help-0

[mighty falcon]

as we only have positive numbers there is no problem

[mortal trellis]

no problem with what

just because something is positive doesn't mean we can do what we want

[mighty falcon]

I was thinking about discontinuities at 0

[mortal trellis]

the 1-norm is the sum of absolute values (of projections)

those are all continuous

so the 1-norm is continuous

do you know that the preimage of a closed set under a continuous function is again closed

[mighty falcon]

Wow I missed a lot of definition in maths
So, P={v∈R^n .... } is in [0,1]^n which is bounded.
We know v1+...+vn = 1 so the 1-norm of v = 1
Because the 1-norm is just the sum of abs which are continuous (as the values >=0? or we don't care?), the 1-norm is continuous

[mortal trellis]

do you know what continuous means

it has nothing to do with being >= 0

[mighty falcon]

yes ok I mixed everything up (with derivation)

I didn't do math since a long time ago this is why I'm struggling so much 🥲

[mighty falcon]

I can't see what's the preimage of P especially, where could this lead to

maybe you mean for Lambda

[mortal trellis]

what is the preimage of {1} under the 1-norm

can you write P as the intersection of that and another closed set

do you know that the intersection of two closed sets is closed

[mighty falcon]

{v1,...,vn}

[mortal trellis]

no

[mighty falcon]

[0,1]^n

I was thinking like:
f^-1({v1,....,vn}) = {1}
Or maybe
f^-1([0,1]^n) = {1}

[mortal trellis]

no

I want f^(-1)({1})

can you write that in set notation

[mighty falcon]

Ok I got it

so f is the 1-norm function and it is true we have f({v1,....,vn}) = R positive

so f^(-1)({1}) = P ?

[mortal trellis]

no

[mighty falcon]

is this wrong?

[mortal trellis]

so we want the set of all vectors that have norm equal to 1

can you write down that set

in set builder notation

[mighty falcon]

Aaaah

Ok P is just a set of real numbers

[mortal trellis]

no

P is a set of vectors

[mighty falcon]

I'm saturated hahaha

[mighty falcon]

My problem now is that i don't see the difference between what you mentioned above and P

[mortal trellis]

all vectors in P only have positive coordinates

[mighty falcon]

Ok

[mortal trellis]

but eg the vector (-1, 0,...,0) has norm 1 but is not in P

[mighty falcon]

Oh I see

I didn't think about that ...

Ok let's consider Q = {w ∈ R^n such that |w1| + |w2| + ... + |wn| = 1}

[mortal trellis]

yes

can you draw that in R^2

[mighty falcon]

is it like a square?

of 1

[mortal trellis]

it is indeed a square

still, can you draw it

eg in paint

[mighty falcon]

something like this?

[mortal trellis]

yes

can you draw P

[mortal trellis]

yes

can you write P as the intersection of Q and some other closed set

read #❓how-to-get-help and get your own channel

[mighty falcon]

With the example above, I would say [0,1]^2

but it is not closed

[mortal trellis]

why is [0,1]^2 not closed

[mighty falcon]

it needs maybe something else

I'm not sure of the definition of a closed space, even I said something about the norm just bc I feel this is right

[mortal trellis]

well then look it up

we are talking about closed sets for hours

[mighty falcon]

🥹

ok y [0,1]^2 is closed I mixed up

Q is closed, [0,1]^n too, so P = Q inter [0,1]^n is closed

[mortal trellis]

yes

so P is closed and bounded

[mighty falcon]

Can we also say consistent?

[mortal trellis]

not sure what you mean by that

[mighty falcon]

ok leave it, I thought there is an adjective to describe a closed and bounded space

[mortal trellis]

compact

ok

now back to the original situation

we have a sequence lambda_m in Lambda that converges to some lambda. we want to show that lambda is in Lambda

with that sequence we have a sequence of vectors v_m in P

so now we have a sequence v_m in a closed and bounded set

what now

[mighty falcon]

is the sequence of vectors v_m a subsequence of lambdam ?

[mortal trellis]

no

.

[mighty falcon]

ok with this I can conclude Lambda is closed

[mortal trellis]

well eventually, yes

but not now

[mighty falcon]

Maybe I have to say first Lambda is included on [0, |A|1]

[mortal trellis]

you need to do a bunch more stuff

you haven't even used bolzano yet

[mighty falcon]

ok with this I could use bolzano

there exists a subsequence of (v_m) in P which is convergent to c ∈ P

[lone heart]

@mighty falcon Has your question been resolved?

[lone heart]

@mighty falcon Has your question been resolved?

[obtuse rose]

@mighty falcon what math level is this?

Or class I guess

[mighty falcon]

I don't really know, I would say 2nd year of university?

[obtuse rose]

Yeah but what class?

[mighty falcon]

what do u mean by class?

[obtuse rose]

Is it Calc

Calc 2

Linear algebra

[mighty falcon]

As I'm not a "math" student, idk :w

Ok finally... There exists a sequence (lambda m) of Lambda which converge to c ∈ Lambda.
The sequence (v{m}) has a subsequence (v{phi(m)}) according to the Bolzano Weierstrass (P is compact)
So lim v{phi(m)} = k ∈ P and lim lambda{phi(m)} = c ∈ Lambda

So finally c x k <= A x k

because c is the upper bound of Lambda, and is included on Lambda, so we can say Lambda is closed

Hahaha I'm really really slow, but I hope with practice, I'll get better and have a correct level
If I'm right, thank you for your patience @mortal trellis 🙏, I'm probably missing some stuff

[lone heart]

@mighty falcon Has your question been resolved?

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[muted marsh]

Hey, I'm brain storming this problem a bit.

We're given these following facts:

We know that if a > 0, then $a^-1) > 0$

[ocean seal]

magilla

[muted marsh]

But how would I first prove that a > 0?

[pliant cedar]

u can try multiplying both sides of ur equation by x

uhm

[muted marsh]

I will follow this lead

[pliant cedar]

wait

but no

do this, turn the left hand side into a single fraction

[muted marsh]

like x + 1 / x?

[pliant cedar]

like take a common denominator

fr example 1 + 1/2 = 3/2

like that

[muted marsh]

Well, isn't our common denominator just x?

[pliant cedar]

yes

[muted marsh]

because right now it's x/x + 1/x

[pliant cedar]

right

[pliant cedar]

so write this as a single faction

this is two fractions

[muted marsh]

(x+1)/(x+x)

[pliant cedar]

?

[muted marsh]

well, you'd cross multiply to add them together like that?

Otherwise I don't get it

[pliant cedar]

when the denominators of two fractions are the same

u can just add the numerators

[muted marsh]

oh, like that

[pliant cedar]

3/5 + 6/5 = 9/5

for example

[muted marsh]

$\frac{x+1}{x}$

[ocean seal]

magilla

[pliant cedar]

yes

so u can first show that if this is >= 2, then x > 0

[pliant cedar]

start by assuming $\frac{x+1}{x}\geq2$

[ocean seal]

SilverSoldier

[pliant cedar]

to get rid of the fraction, we can multiply both sides by x, but coz we dont know the sign of x yet, we cant really do that (if x were negative the inequality sign wud have to change)

if however we can turn the denominator into a qty that is always positive no matter what value x takes, then we can multiply bth sides without worrying about changing the inequality sign

and u know that if x != 0, then x^2 > 0

does this help

[muted marsh]

ah, let me think about this one. It does help.

I get where you're pushing at

[pliant cedar]

btw what u had was x + 1/x

[pliant cedar]

this is not correct

[pliant cedar]

this is what u wud have got if u had 1 + 1/x

[lone heart]

@muted marsh Has your question been resolved?

[muted marsh]

but this IS correct?

[muted marsh]

So wouldn't $\frac{x^2 + 2x +1}{x^2} \geq 2$ be true

[ocean seal]

magilla

[muted marsh]

as x^2/x^2 = 1

then you're left with 2(a real number)

• 1

[tacit arch]

x=-5

[muted marsh]

fair point

Trying to think of where to move from here.

[pliant cedar]

what u shud have done is $x+\frac{1}{x}=\frac{x^2+1}{x}=\frac{x(x^2+1)}{x^2}$

[ocean seal]

SilverSoldier

[pliant cedar]

and solve $\frac{x(x^2+1)}{x^2}\geq2$

[ocean seal]

SilverSoldier

[muted marsh]

Honestly, I would have never contrived this myself, but is this correct?

I'm working on the proof by contradiction right now

[lone heart]

@muted marsh Has your question been resolved?

[tacit arch]

You had the solution the whole time?

Share it to start next time so you don't waste time

[muted marsh]

you guys handheld me to this solution

I wrote it in latex lol

[tacit arch]

Oh then my bad

[muted marsh]

btw riemann

I've been here about a year, glad you finally got honorable

you've helped me a few times

.close

[lone heart]

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[tacit arch]

Appreciate it

[lone heart]

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[alpine sable]

how to divide it

[analog falcon]

factorise

or maybe just long divide directly

do you know how to divide polynomials?

[alpine sable]

no

so i asked

[analog falcon]

This is not really the best place to learn long division

So maybe you can try to factorise those polynomials then cancel out common terms

or if you intend to learn long division then I'd suggest you should go to Youtube or something and watch a tutorial

[alpine sable]

All right, thanks

[analog falcon]

Welcome :^)

[alpine sable]

I remember, you can write down how

(a+b)^4 / (a+b)^3

.close

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[alpine sable]

I can also write it down as a right-hand piece with a denominator

[lone heart]

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[tropic rose]

how would i go about solving this

[tropic rose]

.close

[lone heart]

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[abstract magnet]

How do you create a 3-point moving average graph from using a time series graph?

[lone heart]

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[abstract magnet]

<@&286206848099549185>

[last ether]

Really

[last ether]

Read this

[novel lake]

Send the question

[abstract magnet]

i did ol

my question is above that question thingo

How do you create a 3-point moving average graph from using a time series graph?

[tacit arch]

You posted this in a closed channel

[novel lake]

Ah okay

[tacit arch]

That didn't belong to you

[abstract magnet]

oh lol, that's awkward

[abstract magnet]

got any idea how they work

it's for my year 12 math's assignment

[lone heart]

@abstract magnet Has your question been resolved?

[lone heart]

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[dark dome]

if two planes dont intersect they have to be parallel right

[jagged imp]

yeah (in 3d)

[dark dome]

ok thx

.close

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[alpine sable]

$\frac{8xy^2}{6x^2y^2}$

[ocean seal]

okokok

[alpine sable]

simplify

im thinking factor xy from top and x^2y^2 from bottom

[last ether]

You don't need to factor

As in the verb

Just cancel out any common factors

[alpine sable]

like what ?

[last ether]

Notice how both the numerator and denominator have y factors

But perhaps

Here Gimmie a sec

$\frac{8xy^2}{6x^2y^2} = \frac86 \cdot \frac x {x^2} \cdot \frac{y^2}{y^2}$

[ocean seal]

Umbraleviathan

[last ether]

Hopefully that helps

[alpine sable]

so what do i do

ok how do i get rid of both the y^2

[last ether]

Basic division

What is y^2 / y^2

[alpine sable]

so divide both side by y^2

wouldnt i have to divide the whole thing like

(8xy^2)/y^2

[last ether]

What no

No no what

What are you even doing

[last ether]

_ _

[last ether]

I broke the fraction up into 3 factors

Just simplify each factor

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[odd delta]

I have a question about permutations

[odd delta]

Do permutations have to include all the elements in a list?

I think it's sort of widely known that the number of permutations of a word with n characters is = n!

But if you consider the permutations that use less than all n characters, isn't it n! * n!?

[weary widget]

Yes

[odd delta]

Ok

[odd delta]

Is this correct

permutations with all characters is n!, but if you also need to make the permutations of using n-1 characters, then permutations of using n-2 characters etc

Oh wait no its +

n! + (n-1)! + (n - 2)!

[weary widget]

Review the defination of permutations.

a permutation on $\phi$ is a mapping on $\phi \to \phi$ which is bijective.

[ocean seal]

1048576Prog

[weary widget]

what is the permutations that use less than all n characters?

• $\phi \to \phi$ which is injective?
• $\phi \to \phi$?

[ocean seal]

1048576Prog

[weary widget]

which of these?

[odd delta]

Im not really sure what those mean

I just know permutations from like 11th grade in high school

Im just a freshman in college right now

[weary widget]

what is your defination of permutation?

[odd delta]

A way to rearrange characters with respect to ordering

my very basic high school definition hah

[weary widget]

I'm thinking.

(I'm grade 7 bro)

Like this?

Let $\Sigma$ be a charset.a permutation of $\Sigma$ is a array $a_1,a_2,\dots,a_n \in \Sigma$(which $n$ is the size of $\Sigma$), which ${a_1,a_2,\dots,a_n} = \Sigma$ right？

[ocean seal]

1048576Prog

[weary widget]

hey is it true?

@odd delta

[lone heart]

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[lone heart]

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[alpine sable]

$\frac{(3x+5)(x-1)}{(3x-5)(1-x)}$

[ocean seal]

okokok

[alpine sable]

ok so i can multiply the right by -1 but what about the left

[surreal meadow]

they’re just different

they’re not multiples of each other

[full frost]

-(3x+5)/(3x-5)

[alpine sable]

(5-3x) (3x-5)

[astral briar]

multiply the bottom two terms by negative one

[alpine sable]

oh and then multiply it by -1 again

[astral briar]

$\frac{(3x+5)(x-1)}{(5-3x)(x-1)}$

[ocean seal]

Blighter

[alpine sable]

(5-3x)(x-1)

ok and then multiply the top left by -1

to make it (5-3x)

[astral briar]

see the thing is you have to maintain equality

if you only multiply the top by negative one, then its different

you have to multiply the top and bottom by -1

also, remember that -1 times -1 equals 1

i used this fact that -1 * -1 = 1

[astral briar]

over here

[alpine sable]

so (3x+5)/(5-3x)

no

[astral briar]

yes

wait no

you added an x to 5

[alpine sable]

$\frac{-1(b-a)}{(b-a)}$

[ocean seal]

okokok

[alpine sable]

i only multiplied the num in this one

[astral briar]

no

[alpine sable]

so i must be able to solely multiply the num or denom

[astral briar]

this is wrong because when you factor out -1 from (3x+5), you get (-3x-5)

[alpine sable]

thats from a diff problem

[astral briar]

this problem is the one you are doing right

oh wait nvm

i see now

[astral briar]

where did you derive this from

[alpine sable]

its a diff problem

[astral briar]

(a-b)/(b-a)?

[alpine sable]

yes

[astral briar]

this can be done then

[alpine sable]

(3x+5)/(5-3x) so this is the final answer

[astral briar]

yes

[alpine sable]

i knew it from the start fug

[astral briar]

lol

[alpine sable]

so its ok that i just multiplied the top right by -1

or would i have to also multiply (3x+5) by -1

.close

[lone heart]

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[dusky kernel]

how do i prove this equation has no real solution without actually solving it?

[hybrid walrus]

you can plot both sides

at left is parabolic and right is square root but shifted right

[dusky kernel]

ummmm?

i dont really understand mathematical thing in english

[plush wagon]

Just plot the RHS and LHS on graph

[dusky kernel]

how

[plush wagon]

Put the values

[plush wagon]

And see if they intersect or not

[dusky kernel]

my teacher wont let me use graph

[lone heart]

@dusky kernel Has your question been resolved?

[dusky kernel]

2

[ripe wasp]

You can study function f(y)=y^2-1+y-3*sqrt(y-1) using its derivative and see it never equals zero.

[lone heart]

@dusky kernel Has your question been resolved?

[exotic belfry]

you know that y >= 1 (because of the root on the right side)

you could try to argue like that:

$y^2-1+y=(y+1)(y-1)+y\geq2(y-1)+y>3(y-1)>3\sqrt{(y-1)}$

[ocean seal]

ThM

[exotic belfry]

the first inequaltiy holds for y >=1, the second for all y, and the third for y > 2.

so you have a proof that there is no solution for y > 2, you need to search for better inequalities in the range 1 < y < 2.

[lone heart]

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[green thorn]

In my calculus 2 class, we are learning about area bounded by curves. I was wondering how do I tell which one is the upper and lower inequality of this graph?

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[radiant badger]

2x - -9x + 8 + -12 =

[desert tusk]

????

what are you trying to do

[royal plank]

#❓how-to-get-help

[gray isle]

so you don't need help with your original question anymore?

[radiant badger]

yes

[gray isle]

what's your issue with the current question

[radiant badger]

i dont know how to solve it

[lone ocean]

open the brackets

do bidman

[royal plank]

where are you stuck?
if at the beginning, start by calculating in order of the operations

[lone ocean]

so itl be 15-10/4-1

then do division

[gray isle]

no

[lone ocean]

wait i think i expanded them wrong

just use bidmas, expand them right tho, sorry

[radiant badger]

k

[gray isle]

don't just give solutions away

[lone ocean]

oh shit

sorry

[lone ocean]

sorry

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[alpine sable]

Got this ckeeky one

[alpine sable]

How to start it actually, separate the bases and exponents to LHS and logs to the RHS?

Ah, can't do that, mb. 4^x × log base 2 of x are connected

[small panther]

Yes put the logs together

Even with the 4

@alpine sable

[alpine sable]

Gotcha

[small panther]

Then you have to use a log rule in order to factor by log_2(x)

[alpine sable]

Oh, so 2×log_2(x)

[small panther]

Yes

So you have $(4^x+2)log_2(x)$

[ocean seal]

ByShaDowZ

[small panther]

On the rhs

[alpine sable]

Looks good?

,rccw

[small panther]

Yes mb

That's it

[alpine sable]

No worries

Now I am really stumped

[small panther]

And the rhs

You can multiply and divide by 2

In order to create a $\frac{1}{2}(4-2*4^x)$

[ocean seal]

ByShaDowZ

[alpine sable]

So, you want me to divide the equation by 2?

[small panther]

No multiply and divide by 2

So it multiplies the equation by 1

And doesn't change anything

I'll write it

$4-4^x.2 = log_2(x)(2-4^x)\frac{2}{2}$

[ocean seal]

ByShaDowZ

[small panther]

Like this

Do you understand ? I just added a 2/2

[alpine sable]

Since it's just 1, you multiplied by 1

[small panther]

That's equal to 1 so it doesn't change the lhs

Yes

[alpine sable]

I see now, doing that just with rhs?

[small panther]

Yes

And then

I put the *2 into the parentheses

In order to create a $log_2(x)(4-2*4^x)\frac{1}{2} $

[alpine sable]

Oh my

[small panther]

Do you understand ?

[alpine sable]

Yes, so that *2 multiplies to the 2 things in the parantheses after log

[small panther]

Yes exactly

[alpine sable]

And now we cancel out the 4-2×4^x on both sides

Or reduce

[small panther]

No

[alpine sable]

Oh

[small panther]

Oh yes mb

I misunderstood

[alpine sable]

Ah no worries

LHS becomes 1 right?

[small panther]

Just divide by 4-2x4^x

Yes

[alpine sable]

I can prove that by making an inequality condition for x I guess

[small panther]

But it can be equal to 0

So yes you have to find the condition for x

[alpine sable]

Or maybe make the 4-2×4^x = 0, find x and then make the condition that x can be any real number except the ones which makes the expression =0

X shouldn't be 1/2

[small panther]

But if we say that it's not equal to 0, you can divide and then $1 = \frac{log_2(x)} {2}$

[ocean seal]

ByShaDowZ

[small panther]

Yes

[alpine sable]

Yep, what I got

[small panther]

Then i think you know how to solve this

[alpine sable]

I got x=1

Thanks for the help man. I truly appreciate the explanation

[small panther]

x = 4 ?

I got 4

[alpine sable]

Shoot

[small panther]

2 = log_2(x)

[alpine sable]

Yes, my bad

I thought it was 2^1=2

[small panther]

2^2 = x

[alpine sable]

A little brainfart here

[small panther]

?

[alpine sable]

A saying I heard online

Or something, not native to know all english

Imagine doing all this and messing up on log_2(x)=2, haha

[small panther]

Idk i'm not english

[alpine sable]

I see

Anyways, thanks again for the huge help

[small panther]

You welcome !

[alpine sable]

Have a nice day dude. Good luck!

.close

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[unborn sleet]

Hello I’m trying to study the series in the image, I tried using Leibniz to solve it, the limits to infinity goes to zero, a_n >= 0 but I’m stuck in checking a_n+1 <= a_n, anyone can help?

[lone heart]

@unborn sleet Has your question been resolved?

[lone heart]

@unborn sleet Has your question been resolved?

[marsh rapids]

You can do that by using (n+1)^(3/2) >= n^3/2 + 3/2n I think
Otherwise also notice 5^n + n^5 <= 2*5^n beyond a certain rank, and use the comparison test to show the series is therefore absolutely convergent.

[unborn sleet]

Hi mateo, how did you get 2*5^n, I should not check like the one in the attacked image?

[marsh rapids]

They're totally different methods

[marsh rapids]

The 2nd one proves absolute convergence

And avoids these computations which, although doable, are far less practical

[unborn sleet]

So Instead of Leibniz I should use the absolute convergence and if it converges absolutely it also converges normally?

[marsh rapids]

It's simpler

[unborn sleet]

With absolute convergence I’d only rewrite the sums to infinity without the (-1)^n?

[marsh rapids]

You know what absolute convergence is. You don't need to ask that question

[unborn sleet]

I know but I’ve never used for alternate series

[marsh rapids]

Why would it be any different?

[unborn sleet]

If you give me a few secs I’ll try to write it down if it’s ok for you to check if I did it right

[unborn sleet]

Mins*

@marsh rapids is it okay?

I used also asintotic since n goes to infinity

[marsh rapids]

If you're going to use equivalents then use them from the get go. This is obviously equivalent to n^-3/2

[unborn sleet]

I do not know how to properly use from the get go due to the (-1)^n, that’s why I removed previously with the absolute value the -1 and the used the equivalent, is it wrong how I proceeded?

[marsh rapids]

When you take the absolute value, then afterwards it's clear that it's equivalent to n^-3/2

And no you can't use equivalent theorems and series whose sign isn't constant

[unborn sleet]

Got it so after taking the absolute value without multiplying and dividing by sqrt(n)/sqrt(n) I can take the equivalent asap that's equivalent to n^-3/2 so I can do less steps, thank you so much

[marsh rapids]

As long as you're at a level of study where it doesn't look like bluff to directly assert it, yes

Otherwise I'd first note that (5^n + n^5) / 5^n -> 1 then assert it

[unborn sleet]

Perfect, thank you again

[west bone]

<@&268886789983436800>

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[zinc laurel]

I need help with these

[zinc laurel]

I need a solution asap

No time for explanation 💀

[worn fox]

why asap?

[zinc laurel]

its for someone

[boreal verge]

all of them?

or just one specifically

[zinc laurel]

and i need to help them

all of them yeah

hope its doable

[worn fox]

!nosols

[lone heart]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[alpine sable]

the server is about helping not doing

[zinc laurel]

its not for a homework

and i need the solution ill figure out the rest

if thats not possible lmk

[boreal verge]

we dont just give out solutions for free sorry

[zinc laurel]

okay have a good day

[alpine sable]

we help u get there tho

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@zinc laurel Has your question been resolved?

[lone heart]

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[weary quartz]

hi

[weary quartz]

How would I go about solving this?

We haven’t started trig graphs in class yet

[alpine sable]

Think about what a and b would be doing to the graph

[weary quartz]

do they stretch it?

[alpine sable]

Yes, but how exactly?

[weary quartz]

A vertically B horizontally?

[echo socket]

Or you can try plugging corresponding x and y values into the equations by considering the points (0, 0), (30, 5)

[alpine sable]

Correct, and what happens when you increase A? Does it make it taller or shorter? Same for B, what happens if you increase it? Does it make it longer or shorter?

I'll be back

[weary quartz]

A taller B shorter

[weary quartz]

Ok

[alpine sable]

That's all correct. What are the maximum and minimum values sin(x) can take?

[weary quartz]

Im not sure

0 and 360 cause its degrees?

[alpine sable]

No, those are values of x

[weary quartz]

oh

[alpine sable]

And in truth, x can be bigger than 360 and smaller than 0

If you imagine yourself rotating 365 degrees, you'll see it's the same as rotating 5 degrees

Hence why sin(x) repeats itself infinitely

But what is the maximum value if sin(x)?

Like, imagine you were changing x to try to maximize sin(x), what's the maximum value you could get?

[weary quartz]

i dont know how to do that

[alpine sable]

Hmmm

[weary quartz]

I've never done trig graphs before

[alpine sable]

This has nothing to do with graphs

[weary quartz]

Oh

[alpine sable]

It's purely trigonometry

I'll just tell you: The maximum value sin(x) can take is 1

[weary quartz]

Oh ok

[alpine sable]

Hmmm, have you really never seen that?

That sin(x) and cos(x) go from -1 to 1?

[weary quartz]

No not that I can remember

The only time ive used sin cos etc is for like triangle and bearing length questions

[alpine sable]

Well, do you remember the interpretation of sin(x) where you have a circle of radius 1 and a triangle inside of it?

[wary stream]

You haven't started trig graphs, but you're doing work on it?

[weary quartz]

Yea

Were starting the topic this coming week

So im guessing this question is to do with substitution or something

[wary stream]

So then why don't you wait until you start that topic before you get into that question?

[weary quartz]

The homework is due monday

[alpine sable]

@weary quartz Have you ever seen a diagram like this?

[weary quartz]

Nope

[alpine sable]

Hmmm... Okay, here's a more fundamental question: Do you know the definition of sin(x)?

[weary quartz]

No

[alpine sable]

Ah, you've been doing trig but you haven't even been taught what sin(x) is?

[weary quartz]

No not that I remember

[alpine sable]

Here is a visual definition

sin(x) is just the length of the side of an equilateral triangle opposite to angle X (assuming X isn't the angle opposite to the hypotenuse, in which case it would just be 90°), assuming the length of the hypotenuse is 1

@weary quartz Does this seem confusing?

[weary quartz]

Oh yes I know all this

[alpine sable]

Then you do know the definition of sin(x)

[weary quartz]

Yes I do!

[alpine sable]

Do you understand this circle representation?

[weary quartz]

Yes I do now

[alpine sable]

What theta would you pick to maximize sin(theta°)? (it should be obvious from the circle representation)

@weary quartz Are you still following?

[weary quartz]

1?...

[alpine sable]

1? Okay, well that's the maximum value of sin(theta°)... But I'm asking for a value of theta that would give you that maximum

[weary quartz]

Wait 90?

[alpine sable]

✅

[weary quartz]

Cause sin(90) = 1

Yes

[alpine sable]

And what value of theta would minimize sin(theta°)

[weary quartz]

360

[alpine sable]

That would give you sin(theta°)=0

But you can actually go lower

Do you see how?

[weary quartz]

No

[alpine sable]

What happens when you try a value of theta that's larger than 180, but smaller than 360?

[weary quartz]

you get a negative

[alpine sable]

Yeah...? And a negative is smaller than 0 indeed

So what's the actual value for theta that would minimize sin(theta°)?

[weary quartz]

I dont know

[alpine sable]

Tada!

theta=270 would yield sin(theta°)=-1

@weary quartz Do you understand how?

[weary quartz]

Uhh

At 270 on the graph the y point would be at -1 ?

[alpine sable]

On the graph, sure... But that doesn't give you visual intuition

The graph just tells you it'd be -1, but it's best to know why it equals that

I'll make a Desmos interactive thing to show you hold up a second

[lone heart]

@weary quartz Has your question been resolved?

[alpine sable]

@weary quartz https://www.desmos.com/calculator/upme6qeo0z

t means theta

At the top right, there is a slider that lets you change t

[lone heart]

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[acoustic pivot]

Algebra question: Are all submodules also subrings?

[olive oar]

No

A submodule that is too a subring is a subalgebra

[acoustic pivot]

Thank you!

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[alpine sable]

Good evening

[alpine sable]

I really dont understand why logx>0 between (0,1)

I mean, if i think to the graph, logx Is not positive in that interval.
So to me the function Is not positive.

What do you think guys?

The request comes from and integral exercise, but Is does not matter i think

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[surreal oracle]

where'd sec go 😦

[surreal oracle]

talking about 2nd to 3rd line

nvm y

its factorised

.closed

.close

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[warped sentinel]

I really need help with this question and 3 others, I dont understand them.

[wanton nova]

if x=2 is a root it means that if you plug in 2 for x the quesdratic equals 0

[viscid niche]

Anyone?

[warped sentinel]

hmm ok

[warped sentinel]

what is a quesdratic

[wanton nova]

quadratic*

[jagged cobalt]

A polynomial of degree 2 - the highest power of x is 2

[warped sentinel]

ok

[echo socket]

Apply Vieta's theorem

[tawny condor]

or just find the polynomial directly

[warped sentinel]

idk how to do that, I wasnt at class that day...

[echo socket]

Given that x1 and x2 are the solutions to ax^2 + bx + c = 0, -b/a is the sum of x1 and x2 and c/a is their product

So, in this case, you need -p to be the sum of 2 and 1 (meaning p is -3)

And you need q to be their product

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[tawny moth]

Hi I would like to ask how can I interpret the soil test ?

<@&286206848099549185>

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[swift sky]

Determine if the function sin(1/x ) has any extreme values at (0,1).If so, determine these.

[lone heart]

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[swift sky]

There are infinity extreme values, so I am confused by "determine them if they exist", do they want a formula?

[swift sky]

Wait so I get that the derivative is 0 when x= 1/2pin where n is an integer. I put it in the function and I get sin(2pin)= sin(0) = 0. Is the answer 0? It makes totally sense but I just need to verify

<@&286206848099549185>

[vale wigeon]

Wait so I get that the derivative is 0 when x= 1/2pin where n is an integer
and there you have it

you should have gotten x = 1/(pi n) though not 1/(2pi n)

[swift sky]

Why? Isn't y'= -1/x^2 * cos(1/x) and then cos(1/x)=0 <=> 1/x= (2pi)*n so x= 1/(2pi n)

[vale wigeon]

ah, no, we are both wrong.

cos(1/x) = 0 yields 1/x = pi/2 + pi*n

not 1/x = 2pi*n

cos(2pi*n) isn't even 0

it's 1

[swift sky]

Shit I mixed it up with sin, you're right thanks!

[grave jolt]

i need help here

[swift sky]

Sorry this room is taken

[swift sky]

so x= 2/(pi + 4pi n)

[vale wigeon]

open your own channel. see #❓how-to-get-help for instructions.

[vale wigeon]

4pi n should be 2pi n

[swift sky]

$\frac1{x} = \frac{\pi}2 + 2\pi n <=> x=\frac1{\frac{\pi}2 + 2\pi n}= \frac1{\frac{\pi+ 4\pi n}2} = \frac2{\pi + 4\pi n}$

[swift sky]

but isn't this how it should be

[ocean seal]

afeAlway

[vale wigeon]

1/x is pi/2 + 1pi n

[swift sky]

why is the period 1pi?

[lone heart]

@swift sky Has your question been resolved?

[vale wigeon]

cos(t) = 0 has two solution families, pi/2 + 2pi*k and 3pi/2 + 2pi*k

these are exactly pi units away from each other

[swift sky]

Yeah Ik but I was focusing on one solution at a time. So for pi/2, is my solution right?

[vale wigeon]

...

[swift sky]

yes/ no?

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@swift sky Has your question been resolved?

[lone heart]

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[austere hatch]

Need help finding where I went wrong here. I’m baffled.

[marsh rapids]

The average value is over the length of the interval

Which is 8, not 4

What you do to simplify the integral doesn't change that constant

[austere hatch]

Can you rephrase your response?

[marsh rapids]

Average value = 1/(length of interval) * integral of f over that interval
The length is 8, not 4

[austere hatch]

Oh... duh!

Thanks!!!

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[cinder spindle]

how do i get n for question 6 b

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@cinder spindle Has your question been resolved?

[cinder spindle]

<@&286206848099549185>

.close

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[mossy burrow]

this is what i got

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@mossy burrow Has your question been resolved?

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@mossy burrow Has your question been resolved?

[manic wind]

seems right to me, what's the issue?

you'll want to clean up your notation though, what is "yf" (or uf can't really tell) and why is it equal to both -7.5m/s and 1.23s?

[mossy burrow]

HI

finally

[mossy burrow]

bruh idk lol

that’s how she did it

but

i’m stuck on 20,21,22

[mossy burrow]

plz tell me ur here 😓

[manic wind]

what have you tried?

It's the same equations except you're just solving for different things

[mossy burrow]

yes

my teacher didn’t really explain how

[mossy burrow]

i’m not even sure where to start

i’m guessing look for the max height?

[manic wind]

for 20, you know how tall the building is, and acceleration from gravity is constant, so you should be able to solve for how long it took for the ball to reach the ground

then horizontal velocity doesn't change (since there's no horizontal force), so you can use v = Δx/Δt

[mossy burrow]

how do i find the change in

[lone heart]

@mossy burrow Has your question been resolved?

[mossy burrow]

.cloze

.close

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[jade fox]

Is there something wrong with my working? The question asks:

The answer is apparently wrong and I can't figure out why (although it could just be the answer key that is wrong)

[surreal meadow]

dy/dt looks suspect

[naive valley]

second line seems superfluous, also

[barren portal]

Find dy/dt and dx/dt, later divide both of them?

[jade fox]

I'm not quite sure where you are trying to get at-I will try rework the second line

See if things change

[surreal meadow]

your derivative dy/dt is incorrect

[jade fox]

I see it now

should be 2 not 1

Got the right answer now, thanks everyone 🙂

.close

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[rocky spade]

help

[rocky spade]

10b

[rocky grove]

Hmm

Did you solve 10 a?

@rocky spade

[rocky spade]

yes

[rocky grove]

Okay so what did you get for 10a?

[rocky spade]

this is what i got for a and b

but according to the answer scheme B is wrong

[rocky grove]

,rcw

[rocky grove]

Hmm you can check your answer using lines instead of vectors

[rocky spade]

wdym?

[rocky grove]

Like treat the positional vector of A as coordinates of A

And positional vector of B as coordinates of B

And you can find the slope and see the coordinates of C so that the slope stays the same

[rocky spade]

did you also get the same answer as the answer scheme for B?

[lone heart]

@rocky spade Has your question been resolved?

[lone heart]

@rocky spade Has your question been resolved?

[lone heart]

@rocky spade Has your question been resolved?

[lone heart]

@rocky spade Has your question been resolved?

[patent ledge]

Are you aware of the section formula of normal coordinate geometry?, the same can be used in vectors too, u can solve the question using that

@rocky spade

[patent ledge]

Hope this helps you

[lone heart]

@rocky spade Has your question been resolved?

[rustic coral]

#❓how-to-get-help

Don't post for help in other people's help channels

It defeats the whole purpose of the help channel system

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[lime tangle]

Hello

[lime tangle]

I have question

so here is an integral i have to solve and i did this

$\int tan^5x$

[ocean seal]

IAMTHEFARMER

[lime tangle]

so this is what i did

$ = \int tan^2xtan^3x$

[echo socket]

$=

[wind cloak]

$\int \tan^2 x \cdot \tan^3 x \dd{x}$

[ocean seal]

NEONPerseus

[echo socket]

Btw \tan looks nicer

Yeah

[lime tangle]

yes

[echo socket]

Just like neonperseus did

[lime tangle]

so then i change tan^2 to sec^2-1

then i distrubuted the tan^3x

to get $\int \sec^2x\tan^3x - \tan^3 x \dd{x}$

[ocean seal]

IAMTHEFARMER

[lime tangle]

then seperating the integral:
to get $\int \sec^2x\tan^3x\dd{x} - \int\tan^3 x \dd{x}$

[ocean seal]

IAMTHEFARMER

[wind cloak]

ibp?

[lime tangle]

then i did u sub for the first integral

[wind cloak]

oh right yeah

[lime tangle]

let u = tanx du = sec^2x dx

so

to get $\int u^3 \dd{u} - \int\tan^3 x \dd{x}$

now we deal with the second integral

[ocean seal]

IAMTHEFARMER

[lime tangle]

so for the second integral i did

[wind cloak]

the same?

[lime tangle]

to get $\int u^3 \dd{u} - \int\tan^2x \tan x \dd{x}$

[ocean seal]

IAMTHEFARMER

[lime tangle]

change the tan^2 to sec^2 -1

to get $\int u^3 \dd{u} - \int \tan x (\sec^2 x - 1) \dd{x}$

[ocean seal]

IAMTHEFARMER

[lime tangle]

distribute the tanx

to get $\int u^3 \dd{u} - \int \tan x \sec^2 x - \tan x \dd{x}$

[ocean seal]

IAMTHEFARMER

[lime tangle]

seperate the integrals again

to get $\int u^3 \dd{u} - \int \tan x \sec^2 x + \int \tan x \dd{x}$

[ocean seal]

IAMTHEFARMER

[lime tangle]

u sub for second integral

u = tanx du = sec^2x dx

so

to get $\int u^3 \dd{u} - \int u \dd{u} + \int \tan x \dd{x}$

[ocean seal]

IAMTHEFARMER

[lime tangle]

now we solve

and this seems right to me but its not the answer in my textbook

[wind cloak]

$\int \tan x \dd{x} = \ln |\sec x| + C$

[ocean seal]

NEONPerseus

[lime tangle]

$\dfrac{u^4}{4} - \dfrac{u^2}{2} + ln|\sec x| + C$

[wind cloak]

did you back substitute properly

[lime tangle]

yes i substitue tanx

[ocean seal]

IAMTHEFARMER

[lime tangle]

so

$\dfrac{\tan^4 x}{4} - \dfrac{tan^2 x}{2} + ln|\sec x| + C$

[ocean seal]

IAMTHEFARMER

[lime tangle]

my textbook has

$\dfrac{\sec^4 x}{4} - \tan^2 x + ln|\sec x| + C$

[ocean seal]

IAMTHEFARMER

[lime tangle]

i dont know why the way i did it is wrong

[wind cloak]

,w plot $\frac{\tan^4 x}{4} - \frac{\tan^2 x}{2} + \ln |\sec x|$

[ocean seal]

Results provided by WolframAlpha

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

Requested by NEONPerseus#2128

[wind cloak]

,w plot $\frac{\sec^4 x}{4} - \tan^2 x + \ln |\sec x|$

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by NEONPerseus#2128

[wind cloak]

seriously

,w plot $\frac{\sec^4 (x)}{4} - \tan^2 (x) + \ln (| \sec (x) |)$

[ocean seal]

Results provided by WolframAlpha

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

Requested by NEONPerseus#2128

[wind cloak]

Yeah they're both the same

[lime tangle]

they are the same

wow

ok so i wonder why the texbook didnt give both possibilities

[wind cloak]

I suspect they took the LCM of the denominators and did some simplification

[lime tangle]

yeah

anyway thanks so much for your help it is greatly appreciated

[wind cloak]

np

[lime tangle]

.close

[lone heart]

Channel closed

Closed by @lime tangle

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Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[spiral iris]

Figure shows a triangle ABC

Tell the exact number for sin 2A

(without calculator)

[echo socket]

Recall the identity sin(2A) = 2sin(A)cos(A)

[spiral iris]

yes

[quasi scarab]

and the definition of sin and cos

(also, you need the 3rd side)

[spiral iris]

the third side is 5

[echo socket]

So, given all the sides of the right triangle, what's sin(A) and cos(A)?

[spiral iris]

oh

2 * sin5/13 * cos 12/13

?

[vague mirage]

Sin A= p/h
Cos A=b/h

It is not that complex

[spiral iris]

okay arnab

good for you

i dont know what p b or h is

[vague mirage]

p=perpendicular
b=base
h=hypotenuse

[echo socket]

Yeah just remove the sin and cos here though

[echo socket]

And it'll be fine

[spiral iris]

oh yea

ohh

[echo socket]

Guys they know soh cah toa

[spiral iris]

lol

[vague mirage]

It is not complex compared to a girl

[spiral iris]

What? lmfao

[vague mirage]

Nothin' I just think so now consentrate on your math

[spiral iris]

i get it though

[vague mirage]

Ik

[spiral iris]

Im not talking to you

About the question.

[vague mirage]

I am deaf

[spiral iris]

lmao

[vague mirage]

☠️

[spiral iris]

Thanks guys. And arnab for making it a little more confusing ❤️

.close

[lone heart]

Channel closed

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Use .reopen if this was a mistake.

[vague mirage]

,w plot x^2 + {y -3/4(x^2)^(1/3)}^2 < 1×1

[ocean seal]

Results provided by WolframAlpha

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

Requested by 𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛#6985

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pliant estuary]

reposting my original problem

[tawny condor]

If you have A = P^-1 * D * P

then

A^2 = P^-1 * D * P * P^-1 * D * P

which is P^-1 * D^2 * P

and the same thing will work for any power

so A^100 is P^-1 * D^100 * P

[lone heart]

@pliant estuary Has your question been resolved?

[pliant estuary]

I know, but wouldnt that be just

i will write it down, gimme sec

[tawny condor]

why is that equal to A^100?

[pliant estuary]

well it is, but in different basis right?

like the basis that consisnts of the span of the eigenspace

the P is the basis in which is A diagonal

[tawny condor]

im not sure lol

maybe someone else should help

[pliant estuary]

so the P are linear transformation matrices from one basis to another

in my case

$P = T_{K\to B}$

i think

[ocean seal]

marejak023

[lone heart]

@pliant estuary Has your question been resolved?

[lone heart]

@pliant estuary Has your question been resolved?

[lone heart]

Channel closed

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[quasi vector]

hello, I wanted to know how these integrals arise. I know these can be derived using Ramanujan's Master Theorem, but even WolframAlpha doesn't give this answer, and I don't see how these are derived.
It doesn't make sense to me either. These functions would be non integrable for many values of s would they not?

[vapid shuttle]

well I believe they are derived by using the definition of that function (which I am unfamiliar with)

and I think the answer to your last question is yes? but I am not 100% sure

these functions are non-integrable in terms of elementary functions for many values of s

[quasi vector]

yeah

[vapid shuttle]

that is why that new function is introduced

[quasi vector]

the gamma function?

[vapid shuttle]

perhaps ^ it is only defined at certain values of s?

[quasi vector]

it's just an extension of the factorial

[vapid shuttle]

ah

[quasi vector]

for positive integer values of s it just returns (s-1)!

[vapid shuttle]

well maybe it is just that because there is no elementary antiderivative doesn't mean that there can't be a value that the integral converges too

[quasi vector]

is that a possibility?

[vapid shuttle]

so although the function is not able to have an elementary antiderivative, it still converges to whatever value the gamma function gives * that other term

I believe that is a possibility yes

[vapid shuttle]

@pseudo ice do you know if this is true

[quasi vector]

is there someway I can graph functions in discord itself?

using the bot

im unfamiliar with the notation

[pseudo ice]

It is, if you mean

maybe it is just that because there is no elementary antiderivative doesn't mean that there can't be a value that the integral converges too
there are many examples like that

[vapid shuttle]

well im not sure, but surely you could graph them in desmos

[quasi vector]

yeah

[vapid shuttle]

okay that's what I thought but I wanted confirmation

[quasi vector]

for example

x sin(x) does not converge

[pseudo ice]

,w plot x*sin(x)

[quasi vector]

any positive value of s will not converge i believe