help-23

[kind dove]

are there 3 inversions?

• (odd)

[remote hamlet]

Ok

If you get even for (13) though maybe you didn't exactly get the procedure

[kind dove]

its odd

i missed 1 inversion

[remote hamlet]

Oh, good then

[kind dove]

then (23)

(23)(23) = id

and parity is odd because there is 1 inversion

[remote hamlet]

Yes

[kind dove]

now (123)

i did (123)(123) and i ended up with (312)

and when I composed (123)(312) I ended up again with (312)

[fiery merlin]

(123) = (312). You can rotate the end number to the beginning and have it do the same thing.

[kind dove]

hmm

how to determine order now ,

?

[fiery merlin]

(123)(123)

1 → 2 → 3
2 → 3 → 1
3 → 1 → 2
4 → 4 → 4

So, start with 1 (1⋯), that becomes 3, so write that next (13⋯). 3 becomes 2, so write that next (132⋯). 2 becomes 1, so we're done (132).

(123)(123) = (132).

[kind dove]

hmm

so 132 is same as 312 ?

[fiery merlin]

No, (312) is the same as (123).

You got (312), but that was wrong.

Another way to see it is this.

There's only one identity permutation.

Identity permutation is the one that you apply and it leaves things the same.

(123)(123) = (123) means that (123) is the identity permutation, since it made no change when combined with (123).

But that's false.

(312) is just another way of writing (123).

So, you were saying that:

(123)(123) = (312)
(123)(123) = (123) [rotating the numbers in it leaves it the same]

Like (123) = (312) = (231) = (123).

(12) = (21) = (12)

And so on.

People usually start them off with the lowest number.

So, (231) should start off with 1.

1 is the lowest number, (1⋯).
1 turns into 2, (12⋯).
2 turns into 3, (123⋯).
3 turns into 1, so we've gone through everything, (123).

Does that make sense?

[remote hamlet]

You can start to see why in general a cycle of length n has order n

[kind dove]

so (123)(123) = (132).

and now i have to compose (123)(132) ?

[fiery merlin]

Yes, you can tell by applying the permutations:

1 → 2 → 3
2 → 3 → 1
3 → 1 → 2
4 → 4 → 4

Then, you notice that 1, 2, and 3 are changed.

You write (1⋯). 1 changes to 3, so you put that next (13⋯). 3 changes to 2, so you put that next (132), and you're done because you 've handled all the moved numbers.

[remote hamlet]

Yes

[fiery merlin]

You can skip a bit of work by just doing (123)(123)(123)

1 → 2 → 3 → 1
2 → 3 → 1 → 2
3 → 1 → 2 → 3
4 → 4 → 4 → 4

If you had it written out like that.

[remote hamlet]

In that precisely, you see that for a cycle of length n, each number gets sent in itself after n iterations of the cycle

And no sooner

As if each number "travelled" through all the cycle until it reaches back to its same position

[remote hamlet]

Hence why this

[kind dove]

i think i got it

and parity of (123) should be even

it has two inversions

[remote hamlet]

Yes. Again in general, maybe in the future you'll see that a cycle of length n>=2, has parity (-1)^(n-1)

[kind dove]

and (132) has order 3

(132)(132) = (123)

and (132)(123) = id

and it has even parity

two inversions

[remote hamlet]

Yes

[kind dove]

ok thanks guys a lot for help

[remote hamlet]

Don't you also have to see if H is a subgroup?

[kind dove]

yes i have, but I will try it tomorrow...

[remote hamlet]

Ahah, ok

[kind dove]

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[umbral olive]

need help

[lean otter]

simplify $1 + 1/14$

[flat frigate]

Mrlol22

[lean otter]

what is it

@umbral olive

Remember to find the common factor

[lean otter]

u mean the lcm

Least common factor

Yes

[ruby kettle]

first simplify the mixed fraction

[lean otter]

least common multiple bro

[ruby kettle]

then lcm

[lean otter]

yes i said that

[ruby kettle]

oohok

[lean otter]

is he/she even there?

[lean otter]

My bad Xd

[ruby kettle]

could you come look at mine

[lean otter]

ok

[umbral olive]

yes ngl

[lean otter]

ok hello

have you simplified teh mixed fraction?

u can say yes or no

I can't help u if u don't talk

[umbral olive]

yes i have

[ruby kettle]

could u share what u got

[umbral olive]

yeah its 1 1/14 still

[lean otter]

11/14?

[umbral olive]

no 1. 1/14

[lean otter]

yeah so simplify that

u know how to simplify mixed fractions right?

[umbral olive]

its already simplifed tho

[lean otter]

1+1/14 is simplified?

its a mixed fraction

[safe radish]

@umbral olive Has your question been resolved?

[umbral olive]

wait so how do you simplify mixed fractions again

[cursive saffron]

Here are some examples of mixed fractions being simplified:

3 + 1/2 = 7/2
14 + 5/3 = 47/3
Don't look at this one until you're 100% on your answer
||1+1/14 = 15/14||

[umbral olive]

ah

i think i got it

so it would be - 2/21 + 15/14

[cursive saffron]

Yes, but now there's another issue

You can't add them directly

Do you know why?

[umbral olive]

they're not in their lowest form?

[cursive saffron]

Not quite

The denominators are not equal

[umbral olive]

so i x it by 3?

[cursive saffron]

What do you multiply by 3?

[umbral olive]

15/14 x 3 = 45/42* | 2/21 x 2 = 4/42 | 4 + 45/42 = 49/42

[cursive saffron]

Not quite

The initial question states

-(2/21) + (1+1/14)

15/14 * 3 is 45/42

2/21 * 2 is 4/42

So what's wrong with your answer?

[umbral olive]

not simplifed?

[cursive saffron]

Not quite

It's not correct

You should have -4/42 + 45/42

Which is 41/42

[umbral olive]

ohh

ty

wait wouldnt it be -4/21

[cursive saffron]

No

You're multiplying the numerator and denominator by a scalar

[lean otter]

no need to do all that

just find the lcm of 14 and 21

u know how to add fractions?

[cursive saffron]

Which is the same as multiplying both fractions by scalars...

[lean otter]

maybe he doesn't know scalars and vectors

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[umbral olive]

.reopen

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[umbral olive]

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[runic matrix]

hi

[runic matrix]

what is the soltuion to log3 (x+2)^2=2

i have already found that there are 2 solutions 1 and -5

but i think that -5 is not accepted

the answer says that it is

can someone explain me how to find the existence domain of this logarithm?

never mind i solved it myself sorry

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[lean otter]

how are these two images equivalent?

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@lean otter Has your question been resolved?

[lean otter]

(x1 + y1)^2 = (x1 + y1)(x1 + y1) = (x1)^2 + 2x1y1 + (y1)^2. i understand squaring both sides but how do u expand?

[lean otter]

the expanded form i wrote here doesnt align with the author's intentions

o wow im an idiot lmao

thnx

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[lost tree]

hey so I was having some problems with cleaning up a equation. (xa-4y)^4(x(b^2)/a -y)= y

[lost tree]

I need to find a solution in for y without y in the left side of my equation (if that is even possible)

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[lost tree]

<@&286206848099549185>

I don't really know where to start, I can start solving the equation as much as possible but I'm not sure if that will bring me any farther? is there a effective strategy I can use to tackle problems like this

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[lost tree]

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[strange quest]

Quick physics question, if I had two springs with masses, both vertical, but one with the mass on top and the other with the mass on the bottom

[strange quest]

assuming there is no external forces being applied and energy is conserved

Would they behave the exact same?

[strange quest]

other than gravity

Basically does this

https://cdn.discordapp.com/attachments/609930663076036635/955979458957963274/unknown.png

behave the same way as this

https://cdn.discordapp.com/attachments/609930663076036635/955979782087135312/unknown.png

[static ledge]

i would think so, since the only other force in this scenario would be the applied force of the spring caused by gravity. if you're looking for answers to physics questions, though, i'd recommend you follow the invites in #old-network to the Physics discord server

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[rustic depot]

im stressing out

[rustic depot]

oh wait

this is a math server

oops

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[lean otter]

so there is one tough polynomail i was assigned to fully factor and find the roots of, but there is a small issue, my final pollynomial is impossible to factor, im not sure if im missing any steps

[lean otter]

sorry ill save your eyes by fliping it lol

[dim pecan]

Your first long division is correct

Your second is wrong

[lean otter]

wait how so? final product has a reminder of zero

[dim pecan]

Nevermind, it is right

You can factor that quadratic

I assumed you can't based on what you said

[lean otter]

yeah i was having a little brain fart processing that lol

yeah

thats strange

[dim pecan]

Do the quadratic formula

[lean otter]

yeh ill try that

wow ok this worked out nicely, i did get a zero, 4+-sqrt(0)

i was something not real or at least a fraction

x=2

sweet

thanks for your help @dim pecan

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[sour wraith]

how can i solve this?

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[wanton zodiac]

Plot the point that has the given polar coordinates.

(−1, 7π/6)

Give two other polar coordinate representations of the point, one with r < 0 and one with r > 0.
(r, 𝜃) = (smaller r-value)

[wanton zodiac]

I already plotted the point I just need to understand how to find a smaller value

<@&286206848099549185>

<@&286206848099549185>

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[pliant garnet]

how does this work?

[potent roost]

It's defined that way I think the derivative of e^x is e^x so is the antiderivative

[pliant garnet]

oh you are taking the derivative I had no clue xD

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[toxic stone]

may i know is it true that only 1 and 5 is correct?

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.reopen

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[opaque prism]

try to identify all the elements in 1 to 7

identify one by one

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[toxic stone]

yea i have done it

thus i came up with only 1 and 5 is right, am i right bro?

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[opaque prism]

wrong

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[toxic stone]

Ok bro

[dim pecan]

Just 1

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[drifting cairn]

hello

[drifting cairn]

this is my question:

im confused for c)

i know for a its definite integral basically

d) is FTOC part 2 which is straightforward

and b is just part of application

however for c) im a bit confused

<@&286206848099549185>

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[lean otter]

this is the questions i need help with:

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[calm egret]

Hi There

[calm egret]

I have a question regarding a certain statement

Can anyone describe through FOL how I can setup an infinite set with bounds that do not have numbers in between them?

So I was originally thinking like the set of rationals with upper and lower bounds but

if you pick two elements in the rationals there are numbers in between those rationals

Or perhaps do I have to state specifically that there are no elements in between

Or since the set of rationals is dependent on the denominator that it still is infinite

[drowsy moss]

what is FOL?

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[calm egret]

first order logic

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[idle grove]

What do you exactly mean by bound, because it seems to be a property of real numbers (continuous) and taking any 3 numbers there will be always a number between other two

This is a bit cheating but since complex numbers do not have order you can take a closed region of the complex plane and they will be infinite and with no element between any two element(since there is no order)

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[calm egret]

So

Like from 0 to 1

With two conditions

1. for any element y that isnt the minimum bound, there is some element x such that x < y as well as there should be no elements in between x and y

2. for any element x that isnt the maximum bound, there is some element y such that x < y as well as there should be no elements in between x and y

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[red gust]

what is the law of indices

[red gust]

and how do i apply it too (to?)

[neat spruce]

these are the simple laws of indices

you can express your problem in terms of powers

[red gust]

oooooohhhhhhhh

okay

[neat spruce]

try to express them as powers and then subtract the powers for the division

[red gust]

that makes alot of sense

alot more sense then it written out

thank you for saying something i prolly couldve googled

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[rough socket]

How can I prove that the matrix A is positive definite?

[rough socket]

I found out that the following must hold true for the matrix to be positive definite x^T A x must be greater than 0 where x is a non-zero column vector of real numbers

[hazy veldt]

hi

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[rough socket]

<@&286206848099549185>

[rough socket]

Not how to sure how to apply that to a matrix of arbitrary dimensions

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[cosmic grove]

they didn't give you the dimension of A ?

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[rough socket]

Not a specific dimension, we had to build a recurrsive algorithm for principal minors. I think I managed to prove it though - based on the recursive algorithm for principle minors that they are all greater than 0 so the matrix is positive definite.

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[elfin yew]

@vivid idol what are u tryna do

[vivid idol]

I am trying to solve for m and n

How do I start simplifying this

I have difficulty simplifying the (25/16) ^ 3/4 part

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[dreamy finch]

what is the best way to learn the trig identities that are used for integrating on the ap exam

[dreamy finch]

ap calc bc

i never learned them in my class

[limber smelt]

best way to learn then is by using them alot.

just do alot of practice questions

[dreamy finch]

no but i dont even know what they are

like i literally never touched upon them

[winter pivot]

Mostly cos^2 and sin^2

Those come up in polar integrals

[dreamy finch]

so jsut know that cos^2+sin^2=1?

[winter pivot]

Not just that

Can you integrate cos^2(x)?

[dreamy finch]

i do not know how to do that

that is actually the exact problem that led me here lol

[winter pivot]

The ultimate cheat code is to learn eulers formula

That lets you rederive everything on the spot

[dreamy finch]

oh okay

because my class skipped over eulers method lol

[pulsar condor]

use double angle.

[dreamy finch]

we skipped so many bc subunits

i dont know what that is

[pulsar condor]

$\cos(2t)=\cos^2(t)-\sin^2(t)=1-2\sin^2(t)=2\cos^2(t)-1$

[flat frigate]

Mosh

[dreamy finch]

is that unit 7.5, approximating with eulers method?

[pulsar condor]

no

Euler's formula

$e^{ix}=\cos(x)+i\sin(x)$

[flat frigate]

Mosh

[dreamy finch]

is that in the curriculum, or is that just something that is recommended i learn

so if eulers formula includes e, how could i integrate a function that is cos^2?

[pulsar condor]

You'd use double angle

to which you can rederive the double angles from Euler's Formula

[dreamy finch]

how would i do that since the formula has an e in it?

or should i just watch a video on what eulers formula is because ive never heard it before

[pulsar condor]

The better thing would just be learn the double angles imo

if you havent reached C numbers yet.

[dreamy finch]

are there any other trig identities i should know for integrating?

cuz i know the most basic one since that's easy to remember

[winter pivot]

true. i just personally have a very hard time remembering trig formulas so if i ever need them i just rederive them

[pulsar condor]

memorize all the cos^n and sin^n \s

[dreamy finch]

say what

wait so should i just remember the double angle trig identities?

[pulsar condor]

you should remember the fundamental ones

pythagorean, quotient, reciprocal definitions, double angle

[dreamy finch]

okay thank you

i cant find this in the units online

last question

the first fundamental theorem of calculus (about integrals) states the thing that f(a)-f(b) is the solution to the definite integral, right

the second fundamental theorem is the derivative of the integral, right?

[safe radish]

@dreamy finch Has your question been resolved?

[pulsar condor]

this is poorly phrased imo

$\int_a^b f(x)\dd{x}=F(b)-F(a)$ where $F'(x)=f(x)$ is FTC2

[flat frigate]

Mosh

[dreamy finch]

yeah my bad

but those are still the fundamental theorems of calc

i just didnt fully wanna write them out, but i know in detail the 2 things i just messaged, but those are still the 2 fundamental theorems, righ?

[safe radish]

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[worldly siren]

is there an easy way to do this integral? $\int \frac{4x^2-15x+15}{4x^2-16x+15}$

[flat frigate]

lmaoborghini

[queen parcel]

I can't think of anything immediately, but you can check integral-calculator on Google

What if you added 1 and subtracted 1 in the denominator

You get 4x^2 - 16x + 16 - 1 = (2x - 4)^2 - 1

[worldly siren]

i havent tried doing it that way

[pulsar condor]

$\int 1+\frac{x}{4x^2-16x+15}\dd{x}$ no?

[flat frigate]

Mosh

[worldly siren]

I did it that way

it kinda gets tedious after that tho

i mean its fine as a homework question but I'm worried that it might show up on an exam

so im just wondering if theres some kind of shortcut

[queen parcel]

This approach sounds good on the surface to me

Try it

[worldly siren]

alright

I can't really do anything with it

and when I use a calculator it just ends up expanding the denominator back to the original form

well Ill just hope that stuff like this won't be on the exam. thanks for the help

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[nova solar]

heyyyoo, could yall help me out

[timber atlas]

If an is equal to ef then we can set the equations equal to each other

And solve for x

Similar for rest of the questions

[nova solar]

an?

yea but, how would i get the measurement for AB

[tame raft]

so for example for 1

AB = EF

so 3x - 9 = 2x - 3

[potent roost]

Yes

[nova solar]

then what do i do with this?

[tame raft]

it's a very basic equation

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:linear-equations-variables-both-sides/v/equations-3

here's a video

[nova solar]

alright that helped

so im assuming

that the answer, or the outcome of that equation

is the measurement?

[potent roost]

x wouldn't be the measurement

the question says what the equation for the measurement is

substitute the value of x in it to get the answer

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[abstract drum]

Help I am lost on what to do?

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[trail star]

I solved P(2,4) while Q(6,4)

[trail star]

I also noticed the working to answer that involves using this formula

But how do you determine which values to plug in for y1 and y2?

[crisp oxide]

The points that the two functions intersect

[trail star]

But how to know which is which

[crisp oxide]

you mean which value would be x1 and which would be x2?

[trail star]

yeah which one should be y1 and which one should be y2

[crisp oxide]

Px would be x1 and Qx would be x2 since you integrate from left to right

also

the integral is in terms of x so the limits should be in terms of x

[trail star]

Oh, I was just using y1 and y2 for the lines and curve at the graph

I will substitute them with their respective equation

[trail star]

Ok thx, this is what I wanted to know

[crisp oxide]

👍

[trail star]

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[lean otter]

Simple question, how does the 2 become simplified

In the second to last part

[tepid portal]

distribute it into the squareroot

[lean otter]

Ahh

Right

Thanks

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[spice grove]

What have you tried?

[warm plaza]

17

[spice grove]

17 what?

[warm plaza]

17 days

[spice grove]

How can that be? 12 machines do the work in 20 days.
When there are only 8 working for the first 9 days. That means of course this should take more time, no?

[warm plaza]

Nervermind I have the answer now it was 23 days

[spice grove]

It is.

Correct.

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[keen jasper]

Good morning everyone,

I have to solve an exercise that require to write the cartesian equation of the tangent and normal line for the curve given in polar form:

r(θ)= θ + e^(1+θ), θ in [-1,1]

[lean otter]

Is it possible to convert the polar equation to Cartesian?

[keen jasper]

I'm sure it's possible to convert Cartesian to polar

but i'm not sure about the opposite

Anyway, I think that if I could find a way to convert r(θ) in a function of sin and cos, I would be able to convert it

[lean otter]

Im not sure about this brach of math myself so im just spit balling ideas

It might also be possible to treat the polar equation like a Cartesian one, but just one that has been wrapped around the origin in a spiraling manor, get the derivitive as a cartesean, and somehow transform it back by re wraping it around the origin

[keen jasper]

I don't know what you mean. I can treat the polar eq like a Cartesian one, for example parameterizating (I don't know if this is the right expression in ENG) the eq finding a curve that has the same character of the polar one. But the problem is always converting it to a cartesian equation

You know a way to convert r(θ) in a function of sin(θ) and cos(θ)?

That would help me a lot

[lean otter]

id assume that you could jsut apply the point conversion upon the whole equation

where r (the radius) is r(θ)

but you still have a parametric equation based on θ

so you either have to convert to a Cartesian or take the derivitive as a parametric

you can convert to a carteasen easy enough

$P_x(\theta) = x \ P_y(\theta) = y \ \Rightarrow \ P_x^{-1}(x) = \theta \ \ P_y^{-1}(y) = \theta \ \Rightarrow \ P_y^{-1}(y) = P_x^{-1}(x)$

[flat frigate]

aspwil

[lean otter]

will give you a cartesean equation if the parametric x and y are invertable

do you understand that?

[safe radish]

@keen jasper Has your question been resolved?

[keen jasper]

I need sin(θ) and cos(θ) for exctractin x and y

[keen jasper]

this formula is what I want to use, but for using it, I think that i need θ + e^(1+θ) to be in a sin, cos form

[lean otter]

$x = r(\theta)\cos{(\theta)} \ y = r(\theta)\sin{(\theta)}$

[flat frigate]

aspwil

[lean otter]

the other idea (just for sharing sake) is that you can graph the polar equation as a carteasesan

[keen jasper]

nevermind aspwil, thanks anyway

for trying

[lean otter]

okay

[keen jasper]

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[worthy rain]

Is this correct?

[mortal meteor]

yes, but you can simplify it further

[worthy rain]

With a square root, right?

[mortal meteor]

no: notice that v^2=|v|^2

[worthy rain]

But that's a u not a v.

[lethal musk]

oh

then yeah that's the simplest form

[worthy rain]

Thanks!

how do I close the channel?

[mortal meteor]

that explains it 🙂 Closing is with ".close"

[worthy rain]

Yep

.close

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[lean otter]

y = x + 3 ;

D {3, 4, 5, 6, 7} = ???

[umbral apex]

Uhm well the values can be anything unless you provide with some restrictions to what they should be

[lean otter]

Im still new with this lesson and I do not understand anything at all.

[umbral apex]

Well don't you think the values can be anything?

If you don't restrict the question

[jade gust]

Is the set D the domain restriction?

[lean otter]

Yes

[jade gust]

ok so just substitute those values in?

[umbral apex]

Now I'm getting curious

[jade gust]

Is how you should properly denote it

[lean otter]

Well the instructions say solve for the range of each equation if the given set is the defined domain

[jade gust]

So just insert the lowest and highest value in your restricted domain?

Then the range should be between there

since that's linear

[lean otter]

Ohh alright

Thank you

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[summer jasper]

could someone explain how the equations at the bottom were obtained?

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[summer jasper]

.reopen

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✅

[plucky elk]

where even is the original question?

[summer jasper]

this

[plucky elk]

that's just notes?

notes that are barely legible

can you type what it says here

[summer jasper]

yes, I want to know whether those equations are some kind of standard form

just a moment

[summer jasper]

these are some of the better ones made by my teacher lol

Formation of a PDE(partial differential equation) by elimination of arbitrary constants.

Let f(x,y,z,a,b) = 0
where a and b are arbitrary constants

Differentiate equation 1 partially w.r.t x and y respectively

we get:

It would be great if you could even just point me in the right direction. No one has been able to tell me how we got these equations

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[cunning tundra]

Hi ^^ im really struggling with this question and i feel like i fundamentally dont understand it. Im supposed show that given x_1, x_2, x_3 e R that V = (x_2-x_1)(x_3-x_1)(x_3-x_1) using row operations. I do know however how to use row operations

[iron garden]

what 1+2

[cunning tundra]

what?

[iron garden]

nvm I gotit

[dense kelp]

@iron garden
dont waste time

[iron garden]

did you type for 2 mins to say that

[dense kelp]

yes

#discussion

[cunning tundra]

<@&286206848099549185>

If anything isnt understandable please let me know

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[safe radish]

@cunning tundra Has your question been resolved?

[cunning tundra]

halp

[safe radish]

@cunning tundra Has your question been resolved?

[cosmic grove]

let call the rows respectively r1, r2 and r3
r2 <-- r2 - r1
r3 <-- r3 - r1
you will have :

V = [1 x1 x1² ]
[0 x2-x1 x2²-x1²]
[0 x3-x1 x3²-x1²]

after r3 <-- r3 - r2
you'll be left with :

V = 1 x1 x1²
0 x2-x1 x2²-x1²
0 x3-x2 x3²-x2²

[cunning tundra]

how does this show v = (x_2-x_1)(x_3-x_1)(x_3-x_1)?

[feral linden]

It’s all on the internet, vandermonde determinant

[cunning tundra]

ill look it up

[cunning tundra]

ty you both so much ❤️

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[vapid wasp]

find the remainder when $3^{2^{n}}$ is divided by $2^{n+3}$

[vapid wasp]

I checked for n=1,2,3 and remainder is not constant. therefore there are must be some expression equals to the remainder when n=k for some natural number k

and the pattern was like $2^{n+2}+1$

[vapid wasp]

to prove that I tried to use induction but I got nothing at all

can someone help me please?

[plucky elk]

show your work

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[vapid wasp]

nevermind, just by a tiny mistake I was stuck, induction did work

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[sage brook]

what fomula should i use for this?

ive been trying (1+r/m)^mt

but

i dont knwo if thats riht

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[violet sundial]

for part B would it be a geometric sequence? @sage brook

$P = $200,000, r/m = 5%, mt= 11 and

[sage brook]

nvm got it

.cloes

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[flat frigate]

Vertox

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[ripe gale]

little type in the one before

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[orchid rover]

how do i use the sandwitch theorem to prove the limit of this when (0,0) is 0?

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[zinc berry]

The usual way to do this is to take the absolute value and show that the upper bound tends to 0

In this case, you can prove that |f(x,y)| <= |x| + |y| then the limit of the right side is clearly zero. But there are many inequalities that you can come up with depending on how you play around with things.

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[sharp totem]

how do I prove that the eigenvalues of legendre eq'n are real?

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[golden pecan]

Hello

[golden pecan]

Can someone help me understand this

The exercise is asking me to prove R^2 is a field and gives me this definition

i just dont get how they get this

[crisp linden]

Not really important to your proof

But again, it doesn't matter to you why they chose this definition if you're just asked to prove it's a field under those operations

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[lavish ocean]

This is my lectures worked example on solutions by integrating factors I understand it until it gets to solving for y(x) my thinking was since y(x)x=y(x)r(x) and I have the variables y(x)x and r(x) I could change it to y(x)x/r(x) but that doesn’t line up with the values he got for y(x) sorry if this is confusing to read but help is appreciated as I’m doing an open book coursework with a question similar to this and am stuck on this step

[lavish ocean]

I thought it would be y(x) = (c+x^4/4)/x

<@&286206848099549185>

[crimson field]

,rotate

[crimson field]

You understand all the work and following on from it you get the answer y = (x^4/4 + c)/x but the answer given is different to this?

[lavish ocean]

Yeah the answer the have for y(x) = (c/x)+(x^4/4)

Sorry x^3 not 4

[crimson field]

Observe that (x^4/4 + c)/x = (c/x)+(x^3/4).

Basically, both answers are the same.

[lavish ocean]

That’s helpful could u explain how that is I’m happy that I’ve got the answer right but curious about the form change

[crimson field]

$y = \frac{x^4/4 + c}{x} = \frac{x^4}{4x} + \frac{c}{x} = \frac{x^3}{4} + \frac{c}{x}$.

[flat frigate]

stabulo

[lavish ocean]

Thank you

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[stuck garnet]

0,2/0,25x100 can someone show me this on the paper about how to solve it by steps am confused

[stuck garnet]

as a grade 10 idk how i forgot to make this thingy

[lost ridge]

You can multiply numerator and denominator with 100 (to get rid of decimals) to make the division easier

[stuck garnet]

welp i did but how i can just 2/25

am confused

[lost ridge]

You have a 100 on the numerator too

Your fraction is basically = (0.2 * 100)/0.25 = (20*100)/25

[stuck garnet]

oh

lemme check

welp where i got the 20*100 isnt that goes rip on the turning the 0,2 to 20

am so dumb

[lost ridge]

Umm, you started with (0.2*100)/0.25 right?

[stuck garnet]

yes

no

no

like i started with 0,2/0,25 x100

[lost ridge]

Yes, that's the same haha

[stuck garnet]

am dumb.

[lost ridge]

So, to simply your division you can multiply numerator and denominator with 100

(0.2 x 100/0.25 x 100) x 100

[stuck garnet]

oh

now i got it

thank you friend!!

[lost ridge]

Cheers!

[stuck garnet]

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[visual river]

Question 10 b) is what I need help understanding

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[visual river]

Question 10 b

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[lean otter]

I would be happy to start learning about this cause I know nothing

[warm niche]

this is easy just add up all the sides

for example

first question:

3+8+7+2+16+7 and you also have to add the missing sides: 16-7-3=6 and 14-2-8=4 so its 53cm

[thin bridge]

53cm is incorrect

watch what you're adding

also don't give solutions away

[lean otter]

wait so how to solve it then?

[thin bridge]

one way is to determine the missing sides and add up the values properly

[lean otter]

And how do we find the missing sides?

I see the missing sides

[thin bridge]

segment addition/subraction

[warm niche]

yes what ever that is

[lean otter]

Can you please give or explain it?

[thin bridge]

do you know addition/subraction?

[lean otter]

Yes !

[warm niche]

like a 3 sides add up to 10 two of the sides are 2 and 7 and missing side would be 1

[thin bridge]

segment addition/subtraction is just doing that with lengths of line segments

[warm niche]

for the second question

break the shape down to familiar shapes

like a rectangle

that is called a compound shape

[lean otter]

So for q1 the answer is 54?

[warm niche]

53

you probably miscalculated

[thin bridge]

no

you both miscalculated

[lean otter]

bruh

hmm

Wait then how ? I tried but still 😭

[thin bridge]

you seemed to only identify one of the missing sides

and ignored the other

[warm niche]

oops

wait

let me figure it out

[thin bridge]

and there's a nice trick that i'll reveal that avoids tedious calculations

[warm niche]

okay

can u reveal it lol

i got the answer

i forgot a side

i wait

i think i know what trick it is

[thin bridge]

(after you find it the long way)

[warm niche]

i can just do this right 16x2+14x2

[lean otter]

Wait I think ur correct

Because the same shape

Is a sqaure

And square has same sides

[lean otter]

I feel like this is correct

Hello?

<@&286206848099549185>

Oh wait it didn’t pass 15 minutes

Sorry

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

@helper

<@&286206848099549185>

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[blazing cloud]

am i dumb or can sqrt(1+(1/t^2)) be simplified in a clean way?

[plucky elk]

this channel's occupied. read #❓how-to-get-help

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[bleak kraken]

Can someone explain to me how to solve using z table further? I tried to understand it by reading the instructions on my book but I seriously have no idea what to do

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@bleak kraken Has your question been resolved?

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@bleak kraken Has your question been resolved?

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@bleak kraken Has your question been resolved?

[calm elm]

are you allowed to use calculators?

[bleak kraken]

I'm not sure how I can solve it in calculators but if you mean if we are allowed to solve it with calculators approved by our teacher in class then yea

[calm elm]

so if you use an nspire

oh bruh mines ran out of bat

ok

so

[bleak kraken]

I'm trying so hard to understand how but it's just so many things to take in for my perspective

[calm elm]

the ap exam allows calcs you ill just use it

so the first picture up there

x is the z

[bleak kraken]

So I just put " x = -0.31 "??? (the number 1 in the exam is not included so I'm not putting that)

[calm elm]

wwiat

wait

[bleak kraken]

This (number 1 not included)
I habe to use z table but I'm not sure how to do that 😢 😢

[calm elm]

.1587

[calm elm]

ok lets do that first

yoou here?

[bleak kraken]

Yeah sorry I'm using a Calculator rn to show what I get

[calm elm]

ok

[bleak kraken]

Idk what this is 😭 😭

[calm elm]

hm

question 1

yeah

thats off

you got an nspire?

[bleak kraken]

Question number 1 was not included because our stats teacher already answered it so it's just 2 - 5

[calm elm]

what was the answer for 1 then

[bleak kraken]

Hold on

[calm elm]

yes

thats correct

[bleak kraken]

(I know it looks bad but that's how he writes sorry)

[calm elm]

you got an nspire

?

[bleak kraken]

So the answer that resulted is right?

[bleak kraken]

Also no

[calm elm]

oh...

you gonna need one for status

stats

unless you wanna memorize that whole graph up there 💀

[bleak kraken]

I'm still in online class (yeah ik it sucks) so our teacher doesn't expect us to habe different types of calculators cuz we don't see him eye to eye 💀

[calm elm]

you taking the ap exam?

[bleak kraken]

Yeah, well actually it's just module I need to submit

[calm elm]

well

i strongly

recommend buying the calculator asap

an nspire

because you are allowed to use on in the ap exam

[bleak kraken]

Is there an app like it? If I can't buy it now maybe an app would be faster

[calm elm]

uh

hmmm

lemme see

[bleak kraken]

This?

[calm elm]

wait

im downloading

a file

from the website

gimme a min

[bleak kraken]

Okie

[calm elm]

oh beautiful

[calm elm]

mind if i send a link

[bleak kraken]

Sure

[calm elm]

ok ill dm you

oh uh

[calm elm]

im not friended

[bleak kraken]

Oh sorry

[calm elm]

all good

[bleak kraken]

Turned on dms now

[bleak kraken]

.close

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[regal furnace]

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[trail star]

Can anyone tell me, what is the name of this method of integration?

[trail star]

Integration by substitution?

Oh

So its a distinct method

Ok ok thx

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[lean otter]

I have problems with this

[blazing cloud]

what u looking for?

[lean otter]

Okay I need to know how to get the answers

[blazing cloud]

oh like a b c and d

tghe angles

[lean otter]

Yes

I have to find the missing angles

[blazing cloud]

ok lets look at number 1

look at angle of 60 degrees

it is on a straight line right?

[lean otter]

Yes

[blazing cloud]

so how many degrees is a straight line?

[lean otter]

180 degrees

[blazing cloud]

good

so u have a given 60 degrees,

and u know it totals to 180

now what?

[lean otter]

180-60

[blazing cloud]

bingo!

[lean otter]

120

[blazing cloud]

perfect

now that is that angle to the right of 60degrees

which means the angle diagonol to it

[lean otter]

Which is B= 120

[blazing cloud]

no

b is 60 degrees

im tellin him this becuase it is needed fore the other missing angles

[lean otter]

Oh as they are the smae

*same

[blazing cloud]

now look at angle c

it looks the same as the 60 degrees reight?

[lean otter]

Yes it does but C kinda looks smaller

Ohhhh

[blazing cloud]

i beleive it is the SAS

side angle side

so angle b is 60 degrees which means angle c is also 60 degrees because it is the same as the given 60 degrees

[lean otter]

oh wait

OHH

[blazing cloud]

which makes angle a 60 degrees becuase it is the same as angle b

[lean otter]

this makes so much sense

But doesn’t the A look smaller?

[blazing cloud]

well we know that angle b is 60 degrees right?

now we can compare the given 60 segrees to the c value, which we can conclude that c does infact equal 60,

its this problem where all angles are the same

plus, if u were to add all thoes angles up, you would get a total of 180

per line...

which proves to us that these answers are correct

all these angles are supplementary to eachother

[lean otter]

It’s amazing seeing people have math discussion

[lean otter]

Ohh

[blazing cloud]

also

check it out

u can tell that all thees angles are acute too

they dont look more than 90 degrees

so tahts anotehr hint

which other angle?

well obousoly,,,,

no

nonono

im not sayin that!!!

im saying the 180 applies to the straight line!!!

look at the straight line!!

look at the given angle 60

look here

look at the angle to the right of the 60

its missing right?

its blank right?>

a straight line has a degree of 180

180-60= 120.... which is that missing blank angle

not angle b.... but the missing angle which is blank

it is somewhat relevant here

let me finish son

it is some what relevatn here because you can now determine the other one too

its another way to solve this

since u know that is 120

u can look diagonly to that other angle

which is also 120

applying that same knowlege

120+?= 180?

its 60

so ur answer is 60

for b

actually

yes

this is an elementary problem

no

youre right, a 90 degree angle will have an indicator

so ur proint is wrong

LOL

i just proved to u that it is infact 60 degrees

bnased on supplentary angles

and by looking at it too 🙂

😉

u can tell 10000% that angle b is NOT bigger than 90 degrees

i just told u a valid argument

LOL

youre just adding this extra of looking

supplemntary is pretty valid

LOL

it works in all ways

right, but im trying to word it to this guy who is asking for help

cuase clearly he didnt understand ur method

and he understood mine

amirite?

either method works and i figurfed he understood it

cause he did said he got it

[lean otter]

YE

We could see that the angle known which is 60 is looking same as B , ( and maybe from what I understood is that 180- 60 = 120
120- 60= 60 there fore B is 60

[blazing cloud]

they are just complentary angles

obvously u cant.... but u can tell that its less tha 90 degrees

so that is a hint to what it could be

u will get an indicator saying that it is 90 degrees

not nessesearly

but angle b and the given 60 degree angles are complementary

[lean otter]

Because we have straight line which is 180

And we have known angle which is 60

Subtracting it we get 120

We again