h(2-tau) dtau yes

[stray nova]

oh so we substitute it?

[fickle sky]

do you know what integration is?

[zinc ginkgo]

yes the right side is a function of t

the integral will depend on the value of t

hence why the left side is a function of t

and in particular, t=2 as well

[trim jolt]

@stray nova Has your question been resolved?

[stray nova]

yes why

[stray nova]

ok ,so we plug the shifted value into the g(t-τ) right?

[zinc ginkgo]

the right side has g(t-tau) yes

g(t-tau) is a shift AND reflection

,tex .horz scale

b = -1

actually that doesn't help

g(-tau) as a function of tau is a reflection about 0 of g(tau)

https://www.onlinemath4all.com/reflection-transformation.html

[stray nova]

so its going be h(2-τ)dτ

[zinc ginkgo]

read that

[stray nova]

yes ik that

[stray nova]

is this correct?

[zinc ginkgo]

what is "it"

[stray nova]

im just asking if we shift the h value by 2 then the convolution integrla is going be h(2-τ)dτ

[zinc ginkgo]

the convolution function on the left evaluated at t=2 tells you that you have to shift g(t-tau) to g(2-tau) yes

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[violet elbow]

is the slope not 10

[prime lynx]

,w plot y=5|2x-3|

[solid kiln]

Results provided by WolframAlpha

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

Requested by ishigamisenku_

[marble dagger]

#prealg-and-algebra

[sudden mist]

Does that matter?

[zinc ginkgo]

what does your question have to do with slope

[prime lynx]

You only need to plug in x values tbh

¯_(ツ)_/¯

[violet elbow]

where does that 1.5 come from

i thought it would be 3 on the x axis as a start

[prime lynx]

Which 1.5?

[zinc ginkgo]

comes from setting y=0

[prime lynx]

Oh that

[violet elbow]

wym

why is it 1.5

and not 3

because doesnt the inside of the | | determine the x axis

[violet elbow]

to find f(x) you can use slope

what i did was start at (3,0) and go to -1 at a slope of 10

[sudden mist]

You have the rule given, what gives in doing that way?

[violet elbow]

?

[sudden mist]

you already know what f(x) is

just plug in x

[violet elbow]

if i knew what f(x) is

i wouldve got the answer right

[sudden mist]

??

[violet elbow]

aslan i have to call you out, the way you teach is very belittling

you're very rude

[sudden mist]

How so?

[violet elbow]

you tend to be aggresivly confrontational and expect people without the experience you have in math to get it right away

[sudden mist]

Not all?

[maiden hare]

But you do

[violet elbow]

is that not the slope?

[maiden hare]

Wdym?

It says f(x) = ...

[violet elbow]

we dont have the value of x

[maiden hare]

That's your function

[violet elbow]

how can you solve without hte value of x?

cause you cant plug it in

[sudden mist]

Do you see the table of values in the image?

[maiden hare]

The value of x is what is in the top row of the table

[zinc ginkgo]

absolutely not

[violet elbow]

that's what ive done and it's worked though

[zinc ginkgo]

got lucky then

[violet elbow]

i forgot i could plug it in

[violet elbow]

not really

[zinc ginkgo]

or it was a different question and you weren't paying attention

[violet elbow]

no it was like

the entire math career

up to now

lol!

[maiden hare]

I mean you could use the slope, but that requires getting the point where y=0 correct

[zinc ginkgo]

https://tenor.com/view/doubt-press-x-la-noire-meme-x-button-gif-19259237

[maiden hare]

which you didn't do, and so your method did not serve you well

[violet elbow]

wild ego you have riemann, you dont know me bro

be nice

[sudden mist]

Im assuming theyve only dealt with lines before

[violet elbow]

^

[sudden mist]

maybe thats why?

[violet elbow]

yes

dont yall read #rules

expect that people have no experience in math and build from there

[sudden mist]

Car be nice too? were chatting through text

[violet elbow]

be kind

[violet elbow]

im being plenty nice, calling out people when they're in the wrong is not being mean

it's trying to have people see their own faults so they dont hurt peoples feelings when trying to teach them something new yk

or make them feel stupid

which would suckk cause this server is pretty awesome with all the help it has

anyways i got the answer

thank you @maiden hare

.close

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[zinc ginkgo]

you making rules up and want people to follow all of a sudden?

[sudden mist]

Youre allowed to feel that way, but be mindful that we cant read your mind, we can be as confused as you are?

[violet elbow]

it's in #rules slow poke

[prime lynx]

Can you please stop

[violet elbow]

stop what??

david who are you

you werent even here

[prime lynx]

You will only make things worse by typing

[violet elbow]

being teamed up on when im trying to have others act accordingly isnt exactly pleasent either

[violet elbow]

yeah well what do you think you're doing

💀

[prime lynx]

All I would say is if you want a mute then go on

[violet elbow]

a mute for what? sticking up for myself?

[maiden hare]

.reopen

[trim jolt]

✅

[violet elbow]

ive said nothing wrong

[maiden hare]

@prime lynx you aren't helping

[violet elbow]

yall are just bullying people that are at a lower level of math so yo ucan feed your ego

[prime lynx]

I'm sorry

[violet elbow]

wouldnt exactly call that helpful

nel assisted while being kind

[sudden mist]

Car, if it may not be obvious, context is vital, we had no idea what was going through your mind when you posted the question

[maiden hare]

@violet elbow keep in mind that texting does not always translate intentions well

[violet elbow]

right

forgot about that

[maiden hare]

Also keep in mind that everyone here isn't necessarily a native english speaker

[violet elbow]

I am saying that i'd appreciate if this community was a nice place where the teachers, who are more knowledgeable, would follow the rules where it clearly states that they should be kind to the learner so that they can have an enojyable experience learning and arent turned away from math

because math is a beautiful subject that so many dislike because teachers make them feel stupid for not understanding

i hope i got that across alright

so when im in a situation where it feels like others could interprit something as rude or making them feel stupid, as one of the few very knowledgeable, and ACTIVE teachers in this server, i just wanted to give insight as a student and say how it couldve come across

so they arent turned away

ykk??

[zinc ginkgo]

holy shit

<@&268886789983436800>

[maiden hare]

Yeah, it's fine to have that sentiment, but also every helpee is different, and as helpers we almost never have full context

[zinc ginkgo]

don't waste a channel to whine

.close

[trim jolt]

Channel closed

Closed by @zinc ginkgo

Use .reopen if this was a mistake.

[violet elbow]

you see what i mean @maiden hare ?

[zinc ginkgo]

take it do DMs

[violet elbow]

also @zinc ginkgo it wasnt me who reopened it, i closed it when i got my answer

[somber ginkgo]

wtf happened here lol

[knotty oriole]

Lets slow down ya'll

[prime lynx]

😂

[maiden hare]

Misunderstandings, which can be discussed in the appropriate channels

[knotty oriole]

@violet elbow if there is an issue with a helper that you feel is being overly aggressive, rude or demeaning to you please dm the modmail account.

Most likely engaging them on this kind of thing directly will lead to the issues you already mentioned.

[violet elbow]

apologies, i thought it would be more affective to have a man-to-man conversation that would help us come to an understanding, i saw that i was wrong

[knotty oriole]

And we can't exactly effectively keep track of or moderate that as easily.

[violet elbow]

🫡

i respect the work you do accomplish and appreciate it

[trim jolt]

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[glass summit]

How do i find a range and domain of an equation

[maiden hare]

Domain and range are of a function, not of an equation

I'm assuming you only know up to real numbers, denoted by R

Take f, can you put any value x from R into f? In other words, does f(x) give you an actual value for any x in R?

[trim jolt]

@glass summit Has your question been resolved?

[glass summit]

I keep re reading this and cant figure out what you mean

We learned it a different way, I know that, but I have trouble remembering it so idk it fully

[maiden hare]

Does f(0) make sense? As in, is it a value?

[glass summit]

Yes

Sorry, I was busy

I was gonna ask chat gpt then realized I need to know this later on

[maiden hare]

Does f(1) make sense?

[glass summit]

Yes

[maiden hare]

Does f(pi)?

[glass summit]

Well it could work

Pi is a real number Is it not?

[maiden hare]

Yes

Does f(x) for any x in R?

[glass summit]

Any real number, yes that would work

[maiden hare]

So that's the domain

[glass summit]

I don’t think I can list f(R) as the domain

[maiden hare]

No, it's just R

[glass summit]

I don’t think I could do that either

[maiden hare]

Do you need an interval?

$\mathbb{R}$

[solid kiln]

Nel

[glass summit]

Think so

[maiden hare]

This is perfectly fine to write as a domain

But if you're asked for an interval instead, you can write (-inf, +inf)

[glass summit]

I don’t think I could put that 😭

[maiden hare]

$(-\infty, +\infty)$

[solid kiln]

Nel

[maiden hare]

If you can't use that either, then I don't know

Maybe "the real numbers"

[glass summit]

Idk

Ig ima have to bug my teacher

.close

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[loud flare]

hi

[loud flare]

whats 2+2

<@&286206848099549185>

.close

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[bitter lance]

I'm looking at a particular example for testing whether one set is a subset of another. Where A = {1} and B = {1, {1}}. Now I understand that {{1}} is not the same as {1} but I can't put into words why. Is it because the 1 in set B is a subset of a subset? Trying to conceptialize.

[nova spire]

{1} is a box that contains the number 1

{{1}} is a box that contains {1}

so it contains a box that contains the number 1

the element of the set {{1}} is not the number 1

it's the box that contains it

think of all the boxes as closed

and the elements of a box as "if I open the box, what can I reach inside"

[bitter lance]

Primarily this, I don't understand how A is a Subset of B but that A is also a proper Subset of B

Because how can A be a subset of B if everything in A isn't in B

[nova spire]

?

"proper subset" means "subset that isn't equal"

[nova spire]

I'm gonna go back to my analogy

think of all the sets as closed boxes
and the elements of a set as "if I open the box, what can I reach inside"

what's inside my set A?

I open the box, and I find the element 1

what's inside my set B?

I open the box, and I find:

• the element 1
• a box that contains the element 1

[bitter lance]

But the second box or set isn't defined with a letter but it doesn't matter.

Can A = {1, 1, 1} and B = {1, 1} and not be equal

because i'd find 3 elements of 1

vs 2 elements of 1

[nova spire]

sets are made of distinct elements

if you add copies of something you already have in the box

they don't matter

[bitter lance]

So they just condense

or one max of each instance

[nova spire]

if you have multiple of the same, they condense into 1

[nova spire]

A = {1, 1, 1} = {1}

B = {1,1} = {1}

A = B

[nova spire]

but can you see why B in this question isn't subject to that "copies" rule

[bitter lance]

In the example provided, is this a case of just a bad example?

As I assumed if A is a subset of B that they were equal

because a proper subset A is not equal to B

but in the example I gave it said A is a subset of B and A is a proper subset of B

which contradicts 1 {1} and 1

[nova spire]

no, a subset can either EQUAL or NOT EQUAL the bigger set

when you have a subset

it's either:

• the big set itself

• or a proper subset

[bitter lance]

So subset is more ambigious

[nova spire]

$A\subseteq B$ means either $A=B$ or $A\subset B$

[solid kiln]

rafilou is not not born in 2003

[bitter lance]

I'm thinking of a superset then and misidentifying them

So super set is when they are equal no matter what

[nova spire]

?

you mean $A\supseteq B$?

[solid kiln]

rafilou is not not born in 2003

[nova spire]

it's just $B\subseteq A$

[solid kiln]

rafilou is not not born in 2003

[nova spire]

so same

when you have "A supset B"

you either have A = B or A strict/proper superset of B

[bitter lance]

Oh,. this entire time I was assuming that each subset had one defintion

but it's more ambiguous where each different subset has 2 defintiions

Where a subset means that set a and b are the same, or some part of A is in B.

[nova spire]

uuuh not exactly

A subset B means that A is some part of B, whether some smaller part or the entirety of B

[bitter lance]

Yeah thats what I said

or did I mix it up

[nova spire]

when you said "some part of A is in B"

[bitter lance]

I'm saying Subset C_ is either A=B or A partially equals B

Or like all of A fits into B even if not all of it

[nova spire]

"A partially equals B"?

"all of A fits into B"

that I agree

[bitter lance]

yeah

So subset is where either all of a fits into B or A = B

[nova spire]

all of A fits into B, whether there is wiggle room left or not

[nova spire]

"all of A fits into B" also works if A = B

all of A fits into B, whether there is wiggle room left or not

[bitter lance]

just so confusing because mentally it's hard to understand that

A {1, 2, 3} and B {1, 2, 3, 4} is A = B

unless you're referring to if A = {1} and B = {1} then all of A fits into B

[nova spire]

here we have A subset B because all of A fits into B, even if there is '4' as wiggle room left

[nova spire]

here we have A subset B, even if when we do fit A into B there is no wiggle room left

[bitter lance]

So some sets can be proper subsets and subsets at the same time

[nova spire]

if you're a proper subset, then you are by definition a subset

if you are equal, then by definition you are a subset

here's why keeping the ambiguity is important

when you will want to prove two sets A and B are equal

sometimes the easiest way to do it is this way

you will show A fits into B

and you will show B fits into A

if $A\subseteq B$ and $B\subseteq A$, then $A=B$

[solid kiln]

rafilou is not not born in 2003

[bitter lance]

But in this instance even though a is subset of B they're not equal. So it would not work in this example/you couldn't prove it correct

you could prove A is a subset of B but not B is a subset of A

Unless you already know the A = B and you go through and show your proof

Like this correct?

[nova spire]

yeah sure

but for example

if you wanted to show A = B here

a good way is to show A subset B and B subset A

[bitter lance]

Well thank you, my study time for the night is over I have to move on. I appreciate your help conceptializing it. I think I understand it better now, tommorow I will move on to proving and disproving subset relations.

.close

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[violet elbow]

hey

[violet elbow]

is x^b * x^a = x^b*a

[split chasm]

no

[limpid belfry]

no

[violet elbow]

is it +

[limpid belfry]

yep

[violet elbow]

so x^a * x^b = x^a+b

[split chasm]

missing () around the a+b

important when communicating in text

[violet elbow]

okay

what does ^(2)/(3) mean

conceptually

i forget

[iron vapor]

3√x^2

Idk if thats what u mean tho

[violet elbow]

yes

it is

can you cube root -1

[small root]

Yea

[violet elbow]

what would it be lengthened

like unsimplified

[small root]

(-1)^(1/3) = -1

[violet elbow]

howcome

what does it do to stay the same

[small root]

Because (-1) * (-1) * (-1) = (-1)

[violet elbow]

what's (-1)^(1/2)

[small root]

That's not a real number

[violet elbow]

that's where im confused

thank you

[small root]

?

[iron vapor]

yeah just not sqr root

[violet elbow]

how do you cross multiply

wait

when is cross multiplying valid?

how do you divide exponents over each other when they're fractions?

[wary basin]

can you give an example of what you mean here?

[violet elbow]

u^(3/8) / u^(2/3)

[wary basin]

then you would subtract

[violet elbow]

3/8 - 2/3

?

[wary basin]

=u^(3/8-2/3)

[violet elbow]

ah

so multiplying is adding

dividing is subtracting

squaring is multiplying

and square roooting is dividing

when you have a root on the bottom can it be simplified as a square on the top

[iron vapor]

Think about it like this might be helpful. If I have a fraction for example x/y. If I want y in the numerator I take y to the power of negative 1

In this case its to the power or 2/3 or -2/3 on the top

[violet elbow]

i said 12

m = 12

because of the rule i said above

which is untrue ig

let me show my work rq

[iron vapor]

p^2 and p^3 dont cancel

oh I see

[trim jolt]

@violet elbow Has your question been resolved?

[violet elbow]

so what do you think @iron vapor

[violet elbow]

<@&286206848099549185>

<@&286206848099549185>

[small root]

You can't cancel the 5th root

Like that

[violet elbow]

how then

[small root]

Write it as exponent

Then use
(x^a)/(x^b) = x^ ( a-b)

[violet elbow]

wouldnt that equal the same thing

[small root]

No

[small root]

Oh

Did you raise it to the 5th power?

mb

The mistake is that you raise both sides

So the other side is p^(5m)

[violet elbow]

ahh

?

@small root

[small root]

!noping

[trim jolt]

Please do not ping individual helpers unprompted.

[small root]

No

[violet elbow]

explain

[small root]

How'd you remove the root on p^9

[violet elbow]

took away one of the -1 for p^9 with the additional 5 given from the other power

[small root]

No? That's not how this works

[violet elbow]

explain then

<@&286206848099549185>

[small root]

!noping

[trim jolt]

Please do not ping individual helpers unprompted.

[violet elbow]

tgen help

instead of just saying "that's not it"

cause that's not really helping

<@&286206848099549185>

[mortal elm]

p^43/10

[trim jolt]

@violet elbow Has your question been resolved?

[small root]

I got other stuff dude, I came back cause you pinged me otherwise I wasn't gonna be saying 'that's not it' and leave

Anyways Techno's solution is right

[trim jolt]

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[vale abyss]

Bit confused on how to approach this question

[vale abyss]

I created the linear transformation that represents X1->X2 and Y1 -> Y2

T([x,y]^t) = [x+1, y+1]^t

oh srry

[pearl wind]

I am stuggling with this, i am in 8th grade

[vale abyss]

channel is currently being used

[timid imp]

You need to create your own channel

[pearl wind]

ok my bad

how do i do that

[timid imp]

#❓how-to-get-help

[pearl wind]

thanks

[timid imp]

np

[vale abyss]

.close

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[spiral kettle]

sure is

[marsh forum]

I know

I want to prove this using contradiction

[spiral kettle]

do you have to use contradiction

[marsh forum]

Yes

[spiral kettle]

sob

[marsh forum]

I know it's easy using DP, but c'est la vie

[spiral kettle]

okay, so give me the formal negation of the statement

i can help you translate the original statement to something formal if you want.

[marsh forum]

We wan to prove that if $n \in \Z$ and $n$ is odd, then $n^2$ is odd.We also wish to prove this by contradiction. So we thus wish to prove that the statement if $n$ is odd, then $n^2$ is even is false. As $n$ is odd, it is of the form $n=2q+1$. so $n^2= 2(2q^2+2q)+1$, which is odd. Which is a contradiction, thus our assumption is wrong, $n^2$ must be even.

[solid kiln]

Veni, vidi, perii is not f(wai)

[spiral kettle]

that's not the right statement

[night patio]

should be n is odd and n^2 is even

negation of p implies q turns into p and not q

[spiral kettle]

yes but also there is a universal quantifier at the beginning

[cosmic meadow]

the contrapositive (i think this is the word in english)

[night patio]

oh true

[cosmic meadow]

In the begining

[night patio]

not contrapositive

[cosmic meadow]

What is the word?

[night patio]

contrapositive and negation are 2 different things

[timid imp]

I don't mean to get involved too directly but does the end of the contradiction end up being an even quantity being equal to an odd quantity

[cosmic meadow]

My bad at english then, sorry

[night patio]

contrapositive is not q implies not p <=> p implies q
negation is just ~(bleh)

[timid imp]

asking for myself

[night patio]

nah no worries

[spiral kettle]

yeah in the one that i have in mind.

[timid imp]

sweet

[spiral kettle]

anyways. @marsh forum the negation of the statement would be "there exists an n such that n is odd and n^2 is even"

[marsh forum]

I've written that

[cosmic meadow]

No

You wrote the opposite

[spiral kettle]

you didn't

you are missing a quantifier

[night patio]

and then should be exhcanged for and

implies =/= and

[marsh forum]

Ah yes

got it

:D

[spiral kettle]

okay great.

[marsh forum]

Is the rest of the proof fine?

[spiral kettle]

so now, we are going to derive a contradiction based on the fact that there is some n such that n is odd and n^2 is even.

[spiral kettle]

i really didn't read it, since I figured the entire proof was bsaed off a faulty assumption of what you thought the negation was.

[night patio]

ur concluding statement was flipped

if your assumption is wrong, then n^2 must be odd but u wrote even

[spiral kettle]

it seems like your proof is just the direct proof buried in the language of contradiciton

[marsh forum]

I mean this problems is not something that anyone would ever want to prove by contradiction anyway

[spiral kettle]

okay, here is a contradiction proof that I think you'll find pleasing (and is actually different from the direct proof one)

take n^2 - n

if n is odd and n^2 is even, what parity will n^2 - n be

[marsh forum]

odd

[spiral kettle]

yeah

so now factor n^2 - n

[marsh forum]

$n(n-1)$

[solid kiln]

Veni, vidi, perii is not f(wai)

[spiral kettle]

yeah

but now what parity will that be

[marsh forum]

odd

[spiral kettle]

it's an odd x even

[marsh forum]

wait

oops

even

[spiral kettle]

great

that's a contradiction.

n^2- n would be odd and even.

[marsh forum]

Ah

that's nice

[timid imp]

@spiral kettle what's the other proof you were thinking of

I'd like to see it

[spiral kettle]

yeah this is one of the proofs of all time. of course i think doing it directly is better. I'm not sure what the constructivists think of this proof specifically

[spiral kettle]

what other proof

the one that I had in mind was the one that I just walked through

[timid imp]

nvm

I see lol

[spiral kettle]

I'm assuming you know how to show this directly

[timid imp]

I do

[spiral kettle]

so those are the two proofs that I have for this fact

[timid imp]

I think the way I was doing it was also a contradiction disguised as a direct proof

[spiral kettle]

you can mimic the classic proof here

[marsh forum]

Yeah

[night patio]

or you can use fundamental theorem of arithematic

[night patio]

if u want something a bit different that is

[spiral kettle]

I too can open a lock with a jackhammer

[night patio]

xd

welp fair

it is overkill

[marsh forum]

We wish to prove this by contradiction, so we assume that $(2)^{\frac{1}{3}}$ is rational. so $(2)^{\frac{1}{3}}= \frac{p}{q}$, where p,q are co-prime. so $2q^3=p^3$. If $p,q$ are co prime \frac{p^3}{q^3}$ can't be an integer, so our initial assumption was wrong and $(2)^{\frac{1}{3}}$ is indeed not rational

[timid imp]

@spiral kettle can I dm you the proof I had in mind for the first question? I don't wanna open a help channel for it and I also don't wanna take any space here.

[spiral kettle]

#math-discussion

[timid imp]

👍

[solid kiln]

Veni, vidi, perii is not f(wai)
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[spiral kettle]

why can't p^3/q^3 be an integer.

[marsh forum]

right

I'm confused

[spiral kettle]

you should use the fact that 2q^3 = p^3 at this point

we are going to conclude that p is even.

[marsh forum]

I;m sorry, I think I'll re-read this section and then get bakc to this

[spiral kettle]

okay

[marsh forum]

Thanks!

.close

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[slim mantle]

Howdy, need some assistance with identifying a rational function from its graph. I think I have it mostly solved, but my answer isn't being accepted. Not sure what I'm missing.

[slim mantle]

I determined the x and y intercepts and the vertical asymptotes

x int @ (3, 0)
vertical asymptotes are -3 and 4```

[lilac cloud]

Well think about f(0)

[slim mantle]

yeah, I then used that to solve for a

which i got as a stretch of 4, since f(0)=1

maybe i did an operation wrong tho

the equation i started with was

f(x)=a((x-3)/(x-4)(x+3))

i plugged in f(0)=1

got a((0-3)/(0-4)(0+3))

then that resolved to a(1/4)=1

muliplied both sides by 4 and a = 4

but 4((x-3)/(x-4)(x+3)) wasn't accepted

it looks very similar to me when i graphed it on desmos, so not sure if i'm missing something or if maybe i'm formatting it wrong

oh

it was a formatting error

i needed to distribute the denominator

cool thanks for your insight - it was right on.

.close

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[nimble compass]

Two planes are perpendicular if?

[dusty sleet]

If their normal vectors are perpendicular

[small root]

And if two vectors are perpendicular, their dot product is zero

[empty oasis]

no?

[spiral ocean]

perpendicular not parallel

[small root]

Yea mb

[nimble compass]

Cos90°

So z=4, y=2 are these planes?

@dusty sleet

[dusty sleet]

Yep

[nimble compass]

Can I say are they perpendicular?

[dusty sleet]

Yes

[dusty sleet]

Because of this

[nimble compass]

Let me upload

@dusty sleet

I was trying to check it with an example

[dusty sleet]

I'm not able to answer this, it's too advanced for my skills 😢

[nimble compass]

[trim jolt]

@nimble compass Has your question been resolved?

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[wind python]

I dont get why |A1 n A2| = (3C1)

if x1 > 3 and x2 >4 then x1 + x2 > 7 so shouldnt it be (4C1)?

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[wind python]

<@&286206848099549185>

[wind python]

🤔

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[spiral ocean]

A circus juggler performs an act with balls that he tosses with his right hand and catches with his left hand. Each ball is launched at an angle of $75^{\circ}$ and reaches a maximum height of 90 cm above the launching height. If it takes the juggler 0.2 s to catch with his left hand, pass it to his right hand, and toss it back into the air, what is the maximum number of balls he can juggle?

[solid kiln]

k

[spiral ocean]

dont know where to start

i know projectile

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[wraith arch]

you basically need to find the air time of the ball first

using the information given, just the angle and the maximum height

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@spiral ocean Has your question been resolved?

[spiral ocean]

but isnt 0.2 the air time

@high heron

[wraith arch]

nope

[spiral ocean]

ok

[wraith arch]

0.2 is the time it takes to pass the ball

[spiral ocean]

lemme calculate rq

wait

i made a mistake

0.428 seconds

@wraith arch

[wraith arch]

is that the time it takes to go up only?

cuz i got double that answer

[spiral ocean]

okie

I got it now

what do i do with it

[spiral ocean]

@wraith arch

[spiral ocean]

This is so over

.close

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[zinc zephyr]

i need help

[zinc zephyr]

i dont understand how to get the square roots of decimals

[wraith hinge]

hi

[zinc zephyr]

hi

i can send a pic of the question

[wraith hinge]

Okk

square root of a decimal number can be calculated by using the estimation method or the long division method .

[zinc zephyr]

wdym

[lyric comet]

Convert the decimal into p/q fraction and then take square root of numerator and denominator as they would be positive integers

[zinc zephyr]

ok

thx

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[lethal sigil]

i know the answer, but i'm not sure how to write the equation

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[wraith hinge]

write the number as xy

x,y belongs to [0,9]

so the number would be 10*x + y

[lethal sigil]

okay

so uhh idk where would the 54 come up in the equation

.close

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[rustic nest]

what is the derivative of $\frac{1}{3}\sqrt{y}(y-3)$

[rustic nest]

i did product rulse

f'g+g'f

$\frac{1}{6}\sqrt{y}(y-3) + 1(\frac{1}{3}\sqrt{y})$

[solid kiln]

wakamole

[limpid dawn]

what is dx doing

[solid kiln]

wakamole

[limpid dawn]

your first term looks wrong

[rustic nest]

finally i got $\frac{y-3}{6\sqrt{y}+\frac{1}{3}\sqrt{y} = -\frac{1}{2} + \frac{1}{3}\sqrt{y}$

[solid kiln]

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

bacc the sigma😔🤞

[rustic nest]

but it is 1/3 sqrty

[limpid dawn]

finally i got $\frac{y-3}{6\sqrt{y}+\frac{1}{3}\sqrt{y}} = -\frac{1}{2} + \frac{1}{3}\sqrt{y}$

[solid kiln]

bacc the sigma😔🤞

[limpid dawn]

[limpid dawn]

1/3 is just a factor

[hollow tangle]

Btw bro what time is it for you?

[limpid dawn]

like the 1/6 is correct somehow, but the sqrt(y) should be in the denominator (maybe you meant to do that)?

[tame narwhal]

I need someone to teach me all of geometry by sunday

[limpid dawn]

😂

[hollow tangle]

Bro is geometrymaxxing lmao

[rustic nest]

isnt that what i have

oh i did mean to do that

sry

[limpid dawn]

here it is basically in the numerator

[rustic nest]

my latex

[limpid dawn]

ok I see

[whole coral]

!occupied

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[tame narwhal]

I have to tutor someone on monday and i have never taken geometry a day in my life

[rustic nest]

yes i have it in denominator

yea that is what i hav

[rustic nest]

left term the 1/3 sqrt(y) should be seperated by + sign

but the final i got is correct

in latex...

idk if it is actually correct though

[solid kiln]

bacc the sigma😔🤞

[rustic nest]

yeah i have that

[hollow tangle]

You need f(y)?

[limpid dawn]

Now you put them together

[whole coral]

@hollow tangle

[limpid dawn]

I mean from now it's algebra basically

[rustic nest]

i got. this.. the term on the right

well the first term on the right should also have sqrt(y) in numerator

idk how i got that looking at it now

[limpid dawn]

,w D[sqrt(y)/3 * (y-3),y]

[rustic nest]

i asked wolfram it was horribly wrong for some reason

[solid kiln]

bacc the sigma😔🤞

bacc the sigma😔🤞

bacc the sigma😔🤞

bacc the sigma😔🤞

Results provided by WolframAlpha

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Requested by adoniszgks

[limpid dawn]

there you go

[rustic nest]

wow ty

i am doing arc length so now i can go ahead and setup my integra

[limpid dawn]

yea do that

good luck

[rustic nest]

thanks. is it cool if you remain here?

[limpid dawn]

[rustic nest]

lol

[limpid dawn]

i wanted to eat a sandwich

what do you need

[rustic nest]

i mean how am i supposed to maekt that into a perfect sq

[limpid dawn]

perfect square?

[rustic nest]

ya

[limpid dawn]

what are your bounds

[rustic nest]

1-9

1 to 9

[solid kiln]

bacc the sigma😔🤞

[rustic nest]

i have that